The sum of three numbers is 145. The third number is 4 times the second. The second number is 5 more than the first. What are the numbers?

The Blue line is the translate in the direction of red line by,and therefore has equation y=3(x-4)+5

Answer:

x = 14,641

Step-by-step explanation:

[tex] \sqrt{x} = 121 \\squaring \: both \: sides \\ \implies \: {( \sqrt{x}) }^{2} = {(121)}^{2} \\ \\ \implies \: x = 14,641[/tex]

Answer:

69

Step-by-step explanation:

All angles in a triangle = 180°

35 + x + (x+7) = 180

42 + 2x = 180

2x = 138

x = 69

Hope this helps!

Answer:

y=14,x=8

Step-by-step explanation:

We know that in congruent triangles, angle measures and side lengths are equal.

Therefore <b=<e and AB=DE

80=6y-4

84=6y

y=14

3x-y=10

3x-14=10

3x=24

x=8

Answer:

C=31.4mm

Step-by-step explanation:

Circumfrence formula: π*diameter

diameter =10mm (picture)

C=10mm*3.14

C=31.4 mm

Answer:

31.42

Step-by-step explanation:

use the formula C=2πr

Answer:

C. 1

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\sqrt{\sqrt{\sqrt{x}}} = 16}[/tex]

The equation can be rewritten as:

[tex]\displaystyle \large{\sqrt[8]{x} = 16}[/tex] via surd property.

Since it’s an even surd, that means there only exists zero-positive numbers for value of x.

To solve this surd equation, simply clear out the surd by powering both sides by 8:

[tex]\displaystyle \large{\left(\sqrt[8]{x}\right )^8=(16)^8}[/tex]

Cancel the surd:

[tex]\displaystyle \large{x=16^8}[/tex]

Now, evaluating 16^8 will give up a million and that’s not necessary because we are finding how many solutions this equation has. Since theee only exists one value of x, which is the solution to this equation. Therefore:

Your answer is 1 solution

[tex]y = 14r^2 + 70r + 72\\\text{let}\ y = 0\\12r^2 + 70r + 72 = 0\\6r^2 + 35r + 36 = 0\\(2r + 9)(3r + 4)\\[/tex]

Answer:

768 Square Inches

Step-by-step explanation:

10x18 = 180 (2 rectanlge faces)

12x8 = 96 (2 triangles)

12x18 = 216 (bottom face)

216 + 96(2) + 180(2) =

768

Answer:

B

Step-by-step explanation:

17<9 + x

group like them

17-9 < x

the sign changes due to the negative

8>x

Answer:

differentiation

Step-by-step explanation:

maths class

Answer:

The answer is B, [3,10].

Step-by-step explanation:

Answer:

98 = 2w + 2L,

L = 3w

Step-by-step explanation:

Use the perimeter formula:

2) Perimeter = 2w + 2L (where w is the width and L is the length)

Since the length is three times the width we can write:

L = 3w

We can substitue L with 3w:

Perimeter is equal to 98 so,

98 = 2w + 6w = 8w

W = 98/8

Therefore w is 12.25, and L is 36.75

The lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.

The lateral surface area of a figure is the area of the non-base faces only. The lateral surface of an object is all of the sides of the object, excluding its base and top.

For the given situation,

The diagram shows the cone A and the cylinder B.

Cone A has the radius r and the slant height as h.

Cylinder B has the radius r and the height as h.

The lateral surface area of cone is [tex]\pi rh[/tex]

The lateral surface area of cylinder is [tex]2\pi rh[/tex]

1/2 × lateral surface area of cylinder B,

⇒ [tex]\frac{1}{2} (2\pi rh)[/tex]

⇒ [tex]\pi rh[/tex] = lateral surface area of cone A.

Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.

Learn more about lateral surface area here

https://brainly.com/question/11385509

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Answer:

Hence, the height of the trapezoidal base is 7.2 ft.

Step-by-step explanation:

The height of the trapezoidal base is 7.2 ft.

Step-by-step explanation:

Consider the provided information.

The volume of trapezoidal prism is the area of the cross-section × the length.

Where B is the area of base, H is the length and V is the volume.

The length of the prism is 25.2ft and volume is 1279.152

Hence, the base area is 50.76 ft².

The base is trapezoid.

The area of trapezoid is

Substitute B=50.76,  in above formula.

Hence, the height of the trapezoidal base is 7.2 ft.

Answer:

y = -x - 4

Step-by-step explanation:

y = mx + b

m = rise/run = -5/5 = -1

b = y-intercept = (0, -4)

Answer:

4(2k + j) = 8k + 4j

Step-by-step explanation:

4(2k + j)

Distribute in the 4.

4 * 2k + 4 * j

Multiply 4 and 2k.

8k + 4 * j

Multiply 4 and j.

8k + 4j

Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property:

⇒ A(B+C)=AB+AC

First, multiply by expand.

→ 4*2k=8k

→ 4*j=4j

Rewrite the problem down.

= 8k+4j

[tex]\Longrightarrow: \boxed{\sf{8k+4j}}[/tex]

I hope this helps! Let me know if you have any questions.

Answer:

1. Reflection across y=0

2. Shifted 6 units right

Answer:

Step-by-step explanation:

A translation of 6,-6  followed by a rotation of 180 degrees

2x+9+3x+x=6x+9

⇒ INFINITE SOLUTUIONS

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

[tex]f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}[/tex]

So for f(x) = x² on [1, 5], the AROC of f is

[tex]f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}[/tex]

Answer:

17963.13

Step-by-step explanation:

Answer

-4=lnx

Step-by-step explanation:

So if you raise both side to the ln then the e's cancel out and you are left with lnx=-4

another way to think about it is this:

Answer:

x = 15 , y = 15√(2)

Step-by-step explanation:

The triangle is isosceles where two angles are the same which mean two sides are also the same.

x = 15°

Pythagorean Theorem: a^2 + b^2 = c^2

15^2 + x^2 = y^2

15^2 + 15^2 = y^2

225 + 225 = y^2

450 = y^2

y = √(450) = 15√(2)

Answer:

x=15 and y=15root2

Step-by-step explanation:

tan45=p/b

1=x/15

x=15

again for right angle trangle

h=root (p+b)

=15root2 ans

Answer:

5/12

Step-by-step explanation:

The odds for the die are 5 positive out of 6 possible outcomes

-- 2,3,4,5,6 are the positive outcomes - the ones you want - but there are a total of 6 outcomes or ways the die could land

The odds for the coin are 1 positive outcome out of 2 possible outcomes (heads or tails)

Once you have 5/6 for the die and 1/2 for the coin, you multiply them together.

Answer:

96

Step-by-step explanation:

First solve (10-7)

Then use 21 and ÷ it by 3

Add 89 + 7 and then you'll get your answer

Answer:

UY = 20

WX = 15

VW = 15

Step-by-step explanation:

Given:  UVWXY ~ HDEFG

From inspection of the diagram, the corresponding sides are:

UV~HD

VW~DE

WX~EF

XY~FG

UY~HG

The only pair of sides that both have side lengths are XY and FG. Therefore, we can use these to figure out the scale factor of dilation.

XY = 10 and   FG = 20

⇒ FG/XY= 20/10 = 2

Therefore, HDEFG is an enlargement of UVWXY by a scale factor of 2

If HG = 40

⇒ UY = 40 ÷ 2 = 20

If EF = 30

⇒ WX = 30 ÷ 2 = 15

If DE = 30

⇒ VW = 30 ÷ 2 = 15

Answer:

UY = 20, WX = 15, VW = 15

Step-by-step explanation:

Step 1:  Determine the scale

XY = 10 and FG = 20

[tex]10/20 = 0.5[/tex]

Step 2:  Determine UY

We can determine UY by multipliying GF by 0.5 which will give us the upscaled ratio which will produce UY.

[tex]UY = GF * 0.5[/tex]

[tex]UY = 40 * 0.5[/tex]

[tex]UY = 20[/tex]

Step 3:  Determine WX

We can determine WX by multipliying FE by 0.5 which will give us the upscaled ratio which will produce WX.

[tex]WX = FE * 0.5[/tex]

[tex]WX = 30 * 0.5[/tex]

[tex]WX = 15[/tex]

Step 4:  Determine VW

We can determine VW by multipliying ED by 0.5 which will give us the upscaled ratio which will produce VW.

[tex]VW = ED * 0.5[/tex]

[tex]VW = 30 * 0.5[/tex]

[tex]VW = 15[/tex]

Answer: UY = 20, WX = 15, VW = 15

Answer:

2. The change in expected height for every one additional centimeter of femur length.

Step-by-step explanation:

1. The expected height for someone with a femur length of 65 centimeters.

Doesn't make sense, that would be height value when centimeters = 65.

2. The change in expected height for every one additional centimeter of femur length.

Makes sense, for every increase in one additional centimeter, we can expect the height to be proportional to the slope.

3. The femur length for someone with an expected height of 2.5 centimeters.

Doesn't make sense, the linear relationship relies on the femur length to get the height.

4. The change in expected femur length for every one additional centimeter of height.

Doesn't make sense, again, the linear relationship relies on the femur length.