the velocity v of an object rolled down an inclined plane is given by the formula v equals 26d square-rooted, where d is the distance the object has rolled. solve for d

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x^2-x-4}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

The focus is

[tex]\left(h,\ k+\dfrac{1}{4a}\right)[/tex]

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of a using [tex]k+\dfrac{1}{4a}[/tex]

k = -5

[tex]-5+\dfrac{1}{4a}=-4[/tex]        add 5 to both sides

[tex]\dfrac{1}{4a}=1[/tex]           multiply both sides by 4

[tex]4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4[/tex]

[tex]\dfrac{1}{a}=4\to a=\dfrac{1}{4}[/tex]

Substitute

[tex]a=\dfrac{1}{4},\ h=2,\ k=-5[/tex]

to the vertex form of an equation of a parabola:

[tex]y=\dfrac{1}{4}(x-2)^2-5[/tex]

The standard form:

[tex]y=ax^2+bx+c[/tex]

Convert using

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5[/tex]

use the distributive property: a(b+c)=ab+ac

[tex]y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

8. The volume of the rocket = the volume of the cone + the volume of the cylinder.

The volume of the cone is = [tex]\frac{1}{3} \pi \times radius^{2} (height) = \frac{1}{3} \pi \times 3^{2} \times5 = 15\pi[/tex] [tex]inch^{3}[/tex].

The volume of the cylinder is [tex]\pi \times radius^{2} \times height = \pi \times 3^{2} \times 10 = 90\pi[/tex] [tex]inch^{3}[/tex].

The total volume is [tex]15\pi + 90\pi = 105\pi inch^{3}[/tex].

9. Matt made the error in calculating the volume.

The diameter of the spherical ball is given by 15 centimeter.

The volume of a spherical ball is calculated by the formula [tex]\frac{4}{3} \pi \times radius^{3}[/tex].

Matt put the diameter of the spherical ball instead of its radius.

Answer:

78,732

Step-by-step explanation:

a_1 = 4

a_2 = 12

a_2/a_1 = 12/4 = 3

a_1 = 4

a_2 = 4 * 3 = 4 * 3^1 = 12

a_3 = 4 * 3 * 3 = 4 * 3^2 = 36

a_n = 4 * 3^(n - 1)

For n = 10:

a_10 = 4 * 3^(10 - 1) = 4 * 3^9 = 4 * 19,683 = 78,732

Final answer:

The formula for the nth term of a geometric sequence is a(n) = [tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex], where a(n) is the nth term, a(1) is the first term, and r is the common ratio. In this case, the first term is 4 and the second term is 12. By using the formula, the calculated tenth term is 78,732. Therefore, the correct answer is C.

Explanation:

The formula for the nth term of a geometric sequence is given by:

[tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex]

where:

- [tex]\( a_n \)[/tex] is the nth term,

- [tex]\( a_1 \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the term number.

In this case, the first two terms are given as 4 (which is [tex]\( a_1 \)[/tex]) and 12 (which is [tex]\( a_2 \)[/tex]).

The common ratio ([tex]\( r \)[/tex]) can be found by dividing the second term by the first term:

[tex]\[ r = \frac{a_2}{a_1} = \frac{12}{4} = 3 \][/tex]

Now, you can use this common ratio in the formula to find the 10th term [tex](\( a_{10} \))[/tex]):

[tex]\[ a_{10} = 4 \times 3^{(10-1)} \][/tex]

[tex]\[ a_{10} = 4 \times 3^9 \][/tex]

[tex]\[ a_{10} = 4 \times 19683 \][/tex]

[tex]\[ a_{10} = 78,732 \][/tex]

So, the correct answer is: C) 78,732

Answer:

1) The simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2) The simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) The simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) The simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Step-by-step explanation:

1) Given expression is [tex]\sqrt{36x^2}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^2}[/tex]

[tex]=\sqrt{36\times x^2}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^2}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x\times x}[/tex]

[tex]=6\times x[/tex]

[tex]\sqrt{36x^2}=6x[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2)Given expression is [tex]\sqrt{72x^3}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{72x^3}[/tex]

[tex]=\sqrt{72\times x^3}[/tex]

[tex]=\sqrt{72}\times \sqrt{x^3}[/tex]

[tex]=\sqrt{9\times 8}\times \sqrt{x\times x\times x}[/tex]

[tex]=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}[/tex]

[tex]=3\times 2\sqrt{2}\times x\sqrt{x}[/tex]

[tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) Given expression is [tex]\sqrt{15x^8}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{15x^8}[/tex]

[tex]=\sqrt{15\times x^8}[/tex]

[tex]=\sqrt{15}\times \sqrt{x^8}[/tex]

[tex]=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}[/tex]

[tex]=\sqrt{15}\times x^4[/tex]

[tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

Therefore the simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) Given expression is [tex]\sqrt{36x^7}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^7}[/tex]

[tex]=\sqrt{36\times x^7}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^7}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}[/tex]

[tex]=6\times x^3\sqrt{x}[/tex]

[tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Answer:309.799

Step-by-step explanation:293.08

14.00 =309.799

+ 2.719

Answer: 0.766 = x/12

Final answer:

The correct equation for the triangle is determined by the context provided, which may involve setting up proportions or using trigonometric ratios such as the tangent. Without specific information from a diagram or narrative of the triangle, the correct equation cannot be identified.

Explanation:

The correct equation based on the triangle shown is determined by setting up a mathematical relationship (proportion or equation) that represents the situation described in the diagram or narrative associated with the triangle. Without the specific diagram or narrative details, it is impossible to determine the correct equation. However, generally, if you are given the lengths of sides in different units (for example, feet and inches), you would set up a proportion like

1 foot/12 inches = x feet/y inches

and then cross-multiply to solve for x or y.

If you are dealing with trigonometric functions and are given an angle, you may use a function like sine, cosine, or tangent to find a relationship between the sides. The correct equation could include the tangent ratio if the triangle is right-angled and you have the lengths of the opposite and adjacent sides to the given angle:

tan(theta) = opposite/adjacent

Answer:

The answer 180=3x+90

Answer:

y=3x+-7

Step-by-step explanation:

the standard form is y=mx+b

m being the slope and b being the y intercept

Answer:

3x-7y=14

Step-by-step explanation:

7y=3x-14

3x-7y=14

Answer:

Volume= 3*4*6= 72 cubic feet

Step-by-step explanation:

Whenever finding volume of a simple rectangular prism like that one, simply multiply the Length of one side by the Height of the prism by the Width of the front face and you will get your solution. Length=6 ft, Height=3 ft, Width=4 ft. Hence, V=L*W*H or V=6*4*3=72 cubic feet.

a = –2 and b = 3

Solution:

Given equations are

3a – b = –9 – – – – (1)

–3a – 2b = 0  – – – – (2)

To solve these equations by elimination method.

Elimination method means eliminating one variable to find the other variable.

Add equation (1) with equation (2), we get

3a – b + (–3a – 2b) = –9 + 0

⇒ 3a – b – 3a – 2b = –9

Combine like terms together.

⇒ 3a – 3a – b – 2b = –9

⇒ 0 – 3b = –9

⇒ – 3b = –9

Divide by (–3) on both sides, we get

⇒ b = 3

Substitute b = 3 in equation (1), we get

(1) ⇒ 3a – b = –9

⇒ 3a – 3 = –9

Add 3 on both sides of the equation,

⇒ 3a = –6

Divide 3 on both sides of the equation

⇒ a = –2

Hence, a = –2 and b = 3.

Answer:

X = 0.75

Step-by-step explanation:

0.25[2.5x + 1.5(X-4)]= -X

0.25[2.5x + 1.5x - 6] = -x

0.25[4x -6] = -x

1x + x = 1.5

2x = 1.5

x = 1.5/2

x = 0.75

Answer: 0.112485

Step-by-step explanation: Look below for an attached explanation

Hope this helps!

To find 0.06 divided by 0.5334, multiply both numbers to convert them into whole numbers and then perform long division. The result of the division is approximately 0.1125.

The question asks for the division of two decimal numbers, specifically 0.06 divided by 0.5334. To divide these decimals, you can use long division or a calculator. Here's how to divide them step-by-step using long division:

In this case, 0.06 divided by 0.5334 is approximately 0.1125.

This type of math problem is common in various science calculations, such as determining the concentration of a solution in chemistry or the rate of a reaction in physics.

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Step-by-step explanation:

15x + 21= 3 (5x + 7)

Therefore, greatest common factor is (5x + 7)

Answer:

37.41

Step-by-step explanation:

multiply 4.30 by 10 to get 43

then make it a decimal =0.43

after that multiply it by 13

0.43 times 13 = 5.59

subtract 5.59 from 43

Hope this will help u. If my ans was helpful u can follow me.

THANKYOU.

The expression for the number of words Craig types in m minutes is 20 words/minute × m minutes. This equation can be used to calculate how many words Craig can type in any given number of minutes.

If Craig types at a speed of 20 words per minute, to find the expression for the number of words he types in m minutes, you would use the simple formula of rate times time. The rate is the number of words per minute, and the time is how many minutes he is typing. Therefore, the expression would be:

20 words/minute × m minutes = number of words Craig can type in m minutes.

To find out if Craig can type more than 200 words, you can set m to a value greater than 10, since 20 words/minute for 10 minutes would result in 200 words exactly (20 × 10 = 200).

Step-by-step explanation:

9/8 × (-7/3) =

9 × -7 = -63

8 × 3 = 24

-63/24 simplify

-21/8

Answer:

$722.40

Step-by-step explanation:

2.8% x 4300 = 120.4

120.4 x 6 = 722.40

Answer:

A   =  90,312.5 square feet is the maximum area.

Step-by-step explanation:

Here, the shape of the enclosure  = Rectangle

Now, 3 sides of the rectangle needs to be fenced.

Total length of the fencing wire  = 1000 ft

Let us assume the length of the enclosure = L

The width of the enclose = W

According to question:

The length to fenced = Perimeter of the rectangle - 1 side of Enclosure

⇒ 1000  =  2 (L + W) - L

or, 1000 = L +  2 W

or, L  = 1000 - 2 W  .... (1)

Now, as we need to MAXIMIZE the area of the enclosure:

Area of the enclosure  = L x W    =  (1000 - 2 W) x  W

Now simplifying the area expression, we get:

[tex]A(w) = 1000 w - 2w^2[/tex]

This is a parabola that opens downward so there is a maximum point.

The vertex of the parabola is (h,k) where h is the "maximizing number" and k is the maximum area.

Use the fact that h   =   -b/2 a

h   =    -850/(2*[-2])

h  =   -850/(-4)

h   =   212.5 would be the length of all four sides if it were not for the barn

Therefore you have an extra 212.5 feet

Add the 212.5 feet to the opposite side(length) to get 425 feet.

You have a rectangle that is 212.5 feet by 425 feet by 212.5 feet by "the barn".

The width is 212.5 feet which maximizes the area.

A  =   l w

A  =  425*212.5

A   =  90,312.5 square feet is the maximum area.

We are given a painter can paint 350 square feet in 1.25 hours.

We want to figure out the painting rate in square feet per hour. “Per hour” means for every 1 hour.

To find this, an equation like 350 = 1.25h (h for hours) can be set up. To solve, the only thing we need to do is divide by 1.25 to get h alone:

350/1.25 = 1.25h/1.25 or 280 = h

The painter can paint 280 square feet per 1 hour.

Answer:

x=6

Step-by-step explanation:

2x+(4x+3)=39

2x+4x+3=39

6x+3=39

6x=39-3

6x=36

x=36÷6

x=6

Solving the system of equations y = 4x + 3 and 2x + y = 39, we first substitute y from the first equation into the second. Simplifying, we find x = 6. Substituting x = 6 into the first equation, we find y = 27. Therefore, the solution is x = 6, y = 27.

To find the answer to this system of linear equations using substitution method, we first need to make y the subject of the first equation. From y = 4x + 3, we then substitute y in the second equation, thereby getting 2x + 4x + 3 = 39.

After simplifying, the combined equation becomes 6x + 3 = 39. We then isolate x by subtracting 3 from both sides, giving 6x = 36, and therefore x = 6.

To find y, substitute x = 6 into the first equation, y = 4x + 3. Thus, y = 4*6 + 3, which gives y = 27.

So, for the equations y = 4x + 3 and 2x + y = 39, the solution is x = 6, y = 27.

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Answer:

Answer is: C - hope it helps you!

Answer:

The equation of a line through (5 -3) that is parallel to y = 1/2 x+3 is

y = - 2 x  + 7

Step-by-step explanation:

Let us assume the slope of the line whose equation we need to find is m 1.

The line parallel to the needed line  is:   y=1/2x+3

Comparing it with the general form: y = m x + C

we get m 2 = 1/2

Now, as Line 1 is Perpendicular to Line 2.

⇒ m 1 x m 2  = -1

⇒ m 1 x ( 1/2)  = -1

⇒ m 1  = - 2

Also, the point son the line 1 is given as: (x,y)  = (5,-3)

Put the value of point and Slope in y = m x + C to find the value of Y- INTERCEPT.

we get: -3 = (-2) (5) +  C

or, C = -3 + 10 = 7

⇒ C = 7

The general line equation is given as:  y = m x + C

Substituting  the values of C and m, we get:

y = - 2 x  + 7

Hence, the equation of a line through 5 -3 that is parallel to y = 1/2 x+3 is

y = - 2 x  + 7

Each month for 9 months, Jordan buys 2 sports books. How many more sports books does he need to buy before has bought 25 sports books?

Jordan needs to but 7 more sports book

From given,

Each month for 9 months, Jordan buys 2 sports books

Thus for one month he buys 2 sports books

For, 9 months, number of books is bought is given as:

[tex]\text{Number of books bought in 9 months } = 9 \times 2 = 18[/tex]

Thus, in 9 months he has bought 18 books

He needs to buy 25 sports books

Therefore, remaining books to be bought = 25 - 18 = 7

Thus he needs to buy 7 more books to have 25 of them

Answer: x = -9, x = 115

Step-by-step explanation:

when x = -9 :

5(-9) + 40

-45 + 40

= -5

when x = 15

5(15) + 40

75 + 40

= 115

Answer:

X = -5, 40, 115

Step-by-step explanation:

when x = 0-9

5(0-9) + 40

-45 + 40

= -5

when x = 0T =0

5(0) + 40

0 + 40

= 40

when x = 015=15

5(15) + 40

75 + 40

= 115

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Step-by-step explanation:

[tex]NO+H_{2} O\rightarrow NH _{3}+O_{2}[/tex]

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Answer:

Step-by-step explanation:

so John (lol...who names a snake John)....ok...so at 5 months he was 4 ft...and at 6 months, he was 4'2....means he is growing at a rate of 2 inches per month. So if he continues to grow at 2 inches per month, then this is linear...but if he doesn't, its not linear.

So from 6 months to 1 year, is a period of 6 months...and if he grows at 2 inches per month, in 6 months he should have grown (6 * 2) = 12 inches.

4'2" + 12 inches = 4 ft 14 inches = 5 ft 2 inches......but he is not 5'2" at age 1, he is only 5 ft.....so NO, this is NOT linear.