Given the sequence 2, 10, 50, 250,......where x = 0, 1, 2, 3,....., what is the first term?

A: 2
B: 10
C: 50
D: 250

The answer is 120 because 13 times 8 equals 104, and all you have to do is find the base edge length of the triangle which is found by subtracting 13 from the 17 and getting 4 for the triangle base length, multiplying it by the height (8) which you get 32, dividing it by two to get 16, add 104 and there's your answer.

Answer:

1/5, 1/3, 4/6

Step-by-step explanation:

First, find all the common denominators for these numbers. In this case, it's 30.

1/5 = 10/30

4/6 = 20/30

1/5 = 6/30

Now, you can see which ones are greatest and least.

1. 1/5 (least)

2. 1/3 (middle)

3. 4/6  (greatest)

Answer:

1024πcm²

Step-by-step explanation:

The surface area of a sphere is found using the following formula:n A=4πr². r is the radius while A is the surface area.

in the sphere the radius is 16 cm thus:

A=4×π×16²

=1024π cm²

Answer:

The correct answer is third option 1024π

Step-by-step explanation:

Formula:-

Surface area of sphere = 4πr²

Where r is the radius of sphere

To find the surface area of sphere

Here r = 16

Surface area =  4πr²

  = 4 * π *16²

  = 4 * π * 16 * 16 = 1024π

Therefore surface area of sphere = 1024π

The correct answer is third option 1024π

2times1 because 2.75 take the 75 off and 1.25 take the 25 off so you multiply 2 and 1 so 2times1 equals 2

Answer:

C) 3 x 1

Step-by-step explanation:

First, you round 2.75 to 3 because of the rounding rule- "If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up." Then you round 1.25 to 1 because of the rounding rule. Then you get 3 x 1!

Hope this helps-

maggbaron765

Answer:

Step-by-step explanation:

The calculator says that the answer is 7.36 * 10^-3.

This has been rounded to the proper number of significant digits. 5.02 has only 3 sig digs.

Coefficient: 7.36

Exponent: - 3

Note your calculator might give you 0.00736 but that is really 7.36 * 10^-3

Answer:

7.56932 * 10^-3

The coefficient is 7.35932

The exponent is -3

Step-by-step explanation:

When we multiply numbers in scientific notation, we take the numbers out front and multiply

1.466*5.02 =7.56932

Then we add the exponents on the powers of 10

10^(-8+5) = 10^(-3)

The result is 7.56932 * 10^-3

Using a calculator, we get 0.00735932, which is not in scientific notation.  Your question indicates that you want the result in scientific notation

.00735932 changed to scientific notation

Move the decimal until a nonzero digit is to the left of the decimal

7.35932

We moved it 3 places to the left, that means our exponent is -3

7.35932*10^-3

just about 49. cents a person

Answer:

99.55 – 40x = 19.95 ; $1.99

Step-by-step explanation:

Answer: $1.99

Answer:

[tex] 0.25 [/tex]

Step-by-step explanation:

We are given the following verbal expression and we are to first translate it and then evaluate it:

'6- the square root of 25 divided by 4'

[tex] \frac { 6 - \sqrt { 25 } } { 4 } [/tex]

Taking the square root first to get:

[tex] \frac { 6 - 5 } { 4 } [/tex]

[tex] \frac { 1 } { 4 } [/tex]

[tex] 0.25 [/tex]

Answer:

.25

Step-by-step explanation:

Answer:

squrt6(84)

Step-by-step explanation:

By the law:

squrtn(a^m) = a^(m/n)

Best regards

Answer:

[tex]\large\boxed{The\ vertex:\ (-5,\ 49)}[/tex]

Step-by-step explanation:

[tex]f(x)=ax^2+bx+c\\\\\text{The vertex}\ (h,\ k),\ \text{where}\ h=\dfrac{-b}{2a}\ \text{and}\ k=f(h).\\\\\text{We have:}\ y=-x^2-10x+24\to f(x)=-x^2-10x+24\\\\a=-1,\ b=-10,\ c=24.\\\\\text{Substitute:}\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)+24=-25+50+24=49[/tex]

Answer:

0.00487

Step-by-step explanation:

You move the decimal place back 3 places because it’s 10 to the -3

Answer:

0.00487

Step-by-step explanation:

When you have a negative power, you move the decimal point to the left. In this case, move the decimal three places left.

Answer:

8

Step-by-step explanation:

200 divided by 25 is 8

Answer:

Step-by-step explanation:

The equation of a circle in a standard form:

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

(h, k) - center

r - radius

We have the equation:

[tex]x^2-16x+y^2=36\\\\x^2-2(x)(8)+y^2=36\qquad\text{add}\ 8^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(8)+8^2}_{(*)}+y^2=36+8^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\(x-8)^2+(y-0)^2=36+64\\\\(x-8)^2+(y-0)^2=100\\\\(x-8)^2+(y-0)^2=10^2\\\\\text{Therefore}\\\\center:(8,\ 0)\\radius:10[/tex]

Kash to Gary is 8 miles

Gary to Joan is 5 miles

Use the Pythagorean theorem to calculate the distance from Joan to Kash:

x = √8^2 + 5^2

x = √64+25

x = √89

x = 9.4

Total distance = 5 + 8 + 9.4 = 22.4 miles.

Rounded to nearest mile = 22 miles.

Answer:22 miles

Step-by-step explanation:

Got it right on a quiz

Answer:

1 3/8 ft.

Step-by-step explanation:

The cabinet's center will be at the same place as the wall's center. The wall's center is at its 3 1/8 ft mark. The cabinet's center will also be at the wall's 3 1/8 mark. This means that both sides of the cabinet is 1 3/4 around the center line (if my wording is vague, look at the image). So, we have to find 3 1/8 - 1 3/4, which is 1 3/8 ft.

Subtraction is one of the most basic mathematical operations. The end of the cabinet is 1.375 feet far from the edge of the wall.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The centre of the cabinet will lie at half the width of the cabinet, therefore, the centre of the cabinet will be at,

[tex]\text{Centre of the cabinet}= \dfrac{3\frac{1}{2}}{2}[/tex]

                                  [tex]\rm = \dfrac{\frac{(3 \times 2)+1}{2}}{2}\\\\=\dfrac{7}{2 \times 2} = \dfrac{7}{4} = 1.75\ feet[/tex]

Since Bobby wants the cabinet to be at the centre of the wall horizontally, we need to find the centre point of the wall as well, and then align both the centres together, therefore, the centre of the wall is at,

[tex]\text{Centre of the wall} = \dfrac{6\frac{1}{4}}{2}[/tex]

                            [tex]\rm = \dfrac{\frac{(6 \times 4)+1}{4}}{2}\\\\=\dfrac{25}{2 \times 4} = \dfrac{25}{8} = 3.125\ feet[/tex]

Now, the length between the end of the cabinet from the edge of the wall is the difference between the half the length of the wall and half the length of the cabinet, therefore, the length can be written as,

[tex]\rm Length = \text{Centre of the Wall} - \text{Centre of the Cabinet}\\[/tex]

            [tex]\rm = 3.125 - 1.75\\\\= 1.375\ feet[/tex]

Hence,  the end of the cabinet is 1.375 feet far from the edge of the wall.

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Answer:

y=-5/2x-19/2

Step-by-step explanation:

The vertex of the quadratic equation is (-7,8).

Isolate the variable y for the equation 2x-5y=7

You get y = 2/5x-7/5

The slope we have to find is the inverse of the current slope.

So the slope for the final equation is -5/2.

Then use point slope form to get y - 8 = -5/2 * (x+7)

Then convert it into slope intercept form to get y - 8 = -5/2x - 35/2

Then add 8 to each side to get y=-5/2x-19/2

Answer is A because it’s moved 2 to the right which makes it x-2 and it’s moved 1 down so -1 and it needs to be -x because it’s facing down so the answer is A

Answer:

Option A. f(x) = -(x - 1)² - 1

Step-by-step explanation:

After the transformation of g(x) = x², vertex of the red parabola f(x) is (2, -1).

Therefore, equation of the parabola in the vertex form will be

f(x) = (x - 2)² - 1

Since opening of the parabola is downwards so the function will be

f(x) = - (x - 2)² - 1

This function matches with option A.

Answer:

Step-by-step explanation:

Alright, lets get started.

The total surface area of rectangular pyramid will be the area of all four faces and area of base.

The faces are triangular, so area will be = [tex]\frac{1}{2}*base*height[/tex]

Area of face = [tex]\frac{1}{2}*16*14=112[/tex]

Another face area = [tex]\frac{1}{2}*12*15=90[/tex]

Each face has its similar another face. So total area of faces will be = [tex]112+112+90+90=404[/tex]

Area of base = [tex]12*16=192[/tex]

So total surface area = [tex]404+192=596[/tex] square feet

Hence the total surface area is 596 square feet.   :   Answer

Hope it will help :)

Answer:596 square feet

Step-by-step explanation:

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=9\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=\stackrel{r}{3^2}~\hfill \begin{cases} center~(3,7)\\ radius=3 \end{cases}[/tex]

Final answer:

The radius of the circle with the equation (x − 3)² + (y − 7)² = 9 is found by taking the square root of 9, which is 3. Therefore, the correct answer is A) 3.

Explanation:

The question asks to find the radius of a circle given its equation. The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Comparing this with the given equation (x − 3)² + (y − 7)² = 9, we see that the value of r² is 9.

Therefore, the radius r of the circle is the square root of 9, which is 3.

Hence, the correct answer is A) 3.

40+20=72-12 is how you rewrite it

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. The equation can be correctly rewritten as 60=60.

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. Starting with the left side, we have 4(10+5). Using the distributive property, this becomes 4(10) + 4(5) = 40 + 20 = 60. Now, let's apply the distributive property to the right side of the equation. We have 6(12-2), which becomes 6(12) - 6(2) = 72 - 12 = 60. Therefore, the equation 4(10+5)=6(12-2) can be correctly rewritten as 60=60 using the distributive property.

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Answer:

The answer is 9x² - 6x - 1

Step-by-step explanation:

∵ (6x³ + x² - 10x - 1) - (6x³ - 8x² - 4x) =

    0 + 9x² - 6x - 1 = 9x² - 6x - 1

Answer:

The result is : [tex]9x^{2} -6x-1[/tex]

Step-by-step explanation:

The given terms to be subtracted are ;

[tex]6x^{3}+x^{2} -10x-1[/tex] and

[tex]6x^{3}-8x^{2} -4x[/tex]

So, subtracting each term to be more clear we get:

[tex]6x^{3}-6x^{3}=0[/tex]

[tex]x^{2} -(-8x^{2} )=x^{2} +8x^{2} =9x^{2}[/tex]

[tex]-10x-(-4x)=-10x+4x=-6x[/tex]

[tex]-1+0=-1[/tex]

So, the answer will be :

[tex]9x^{2} -6x-1[/tex]

Answer:

4 inches long each i think im not completely sure

Step-by-step explanation:

Rectangle has its adjacent sides perpendicular to each other. The lengths of the sides of the considered rectangle are: 5 inches and 12 inches.

Its the sum of length of the sides used to made the given figure.

For a rectangle, as the rectangle has two of its sides equal to its length, and rest two are equal to its width, thus,

perimeter of rectangle = twice of (width + length)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]  

where |AB| = length of line segment AB.

In a rectangle, its adjacent sides are perpendicular to each other(making 90 degrees with each other), thus, when its diagonal is drawn, we can use Pythagoras theorem to relate its length, width and length of the diagonals (both of diagonals of a rectangle are of same length).

Thus,  using Pythagoras theorem, we get:

[tex](|Diagonal|)^2 = |Length|^2 + |Width|^2[/tex]

Suppose its length and width are L and W, then we get two equations:

Perimeter = 2(L + W) = 34 inches

Diagonal² = 13² = 169 = L² + W²

From the first equation, getting L in terms of W, we get:

[tex]L = 17 - W[/tex]

Putting this value in second equation, we get:

[tex]L^2 + W^2 = 169\\(17-W)^2 + W^2 = 169\\289 + W^2 + W^2 -34W = 169\\2W^2 -34W + 120 = 0\\W^2 - 17W + 60 = 0\\W^2 -12W - 5W + 60 = 0 \\W(W - 12) - 5(W - 12) = 0\\\\(W-5)(W-12) = 0\\W = 5, 12[/tex](in inches)

Thus, we get L= 17-W = 12 or 5,

Thus, dimensions of the considered rectangle are 5 inches and 12 inches.

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The solution to the equation j/3 = 4.5 is j = 13.5

From the question, we have the following parameters that can be used in our computation:

j/3 = 4.5

Multiply both sides of the equation by 3

So, we have

3 * j/3 = 4.5 * 3

Evaluate the products

This gives

j = 13.5

Hence, the solution to the equation is 13.5

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This means that everything in between those numbers is correct

To find which binomial is a factor of the polynomial x^2 - x - 6, one needs to factor the polynomial and find its roots. The factored form of the polynomial is (x -2)(x +3), indicating that the roots are x = 2 and x = -3. Consequently, the correct answer is (X - 2).

The question is asking us to identify which of the listed binomials is a factor of the polynomial x^2 - x - 6. A factor of a polynomial is a polynomial which divides the original polynomial exactly. To find the factors of the polynomial x2 - x - 6, we have to solve the equation for it equal to zero, x2 - x - 6 = 0. This is a quadratic equation, and we can find its roots via factoring. The factored form of the polynomial is (x - 2) (x + 3). From the factored form, we see that the roots or zeros of the polynomial are x = 2 and x = -3. Hence, the answer is (X - 2).

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[tex]7\frac{4}{5} = \frac{28}{5}[/tex]

because 7 x 4 = 28

[tex]4\frac{7}{5} = \frac{28}{5}[/tex]

because 4 x 7 = 28

This means that

[tex]7\frac{4}{5} = [tex]4\frac{7}{5}[/tex]

[tex]6\frac{12}{5} = \frac{72}{5}[/tex]

because 6 x 12 = 72

This means

[tex]7\frac{4}{5} = [tex]6\frac{12}{5}[/tex]

Answer:

The area of the regular hexagon is [tex]166.3\ units^{2}[/tex]

Step-by-step explanation:

we know that

The regular hexagon can be divided into 6 equilateral triangles

so In this problem

The radius is equal to length side of the polygon

The area of the regular hexagon is equal to the area of six equilateral triangle

[tex]A=6[\frac{1}{2}(b)(h)][/tex]

we have

[tex]b=r=8\ units[/tex] ---> the base of each triangle is equal to the radius

[tex]h=4\sqrt{3}\ units[/tex] ---> the height of each triangle is equal to the apothem

substitute

[tex]A=6[\frac{1}{2}(8)(4\sqrt{3})]=96\sqrt{3}\ units^{2}[/tex]

[tex]96\sqrt{3}=166.3\ units^{2}[/tex]

The volume of a cylinder,

πr^2h => π x 3^2 x 2.033 = 57.48 cubic ft

67 cubic feet Tank hold 500 Gallons

57.48 cubic feet Tank will hold less than 500 Gallons

Yes you can win.

The volume of a cylinder in cubic feet is equal to π times the radius in feet squared times the height in feet. π is roughly equal to 3.1415. If you know the diameter of the cylinder, you can find the radius by dividing the diameter by two, or just use our circle diameter calculator.

To calculate the volume of a cylinder, you need the radius or diameter of the circular base or top and a cylinder's height. The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.

Cubic feet by multiplying three linear measurements—length, width, and height—in feet.π r2 h

The volume of a cylinder is given by the formula – π r2 h, where r is the radius of the cylinder and h is the height.

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QUESTION 1

The tangent ratio is the ratio of the length of the opposite side of the length of the adjacent side.

From ΔVWX,

[tex]\tan(X)=\frac{VW}{WX}[/tex]

From ΔYZX,

[tex]\tan(X)=\frac{YZ}{XZ}[/tex]

[tex]\therefore \tan(X)=\frac{VW}{WX}=\frac{YZ}{XZ}[/tex]

QUESTION 2

We use the tangent ratio to obtain;

[tex]\tan(V)=\frac{Opposite}{Adacent}[/tex]

[tex]\tan(V)=\frac{WX}{VW}[/tex]

QUESTION 3

From ΔVWX,

[tex]\tan(X)=\frac{VW}{WX}[/tex]

We take the inverse tangent of both sides to obtain;

[tex]X=\tan^{-1}(\frac{VW}{WX})[/tex]

[tex]\therefore \tan^{-1}(\frac{VW}{WX})=X[/tex]

QUESTION 4

From ΔVWX,

[tex]\tan(V)=\frac{WX}{VW}[/tex]

Taking the inverse tangent of both sides, we obtain;

[tex]V=\tan^{-1}(\frac{WX}{VW})[/tex]

[tex]\therefore \tan^{-1}(\frac{WX}{VW})=V[/tex]

QUESTION 5.

We know that

[tex]\tan(V)=\frac{WX}{VW}[/tex]

and

[tex]\tan(X)=\frac{VW}{WX}[/tex]

[tex](\tan X)(\tan V)=(\frac{VW}{WX})(\frac{WX}{VW}=1[/tex]

QUESTION 6.

[tex]\tan^{-1}(\frac{VW}{WX})=X[/tex]

[tex]\tan^{-1}(\frac{WX}{VW})=V[/tex]

This implies that;

[tex]\tan^{-1}(\frac{VW}{WX})+\tan^{-1}(\frac{WX}{VW})=X+V[/tex]

QUESTION 7

[tex]\tan 23\degree =0.4244[/tex]

We round to the nearest 0.01 to obtain;

[tex]\tan 23\degree =0.42[/tex]

QUESTION 8

[tex]\tan 43\degree =0.9325[/tex]

We round to the nearest 0.01 to obtain;

[tex]\tan 43\degree =0.92[/tex]

QUESTION 9

[tex]\tan ^{-1} 0.14=7.9696\degree[/tex]

We round to the nearest 0.01 to obtain.

[tex]\tan ^{-1} 0.14=7.97\degree[/tex]

QUESTION 10

[tex]\tan ^{-1} 1=45.00\degree[/tex]

QUESTION 11

[tex]\tan ^{-1} 0.14=7.97\degree[/tex]

This implies that;

[tex]\tan 7.97\degree=0.14[/tex]

QUESTION 12

[tex]\tan ^{-1} 1=45.00\degree[/tex]

This implies that;

[tex]\tan 45.00\degree=1[/tex]

Answer:

YES

Step-by-step explanation:

3x+4y=33

2x+y=17 ➡ y=-2x+17

2x+(17-2x)=17

2x+17-2x=17

2x-2x+17=17

17=17

same number on both sides means   Infinitely many solutions

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