Given \(\triangle DEF\ :\ \triangle RST\), find the scale factor.

Answer:

x=60+70=130(exterior angle of a triangle is equal to the sum of two opposite interior angle)

Answer:

its purple

Step-by-step explanation:

x = 3

-4x - (-3 - 5x) =  -3(2x - 8)

x + 3 = -6x + 24

x + 3 - 3 = -6x + 24 --3

x = -6x + 21

x + 6x = -6x + 6x + 21

7x = 21

7x / 7 = 21 / 7

- PNW

If the value of x is 3 then the equation  -4x-(-3-5x)= -3(2x-8) will be true.

Two or more expressions with an Equal sign is called as Equation.

The given equation is -4x-(-3-5x)= -3(2x-8)

We need to find the value of x which makes the equation as true.

Minus four times of x minus of minus three minus five times of x equal to minus three times of two x minus eight.

-4x-(-3-5x)= -3(2x-8)

-4x+3+5x= -6x+24

Take all the terms to the left hand side

-4x+3+5x+6x-24=0

Add the like terms

7x-21=0

Add 21 on both sides

7x=21

Divide both sides by 7

x=3

Hence, if the value of x is 3 then the equation  -4x-(-3-5x)= -3(2x-8) will be true.

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Answer:

15 is the answer

Answer: 1071.0 prep

Step-by-step explanation:

Answer:

The first one is complementary and the second one is supplementary, the third and fourth are neither.

Step-by-step explanation:

Answer:

The first picture is Complementary, the second picture is neither, and the third picture is supplementary

Step-by-step explanation:

The first picture is complementary because both angles measure 90 degress,  the second picture is neither because both angles do not add to a 90 or 180 sum. and the third picture is supplementary because both angles measure 180 degress.

Answer:

We know that the area of a square of sidelength L, is:

Area = L^2

In this case, we have:

L = 2cm + x cm

And we know that the area of the square is 7cm, then:

Area = 7cm^2 = (2cm + x cm)^2

7cm^2 =  4cm^2 + 4cm*xcm + (x cm)^2

7cm^2 = 4cm^2 + (4*x)cm^2 + x^2 cm^2

Now we can remove all the "cm^2" and just get the numbers:

7 = 4 + 4*x + x^2

We can subtract 4 in both sides to get

7 - 4 = 4 + 4*x + x^2 - 4

3 = 4*x + x^2

This is what whe wanted to prove.

Answer:

11.65$ : 100% = x : 94

94 because 100 - 6

Step-by-step explanation:

Do this:

11.65 x 94 = ?

divide the answer by 100

and that is your answer

Answer:

CVS

Step-by-step explanation:

i am pretty sure

Answer:

a) x =  7.5

b) x = 1

Step-by-step explanation:

a)

b)

Answer:

25+3(a−5)+7a.

25+3a-15+7a

7a+3a+25-15

10a+10

10(a+1)

Answer:

the answer is c

Step-by-step explanation:

Answer:

A = 48.81°

Step-by-step explanation:

Angles in a Right Triangle

When the side lengths of a right triangle are known and an angle must be determined, we can use the trigonometric ratios that relate angles and sides.

The tangent ratio is defined as:

[tex]\displaystyle \tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

Opposite leg to angle A is 8 and adjacent leg is 7, thus:

[tex]\displaystyle \tan A=\frac{8}{7}[/tex]

Using the inverse tangent funcion:

[tex]\displaystyle A=\arctan\frac{8}{7}[/tex]

Calculating:

A = 48.81°

Answer:

the answer is A

Step-by-step explanation:

5 * 8 = 40

300/40 = 7.5

Answer:

18 feet

Step-by-step explanation:

Answer:

Not teenagers = 1120

Step-by-step explanation:

Total number of audience members = 1600

30% of the audience were teenagers.

It means 70% of the audience were not teenagers. It can be given by :

x = 70% of 1600

[tex]x=\dfrac{70}{100}\times 1600\\\\x=1120[/tex]

Hence, 1120 audiences were not teenagers.

Answer:

10

Step-by-step explanation:

68 screwdrivers will be leftover at the end of day.

A division is a process of splitting a specific amount into equal parts.

Given that At the Medal Factory, the assembly line produces 98 screwdrivers in a batch.

The screwdrivers are packaged in boxes with 12 each.

If 5 batches are made in one day

We need to find  how many screwdrivers will be leftover at the end of it.

12 screwdrivers in each batch.

So for 5 batches there are 5×12=60 screwdrivers.

The left screwdrivers are 98-60=38

Hence, 68 screwdrivers will be leftover at the end of day.

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Answer:

15% chance

Step-by-step explanation:

The required probability is 0.0166 that you will dress all in a brown shirt, pants, socks, and shoes.

The probability that you will dress all in brown is the product of the probability of selecting each brown item.

There is only one choice of brown shirt out of a total of 5 shirt choices, so the probability of selecting a brown shirt is 1/5.

Similarly, there is only one choice of brown pants out of a total of 3 pant choices, so the probability of selecting brown pants is 1/3.

There is also only one choice of brown socks out of a total of 4 sock choices, so the probability of selecting brown socks is 1/4.

Finally, there is also only one choice of brown shoes out of a total of 3 shoe choices, so the probability of selecting brown shoes is 1/3.

To find the overall probability of dressing all in brown, you need to multiply these probabilities together: (1/5) × (1/3) × (1/4) × (1/3) = 1/60.

This means the probability of dressing all in brown is approximately 0.0166, or about 1.7%.

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Answer:

There were 120 questions on the test.

Step-by-step explanation:

It is given that:

Number of questions answered = 54

Grade percent = 45%

Let,

x be the total number of questions

45% of x = 54

[tex]\frac{45}{100}x=54\\0.45x = 54[/tex]

Dividing both sides by 0.45

[tex]\frac{0.45x}{0.45}=\frac{54}{0.45}\\x=120[/tex]

Therefore,

There were 120 questions on the test.

Answer: The population in 2025 will be 7669

Step-by-step explanation:

a) When we have an initial quantity A, and we have an increase of the X%, the new quantity is written as:

new quantity = A + A*(X%/100%) = A*(1 + X%/100%)

In this case, our initial quantity is 3500, the town's population in 2005.

And X% = 4%.

We know that each year, the population increases by 4%.

Then if P(1) is the population one year after 2005, this is:

P(1) = 3500*(1 + 4%/100%) = 3500*(1.04)

After another year, the population increases again:

P(2) = (3500*(1.04))*(1 + 4%/100%)) = 3500*(1.04)*(1.04) = 3500*(1.04)^2

Well, we already can see the pattern here, the population N years after 2005 will be:

P(N) = 3500*(1.04)^N

b) Now we want to know the population in 2025.

N represents the number of years after 2005, then we will have:

N = 2025 - 2005 = 20

2025 is 20 years after 2005.

Then the population in 2025 will be:

P(20) = 3500*(1.04)^20 = 7,668.9

And we can not have a 0.9 of a person, so we should round it up to the next whole number, then the population in 2025 will be 7669

To answer the questions, we need to understand the utility functions and budget constraints for both Joey and Jim. Let's break it down step by step:

Joey's Utility Function and Budget Constraint:

Joey's utility function for whisky (w) and beer (b) is given by: U(w, b) = 5 + (w^0.3 * b^0.7)

w: The quantity of whisky (in bottles) consumed by Joey

b: The quantity of beer (in cans) consumed by Joey

Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.

To find how many cans of beer and bottles of whisky Joey consumes, we need to maximize his utility function while staying within his budget constraint.

Joey's Budget Constraint:

Joey's total expenditure on drink (E) is given by: E = 2b + 6w

And we know that E = £75.

So, the budget constraint is: 2b + 6w = 75

Now, we can solve this problem using optimization techniques. However, without specific numerical values for the utility function and budget constraint, it's not possible to determine the exact quantities of beer and whisky consumed by Joey. We can only find the optimal consumption bundle if the specific values are given.

Joey's Indifference Curve and Budget Constraint Diagram:

To illustrate Joey's optimal consumption bundle, we would need to plot his indifference curve (representing his preferences) and his budget constraint (showing all possible affordable combinations of beer and whisky). However, without the exact values, we cannot draw the diagram.

Jim's Utility Function and Consumption:

Jim's utility function for beer (b) and whisky (w) is given by: U(b, w) = min{5, (w^0.3 * b^0.7)}

Jim's utility function shows that he insists on drinking beer and whisky together, and his utility is the minimum of 5 and the product of whisky and beer raised to certain powers.

Again, without specific numerical values for the utility function, we cannot determine the exact quantities of beer and whisky consumed by Jim.

In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint. With those values, we could then calculate the optimal consumption bundles for both Joey and Jim.

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Answer:

1.5 hours = 1 hour 30 mins

Step-by-step explanation:

3/4 = 0.75

0.75 x 2 = 1.5

Answer:

14 9/12

Step-by-step explanation:

Add the whole numbers then try to come up with a common denominator.

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. A base can be any whole number greater than 0. The most commonly used number system is the decimal system, commonly known as base 10. ... Binary is the most commonly used non-base 10 system.

Step-by-step explanation:

hope it helps ☺️