Hermina cut a 10" by 15" piece of cardboard down the diagonal

Answers

Answer 1

When you cut along the diagonal, a right triangle is formed where the hypotenuse is the diagonal and the legs are the length and width of the rectangle (10 and 15 in this case)
Now use the pythagorean theorem to solve
10^2+15^2=325=c^2
c= approx 18.02775=length of the diagonal

Answer 2

Final answer:

Hermina can calculate the length of the diagonal on her 10" by 15" rectangle of cardboard by using the Pythagorean theorem. The formula states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides, the length and the width. Thus, by inputting the values into the formula, we get a diagonal length of about 18.03".

Explanation:

The question involves calculating the length of the diagonal on a rectangular piece of cardboard. In mathematics, the Pythagorean theorem is used to calculate the length of a diagonal. In this case, the length and width of the rectangle are given as 10" and 15" respectively. We can apply the theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The diagonal here acts as the hypotenuse, with the other two sides being the length and width of the rectangle. Therefore, the length of the diagonal is the square root of the sum of squares of these sides, which would be sqrt(10^2 + 15^2), resulting in approximately 18.03".

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Related Questions

how would you simplify -2+3i/-3-2i (im doing conjugates in math right now)

Answers

[tex] \cfrac{-2+3i}{-3-2i}= \\ \\ \\ \cfrac{(-2+3i)(-3+2i)}{(-3-2i)(-3+2i)}= \\ \\ \\ \cfrac{6-4i-9i+6i^2}{9-4i^2}= \\ \\ \\ \cfrac{6-13i-6}{9+4}= \\ \\ \\ \cfrac{-13i}{13}=-1i [/tex]

hope this helps

Final answer:

To simplify -2+3i/-3-2i, multiply both the numerator and denominator by the conjugate of the denominator (-3+2i).

Explanation:

To simplify -2+3i/-3-2i, we can multiply both the numerator and denominator by the conjugate of the denominator, which is -3+2i. This will help us eliminate the imaginary terms in the denominator.

Multiplying the numerator and denominator, we get:

(-2+3i)(-3+2i) / (-3-2i)(-3+2i)

Expanding and simplifying:

(6i+4i^2-9+6i) / (9+4)

Combining like terms:

(-9+12i+4i^2) / 13

Since i^2 is equal to -1, the expression becomes:

(-9+12i-4) / 13

Combining like terms:

(-13+12i) / 13

Therefore, the simplified form of -2+3i/-3-2i is (-13+12i) / 13.

NEED HELP FAST!
(08.02 MC)
Which of the following graphs shows a pair of lines that represents the equations with the solution (2, –5)? (1 point)

Answers

The third graph shows this

The third graph because the two lines meet or cross at the point (2,-5) so that means that (2,-5) is the solution two the lines.

The weight of a sack of potatoes was more than 11 pounds. Shana wants to write an inequality for the weight of the sack of potatoes. What constant should she use in the inequality?

Answers

Answer: The constant that Shana should use in the inequality is 11.

Step-by-step explanation: Given that the weight of a sack of potatoes was more than 11 pounds and she wants to write an inequality for the weight of the sack of potatoes.

We are to find the constant that she should use in the inequality.

Let x pounds represents the weight of the sack of potatoes.

Then, according to the given information, the inequality can be written as

[tex]x>11.[/tex]

Thus, the required constant that Shana should use in the inequality is 11.

In the portion of the shuffleboard court shown above, . What additional piece of information do you need to show that using the SSS similarity theorem?

Answers

The additional piece of information to show that ∆RST∼QSU uses the SAS similarity theorem is <SRT≅<SQU.

What is the similarity theorem?

The fundamental theorem of similarity states that a line segment divides two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

In this case, the additional piece of information to show that ∆RST∼QSU uses the SAS similarity theorem is <SRT≅<SQU.

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it takes trevon ten hours to clean an attic. cody can clean the same attoc in seven hours.find how long it would take them if they worked together.

Answers

(17/70)x = 70/70(17x)/70 = 70/7017x = 70x = 70/17x ≈ 4.1176

Final answer:

If Trevon takes 10 hours to clean the attic and Cody takes 7 hours to clean the same attic, it would take them approximately 4.11 hours to clean the attic if they worked together.

Explanation:

If Trevon takes 10 hours to clean the attic and Cody takes 7 hours to clean the same attic, we can find the rates at which they clean per hour. Trevon cleans at a rate of 1/10 of the attic per hour, and Cody cleans at a rate of 1/7 of the attic per hour. To find out how long it would take them if they worked together, we add their rates: 1/10 + 1/7 = 17/70. This means that together, they can clean 17/70 of the attic per hour.

To find out how long it would take for them to clean the whole attic, we divide 1 (representing the full attic) by their combined rate: 1 / (17/70) = 70/17 = 4.11 hours (rounded to the nearest hundredth).

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Solve the equation. 3.1x + 4.6 = 10.8

Answers

x = 2

3.1x + 4.6 = 10.8

3.1x + 4.6 - 4.6 = 10.8 -4.6
3.1x = 6.2
3.1x/3.1 = 6.2/3.1
x=2

3.1x+4.6=10.8
3.1x+4.6(−4.6)=10.8(−4.6)
3.1x=6.2

3.1x/3.1=6.2/3.1

x=2

3.1(2)+4.6=10.8

Solve.
(3x)^2 - 7y^2 when x = 3 and y = 2

Answers

The answer is 53. you can substitute x and y in equation

81-28-53 the answer is 53

An arithmetic sequence has a first term of 6.3 and a second term of 8.8 Which term has a value of 78.8?

Answers

First term [ a ] = 6.3

Common difference [ d ] = 8.8 - 6.3 = 2.5

Using general term formula,

[tex]t_{n} = a + (n-1)d[/tex]

78.8 = 6.3 + (n-1)*2.5

2.5*(n-1) = 72.5 [ Dividing both sides by 2.5 ]

n-1 = 29

n = 30

Hence, 78.8 is the 30th term in the arithmetic series.

What is the answer to the question

Answers

The answer to 87.48/5.4 is 16.2.

All you have to do is multiply the numerator and the denominator by 10, giving you 874.8over54. THen just put that in long division format. Divide 87 by the 54 and you simply get 1. Multiply the quotient by the divisor subract 54 from 87 Then bring down the next number, Multiply the quotient by 6 then subtract 324 from 334. The rest is pretty simple. Once done, you get 16.2 as your final answer!

~I hope this helped!

I am, yours most sincerely,
Joshua A. Bunn

what is 1/4 of 3200?

Answers

Answer: 800

Divide 3200 by 4 to get 800.

800 is the answer to the question, What is one fourth of 3200?

solve for y 7y - 6y - 10 = 13

Answers

7y-6y-10=13

7y-6y = y

y-10=13

add 10 to both sides

y = 23

7y-6y = 1y and 1=y≡

...

Jacob walked for x miles and then cycled for y miles between his home and the library. the number of miles Jacob cycled was 3 miles more than twice the number of miles he walked. the total number of miles Jacob walked and cycled was 6 miles. how many miles did Jacob walk and cylcle?

Answers

Walk: 1
Bike: 5

y=2x+3
x+2x+3=6
3x+3=6
3x=3
x=1
6-1=5

Walk: 1

Bike: 5

y=2x+3

x+2x+3=6

3x+3=6

3x=3

x=1

6-1=5

The low temperature in Anchorage, Alaska, one day was -9 degrees F. On the same day, the low temperature in Flagstaff, Arizona, was 26 degrees F. Write an inequlity to compare the temperatures.Explainthe meaning of the inequality.

Answers

26>-9

This states that 26 is greater than -9. Look at the > sign like it's an alligator's mouth - the alligator wants to eat the bigger side, and 26 is clearly bigger than -9, so the alligator wants to eat 26!

Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).

What formula can he use to determine the distance from point C to point D?

Answers

The formula used to find the length of a line segment is the same formula as the Pythagoras theorem.

We take CD as the hypotenuse of the right-angled triangle and the distance between the x-coordinates and y-coordinates as the length of two short sides.

We can write the formula as
CD = [tex] \sqrt{( x_{1}- x_{0}) ^{2}+ ( y_{1}- y_{0}) ^{2} } [/tex]
CD = [tex] \sqrt{(a-0)^{2}+ (b-b)^{2} } [/tex]

Wrong on apex is is a-0+(b-b)2=a2=a

Find the product of 6, m and 5. Then, identify the coefficient.

Answers

The product of 6 m and 5 would be 30m.
The coefficient is 30, since the coefficient is the number next to the variable.

Write the decimal number in standard form

Six and five hundred and sixteen ten-thousandths

Answers

Final answer:

The decimal number 'six and five hundred and sixteen ten-thousandths' in standard form is 6.0516, which combines the whole number six with the fractional part written as a decimal. Scientific notation is not necessary here since the number is already reasonably simple.

Explanation:

To express the number six and five hundred and sixteen ten-thousandths in standard form, you start by identifying the whole number and the fractional part. The whole number is six, which is straightforward. The fractional part is five hundred and sixteen ten-thousandths, which refers to 516 over 10000. In decimal form, this is written as 0.0516. Combining the whole number with the fractional part gives us the decimal 6.0516. This is the number in standard notation.

Scientific notation simplifies the expression of very large or very small numbers. For example, a large number like 306,000,000 can be written as 3.06 × 108, and a small number like 0.000028 can be expressed as 2.8 × 10-5. However, the number 6.0516 is already concise enough that converting it to scientific notation isn't necessary.

What is the best name for angle Y?

Answers

the answer to the question is B

a triangle with side lengths of 32, 60 and 68 is a right triangle?
true or false

Answers

I believe that it would come out to become true

The triangle with side lengths of 32, 60, and 68 is a right triangle is true.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

We can use the Pythagorean theorem to check if a triangle with side lengths of 32, 60, and 68 is a right triangle:

a² + b² = c²

where a, b, and c are the side lengths of the triangle and c is the hypotenuse.

Plugging in the values, we get:

32² + 60² = 68²

Simplifying:

1024 + 3600 = 4624

So, the equation holds true, which means that the triangle with side lengths of 32, 60, and 68 is a right triangle.

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The width of a rectangle is 8 units less than the length. If the area is 153 square units, then find the dimensions of the rectangle.

Answers

Length: 17 units
Width: 9 units. i think this is right

What is 42.2% of 635.4 explain how you found your answer

Answers

it is 268.1
10% of 635.4 is 63.54 and i just multiply that by 4 to get 254.16.
1% of 635.4 is 6.354 and multiply that by 2 to get 12.708.
.1% of 635.4 is .6354 multiply that by 2 to get 1.2708.
add up all the totals to get 268.1

What I did is turn 42.2% into a fraction 422/10 and multiply it with 635.4: after reducing the fraction 422/10 to 211/5. I multiply the numerators: to get 268138.8 and divide 5 to get 268.1388

how to find the density of a unknown liquid, the volume is 12.0mL and the mass is 6g.

Answers

mass divided by volume

Final answer:

To calculate the density of an unknown liquid given its mass of 6g and volume of 12.0mL, divide the mass by the volume, resulting in a density of 0.5 g/mL.

Explanation:

To find the density of an unknown liquid with a volume of 12.0mL and a mass of 6g, you need to use the formula for density which is density = mass/volume. Given the mass is 6g and the volume is 12.0mL, you substitute these values into the formula to calculate the density.

Therefore, the calculation would be: density = 6g / 12.0mL = 0.5 g/mL.

This states that the density of the unknown liquid is 0.5 g/mL, which means for every milliliter of this liquid, it weighs 0.5 grams. Understanding the density of a substance can be crucial in identifying it since density is a characteristic property.

A triangle has vertices (-1, 2), (3, 1), and (7, 2). What is the approximate perimeter of the triangle? Round your answer to the nearest hundredth.

Answers

Use the distance formula to find the length of the sides, then add them up to find the perimeter.

[tex]\sf d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For points in the form of (x1, y1), (x2, y2).

(-1, 2), (3, 1)

[tex]\sf d=\sqrt{(3+1)^2+(1-2)^2}[/tex]

[tex]\sf d=\sqrt{(4)^2+(-1)^2}[/tex]

[tex]\sf d=\sqrt{16+1}[/tex]

[tex]\sf d=\sqrt{17}[/tex]

(3, 1), (7, 2)

[tex]\sf d=\sqrt{(7-3)^2+(2-1)^2}[/tex]

[tex]\sf d=\sqrt{(4)^2+(1)^2}[/tex]

[tex]\sf d=\sqrt{16+1}[/tex]

[tex]\sf d=\sqrt{17}[/tex]

(7, 2), (-1, 2)

[tex]\sf d=\sqrt{(-1-7)^2+(2-2)^2}[/tex]

[tex]\sf d=\sqrt{(-8)^2+(0)^2}[/tex]

[tex]\sf d=\sqrt{64+0}[/tex]

[tex]\sf d=\sqrt{64}=8[/tex]

So the perimeter will be:

[tex]\sf 8+\sqrt{17}+\sqrt{17}\approx\boxed{\sf 16.25}[/tex]

Answer:

Step-by-step explanation:

Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$ is divided by 7?

Answers

[tex]\begin{cases}a\equiv1\pmod7\\b\equiv2\pmod7\\c\equiv6\pmod7\end{cases}[/tex]

[tex]a^{81}\equiv1^{81}\equiv1\pmod7[/tex]

[tex]b^{91}\equiv2^{91}\pmod7[/tex]

[tex]2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7[/tex]
[tex]8\equiv1\pmod7[/tex]
[tex]2\equiv2\pmod7[/tex]
[tex]\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7[/tex]

[tex]c^{27}\equiv6^{27}\pmod7[/tex]

[tex]6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7[/tex]

[tex]\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7[/tex]

Answer:

5 (mod 7)

Step-by-step explanation:

Consider the following piecewise-defined function, find f(-4)
f(x)=x^2-5,x<3
2x+5,x>3

Answers

(-4)^2-5, since its less than 3
16-5
= 11

(-4)^2-5, since its less than 3
16-5
= 11 i believe this is your answer

If 2/3=x/12 , what is the value of x?

Answers

2/3=x/12
Use cross multiply
2*12=3*x
24=3x
Divided both side by 3
24/3=3x/3
x=8
Check:
2/3=x/12
Substitute x with 8
2/3=8/12
2/3=(8/4)/(12/4)
2/3=2/3. As a result, x=8. Hope it help!

Answer:

the answers 8,just cross multiple and divide.

Step-by-step explanation:

Seven students—four girls and three boys—have volunteered to direct the class play. Mrs. Barry decides the only fair way to pick a director is to put all of their names in a hat and draw a name. What is the theoretical probability that a boy's name will be chosen? 3/4, 4/7, 3/7, 7/3

Answers

the probability would be 3/7

Answer:

Step-by-step explanation:

A. 3/7 is right

Write two decimal that are equivalent to2.50

Answers

2.5 and 2.500 could be alternative ways of writing this decimal although they will be equivalent to one another.....

Hope this helped

h(x)=|x+2| Find h(-10)

Answers

Plugging in,
H(10) = |-10+2|
= |-8|
= 8
The answer is 8.

44 points

The computer store pays its employees $150 per day plus a commission of 15% of their sales. Teagan wants to make at least $450 today. Which equation will help Teagan determine how much he has to sell today?

Answers

he makes 150 plus 15% of what is sold

so 150 + 0.15x has to equal at least 450

so the correct answer is B to find out the total he as to sell

You do Time4Learning to?

Which of the following statements is true?

Question 9 options:

0 < -3.2

-5.9 > 1.2

-2.8 < -7.4

-1.9 > -6.0

Answers

The true statement is: -1.9 > -6.0

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