The graph represents the piecewise function

3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. In actuality, 3^2 + 3^3 = 36, while 3^5 = 243.

No, 3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. This is a common misconception when dealing with exponents. To clear this up, let's look at what these expressions actually mean:

3 to the 2nd power (3^2) = 3*3 = 9

3 to the 3rd power (3^3) = 3*3*3 = 27

So, 3^2 + 3^3 = 9 + 27 = 36

However, 3 to the 5th power (3^5) = 3*3*3*3*3 = 243

So, as you can see, 36 does not equal 243.

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Answer:

x = 7/2 ±sqrt(65)/ 2

Step-by-step explanation:

x^2=7x+4

Subtract 7x from each side

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

x^2 -7x =4

Complete the square

Take the coefficient of x and divide by 2

-7/2

Then square it

(-7/2)^2 = 49/4

Add this to each side

x^2 -7x +49/4 =4+49/4

(x-7/2)^2 = 4 +49/4

(x-7/2)^2 = 16/4 +49/4

(x-7/2)^2 =65/4

Take the square root of each side

sqrt((x-7/2)^2) =±sqrt(65/4)

x-7/2 = ±sqrt(65)/ sqrt(4)

x-7/2 = ±sqrt(65)/ 2

Add 7/2 to each side

x-7/2 +7/2=7/2 ±sqrt(65)/ 2

x = 7/2 ±sqrt(65)/ 2

The solutions to the quadratic equation x^2 = 7x + 4 are x = 3 and x = -7, found using the quadratic formula and verified by substitution into the original equation.

To solve the quadratic equation x^2 = 7x + 4, we first need to bring all terms to one side of the equation to get it into the standard form ax^2 + bx + c = 0. This gives us x^2 - 7x - 4 = 0. We can then apply the quadratic formula, which is x = (-b \/- sqrt(b^2 - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax^2 + bx + c = 0.

For our equation, a = 1, b = -7, and c = -4. Substituting these values into the quadratic formula gives us two solutions, which result in x = 3 and x = -7 as the solutions to the problem. To verify these solutions, we can substitute them back into the original equation and confirm they satisfy the equation, thus proving they are correct.

Answer:

The correct option is A

Step-by-step explanation:

(x^2+x+9)+(7x^2+5)​

Open the parenthesis:

=x²+x+9+7x²+5

Now add the like terms:

=8x²+x+14

Therefore the correct option is A...

Answer:

A

Step-by-step explanation:

The solutions to the quadratic equation are x = -1/4 and x = -5.

First, we look at the coefficient of x², which is 4 in this case. We need to find two numbers whose product is 4 times 5 (the constant term) and whose sum is the coefficient of x (12 in this case). These numbers are 1 and 20, as 1 * 20 = 20 and 1 + 20 = 21.

Next, we rewrite the middle term (12x) of the quadratic expression as the sum of these two numbers:

4x² + 1x + 20x + 5 = 0.

Now, we group the terms in pairs:

(4x² + 1x) + (20x + 5) = 0.

Next, we factor out the greatest common factor from each group:

x(4x + 1) + 5(4x + 1) = 0.

Notice that we have a common binomial factor, (4x + 1), which we can factor out:

(4x + 1)(x + 5) = 0.

Now, we apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor to zero and solve for x:

   1. 4x + 1 = 0 => 4x = -1 => x = -1/4.

   2. x + 5 = 0 => x = -5.

Answer: x = -1/4, -5.

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Answer:

1/32

15/32

Step-by-step explanation:

For a fair sided coin,

Probability of heads, P(H) = 1/2

Probability of tails P(T)  = 1/2

For a coin tossed 5 times,

P( All heads)

= P(HHHHH),

= P (H) x P(H) x P(H) x P(H) x P(H)

= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/32 (Ans)

For part B, it is easier to just list the possible outcomes for

"at most 2 heads" aka "could be 1 head" or "could be 2 heads"

"One Head" Outcomes:

P(HTTTT), P(THTTT) P(TTHTT), P(TTTHT), P(TTTTH)

"2 Heads" Outcomes:

P(HHTTT), P(HTHTT), P(HTTHT), P(HTTTH), P(THHTT), P(THTHT), P(THTTH), P(TTHHT), P(TTHTH), P(TTTHH)

If we count all the possible outcomes, we get 15 possible outcomes representing "at most 2 heads)

we know that each outcome has a probability of 1/32

hence 15 outcomes for "at most 2 heads" have a probability of

(1/32) x 15  = 15/32

The aquarium, which has a volume of 770 cubic feet, can hold approximately 5,760 gallons of water when taking into consideration the conversion rate of 7.48 gallons per cubic foot.

To calculate the volume of water an aquarium can hold, we need to first calculate the volume of the aquarium itself, which is determined by multiplying the length, width, and height together. In this case, we have an aquarium that measures 11 feet wide, 10 feet long and 7 feet deep, so multiplying these dimensions together gives us a volume of 770 cubic feet.

Next, we need to convert this volume into gallons. We're given the conversion rate of 7.48 gallons per cubic foot of water, so we multiply our previously obtained volume by this rate. This gives us: 770 cubic feet * 7.48 gallons per cubic foot, which equals 5,759.6 gallons.

So, the aquarium can hold approximately 5,760 gallons of water.

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Answer:

[tex]\large\boxed{y=\dfrac{15}{14}x+1.5}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

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

You must solve the system of equations:

[tex]\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ[/tex]

[tex]\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}[/tex]

Answer:

D. Linear decay.

Step-by-step explanation:

The data decays and lowers.

Answer with explanation:

If you will look at the graph of function, it is not a straight line.

Horizontal Asymptote is, y=0.

There is no vertical Asymptote.

Either it can be growth function or decay function.

But , if you will look at the graph of growth function, it begins from negative infinity and then starts increasing.

In this case graph is decreasing function.

So, The function represents

Option C:→ Exponential Decay

Answer:

The correct answer option is C. [tex]y>\frac{2}{3}x+3[/tex].

Step-by-step explanation:

We are given a graph and we are to determine whether which linear  inequality is represented by the graph.

We know that the grey part on the graph represents the the region which is not included in the inequality.

Also, when x = 0, the values of y can only be less than 3.

So we choose two points on the graph and we find the slope.

For example, we take the points [tex](0,3)[/tex] and [tex](3,5)[/tex].

Slope = [tex]\frac{5-3}{3-0} =\frac{2}{3}[/tex]

which makes the equation of the line [tex]y=\frac{2}{3}x+3[/tex] and inequality [tex]y>\frac{2}{3}x+3[/tex].

Answer:

Option A (Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance).

Step-by-step explanation:

Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. It is important to note that correlation shows a relationship between the two variables but it cannot determine the causation i.e. it cannot be concluded that one variable caused the other variable to occur. Even though having a strong correlation does not mean causal relationship. Therefore, correlation does not prove causation. This is because there are several other lurking and unobserved variables which affect the observed variables. The former class of variables are not accounted for in the correlation. Therefore, the exact magnitude of the causal relationship cannot be determined. Therefore, Option A is the correct choice!!!

Answer:

OPTION A: Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.

Step-by-step explanation: I got it right on the test.

Answer:

jjjjjj

Step-by-step explanation:

it would be the same as before because translated means it stays the same

Answer:

2.25

Step-by-step explanation:

Answer:

x = 2.25

Step-by-step explanation

using process of elimination the only viable answer is 2.25

Answer:

x = 4.2, LJ = 14.2

Step-by-step explanation:

When 2 chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

10x = 6 × 7 = 42 ( divide both sides by 10 )

x = 4.2

Hence LJ = 10 + x = 10 + 4.2 = 14.2

Elisa's distance from home (in miles) equals her walking speed (2 mph) multiplied by time spent walking (t hours).

To model Elisa's distance from home based on the time spent walking, we can use the formula for distance, which is:

[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\\[/tex]

Given that Elisa walks at a steady pace of 2 miles per hour, her rate (or speed) is 2 miles per hour. Let's denote this rate as [tex]\( r = 2 \)[/tex] mph.

The time Elisa spends walking can vary, so let's denote it as [tex]\( t \)[/tex] (in hours).

Now, to find Elisa's distance from home, we'll substitute the values into the formula:

[tex]\[ \text{Distance} = r \times t \]\[ \text{Distance} = 2 \times t \][/tex]

Since Elisa's distance from home is what we're interested in, this equation models her distance from home based on the time spent walking. It shows that her distance from home increases linearly with time as she walks at a steady pace.

Answer:

y = - 3x + 3

Step-by-step explanation:

The equation of a line in slope intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3, hence

y = - 3x + c ← is the partial equation of the line

To find c substitute (- 1, 6 ) into the partial equation

6 = 3 + c ⇒ c = 6 - 3 = 3

y = - 3x + 3 ← equation of line

Answer: A

Step-by-step explanation:

FLVS Question, the answer is A !!

Answer:

6x + 8y

Step-by-step explanation:

Distribute 2:

Note: This means to multiply 2 with the numbers inside the parentheses.

2 * 3x = 6x

2 * 4y = 8y

Our answer would be 6x +8y

Answer:

I think A and C are because they all go back to the original equation.

Step-by-step explanation:

Hope my answer has helped you and if not i'm sorry.

Answer:

7.6 inches

Step-by-step explanation:

First of all we have to define range.

Range gives us the difference of two values between which the data is spread.

the formula for range is:

Range = Highest value - lowest value

By observing the diagram, we can see that

The highest value is = 8.5 inches

The lowest value is: 0.9 inches

So,

Range = 8.5 - 0.9

= 7.6 inches

So, the range is 7.6 inches ..

[tex]\bf \cfrac{1+cot^2(\theta )}{1+csc(\theta )}=\cfrac{1}{sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\implies \cfrac{1+\frac{cos^2(\theta )}{sin^2(\theta )}}{1+\frac{1}{sin(\theta )}}\implies \cfrac{~~\frac{sin^2(\theta )+cos^2(\theta )}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}\implies \cfrac{~~\frac{1}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}[/tex]

[tex]\bf \cfrac{1}{\underset{sin(\theta )}{~~\begin{matrix} sin^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}\cdot \cfrac{~~\begin{matrix} sin(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{sin(\theta )+1}\implies \cfrac{1}{sin^2(\theta )+sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\ne \cfrac{1}{sin(\theta )}~\hfill[/tex]

Answer:

Rosa is closer to the correct depth.  

Step-by-step explanation:

To show that two measurements are nearly equivalent, we must convert one of the measurements to the other unit.

1 m = 3.281 ft

[tex]\text{Depth } = \text{1644 ft} \times \dfrac{\text{1 m}}{\text{3.281 ft}} = \textbf{501.1 m}[/tex]

Neither is correct but Rosa is closer to the correct depth.

Answer:

(72/17) hours

Step-by-step explanation:

Time Jackie would take alone , J = 8 hrs

Time Patricia would take alone , P = 9 hrs

Let the time they will take together be T

use the formula for shared unit rate

[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{J}[/tex] + [tex]\frac{1}{P}[/tex]

[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{9}[/tex]

[tex]\frac{1}{T}[/tex] = [tex]\frac{17}{72}[/tex]

T = [tex]\frac{72}{17}[/tex] hours (or 4.24 hours)

It takes them to work together for 4 hours and 14 minutes.

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

Jackie was to paint her living room alone. It would take 8 hours.

Her sister Patricia could do the job in 9 hours.

How long would it take them to work together?

We know the work is inversely proportional to the time. And formula we have

[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{T_1} +\dfrac{1}{T_2}[/tex]

We have

[tex]\rm T_1 = 8, \ \ \ and\ \ T_2 = 9[/tex]

Then by the formula.

[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{8} +\dfrac{1}{9}\\\\\rm \dfrac{1}{T_f} = \dfrac{8+9}{8*9} \\\\\rm \dfrac{1}{T_f} = \dfrac{17}{72} \\\\T_f \ = \dfrac{72}{17}\\\\T_f \ = 4.24[/tex]

Then the time 4.24 will be 4 hours and 14 minutes.

Thus, it takes them to work together for 4 hours and 14 minutes.

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Step-by-step explanation:

The y-intercept is the value of the function at x = 0.

f(0) = -3(0) + 2 = 2

g(0) = -3

h(0) = 4 sin(0 + π) + 3 = 3

h(x) has the greatest y-intercept.

Answer:

The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.

Step-by-step explanation:

The given function is

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

Substitute x=0, to find the y-intercept of the function.

[tex]f(0)=-3(0)+2[/tex]

[tex]f(0)=0+2[/tex]

[tex]f(0)=2[/tex]

The y-intercept of the function f(x) is 2.

From the given graph it is clear that the graph of g(x) intersect the y-axis at y=-3.

Therefore the y-intercept of the function g(x) is -3.

The given function is

[tex]h(x)=4\sin (2x+\pi)+3[/tex]

Substitute x=0, to find the y-intercept of the function.

[tex]h(0)=4\sin (2(0)+\pi)+3[/tex]

[tex]h(0)=4\sin (0+\pi)+3[/tex]

[tex]h(0)=4\sin (\pi)+3[/tex]

[tex]h(0)=4(0)+3[/tex]

[tex]h(0)=3[/tex]

The y-intercept of the function h(x) is 3.

The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.

Answer:

6 Hours

Step-by-step explanation:

360 is half of 720, so it would take half the time to travel. half of 12 is 6

At a constant speed of 60 miles per hour, it would take 6 hours to travel 360 miles, which is a reasonable answer since the time required is halved when the distance is halved.

The question involves calculating the time it would take to travel a certain distance given a constant speed which is a basic concept in mathematics, more specifically in the topic of rates and ratios.

If you travel 720 miles in 12 hours, you are traveling at a speed of 720 miles / 12 hours = 60 miles per hour. Now, to find out how long it would take to travel 360 miles at this constant speed, you divide the distance by the speed to get the time: 360 miles / 60 miles per hour = 6 hours. So, it would take 6 hours to travel 360 miles if you maintain the same speed.

When you check if the answer is reasonable, consider if the distance is halved, the time should also be halved if the speed remains constant. Since 360 miles is half of 720 miles, and 6 hours is half of 12 hours, the answer is indeed reasonable.

Answer:

1. 24

2. 30

3. 20

4. 12

5. 6

Answer:

x = 7.5

Step-by-step explanation:

Given

- 15 = [tex]\frac{x}{-0.5}[/tex]

Multiply both sides by - 0.5

- 0.5 × - 15 = x, hence

x = 7.5

Answer:

7.5.

Step-by-step explanation:

-15 = x / -0.5

Cross multiplying:

x =  -15 * -0.5

= 7.5.

Answer:

see explanation

Step-by-step explanation:

81[tex]a^{6}[/tex] - 100 ← is a difference of squares which factors in general as

a² - b² = (a - b)(a + b)

81[tex]a^{6}[/tex] = (9a³ )² ⇒ a = 9a³ and 100 = 10² ⇒ b = 10

Hence

81[tex]a^{6}[/tex] - 100

= (9a³)² - 10²

= (9a³ - 10)(9a³ + 10)

Answer:

C

Step-by-step explanation:

Unit Test Is a pain I know

Answer: So the sum of all of the measures of the interior angles of a 16-sided polygon is 2520 degrees.

The sum of the interior angles of a 16-sided polygon is 2520 degrees.

The sum of the interior angles of a 16-sided polygon, or hexadecagon, is 2520 degrees, which can be calculated using the formula (n-2) x 180 degrees.

The sum of the interior angles of any polygon can be found using the formula (n-2)  imes 180 degrees, where n is the number of sides of the polygon. A 16-sided polygon is known as a hexadecagon. Using the formula, we have:

Sum of interior angles = (16-2)  imes 180 degrees

Sum of interior angles = 14  imes 180 degrees

Sum of interior angles = 2520 degrees

Therefore, the sum of the interior angles of a 16-sided polygon is 2520 degrees.

Answer:

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin30° = [tex]\frac{1}{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex] = [tex]\frac{1}{2}[/tex]

Cross- multiply

y = 2 × 17 = 34

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{x}{34}[/tex] and

[tex]\frac{x}{34}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 34[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 17[tex]\sqrt{3}[/tex]

Hence

x = 17[tex]\sqrt{3}[/tex] and y = 34

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below a line or to the left if is a vertical line

>, ≥ - shaded region above a line or to the right if is a vertical line

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

We have x ≥ 4:

solid vertical line x = 4

shaded region to the right

Answer:

C.

Step-by-step explanation:

You are given 3x-4y<16 and we want to see which of the ordered pairs is a solution.

These ordered pairs are assumed to be in the form (x,y).

A. (0,-4) ?

3x-4y<16 with (x=0,y=-4)

3(0)-4(-4)<16

0+16<16

16<16 is not true so (0,-4) is not a solution of the given inequality.

B. (4,-1)?

3x-4y<16 with (x=4,y=-1)

3(4)-4(-1)<16

12+4<16

16<16 is not true so (4,-1) is not a solution of the given inequality.

C. (-3,-3)?

3x-4y<16 with (x=-3,y=-3)

3(-3)-4(-3)<16

-9+12<16

   3<16 is true so (-3,-3) is a solution to the given inequality.

D. (2,-3)?

3x-4y<16 with (x=2,y=-3)

3(2)-4(-3)<16

6+12<16

18<16 is false so (2,-3) is not a solution to the given inequality.

Answer:

3

Step-by-step explanation:

Plug in the values for a and b=     -7(-1)-2(2)

Multiply=   7-4

Subtract=   3

Hope this helps ^-^

Answer:

3

Step-by-step explanation:

We'd just substitute the value provided to us with the variable.

-7(-1) - 2(2)

-7 * -1 = 7

-2(2) = -4

7-4 = 3

Our answer is 3