Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
O A. y = 3x + 4
OB. y= 3x - 14
O C. y= 3x - 4
OD. y = 3x + 12

Answer:

[tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

The quickest way to solve this is to recognize this as a 30-60-90 triangle. The smallest angle is 30 degrees, and the answer is simply cos 30º.

You can also use the pythagorean theorem to find the length of the hypotenuse, then use SOH-CAH-TOA to get the answer.

Answer:

Volume of a pyramid is

[tex] \frac{1}{3 } \times (area \: \: of \: base) \times height[/tex]

Since it's a square pyramid the base is a square

So we have

Area of a square = l²

where l is the length of one side

Area of square = 22²

= 484 cm²

So volume of the pyramid is

[tex] = \frac{1}{3} \times 484 \times 8 = 1290.7 {cm}^{3} [/tex]

Hope this helps you

Answer:

The rise is -6.

Step-by-step explanation:

For this problem, the direction of the vector gives the indication of a negative slope.  We know that the equation to find slope = rise/run meaning y/x values.  So for this, we can see the y-value of the blue triangle (the rise) to be 6, and the x-value of the blue triangle (the run) to be 3.  And as stated before, this is a negative slope, in the y-direction.  Hence, the rise is -6 for the blue triangle.

Answer:

1/5

Step-by-step explanation:

The stick has a length of 5 units

The stick is broken at two points chosen at random

First break: the probability that you get a piece that is 1 unit or longer than 1 units= 1/5.

Second break, the probability that you get a piece that is 1 unit or longer than 1 units is 1/5.

Therefore,

The total probability =probability of first break * probability of second break * original stick unit

=1/5 * 1/5 * 5

= 1/25 *5

=5/25

=1/5

Answer:

[tex]\large \boxed{\sf \ \ x^2 + 7x + 5 \ \ }[/tex]

Step-by-step explanation:

[tex]\mathrm{\sf (-3x^2 + 2x -4) + (4x^2 + 5x + 9)}[/tex]

Remove brackets.

[tex]\large{\sf -3x^2 + 2x -4 + 4x^2 + 5x + 9}[/tex]

Group like terms.

[tex]\large{\sf -3x^2 + 4x^2 + 2x + 5x + 9 -4}[/tex]

Combine like terms.

[tex]\large{\sf x^2 + 7x + 5}[/tex]

The simplified form of this expression (-3x² + 2x − 4) + (4x² + 5x + 9) is determined as x² + 7x + 5.

To simplify the given expression, we need to combine like terms.

The given expression;

(-3x² + 2x − 4) + (4x² + 5x + 9)

Let's start by combining the terms with the same degree of x:

Combine the x² terms:

(-3x² + 4x²) + 2x - 4 + 5x + 9

Simplify further;

x² + 7x + 5

Thus, the simplified form of this expression (-3x² + 2x − 4) + (4x² + 5x + 9) is determined as x² + 7x + 5.

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Let d equal the final amount it depreciates.

Let m equal the number of months.

Since d is the final amount, we put this at the very end of the equation.

Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).

The final equation comes out too: d = 650 - 25m

Best of Luck!

Answer:

a. TRUE.

Step-by-step explanation:

If the pair of opposite sides are both parallel and congruent, the other two sides will have to fit in between the two lines. That will make the other two sides both parallel and congruent, so the quadrilateral is a parallelogram.

Answer:

a. True

Step-by-step explanation:

A parallelogram is a quadrilateral. A parallelogram has two pairs of opposite parallel sides. The opposite parallel sides are equal in length and are congruent.

Answer: D

Step-by-step explanation:

If we substitute -12 into this equation we get:

[tex]-3[-12-8]+1.5[/tex]

[tex]-3[-20]+1.5[/tex]

Because -20 is in absolute value, we simply just use 20.

Thus,

[tex]-3(20)+1.5\\= -60+1.5\\= -58.5[/tex]

Answer:

D

Step-by-step explanation:

Answer:

Sample Answer: First determine the integers the x-coordinate and the y-coordinate are between. Then look at each to decide which integer the x- or y-value is closer to, and approximate the coordinate value to the tenths place.

Step-by-step explanation:

To estimate to the tenths place, you have to determine the actual solution and the approximate.

Assume the solution to the system of equation is:

[tex]\mathbf{(x,y) = (1.25, 1)}[/tex]

1.25 is to the hundredth place.

So, the next thing is to approximate 1.25 to 1.3 (the tenth place).

So, we have:

[tex]\mathbf{(x,y) = (1.3, 1)}[/tex]

Hence, the actual solution must be approximated to the tenths place.

Read more about system of equations at:

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Answer:

I'd cross multiply to solve this equation.

Step-by-step explanation:

Since we have a fraction where we're finding a ratio:

[tex]\frac{3}{x} = \frac{6}{14}[/tex],

I'd find it easiest to cross multiply. This is because we are finding an equivalent to a ratio, so cross multiplication works best here.

Let's solve it.

[tex]14\cdot 3 = 42\\42\div6=7[/tex]

x = 7

Hope this helped!

Answer:

Its the last option. On the bottom.

Step-by-step explanation:

You need to Solve for x to find the zeroes of the equation.

x-1=0 So one x is at 1.

x+4=0 So the other x is at -4.

This graph is also not negative so it does not get flipped across the x-axis

The graph of the function [tex]f(x) = (x - 1)(x + 4)[/tex] is graph (d)

The equation of the function is given as:

[tex]f(x) = (x - 1)(x + 4)[/tex]

From the above function, we have the zeros of the function to be:

1 and -4

This means that:

Hence, the graph is graph (d)

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Answer:

I think it's x-axis.

Step-by-step explanation:

but me could me wrong

Answer:

The correct answer to this question would be C.

Step-by-step explanation:

took the test. Hope this helps!

Step-by-step explanation:

At t = 20 min, V = 45,000 L.

At t = 70 min, V = 0 L.

a) The rate is the slope:

m = ΔV/Δt

m = (0 L − 45,000 L) / (70 min − 20 min)

m = -900 L/min

b) Using the slope to find V when t = 0 min:

m = ΔV/Δt

-900 L/min = (V − 0 L) / (0 min − 70 min)

V = 63,000 L

c) Use slope-intercept form to find the equation.

V = -900t + 63,000

d) At t = 62 min:

V = -900(62) + 63,000

V = 7200

Answer:

a. -900 L/min

b. Vo = 63,000 Liters

c. V ( t ) = 63,000 - 900*t

d. 7,200 Liters

Step-by-step explanation:

Solution:-

We have a swimming pool which is drained at a constant linear rate. Certain readings were taken for the volume of water remaining in the pool ( V ) at different instances time ( t ) as follows.

                t = 20 mins ,   V = 45,000 Liters

                t = 70 mins , V = 0 Liters

To determine the rate ( m ) at which water drains from the pool. We can use the linear rate formulation as follows:

                             [tex]m = \frac{V_2 - V_1}{t_2 - t_1} \\\\m = \frac{0 - 45000}{70 - 20} \\\\m = \frac{-45,000}{50} = - 900 \frac{L}{min}[/tex]

We can form a linear relationship between the volume ( V ) remaining in the swimming pool at time ( t ), using slope-intercept form of linear equation as follows:

                              [tex]V = m*t + V_o[/tex]

Where,

                  m: the rate at which water drains

                  Vo: the initial volume in the pool at time t = 0.

We can use either of the data point given to determine the initial amount of volume ( Vo ) in the pool.

                           [tex]0 = -900*( 70 ) + V_o\\\\V_o = 63,000 L[/tex]

We can now completely express the relationship between the amount of volume ( V ) remaining in the pool at time ( t ) as follows:

                             [tex]V ( t ) = 63,000 - 900*t[/tex]

We can use the above relation to determine the amount of volume left after t = 62 minutes as follows:

                           [tex]V ( 62 ) = 63,000 - 900*(62 )\\\\V ( 62 ) = 63,000 - 55,800\\\\V ( 62 ) = 7,200 L[/tex]

Answer:

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Step-by-step explanation:

x ^ 1.4

Rewriting the decimal as an improper fraction

x ^ 14/10

x ^ 7/5

The top is the power and the bottom is the root

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

S - a randomly chosen pregnancy result in a successful delivery

C - a randomly chosen pregnancy ending in a C section

Answer:

Jesse

Step-by-step explanation:

Everyone except for Jesse and Trey asked other grades but Jesse and Trey was the only one that asked 6th graders. The reason why I thought Trey might be biased is he asked HIS class while Jesse asked random people.

Hope this helped! :)

Answer:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]

Step-by-step explanation:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.

Then do 16*13=208.

Simplify by dividing both by 2.

You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].

Your final simplified answer is [tex]\frac{-21}{104}[/tex]

I hope this helps!

triangle is the best answer

Answer:

Step-by-step explanation:

Answer:

<B = 32°

c = 9.43

Step-by-step explanation:

To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.

58° + 90° = 148°

180° - 148° = 32°

The measure of <B is 32°.

To find the length of side c, use the Pythagorean Theorem.

a² + b² = c²

5² + 8² = c²

25 + 64 = c²

89 = c²

c = √89

c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)

The length of side c = 9.43.

Hope that helps.

Answer: negative 2 minus radical 3

Step-by-step explanation:

We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:

tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]

Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.

Substituting these values, we get:

tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]

= ±√[(2+sqrt(3))/(2-sqrt(3))]

Multiplying the numerator and denominator by (2+sqrt(3)), we get:

= ±√[(2+sqrt(3))^2/(4-3)]

= ±√[(2+sqrt(3))^2]

= ±(2+sqrt(3))

Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)

Step-by-step explanation:

I would suggest that she studies or do a cost analysis of what it will cost her to transport to the library to request for the book and return it, if it is not expensive as compared to the cost of the book she should travel down to request for it. else she should purchase the book

Or

Fareeda can simply check if the second library has a distant library services so that the book can be either

1. Sent to her home or placement address, or

2.Scans of book chapters and articles be emailed to her.

Step-by-step explanation:

The 20° angle is equal to the angle next you friend.

since they are interior alternate angles

The height of the ballon is 600 feet

Let x be the missing distance we are looking for

so the missing distance is 1754 feet

Here I represented the situation to visualize the problem

Let h be L be the length of the ladder

so the ladder is 14 ft

Answer:

0.897

Step-by-step explanation:

Brahmagupta formula for quadratic equation [tex]ax^2+bx=c[/tex] is

[tex]x=\dfrac{\sqrt{4ac+b^2}-b}{2a}[/tex]

It involved only one solution.

The given equation is

[tex]3x^2+4x=6[/tex]

Here, a=3, b=4 and c=6. Put these values in the above formula.

[tex]x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}[/tex]

[tex]x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}[/tex]

[tex]x=\dfrac{\sqrt{72+16}-4}{6}[/tex]

[tex]x=\dfrac{\sqrt{88}-4}{6}[/tex]

[tex]x\approx \dfrac{5.38}{6}[/tex]

[tex]x\approx 0.897[/tex]

Therefore, the required solution is 0.897.

Answer:

paid vacation

paid medical

401k

Answer:

0.007349 to 3 significant figure=0.00735

Step-by-step explanation:

Approximate 0.007349 to 3 significant figure

Significant figure start from 1 to 9 with the exclusion of 0

From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.

0.007349

The first significant number is 7 after 0

The second significant number is 3

The next

The third significant number is 4

The fourth significant number is 9

We want to approximate to three significant figure, so, all figure after 4(third significant figure) will be rounded up or down.

If the numbers are below 5(0, 1,2,3,4) they will be rounded down to 0

If the numbers are above 4(5,6,7,8,9), they will be rounded up to 1

So the number after 4 is 9, therefore it will be rounded up to make 4=5

0.007349 to 3 significant figure=0.00735

Answer:

-11

Step-by-step explanation:

f(x)=-2x-5

Let x = 3

f(3) = -2 *3 -5

     = -6 -5

     = -11

Answer:

the inverse of the function f^-1(x)=(x-3)/(4+5x)

Step-by-step explanation:

( 3+4x)/(1-5x)

y=4x+3/1-5x swap the variables

x=4y+3/1-5y solve for y

y=x-3/4+5x

The inverse of a function is :y=x-3/4+5x

What is inverse of a function?

The inverse function returns the original value for which a function gave the output.

If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.

Steps are:

for example:

Suppose, f(x) = 2x + 3 is a function.

Let f(x) = 2x+3 = y

y = 2x+3

x = (y-3)/2 = f-1(y)

This is the inverse of f(x).

Given function:

f(x)= ( 3+4x)/(1-5x)

now, swap the variables x and y.

y=4x+3/1-5x

Now solving for y

x=4y+3/1-5y

y=x-3/4+5x

Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).

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Answer: y = 3(x - 5)² + 4

Step-by-step explanation:

Use the Vertex form:  y = a(x - h)² + k to find the a-value

Given: (x, y) =(0, 79) and (h, k) = (5, 4)

79 = a(0 - 5)² + 4

79 = 25a + 4

75 = 25a

3 = a

Input a = 3 and (h, k) = (5, 4) into the Vertex form:

y = 3(x - 5)² + 4

Answer:  [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.

Step-by-step explanation:

A series can be represented in a summation or sigma notation.

Greek capital letter, ∑ (sigma), is used to represent the sum.

For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.

The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .

So , we can write it as

[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.

Answer:

B=6

C=n^2

Just did the test

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

Inversely proportional means that the two variables (price and weight in this case) will always have the same product. Therefore, we can write the following equation:

25 * x = 20 * 30 (where x is the price of a 25 oz. racquet)

25x = 600

x = $24