Use the power reducing fabulous rewrite the identity in terms of the first power of cosine

Based on the definition of the median and applying the centroid theorem, the length of WI is calculated as: 6 units.

The line that joins the vertex of a triangle to the midpoint of the side it is directly opposite is called the median of a triangle.

Medians intersect each other at a point inside the triangle that is called the centroid. Based on the centroid theorem, since J is the centroid of triangle XYW, then:

the length of IE is one-third of the length of segment EW (referring to the image given in the question that shows triangle XYW)

Thus, we have the equation that relates the length of the segments as shown below:

IE = 1/3(EW)

Given that:

IE = 3 units

Substitute the value of IE into the equation:

3 = 1/3(EW)

3(3) = EW

9 = EW

EW = 9 units

Therefore:

Length of WI = the length of EW - the length of IE

Substitute

Length of WI = 9 - 3

Length of WI = 6 units.

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Answer:

0 (its a straight line horizontal)

Step-by-step explanation:

-3+3=0

18-3=15

0/15 = 0

slope=0

Given:

The linear equations are,

The objective is to solve by elimination method.

The equations can be rearranged as,

To solve the equation, multiply equation (1) b

Answer:

1)

The hypotenuse is the longest side of a triangle. It is ALWAYS the one across from the right angle (depicted as the box in the corner at 90 degrees). Therefore the 2 sides that intersect the 90-degree angle are "leg" and "leg" and the longest side is the"hypotenuse"

2)

The Pythagorean theorem states: [tex]a^{2} + b^{2} = c^{2}[/tex]  where a and b are sides and c is the hypotenuse.

[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 6^{2} = c^{2} \\64 + 36 = c^{2} \\100 = c^{2} \\\sqrt{100} = c\\10 = c[/tex]

For your purposes, a and b do not matter which number you choose as long as you make sure that they are sides and not the hypotenuse.

3)

The Pythagorean theorem states: [tex]a^{2} + b^{2} = c^{2}[/tex]  where a and b are sides and c is the hypotenuse.

[tex]a^{2} + b^{2} = c^{2} \\4^{2} + 7^{2} = c^{2} \\16 + 49= c^{2} \\65 = c^{2} \\\sqrt{65} = c\\8.0622 = c[/tex]

Hope that helps!

Answer:

150 gram is the word

Answer:

a. (7x²+2) + (2x²+3)

= 9x² + 5

b. (5x + 2) + (8x + 3)

= 13x +5

c. (5x)(8x + 3)

= 40x² + 15x

Answer:

here you go I guess

Step-by-step explanation:

Answer:

Explanation:

Terry bought 2 shirts for $14 each.

That is $28 on shirts

2 pair of socks for $2.99

That is $5.98 on socks

A pair of slacks for $25

The sales tax rate is 6.5% or 6.5/100 or 0.065

We want to know how much he paid.

Adding all the items he bought together, we have:

$28 + $5.98 + $25

= $58.98

Next, we apply the sales tax rate.

Take 6.5% of $58.98

This is: $58.98 * 0.065

= $3.83

Finally, add the sales tax with the amount we got

$58.98 + $3.83

= $62.81

He paid $62.81 in total

Answer:

-9,-3

Step-by-step explanation:

-4+-5 = -9

1+-4 = -3

Think about a number line to help you

Answer: -4 + (-5) = -9

1 + (-4) = -3

Step-by-step explanation: Subtract -4 and -5 and u get -9. Subtract 4 and 1 to get -3

Answer:8 dollars

Step-by-step explanation:

20-12=

The distance between Noor's house and her grandparent's house is 37.40 miles or if rounded off to the nearest tenth, it will be 40 miles using the estimation concept.

As per the question statement, Noor’s family is meeting her grandparents at a restaurant and the restaurant is 24.5 miles from Noor’s house but this is 65.5% of the distance from Noor’s house to her grandparents’ house.

We are supposed to find the distance between Noor's house and her grandparent's house. We will use the concept of estimation.

Distance between Noor's house and restaurant = 24.5 miles

Let distance between Noor's house and her grandparent's house be "x" miles.

So the distance between grandparent's house and restaurant = x - 24.5

Now it is given that 24.5 miles is 65.5% of the distance from Noor’s house to her grandparents’ house.

So, 65.5% of x = 24.5

(65.5*x)/100 = 24.5

65.5*x = 2450

x = 2450 / 65.5

x = 37.40 miles

If rounded off to the nearest tenth mile, we get

x = 40 miles.

So, the distance between Noor's house and her grandparent's house is 37.40 miles or if rounded off to the nearest tenth, it will be 40 miles.

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Answer:  76           Mr Helmer had 76 inches left.

Step-by-step explanation:  All you do is you subtract 9 from 85.

Or 85-9=X

With the concepts of percentages and calculations, the percent decrease in the number of people who went to the pool over these four weeks is 10%

Take the base as 100 and convert the percentage to numbers and then proceed with the same.

Now, the initial number of people in the local swimming pool is 1020, after which 100 fewer went, hence 920 people

Now, 135 people more people need to be added, thus 1055 people.

Now, 137 fewer people went, so 918 people went to the pool in the four weeks.

Therefore percent decrease = Difference/No. of people in the first week * 100

Thus, the percent decrease =  102/1020*100=10%

Hence 10% of people went less in the fourth week as compared to the first week.

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The given inequality is,

The graph of the inequality will be shown below

72, 108, and 108 are the other three angles formed by the two straight lengths of wire.

For the given question.

Two straight lengths of wire are put on the ground, to form vertical angles.

Because vertical angles have always been congruent, 72 is the vertical angle to 72.

Because the line is straight, the answer is 180.

180 - 73 equal 108. (supplement angles)

Because they are both vertical angles, there are two 180s.

Thus, the three angles formed are 72, 180 and 180 degrees.

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8 × [tex]10^5[/tex] is 200 times greater than 4 × [tex]10^3[/tex]  as according to multiplying and dividing as per the scientific notation of multiplication and division.

A kind of representation of number which is some power of 1/10 can also be expressed in as easily in scientific notation.

1/10 = [tex]10^{-1[/tex]  (“ten to the minus one power”)

More generally, the expression “[tex]10^{-n[/tex]” (where n is a whole number) means (1/10) n. Thus

[tex]10^{-3[/tex] = [tex]\frac{1}{10}^{-3}[/tex]

= 1/1000

[tex]10^{-8[/tex] = [tex]\frac{1}{10}^{-8[/tex]

= 1/100,000,000

Scientific notation was invented to help scientists (and science students) deal with very large and very small numbers, without getting lost in all the zeros.

Herein this question

8 × [tex]10^5[/tex] can also thus be written as 2 x 4 × [tex]10^5[/tex]. On dividing with 4 × [tex]10^3[/tex] we get 2 x [tex]10^2[/tex]. Thus, it is 2 x [tex]10^2[/tex] i.e., 200 times larger than 4× [tex]10^3[/tex].

The expression “10n”, where n can be stated as a whole number, simply means that “10 is raised to the nth power,” or in other words, a number that is got by using 10 as a factor n times.

You can also notice that the number of zeros that are present in the ordinary decimal expression is absolutely equal to the power to which thus 10 is raised.

If any kind of number is expressed in words, first we have to write it down as an ordinary decimal number and then we have to convert it. Thus, the value “ten million” becomes 10,000,000. There are a total of seven zeros, so in powers of ten notation ten million is written [tex]10^7[/tex].

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Answer:

1,897,055

Step-by-step explanation:

1,381,069+515,986​=1,897,055

The width of the plywood = 23/8 ft

The two rectangular pieces of plywood had equal widths.

The length of first rectangular piece = 6 ft

The length of second rectangular piece = 5 1/2 ft = 11/2 ft

The two pieces are joined to make a single rectangular stage.

Then the total length of the stage = 6 + 11/2 = 23/2 ft

Now area of the rectangular stage = 66 1/8 = 529/8 square feet.

⇒ length x width = 529/8

⇒ 23/2 x width = 529/8

⇒ width = 529/8 x 2/23 = 23/4 ft

Let 'x' be the width of a rectangular plywood.

Then 2x = width of the stage

⇒ 2x = 23/4

⇒ x = 23/8 ft

Hence width of the plywood = 23/8 ft

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Using properties of exponents, it is found that Mia's first mistake is described as follows:

Mia made a mistake in Step 3. She simplified the exponents 16 and -8 incorrectly. She should have subtracted them.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, as follows:

3^0 x 3^(16) = 3^(0 + 16) = 3^16.

Hence the Step 1 is correct.

For the power of power rule, we keep the base and multiply the exponents, hence:

(3^(-4))² = 3^(-4 x 2) = 3^(-8).

Hence the Step 2 is correct.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, as follows:

3^16/(3^(-8)) = 3^(16 - (-8)) = 3^(16 + 8) = 24.

Which is Mia's mistake, as she did not subtract the exponents.

The steps are missing and are given by the image at the end of the answer.

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character character character

The percent sales tax of the purchase is 3 %.

A sales tax is a consumption tax imposed by the government on the sale of goods and services.

She went shopping for a new pair of sneakers.

The listed price of the pair of sneakers was $43, but the price with tax came to $44.29.

Therefore, the percent sales tax can be found as follows:

sales tax = 44.29 - 43

sales tax = $1.29

Therefore,

percent sale tax = sale tax / cost with tax × 100

percent sale tax =  1.29 / 43 × 100

percent sale tax = 129 / 43

Therefore,

percent sale tax = 3%

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The price per one pound of almonds equal $2.20/0.65 lb

0.65 pounds of almonds cost $2.20

Verify each case

case 1) The price per one pound of almonds equal $2.20/0.65 lb

The statement is true

To find the price per one pound calculate the unit rate

So,

$2.20/0.65 lb=$3.38 per one pound

case 2) 2.2 pounds of almonds cost $0.65

The statement is not True

The correct is 0.65 pounds of almonds cost $2.2

case 3) Each bag of almonds weighs 2.2 pounds

Cannot be determined

In the problem there is no information about how much each bag of almonds weighs

case 4) 0.65 pounds of almonds cost $2.20

The statement is True

The point (0.65,2.20) lie to the line of the the graph.

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Answer:

A

Step-by-step explanation:

Given:

Area of large rectangle = (8x + 1)(5x)

Area of small rectangle = (4x)(2x)

To find area of the shaded region, subtract the area of the small rectangle from the large rectangle.

We have:

Area of large rectangle =

Area of small rectangle =

Area of shaded region =

Therefore, the area of the shaded region is = 32x² + 5x

ANSWER:

Answer:

1 ; -2·i ; 2·i

Because x = -1 is a real root, you can divide

(x^3 + x^2 + 4·x + 4)/(x + 1) = x^2 + 4

Roots of x^2 + 4 are

x^2 + 4 = 0

x^2 = -4

x = ± 2·i

All real and complex roots are

1 ; -2·i ; 2·i

the answer to tuis problem is x=4.

Answer:   width=8, length=24

Step-by-step explanation:

2(x+3x)=64

2x+6x=64

x=8

width (x)=8

length (3x)=24

perimeter=2(x+3x)=64

Answer:

Step-by-step explanation:

i think its undefined