A right triangle has legs with lengths 61 cm and 60 cm. What is the length of the hypotenuse

Answer:

A) x = 5 or x = 6

B) x = 0.298 or 6.702

C) x = 3

D) x = ±1

Step-by-step explanation:

A) Values of x for which;

x² − 11x + 31 = 1

x² - 11x + 30 = 0

Using quadratic formula, we have;

x = 5 and x = 6

B) Values of x for which;

x² − 5x − 3 = 2x − 5

x² − 5x - 2x - 3 + 5 = 0

x² - 7x + 2 = 0

Using quadratic formula, we have;

x = 0.298 or 6.702

C) Values of x for which;

7x + 1 = 3x² − 2x + 1

3x² - 2x - 7x + 1 - 1 = 0

3x² - 9x = 0

3x² = 9x

Divide both sides by 3x to get;

x = 3

D) Values of x for which;

−2x² + 5x + 6 = 4x² + 5x

Rearranging, we have;

4x² + 2x² + 5x - 5x - 6 = 0

6x² - 6 = 0

x² = 6/6

x² = 1

x = √1

x = ±1

The values of [tex]x[/tex] for the given situations would be as follows:

A). [tex]x = 5[/tex] or [tex]x = 6[/tex].

B). [tex]x = 0.298[/tex] or [tex]6.702[/tex]

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

D). [tex]x =[/tex] ±[tex]1[/tex]

a). [tex]x^2 - 11x + 31 = 1[/tex]

⇒ [tex]x^2 - 11x + 30 = 0[/tex]

by employing the quadratic equation, we have the values of [tex]x[/tex];

Considering

a = 1

b = -11

c = 30

⇒ {[tex]-(-11)[/tex] ± [tex]\sqrt{(-11)^2 -4 .1. 30 }[/tex]}[tex]/2.1[/tex]

Now,

[tex]x =[/tex] ([tex]11[/tex] ± [tex]1)/2[/tex]

Thus, the values for which the given trinomial would be equivalent to 1 would be:

∵ [tex]x = 5[/tex] and [tex]x = 6[/tex]

b). [tex]x^2 - 5x - 3 = 2x - 5[/tex]

⇒ [tex]x^2 - 5x - 2x - 3 + 5 = 0[/tex]

⇒ [tex]x^2 - 7x + 2 = 0[/tex]

by employing the quadratic equation, we have the values of [tex]x[/tex];

Therefore, the values of polynomials [tex]x^2 - 5x - 3 = 2x - 5[/tex] when:

∵ [tex]x = 0.298[/tex] or [tex]x = 6.702[/tex]

c). [tex]7x + 1 = 3x^2 - 2x + 1[/tex]

⇒ [tex]3x^2 - 2x - 7x + 1 - 1 = 0[/tex]

⇒ [tex]3x^2 - 9x = 0[/tex]

⇒ [tex]3x^2 = 9x[/tex]

by dividing both the sides by [tex]3x[/tex] to receive;

Hence, the binomial and trinomial [tex]7x + 1 = 3x^2 - 2x + 1[/tex] when:

∵ [tex]x = 3[/tex]

d). [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex]

by arranging them again, we get;

[tex]4x^2 + 2x^2 + 5x - 5x - 6 = 0[/tex]

⇒ [tex]6x^2 - 6 = 0[/tex]

⇒ [tex]x^2 = 6/6[/tex]

The trinomial and binomial [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex] would be when:

∵  [tex]x =[/tex] ±[tex]1[/tex]

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It's B isn't it? If this is the question I'm thinking of. No image here so I'm just guessing.

Answer:

the square root of 169 is 13 then ×2

26

I hope I am correct mate

enjoy your day

#Captainpower

Answer:

Step-by-step explanation:

(1-0.32)p=357

0.68p=357

p=$525

Answer:

471.24

Step-by-step explanation:

First you want to find 32% of 357, which is 114.24. Then you want to add that onto 357. Hope this helps!

Answer:

Step-by-step explanation:

theres no information

Answer:

none because there are no numbers there I'll help you when you add the numbers

Step-by-step explanation:

but have a good rest of your day :) ❤

Answer:

D

Step-by-step explanation:

supplementary means two angles that there sum will be 180. and 30 x 4 = 120 + 20 = 140 and if you add the other angle 40 that's 180.

Answer: I wasn't sure if number 18 was 350.00 but that's what I put down to do the problem hope I'm not too late.

9. $72.45

10. $15.52

11. $30.69

12. $48.95

13. $6.39

14. $67.6

15. $18.02

16. $51.6

17. $11.25

18. $175.00

19. $3.20

20. $10.00

21. $31.25

22. $45.90

Step-by-step explanation:

The radius of the circle is 3

Answer: 450 cm³ is the volume

Step-by-step explanation:

Volume of pyramid = L x W x H divide by 3

The required volume of the given square pyramid is 20,250 cubic centimeters.

Given that,
The side length of the base of a square pyramid is 30 centimeters. The height of the pyramid is 45 centimeters. The volume of the pyramid in cubic centimeters is to be determined.

Volume is defined as the ratio of the mass of an object to its density.

Here,
The volume of the square pyramid is given as,
= 1/2 area of base × height
= 1/2[30×30]×45
= 900 × 45 / 2
= 20,250 cubic centemeters.

Thus, the required volume of the given square pyramid is 20,250 cubic centimeters.

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Data for the question :

1 3/4, 2 1/2, 2, 2 3/4, 1, 1 3/4, 1 1/4, 3, 3 1/4, 3 3/4, 2, 2

Answer:

Julie is Incorrect

Step-by-step explanation:

Given the data:

1 3/4, 2 1/2, 2, 2 3/4, 1, 1 3/4, 1 1/4, 3, 3 1/4, 3 3/4, 2, 2

The least amount of time spent is : 1

The most amount of time spent is 3 3/4

According to Julie ; the most amount of time spent is equal to 1 1/2 the least amount of time spent.

That is,

3 3/4 = 1 * 1 1/2

3 3/4 = 15/4

1 * 3/2 = 3/2

Hence, she is incorrect ;

15/4 ≠ 3/2

Answer:

r = 1

Step-by-step explanation:

Answer:

correct students

-5+2x=15

2x=15+5

2x=20(divided by 2 both sides)

x=10

mistake students

-5+2x=15

-3x=15(divided by - 3 both sides)

x=-5

The required simplified value of the given expression is given as x = 10.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
-5 + 2x = 15

Now,
Adding 5 on both sides,
2x = 15 + 5
2x = 20

Divide by 2 into both sides
x = 10

Thus, the required simplified value of the given expression is given as x = 10.

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The question is incomplete, the correct solution is given above, to determine the mistake of the student, compare the above solution with the student solution.

Answer:

√16 or 4

hope this helps!

Answer:

5%

Step-by-step explanation:

As given,

The population of the town increased from 175000 to 262500 in a decade.

⇒ In 10 years , population increased from 175000 to 262500

⇒% increase = [tex]\frac{262500 - 175000}{175000}[/tex]× 100% = [tex]\frac{87500}{175000}[/tex]×100% = 0.5×100% = 50%

Now,

Average % increase = [tex]\frac{percent increase}{Total years}[/tex] = [tex]\frac{50}{10}[/tex]% = 5%

∴ we get

Average percent increase of population per year = 5%

Answer:

Chromebook: 0.25 percent per minute

iPhone: 0.5 percent per minute

1) The phone

2) Faster by 0.25 percent per minute, or 1 percent every four minutes

3) The phone

4) 25 percent more

5) The phone

Hi! Your answer is 125/3 π

Please see an explanation for a clear understanding to the problem.

Any questions about the answer/explanation can be asked through comments! :)

Step-by-step explanation:

For this problem, I'll be demonstrating two methods to solve your problem which are Integration method and Formula method. Let's start with Formula method first!

Formula Method

Volume of Cone Formula

[tex]V=\huge{\frac{1}{3}\pi r^2h}[/tex]

r is a radius. Therefore, r² is a diameter.

h is height of cone.

Our r is 5. Therefore, 5² = 25.

Our h is 5.

Substitute these values in the equation.

[tex]V=\huge{\frac{1}{3}\pi (5)^2(5)}\\V=\huge{\frac{1}{3}\pi (25)(5)} \\V=\huge{\frac{1}{3}\pi (125)}\\V=\huge{\frac{125}{3}\pi}[/tex]

Hence, the volume of a cone is 125/3 pi. If you want in Mixed Number form then It'd be 41 and 2/3 pi [ 41 2/3 pi]

Integration Method - Proof

Let r':r = x:h

Therefore,

[tex]\huge{\frac{r'}{r}=\frac{x}{h}}\\\huge{r'=\frac{x}{h}r[/tex]

r and h both are same (r is still radius while h is still height)

[tex]\huge{S(x)=\pi(r')^2[/tex]

The reason why we add pi because the surface is a circle. If the surface is not a circle, we don't add pi.

[tex]\huge{S(x)=\pi(\frac{x}{h}r)^2}\\\huge{S(x)=\pi(\frac{x^2r^2}{h^2})}\\\huge{S(x)=\frac{\pi r^2}{h^2}x^2}\\[/tex]

The range starts from 0 ≤ x ≤ h

[tex]\huge{V=\int\limits^h_0 {S(x)} \, dx[/tex]

Substitute S(x) in.

[tex]\huge{V=\int\limits^h_0 {\frac{\pi r^2}{h^2}x^2 } \, dx[/tex]

Integrate, separate everything in the integrand out except for x^2

[tex]\huge{V=\frac{\pi r^2}{h^2} \int\limits^h_0 {x^2} \, dx}\\\huge{V=\frac{\pi r^2}{h^2}[\frac{1}{3}x^3]^h__0}}\\\huge{V=\frac{\pi r^2}{h^2}[\frac{1}{3}h^3]}\\\huge{V=\pi r^2[\frac{1}{3}h]}\\\huge{V=\frac{1}{3}\pi r^2h}[/tex]

As you notice, Integration method is pretty useful, but it's mostly for an advanced volume lesson only.

Integration Method - Problem Solving

Let r':r = x:h

r is given as 5

h is given as 5 as well.

Therefore, r':5 = x:5

[tex]\huge{\frac{r'}{5}=\frac{x}{5}}\\\huge{r'=\frac{x}{5}(5)}\\r'=x[/tex]

[tex]\huge{S(x)=\pi(r')^2}\\\huge{S(x)=\pi(x^2)}\\\huge{S(x)=\pi x^2}[/tex]

The range of volume starts from surface to height. Therefore the range is 0 ≤ x ≤ 5

[tex]\huge{V=\int\limits^5_0 {S(x)} \, dx }\\\huge{V=\int\limits^5_0 {\pi x^2} \, dx }\\\huge{V=\pi\int\limits^5_0 {x^2} \, dx }\\\huge{V=\pi[\frac{1}{3}x^3]^5__0}}\\\huge{V=\pi[(\frac{1}{3}(5)^3-\frac{1}{3}(0)^3]}\\\huge{V=\pi[(\frac{1}{3}(125)-0)]}\\ \huge{V=\pi[(\frac{1}{3}(125)]}\\\huge{V=\pi(\frac{125}{3})}\\\huge{V=\frac{125}{3}\pi}[/tex]

Notice that both methods have same answer. Hence, we can conclude that the volume of a cone is 125/3 pi units²

Answer:

The Manchester, England sweater is more expensive.

27 GBP is equal to 49.52 CAD, which is more than the 38 CAD from the afterwards.

Step-by-step explanation:

Answer:

AC = 4.7 feet

Step-by-step explanation:

cos 20° = x

                5

5 · cos 20° = x

4.7 = x

Answer:

Area=190.091 cm^2

Step-by-step explanation:

Area = 1/2(Pi x r^2)    one-half because it's a semi-circle

Area=1/2(3.14 x 11^2)

11^2=121 so, Area=1/2(3.14 x 121)

Area=1/2(379.94)

Area=189.97 cm^2

adjustment:

Area=1/2(3.142 x 11^2)

Area=1/2(3.142 x 121)

Area=1/2(380.182)

Area=190.091

Answer:

Three perpendicular bisectors are required

Step-by-step explanation:

A perpendicular bisector of a line segment is a line that cuts the line segment at a 90° angle, dividing it into two equal halves.

In this example, one bisector produces two equal parts of the segment

two bisectors produce three segments and three bisectors, four segments as shown in the diagram.

Perpendicular bisectors are constructed using a compass and a pencil, you can check out how to construct one, it is pretty interesting.

Answer: 5

Step-by-step explanation:

Terms are single numbers, variables, or the product of a number and variable.

Answer:

3

Step-by-step explanation:

Answer:

3 terms are given

Step-by-step explanation:

Answer:

-1.3

Step-by-step explanation:

number line will go all the way to the left and then 7 to the right. which is -1.3

The value of -2 - -7 as modelled in the attached image is; -1.3

According to the question;

The number line model given can be used to evaluate -2 - -0.7 by simply finding the distance between -2 and -0.7 as in the attached image.

Ultimately, the value of -2 - -0.7 is; -1.3

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Answer:

Angle x = 38°

Step-by-step explanation:

It is important to note that:

Two angles are called supplementary when their measures add up to 180 degrees.

Angle x and y are supplementary

Angle y = 142°

Hence,

Angle x = 180° - 142°

Angle x = 38°