The graphs of f(x) and g(x) are shown below:


PIC


What are the solutions to the equation f(x) = g(x)?


x = −3, 4

x = −3.8, −0.4

x = −3.8, 3

x = 6.5, −6

Answer:

the correct solution is letter A.

Step-by-step explanation:

We have the following expression:

6sqrt(7) - 5x*sqrt(7) - x*sqrt(7)

Grouping the expression, we have:

=sqrt(7)*[6 - 5x - x]

=sqrt(7)*[6 - 6x]

=  6*sqrt(7)- 6x*sqrt(7)

So the correct solution is letter A.

For this case we have the following equation:

[tex]3-2z = \frac {1} {10}[/tex]

We must find the value of z that represents the solution of the equation:

We follow the steps below:

We multiply by 10 on both sides of the equation:

[tex]10 (3-2z) = 1[/tex]

We apply distributive property to the terms of parentheses;

[tex]30-20z = 1[/tex]

We subtract 30 from both sides of the equation:

[tex]-20z = 1-30\\-20z = -29[/tex]

We divide between -20 on both sides of the equation:

[tex]z = \frac {-29} {- 20}\\z = \frac {29} {20}\\z = 1.45[/tex]

If we substitute the value of z in the original equation, equality is satisfied.

Answer:

[tex]z = 1.45[/tex]

Answer:

f(x) = x3 + 3x2 − 4x − 12

Step-by-step explanation:

A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.

(x+3)(x+2)(x-2)

(x^2 + 3x + 2x + 6)(x-2)

(x^2 + 5x + 6)(x-2)

x^3 + 5x^2 + 6x -2x^2 - 10x - 12

x^3 + 3x^2 - 4x - 12

Answer:

y = 3 cos (x + π/2) + 2

Step-by-step explanation:

The transformed equation of y = Cos x  is  y=a cos⁡(x−c)+d

Where

Keeping these points in mind, the correct equation should have a = 3, c = + π/2, and d = +2

So we can write:

y = 3 cos (x + π/2) + 2

first answer choice is right.

Answer:

[tex]\boxed{\text{TRUE}}[/tex]

Step-by-step explanation:

If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.

For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.

However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.

Answer:

D

Step-by-step explanation:

I usually use a z-score table, but you can do this with a calculator.

If we go to a z-score table, we first look up the first two digits (in this case, 2.8) in the far left column.  Then we find the hundredths digit in the top row (0.07).  Where they intersect is P(z < 2.87).

P(z < 2.87) = 0.9979

Answer D.

Using the normal distribution, it is found that the correct option regarding P(z < 2.87) is given by:

D. 0.9979

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, P(z < 2.87) is the p-value of Z = 2.87, which is of 0.9979, hence option D is correct.

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Answer:

5

Step-by-step explanation:

since -4 *-2 = 8 and -8+8=0

0*-2=0

0+5=5

Answer:

The price of one gallon of milk is $3.5

Step-by-step explanation:

Let

x----> the price of one loaves of bread

y----> the price of one gallon of milk

we know that

4x+y=12.50 ----> equation A

2x+2y=11.50 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (2.25,3.5)

see the attached figure

therefore

The price of one loaves of bread is $2.25

The price of one gallon of milk is $3.5

He would have to make 10 visits at the ($12 per month + $4 each visit) gym to make the ($50 per month for unlimited visits) gym the cheapest option.

Explanation:

12 + (4 x 10) =

12 + (40) = $52

Answer:

He would have to use it more than 10 times in the month.

Step-by-step explanation:

4x+12>50

4x=38

x> 9.5

4(10)+12>50

52>50

The best prediction for the fish population is 16,079.

Hello i hope you are having a good day :)

Question 1 : A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year. Which is the best prediction for the number of regular viewers the show will have in 6 years? = y = 223000(1-0.047)⁶ = 223000(0.953)⁶ = 167,056.

Question 2 : A population of 30,000 fish is expected to shrink at a rate of 7.5% per year.  Which is the best prediction for the fish population in 8 years?       = 30,000(1−7.5/100)8≈ 16078.9

Question 3 : Bromine-82 has a half-life of about 35 hours.  After 140 hours, how many millilitres of an 80 ml sample will remain?  = Divide 80(1/2)^4 to get 5.

Question 4 : Polonium-218 has a half-life of about 3 minutes.  After 15 minutes, how many milligrams of a 120 mg sample will remain? = 3.75 mg

Question 8 : Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string.  To the nearest tenth of a meter, how high above the ground is the kite? = 68.2 m

Question 9 : Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff.  To the nearest tenth of a meter, how high above the ground is the eagle? = 91.9 m

Question 10 : A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? =  37.4 m

Answer:

552.16 cm^3

Step-by-step explanation:

Just multiply the lenght together.

The volume of the rectangular prism is approximately 552.16 cubic cm.

To find the volume of a rectangular prism, you need to multiply its length, width, and height.

Given that the length is 14 cm, the width is 3.4 cm, and the height is 11.6 cm, we can calculate the volume as follows:

Volume of a rectangular prism = Length × Width × Height

Volume of a rectangular prism = 14 cm × 3.4 cm × 11.6 cm

Volume of a rectangular prism ≈ 552.16 cm³ (rounded to the nearest tenth)

Therefore, the volume of the rectangular prism is approximately 552.16 cubic cm.

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Answer:

(a)

Step-by-step explanation:

Using Pythagoras' theorem

11² + 12² ? 16²

121 + 144 ? 256

265 > 256 ⇒ acute triangle

If the left side < right side then obtuse

If the left side = right side then right

Answer:

Step-by-step explanation:

I will assume that you meant F(x)= 12x + 12.  If you meant a fraction, write 1/2.

Then F(3) = 12(3) + 12 = 48

F(-12) = 12(-12) + 12 = -132.  

F(1/3) = 12(1/3) + 12 = 4 + 12 = 16

Please verify what you meant.  Then I will answer the remaining questions.

[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]

To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:

1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.

2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.

3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]

4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]

5. F(k): Substitute x = k into the function: F(k) = 12k + 12.

6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]

7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.

8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.

These are the values of the function for the given inputs.

60.0 is the area of the triangle

Answer: Option B

Step-by-step explanation: If You Found The Area Of The Triangle You Would Get An Answer Of 36 Square Inches. Have A Great Day!

The area of a triangle with a base of 9 inches and a height of 8 inches is found using the formula A = ½ × base × height, resulting in 36 square inches.

To find the area of a triangle, the formula A = ½ × base × height is used, where A represents the area, base is the length of the base of the triangle, and height is the measure from the base to the opposite vertex at a right angle. In this instance, the base of the triangle is 9 inches and the height is 8 inches. By plugging these values into the formula, you get the following calculation:

A = ½ × 9 in × 8 in = ½ × 72 in² = 36 in²

Therefore, the area of the triangle is 36 square inches.

The 10 cm string is 7 times smaller than the 70 cm string

Answer: Option D

D. [tex]880 = 45d + 70[/tex]; [tex]18\ days[/tex]

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call "d" the number of days that Barry attends school

So the cost was:

[tex]45d + 70 = 880[/tex]

Now we solve the equation for the variable d

[tex]45d= 880-70[/tex]

[tex]d= \frac{810}{45}[/tex]

[tex]d= 18\ days[/tex]

Therefore answer is the option D

Answer:

C. 1/8

Step-by-step explanation:

This is because the number two goes into sixteen eight times. This is the simplest form of the fraction.

Step-by-step explanation:

A, B, and C have the same area.  So P(A) = 1/3 and P(B) = 1/3, which means P(A or B) = 2/3.

P(success) = 2/3 and P(failure) = 1/3.

The probability of 2 failures is:

P = (1/3)² = 1/9

The probability of 2 successes is:

P = (2/3)²= 4/9

The probability of 1 success and 1 failure can be found either with binomial probability, or simply by subtracting the probabilities we found earlier from 1.

P = 1 - 1/9 - 4/9

P = 4/9

So the answer is the one in the bottom left corner.

Answer: C

X              P

0             1/9

1              4/9

2             4/9

Step-by-step explanation:

Screenshot provided

Answer:

tan(B)

Step-by-step explanation:

we know that

The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

In this problem

tan(B)=AC/AB

substitute

tan(B)=8/15

Do 15 divided by 3 equals 5

Final answer:

To determine Alyssa's age, we set up the equation 15 = 3A, based on the assumption that Eric being '3 times older' than Alyssa means he is 3 times her age. We divide both sides by 3 to get Alyssa's age, which is 5 years old.

Explanation:

To find Alyssa's age, we need to write an equation based on the information provided: Eric is 3 times older than his sister Alyssa, and we know that Eric is 15 years old. The phrase '3 times older' would technically mean 3 times Alyssa's age plus her age again (Alyssa's age times 4). However, this phrase can sometimes be used colloquially to mean '3 times Alyssa's age,' which is more common. So, we need clarification on the intended meaning. If we assume the latter, more common interpretation, the equation based on the information provided would be:

Let A be Alyssa's age. Since Eric is 15 years old and 3 times Alyssa's age, we have: E = 3A, where E is Eric's age.

Substituting Eric's age into the equation, we get: 15 = 3A

To find Alyssa's age, we then divide both sides by 3: 15 / 3 = A

Alyssa's age A would then be 5 years old. So, the equation to find Alyssa's age is: 15 = 3A

Answer:

x = 3

Step-by-step explanation:

It should NOT be "fight of the origin", rather "right of the origin".

Now let's move on to solve the question...

The x-intercept is found by setting the function equal to 0. Thus:

0 = x^3 - 9x

Let's solve this using algebra:

[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]

Hence, x = -3 and x = 3

The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.

Answer:

40 units^2

Step-by-step explanation:

This is because your figure has a height of 8 and a width of 5. 8*5=40 so there u go! Please mark brainliest

Answer:

Area of rectangle = 40 square units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Area of rectangle = Length * Breadth

To find the length and breadth

Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)

Length1 =  √[(x₂ - x₁)² + (y₂ - y₁)²]

√[(12 - 7)² + (3 - 3)²] = √5² = 5

Length2 =  √[(x₂ - x₁)² + (y₂ - y₁)²]

√[(12 - 12)² + (11 - 3)²] = √8² = 8 units

Therefore Length of rectangle = 8 and  

Breadth of rectangle = 5 units

To find the area of rectangle

Area = Length * Breadth

  = 8 * 5 =  40 square units

Answer:  C & D

Step-by-step explanation:

A binomial experiment must satisfy ALL four of the following:

A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

  → #3 is not satisfied  (#4 is also not satisfied)

B) When the spinner is spun multiple times ...

    → #1 is not satisfied

C)  When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

    → Satisfies ALL FOUR

D) When the spinner is spun five times, X is the number of times the spinner lands on 1.

   → Satisfies ALL FOUR

The answer is:

The equation is:

[tex]Total(t)=5200*(2)^{t}[/tex]

It's an exponential growth problem, we can calculate the exponential growth using the following equation:

[tex]Total(t)=StartPopulation*(1+r)^{\frac{t}{2}}[/tex]

Where,

Total, is the total population after "t" time in days.

Start population, for this is equal to 5,200

r,is equal to the percent of growth, for this case it's 100% each day.

t, is the time elapsed.

So, rewriting the equation, we have:

[tex]Total(t)=5200*(1+\frac{100}{100})^{t}[/tex]

[tex]Total(t)=5200*(1+1)^{t}[/tex]

[tex]Total(t)=5200*(2)^{t}[/tex]

Have a nice day!

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt{73}}{4}\ or\ x=\dfrac{5+\sqrt{73}}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two different solutiions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has no solution.}[/tex]

[tex]\text{We have}\ 2x^2=5x+6.\ \text{Convert to the form of}\ ax^2+bx+c=0:\\\\2x^2=5x+6\qquad\text{subtract}\ 5x\ \text{and}\ 6\ \text{from both sides}\\\\2x^2-5x-6=0\\\\a=2,\ b=-5,\ c=-6\\\\b^2-4ac=(-5)^2-4(2)(-6)=25+48=73>0\\\\x=\dfrac{-(-5)\pm\sqrt{73}}{2(2)}=\dfrac{5\pm\sqrt{73}}{4}[/tex]

Answer:

D

Step-by-step explanation:

The reflection across the y-axis has the rule:

(x,y)→(-x,y).

So, the vertices of the triangle ABC after reflection across the y-axis will have coordinates:

Hence, correct option is D

Answer:

d (-5,3)

Step-by-step explanation:

just flip it over to the other side.

None of the above (0)

Only two cards are drawn, so it is impossible for three of them to be pink.

If you meant to type that two of them were pink cards, then the answer is B. 2/15

First, find the probability of drawing a pink card first. There are 10 cards, and 4 of them are pink, so the probability is 4/10, which can be simplified to 2/5.

Now find the probability for the second card to be pink. There are now 9 cards, and 3 of them are pink, so the probability is 3/9, or 1/3.

Finally, multiply the probabilities together. First, multiply the numerators together. 2 * 1 = 2. Now, multiply the denominators together. 5 * 3 = 15. So, the final probability is 2/15

Answer:

  360 minutes

Step-by-step explanation:

(1.5 h/wk)·(4 wk)·(60 min/h) = 1.5·4·60 min = 360 min

Multiply reading time per week by the number of weeks to get reading time. Multiply the number of hours by the number of minutes in an hour to get minutes.

Answer:

Just finished test answer is 17

Step-by-step explanation:

The length of the side BC of the triangle ABC will be 17 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

The triangle is an isosceles triangle. Then the side AB is equal to the side AC. Then the value of 'x' is given as,

AB = AC

2x - 8 = x + 9

2x - x = 8 + 9

x = 17

The length of the side BC of the triangle ABC will be 17 units.

More about the triangle link is given below.

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