Simplify the expression. Write your answer as a power.
((-3)²)⁴
The simplified expression is

Applying the Pythagorean theorem, the missing lengths in the right triangles are:

1. √19 ≈ 4.4

2. √96 ≈ 9.8

3. √60 ≈ 7.7

4. √231 ≈ 15.2

5. √21 ≈ 4.6

6. √24 ≈ 4.9

The Pythagorean theorem is a formula that can be used to find the leg of a  right triangle, and is given as: c² = a² + b², where a and b are the smaller legs and c is the longest leg/hypotenuse.

1. missing leg = √(10² - 9²) = √19 ≈ 4.4

2. missing leg = √(11² - 5²) = √96 ≈ 9.8

3. missing leg = √(8² - 2²) = √60 ≈ 7.7

4. missing leg = √(16² - 5²) = √231 ≈ 15.2

5. missing leg = √(5² - 2²) = √21 ≈ 4.6

6. missing leg = √(7² - 5²) = √24 ≈ 4.9

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Answer:

5 gallons

Given:

• Liters in 1 gallon

• Cooler holds 18 liters

Step-by-step explanation:

[tex]\sf 18L \div 3.785 = 4.75G[/tex]

≈ [tex]\sf 5G[/tex]

Answer:

5 gallons

Step-by-step explanation:

Unit conversion (given) : 1 gallon = 3.785 liters

Here, we are given 18 liters.

Then, let the value in gallons be x. We can take the values in proportion.

⇒ [tex]\frac{x}{1} = \frac{18}{3.785}[/tex]

⇒ [tex]x = \frac{18}{3.785}[/tex]

⇒ [tex]x = 4.75561427[/tex]

⇒ x = approximately 5 gallons

Answer:

4

Keys:

Step-by-step explanation:

[tex]4\left(\left(2\right)\cdot \:2+2\left(-2\right)\right)-2\left(-2\right)\\\left(2\right)\cdot \:2+2\left(-2\right)\\=4+2\left(-2\right)\\=4-4\\=0[/tex]

[tex]=4\cdot \:0-2\left(-2\right)\\4\cdot \:0\\=0\\=0-2\left(-2\right)[/tex]

[tex]2\left(-2\right)\\=-4\\=0-\left(-4\right)[/tex]

[tex]0-\left(-4\right)\\=0+4\\=4[/tex]

Answer:

Step-by-step explanation:

The mean is the average value: the sum divided by the number of numbers. The median is the middle number when they are written in increasing order. The mode is the number that appears most often. The range is the difference between the highest and lowest values.

__

Sorted into increasing order, the numbers are ...

  43, 57, 67, 87, 98

The total of these values is

  43 +57 +67 +87 +98 = 352

The mean is this sum divided by the number of contributors:

  mean = 352/5 = 70.4

__

The median of the 5 numbers is the middle (3rd) one:

  median = 67

__

The mode is the most-repeated number. All of the numbers show up exactly once, so there is no mode.

  mode: none

__

The range is the difference between the highest and lowest values:

  range = 98 -43

  range = 55

Types of Triangles (Angles):

---Acute = all angles are less than 90 degrees

---Right = one angle is equal to 90 degrees

---Obtuse = one angle is greater than 90 degrees

Types of Triangles (Side Lengths):

---Equilateral = all sides are the same length

---Isosceles = two sides are the same length

---Scalene = all sides are different lengths

The following triangle is obtuse and scalene. It has one angle that is greater than 90 degrees and its sides are all different lengths.

Hope this helps!

B. Scalene

E. Obtuse

Triangles can be classified in 2 different ways. They can be classified based on their sides and angles.

Sides

There are 3 different categories for the sides: scalene, isosceles, and equilateral.

Angles

Triangles can be classified as acute, obtuse, or right based on their angles.

Scalene Obtuse Triangle

The triangle above has no equal sides, so it must be scalene. Additionally, because one of the angles is 132 degrees, it must be an obtuse triangle.

The student is incorrect, the actual x-intercept is (5, 0).

Here we have the equation:

x + 2y = 5

The student says that the x-intercept is the point (0, 5).

So if you look at the point you already can see that the student is incorrect, this is because the x-intercept always must have a y-value of 0. (the graph only intercepts the x-axis when y = 0).

So the point (0, 5) can't be an x-intercept.

For the given function:

x +2y = 5

The x-intercept is given by:

x + 2*0 = 5

x = 5

So it is (5 , 0).

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To find the area of a complex shape:

 ⇒ must cut the whole shape into a simpler shape

Let's calculate:

             [tex]Area = \frac{1}{2}*4*8 + \frac{1}{2}*4*8=16+16=32\\[/tex]

             [tex]Area = \frac{1}{2}*4*10 + \frac{1}{2}*4*10=20+20=40[/tex]

             [tex]Area = 4 * 4=16[/tex]

Total Area: 32 + 40 + 16 = 88 in²

Answer: 88 in²

Hope that helps!

Answer: 1190 pages

Step-by-step explanation:

The word problem states that Grace has a set of 14 notebooks, and each notebook has 85 pages. To find the total number of pages, we want to multiply the number of pages in each book by how many books there are.  

14×85=1190 pages

Answer:

[tex]9.5 \div 100 \times 841.99 = 79.99 \\ \\ 841.99 + 79.99 \\ 921.98[/tex]

Answer:

$921.98905

Step-by-step explanation:

To find the sales tax amount we need to find 9.5% of 841.99

for this we can use 2 methods:

Method 1-

P%* X= Y

9.5%*841.99= Y

Convert 9.5% to a decimal by removing the percent sign and dividing by 100: 0.095

Substitute 0.095 for 9.5% in the equation: 9.5% * 841.99 = Y becomes 0.095 * 841.99 = Y

Do the math: 0.095 * 841.99 = 79.98905

OR

method 2-

9*841.99

=7998.905

÷100

=79.98905

Now that we know how much the the amount is all we have to do is add the amount with the original price of the tv

$841.99 + $79.97905= $921.98905

Answer:

Plan B

Step-by-step explanation:

If you multiply 21 by $2.50 you get $52.5 then add $5 you get 57.5 and that's you outcome for Plan A

but if you multiply 21 by $1.50 you get $31.5 then add $24 you get $55.5 so the best and cheapest plan would be Plan B

The inequality equation will be 0 < -15 - y. Then the value of the variable y is less than negative 15.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Zero is less than negative fifteen decreased by y, can be written as mathematically

0 < -15 - y

Then solving for y, we have

y < -15

The value of the variable y is less than negative 15.

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The volume of the sphere will be 49π cubic cm. Then the correct option is C.

Let r be the radius of the sphere.

Then the volume of the sphere will be

V = 4/3 πr³ cubic units

The figure shows a vertical cross-section of a sphere inscribed in a right cone.

A vertical cross-section of a sphere inside a cone has a radius labeled as r. The height of the cone is 12 centimeters. The half length of the face of the cone is 5 centimeters.

Then the volume of the sphere will be

In ΔADF, we have

tan a = 5 / 12

      a = 22.61°

Then in triangle ΔABC, we have

   sin 22.61° = r / (12 - r)

           0.38 = r / (12 - r)

4.62 - 0.38r = r

           1.38r = 4.62

                  r = 3.34 cm

Then the volume of the sphere will be

V = 4/3 π(3.34)³

V = 49π cubic cm

Then the correct option is C.

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Answer:

49cm

Step-by-step explanation:

49cm i got it right on edmentum

Answer:

10.19

Step-by-step explanation:

Use the Pythagorean Theorem:

[tex]a^{2}+b^{2}=c^{2}[/tex]

Substitute the numbers given:

[tex]11^{2}+b^{2}=15^{2}[/tex]

[tex]121+b^{2}=225\\ b^{2}=225-121\\ b^{2}=104\\ \sqrt b^{2}= \sqrt{104} \\ b=10.19[/tex]

Answer:

63.5 m from the ground

answer is 66.9 ft

top is the step by step explanation, hope it helps <3

Answer:

Step-by-step explanation:

According to definition, angles 4 and 2 are exterior angles.

The matching answer choices are E and F

Answer: The number of sides of the base of a prism and the number of lateral faces is equal.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

edge exam

Answer: 8

Step-by-step explanation:

The triangles are congruent by SAS, so using CPCTC, the answer is 8

The positive measure is 220° and the negative measure is -140°.

First, we know that the reference angle is 40°, and it lies on the third quadrant.

So these 40° are measured from the negative x-axis (the axis where the quadrant starts).

This means that the angle measured in the standard way (from the positive x-axis) measures:

M = 40° + 90° + 90° = 220°.

To find the negative measure, we remember that any angle A is equivalent to:

B = A + n*360°.

Where n is an integer.

If we take n = -1 for our angle, we get:

M' = 220° + (-1)*360° = -140°.

So the positive measure is 220° and the negative measure is -140°.

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Answer:

7/6

Step-by-step explanation:

6*1=6

6+1=7

7/6

Hope this helped! :)

The angles NOS, NOT, NOU, VOR, VOQ, VOP​ are obtuse angles

An angle whose measure is more than 90 degree is called an obtuse angle.

In the given figure , the angles which have value more than 90 degree needs to be found.

The angles NOS, NOT, NOU, VOR, VOQ, VOP​ are obtuse angles as their measure is more than 90 degree.

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Answer:

Answer E is correct

Step-by-step explanation:

We know that,

[tex](x^ay^b)^c=x^a^cy^b^c[/tex]

Let us use the above to find the answer to this question.

Let us solve it now.

[tex](a^\frac{2}3} b^\frac{1}{3})^\frac{1}{2}[/tex]

[tex]a^\frac{2}3}^*^ \frac{1}{2} *b^\frac{1}{3}^*^\frac{1}{2}[/tex]

[tex]a^\frac{2*1}{3*2} * b^\frac{1*1}{3*2}[/tex]

[tex]a^\frac{2}{6} * b^\frac{1}{6}[/tex]

Here, we can simplify the [tex]a^\frac{2}{6}[/tex] as [tex]a^\frac{1}{3}[/tex] by dividing the numerator and denominator by 2.

Therefore, the answer will be,

[tex]a^\frac{1}{3} b^\frac{1}{6}[/tex]

By applying the law of sines, the length of side PQ is equal to 7.1 units.

The law of sines is also referred to as sine law and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

Mathematically, the law of sines is given by this equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

Substituting the given parameters into the formula, we have;

[tex]\frac{sin80}{PQ} =\frac{sin42}{4.8} \\\\\frac{0.9848}{PQ} =\frac{0.6691}{4.8}\\\\0.6691PQ = 4.7270\\\\PQ = 4.7270/0.6691[/tex]

PQ = 7.1 units.

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Answer:

16 red marbles

Step-by-step explanation:

8 red

9 yellow

7 green

total = 8 + 9 + 7

p(red) = 8/24 = 1/3

Add r number of red marbles to the total.

8 + r red

9 yellow

7 green

total = 8 + r + 9 + 7 = r + 24

p(red) = (8 + r)/(r + 24) = 3/5

Cross multiply.

40 + 5r = 72 + 3r

2r = 32

r = 16

Answer: 16 red marbles

Answer:

16

Step-by-step explanation:

bag red: 8 + x

yellow:9

green 7/24

3/5 = 8+ x/24+ x

5(8 + x) = 3 (24 + x)

40 + 5x

-40 -3x = 72 + 3x

-40 -3x    -40 - 30

2x/2 = 32/2  so,x = 16

The inequality that represents the possible length of the patio is √A < 625.

Maddie's backyard is 25 meters by 25 meters.

Therefore,

area of the backyard = 25 × 25  = 625 m²

Hence,

She wants to put a square cement patio in her backyard.

A = area of the patio, in square meters.

Hence,

area of the backyard = 625 m²

Therefore, the inequality that represents the possible length of the patio is √A < 625.

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