Pre-image point N(6, -3) was dilated to point N'(2, -1). What was the scale factor used?
What is the midpoint between (-8, 5) and (2, -2)?

ANSWER

[tex]\sqrt{5} [/tex]

EXPLANATION

The given radical expression is

[tex]5 \div \sqrt{5} [/tex]

This can be rewritten as

[tex] \frac{5}{ \sqrt{5} } [/tex]

We rationalize the denominator to get:

[tex]\frac{5}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } [/tex]

Recall that

[tex] \sqrt{x} \times \sqrt{x} = x[/tex]

This implies that,

[tex] \frac{5 \sqrt{5} }{5} [/tex]

Cancel out the common factors to get,

[tex] \sqrt{5} [/tex]

Answer:

Take x and 5x for example.

5x is a multiple of x.

If you were to add x and 5x, you'd get 6x.

So basically, when you add x and a multiple of x, just add 1 to the number in front of the multiple of x.

[Like how we did earlier, 5x + (1)x = 6x]

Answer:

add x and a multiple of x, and 1

Step-by-step explanation:

Answer:

The sales tax is equal to [tex]\$2.3[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

y-----> the cost of the purchase

x ----> the sales tax

step 1

Find the value of k

For [tex]y=76, x=3.80[/tex]

substitute

[tex]k=y/x[/tex]

[tex]k=76/3.8[/tex]

[tex]k=20[/tex]

The linear equation is equal to

[tex]y=20x[/tex]

step 2

what would be the sales tax on a purchase of $46

For [tex]y=46, x=?[/tex]

substitute in the equation

[tex]46=20x[/tex]

[tex]x=46/20[/tex]

[tex]x=\$2.3[/tex]

Answer:

$2.30

Step-by-step explanation:

We have been given that the amount of sales tax varies directly with the cost of the purchase.

We know that a direct variation in in form [tex]y=kx[/tex], where, y varies directly with x and k is constant of variation.

First of all, we will find constant of variation as:

[tex]\text{Sales tax}=k*\text{Cost of purchase}[/tex]

[tex]\$3.80=k*\$76[/tex]

[tex]\frac{\$3.80}{\$76}=\frac{k*\$76}{\$76}[/tex]

[tex]0.05=k[/tex]

To find the amount of sales tax on a purchase of $46, we will substitute [tex]k=0.05[/tex] in our equation as:

[tex]\text{Sales tax}=0.05*\$46[/tex]

[tex]\text{Sales tax}=\$2.30[/tex]

Therefore, the sales tax would be $2.30.

Answer:

Assuming that you're calculating surface area it would be:

16+10+10+10+10 or B

Step-by-step explanation:

Answer:

AC=16.2 units

Step-by-step explanation:

we know that

The triangle ABC is an isosceles triangle

so

AX=XC

because triangles ABX and CBX are congruents

AC=2*AX

see the attached figure to better understand the problem

therefore

AC=2*8.1=16.2 units

Final answer:

To find the length of AC, we add the lengths of segments AX and BC, giving us AC = 8.1 + 18.5, which equals 26.6 units.

Explanation:

If we are given that AB = 18.5 units, AX = 8.1 units, and BC = 18.5 units, then to find the length of AC, we simply need to add the lengths of segments AX and BC together, since AX and BC are adjacent segments on line AC. The formula to calculate AC in this situation is:

AC = AX + BC

Substituting the given values into this formula gives us:

AC = 8.1 units + 18.5 units = 26.6 units

Therefore, the length of segment AC is 26.6 units.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 8 = - [tex]\frac{1}{9}[/tex] (x - 7) is in this form

with slope = - [tex]\frac{1}{9}[/tex] and (a, b) = (7, - 8)

Answer:

B. 25

Step-by-step explanation:

We can use the altitude theorem, to quickly find the value of x.

According to this theorem; the altitude  of the triangle is equal to the geometric mean of the product of the two segments created by the leg of the altitude on the hypotenuse.

We apply this theorem to obtain:

[tex]10=\sqrt{4x}[/tex]

This implies that:

[tex]10^2=4x[/tex]

[tex]100=4x[/tex]

Divide both sides by 4 to obtain:

[tex]\frac{100}{4}=x[/tex]

[tex]x=25[/tex]

Answer:

$50

Step-by-step explanation:

So that means 40 percent is equal to $20 do

40:20

Divided by 2

20:10

Times 5

100:50

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

To calculate the cost per cup of bleach, first convert the quantity from gallons to cups. A 3-gallon bottle equals 48 cups. Divide the total cost ($13.92) by the total number of cups (48) to determine the cost per cup, which is $0.29.

This problem involves finding out the unit cost or, in this case, the cost per cup of bleach. One gallon is equivalent to 16 cups, hence a 3-gallon bottle is equivalent to 48 cups.

So, if $13.92 buys you 48 cups, you can calculate the cost per cup by dividing the total cost by the number of cups.

Proceed with the following calculation: $13.92 costs /48 cups = $0.29 per cup of bleach costs.

In conclusion, each cup of bleach from this 3-gallon bottle would cost you $0.29.

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To find the price per cup of bleach from a 3-gallon bottle costing $13.92, we multiply 3 gallons by 16 cups per gallon to get 48 cups, and then divide $13.92 by 48 to find the cost per cup, which is approximately $0.29.

To calculate the price per cup of bleach when given the price per gallon, we need to know how many cups are in a gallon and then divide the total cost by the total number of cups.

First, we establish that there are 16 cups in a gallon. Since we are dealing with a 3-gallon bottle, the total number of cups will be 3 gallons times 16 cups per gallon, which equals 48 cups.

Next, we take the total cost of the 3-gallon bottle, which is $13.92, and divide it by the total number of cups, 48. Performing this division gives us the cost per cup. So, $13.92 divided by 48 cups equals approximately $0.29 per cup.

This method demonstrates how to break down bulk costs into more manageable unit prices and can be applied across various products and measurements.

Answer:

3

Step-by-step explanation:

The given function is

[tex]f(x)=-x^2+6x+13[/tex]

The average rate of change is simply the slope of the secant line connecting any two point on the graph of the function.

The average rate of change  of this function over the interval;

[tex]-1\le x\le 5[/tex] is given by:

[tex]\frac{f(5)-f(1)}{5-1}[/tex]

[tex]f(5)=-(5)^2+6(5)+13[/tex]

[tex]f(5)=-25+30+13=18[/tex]

[tex]f(-1)=-(-1)^2+6(-1)+13[/tex]

[tex]f(-1)=-1-6+13=18[/tex]

[tex]f(-1)=6[/tex]

The average rate of change now becomes;

[tex]\frac{18-6}{4}[/tex]

[tex]\frac{12}{4}=3[/tex]

Answer:40.85

Step-by-step explanation:

43x5/100=2.15

43-2.15= 40.85

Answer:

The sale-price of this dress is $40.85

Step-by-step explanation:

Multiply 95 by 43 (since the dress is 5% off, it 95% of it's normal sales price). Divide that number by 100:

(95 × 43) ÷ 100

Solving both equations individually, we derive n = -5 from the first and n < 2 from the second. No common solution exists due to the nature of these equations.

This problem involves two separate equations where you’re asked to find the value of n that satisfies both. We solve this by treating each equation individually.

First equation: -1 + 5n = -26

 To resolve for n we can simply add '1' to both sides, which result in: 5n = -25. Then divide both sides by '5' to isolate n, implying n = -5.

Second equation: 7n - 2 < 12

We will apply the same logic and add '2' to both sides, which gives 7n < 14. Afterwards, dividing through by '7', which gives us n < 2.

From these two solutions, there is no value of n that validates both equations simultaneously.

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Answer:

$0.036

Step-by-step explanation:

I will be solving this questions in a rational, proportional way.

This question given is directly proportional. There are two types of proportion.

Direct - Let's say there are two values, x and y. In direct proportion, while x   increases, y increases with it.  

Inverse- Taking x and y, in inverse proportion, while x increases, y decreases or while y increases, x decreases.

In the given example, there are two values, number of plates and cost of plates. While the number of plates increases, the cost would surely increase. Therefore, giving us that it is a direct proportion.

500 plates : $18.00 :: 1 : $x

500 plates is to 18 dollars, then, 1 plate is to how many dollars?

In direct proportion, the product of extremes is equal to the product of means.

500(x) = 18(1)

500x = 18

x = 18 / 500

x = 0.036

Hence, one plate costs $0.036 or 3.6 cents

Answer:

each plate cost:  .036 each

18.00 divided by 500

Step-by-step explanation:

Answer:

Isosceles

Step-by-step explanation:

Consider triangle ABC, BD is the median and the altitude drawn to the side AC. This segment (BD) divide the triangle ABC into two triangles: ABD and CBD.

In these triangles:

Thus, by SAS postulate, triangles ABD and CBD are conruent. Congruent triangles have congruent corresponding sides. Hence, AB=CB.

If in triangle ABC, AB=BC, then this triangle is isosceles.

Answer:

Isosceles (apex)

Step-by-step explanation:

let's bear in mind that 1 Cup = 8 fl oz.

a) is absolutely correct, 18oz and thus they can fit fine in the 24oz container.

b) is correct, 24 - 18 = 6, we can fit in 6 more oz, which is 3/4 of a cup.

c) is correct as well

d)

we just need to convert c) units to fluid ounces

[tex]\bf 2\frac{1}{4}\implies \cfrac{9}{4}\cdot 8\implies \boxed{18}~\hfill 3\cdot 8\implies \boxed{24} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{juice}}{18}+\stackrel{\textit{water}}{12}+\stackrel{\textit{ice cream}}{24}\implies 54~\textit{fluid ounces}[/tex]

Answer:

1/2x-5=13

Step-by-step explanation:

Let x= Frankie’s mother’s age

Half his mother’s age= 1/2x

5 less than that=1/2x-5

We know that Frankie is 13 so that equation is equal to Frankie’s age, which is 13.

Hope this helps.

To determine Franky's mother's age, we can create an equation using the given information. By solving the equation, we find that Franky's mother is 36 years old.

To determine Franky's mother's age, we can create an equation based on the given information. Let's assume Franky's mother's age is M. According to the information given, Franky's age is 5 years less than half of his mother's age. So, Franky's age can be represented as (1/2)M - 5.

We are also given that Franky is 13 years old. So we can set up the equation:

(1/2)M - 5 = 13

To solve for M, we can simplify the equation:

(1/2)M = 13 + 5

(1/2)M = 18

M = 18 * (2/1)

M = 36

Therefore, Franky's mother's age is 36 years old.

Answer:

8

Step-by-step explanation:

The number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1 are:

                               36

We are asked to find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

We know that a number is even if the last digit of the number is divisible by 2 i.e. even.

Hence, the only digits among the given digits which is even is: 8

Now, at the first place any of the 6 digits could come up.

( Since, the digits could be repeated)

Also, at the second palace any of the 6 digits could come up.

Hence, the total number of such numbers possible are:

                 6×6×1=36

Answer:  B) 160

Step-by-step explanation:

Since the Standard deviation of 21 bins is 3 bins, then the first 7 bins falls in the first 2.5% edge of the bell curve.

2.5% of 21 times 1000 = (0.025)(21)(1000) = 160

ANSWER

[tex](b + 3)(1 - c)[/tex]

EXPLANATION

The given expression is:

[tex](b + 3) - c(b + 3)[/tex]

We can rewrite this to reveal the invisible 1 multiplying the first term.

[tex]1(b + 3) - c(b + 3)[/tex]

There is a common factor of (b+3).

We factor to get;

[tex](b + 3)(1 - c)[/tex]

Therefore the completely factored form of the given expression is

[tex](b + 3)(1 - c)[/tex]

What your are going to want to do is look for the average of the number (hope this helps some what!) good luck

Answer:

[tex]y(t) = 750 -50t[/tex]

Step-by-step explanation:

We want to model the position of the submarine as a function of time.

Notice that we have a constant amount. The initial depth: 750 meters

 Then we have a factor that varies over time. Every hour the submarine ascends 50 meters. therefore as t increases the depth y(t) of the submarine decreases. Then the factor is:

-50t.

Where t represents the time in hours.

Then the equation that represents the new position of the submarine in relation to the level of the sea:

[tex]y(t) = 750 -50t[/tex]

Answer:

im pretty sure it's -750 + 4 x 50

Step-by-step explanation:

This is the only answer that really makes sense to me

Answer: 15 feet

Step-by-step explanation: 28-13

The answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

To find the required function f(3), we need to use the given function f(x) and evaluate "x" equal to 3 (input).

We are given the function:

[tex]f(x)=(\frac{1}{6})^{x}[/tex]

Then, evaluating "x" equal to 3, we have:

[tex]f(3)=(\frac{1}{6})^{3}[/tex]

[tex]f(3)=(\frac{1}{6})^{3}=(\frac{1}{6})*(\frac{1}{6})*(\frac{1}{6})=(\frac{1}{6*6*6})[/tex]

[tex]f(3)=(\frac{1}{6*6*6})=(\frac{1}{216})[/tex]

Hence, we have that the answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Have a nice day!

Jared is correct because if you substitute a random number in for x 2 for example

2+10=12

2-10 doesn’t =12

Answer:

Both Jared and Nicole are correct. You can solve for either variable and use the equivalent expression to create a one-variable equation. Then you can solve. Jared would have created a one-variable equation that can be used to solve for x, whereas Nicole would have created a one-variable equation that can be used to solve for y.

Step-by-step explanation:

The phrase "eight times the sum of a number and 16 is at least -28" translates into the inequality 8(w + 16) >= -28. After solving, it shows that w must be greater than or equal to -19.5.

The student's question involves creating and solving an inequality. The inequality represents the phrase 'eight times the sum of a number and 16 is at least -28' and uses the variable w for the unknown number. The inequality in mathematical terms is:

8(w + 16) = -28

To solve the inequality, we first distribute 8 across the parenthesis:

8w + 128 = -28

Subtract 128 from both sides to get:

8w =-28 - 128

8w = -156

Now divide both sides by 8:

w = -19.5

This inequality shows that the number w must be greater than or equal to -19.5 to satisfy the original statement.

The solution to the inequality is [tex]\( w \geq -19.5 \)[/tex]

[tex]\[ w \geq \frac{-28 - 8 \times 16}{8} \][/tex]

[tex]\[ w \geq \frac{-28 - 128}{8} \][/tex]

[tex]\[ w \geq \frac{-156}{8} \][/tex]

[tex]\[ w \geq -19.5 \][/tex]

To solve this inequality, we'll first rewrite the given statement in mathematical terms. The problem states that "eight times the sum of a number and 16 is at least -28." Let's represent the unknown number by [tex]\( w \)[/tex]. According to the statement, we can write the inequality as:

[tex]\[ 8(w + 16) \geq -28 \][/tex]

To solve for [tex]\( w \)[/tex], we'll isolate it by performing operations to both sides of the inequality. First, we distribute the 8:

[tex]\[ 8w + 128 \geq -28 \][/tex]

Next, we'll subtract 128 from both sides to isolate the [tex]\( 8w \)[/tex] term:

[tex]\[ 8w \geq -28 - 128 \][/tex]

[tex]\[ 8w \geq -156 \][/tex]

Now, to solve for [tex]\( w \)[/tex], we divide both sides by 8:

[tex]\[ \frac{8w}{8} \geq \frac{-156}{8} \][/tex]

[tex]\[ w \geq -19.5 \][/tex]

So, the solution to the inequality is [tex]\( w \geq -19.5 \)[/tex]. This means that any number greater than or equal to -19.5 will satisfy the given condition. Therefore, the set of solutions is all real numbers greater than or equal to -19.5.

Complete question:

Eight times the sum of a number and 16 is at least -28 Use the variable w for the unknown number

Answer: 432ft. shadow

Step-by-step explanation:

Because Nora is 5’3”, you need to convert every numerical value into inches by multiplying them by 12 (12in = 1 ft.)

5’ x 12 = 60” + 3” = 63”

9’ x 12 = 108”

252’ x 12 = 3,024”

Then create equivalent fractions.

63/108 = 3,024/x

108 x 3024 = 326,592/63 = 5,184in.

Then convert it back into feet.

5,184/12 = 432ft.

Final answer:

Using the proportion of similar triangles, we find that if Nora, who is 63 inches tall, casts a 108-inch shadow, then the 3024-inch tall monument will cast a shadow that is 5184 inches long, or 432 feet.

Explanation:

To find the length of the shadow casted by the monument, we can use the concept of similar triangles. The proportion between the heights and shadows of Nora and the monument will be the same because the angle of the sunlight is the same for both. Nora is 5'3" tall, which is 63 inches, and she casts a 9-foot shadow, which is 108 inches. The monument is 252 feet tall, which is 3024 inches. Setting up the proportion, we have:

Nora's height : Nora's shadow = Monument's height : Monument's shadow

63 inches : 108 inches = 3024 inches : x inches

To solve for x (the length of the monument's shadow in inches), we cross-multiply and divide:

63 * x = 3024 * 108

x = (3024 * 108) / 63

x = 5184 inches

To convert this back to feet, we divide by 12 inches per foot:

x = 5184 inches / 12 inches/foot

x = 432 feet

Therefore, the length of the shadow cast by the monument is 432 feet.

Answer:

Answer D:  7/5

Step-by-step explanation:

Combine like terms:  add 21 to both sides, obtaining:

25n = 35, or n = 35/25, or n = 7/5 (Answer D)

Answer:

D. 7/5

Step-by-step explanation:

To solve -21 + 25n = 14 for n, you must first isolate the variable.To do this add 21 on each side of the equation, 21+-21 cancels out and 21 + 14 equals 35.

You now have 25n = 35. To then further isolate the variable, divide each side by 25.25 and 25 cancels out so you get n = 1.4.

7/5 is equal to 1.4

So it is D!!!!!!!!!!!!!

Answer:

A. A tennis tournament in which after each round, half the players are eliminated.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=40ft,\ leg=30ft,\ hypotenuse=x[/tex]

Substitute:

[tex]40^2+30^2=x^2\\\\1600+900=x^2\\\\2500=x^2\to x=\sqrt{2500}\\\\x=50\ ft[/tex]

You can see that you have a right triangle in the figure is a right triangle, which means that you can find the hypotenuse using the Pythagorean theorem:

[tex]d = \sqrt{30^2+40^2}=\sqrt{900+1600}=\sqrt{2500} = 50[/tex]

Answer:

12.56

Step-by-step explanation:

using the formula 2piR

Answer:

12.56 feet

Step-by-step explanation:

C= pie times diameter

Or

C= 2 times pie times radius

C= 3.14 times 4

Therefore, the circumference equals 12.56 feet