how do you solve this problem ??

Congruent triangles have congruent corresponding sides and angles, while similar triangles may or may not be congruent

The congruence statement is given as:

ΔPOG ≅ ΔSOR

The above means that:

Points P, O and G correspond to the points S, O and R

Hence, the corresponding side of PO in ΔPOG ≅ ΔSOR is SO

The congruence statement is given as:

ΔPOG ≅ ΔSOR

Hence, the congruent triangles are ΔPOG ≅ ΔROS

In figure 2, we have:

2 congruent sides, and 1 congruent angle between the congruent sides

Hence, the congruence postulate is SAS

The congruence statement is given as:

ΔABC ≅ ΔXYZ

The above means that:

Point A corresponds to the point X

Hence, the congruent angle of <A is <X

Read more about congruent triangles at:

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Given :

To Find :

Solution :-

Let us take that ,

→ number of flags sold = f

→ number of pennant sold = p

Money earned by selling flags

→ Money = $6 * f = $6f

Money earned by selling pennants

→ Money = $1*p = $1p

Total money earned

→ Total Money = $6f + $1p

Total items sold

→ Total items = f + p = 50 . . . . . (i)

According to the question ,

→ 6f + p = 115 . . . . . (ii)

Solving equations (i) and (ii) ,

On subtracting them ,

→ 6f - f = 115 -50

→ 5f = 65

→ f = 65/5

→ f = 13

Substitute this in equation (i) ,

→ 13 + p = 50

→ p = 50 -13 = 37

Hence they sold 13 flags and 37 pennants .

I hope this helps .

Answer:

116

Step-by-step explanation:

3 to the power of 4 is 81. 7x5 =35+81=116

Answer:

   -2.5 m/s^2

Step-by-step explanation:

From 2 seconds to 8 seconds (the last 6 seconds), the speed decreased from 15 m/s to 0. The average acceleration is ...

  (-15 m/s)/(6 s) = -2.5 m/s^2

Answer:

-84

Step-by-step explanation:

Let the number be x. Then we have,

[tex]\frac{x}{-7}[/tex] (the quotient of a number and -7)

[tex]\frac{x}{-7}-2[/tex] (decreased by 2)

[tex]\frac{x}{-7}-2=10[/tex] (is 10)

Now we can solve for x,:

[tex]\frac{x}{-7}-2=10[/tex]

[tex]\frac{x}{-7}=12[/tex]

[tex]x=-84[/tex]

So, the original number is -84

Answer:

-84

Step-by-step explanation:

[tex]\frac{n}{-7}[/tex] -2 = 10

add 2 to each side to get:

[tex]\frac{n}{-7}[/tex] = 12

multiply each side by -7 to get:

n = -84

Answer:

[tex]4p^2q-4q+8p[/tex]

Step-by-step explanation:

[tex](12p^2q+p-3pq^2)-(4q-7p+8p^2q-3pq^2)[/tex]

Apply rule [tex]-(-a)=a[/tex] and [tex]-(a)=-a[/tex]:

[tex]\implies 12p^2q+p-3pq^2-4q+7p-8p^2q+3pq^2[/tex]

Collect like terms:

[tex]\implies 12p^2q-8p^2q-3pq^2+3pq^2-4q+7p+p[/tex]

Combine like terms:

[tex]\implies 4p^2q-4q+8p[/tex]

Answer:

the zeroes are -2 and 8

Step-by-step explanation:

[tex]-x^2 +6x+16\\\implies -(x^2-6x-16)\\\implies -(x+2)(x-8)[/tex]

Therefore, the zeroes are -2 and 8

Ratio compares two quantities. The amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.

Given to us

The solubility of calcium carbonate is 14.

We know that to dissolve 14 milligrams of calcium carbonate we will need 1 liter of water. therefore, the ratio of water and calcium carbonate can be written as,

[tex]\rm \dfrac{calcium\ carbonate}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]

We need to find the amount of water needed to dissolve 14 grams of water, therefore, we will convert grams to milligrams,

1 gram = 1000 milligram

14 gram = 14,000 milligram

Using the same ratio,

[tex]\rm \dfrac{14,000\ milligram}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]

[tex]\rm {water} = \dfrac{14000\ milligram \times 1\ liter}{14\ milligram}[/tex]

water = 1000 liters

Hence, the amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.

Learn more about Ratio:

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Answer:

11700 m²

Step-by-step explanation:

Split the shape in two. One rectangle 150x30 and one triangle 180x80.

Find the areas of both and add them:

A = bh + 1/2bh

A = 150(30) + 1/2(180)(80)

A = 4500 + 7200

A = 11700

Answer:

One senior citizen ticket costs 4 dollars and one child ticket costs 7 dollars

Step-by-step explanation:

Let x be the cost of a senior ticket and y be the cost of a child ticket then...

3x+9y=75

8x+5y=67

We can simplify the first equation by dividing everything by 3...

x+3y=25

Now, isolate x by subtracting 3y from both sides

x=25-3y

We can solve this system of equations using substitution (substitute 25-3y for x)...

8(25-3y)+5y=67

200-24y+5y=67

Combine like terms

-19y+200=67

Subtract 200 from both sides

-19y=-133

Divide both sides by -19

y=7

Plug 7 back in for y to solve for x

x=25-3(7)=25-21=4

One senior citizens ticket costs 4 dollars and one child ticket costs 7 dollars.

Answer:

the regions whose populations have 9 as the power include Africa and Asia.

Step-by-step explanation:

Answer:

africa and asia

Step-by-step explanation:

Answer:

More than sign as the first equation will give 40 whereas the second one is 0 so the first equation is larger

Therefore more than

Answer:

B. card I'' increased by 1.2986 = 13 more than card H's

Step-by-step explanation:

Answer:D

Step-by-step explanation:

D

Answer:

I think the answer is letter C.15

Correct me if im wrong

#Thank you

Answer:

4 and 5

Step-by-step explanation:

Answer:

x >= 1/5

Step-by-step explanation:

2 + 5x >= 3

5x >= 1

x >= 1/5

Answer:

Find the inverse of g(x)=1/x-1+2 :

[tex]g^{-1} (x)=\frac{1}{x-1}[/tex]

The length of the other leg of the right triangle is; 89.44 centimetres

According to the question;

By the Pythagoras theorem;

Hence, It follows that;

Find the square root of both sides of the equation;

x = 89.44 centimeters

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Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I= PRT

[tex]simple \: interest = \frac{500 \times 3 \times 1}{100 \times 2} [/tex]

[tex] = \frac{1500}{200} [/tex]

=$7.50

Answer:

Angle C prime

Step-by-step explanation:

First design and sketch it:

Make a rectangle with corners C D E and F. 90 degrees each. Now rotate it 45 degrees to the left. Angle D is diagonally from Angle C.

I hope this helps! :)

According to the given confidence interval, we have that:

a) Since 12 ounces is part of the confidence interval, the interval does not provide convincing evidence that the true mean volume is different than 12 ounces.

b) Since 12 ounces is part of the confidence interval, the interval provides convincing evidence that the true mean volume is 12 ounces.

It is being tested if the true mean volume is different of 12 ounces, hence:

In this problem, the interval is (11.97, 12.05), hence it provides convincing evidence that the true mean volume is 12 ounces, and basically, item a is False and item b is True.

You can learn more about confidence intervals at brainly.com/question/16236451

Velocity can be represented in horizontal and vertical components

The horizontal component form of the velocity is 12.5 mph

The given parameters are:

Velocity = 25 mph

Angle = 60 degrees

The horizontal component form of the velocity is then calculated as:

[tex]v_x = 25 * \cos(60)[/tex]

Evaluate the product

[tex]v_x = 12.5[/tex]

Hence, the horizontal component form of the velocity is 12.5 mph

Read more about velocity at:

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Answer:

Answer: ¾

Step-by-step explanation:

» From the trigonometric identities:

[tex]{ \tt{ \sin {}^{2} \theta + \cos {}^{2} \theta = 1 }}[/tex]

» Substitute to the formular:

[tex]{ \tt {( \frac{ \sqrt{7} }{4} )}^{2} + { \cos }^{2} \theta = 1 } \\ \\ { \tt{ \frac{7}{16} + { \cos}^{2} \theta = 1 }} \\ \\ { \tt{ \cos {}^{2} \theta = 1 - \frac{7}{16} }} \\ \\ { \tt{( \cos\theta) {}^{2} = \frac{9}{16} }} \\ \\ { \tt{ \sqrt{ {( \cos \theta}^{2}) } = \sqrt{( \frac{9}{16}) } }} \\ \\ { \tt{ \cos \theta = \frac{ \sqrt{9} }{ \sqrt{16} } }} \\ \\ { \boxed{ \tt{ \cos \theta = \frac{3}{4} }}}[/tex]

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

As we observe the points, we can conclude that :

Translation along x axis is ~

[tex]\qquad \sf  \dashrightarrow \: 1 - ( - 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 \: \: units \: \: towards \: \: left[/tex]

Translation along y axis ~

[tex]\qquad \sf  \dashrightarrow \: - 8 - ( - 13)[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 8 + 13[/tex]

[tex]\qquad \sf  \dashrightarrow \:5 \: \: units \: \: towards \: \: down[/tex]

So, same goes with translation of (-5 , 9)

[tex]\qquad \sf  \dashrightarrow \: x \: \:coordinate = - 5 - 4 = - 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: y \: \:coordinate = 9 - 5 = 4[/tex]

So, the required coordinates of the image under same translation is ~

[tex]\qquad \sf  \dashrightarrow \:(-9, 4)[/tex]

Answer:

Please help look at the image I need help with number 4. I already did the line plot for number 3 and the data in on the chart. Thank you! :)

The total percent of decrease in price of the shares of Selena's stock which Selena first buys and then sold is 11.5 percent.

Percentage decrease in a number is the ratio of total decrease in the original value of a number to the decreased value in the percentage form.

Given information-

The total stock buy by the Selena in $32.

The total stock sold by the Selena in $28.32.

As the total stock buy by the Selena in $32, and the total stock sold by the Selena in $28.32. Thus the total decrease in the price of stock is,

[tex]C_s=32-28.32\\C_s=3.68[/tex]

Thus the total decrease in the price of stock is $3.68.

As the cost price of the stock is $32 and the total decrease in the price of stock is $3.68. Thus the total percent of decrease in the price of the stock is,

[tex]\Delta C_s=\dfrac{3.68}{32}\times100\\\Delta C_s=11.5[/tex]

Thus the total percent of decrease in the price of the stock is 11.5 percent.

Learn more about the percentage decrease here;

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