If triangle RAT was rotated 270° clockwise about the origin to create triangle R’S’T, what would be the length of segment S’T’?

let's firstly convert the mixed fractions to improper fractions and then multiply.

[tex]\bf \stackrel{mixed}{5\frac{3}{7}}\implies \cfrac{5\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{38}{7}}~\hfill \stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{38}{7}\cdot \cfrac{16}{7}\implies \cfrac{(38)(16)}{(7)(7)}\implies \cfrac{604}{49}\implies 12\frac{20}{49}[/tex]

The volunteers gave 1368 fliers in total.

Step-by-step explanation:

Given,

Fliers given by volunteers in first neighborhood = [tex]\frac{21}{38}[/tex]

Remaining fliers = 612

Fraction of remaining fliers = [tex]1-\frac{21}{38}=\frac{38-21}{38}[/tex]

Fraction of remaining fliers = [tex]\frac{17}{38}[/tex]

Let,

x be the total fliers given by volunteers.

[tex]\frac{17}{38}\ of\ x=612[/tex]

[tex]\frac{17}{38}x=612[/tex]

Multiplying both sides by [tex]\frac{38}{17}[/tex]

[tex]\frac{38}{17}*\frac{17}{38}x=612*\frac{38}{17}\\\\x=\frac{23256}{17}\\\\x=1368[/tex]

The volunteers gave 1368 fliers in total.

Keywords: fraction, division

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Answer:

C. and A.

Step-by-step explanation:

4. 5(x + 3) - 2x

5x + 15 - 2x

3x + 15

5. -6x + 2.5(x - 1) - 5x

-6x + 2.5x - 2.5 - 5x

-8.5x - 2.5

Answer:

5 years = 89,940

10 years = 107, 856

Step-by-step explanation:

75000 * 1.037 ^ 5 for the 5 years one

Then do the answer (89940) and times by 1.037 ^ 5. For 10 years

You do it to the power of 5 because you are adding on another 5 years

Answer:

[tex]\frac{104}{5}[/tex] weeks or [tex]20\frac{4}{5}[/tex] weeks

Step-by-step explanation:

To do this we can set up a proportion

[tex]\frac{52}{1} *\frac{2}{5}[/tex]

This will tell us how many weeks are in 2/5 of a year

Let's evaluate this

[tex]\frac{104}{5}[/tex]

We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below

[tex]20\frac{4}{5}[/tex] weeks

[tex]\text{We're trying to find how many weeks Ben has lived in London}\\\\\text{We know that there are 52 weeks in a year}\\\\\text{We also know that he's been in London for 2/5 of a year, or 40\%}\\\\\text{To find your answer, you could multiply 52 by 0.40}\\\\52*0.40= 20.8\\\\\boxed{\text{Ben has been in London for 20.8 weeks}}[/tex]

The value of expression is 63 when e = 4 and g = 6

Solution:

Given expression is:

[tex]5e^2-4g+7[/tex]

We have to solve the expression

Given that e = 4 and g = 6

Substitute e = 4 and g = 6 in given expression

[tex]\rightarrow 5(4)^2 -4(6) + 7\\\\Simplify\ the\ above\ equation\\\\\rightarrow 5(16) -24 + 7\\\\\rightarrow 80-24+7\\\\Simplify\\\\\rightarrow 56+7=63[/tex]

Thus value of expression is 63

Answer:

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.

Step-by-step explanation:

Let an exponential growth function is given by [tex]f(x) = a(b)^{x}[/tex]

So, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex], [tex]f(x) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex]

Therefore, this series of values corresponding to the x-value 1, 2, 3, and 4 are in G.P. and the common ratio is b.

Now, from the given tables in the options only the second option i.e. a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16 satisfies an exponential function.

Since, f(1) = 2, f(2) = 4, f(3) = 8 and f(4) = 16 are in G.P.(Answer)

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

94 dollars

Answer:

The discount would be $94.50 but the final price would be $220.25.

Hope this helps!

Answer:

∠A = 45°

Step-by-step explanation:

The sum of angles in a triangle = 180°.

That means in the triangle ABC, ∠A + ∠B + ∠C = 180°.

Given ∠B = 90° and ∠C = 45°.

⇒ ∠A + 90° + 45° = 180°

⇒ ∠A = 180 - 90 - 45

⇒ ∠A = 45° is the required answer.

Answer:

x=8

NR=5 units

BI=10 units

Step-by-step explanation:

In  a rectangle BRIA

AN=5 units

NR=x-3

We have to solve for x , NR and BI.

We know that

Diagonals of rectangle bisect to each other.

BI and AR are the diagonals of rectangle BRIA and intersect at point N.

AN=NR

[tex]5=x-3[/tex]

[tex]x=5+3=8[/tex]

[tex]x=8[/tex]

Substitute the value of x

NR=8-3=5

By property of rectangle

BI=AR=AN+NR=5+5=10 unit

BI=10 units

Answer:

y + 4 ≥ 25

if y is increased by 4 and is at least 25

Step-by-step explanation:

The given table:

X       Y

3    − 2

6    − 4

9   − 6

12  − 8

To find, the constant ratio, [tex]\dfrac{y}{x}[/tex] = ?

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-2}{3}[/tex],

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-4}{6}[/tex] = [tex]\dfrac{-2}{3}[/tex],

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex] and

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex]

Thus, the required option A) yes; [tex]\dfrac{-2}{3}[/tex] is correct.

Answer:

5x + 15 = -5x - 15

10x = -30

x = -3

y = 5(-3) + 15 = -15 + 15 = 0

(-3,0)

Step-by-step explanation:

Answer:

36 batches

Step-by-step explanation:

we know that

Each bath of cookies used 2/9 cup of sugar

so

using proportion

Find out how many batches of cookies Melinda makes for 8 cups of sugar

[tex]\frac{1}{(2/9)}\ \frac{bath}{cups}=\frac{x}{8}\ \frac{bath}{cups}\\\\x=8/(2/9)\\\\x=36\ batches[/tex]

Answer:

300.

Step-by-step explanation:

256 is closer to 300 than it is to 200 so it rounds to 300.

Answer:300

Step-by-step explanation:

Total area is 102.3 yd²

Step-by-step explanation:

Total area = area of the parallelogram + area of the right triangle

Calculate the area of the parallelogram.

Base = 11 yd, Height = 6.2 yd

⇒ Area of the parallelogram = Base × Height = 11 × 6.2 = 68.2 yd²

Calculate the area of the right triangle.

Height = 6.2 yd, Base = 11 yd (Since opposite sides of a parallelogram are equal)

⇒ Area of the triangle = 1/2 × base × height = 1/2 × 11 × 6.2 = 34.1 yd²

Calculate the total area.

⇒ Total area = 68.2 + 34.1 = 102.3 yd²

Answer:

a = 58

b = 34

Step-by-step explanation:

a + b = 92

a - b = 24

add

a + b + a - b = 92 + 24

2a = 116

a = 116 : 2

a = 58

b = 92 - 58

b = 34

Answer:

Step-by-step explanation:

Let the numbers be x and y

x + y = 92..........(1)

x - y = 24..........(2)

Adding (1) and (2)

2x = 116

x = 116/2

x = 58

From (1)... x + y = 92

58 + y = 92

y = 92 - 58

y = 34

Answer:

D

Step-by-step explanation:

When Y is a function of X, the graph is a v shape.

Answer:

1st triangle = 1

2nd triange= 3

3rd triangle = 9

4th triangle = 27

A triangle exists a three-sided polygon with three vertices and three edges. The number of triangles in the given figure exists 1, 3, 9, and 27.

A triangle exists a three-sided polygon with three vertices and three edges. It exists one of the major fundamental geometric forms.

The number of shaded triangles in each of the triangles exists shown below, thus, the number of triangles in each triangle can are:

1st triangle = 1

2nd triangle = 3

3rd triangle = 9

4th triangle = 27

Therefore, the number of triangles in the given figure exists 1, 3, 9, and 27.

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Answer:

The cross section would be a square.

Step-by-step explanation:

The 2 ends of the rectangular prism are squares while the other 4 sides are rectangles. A cross section would be perpendicular to the rectangles, making the cross section a square. The cross section would be parallel to the end squares.

a) ASA congruency

b)SAS congruency

c)SSS congruency

d) Not congruent

Step-by-step explanation:

Step 1:

a)

Angle PRQ = Angle RQS

Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.

QR is the common Side

Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.

Step 2 :

b)

Angle IGH = Angle EDF

Side IG = DF and Side GH = DE

Here 2 of the sides of the triangle are same and the Angle which is included are same.

Hence the given triangles are equal

Step 3:

c)

In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.

Step 4:

d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent

Answer:the answer is B

Step-by-step explanation:

The function that represents the exponential growth is

f(x) = 4 x [tex]1.05^n[/tex].

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

An exponential growth function.

Rate of change = 5%

This means,

There is a growth per year of 5%.

The function can be represented as,

f(x) = a [tex](1 +0.05)^n[/tex]

f(x) = a x [tex]1.05^n[/tex]

Where 100% = 1 and 5% = 0.05

Let a = 4

f(x) = 4 x [tex]1.05^n[/tex]

Thus,

The exponential growth function is

f(x) = 4 x [tex]1.05^n[/tex]

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The commission would be $2095.

Step-by-step explanation:

Given,

Commission on first $1000 = 7%

Amount of commission = 0.07*1000 = $70

Worth of sold items = $14,500

We will subtract $1000 from it.

Balance = 14500-1000 = $13500

Commission on balance = 15% = 0.15

Amount of commission = 0.15*13500

Amount of commission = $2025

Total commission = 70+2025 = $2095

The commission would be $2095.

Keywords: percentage, subtraction

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McKenzie would earn $2,095 in commission if her sales for the month were $14,500.

To calculate McKenzie's commission, we need to determine the amount of sales that fall under the 7% rate and the amount that falls under the 15% rate. First, we calculate the commission on the first $1,000 in sales: 7% of $1,000 = $70. Next, we calculate the commission on the remaining sales: $14,500 - $1,000 = $13,500. 15% of $13,500 = $2,025.

Finally, we add the two commissions together to get the total commission: $70 + $2,025 = $2,095. So McKenzie would earn $2,095 in commission if her sales for the month were $14,500.

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Answer:

6km

Step-by-step explanation:

Area of circle = πr²

Where r = radius,  π= 3.14, A = 28.26km²

A = 3.14 x r²

3.14 r2 = 28.26

Divide both sides by 3.14

r²= 28.26/3.14

r² = 9

Square root both sides

r= √9

r= 3

Radius = 3km

Note : Diameter = 2 x radius

Diameter = 3 x 2

Diameter = 6km

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Answer:

Option B

Step-by-step explanation:

The function in the graph is an exponential growth function.

Therefore its equation is [tex]g(x)=3^x[/tex]

A transformation that shrinks this graph is of the form: [tex]f(x)=k*3^x[/tex] where [tex]0\:<\:k\:<\:1[/tex]

From the given options, we must have [tex]k=\frac{1}{2}[/tex]

This implies that:

[tex]f(x)=\frac{1}{2} (3)^x[/tex]

Answer:

B

Step-by-step explanation:

Answer:

{x| x < 10 and x > 14} is an empty set.

there cannot be any intersection between the two ranges that is , x< 10 and x>14.

Step-by-step explanation:

x < 10 and x > 14 will lead to an empty set.

there cannot be any intersection between the two ranges that is , x< 10 and x>14.

Final answer:

The set with condition { | < 10 and > 14} is the empty set, as no elements can satisfy being both less than 10 and greater than 14 simultaneously.

Explanation:

The set being asked about is defined as { | < 10 and > 14}.

To determine if this set is the empty set, interpret the conditions placed upon the members of the set.

The description says that an element must be both less than 10 and greater than 14 at the same time, which is an impossible condition. Since no number can satisfy both conditions simultaneously, no elements can exist within this set, making it the empty set, often denoted by Ø.

Answer:

$8.60

Step-by-step explanation:

Answer:

$8.60

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

7x3=21

Answer:21

Step-by-step explanation:

You can get it srry if that was mean

Answer:

The measure of side AC is 6 cm.

Step-by-step explanation:

The information for the triangle ABC are:

AB = 6 cm

m∠A = 80°

m∠B = 50°

The sum of all angles of a triangle is 180°.

Compute the value of m∠C as follows:

m∠A  + m∠B + m∠C = 180°

m∠C = 180° - 80° - 50°

        = 50°

Thus, the angles, m∠C = m∠B.

Consider the triangle below.

If two angles of a triangle are equal or similar then that triangle is known as an isosceles triangle.

And in an isosceles triangle the sides corresponding to the equal angles are equal.

Then in this case as m∠C = m∠B then sides AC = AB.

The measure of the side AC is 6 cm.

Final answer:

To find the new temperature of the soup after cooling for 25 minutes, multiply the rate of decrease, 2.3 F/min, by 25 minutes to find the total decrease in temperature, which is 57.5 F. Then subtract this from the initial temperature of 192.7 F to get the final temperature of 135.2 F.

Explanation:

The question is about calculating the new temperature of chicken soup after it cools for a certain period. The initial temperature of the soup is 192.7 F, and it's stated that the soup temperature decreases by 2.3 degrees per minute. Since it's asking for the temperature after 25 minutes, we need to multiply the rate of cooling by the number of minutes.

To calculate the new temperature:
Decrease in temperature = 2.3 F/min × 25 min = 57.5 F

The new temperature would then be:
Initial temperature - Decrease in temperature = 192.7 F - 57.5 F = 135.2 F.

Problem Solving Strategies for the Effects of Heat Transfer

Although the question does not require complex problem-solving strategies involving specific heat capacity or mass of the substance, it does simulate a simplified version of heat transfer where we only consider the overall change in temperature over time.