Answer: 20 feet
Step-by-step explanation: To find the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two other sides are the length and the width of the room, so we have:
diagonal^2 = 12^2 + 16^2
diagonal^2 = 144 + 256
diagonal^2 = 400
Taking the square root of both sides, we get:
diagonal = √400
diagonal = 20 feet
Therefore, the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom is 20 feet.
A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 110 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
22 gallons of the first brand (35% pure antifreeze) and 88 gallons of the second brand (60% pure antifreeze) to make 110 gallons of a mixture that contains 55% pure antifreeze.
Let x be the number of gallons of the first brand (35% pure antifreeze) needed, and y be the number of gallons of the second brand (60% pure antifreeze) needed to make the desired mixture.
We know that the total volume of the mixture is 110 gallons and the desired concentration of antifreeze is 55%.
We can set up two equations based on the amount of antifreeze and the total volume of the mixture:
0.35x + 0.6y = 0.55(110) (amount of antifreeze)
x + y = 110 (total volume)
Simplifying the first equation, we get:
0.35x + 0.6y = 60.5
Now we can use substitution or elimination to solve for x and y. Here's one way to use substitution method
x + y = 110 (equation 1)
x = 110 - y (solve for x)
0.35x + 0.6y = 60.5 (equation 2, substitute x)
0.35(110 - y) + 0.6y = 60.5 (substitute x into equation 2)
38.5 - 0.35y + 0.6y = 60.5 (distribute 0.35)
0.25y = 22 (combine like terms)
y = 88 (divide both sides by 0.25)
So we need 88 gallons of the second brand (60% pure antifreeze). To find the amount of the first brand (35% pure antifreeze), we can substitute y back into equation 1:
x + y = 110
x + 88 = 110
x = 22 gallons
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Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m ≥ 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m
The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:
Step 1: Assume n = m², for some non-negative integer m.
Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².
Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.
Step 4: Let's assume m ≥ 1.
Step 5: Hence, n + 2 is not a perfect square.
The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.
In the final step, we conclude that n + 2 is not a perfect square.
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Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?
Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
What is social security benefits retirement age?The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.
Given that, Juanita started collecting benefits at age 65.
Thus, her benefits reduced by 13.3%.
0.133 x $2,128 = $283.10
Deducting the reduction amount from the total:
$2,128 - $283.10 = $1,844.90
Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
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Can someone help me with this
Answer:
corn dogs: $1.25fries: $3.50Step-by-step explanation:
You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.
SetupThe cost of each purchase can be represented by the equations ...
2d +3f = 134d +f = 8.50SolutionSubtracting the second equation from twice the first gives ...
2(2d +3f) -(4d +f) = 2(13) -(8.50)
5f = 17.50 . . . . . . simplify
f = 3.50 . . . . . . . divide by 5
4d = 8.50 -f = 5.00 . . . . use the second equation to find d
d = 1.25 . . . . . . divide by 4
Corn dogs cost $1.25; chili-cheese fries cost $3.50.
__
Additional comments
Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.
The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.
math question please help
Answer:
Step-by-step explanation:
only the 1st and 5th statements are true
Proving Triangle Similarity
The proof is completed using two column proof as follows
Statement Reason
QT ⊥ PT Given
∠ QRP ≅ ∠ SRT = 90 definition of perpendicularity
∠ QPR ≅ ∠ STR Given
Δ PQR is similar to Δ TSR AA similarity theorem
What is AA similarity theorem?The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.
In the given triangle, the two angles given to be equal are
∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STRHence the triangles are similar
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Answer:
:)
Hopefully this helps you guys :)
good luck :D
What is the area of the triangle?
Answer:
Step-by-step explanation:
Given:
Side a and Side b are 6 and 5.
The angle C is 131.
This is an obtuse scalene triangle as identified.
Area = ab * sin (C)/2 = 11.32064
florian bought his first car for $6,040. he saved up $1,000 gor a down payment and takes out a loan for the rest.the loan will allow him to pay $140 per month for the remaining balance. how much will he own on his car for 3 months?
Florian has to pay $2,013.3, then he own on his car for 3 months
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
6040 is the total amount
he has to repay in 3 months
dividing the total amount/3
6040/3
$2,013.3
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Simplify (cos^2a - cot^2a)/(sin^2a - tan^2a)
Answer:
The simplified expression is sec^2a
Step-by-step explanation:
We can start by using the trigonometric identities:
cot^2 a + 1 = csc^2 a
tan^2 a + 1 = sec^2 a
Using these identities, we can rewrite the expression as:
(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)
= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))
= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)
Now we can use the identity:
sin^2 a + cos^2 a = 1
to rewrite the expression further:
= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)
= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)
= sin^2 a / sin^2 a (1 - cos^2 a)
= 1 / (1 - cos^2 a)
= sec^2 a
Therefore, the simplified expression is sec^2 a.
Isosceles Trapezoids: Only one pair of opposite sides are _______
Answer:
equal
Step-by-step explanation:
You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.
we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;
tan 68° = 125/x {opposite/adjacent}
x = 125/ tan 68° {cross multiplication}
x = 50.5033
tan 71° = y/50.5033
y = 50.5033 × tan 71°
y = 144.6722
height of the antenna = 144.6722 - 125
height of the antenna = 19.6722
Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
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The expression tan(0) cos(0) simplifies to sin(0) . Prove it
Using the definitions of trigonometric functions for x = 0, we have tan(0) = 0 and cos(0) = 1, which simplifies to 0 * 1 = 0, and sin(0) = 0,
therefore tan(0) cos(0) = sin(0).
Define trigonometric.
Trigonometric refers to the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their properties and applications in various fields including mathematics, science, engineering, and navigation.
For any angle x, we have the identity:
tan(x) = sin(x) / cos(x)
Setting x = 0, we get:
tan(0) = sin(0) / cos(0)
Since tan(0) = 0 and cos(0) = 1, we can simplify this equation to:
0 = sin(0)
which is true, since the sine of 0 degrees is 0. Therefore, we have shown that:
tan(0) cos(0) = sin(0)
Therefore, the identity tan(0) cos(0) = sin(0) is proven.
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A circular flower garden has an area of 314m². A sprinkler at the center of the garden can cover an area of 12 m. Will the sprinkler water the entire garden?
Step-by-step explanation:
No,
if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular
A=πr2
A=3.142*36
A=113.112 cm3
What is the answer to this math problem? I can’t seem to figure it out.
Answer:
X
Step-by-step explanation:
We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.
Hope this helps!
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}.
The decision boundary is the line that separates the two classes. When it comes to the nearest neighbour method, the boundary of a class is determined by the closest data point in the other class.What is the nearest neighbour method?The nearest neighbour method (NNM) is a type of lazy learning method in which the data is stored and the computation is deferred until the classification phase.
The goal of the nearest neighbor technique is to use the pattern of the closest data point to classify a new sample. It's also one of the simplest non-parametric classification methods, and it's based on the assumption that the feature spaces used by each class are continuous regions.For Class 1, there are two labeled training data points: (0, 0)T and (0, 1)T. Similarly, for Class 2, there are two labeled training data points: (1, 0)T and (0, 0.5)T.
To generate decision boundaries, follow the steps below:Step 1: Plot the given labeled training data. They are shown in the figure below. Step 2: Label the data points according to their class: Class 1 and Class 2.Step 3: Now, we need to find the nearest neighbors. Find the nearest neighbor for each of the labeled training data points from the opposite class. The distances are calculated as follows:For the Class 1 data points, the nearest neighbor is Class 2's (1, 0)T data point.
For the Class 2 data points, the nearest neighbour is Class 1's (0, 1)T data point.Step 4: Connect the nearest neighbour's labeled training data points with a line. These are the decision boundaries. The red line represents the decision boundary between Class 1 and Class 2. The green line represents the decision boundary between Class 2 and Class 1. The slopes of the decision boundaries are -1 for the red line and 1 for the green line. These slopes are the result of the negative reciprocal of the nearest neighbour's slope. The break point for the red line is 0.5, while the break point for the green line is 0. A break point is the point at which the decision boundary intersects the y-axis.
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Find m ∠ JKL using the picture
The value of m∠JKL is 34°
How to find the value of m∠JKL?An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.
Based on the theorem above, we can say:
m∠JKL = 1/2 * (159 - 91)
m∠JKL = 1/2 * 68
m∠JKL = 34°
Therefore, the value of m∠JKL in the circle is 34°.
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Let X1, X2,..., Xn be i.i.d. random variables from a double exponential distribution with density f(x) = 1/2*λ*exp(−λ|x|). Derive a likelihood ratio test of the hypothesis H0: λ=λ0 versus H1: λ=λ1, where λ0 and λ1 > λ0 are specified numbers. Is the test uniformly most powerful against the alternative H1: λ > λ0?
The bearing of part A from part B is 074 deg. What is the bearing of part A from part B
The bearing of part A from part B is 254 degrees.
Enter the correct answer in the box.
Write this expression in simplest form.
Don’t include any spaces or multiplication symbols between coefficients or variables in your answer.
16h^(10/2) *remove the root sign
16h^5 *simplify the exponent
Answer: 16h^5
Step-by-step explanation: im correct
4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
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Select all of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders.
A double box plot showing hours sleeping. For seventh graders, the left whisker is at 7.5, the left edge of the box is at eight, the line inside the box is at 8.5, the right edge of the box is at nine, and the right whisker is at 9.5. For eighth graders, the left whisker is at seven, the left end of the box is at 7.5, the line inside the box is at eight, the right end of the box is at 8.5, and the right whisker is at nine. Screen reader support enabled.
All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:
A. The data are evenly distributed between 7 hours and 9 hours.
D. There is no outlier in the data.
What is a range?In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
Mathematically, the range of a data set can be calculated by using the following mathematical equation;
Range = Highest number - Lowest number
By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.
In conclusion, the box-and-whisker plot or box plot is symmetrical.
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Answer:
Step-by-step explanation:
Yeah what the other guy said
 choose all the shapes with at least one pair of perpendicular sides
According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.
What is the definition of perpendicular sides?Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:
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if the area of the quadrilateral ABCS is 924cm^2 and the length of the diagonal AC is 33cm,find the sum of lengths of the perpendicular from points B and D to AC.
please answer with full steps asap
3BE² + 3DF²- (2AC²- AB) is the answer of the following question
The calculation is as follows
Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.
Since ABCS is a quadrilateral, we have:
Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)
Substituting the given values, we get:
924 = (1/2) * 33 * BD * sin(angle between AC and BD)
sin(angle between AC and BD) = 924 / (16.5 * BD)
Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:
AB² + BC² = AC² (1)
CD²+ BC² = AC² (2)
Adding equations (1) and (2), we get:
AB² + 2BC²+ CD²= 2AC²
Substituting AC = 33 and rearranging, we get:
BC² = (2AC²- AB² - CD²) / 2
We can also write:
BE²= AB²- AE² (3)
DF² = CD²- CF²(4)
Adding equations (3) and (4), we get:
BE² + DF²= AB²+ CD² - AE²- CF²
Substituting BC²from earlier, we get:
BE²+ DF² = 2AC² - BC²- AE²- CF²
We want to find BE + DF. Squaring both sides of equation (3), we get:
BE²= AB² - AE²
AE²= AB²- BE²
Similarly, squaring both sides of equation (4), we get:
DF²= CD²- CF²
CF²= CD² - DF²
Substituting these expressions into the equation for BE²+ DF², we get:
BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)
Simplifying, we get:
BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²
Collecting like terms, we get:
BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²
Simplifying, we get:
BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²
Substituting the values we know, we get:
BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²
Rearranging, we get:
3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924
Substituting BC^2 from earlier, we get:
3BE²+ 3DF² - (2AC²- AB)
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8hr/2days=28hr/?days
find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
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Marcus bought a booklet of tickets to use at the amusement park. He used 25% of the tickets on rides, 1 2 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 23% of the tickets in the batting cage. Do you agree? Complete the explanation.
Answer: Do not agree.
Step-by-step explanation:
To determine if we agree with Marcus, we need to verify if the percentages he used on rides, video games, and batting cage add up to 100%.
Marcus used 25% of the tickets on rides and 1/2 on video games. So, the total percentage of tickets he used is:
25% + 1/2 × 100% = 25% + 50% = 75%
This means that Marcus should have used 25% of the tickets in the batting cage. If he said he used 23% of the tickets in the batting cage, then we do not agree with him.
James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Answer:
ames have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Step-by-step explanation:
Let's start with the amount of water in tank 1 as x liters.
I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.
II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.
III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.
We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.
3/8 * x + 3/8 * x + 1/8 * x = 18
Simplifying the equation, we get:
7/8 * x = 18
x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)
Therefore, the amount of water in each tank is:
Tank 1: 3/8 * x = 7.71 liters
Tank 2: 3/8 * x = 7.71 liters
Tank 3: 1/8 * x = 2.57 liters
A landscaper needs to mix a 80% pesticide solution with 35 gal of a 30% pesticide solution to obtain a 55% pesticide solution. How many gallons of the 80%
solution must he use?
By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.
What is equation?In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Let's say a landscaper needs to use x gallons of an 80% pesticide solution.
The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.
After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.
Since we need a 55% pesticide solution, we can set the following formula:
[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]
Therefore, landscapers should use 35 gallons of an 80% pesticide solution.
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If the angles of a pentagon are xº, x°, 2xº, (2x +
40), (2x+10)º, find the value of the biggest
angle
Answer:
285°
Step-by-step explanation:
x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180
8x + 50 = 540
8x = 490
x = 61.25
2x + 40 = 2(61.25) + 40 = 285
Answer:
Step-by-step explanation:
Interior angles in a pentagon equal 540°.
Simplify
x°,x°,2x°, (2x+40) and (2x+10) = 8x+50
Calculate x
8x + 50 = 540
8x = 540 - 50 = 490
x = 490/8
x = 61.25°
Calculate largest angle
2x + 40, where x = 61.25°
=162.5°
Schools have different ways of fund raising. The parents and the SGB of Progress High School agree that each learner should donate an amount to the school. The money is payable during the first month of the year. 1.1 Use TABLE 1 to answer the questions that follow. Write down the donation per leamer. 1.2 TABLE 1: INCOME IN RANDS OF FUND RAISING Number of learners that paid Income (R) 1 200 1.3 1.5 Calculate the missing value A. 10 2 000 20 45 215 4 000 9 000 A [Adapted from original school financial books ] Use TABLE 1 and write down the dependent variable. 1.4 Write the income received from 10 leamers to the income received from 45 learners, in a ratio in its simplest form. (3) (2) (2) (2) have The SGB chairperson claims that if 80% of the leamers paid, the school would raised more than R170 000. There are 1 100 learners enrolled at the school. Verify, by showing ALL calculations, whether his statement is valid. (4)
Answer: 1.1. The donation per learner cannot be determined from the given table.
1.2. TABLE 1: INCOME IN RANDS OF FUNDRAISING
Number of learners that paid Income (R)
1 200
1.3. To calculate the missing value A, we need to add up all the given incomes and subtract it from the total income for 45 learners, which is 45 x A. Then we can solve for A:
Total income = 200 + 150 + 10(2,000) + 20(45) + A + 4,000 + 9,000
Total income = 45A
45A = 25,150
A = 558.89
Therefore, the missing value A is R558.89.
1.4. The dependent variable in the table is the income received from fundraising.
To find the ratio of income received from 10 learners to income received from 45 learners, we need to divide the income received from 10 learners by the income received from 45 learners and simplify the fraction:
Income from 10 learners = R1,100 (since each learner donates R110)
Income from 45 learners = R215
Ratio = Income from 10 learners : Income from 45 learners
= 1,100 : 215
= 20 : 3 (in its simplest form)
The total number of learners enrolled at the school is 1,100. If 80% of the learners paid, then the number of learners who paid is:
80% of 1,100 = 0.8 x 1,100 = 880 learners
The minimum income that the school can raise if 80% of the learners paid is when each of the 880 learners paid the minimum donation, which is R150:
Minimum income = 880 x 150 = R132,000
Since R132,000 is less than R170,000, the SGB chairperson's statement is not valid.
Step-by-step explanation:
