The hypotenuse of a 45°-45°-90° triangle measures 128 cm. What is the length of one leg of the triangle? 64 cm cm 128 cm cm

Answer:

Value of h is 4.5 unit.

Step-by-step explanation:

Given:

MO = 12 and PO = 2

∠N and ∠p are right angle

To find: Value of h.

In ΔMNO and ΔONP

∠MNO = ∠OPN = 90°

∠MON = ∠NOP  ( common angle)

⇒ ΔMNO and ΔONP are similar triangle by AA Similiarity criteria.

Corresponding part of similar triangles are ,

∠OMN = ∠ONP

[tex]\frac{OM}{ON}=\frac{MN}{PN}=\frac{ON}{OP}[/tex]

Consider,

[tex]\frac{OM}{ON}=\frac{ON}{OP}[/tex]

[tex]OM\times OP=ON^2[/tex] .................(1)

Now in ΔONP,

using Pythagoras Theorem

ON² = NP² + OP²

ON² = h² + 2²

ON² = h² + 4 .............(2)

From (1) and (2), we have

12 × 2 = h² + 4

h² = 24 - 4

h² = 20

[tex]h=\sqrt{20}[/tex]

[tex]h=2\sqrt{5}[/tex]

h = 2 × 2.236  ( Value of √5 is 2.236 )

h =  4.472

h = 4.5 unit

Therefore, Value of h is 4.5 unit.

Answer: 3 units

Step-by-step explanation:

Answer:

3 units

Step-by-step explanation:

The approximate surface area of Arizona is calculated as 19.4% of Alaska's surface area, which is 588,000 square miles. By converting the percentage to a decimal and multiplying, we find that Arizona's surface area is approximately 114,072 square miles.

The question asks us to find the approximate surface area of the state of Arizona if it is 19.4% of the surface area of Alaska. To find this, we can use the known surface area of Alaska, which is approximately 588,000 square miles.

Here are the steps to calculate the surface area of Arizona:

So, the approximate surface area of the state of Arizona is 114,072 square miles.

The approximate surface area of the state of Arizona is 114,072 square miles, calculated as 19.4% of Alaska's surface area of 588,000 square miles.

To find the surface area of Arizona, we utilize the fact that it constitutes approximately 19.4% of Alaska's surface area.

This means that the surface area of Arizona is roughly 19.4% of the surface area of Alaska.

Given that the surface area of Alaska is approximately 588,000 square miles, we can calculate the surface area of Arizona by multiplying this value by 19.4%.

Mathematically, this can be expressed as:

[tex]\[ \text{Surface area of Arizona} = 0.194 \times \text{Surface area of Alaska} \][/tex]

Substituting the known value for the surface area of Alaska:

[tex]\[ \text{Surface area of Arizona} = 0.194 \times 588,000 \][/tex]

Calculating this yields:

[tex]\[ \text{Surface area of Arizona} \approx 0.194 \times 588,000 \][/tex]

[tex]\[ \text{Surface area of Arizona} \approx 114,072 \][/tex]

Therefore, the approximate surface area of the state of Arizona is 114,072 square miles, calculated as 19.4% of Alaska's surface area of 588,000 square miles.

This demonstrates the relative size of Arizona compared to Alaska.

Answer:

Think simple.

angle 1 and the angle with the measurement of 110° are subplementary angles, therefore:

∠1 + 110° = 180°

∠1           = 180° - 110° = 70°

Answer:

Step-by-step explanation:

The point-slope equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation

[tex]y-4=3(x+2)\\\\y-4=3(x-(-2))[/tex]

Therefore

m = 3

(x₁, y₁) = (-2, 4)

Answer:

Its A. on edge

Step-by-step explanation:

could that really be simplified anymore!!!!!

The simplified expression of (√12+6)(-√8-√2) is  -6(√6 + √2).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(√12 + 6) ( -√8 - √2)

√12 x -√8 - √12 x √2 + 6 x -√8 - 6 x -√2

-√96 - √24 - 6√8 + 6√2

-√(16x6) - √(4x6) - 6√(4x2) + 6√2

-4√6 - 2√6 - 12√2 + 6√2

-6√6 - 6√2

-6(√6 + √2)

Thus,

-6(√6 + √2) is our final expression.

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Answer:

the solution set consists of {x < -2 ∪ x > 10/3}

Step-by-step explanation:

|3x - 2| > 8 is equivalent to the following set of inequalities:

1) 3x - 2 > 8

and

2) -(3x - 2) > 8

In case 1, above, add 2 to both sides, obtaining 3x > 10, or x > 10/3.

In case 2, above, carry out the indicated multiplication first:

-3x + 2 > 8.  Next, subtract 2 from both sides:  -3x > 6.

Next, divide both sides by -3, remembering to reverse the direction of the inequality sign:  x < -2.

Thus, the solution set consists of {x < -2 ∪ x > 10/3}

Answer:

x < -2 or x > 10/3

Step-by-step explanation:

3x - 2 > 8

3x > 10

x > 10/3

-3x + 2 > 8

-3x > 6

x < -2

x < -2 or x > 10/3

Answer:

1. y-intercept: [0, 500]; Slope: 200

3. Graph this equation with a POSITIVE slope of 0.25 and a y-intercept of 20.

Step-by-step explanation:

The keywords in #1 are "receives [y-intercept]" and "a day [Rate of Change (Slope)]".

The probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39, is 96.18%

To find the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39, we need to standardize the values using the z-score formula. The z-score is calculated as (x - mean) / standard deviation. In this case, the mean proportion of registered voters who vote is 0.38 and the standard deviation is 0.0485. So, for 0.37:

z = (0.37 - 0.38) / 0.0485 = -2.0619

Using the standard normal table, we can find the area to the left of -2.0619, which is approximately 0.0191. For 0.39:

z = (0.39 - 0.38) / 0.0485 = 2.0619

Again, using the standard normal table, we can find the area to the left of 2.0619, which is approximately 0.9809.

To find the probability between 0.37 and 0.39, we subtract the smaller area from the larger area: 0.9809 - 0.0191 = 0.9618, or 96.18%.

Answer:15%

Step-by-step explanation:

Divide 20 by 4 then 3/4th are boys so take the answer and add it 3 times.

Given that 50% of the class are boys and 20% are blonde-haired, if there are three times as many blonde boys, the percentage of blonde boys in the class is 60%.

The question can be interpreted as looking for the percentage of boys with blonde hair in the entire class. We know that 50% of the class are boys and that there are three times as many boys that are blonde as the 20% that are generally blonde-haired. This means that 60% of the class are boys who have blonde hair.

We can calculate this by multiplying the total percent of blondes (20%) by 3, as we are told there are three times as many blonde boys. Hence, the percentage of blonde boys in the entire class is 60%.

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Answer:

192 mm

Step-by-step explanation:

Volume of rectangle = L * B * H

= 6 mm * 4 mm * 8 mm

= 192 mm

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Answer:

18

Step-by-step explanation:

9 + 9 = 18

Answer:

It equals 18.

Step-by-step explanation:

Nine is worth 9 1's.

Nine is also worth 9 1's.

So if you count up all the 1's, it will equal 18.

I just took a quiz with this question. I got 100% and my answer to this question was 11.0.

Final answer:

To find x to the nearest tenth in the given numbers, move the decimal point ten places to the left to get -10.0.

Explanation:

Move the decimal point ten places to the left to get 0.00000000067.

When dividing by powers of 10, shift the decimal to the left by the number of zeros in the power of ten.

To find x to the nearest tenth in 11.012.9-10.0-6.3, the result would be -10.0.

Answer:

[tex]0.0134[/tex]

Step-by-step explanation:

we have

[tex]2(e^{-5})[/tex]

Using a calculator

[tex](e^{-5})=0.0067[/tex]

substitute

[tex]2(0.0067)=0.0134[/tex]

ANSWER

[tex]y = - 4x + 8[/tex]

EXPLANATION

The given line passes through (1,4) and (3,-4).

The slope of this line is calculated using the formula:

[tex]m =\frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points into the slope formula to get:

[tex]m = \frac{ - 4 - 4}{3 - 1} [/tex]

[tex] \implies \: m = \frac{ - 8}{2} [/tex]

[tex]m = - 4[/tex]

We substitute the first point and slope into the point-slope formula

[tex]y-y_1=m(x-x_1)[/tex]

This implies that

[tex]y - 4 = - 4(x - 1)[/tex]

We expand to get

[tex]y - 4 = - 4x + 4[/tex]

[tex]y = - 4x + 2/4+ 4[/tex]

[tex]y = - 4x + 8[/tex]

Answer:

TRUE

Step-by-step explanation:

TRUE

a_1 = 2

a_n = 2*(an_1)

if we start with 2, we would get

a_2 = 2*(a_1) = 2*(2) = 4

a_3 = 2*(a_2) = 2*(4) = 8

a_4 = 2*(a_3) = 2*(8) = 16

a_5 = 2*(a_4) = 2*(16) = 32

.

.

.

and so on

Answer:

the answer is TRUE

Answer:

y-2=4/3(x-2)

Step-by-step explanation:

Pick one coordinate and then plug the x value and the by value into the formula and then to find the slope and count up 4 and to the right 3.

The probability of a dart (thrown at random) landing in the area marked F is:

                                      1/16

We know that the probability of an outcome is defined as the chance of occurrence of an outcome and it is calculated as the ratio of number of favorable outcomes to the total number of outcomes.

We first make equal sections i.e. we divide the figure into equal sections and observe that:

A and D is made up of 4 sections.

B,C and E is made up of 2 sections.

F and G are made up of 1 section.

This means that the total number of sections are: 4+4+2+2+2+1+1=16

Hence,

Probability(landing on F)=1/16

( Since there are total 16 sections and F is made up of 1 )

For this case we have by definition, that the sum of the internal angles of a triangle is 180 degrees.

Then, according to the figure we have to:

[tex]x + y + y = 180[/tex]

Where "x" represents the angle of the left side of the triangle, we have that "x" is given by:

[tex]x = 180-114\\x = 66[/tex]

So we have to:

[tex]66 + 2y = 180\\2y = 180-66\\2y = 114\\y = \frac {114} {2}\\y = 57[/tex]

Finally, "y" is equal to 57 degrees.

Answer:

Option C

The value of y in the triangle is,

⇒ y = 57 degree

For this case we have by definition, that the sum of the internal angles of a triangle is 180 degrees.

Then, according to the figure we have to:

⇒ x + y + y = 180

Where "x" represents the angle of the left side of the triangle, we have that "x" is given by:

x = 180 - 114

x = 66 degree

So we have to:

66 + 2y = 180

2y = 180 - 66

2y = 114

y = 57 degree

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Answer:

(B). [tex]y=9x[/tex]

Step-by-step explanation:

We have been given 4 equations. We are asked to choose an equation which has constant of proportionality equal to 9.

We know that two proportional quantities are in form [tex]y=kx[/tex], where k is constant of proportionality.

(A). [tex]y=\frac{81}{3}x[/tex]

[tex]y=27x[/tex]

We can see that value of k is 27, therefore, option A is not a correct choice.

(B). [tex]y=9x[/tex]

We can see that value of k is 9, therefore, option B is the correct choice.

(C). [tex]y=3x[/tex]

We can see that value of k is 3, therefore, option C is not a correct choice.

(D). [tex]y=\frac{1}{9}x[/tex]

We can see that value of k is 1/9, therefore, option D is not a correct choice.

Answer:

5x2 - x + 6

Step-by-step explanation:

(6x2-x+8)-(x2+2)

We gonna use KCC which is Keep Change Change and distributing property

multiple (6x2-x+8) by 1 and (x2+2) by -1

6x2-x+8 -x2 - 2

combine the like terms

6x2 - x2 + 8 - 2 - x

5x2 + 6 - x

arrange in order

5x2 - x + 6

Let the Total Amount of money won in Lottery be : L

Given - Jane and Ben share the Lottery in the Ratio 7 : 3

[tex]\implies \mathsf{Jane\;share\;of\;money = \left(\dfrac{7}{7 + 3}\right) \times L}[/tex]

[tex]\implies \mathsf{Jane\;share\;of\;money = \dfrac{7L}{10}}[/tex]

Given : Jane's share of money is $5600

[tex]\mathsf{\implies \dfrac{7L}{10} = 5600}[/tex]

[tex]\mathsf{\implies L = \dfrac{56000}{7}}[/tex]

[tex]\mathsf{\implies L = 8000}[/tex]

[tex]:\implies[/tex]  Total Lottery Money = $8000

[tex]\implies \mathsf{Ben's\;Share = \left(\dfrac{3}{7 + 3}\right) \times 8000}[/tex]

[tex]\implies \mathsf{Ben's\;Share = \left(\dfrac{3}{10}\right) \times 8000}[/tex]

[tex]\implies \mathsf{Ben's\;Share = \left(3 \times 800\right)}[/tex]

[tex]\implies \mathsf{Ben's\;Share = 2400}[/tex]

Answer : Ben received $2400

Answer:

Ben's share =  $2400

Step-by-step explanation:

Ratio = 7:3

Jane's share = 7x

Ben's share = 3x

7x = 5600

x = 5600/7 = $ 800

Ben's share =  3x = 3*800 = $2400

Jacob bought 3 medium and 6 large pizzas for his class party, as the large pizzas were twice the amount of medium pizzas and the total number was 9.

Jacob bought a total of 9 pizzas for his class party. The condition given is that the amount of large pizzas was twice the amount of medium pizzas. Let's define the number of medium pizzas as x. Therefore, the amount of large pizzas would be 2x. Since the total number of pizzas is 9, we can write the equation x + 2x = 9. Adding the terms together gives us 3x = 9. Dividing both sides of the equation by 3, we find that x = 3. This means Jacob bought 3 medium pizzas and 2 times 3, which is 6 large pizzas for his class party.

Answer:This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).

Step-by-step explanation: If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).

Basically what this assignment sais is to write a function, input the data and write input and output as an ordered pair.

[tex]f(x)=3.75x[/tex]

Where f(x) equals y and 3.75 times x is cost of number of gallons x.

So we have:

[tex]

f(x)=12\Longrightarrow 12=3.75x \\

12=3.75x\Longrightarrow x=\dfrac{12}{3.75}=3.2

[/tex]

So the ordered pair is in a form of:

[tex](x, f(x))\Longleftrightarrow(x,y)[/tex]

We have x is 3.2 and y is 12. So the ordered pair is:

[tex]\boxed{(3.2, 12)}[/tex]

Hope this helps.

r3t40

ANSWER

-4.0

EXPLANATION

The given trigonometric equation is

[tex] \tan \: 45 \degree - 10 \: \cos \: 60 \degree[/tex]

From special angles or using the unit circle.

[tex]\tan \: 45 \degree = 1[/tex]

[tex] \cos \: 60 \degree = \frac{1}{2} [/tex]

We make the substitution to get:

[tex]1 - 10 ( \frac{1}{2} ))[/tex]

This simplifies to:

[tex]1 - 5 = - 4[/tex]

Hence the correct answer is -4.0

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Answer:

Your answer would be a) about 1.4 miles

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Step-by-step explanation:

In order to solve this problem, we're going to need to round to the tenths place.

The tenths place is the decimal place to the right of the decimal.

Example: 0.54  --- 5 would be in the tenths place.

We would use the number next to it to see if we're going to round up or stay the same.

3.45 --- 4 is in the tenths place. When we look at the number next to it, 5, we would notice that it's big enough to make 4 round up. You would round 4 up to 5.

Your decimal should look like this: 3.5

1.23 --- 2 is in the tenths place. When you look at the number next to it, 3, it's not big enough for us to round it up, so we would keep the number 2 the same.

Your decimal should look like this: 1.2

0.85 --- 8 is in the tenths place. When you look at the number next to it, 5, you would see that it's big enough for you to round up, so you would round the 8 to a 9.

Your decimal should look like this: 0.9

Our rounded decimals:

3.5

1.2

0.9

Now, we have our rounded decimals. We're going to need to find how much Molly walked more than her sister and brother.

Molly walked 3.5

Her sister walked 1.2

Her brother walked 0.9

To solve that question, we would get 3.5 and subtract it with the rest of the numbers, since we are subtracting Molly's walk length to her brother and sister's combined walked length.

[tex]3.5 - 1.2-0.9= 1.4[/tex]

You should get 1.4

Therefore, Molly walked 1.4 miles more than her sister and brother combined.

A). about 1.4 miles should be your FINAL answer.

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