Please help. Solve the system of equations.
Y=2x
Y=x^2-8
The solution of the system of equation is as follows;
when x = -2 , y = -4
when x = 4, y = 8
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let solve the system of equation by substitution method.
Therefore,
y = 2x
y = x² - 8
Using substitution,
2x = x² - 8
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) - 4(x + 2) = 0
(x - 4)(x + 2) = 0
x = -2 or 4
Hence,
when x = -2
y = 2(-2) = -4
when x = 4
y = 2(4) = 8
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In △QRS , ∠R is a right angle.
If
QS
= 20 and m∠Q = 49° , what is the length of
QR
?
HELP IM TAKING MY GEOMETRY FINAL AND I DONT KNOW ANYTHING
Answer:
Bellow
Step-by-step explanation:
QS =√c2 - b2
= √202 - 15.0941916044552
= √172.16537980799
= 13.12118
Find the area of the figure.
The area of the figure in the first, second, and third cases will be 76 square ft, 120 square cm, and 87.5 square in, respectively.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The area of the trapezoid will be calculated as,
A = 1/2(sum of parallel sides) x height
8. The area of the figure is calculated as,
A = 1/2 (6 + 6 + 7) x 8
A = 76 square ft
9. The area of the figure is calculated as,
A = 1/2 (8 + 4) x 4 + 8 x 12
A = 24 + 96
A = 120 square cm
10. The area of the figure is calculated as,
A = 1/2 (5 + 10) x 5 + 5 x 10
A = 37.5 + 50
A = 87.5 square in
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what is the total surface area of the triangular prism in square centimeters?
A 240 cm^2
B 368 cm^2
C 320 cm^2
D 344 cm^2
Answer:
D
Step-by-step explanation:
base area = (6 · 4)/2 = 24/2 = 12 cm²
half base length = 6 : 2 = 3 cm
leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm
perimeter = (5·2) + 6 = 10 + 6 = 16 cm
lateral area = 16 · 20 = 320 cm²
surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²
a biologist records the average weight of the brain and body for a number of mammal species the biologist uses the inequality [tex]60\leq 0.5x+2.5\leq 250[/tex] to determine the weight of the mammals whose brain weighs between 60 pounds(lb) and 250 lb. solve the inequality
The inequality is [tex]115\leq x\leq 495[/tex]
What is inequality?
A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
Given [tex]60\leq 0.5x+2.5\leq 250[/tex]
splitting the equation:
[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]
[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]
also
[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]
therefore the equation is
[tex]115\leq x\leq 495[/tex]
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Please please please help me I need it asap! Please!!
Point A, located at (-11, -7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C.
What are the coordinates of points B and C?
A: Point B: (-11, 7) Point C: (11, -7)
B: Point B: (11, -7) Point C: (11, 7)
C: Point B: (11, -7) Point C: (-11, 7)
D: Point B: (-11, 7) Point C: (11, 7)
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The true statements about the circle are
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. How to determine the true statements about the circle?From the question, we have the following parameters that can be used in our computation:
x² + y² - 2x - 8 = 0
Generally, To convert this equation to standard form, we need to complete the square.
First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:
x² - 2x + y² - 8 = 0
Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.
To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:
So, we have
x² - 2x + (1²) + y² - 8 = 0 + (1²)
Evaluate
(x - 1)² + y² - 8 = 1
Finally, we can rearrange the terms
So, we have
(x - 1)² + y² = 9
Express 9 as the square of 3
(x - 1)² + y² = 3²
So, the standard form of the equation is (x - 1)² + y² = 3²
The standard equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
When these equations are compared, we have
Center = (a, b) = (-1, 0)
Radius = r = 3
The point (-1, 0) lies on the x-axis
This means that the center is on the x-axis.
Also, it means that the radius of the circle is 3 units
This radius is the same for a circle that has the form x² + y² = 9
This is so because 9 can be expresses as the square or 3, and r = 3
Hence, the correct statements are (a), (b) and (e)
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Complete Question
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?
Select three options.
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.In circle C, mCG= 148°, mCD = 86°, and m∠EPF = 116°. What is the measure of arc FG?
Answer:
The measure of arc FG is 148°
Step-by-step explanation:
Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.
5. The roof drawn below is made up of six pieces of lumber and is symmetrical. There is 1
foot of overhang on both sides.
Use the dimensions given in the diagram, determine how much total lumber would be
needed to create this roof (i.e. how many feet of wood does it take to build this roof?).
It is a good idea to label all of the vertices before beginning (6 marks).
Answer:
72+20sqrt3
Step-by-step explanation:
check the attached file
Bob lifts a 15N rock through a distance of 1.7m. How much work does Bob do
Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do
What is work done?An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.
The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.
Work done (W) = F × s
Where, F = force
s = displacement
Now putting the values, we get-
or, W = 15 N × 1.7 m
or, W = 25.5 N-m or Joule
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An elected official surveyed residents of a town to assess their satisfaction with city services. the survey includes both those who own and those who rent their homes. level of satisfaction high medium low total owners 26 34 18 78 renters 15 12 5 22 total 41 46 23 110 what proportion of those surveyed have low satisfaction with city services? 0.2091 0.2308 0.2644 0.3727
The proportion we get is 0.291 and that matches up with our first choice that we see.
What is proportion?A proportion simply means the amount or quantity of a thing present in another thing taken as whole.
What are the applications of proportion?The main purpose of stating stuff in proportions is to compare shares. If 2 people receive shares in a 1:1 proportion, it means they have exactly equal shares. If 2 people invest in something and one partner invests $3 for every $2 the other invested, the major partner would expect the profits to be divided 3:2 in their favor.
This issue informs us that a town's residents were polled by an elected official to see how satisfied they were with the town's services. Both homeowners and renters were included in the survey. The following charts show the percentage of respondents that are unsatisfied with city services. In order to calculate the percentage of surveys with low satisfaction, we only need to consider the third column to the right, which is labeled "low satisfaction," and the number we are interested in is the 1, which corresponds to the row labeled "total," because it represents the total number of survey respondents who have low satisfaction, whether or not they are home owners or renters. This number is 23 points.
But that only represents the whole population of those with low levels of satisfaction. We can find the total number of respondents in the cross section between the total column and the total row, giving us 110 points. We wish to multiply that total for the low level by the entire number of respondents. Therefore, if we want that proportion right away, we need divide 23 by 110 points. When we round off to four decimal places, the result is 0.291, which corresponds to our initial option that we see.
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Answer:
A - 0.2091
Step-by-step explanation:
I took it
-2y + 3 =21 solve linear equations
Answer:
y= -9
Step-by-step explanation:
Subtract 3 from both sides
-2y + 3-3= 21-3
-2y=18
Divide both sides by the same factor
-2y/-2 = 18/-2
y= -9
Answer: y = -9
Step-by-step explanation:
-2y+3=21
-2y=21-3
-2y=18
Divide that by -2:
y=-9
A car dealership pays $8350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this deallership
The retail price of the car is $ 9802.9.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.A car dealership pays $8350 for a car.
They mark up the price by 17.4%
8350 * 17.4% = 1452.9
retail price = 8350 + 1452.9 = $ 9802.9
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In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
Answer:
c = 14
Step-by-step explanation:
If the price of a certain stock is $55.00 per share and its earnings are $2.75 per share, what is the ratio of the earnings to the stock’s price in lowest terms?
The earnings-to-stock-price ratio in simplest terms is 20.
What is PE ratio?A stock's P/E ratio is calculated by dividing its price by its annual earnings per share.The P/E ratio assists investors in determining whether a company's stock is overvalued or undervalued in relation to its earnings. The ratio measures what the market is willing to pay for the company's current operations as well as its potential growth. If a company has a high P/E ratio, the market believes in its growth potential and is willing to overspend today based on future earnings.
Here given,
Stock price = $55.00
Earnings per share = $2.75
We have to find ratio od earnings,
The formula is,
Ratio is : P/E
By substituting the values,
Ratio = $55.00 / $2.75
= 20
write an equation for the line for each graph
The equation of each of the lines are:
1. y = 1/3x - 1
2. y = 3x + 1
3. y = 2/3x - 1
4. y = 3x
5. y = -2/3x - 1
6. y = 1/3x - 1
7. y = -3x + 2
How to Write the Equation of a Line?To write the equation of a line, find the following:
Slope (m) = rise/runy-intercept (b) = the point where the line intersects the y-axis.1. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
2. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 1.
To write the equation, substitute m = 3 and b = 1 into y = mx + b:
y = 3x + 1
3. Slope (m) = rise/run = 2/3
y-intercept (b) = -1.
To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:
y = 2/3x - 1
4. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 0.
To write the equation, substitute m = 3 and b = 0 into y = mx + b:
y = 3x
5. Slope (m) = rise/run = -2/3
y-intercept (b) = -1.
To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:
y = -2/3x - 1
6. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
7. Slope (m) = rise/run = -3/1 = -3.
y-intercept (b) = 2.
To write the equation, substitute m = -3 and b = 2 into y = mx + b:
y = -3x + 2
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Assume that when adults with smartphones are randomlyselected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. Round to 4 decimals
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
what is probability?The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
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HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:7.48521878104
if 87.5 percent of a sample of pure 131i decays in 24 days, what is the half-life of 131i?
If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.
In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days
We need to find the the half-life of 131i
We know that the rate constant expression is given as :
k = (2.303/t)*(log (a / a-x))
where, t = 24 days
a = 100
a -x = 100 - 87.5
= 12.5 g
From the rate constant expression,
k = (2.303 / 24) * (log(100/12.5))
k = 0.0866
Now, the half life is given as :
k = 0.693 / t(1/2)
t1/2 = 0.693 / 0.0866
t1/2 = 8 days.
Therefore, the half-life of 131 i is 8 days.
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What is the vertical asymptote of the function? x = –3 x = –2 x = 0 x = 3
Answer:4
Step-by-step explanation:i did the quiz
Find the value of x using the picture
The value of x is 91/9.
What is the value of X triangle?
The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
(9x+1)+ 88
Remove parentheses: (a)=a
9 x+1+88=180
Add the numbers: 1+88=89
9 x+89=180
Move 89 to the right side
9 x=91
Divide both sides by 9
[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]
Simplify
[tex]x=\frac{91}{9}$$[/tex]
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Answer:
x = 5
Step-by-step explanation:
You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.
Base angleEach base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...
9x +1 = 90 -(88/2)
9x = 45 . . . . . . . . . . subtract 1
x = 5 . . . . . . . . . divide by 5
Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2003 through 2014 can be approximated by 7.4x-y=-254 The number of network and data analyst jobs for the same years can be approximated by 12.4x-y=-231. For both equations, x is the number of years since 2003 and y is the number of jobs in thousands.
a. Use addition method to solve the following system of equations
{7.4x-y=-254
{12.4x-y=-231
The solution, rounded to the nearest whole number is: ?
Pls help!!!
Number of years since 2003 x=5 years and number of jobs in thousand y=288.
What is addition method of algebra?In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.
Why is addition method called elimination method?while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.
Given equation, 7.4x-y= -254
12.4x-y = -231
using addition method
-5x= -23
after solving x=4.6
x= 5 (nearest whole number)
y = 288.04
y =288
hence, number of years 5
number of jobs in thousand =288
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A photo is being resized to sell at a gallery. The original photo is 4 inches by 6 inches. Using the dimensions of 3 yds by 4.5 yds, find the scale factor.
The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.
What is the scale factor?The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
Given:
The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,
Calculate the scale factor as shown below,
Scale factor = Original dimension / new dimension
Scale factor = (4 × 6) / (3 × 4.5)
Scale factor = 1.8
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what is the difference between a squared number and a cubed number
this is the explanation above with some examples
11.3 is 7% of what?
Answer: 157.14
Step-by-step explanation: SDHU IK
The sum of two numbers is 57 and the difference is 3. What are the numbers?
Answer:
The 2 numbers are 27 and 30
Step-by-step explanation:
Let call them x and y where x is the larger number and y is the smaller number :
x + y = 57 (obtained from the first line of the question)
x - y = 3 (obtained from the second line of the question)
Now we are going to use the rules of simultaneous equations to find x and y :
I will use elimination method :
Add the 2 equations to eliminate the y :
2x = 60
x = 30
Substitute x into equation 1 :
(30) + y = 57
Subtract 30 from both sides :
y = 57 - 30
y = 27
So
x = 30 and y = 27
As you can see the difference is also 3
The 2 numbers are 27 and 30
Hope this helped and have a good day
a. 1 /2 + 5 12 greater than 1 less than 1 b. 2 7/8 – 1 7/9 greater than 1 less than 1.
nj bought a car for $20,000. two years later, the car has depreciated to a value that is 81% of what he paid. which equation(s) represent the exponential relationship?
V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.
The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.
One equation that represents this relationship is:
V = 20,000 * 0.81^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.
Another equation that represents this relationship is:
V = 20,000 * (1 - 0.19)^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.
Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.
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A man spends 70% of his income and craves rs 2580 What is his income? Full explanation please
Answer:
• Statement of the given problem,
⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?
According to above data,
⚫ the required income of the
given man
= 2550/(1 - 70/10)
☐ = 2550/0.30
= 8,500 (Rs) [Ans]
. Stanley needs to get 12 gallons of gas. He finds a gas station that is advertising their price at $3.479/gallon.
A. What will the cost be if the gas station rounds the final cost of gas (to the nearest hundredth) after all calculations?
B. What will the cost be if the gas station rounds their price per gallon (to the nearest hundredth) and then calculates the total price?
C. Which option will save Stanley money?
In case A:
The amount to be paid = $41.75
In case B :
The amount to be paid = $41.76
So, the Case A is better option.
Finding the right answer using the round off to nearest hundredth.
How to change any value to it's nearest hundredth ?
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
Steps to find nearest hundredth of any value:
Step 1:
Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.
Step 2:
Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.
Step 3:
If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.
Step 4:
If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.
Case A :
The price for each gallon = $3.479
So, the total price for 12 gallon = $41.748
In case A total amount is rounded off
So, the price = $41.75
Case B :
The price for each gallon = $3.479
Rounding off the price for each gallon = $3.48
So, the total amount for 12 gallon = $41.76.
So, the case A is better option.
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