For what value of the constant c is the following function continuous at x = −7?

\(9 \times \frac{1}{4} = \frac{9}{4} \)✅

Option A⤵

\(5 \times \frac{1}{2} = \frac{1}{10} \\ ⇢  \frac{5}{2} ≠ \frac{1}{10} \)

Option B⤵

\(4 \times \frac{1}{3} = \frac{4}{12} \\ ⇢ \frac{4}{3} ≠ \frac{4}{12} \)

Option C⤵

\(9 \times \frac{1}{4} = \frac{9}{4} \\ ⇢ \frac{9}{4} = \frac{9}{4} \)

Option D⤵

\(8 \times \frac{1}{ 5} = \frac{9}{5} \\ ⇢ \frac{8}{5} ≠ \frac{9}{5} \)

Hence, option C is correct.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

-3/4

Step-by-step explanation:

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.

Answer:

0 :/

Step-by-step explanation:

S(48) = (48/2)(2a+47d),

S(36) = (36/2)(2a+35d).

Now S(48) = 4S(36)

24(2a+47d) = 4*18(2a+35d) = 72(2a+35d).

Then 2a+47d = 3(2a+35d) and

6a +105d -2a -47d = 0,

4a +58d = 0,

2a+29d = 0.

Now S(30) = (30/2)(2a+29d) = (15)(2a+29d)=0

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:

r = 0.06/12 = 0.005

Next, we can substitute the given values into the formula and solve for P:

12,000 = P(1 + 0.005/12)^(12*3)

12,000 = P(1.005)^36

P = 12,000/(1.005)^36

P ≈ $9,883.86

Therefore, the amount of money that should be deposited today is approximately $9,883.86.

Step-by-step explanation:

Answer:

1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.

2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.

3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.

4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.

The gradients of line equations are listed below:

In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:

m = Δy / Δx

Where:

Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)

m = [2 - (- 4)] / [1 - (- 1)]

m = 3

Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)

m = [3 - (- 1)] / [0 - (- 1)]

m = 4

Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)

m = [3 - (- 1)] / [1 - (- 1)]

m = 2

Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)

m = (- 2 - 4) / (2 - 0)

m = - 3

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Answer: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... the line y = x is the point (y, x). The reflection of the point (x,y) across. the line y = -x is the point (-y, -x).

Step-by-step explanation: I hope this helped! Actually, I just hope that my answer is correct but whatevs lol :)

Answer:

  -225°, 135°, 495°

Step-by-step explanation:

Adding or subtracting multiples of 360° will give angle values that are coterminal with a given angle.

  -225° -360° = -595° (not on the list)

  -225° +0·360° = -225°

  -225° +360° = 135°

  -225° +2·360° = 495°

Angles -225°, 135°, 495° are coterminal with -225°.

Answer:

x = 3, x = -5

Step-by-step explanation:

A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:

a^2 = x^2

a = x

Now, we can substitute x for a in the other expression to create the equation:

2ab = 2x

2(x)b=2x

b = 1

From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:

x^2 + 2x = 15

x^2 + 2x + 1 = 16

Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:

(x + 1)^2 = 16

Now, we take the square root of both sides:

x + 1 = ± 4

We can separate this into two equations and solve:

x + 1 = 4

x = 3

x + 1 = -4

x = -5

Answer:

Step-by-step explanation:

x^2 + 2x = 15

x^2 + 2x + [1/2(2)]^2 = 15 +  [1/2(2)]^2

(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2

(x + 1)^2 = 15 + 1^2

(x + 1)^2 = 15 + 1

(x+1)^2 = 16                       Take the square root of both sides.

sqrt( (x + 1)^2 ) = sqrt(16)

x + 1 = +/- 4

x + 1 = 4

x = 4 - 1 = 3

x + 1 = -4

x = -4 - 1

x = - 5

So the roots are 3 and - 5

Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Answer:

u = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = sqrt(2) / u

u cos 45 = sqrt(2)

u = sqrt(2) / cos 45

u = sqrt(2) / 1/ sqrt(2)

u = sqrt(2) * sqrt(2)

u =2

u=2

Answer:

Solution given:

Cos 45°=base/hypotenuse

\(\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}\)

doing crisscrossed multiplication

\(\sqrt{2}*\sqrt{2}=1*u\)

u=2

Answer:

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

The probability that one will get the required result on the next roll as described in the game is; 1/36.

It follows from the task content that to secure a win in the back gammon game using the standard dice, one must roll double threes.

Hence, the probability of such result to occur can be evaluated as follows;

P (double threes) = 1/6 × 1/6

= 1/36.

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Hey there!

The answer to your question is 3480

There are two ways we can do this. I will show you both, so you know how to do it in the future:

The First Way ~ Parantheses First:

Step 1.) Add \(86\) and \(34\)

\(29(120)\)

Step 2.) Multiply

\(3480\)

The Second Way ~ Distribute First

Step 1.) Multiply \(29\) and \(86\)

\(29(34)+2494\)

Step 2.) Multiply \(29\) and \(34\)

\(986+2494\)

Step 3.) Add \(986\) and \(2494\)

\(3480\)

Have a terrificly amazing day!

Answer:

you would still pay the normal amout of tax of other normal technology. The tax would change depending on e=what state your in tho

Step-by-step explanation:

Answer:

A

False

Step-by-step explanation:

Answer:

1) increase

explanation: In most plants, the uptake of CO2 through photosynthesis is reduced by a side reaction called photorespiration. The research group has now found that the CO2 increase in the atmosphere over the 20th century has shifted the balance between photosynthesis and photorespiration toward photosynthesis.

2) think its false

P(A or B) =

Formula: P(AUB)=P(A)+P(B)-P(A n B)

We roll six-sided die.

Then sample space ={1,2,3,4,5,6}

And

Event A: Roll an odd number.

Odd numbers are {1,3,5}

Event B: Roll a number less than 5

Number less than 5 are {1,2,3,4}

So, Probability P(A)=

Probability P(B)=

Now, the odd number which is less than 5 are {1,3}

So, P(A n B)=

Since P(AUB)=P(A)+P(B)-P(A n B)

Therefore, P(A or B) = 1/6

Answer:

A, B, and E. Hope this helps!

f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.

So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.

To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.

Applying the power rule, we differentiate each term separately:

f'(x) = d/dx (x^1) + d/dx (2)

The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.

The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.

Therefore, f'(x) = 1 + 0 = 1.

So, the derivative of f(x) = x + 2 is f'(x) = 1.

To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).

In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).

Applying the power rule and the constant multiple rule, we differentiate each term separately:

f'(x) = d/dx (2 * x^(-2))

Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.

Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.

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==========================================================

Explanation:

If you plug in x = -2, then,

y = 4x-2

y = 4(-2)-2

y = -8-2

y = -10

This shows that the answer must be choice D, as this is the only answer that has x = -2 lead to y = -10. Note the first column of table D.

We could stop here if you wanted.

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

If we kept going and plugged in x = 0, then,

y = 4x-2

y = 4(0)-2

y = 0-2

y = -2

We have x = 0 lead to y = -2. This matches with the second column of table D.

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

Lastly, if we plugged in x = 2, then we get,

y = 4x-2

y = 4(2)-2

y = 8-2

y = 6

So the third column of table D is also confirmed.

Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

Correct Answer:

x(t) = 9cos(t)

y(t) = 9sin(t)

z(t) = 54sin(t)cos(t)

What is the parametric equation?

The parametric equation of a curve is a representation of the curve in terms of one or more independent variables (known as parameters), usually represented as t. Each parameter value t corresponds to a unique point (x, y, z) on the curve.

For the given curve, the intersection of the cylinder x²  + y² = 81 and the surface z = 6xy can be found by setting the equation of the cylinder equal to the equation of the surface and solving for x, y, and z in terms of a single parameter t.

Starting with the cylinder: x²  + y² = 81, we can parameterize x and y as follows:

x(t) = 9cos(t)

y(t) = 9sin(t)

Substituting these expressions into the equation of the surface:

z(t) = 6x(t)y(t) = 6 * 9cos(t) * 9sin(t) = 54sin(t)cos(t)

So, the parametric equations of the curve given by the intersection of the cylinder x² + y² = 81 and the surface z = 6xy are:

x(t) = 9cos(t)

y(t) = 9sin(t)

z(t) = 54sin(t)cos(t)

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Answer:

ans:- B and E

Step-by-step explanation:

\(\pi \: r {}^{2} \)

so pie into 1×1

Answer:

7

Step-by-step explanation:

Two numbers are additive inverses if they add to give a sum of zero. 3 and -3 are additive inverses since 3 + (-3) = 0. -3 is the additive inverse of 3. 3 is the additive inverse of -3.

The additive inverse of a number is a number that is the same distance from 0 on the number line, but in the opposite direction. It can also be thought of as the number that you need to add to a number in order for the result to be 0.

Examples

In the number line below, -3 and 3 are additive inverses. If we add the other value to either of the two values, the result will be 0.

-3 + 3 = 0

3 - 3 = 0

The same is true of the other corresponding values on the number line; 5 and -5, 4 and -4, 2 and -2, 1 and -1, and even 0 and 0, are all also additive inverses.

Answer:

7

Step-by-step explanation:

The additive inverse of a number is is the number that, when added to it, yields zero.

Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

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