The functions f(x) and g(x) are defined below.
f(x)= 2e^x + 1
g(x)= 1/2e^x + 5/2

Determine where f(x) = g(x) by graphing.

A. x = 0
B. x = 0; x = 3
C. x = 1; x = 3
D. x= 3

Answer:

X²+6X=112

Step-by-step explanation:

area=1/2 base x height

56=x(x=6)/2

Multiply each side by two to eliminate the denominator

112=x(x=6)

112=x²+6x

Answer:

Option B, 1/4 (x - 5) = 13

Step-by-step explanation:

An inequality has a less than, greater than, less than or equal to, and greater than or equal to.  But, there are no equal signs allowed in a inequality.  That makes it an expression.

Answer:  Option B, 1/4 (x - 5) = 13

Answer:

B

Step-by-step explanation:

Answer:5 1/3

Step-by-step explanation:

number = n

second number = s

6n + 3s = 27

2n + 1 = s

6n + 3(2n + 1) = 27

6n + 6n + 1 = 27

12n = 26

n = 26/12

n = 2 1/6

2(2 1/6) + 1 = s

4 1/3 + 1 = s

5 1/3 = s

Final answer:

To find the second number, we create a system of linear equations using the given information and solve for the variables. The solution shows that the second number is 5.

Explanation:

The student's question involves setting up a system of two linear equations and solving them to find the values of two unknown numbers.

Let the first number be x and the second number be y. We are given the following equations based on the problem:

6x + 3y = 27

y = 2x + 1

First, we can substitute the second equation into the first to solve for x:

6x + 3(2x + 1) = 27

6x + 6x + 3 = 27

12x + 3 = 27

12x = 24

x = 2

Now, substitute x = 2 into the second equation to find y:

y = 2(2) + 1

y = 4 + 1

y = 5

Therefore, the second number, y, is 5.

Answer:

36

Step-by-step explanation:

30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120

120 × 0.30 = 36

mixed fraction​​ [tex]16\frac{2}{3}[/tex]

Step-by-step explanation:

Decimal Form: 16.666667

Answer:

190 cm^2

Step-by-step explanation:

Base: 10 × 3 = 30 (×2 = 60)

Small faces: 5 × 3 = 15 (×2 = 30)

Larger faces: 5 × 10 = 50 (×2 = 100)

Add: 100 + 60 + 30 = 190

Answer:1440

Step-by-step explanation:

I’m guessing that’s cuz 300/15 is 60 then 60 times 24?

First, let's start by figuring out how much Kendra gets paid per day. To do this, we can divide 300 by 5. 300 / 5 equals $60 per day.

Next, we can take the amount she gets paid per day and multiply it by the number of days, 24. 24 * 60 = $1440.

At the rate of $60 per day, Kendra will get paid $1440 for working 24 days.

Hope this helps!! :)

Answer:

-0.625

Step-by-step explanation:

The stock's value decreased by -0.625 each day over a period of four days, calculated by dividing the total decrease of -2.5 by the number of days.

The student's question pertains to finding the amount by which a stock's value decreased each day over four days, given that the total decrease was -2.5. To solve this problem, we use the concept of an arithmetic series, where each term changes by a constant difference. Since we know the total change in the stock's value was -2.5 over four days, we divide the total change by the number of days to find the daily change.

To calculate the change in stock value each day, we can use the formula:

Daily Change = Total Change / Number of Days

Plugging the values into the formula, we get:

Daily Change = -2.5 / 4 = -0.625

Therefore, the stock value decreased by -0.625 each day for the 4-day period.

Answer:

1/243 for edge

Step-by-step explanation:

The simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.

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

To simplify the quotient 3⁻¹ divided by 3⁴, we can use the rule that says when we divide two exponential expressions with the same base, we can subtract their exponents.

So, we have:

3⁻¹ ÷ 3⁴

3⁻¹ divided by 3⁴ = 3⁻¹⁻⁴

Now, we can simplify the expression by subtracting the exponents:

3⁻¹⁻⁴ = 3⁻⁵ = 1/3⁵ = 1/243

So, the simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.

Learn more about quotient here:

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Answer:

2/6<2/4

Step-by-step explanation:

We can start by simplifying the two fractions. 2/6=1/3 and 2/4=1/2. 1/3<1/2 so 2/6 is smaller than 2/4.

Answer:

Option B

Step-by-step explanation:

Using the law of logarithms

[tex]n log x= log x^{n}[/tex]

Therefore, since all the logs are to the same base, I will assume the base.

Also, when the bases are the same

log y+ log x= log (x+y)

[tex]\frac {1}{2}(log 4+ log 16)=log 4^{0.5}+log 16^{0.5}=log 2+log 4=log 6[/tex]

Now log 6-log 2= log (6-2)= log 4

Therefore, option B is correct

Answer:

put the ^ when you do exponents!

Step-by-step explanation:

There are three parts to graphing an inequality.

1. determine if the line will be dashed or solid

2. determine where you will shade in

3 graph with the appropriate line and shade

1. it is just > and not ≥ so the line will be dashed, which means the line itself is not part of the answer.

2. it is y> so you shade in the area inside the parabola.  if y was an actal number it might be more complicated

3. graph x^2 - 6x + 11.  If that seems a bit hard, put it into vertex form by completing the square.

y = x^2 - 6x + 11

y = (x - 3)^2 +2

Since x^2 is positive it opens upward and then plug in 0 for x and y in y = (x - 3)^2 +2 to get the x and y intercepts and the -3 and +2 tells you the vertex (in this case the minimum) is at (3,2),  then remember the points are mirrored on either side of the vertex.  so if the y intercept is 2 to the left and one higher than the vertex, there will also be a point 2 to the RIGHT and 1 up.  then just connect the dots.  Keep in mind there may not be any x intercepts if it never goes below the x axis *hinthintwinkwink*

if all else fails just graph a handful of points to get the idea of the shape.  Just remember you are shading inside of the parabola and using dashed lines.  

Answer:

6

Step-by-step explanation:

18/3=6 You have to divide 18 by 3 in order to know how many times older Jill is than her sister.

Answer: Slope: -1/4

Y-intercept: -8

Answer:Dante’s soccer team sells T-shirts to raise money for new equipment. For each T-shirt sold, the team raises $8. Parents also make a donation of $100 toward the equipment.

What is the equation that represents the total amount raised, y, if x T-shirts are sold?

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Parallel lines will always have the same slope, but their y-intercepts can be any real number.

Good morning ☕️

Answer:

Step-by-step explanation:

-7x + 5 = 8x - 25

then

25 + 5 = 8x + 7x

then

15x = 30

then

x = 2

___________________

:)

Answer:

    [tex]x=2[/tex]

Step-by-step explanation:

Given equation:

[tex]-7x + 5 = 8x - 25[/tex]

To find the value of 'x', take the terms of 'x' to one side and the constants to the other side:

Subtracting '[tex]5[/tex]' to both side:

   [tex]-7x+5-5=8x-25-5\\\\-7x=8x-30[/tex]

Subtracting '[tex]8x[/tex]' both side:

   [tex]-7x-8x=8x-8x-30\\\\-15x=-30[/tex]

          [tex]x=\frac{-30}{-15}[/tex]

          [tex]x=2[/tex]

Given:

ABCD is a cyclic quadrilateral.

m∠C = 43°

To find:

The measure of ∠A.

Solution:

In cylic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ m∠A + 43° = 180°

Subtract 43° from both sides.

⇒ m∠A + 43° - 43° = 180° - 43°

⇒ m∠A = 137°

The measure of ∠A is 137°.

Answer:

Final answer:

The probability of drawing a blue marble from a box containing 8 red, 9 blue, and 11 yellow marbles is calculated by dividing the number of blue marbles (9) by the total number of marbles (28), resulting in a probability of 9/28.

Explanation:

The question asks for the probability that a marble chosen randomly from a box is blue, given that the box contains 8 red marbles, 9 blue marbles, and 11 yellow marbles. To find this probability, you divide the number of blue marbles by the total number of marbles. Here's the calculation:

Therefore, the probability of drawing a blue marble from the box is 9/28.

Answer:

8% is 0.08

275 + 0.08s > 560

0.08s > 285

s > 3562.5

Answer:

(x - 2)² + (y + 3)² = 9

Step-by-step explanation:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - (-3))² = 3²

(x - 2)² + (y + 3)² = 9

The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

The correct option is (B).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

As per the given data:

We are given the coordinates for the center of a circle and the measure of the radius of the circle. We have to find out the equation of the circle

The coordinates of the center of the circle (O) = (2, -3)

The radius of the circle = 3

The standard equation of the circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

By substituting (h, k) ⇒ (2, -3) and r = 3

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

= (x - 2)^2 + (y + 3)^2 = 9

The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

Hence, The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

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Answer:100cm

Step-by-step explanation:

Answer:

-1 case D)

Step-by-step explanation:

5-x=-(x-5) so the unknown factor is -1

b-k=-(k-b), again, -1

Similar for third case.

Answer:

The correct answer is B. 3/8 = 9/24

Answer:

2a² + a   (   or a(2a+1)   )

Step-by-step explanation:

(6a²+3a) - (4a² + 2a)  (expand parentheses)

= 6a²+3a - 4a² - 2a   (group like terms)

= 6a²- 4a²+3a- 2a

= 2a² + a

= a(2a+1)

Answer:

2a^2+a

Step-by-step explanation:

This is an algebra. An algebra is an expression with no equality sign, and it will be expressed till the simplest form.

(6a^2+3a) - (4a^2 + 2a)

Remove the brackets

6a^2+3a-4a^2-2a

6a^2-4a^2+3a-2a

2a^2+a

Answer:

16.75

Step-by-step explanation:

do pie times 4/3 times the radius and you will get your answer

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ V=\cfrac{256\pi }{3}\implies V\approx \stackrel{in^3}{268.08}[/tex]

Answer:

45 in.

Step-by-step explanation:

6 x 8 = 48

.75 x 4 = 3

48 - 3 = 45

45 inches left

After cutting out four square corners, each with a side length of 3/4 inch from a 6 by 8 inches rectangular piece of paper, 45.75 square inches of paper is left.

To solve how much paper is left after the corners are removed, we need to calculate the total area of the paper and subtract the total area of the corners that were cut out.

The original dimensions of the paper are 6 inches by 8 inches, so its total area is:

Area of rectangle = width times length = 6 inches times 8 inches = 48 square inches.

Each corner is a square with a side of 3/4 inch, so the area of one corner is:

Area of one square corner = (3/4 inch) times (3/4 inch) = 9/16 square inches.

Since there are four corners:

Total area removed = 4 inches (9/16 square inches) = 9/4 square inches = 2.25 square inches.

Finally, subtract the area removed from the total area to find the remaining area:

Remaining area = Total area of rectangle - Total area removed

Remaining area = 48 square inches - 2.25 square inches = 45.75 square inches.

Therefore, after cutting out the corners, 45.75 square inches of paper is left.

Answer:

n = 5

n = 8

Step-by-step explanation:

n^2 - 13n = -40

Equate everything to zero

n^2 - 13n + 40 = 0

Factorise

(n - 5)(n - 8) = 0

Either

n - 5 = 0

Add 5 to both sides

n - 5 + 5 = 0 + 5

n = 5

Or

n - 8 = 0

Add 8 to both sides

n - 8 + 8 = 0 + 8

n = 8

n = 5 or

n = 8

It has two real solutions

Answer:

100 : 175

Step-by-step explanation:

Divide 275 into two parts which are in the ratio 4:7?

To divide 275 into 4 :7, we will follow the steps below

First, We will add the ratio numbers together, that is; 4 + 7 = 11  

4 : 7 of 275 will be;

4/11  × 275

=4 × 275    /   11

=1100/11

=100

Then we will now proceed to the second part;

7/11  × 275

=  7 × 275  / 11

=1925/11

=175

Therefore dividing 275 into 4 : 7 yields    100 : 175

Answer:

attatch a picture

line AB im assuming

Step-by-step explanation: