A student is taking an exam with 40 questions on it.To pass the exam she needs to answer 70% of the questions correctly. Unfortunately she answered only 40% of the 15 questions correctly. What percent of the remaining 25 questions does she have to answer correctly to pass the exam?

The vertex form of the equation is y = 3(x + 2)^2 - 5

The equation is given as:

y = 3x^2 + 12x + 7

Set to 0

3x^2 + 12x + 7 = 0

Subtract 7 from both sides

3x^2 + 12x = -7

Divide through by 3

x^2 + 4x = -7/3

-------------------------------------------------------------------

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)^2 = 4

-------------------------------------------------------------------

So, we add 4 to both sides of x^2 + 4x = -7/3

x^2 + 4x + 4 = -7/3 + 4

Express as perfect square

(x + 2)^2 = -7/3 + 4

Multiply through by 3

3(x + 2)^2 = -7 + 12

Evaluate

3(x + 2)^2 = 5

Subtract 5 from both sides

3(x + 2)^2 - 5 = 0

Rewrite as

y = 3(x + 2)^2 - 5

Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5

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The point that the graphs of f and g have in common are (1,0)

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

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Answer:

Its (1,0)

and the second one is A. F

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 7, 8 ] , then

f(b) = f(8) = 20 ← point (8, 20 ) on graph

f(a) = f(7) = - 20 ← point (7, - 20 ) on graph

average rate of change = [tex]\frac{20-(-20)}{8-7}[/tex] = [tex]\frac{20+20}{1}[/tex] = 40

Answer:

t=20

Step-by-step explanation:

t-19=1

t-19(+19)=1+19

t=20

The value of x from the given diagram is 100 degrees

From the given diagram, we will use the theorem "angle at the vertex is half that at the centre.

<50 = 1/2 x

Cross multiply

50 * 2 = x

x = 50 * 2

x = 100 degrees

Hence the value of x from the given diagram is 100 degrees

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Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

Answer:

im not sure the answer tho- just trying

Answer:

[tex]tan(30) = \frac{5}{b} [/tex]

Step-by-step explanation:

Trigonometric Ratios.

To solve for b, we check the parameters that are given in the triangle.

If we're considering 30°, we can see that the opposite is given as 5cm and the adjacent is b.

Applying:

[tex]tan \alpha = \frac{oppsite}{adjacent} \\ \\ tan \: (30) = \frac{5}{b} [/tex]

Answer:

a

Step-by-step explanation:

just did the quiz!!!!

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

An equation is an expression that shows the relationship between two or more variables and numbers.

The greatest common factor is the highest number that all the numbers share.

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

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Using translation concepts, it is found that the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering the translations, the equivalent point is found as follows:

Hence the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

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Answer:

2x+9=1x-5

2x-1x=-5-9

x=-14

The fat percentage in the second type(40 liters) of milk is 1%

Fats in 40 liters of milk = Total fat - fats in 80 litrrs milk

= 3% - 2%

= 1%

Therefore, the fat percentage in the second type of milk is 1%

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The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

From the question, we are to determine the area of the shaded part

In the given diagram, the shaded part is a rectangle

Area of a rectangle = Length × Width

Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches

Width of the shaded part = 6 inches - 2inches = 4 inches

Then,

Area of the shaded part = 13 inches × 4 inches

Area of the shaded part = 52 sq. inches

Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

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[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{3}\\ r=3 \end{cases}\implies s=(3)(\frac{7\pi }{3})\implies s=7\pi \implies s\approx 21.99~in[/tex]

Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The measures are direct proportional, hence the rule of three is:

11 lb - 9 inches

22 lb - n inches

Applying cross multiplication:

11n = 9 x 22

n = 9 x 2

n = 18 inches.

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Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are:

P = 250000, r = 0.05, n = 12 x 30 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Then:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]

A = $1,342.12

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based on the given results, the coefficient of variation can be found to be 45.54.

first, find the mean:
= (30 + 60 + 90 + 45) / 4

= 56.25

find the standard deviation using a spreadsheet:

= 25.61737691

the coefficient of variation is therefore:

= standard deviation / mean x 100

= 25.61737691 / 56.25 x 100

= 45.54

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Answer:

c

Step-by-step explanation:

Aight, let's hop to it:

So we got

[tex] \frac{5x}{45} = \frac{20}{36} = = > \\ \frac{x}{9} = \frac{5}{9} = = > \\ x = 5[/tex]

and boom

The expression that we need to get is:

[tex]N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the correct option is the second one.

We know that 1 gallon is enough to cover 200 ft².

We have two rectangular areas, one of:

23 feet by 10.4 feet, and other of 10.5 feet by 7.2 feet.

Then the total area is:

A = (23 ft)*(10.4 ft) + (10.5ft)*(7.2 ft)

The number of gallons needed is given by the quotient between the area that we want to cover, and the area that covers one gallon, so the expression is:

[tex]N = \frac{(23ft)*(10.4ft) + (10.5ft)*(7.2ft)}{200ft^2} \\\\N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the corerect option is the second one.

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Put brackets equal 0

(2x + 1) (x - 1) = 0

(2x + 1) = 0

-1, then ÷2

x = - 1/2 or - 0.5

(x - 1) = 0

+1

x = 1

So, x = - 0.5 & x = 1

Hope this helps!

Answer:

x = -0.5

x = 1

Step-by-step explanation:

Hello!

We can set each factor to 0 and solve for x in both.

There are 2 solutions for x, -0.5 and 1.

The factored form of the related polynomial is (x - 1)(x - 9)

In this question, the given parameter is the attached graph

From the graph, we can see that the curve crosses the x-axis at two different points

These points are the zeros of the polynomial function.

From the graph, the points are

x = 1 and x = 9

Set these points to 0

x - 1 = 0 and x - 9 = 0

Multiply the above equations

(x - 1)(x - 9) = 0

Remove the equation

(x - 1)(x - 9)

Hence, the factored form of the related polynomial is (x - 1)(x - 9)

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Answer:

  x = 3

  y = 8

Step-by-step explanation:

A matrix product exists if and only if the number of columns in the left matrix is equal to the number of rows in the right matrix.

For AB to exist, we must have ...

  columns of A = rows of B

  x +5 = y

For BA to exist, we must have ...

  columns of B = rows of A

  11 -y = x

Using the second equation to substitute for x in the first equation, we have ...

  (11 -y) +5 = y

  16 = 2y

  8 = y

Then the value of x is ...

  11 -8 = x = 3

The values of x and y are ...

__

Additional comment

The dimensions are A = 3×8; B = 8×3.

The domain f the function is (-∞, 1/3) U (1/3, ∞)

The composite functions are also known as function of a function

Given the following functions

f(x) = √2-6x

g(x) = -1/x

In order to determine the composite function g(f(x))

g(f(x)) = g(√2-6x)

Replace x with √2-6x in g(x)

g(f(x))  = -1/√2-6x

The expression does not exist when √2-6x = 0

2-6x = 0

x = 1/3

The values shows that the domain of the function exists on all real numbers except 1/3.

Hence the domain f the function is (-∞, 1/3) U (1/3, ∞)

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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There are 238 passengers in the plane in 2010

The given parameters are:

Weight = 150 pounds and Passenger = 270 --- Year 2000

Weight = 170 pounds --- Year 2010

Represent the parameters using the following inverse proportion

Weight * Passenger= Fixed

So, we have:

150 * 270 = 170 * Passenger

Divide both sides by 170

150 * 270/170 = Passenger

Evaluate

238 = Passenger

Rewrite as

Passenger = 238

Hence, there are 238 passengers in the plane in 2010

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From the calculation, the growth rate is 0.88.

To find the relative growth rate

P1 = Poe^rt

P2 = Poe^rt

Thus;

1920 = Poe^4r ------ (1)

1966080 =Poe^12r -------(2)

P2/P1 gives;

1966080/1920 = Poe^12r/Poe^4r

1024 = e^12r/e^4r

1024 =e^8r

1024 = (e^r)^8

2^10 = (e^r)^8

e^r = 2^1.25

e^r = 2.38

r = ln(2.38)

r = 0.88

The initial size of the culture is;

1920 = Poe^(0.88 * 4)

Po = 1920/e^(0.88 * 4)

Po = 57

The  expression for the exact number of bacteria after t hours is

P(t) = 57e^0.08t

The growth (in bacteria per hour) after 9.5 hours is

P(t) = 57e^(0.88 * 9.5)

P(t) = 243544

For the number to reach 72,000;

72,000 =  57e^0.88t

72,000/57 = e^0.88t

ln 126 = ln[e^0.88t]

4.8 = 0.88t

t = 4.8/0.88

t = 5.5 hours

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The temperature does not change after the percentage increase and decrease.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Assume the initial temperature is 10.

Temperature after the 50% increase : (1 + 0.5) x 10 = 15

Temperature after the 33 1/3% decrease : (1 - 0.333) x 15 = 10.00

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The annual breakeven point is $550157

Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.

The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.

The sales price is $31 and the total variable cost is $21.10.

Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get

Contribution margin= Sales price-Total sales price

Contribution margin=31-21.10

Contribution margin=9.9

Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get

contribution margin ratio=contribution margin/Sales price

contribution margin ratio=9.9/31

contribution margin ratio=0.319

contribution margin ratio=31.9%

Furthermore, we will find the break-even point, we get

Break-even point=Fixed cost/contribution margin

Break-even point=175500/9.9

Break-even point=17727.27

Now, we will find the break-even sales in dollars, we get

Break-even sales=Fixed cost/contribution margin ratio

Break-even sales=(175500/31.9)×100

Break-even sales=550157

Hence, the annual breakeven point in unit sales is calculated to be $550157.

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The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

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Answer: Option 2 or B.  AC + CB < AB

Step-by-step explanation: Trust Me!  It is correct on Edge!

Q: Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

A: AC + CB < AB