Which of the following represents all solutions to the equation
1/3x^2 +10 = 7

Answer:

subtraction

Step-by-step explanation:

If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.

7 - 4

= 3 she has 3sqft of construction paper left.

Answer:

The equation of the line is y = -1.x + 9

Graph is provided in the attached figure

Step-by-step explanation:

The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation

[tex]y = mx + c[/tex]

where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0

Given slope = -1, we can find c and the equation of the line

Since (3,6) is a point on the graph, these coordinates must satisfy the above equation

Substitute for y = 6 and x = 3

[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]

In the attached figure you can see that (3,6) is on the line

Answer:

[tex]5x^{2} -4x-9[/tex]

Step-by-step explanation:

f(x)+g(x)

[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]

The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9

Given that:

Functions, f ( x ) = 3x² - 6x + 2

And g ( x ) = 2x² + 2x - 11.

Then find f ( x ) + g ( x ).

To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.

To find f(x) + g(x), add the coefficients of the corresponding terms:

f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)

Now, combine like terms:

f(x) + g(x) = 5x² - 4x - 9

So, the sum of the two functions is:

f(x) + g(x) = 5x² - 4x - 9

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The number of months taken for the toenail to completely regenerate itself is 13 months

It is the quantity of an amount of something at a rate of one of another quantity.

We have,

Toenail grows:

0.05 mm per day

0.05 mm = 1 day

[ 1 inch = 25.4 mm ]

So,

1 mm = 1/25.4 inch

0.05 x 1/25.4 inch = 1 day

0.0019 inch = 1 day

Divide both sides by 0.0019

1 inch = 1/0.0019 day

1 inch = 526.32 days

Multiply 3/4 on both sides.

3/4 inch = 3/4 x 526.32 days

3/4 inch = 395 days _____(1)

We can assume,

1 month = 30 days

Multiply 395/30 on both sides.

395/30 months = 395 days

13 months = 395 days _____(2)

From (1) and (2) we get,

3/4 inch = 13 months

Thus,

The number of months taken for the toenail to completely regenerate itself is 13 months.

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The given height of the shape is calculated to be 1,895.04 inches.

We have the following details required to solve this problem

The distance b1 = 800 m

The angle of elevation β1 = 50°

distance b2 = 1450 m

- The new angle of elevation  α = 33°

We first have to find the height of h1

800 x tan 50 degrees

= 953.40

The height of h2

1450 x tan 33

= 941.641

The height of the shape is the sum of the heights of h1 and h2

953.40 + 941.641

= 1,895.04

Hence the height of the shape is given as 1,895.04 inches.

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Answer:

$140

Step-by-step explanation:

interest = 8x5 = 40

total = time + interest

total = 100 + 40 = $140

The average number of pages she reads per hour is 19 pages per hour

The given parameters are:

Number of pages = 76 pages

Number of hours = 4 hours

The average number of pages she reads per hour is calculated using the following formula

Average = Number of pages/Number of hours

Substitute the known values in the above equation

Average = 76 pages/4 hours

Evaluate the quotient

Average = 19 pages per hours

Hence, the average number of pages she reads per hour is 19 pages per hours

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Answer:

350

Step-by-step explanation:

Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).

We now have

x+(x–54)=646

2x=700

x=350

Therefore, 350 adult tickets were sold.

Answer:

2 dogs

Step-by-step explanation:

Answer:

8 ^-11

Step-by-step explanation:

It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:

8^-2 × 8^-9

= 8^(-2 + -9)

= 8^-11

1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.

Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.

If in a triangle ΔABC,

Here it is given that,

67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.

By using the formula of Area of a Triangle with 2 Sides and Included Angle,

Area of the cheetah area = 1/2 × bc × sin(A)

Area of the cheetah area = 1/2 × (67)(48) × sin(72°)

sin(72°) = 0.951056516

Area of the cheetah area = 1608 × 0.951056516

Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit

Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.

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Answer:

h = -14

Step-by-step explanation:

-7πh = 98π

⇔ -7h = 98   (Just Divide both sides by π)

⇔ h = 98 ÷ (-7) = -14

Hi :)

We should find h. All it takes is some algebra skills ^•^

First off, you can see than we have π on both sides. So, why not divide both sides by π and get it out of the way?

We end up with

[tex]\boldsymbol{-7h=98}[/tex]

Super! Now all we have to do is divide both sides by -7

We end up with

[tex]\boldsymbol{h=-14}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

The attached figure represents the array for 237 x 43

The array is given as:

237 x 43

An array is represented as:

Row x Column

This means that:

Row = 237

Column = 43

i.e. the array has 237 rows and 43 columns

The numbers are large, so the cells would be small when the arrays are drawn

See attachment for the array

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The three dimensional shape formed by the net shown below is a cube.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

The cube is a a three-dimensional solid object bounded by six square faces.

The three dimensional shape formed by the net shown below is a cube.

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Answer:

6

Step-by-step explanation:

Solve for y:

[tex]y/8=9/12[/tex]

Multiply both sides by 8:

[tex]y=72/12[/tex]

Solve fraction

[tex]y=6[/tex]

The probability that a randomly selected member did not volunteer for the recent activity is 19/43.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered

1 - 24/43

(43/43) - (24/43) = 19/43

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.

By using similarity, ratio of their corresponding sides must be equal as well~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 3 \times 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 9 \: \: units[/tex]

Answer:

x = 1.086

Step-by-step explanation:

Formula

6^x = 7                     Take the log of both sides.

Solution

log 6^x = log 7         Bring the power down You are now dealing with log 6

x * log 6 = log 7        Divide by log 6

x = log 7/log 6

x = .8451 / .7782       Divide

Answer

x = 1.086

Answer:

13

Step-by-step explanation:

The range of the data set can be defined as: max-min, and in a sorted data  set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.

With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.

This means the range is defined as: 30 - 17 = 13

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]

[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]

[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]

[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\text{24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{30}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{17}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\rm{30 - 17}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

43 degrees

Step-by-step explanation:

First, notice that we can draw a right triangle to represent this situation. The vertical leg of the triangle corresponds to the tower, and the horizontal leg corresponds to the shadow. The height of the tower, 114, is OPPOSITE, and the length of the shadow, 121, is ADJACENT to the angle of elevation to the top of the tower. Remember SOH CAH TOA, we can use TAN to find the angle since we know the values of O and A.

TAN(x) = O/A

TAN(x) = 114/121

x = ARCTAN(114/121)

x = 43

Step-by-step explanation:

Here! ●□●□●□●□● THIS IS THE ANSWER BRO

The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

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If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]

Given an expression 8v(v+3)(v+3).

We are required to rewrite the given expression.

Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.

The expression is 8v(v+3)(v+3). There are three terms in which variable is v.

To rewrite the expression we have to multiply all the three terms with each other which can be done as under:

=8v(v+3)(v+3)

=[tex](8v^{2}+24v)(v+3)[/tex]

=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]

=[tex]8v^{3}+48v^{2} +72v[/tex]

Now divide it by 8.

=[tex]v^{3}+6v^{2} +9v[/tex]

Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .

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If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.

We are required to find the first term of the arithmetic sequence.

Arithmetic sequence is a series in which all the terms have equal difference.

Nth term of an AP=a+(n-1)d

[tex]A_{3}[/tex]=a+(3-1)d

126=a+2d--------1

[tex]A_{64}[/tex]=a+(64-1)d

3725=a+63d------2

Subtract second equation from first equation.

a+2d-a-63d=126-3725

-61d=-3599

d=59

Put the value of d in 1 to get the value of a.

a+2d=126

a+2*59=126

a+118=126

a=126-118

a=8

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

=8+0*59

=8

Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

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The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

In this problem we have a function in implicit form, that is, an expression of the form: f(x, y, c) = 0, where c is a constant. Then, we should apply implicit differentiation twice to determine the second derivative of the function:

Original expression

x · y - 1 = 2 · x + y²

First derivative

y + x · y' = 2 + 2 · y · y'

(x - 2 · y) · y' = 2 - y

y' = (2 - y) / (x - 2 · y)

Second derivative

y' + y' + x · y'' = 2 · (y')² + 2 · y · y''

2 · y' - 2 · (y')² = (2 · y - x) · y''

y'' = 2 · [y' - (y')²] / (2 · y - x)

y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]]

The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

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Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.3, n = 6.

The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595

0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

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Let the two exponential functions be

[tex]$f(x) = (4/5)^x[/tex] and

[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]

Both of these exist exponential functions with positive bases, we end that the range for both exists: {y| y > 0}.

Therefore, the ranges of the two functions exists {y| y > 0}.

Let the two exponential functions be

[tex]$f(x) = (4/5)^x[/tex] and

[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]

Both of these exist exponential functions with positive bases, then neither of these can contain negative outcomes, while, as x increases, the outcome will also increase.

Then both the functions exist exponential growths, so the range for both of these exists the set of all real positive values, written in both cases as: {y| y > 0}.

Therefore, the ranges of the two functions exists {y| y > 0}.

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Answer:

12. standard deviation =6.22972...

. variance = 38.80952...