Determine the x- and y- intercepts for the graph defined by the given equation.
y = 7x + 3

Answer:

c for the question that says what point is on [tex]y=\log_a(x)[/tex] given the options.

9  for the question that reads: "If [tex]\log_a(9)=4[/tex], what is the value of [tex]a^4[/tex].

Step-by-step explanation:

We are given [tex]y=\log_a(x)[/tex].

There are some domain restrictions:

[tex]a \text {is number between } 0 \text{ and } 1 \text{ or greater than } 1[/tex]

[tex]x \ge 0[/tex]

a) couldn't be it because x=0 in the ordered pair.

b) isn't is either for the same reason.

c) \log_a(1)=0 \text{ because } a^0=1[/tex]

So c is so far it! Since (x,y)=(1,0) gives us [tex]0=\log_a(1)[/tex] where the equivalent exponential form is as I mentioned it two lines ago.

d) Let's plug in the point and see: (x,y)=(a,0) implies [tex]0=\log_a(a)[/tex].

The equivalent exponetial form is [tex]a^0=a[/tex] which is not true because [tex]a^0=1 (\neq a)[/tex].

If [tex]\log_a(9)=4[/tex]. then it's equivalent exponential form is: [tex]a^4=9[/tex].

Guess what it asked for the value of [tex]a^4[/tex] and we already found that by writing your equation [tex]\log_a(9)=4[/tex] in exponential form.

Note:

The equivalent exponential form of [tex]\log_a(x)=y[/tex] implies [tex]a^y=x[/tex].

Answer:

126 trees should she plant per acre to maximize her harvest.

Step-by-step explanation:

Let x be the additional tress that must be plant after planting 100 tress.

So, total number of trees = 100 + x trees

Also, Each additional tree planted decreases the yield of each tree by 3 bushels.

So , net bushels by each tree = 35 - 3x

The revenue function becomes

f(x) = (100 + x)(35 - 3x)

Thus,

Differentiating it by using chain rule as:

f'(x) = (100 + x)35 + 100(35 - 3x)

f'(x) = 3500 + 35x + 3500 - 300x

f'(x) = 7000  - 265x

For maxima of f(x), f'(x) = 0

7000  - 265x = 0

Thus,

x = 26.4151

Since, x represents tress, so, x is 26.

So, total tress she would plant to earn maximum revenue = 100 + 26 = 126 trees

Check the picture below.

Answer:

I don't know if you want to find this answer using the quadratic formula or not, the question is no the greatest but i will solve it the best that i can. Or

Step-by-step explanation:

I used the discriminant which is √[tex]b^{2}[/tex]-4ac

Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.

Hoped this helped thanks, if you need more help let me know.

The required value of the given expression is (-9). which is the correct answer would be an option (B).

A quotient is defined as when dividing one number by another, the result is called the quotient.

To determine the value of the expression.

The given expression is given in the question.

⇒ 3b ÷ c⁽¹⁻ᵃ⁾

Here a = 4, b = 9, and c = 1

Substitute the value of a,b, and c in the expression

⇒ 3(9) ÷ (1)⁽¹⁻⁴⁾

⇒ 27 ÷ (1)⁽¹⁻⁴⁾

⇒ 27 ÷(1)⁽⁻³⁾

Reciprocal the term in the denominator,

⇒ 27 × (1 /(-3)

⇒ 27/(-3)

Apply the division operation,

⇒ (-9)

Therefore, the required value of the given expression is (-9).

Hence, the correct answer would be an option (B).

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The question seems to be incomplete the correct question would be

Evaluate the expression if a = 4, b = 9, and c = 1.

3b ÷ c⁽¹⁻ᵃ⁾

A. –27 B. –9 C. 9 D. 27

Answer:

The center of the hyperbola is (-5 , 7)

The left vertex is (-5 , -6)

The other vertex is (-5 , 20)

Step-by-step explanation:

* Lets explain the equations of the hyperbola

- The standard form of the equation of a hyperbola with  center (h , k)

  and transverse axis parallel to the x-axis is (x - h)²/a² - (y - k)²/b² = 1

- The hyperbola is open horizontally

- The coordinates of the vertices are (h ± a , k)

- The standard form of the equation of a hyperbola with center (h , k)

  and transverse axis parallel to the y-axis is  (y - k)²/a² - (x - h)²/b² = 1

- The hyperbola is open vertically

- The coordinates of the vertices are (h , k ± a)

* Lets solve the problem

∵ The equation of the hyperbola is - (x + 5)²/9² + (y - 7)²/13² = 1

- Lets rearrange the terms of the equation

∴ The equation is (y - 7)²/13² - (x + 5)²/9² = 1

∴ The hyperbola opens vertically

∵ (y - k)²/a² - (x - h)²/b² = 1

∴ a = 13 , b = 9 , h = -5 , k = 7

∵ The coordinates of its center are (h , k)

∴ The center of the hyperbola is (-5 , 7)

∵ The hyperbola opens vertically

∴ Its vertices are (h , k - a) the bottom one and (h , k + a) the up one

∴ The bottom vertex is (-5 , 7 - 13) = (-5 , -6)

∴ The bottom vertex is (-5 , -6)

∴ The other vertex is (-5 , 7 + 13) = (-5 , 20)

∴ The other vertex is (-5 , 20)

Answer:

Center: (-5,7)

Opens Vertically: (-5,-6)

The other vertext : (-5, 20)

Step-by-step explanation:

Answer:

  a) 15

  b) 2

Step-by-step explanation:

a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.

We know that there are 10 students triply-enrolled, so the difference ...

  (60 +45 +30) -2(10) = 15

is the number of doubly-enrolled students.

There are 15 students enrolled in exactly 2 science classes.

__

b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.

Answer:

a) 15

b) 2

Step-by-step explanation:

There are 15 students in 2 science classes.

2 students enrolled in both chemistry and biology, but not physics.

15 -13 = 2

C.) Are the same length

How you know-

No matter how long the rectangle is the diagonals always will measure the same length. Think about two sides of a square, they have to equal the same length because if they were not the same then the shape wouldn't be a square.

The best answer is the diagonals of the rectangle are the same length.

The diagonal of rectangle is a line segment drawn between the opposite vertices of the rectangle. The properties of diagonals of a rectangle are as follows:

1. The two diagonals of a rectangle are congruent. In other words, the length of the diagonals is equal.

2. The two diagonals bisect each other and divide the rectangle into two equal parts.

3. The length of the diagonal of rectangle can be obtained using the Pythagoras theorem.

4. When the diagonals bisect each other, the angles of a rectangle at the center become one obtuse angle and the other an acute angle.

5. When two diagonals bisect each other at 90° it is called a square.

6. Since the diagonal of rectangle divide the rectangle into two right-angled triangles, it is considered the hypotenuse of these triangles.

We know the diagonal property of rectangle that

1. The diagonals of the rectangle bisect each other.

2. The diagonals of the rectangle are equal.

The best answer is the diagonals of the rectangle are the same length.

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Answer:

  a.  0.6975

  b.  0.833625

Step-by-step explanation:

a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.

__

b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.

Answer:

B. Discontinuity at (−2, 1), zero at (−3, 0)

Step-by-step explanation:

The given function is:

[tex]\frac{x^{2}+5x+6}{x+2}[/tex]

The expression in numerator can be expressed as factors as shown below:

[tex]\frac{x^{2}+5x+6}{x+2}\\\\ =\frac{x^{2}+2x+3x+6}{x+2}\\\\ =\frac{x(x+2)+3(x+2)}{x+2}\\\\ =\frac{(x+2)(x+3)}{x+2}[/tex]

Note that for x = -2, both numerator and denominator will be zero. When both the numerator and denominator of a rational function are zero for a given value of x we get a discontinuity at that point. This discontinuity is known as a hole. This means there is a hole at x = -2

Cancelling the common factor from numerator and denominator we get the expression f(x) = x + 3

Using the value of x = -2 in previous expression we get:

f(x) = -2 + 3 = 1

Thus, there is a discontinuity(hole) at (-2, 1)

For x = -3, the value of the expression is equal to zero. This means x = -3 is a zero or root of the function.

Thus, (-3, 0) is a zero of the function.

Therefore, option B would be the correct answer.

Answer:

Part 1) The function of the First graph is [tex]f(x)=(x-3)(x+1)[/tex]

Part 2) The function of the Second graph is [tex]f(x)=-2(x-1)(x+3)[/tex]

Part 3) The function of the Third graph is [tex]f(x)=0.5(x-6)(x+2)[/tex]

See the attached figure

Step-by-step explanation:

we know that

The quadratic equation in factored form is equal to

[tex]f(x)=a(x-c)(x-d)[/tex]

where

a is the leading coefficient

c and d are the roots or zeros of the function

Part 1) First graph

we know that

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive

The function is equal to

[tex]f(x)=a(x-3)(x+1)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (1,-4)

substitute and solve for a

[tex]-4=a(1-3)(1+1)[/tex]

[tex]-4=a(-2)(2)[/tex]

[tex]a=1[/tex]

therefore

The function is equal to

[tex]f(x)=(x-3)(x+1)[/tex]

Part 2) Second graph

we know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to

[tex]f(x)=a(x-1)(x+3)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

substitute and solve for a

[tex]8=a(-1-1)(-1+3)[/tex]

[tex]8=a(-2)(2)[/tex]

[tex]a=-2[/tex]

therefore

The function is equal to

[tex]f(x)=-2(x-1)(x+3)[/tex]

Part 3) Third graph

we know that

The solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to

[tex]f(x)=a(x-6)(x+2)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

substitute and solve for a

[tex]-8=a(2-6)(2+2)[/tex]

[tex]-8=a(-4)(4)[/tex]

[tex]a=0.5[/tex]

therefore

The function is equal to

[tex]f(x)=0.5(x-6)(x+2)[/tex]

For the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the first graph, the x-intercepts are x = -1 and x = 3, and it is opening up-side, so the function:

f(x) = (x - 3)(x + 1)

Second graph: x-intercepts are x = -3 and x = 1 and opening down-side.

Also, the vertex is at (-1, 8) so the function:

f(x) = -2(x - 1)(x + 3)

Third graph: x-intercepts are x = -2 and x = 6, and it is opening up-side, Also the vertex is at (2, -8) so the function:

f(x) = 0.5(x-6)(x+2)

Thus, for the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).

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Answer:

B, the x coordinate is zero

Step-by-step explanation:

The y axis is the line where the x coordinate is zero

The x axis is the line where the y coordinate is zero

We are looking for the y axis, so x=o

Answer:

For me the answer was B (the x-coordinate is 0)

Step-by-step explanation:

Answer:

(0, -3)

Step-by-step explanation:

The vertex is halfway between the directrix and the focus.  The vertex is at (0, 0) and the directrix is a (0, 3).  There are 3 units between them, so that means that the focus is 3 units the other way at (0, -3).

Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).

A parabola is known to be a kind of plane curve that is said to be often mirror-symmetrical  and it is one that can be called closed to U-shaped.

Note that the vertex is said to be in the middle between the directrix and the focus.  So the vertex is at (0, 0) and also the directrix is a (0, 3).  

Since there are found to be 3 units between them, we can say that  the focus is 3 units the other part at (0, -3).

Therefore, Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).

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Answer:

Earnings per share is $2.93

Step-by-step explanation:

Given data

shares = 450

assets =  $28,900

net income = $1,320

to find out

earnings per share

solution

Earnings per share is directly calculate by net income / total share

here we know net income and that share i.e.450

so

Earnings per share = net income / total share

Earnings per share = 1,320 / 450

Earnings per share = $2.93

so option C is right i.e. $2.93

Answer:

A.

Step-by-step explanation:

(x − 7)^2=

=x^2 − 14x + 49

Answer:

x^2 -14x+49

Step-by-step explanation:

(x − 7)^2

(x-7) (x-7)

FOIL

first x*x = x^2

outer -7*x = -7x

inner -7*x = -7x

Last = -7*-7 = 49

Add them together

x^2 -7x-7x +49

x^2 -14x+49

D) 13.5 cm squared (13.5 cm²)

In this question, it's asking you to find the area of the rectangle.

In order to solve this question, we need to use the helpful information that the question gives us.

Important Information:

With the information above, we can solve the problem.

To find the area of the rectangle, we would need to multiply the length times the width.

length × width (or l × w)

We know that the length is 3 and the width is 4.5, so we would multiply 3 and 4.5 in order to get the area of the rectangle.

[tex]3 * 4.5=13.5[/tex]

When you're done multiplying, you should get 13.5. With the unit, it would be 13.5 cm² (area of a rectangle is always squared).

This means that the area of the rectangle is 13.5 cm²

Answer:

Either:  1 neg, 3 pos, 0 imaginary; 1 neg, 1 pos, 2 imaginary

Step-by-step explanation:

Look for the positive possibilities first.  Count the numbe of sign changes then subtract 2, if possible, as many times as you can.

There are 3 sign changes.  So the possible positive roots are either 3 or 1.

Now look for the negative possibilities.  Replace each x with a -x and then count the sign changes.  Replacing with -x's gives you this polynomial:

[tex]f(-x)=-3x^4-5x^3-x^2-8x+4[/tex]

There is only one sign change here, so the possible negative roots is 1.  Start with the negative roots to find the possible combinations of positive, negative, and imaginary, since there is only 1.

-     1       1

+    3       1

i     0       2

Since this is a 4th degree, the number of roots we have has to add up to equal 4.

I assume the question is to find [tex](g\circ f)(-4)[/tex]

[tex](g\circ f)(x)=(-2x-5)^4\\\\(g\circ f)(-4)=(-2\cdot(-4)-5)^4=3^4=81[/tex]

Answer:

1 in 18

Step-by-step explanation:

The highest possible number Hillary can get is 12, meaning that the only odd number above 10 which she can get is 11.

There are two possible ways in which Hillary can get 11:

(a) Hillary rolls a 5 on her first cube and a 6 on her second cube

(b) Hillary rolls a 6 on her first cube and a 5 on her second cube

There are 34 other possible outcomes which Hillary can have when rolling her number cubes, for a total of 36 possible outcomes.

Since 2 of these outcomes result in a roll of 11, Hillary has a 2 in 36 chance of rolling an 11, which can be simplified as 1 in 18.

Answer:

1/18

Step-by-step explanation:

Answer:

The average price of a gallon of orange increased by $0.03 each month.

Step-by-step explanation:

It is 11 months between October 2013 and September 2014 so the price after 11 months =

f(11) = 6.12 + 0.03(11)

= 6.12 + 0.33

= $6.45.

This is an increase of 0.33 / 11 = 0.03 / month.

Answer:

38.7°

Step-by-step explanation:

Use the Law of Cosines:

[tex]7^2=11^2+10^2-2(11)(10)cosT[/tex] and

49 = 121 + 100 - 220cosT so

-172 = -220cosT and

.781818181 = cosT

Using the inverse cosine function on your calculator, you find that angle T = 38.7 degrees

Answer:

Explanation:

You can convert the percent markup into a multiplicative factor in this way:

Base price:                     15,800 . . . (cost to the seller)

Percent mark up:           115% . . .  (based on the cost to the seller)

Sale price:                      15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =

                                        = 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970

The markup is:

And the percent markup based on the sale price is:

            = 53.49 %

Rounding to the nearest tenth percent that is 53.5 %.

Answer:

Option B

Step-by-step explanation:

The two acute angles of a right triangle are equal.

[tex] \angle \: A + 18 = 180[/tex]

[tex]\angle \: A= 90 - 18 = 72 \degree[/tex]

Recall the mnemonics SOH-CAH-TOA

The tangent ratio is opposite over adjacent.

[tex] \tan(18) = \frac{AC}{21} [/tex]

[tex]AC = 21 \tan(18) [/tex]

[tex]AC = 6.8[/tex]

The sine ratio is opposite over hypotenuse

Using the sine ratio,

[tex] \sin(72) = \frac{21}{AB} [/tex]

[tex]AB = \frac{21}{ \sin(72) } = 22.1[/tex]

Answer:

it 55

Step-by-step explanation:

Answer:

  29°, 58°, and 93°

Step-by-step explanation:

If the angles opposite are equal, the sides are equal. In order to have three different side lengths, you must have three different angles.

Answer:

  Both A and B . . . . . and 2 more answers

Step-by-step explanation:

Completing the square, you get

  tan²(x) -tan(x) +0.25 = 2.25 . . . . . add 0.25

  (tan(x) -0.5)² = 1.5²

  tan(x) = 0.5 ± 1.5 = {-1, 2}

For tan(x) = -1, the solutions are ...

  x = arctan(-1) = 135°, 315°

For x = 2, the solutions are ...

  x = arctan(2) ≈ 63.435°, 243.435°

Answer:

C

Step-by-step explanation:

Answer: OPTION C

Step-by-step explanation:

You need to follow these steps:

- Carry the number 1 down and multiply it by the number 2.

- Place the product obtained above the horizontal line, below the number 5 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number 2.

- Place the product obtained above the horizontal line, below the number -14 and add them.

Then:

[tex]2\ |\ 1\ \ 5\ -14\\\\.\ \ |\ \ \ \ 2\ \ \ 14\\------\\.\ \ \ 1\ \ \ 7\ \ 0[/tex]

Therefore, the quotient in polynomial form is:

[tex]x+7[/tex]

Answer:

  x° = 109°

Step-by-step explanation:

x° is a "corresponding angle" to either of the upper left or lower right interior angles of the parallelogram. (The lines marked with a single arrow are parallel, as are the lines marked with a double arrow.)

Either of those angles is supplementary to the one marked 71°, so x° and all corresponding angles are 180° -71° = 109°.

Answer:

  x = 8.75

Step-by-step explanation:

The measure of angle C is half the measure of arc RS, so ...

  6x = (1/2)(105)

  x = 105/12 = 8.75 . . . . divide by 6

Answer:

[tex]x=8.75[/tex]

Step-by-step explanation:

We have been given a circle. We are asked to find the value of x for our given circle.

Upon looking at our given circle, we can see that angle RCS is an inscribed angle of arc RS.

We know that measure of an inscribed angle is half the measure of its intercepted arc, so we can set an equation as:

[tex]m\angle RCS=\frac{\widehat{RS}}{2}[/tex]

[tex]6x^{\circ}=\frac{105^{\circ}}{2}[/tex]

[tex]6x^{\circ}=52.5^{\circ}[/tex]

[tex]\frac{6x^{\circ}}{6}=\frac{52.5^{\circ}}{6}[/tex]

[tex]x^{\circ}=8.75^{\circ}[/tex]

[tex]x=8.75[/tex]

Therefore, the value of x is 8.75 for the given circle and option A is the correct choice.

Answer: 8359

Step-by-step explanation:

The formula for sample size needed for interval estimate of population proportion :-

[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]

Given : The significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}}=z_{0.025}=\pm1.96[/tex]

Previous estimate of proportion : [tex]p=0.32[/tex]

Margin of error : [tex]E=0.01[/tex]

Now, the required sample size will be :-

[tex]n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359[/tex]

Hence, the required sample size = 8359

To estimate the proportion of adults with high-speed Internet access with a 95% confidence level and a margin of error of 0.01, a sample size of 752 should be obtained.

To estimate the proportion of adults who have high-speed Internet access with a 95% confidence level and a margin of error of 0.01, we can use the formula:

Sample Size = (Z^2 * p * (1-p)) / (E^2)

Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion from a previous study, and E is the desired margin of error.

With a previous estimate of 0.32, a confidence level of 95% (corresponding Z-score of 1.96), and a margin of error of 0.01, the sample size required would be:

(1.96^2 * 0.32 * (1-0.32)) / (0.01^2) = 752

A sample size of 752 should be obtained to achieve the desired confidence level.

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For the given equation, if b=30, then the value of a will be equal to 60.

Like the given equation is a linear equation with two variables (a and b). You can solve this equation replacing b for the informed value (30).

Here it is important to remember the rules to the addition and the mutiplication  of integers numbers:

The rules to addition of numbers are:

+  +  

Add  Final result (+)  

-   -    

Add  Final result (-)  

+  -    

Subtract  Final result (the sign of the integer having greater value )

-   +  

Subtract  Final result (the sign of the integer having greater value )

The rules to multiplication of numbers are:

+  +  or  -   -

The result presents a positive sign (+) because the signs are same.

+  - or   -   +

The result presents a negative sign (-) because the signs are different.

If b=30, then you can find the value for a from steps below.

                                          [tex]\frac{1}{2}*a +\frac{2}{3} *b=50\\ \\ \frac{1}{2}*a +\frac{2}{3} *30=50\\ \\ \frac{1}{2}*a +2*10=50\\ \\ \frac{1}{2}*a +20=50\\ \\ \frac{1}{2}*a =50-20\\ \\ \frac{1}{2}*a=30\\ \\ a=30*2\\ \\ a=60[/tex]

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Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The volume of a rectangular pyramid is equal to

[tex]V=\frac{1}{3}LWH[/tex]

where

L is the length of the rectangular base

W is the width of the rectangular base

H is the height of the pyramid

If the pyramid is scaled proportionally by a factor of k

then

the new dimensions are

L=kL

W=kW

H=kH

substitute and find the new Volume V'

[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex]

[tex]V'=\frac{1}{3}(k^{3})LWH[/tex]

[tex]V'=(k^{3})\frac{1}{3}LWH[/tex]

[tex]V'=(k^{3})V[/tex]

The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume

Answer:

V = πr2h

V' = π × (k × r)2 × (k × h)

   = π × k2 r2 × kh

   = k3 × πr2h

   = k3 × V

Step-by-step explanation: