Answer:
the value of x is 3.5.
Step-by-step explanation:
To find the perimeter of a rectangle, we need to add up the lengths of all four sides. In the given rectangle, the lengths of the sides are 4x-3, 7x+2, 4x-3, and 7x+2. We can write this as:
Perimeter = (4x-3) + (7x+2) + (4x-3) + (7x+2)
Perimeter = 2(4x-3) + 2(7x+2)
Perimeter = 8x - 6 + 14x + 4
Perimeter = 22x
We are told that the perimeter is 64, so we can set up the equation 22x = 64 and solve for x.
22x = 64
x = 64 / 22
x = 3.5
Therefore, the value of x is 3.5.
find the number of different ways that an instructor can choose 3 students from a class of 24 students for a field trip.
There are 2024 ways in which the instructor can choose 3 students from a class of 24 students for the field trip.
A combination is a mathematical technique for calculating the number of possible arrangements in a set of items where the order of the selection is unimportant.You can choose the items in any order in combinations.
Permutations and combinations are often confused. In permutations, however, the order of the selected items is critical. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), but different in permutations.
There is a way you can calculate combinations using a formula. This formula is:
[tex]nC_r = \frac{n! }{ r!(n-r)! }[/tex]
where
n = total no. of items;
r = items selected for the combination;
"!" is the factorial
Given,
Total number of students in class , n = 24
Number of students selected, r = 3
So, the number of ways that 3 students can be selected from 24 students is
[tex]24C_3=\frac{24 !}{3!(24-3) !}\\\\=\frac{24 !}{3!*21 !}\\\\=\frac{3!*24*23*22*21 !}{3!*21 !}\\\\=\frac{24*23*22}{3*2*1}\\\\=2024[/tex]
Hence, the students can be selected in 2024 ways for the field trip.
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Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
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 =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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at a certain gas station, 35% of the customers use regular unleaded gas, 35% use extra unleaded gas, and the remainder use premium unleaded gas. of those using regular gas, only 50% fill their tanks. of those customers using extra unleaded, 30% fill their tanks, whereas of those using premium unleaded, 30% fill their tanks. if the next customer fills the tank, what is the probability that extra unleaded gas was requested? (give your answer in percentage terms with one decimal point of precision.)
The probability that extra unleaded gas was requested is 35%.
To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.
Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.
Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.
This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.
The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.
To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.
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Match each theorem with its description.
(3) Isosceles triangle Theorem
(8) Same side Interior angle Theorem
(2) Triangle sum Theorem
(1) Vertical angle Theorem
(7) Alternate exterior angle Theorem
(5)Corresponding angle Postulate
(6)Alternate exterior angle Theorem
(4) Triangle midsegment Theorem
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Isosceles triangle Theorem: A triangle's opposite angles are also congruent if its two sides are.
Same side Interior angle Theorem:
The same side interior angles are additional when two parallel lines are cut by a transversal.
Triangle sum Theorem:
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Vertical angle Theorem:
When two straight lines collide, two sets of linear pairs with identical angles are created.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Corresponding angle Postulate:
The related angles are equivalent if a transversal cuts two parallel lines.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Triangle midsegment Theorem:
The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depe
The graph of a function f(x) passes through the following points:
(0,2), (1, 0), (- 1,-4)
Which of the following could be f(x)?
Of(x) = 2x² - 2
O f(x) = 2√x-2
Of(x) = 2x - 2
Of(x) = 2x - 2
The option that represents the function of the graph of the output f(x) which passes through the points (0, 2), (1, 0), (-1, -4), is the option;
f(x) = 2·x - 2
What is a mathematical function?A function is a rule, law, or expression, defining the method by which a value is mapped unto another value.
The points of the graph of f(x) obtained from a similar question online are;
(0, -2), (1, 0), (-1, -4)
The value of the output of the function, f(x), when the input value, x, is 0, f(0), is the same as the constant term.
The coordinates of the point where x = 0 is (0, -2)
Therefore, f(0) = -2
All of the possible functions, have a constant of -2, therefore, f(0) = -2, for all the functions.
At the point (1, 0), we get;
f(1) = 0
The functions that have an output of 0 when the input value, x = 0, are also all the possible functions
However, the function that has an output value of -4 when the input value is (-1) is the function, f(x) = 2·x - 2
The function, f(x) could be is therefore, f(x) = 2·x - 2
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In a school Auditorium, there are three types of rows arrangement
possible for watching programs: rows of 20 students per row, or rows
of 25 students ver row, or rows of 40 students per row. Find the least
number of students required for any one of these arrangements so
that all the students can be accommodated in each of these
arrangements.
I think
it should be 200 as it's the first common multiple of 20 40 and 25
Which expressions are equivalent to
[tex] {5}^{18} [/tex]
select all that apply
Answer:
B and C
Step-by-step explanation:
(5⁷)¹¹ = 5⁷⁷
5⁹ × 5² = 5¹¹
Answer:
[tex] {5}^{12} \times {5}^{6} and \: \frac{ {5}^{24} }{ {5}^{6} } \\ option \: b \: and \: c[/tex]
Step-by-step explanation:
[tex] {a}^{b} \times {a}^{c} = {a}^{(b + c)} \\ \frac{ {a}^{b} }{ {a}^{c} } = {a}^{(b - c)} [/tex]
[tex] {5}^{12} \times {5}^{6} = {5}^{(12 + 6} = {5}^{18} \\ \frac{ {5}^{24} }{ {5}^{6} } = {5}^{(24 - 6)} = {5}^{18} [/tex]
A patient recovering from a heart attack is advised to start a regular walking workout. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week, and so on. Recursive Write the sequence formulas that model this situation. Use no spaces, use (shift-8) for multiplication, use (shift-6) for exponents. A f(1) = -1 A f(n) 1 pts Explicit f(n) =
Answer:
Step-by-step explanation: At that point, the patient is to maintain the distance walked during the 10th week. To Find- How far will the patient walk during the 10th week? So, in till tenth week patient will walk 32 km.
The factors of the function are (x + 1), (x - 1) and (x-4). Which equation could describe the function?
The function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
What are factors?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given, the factors of a function are (x+1), (x-1) and (x-4)
We know that if the factors of a function are (x-a) and (y-b), it would mean that the function is (x-a)(y-b) = 0
Similarly, taking the above factors given in a function, the function would be:
(x+1)(x-1)(x-4)=0
⇒ (x²-1)(x-4)=0
⇒ x³-4x²-x+4 = 0
Hence, the function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
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What is the approximate perimeter of the parallelogram shown in the below coordinate plane?
Answer: C
Step-by-step explanation:
Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?A. 2w^2 + 5w, where w is the widthB. 2w^2 + 5, where w is the widthC. 2w^2, where w is the widthD. 10w^2 + 5 w, where w is the width
The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.
What is the area of rectangular shape?
In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.
Given that the length of a cabin is equal to 5 feet more than twice the width.
Assume that the width of the cabin be w.
Then the mathematical expression of twice the width is 2w.
Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.
The area of rectangular shape is product of length and width.
The area of the cabin is (2w + 5)w
Apply distributive property:
= 2w × w + 5 × w
= 2w² + 5w
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Which expression is equivalent to 30+42?
6 ( 7 + 5 ) expression is equivalent to 30+42.
what is algebraic expressions ?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.It shows that the expressions printed on the left and right sides have an equal relationship.Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. When creating an equation, the "=" symbol and terms on both sides are a need.
given the data,
Let's say the equation looks like this: A
Currently, A's value is given as
A = 42 + 30 be formula (1)
When we simplify the equation, we obtain
A = 72
The equation (1) can now be factored as follows:
By using the equation's common term, we obtain
A = 6 ( 7 + 5 ) = 72 be equation (2)
So , on simplifying the equation (2) , we get
A = 6 ( 7 + 5 )
A = 6 ( 12 )
A = 72
Therefore , the value of equation A is 72
Hence , the equation can be factorized as 6 ( 7 + 5 )
complete question :
Which expression is equivalent to 42 + 30? (
A.6(36 + 24)
B.7(6 + 30)
C.6(7 + 5)
D.5(37 + 25)
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in a poll, respondents were asked whether they were planning to vote in the local election. 315 respondents indicated that they were planning to vote and 217 said that they were not. what is the probability that the next respondent questioned will indicate that they are planning to vote?
The probability that the next respondent questioned would say they plan to vote is 0.59.
What is probability?
The ratio of the number of favorable outcomes to the total number of outcomes of an event is defined as probability.
We know that the probability of an occurrence =the number of favorable outcomes divided by the total number of events.
Given that, 315 respondents stated they planned to vote, while 217 said they did not.
Now, the probability of voting is:
P(voting)=315(315+217)
= 315/532
= 0.59
As a result, the likelihood that the next respondent questioned would say they plan to vote is 0.59.
The probability that the next respondent questioned would say they plan to vote is 0.59.
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james is painting an L- shaped piece of wood that is made up of two rectangular prisms
6 in
5 in
1 in
7 in
11 in
How many square inches does he need to paint?
Applying the surface area of a rectangular prism, the number of square inches hat will be painted is, 346 in.².
How to Find the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(wl + hl + hw), where:
length - lwidth = wheight = hThe L-shaped piece of wood is composed of two rectangular prisms, therefore:
The square inches of paint needed = surface area of prism 1 + surface are of prism 2 - 2(area where both prism meet).
Prism 1 surface area:
l = 7 in.
w = 6 in.
h = 5 + 1 = 6 in.
Surface area = 2·(6·7+7·7+7·6) = 266 in.²
Prism 2 surface area:
l = 7 in.
w = 11 - 6 = 5 in.
h = 1 in.
Surface area = 2·(5·7+1·7+1·5) = 94 in.²
Area where both prism meet = (l)(w) = (7)(1) = 7 in.²
Number of square inches that needs to be painted = 266 + 94 - 2(7)
= 346 in.²
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each student at william elementary can only participate in one fall activity. there are 65 students on the football team and twice that number in band. there are 61 students on each of the two soccer teams. how many students participate in fall activities
Answer:191
Step-by-step explanation:
65x2=130
130+61=191
Is 9,40,41 a right triangle
Using pythagoras theorem, the values given in the question 9, 40 and 41 represents a right angle triangle
Pythagoras TheoremThis theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle are named the perpendicular, base and hypotenuse. In this case, the hypotenuse is always longest side, as it is opposite to the angle 90°
Mathematically Pythagoras theorem is given as;
x² = y² + z²
x = hypothenusey = legz = legLet's substitute the values into the formula and check if the values are a right angle triangle.
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681
The values 9, 40, 41 represents a right angle triangle
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Helen has a new beaded necklace. The necklace has 69 blue beads and 23 white beads. What percentage of the beads on Helen's necklace are blue?
63.48 percent of the beads on Helen's necklace are blue.
What is the percentage?The ratio's numerical value is multiplied by 100 to obtain the percent value.
Given, A new beaded necklace belongs to Helen. 23 white beads and 69 blue beads make up the necklace. Hence,
Total beads in Helen's necklace = 23+69 = 92
percentage of blue beads in the necklace = 69 * 92 /100
percentage of blue beads in the necklace = 63.48
Therefore, The blue beads make up 63.48 percent of Helen's necklace.
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in 12 years a man will be twice as old as he was 12 years ago . find his present age
His present age is 36 years.
Let his present age = x
Given,
2(x − 12) = x +12
2x - 24 = x + 12
2x - x = 12 + 24
x = 36
Therefore, his present age is 36 years.
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Can you please give me the answer you don’t have to solve all but please!!!!!!
Answer: Reduction: 1/3
Step-by-step explanation:
Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.
Answer: Reduction 1/3.
Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.
Have a great day! :)
Solve the inequality.
$-12
Solve
e + 0.05 = 9.21
Answer: e = 9.16
Step-by-step explanation: Although it's not necessary, I would first get rid of the decimals by multiplying both sides of the equation by 100.
That gives is 100e + 5 = 921 which has no decimals.
Now just subtract 5 from each side to get 100e = 916 and
dividing both sides by 100 from here, e = 9.16.
make g the subject of 3e+4g=7+9eg
Answer:
the answer is g = (7 - 3e) / (4 - 9e)
Step-by-step explanation:
The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.
The given equation subject of equation is 3e + 4g = 7 + 9eg
Subtraction of 9eg from both sides of the equation
3e + 4g - 9eg = 7 + 9eg - 9eg
3e + 4g - 9eg = 7
Subtract 3e on both sides of the equation
3e + 4g - 9eg - 3e = 7 - 3e
4g - 9eg = 7 - 3e
Factorize g on left side of the equation,
g (4 - 9e) = 7 - 3e
Then divide (4 - 9e) on both sides of the equation,
g = (7 - 3e) / (4 - 9e)
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10. Open-Ended Complete the addends so you need to regroup to add. Then find the sum. 4, _ 37 + 1,28_
The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.
the addends. 4, 837 + 1,287
the sum is 6124
What is regrouping?Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.
When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.
Using regrouping for the addition problem
addend 4 8 3 7
addend 1 2 8 7
sum 4
1 regrouped to tens column
addend 4 8 3 7
addend 1 2 8 7
sum 2 4
1 regrouped to hundreds column
addend 4 8 3 7
addend 1 2 8 7
sum 1 2 4
1 regrouped to thousands column
addend 4 8 3 7
addend 1 2 8 7
sum 6 1 2 4
the sum is 6124
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There are 30 students in Mrs. Woodward's class and 1/5 of the class has their own cell phone. Of the students that have cell phones, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?
Answer: 3 people
Step-by-step explanation:
1/5 of 30 will give us the number of students.
6
1/2 of 6, will give us the number of people who can use social media.
3 people.
Consider the function
What is
f(x) = -2/3x + 5.
ƒ ( − 1/2 )
?
Answer:
Step-by-step explanation:
0
Answer:
f(1/2) = 5 1/3
Step-by-step explanation
All you need to do is replace each x in the function with -1/2, and you have your answer!
Hope this helps :)
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Trolley Train and the Silly Slide.
25 units
7 units
5 units
3 units
The distance between the Trolley Train and the Silly Slide is 5 units. The 3rd option is the answer
How to determine the distance between the Trolley Train and the Silly Slide?From the map, the coordinate of the Trolley Train is (-2, -6) and the coordinate of the Silly Slide is (2, -3)
The formula for finding the distance between the two points is given as:
d=√(x₂ – x₁)² + (y₂ – y₁))²).
where
x₁ = -2,
y₁ = -6 (Trolley Train)
x₂ = 2
y₂ = -3 (Silly Slide)
d = √((2 – (-2))² + (-3 – (-6))²)
d = √((4)² + (3)²)
d = √25
d = 5 units
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Sometimes business partners do not share the ownership of a
business equally. Instead, they own a percentage of the
business, and each receives that percent of the profits.
Alvarez, Brown, and Chow are partners in a business that
earned $500,000. Alvarez owns 40% of the business. Chow
received $175,000. How much money did Alvarez make?
Alvarez received $200,000 which is 40% of the profit.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it. Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Given
Profit $500000
Alvarez owns 40% of the business.
Percentage
500000 × 40%
200000
Alvarez received $200,000 which is 40% of the profit.
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find f(20) if f(x)=[tex]\frac{1}{4}x+5[/tex]
Answer:
f(20) = 10
Step-by-step explanation:
hii please help I'm super confused !
Answer:
Below
Step-by-step explanation:
Two points are given....calculate the slope, m = (y1-y2) / (x1-x2)
= ( 3-1) / ( 0 - - 8) = 2/8 = 1/4
Only equation II has slope = 1/4
four cubes of volumes $1 \text{ cm}^3$, $8 \text{ cm}^3$, $27 \text{ cm}^3$, and $125 \text{ cm}^3$ are glued together at their faces. what is the number of square centimeters in the smallest possible surface area of the resulting solid figure?
Answer: 194
Step-by-step explanation:
From the volumes, we deduce that the side lengths of the cubes are 1 cm, 2 cm, 3 cm, and 5 cm. We position the cubes as follows:
[asy]
unitsize(0.5 cm);
draw((0,0)--(5*dir(-30))--(5*dir(-30) + 5*dir(30))--(10*dir(-30))--(5*dir(-30) + 5*dir(-90))--(5*dir(-90))--(0,0));
draw((5*dir(-30))--(5*dir(-30) + 5*dir(-90)));
draw((0,0)--(0,2)--((0,2) + 2*dir(-30))--(2*dir(-30)));
draw((0,2)--((0,2) + 2*dir(30))--((0,2) + 2*dir(30) + 2*dir(-30))--(2*dir(30)));
draw((2*dir(-30))--(2*dir(-30) + dir(30))--(2*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,2)));
draw((2*dir(-30) + dir(30))--(3*dir(-30) + dir(30))--(3*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + dir(30) + (0,1)));
draw((3*dir(-30) + dir(30) + (0,1))--(3*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1)));
draw((2*dir(30) + (0,2))--(2*dir(30) + (0,3))--(2*dir(30) + 3*dir(-30) + (0,3))--(2*dir(30) + 3*dir(-30))--(dir(30) + 3*dir(-30)));
draw((2*dir(30) + (0,3))--(5*dir(30) + (0,3))--(5*dir(30) + 3*dir(-30) + (0,3))--(5*dir(30) + 3*dir(-30))--(5*dir(30) + 5*dir(-30)));
draw((3*dir(-30) + 2*dir(30))--(3*dir(-30) + 5*dir(30)));
draw((3*dir(-30) + 2*dir(30) + (0,3))--(3*dir(-30) + 5*dir(30) + (0,3)));
[/asy]
The surface area of a cube with side length $s$ is $6s^2$, so the total surface area of the cubes is $6 \cdot 1^2 + 6 \cdot 2^2 + 6 \cdot 3^2 + 6 \cdot 5^2 = 234$.
Note that every pair of cubes touches, and furthermore, they have maximum contact. (This is why this solid has the smallest possible area.) The area of contact of the 1-cube and the 2-cube is 1 square centimeter, so we must subtract this twice from 234 (because this portion of the area from both the 1-cube and 2-cube is not seen anymore).
Doing this for every pair of cubes, we find that the surface area of this solid is $234 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 2^2 - 2 \cdot 2^2 - 2 \cdot 3^2 = \boxed{194}$.
