An isosceles trapezoid has base lengths of 12 in and 18 in. If the area of the larger shaded triangle is 72 square inches, find the area of the smaller shaded triangle.

Answer: C. y - 1 = 1/2(x-5)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = 1/2

y1 = 1

x1 = 5

y - 1 = 1/2(x-5)

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4}\implies A=4000(1.0125)^{16}\implies \boxed{A\approx 4879.56} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}}[/tex]

[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4}\implies A=4000(1.0275)^8\implies \boxed{A\approx 4969.52}[/tex]

well, "better" meaning more amount per same 4000, clearly the latter will be better.

Answer:

Rosemont Savings Bank; interest is $969.52

Step-by-step explanation:

because i said so <3

If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Density = mass/volume

A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.

Then the approximate density of the aluminum will be

The volume of the aluminum brick will be

V = 29 x 15 x 5.1

V = 2218.5 cubic cm

Then the density will be

D = 19,745 / 2218.5

D = 8.900 gram per cubic cm

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Answer:

25

Step-by-step explanation:

50/2=25

The similarity ratio by taking the cube root of each volume is 8/13,  ratio of the surface areas is 64/169, and surface area of the larger solid is 2535 square cm.

It is defined as a three-dimensional space enclosed by an object or thing.

Part 1:

Volume of larger solid = (512) cubic cm

Volume of small solid = 2197 cubic cm

Ratio of the volumes = 512/2197

Taking cube root:

Similarity ratio = 8/13

Part 2:

Similarity ratio by taking the cube root of each volume = 8/13

Taking the square of the above ratio:

= 64/169

Part 3:

64/169  = 960/SA(larger)

SA(larger) = 2535 square cm

Thus, the similarity ratio by taking the cube root of each volume is 8/13,  ratio of the surface areas is 64/169, and surface area of the larger solid is 2535 square cm.

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The cost of one pair of shoes is $8.

The cost of one shirt is $12.

2a + b = 32 equation 1

2a + 3b = 48 equation 2

Where:

Subtract  equation 1 from  equation 2

2b = 16

b = 16/2

b = $8

Substitute for b in equation 1

2a + 8 = 32

2a = 32 - 8

2a = 24

a = 24 / 2

a = $12

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The pair of rational numbers with their sum are matched.

The numbers in the form of p/q is called the rational number.

1. -2/a²b +2/ab² = ( -2ab² +2a²b) / a³b³

                          = 2(a-b)/a²b²

2. 1/2ab -1/4a²b² =( 4a²b² -2ab) / 8a³b³

                            = 2ab -1 /4a²b²

3. 2/a²b³ -2/ab = (2ab -2a²b³) / a³b⁴

                         = 2( 1- ab²) /a²b³

4. 1/ab³ -1/a²b = a²b - ab³ / a³b⁴

                       = (a - b²) / a²b³

Thus, all the rational numbers are matched with their sum.

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Answer:

x = 5 only

≡ On a graph, the point touches (5, 0), making x equal to 0.

≡ In other words, you must replace y with 0 to solve for x. There is no y term in this problem, so you must determine y by separating the coefficients into groups and determining each part.

The mistake he made is that he Yuri divided by n instead of n -1.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.

In order to determine the standard deviation, take the following steps:

• Determine the mean of the observation: 14

Determine the difference between each value and the mean and then square the result: (12 - 14)² + (14 - 14)² + (9 - 14)² + (21 - 14)² = 78

Determine the mean of the sum of the squared differences and then find the square root of the mean: √78/(n - 1) = 5.1

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Answer:

Yuri divided by n instead of n -1.

Step-by-step explanation:

The answer above is correct.

Answer:

hre is your tense chart

Step-by-step explanation:

mark me brainliest

Answer:

y = 3x + 7

Step-by-step explanation:

apply the rule

[tex]y-y_{0} =m(x-x_{0} )[/tex]

where

[tex]x_{0}, y_{0}[/tex]

they are taken from the point  (-2, 1), and "m" is the slope (3)

Then

[tex]y-1=3(x--2)[/tex]

[tex]y-1=3(x+2)[/tex]

[tex]y=3x+6+1[/tex]

[tex]y=3x+7[/tex]

Hope this helps

Answer:

y=-2x+10

Step-by-step explanation:

i graphed it i graphed all of them

Answer:

y-2x-2

Step-by-step explanation:

The way I would do this is by first using the information given and making an equation in point-slope form, before bringing it to y=mx+b.

We know that the slope is -2, and we have a point, (2,-6). The formula for equations in point slope form is [tex]y-y_{1} =m(x-x_{1} )[/tex]. So, we can insert the given information into this formula to get [tex]y+6=-2(x-2)[/tex].

Next, we distribute the slope to the the parenthesis to get [tex]y+6=-2x+4[/tex]

Then, we subtract 6 from both sides to get [tex]y=-2x-2[/tex]

Since this equation is now in the form [tex]y=mx+b[/tex], the answer is [tex]y-2x-2[/tex]

Hope this helps! :)

Answer:

No solution.

Step-by-step explanation:

When two lines have the same slope but different y-intercepts, they are parallel.  Parallel lines never intersect, and therefore there is no solution.

The true statements about the diagram given are:

3. m∠JKL = 45°

4. m∠MKQ + m∠PKQ = m∠PKM

5. PK is an angle bisector

An angle bisector is a segment that divides a given angle into two parts that are congruent to each other.

The missing part of the question is in the image attached below.

In the image given, PK bisects the straight angle JKM since angles JKP and MKP both equal 90 degrees (right angle).

Therefore, m∠JKL = m∠PKL = 45°

m∠MKQ + m∠PKQ = m∠PKM based on the angle addition theorem.

Therefore, the true statements are:

3. m∠JKL = 45°

4. m∠MKQ + m∠PKQ = m∠PKM

5. PK is an angle bisector

(see image attached below)

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Answer:

hope you can understand

Answer:

0.0178 is the answer

Answer:

x = ±2

Step-by-step explanation:

Given :

y = 64 - 16x²

=========================================================

Add 16x² to each side (take y = 0) :

⇒ 0 + 16x² = 64 - 16x² + 16x²

⇒ 16x² = 64

=========================================================

Divide both sides by 16 :

⇒ 1/16 × 16x² = 1/16 × 64

⇒ x² = 4

=========================================================

Taking square root on both sides :

⇒ √(x²) = √4

⇒ x = ±2

[tex]\text{Given that,}\\\\~~~~~~~2x^4 +2y^4 +2z^4 = 144\\\\\implies 2(x^4+y^4 +z^4) = 144\\\\\implies x^4 +y^4 +z^4 = \dfrac{144}{2}\\\\\implies x^4 +y^4 +z^4 = 72\\\\\text{Mean} = \dfrac{x^4+y^4+z^4}{3}\\\\~~~~~~~~=\dfrac{72}{3}\\\\~~~~~~~~=24[/tex]

Inequalities help us to compare two unequal expressions. (-6, 3) is not the solution to the system of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The graph of y ≥ −3x + 3 will be a solid line with the equation y=−3x + 3, this solid line signifies that the value on this line is also included in the solution. Since the symbol is '≥' therefore the area above the line will have the solutions.

The graph of y<(3/2)x -6 will be a dashed line with the equation y=(3/2)x - 6, this dashed line signifies that there is no solution on the line. since the inequality symbol is '<' therefore, the area under the dashed line will have all the solutions.

The area where both shaded areas meet is the area that will have all the possible solutions.

PartB:

y ≥ −3x + 3

3 ≥ -3(-6) + 3

3 ≥ 18 + 3

Since the above inequality is not satisfied, (-6, 3) is not the solution to the system of inequalities.

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Answer:

Solution and how to convert 8 / 21 into a percentage

0.38 times 100 = 38.1. That's all there is to it!

Step-by-step explanation:

hope this helps

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex](\frac{1}{4}) ^{2}[/tex] can also be written as [tex](\frac{1}{4} )(\frac{1}{4} )[/tex]

So the answer is just [tex]\frac{1}{16}[/tex]

Answer:

72 mins or 1 hour 12 mins

Step-by-step explanation:

1 miles = 9 mins

8 miles = 9×8 mins

8 miles = 72 mins = 1 hour 12 mins

Hope this helped and brainliest please

The cost of a tea cup and a cup of coffee in the shop is £0.90 and £1.50 respectively.

let

x + 2y = 3.90

3x + y = 4.20

Multiply (1) by 3 to eliminate x

3x + 6y = 11.70

3x + y = 4.20

5y = 7.50

y = 7.50/5

y = 1.50

Substitute y = 1.50 into (1)

x + 2y = 3.90

x + 2(1.50) = 3.90

x + 3 = 3.90

x = 3.90 - 3

x = 0.90

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Answer:

Step-by-step explanation:

2500( 7 years )

????? (15 years )

15*2500=37 500

[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]

[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]

As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.

Answer:

This is put together very weird, can you put the answers more clearly?

Step-by-step explanation:

?

The final coordinates after the transformations will be:

A" is (-1, 5),

B" is (0, 1),

C" is (-3, -1).

Reflect across the y-axis: For any point (x, y), the reflection across the y-axis is (-x, y).

Translation by vector <1, 3>: For any point (x, y), the new coordinates after translation are (x + 1, y + 3).

Let's apply these transformations step by step:

A (2, 2):

Reflect across y-axis: (-2, 2).

Translate by <1, 3>: (-2 + 1, 2 + 3) = (-1, 5).

So, A" is (-1, 5).

B (1, -2):

Reflect across y-axis: (-1, -2).

Translate by <1, 3>: (-1 + 1, -2 + 3) = (0, 1).

So, B" is (0, 1).

C (4, -4):

Reflect across y-axis: (-4, -4).

Translate by <1, 3>: (-4 + 1, -4 + 3) = (-3, -1).

So, C" is (-3, -1).

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Answer:

x = 7 or -6

Step-by-step explanation:

Let a number be x.

Its square = x²

x - x² = 42

-x² + x - 42 = 0

-(x² - x + 42) = 0

x² - x + 42 = 0

(x - 7)(x + 6) = 0

x - 7 = 0 or x + 6 = 0

x = 7 or x = -6

Answer:

-1 and -4

Step-by-step explanation:

-1 + -4 = -5

-1 times -4 = 4

give brainiest please!

hope this helps ;)

Some examples of additions with integers with 5 terms or more are:

In mathematics, an integer is a whole number that is used to represent a value and is not a fraction.

Furthermore, we can make the addition of integers as they would increment based on the number they are being incremented with and this has been shown above.

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