Graph the line with slope
3/4
passing through the point (-4,-1)
.

The required, difference between the perimeters of the two rectangles is,

⇒ 46.03 in.

Since, rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k.

Then, We get:

k = XY / LM

k = 2.22 / 19

To find the value of k, we can divide 2.22 by 19:

k ≈ 0.117

Hence, The area of rectangle LMNP is given as,

140.6 in².

We can use this to find the length of NP:

LM x NP = area of LMNP

19 x NP = 140.6

NP ≈ 7.4 in

Since, the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:

XY / YZ = LM / NP

2.22 / YZ = 19 / 7.4

YZ ≈ 1.167 in

Now we can calculate the perimeters of both rectangles:

Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in

Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in

Thus, The difference between the perimeters is:

52.8 - 6.77 = 46.03 in

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Answer:

  58.85°

Step-by-step explanation:

You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.

The cosine function relates angles and sides by ...

  Cos = Adjacent/Hypotenuse

  cos(x) = 15/29

The inverse function is used to find the angle value:

  x = arccos(15/29) ≈ 58.85°

The value of x is about 58.85°.

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Answer:

4 minutes and 44 seconds.

Answer:

Step-by-step explanation:

The requried line of reflection is the x-axis.

To determine the line of reflection, we need to find the line that maps each vertex of the first polygon to the corresponding vertex of the second polygon.

We can start by reflecting the first polygon across the x-axis. This will map V to V', W to W', X to X', Y to Y', and Z to Z', as shown below:

First Polygon (VWXYZ) Second Polygon (V'W'X'Y'Z')

(3, 2) V (3, -10) V'

(3, 0) W (3, -8) W'

(6, -7) X (6, -1) X'

(9, 0) Y (9, -8) Y'

(9, 2) Z (9, -10) Z'

Next, we can compare the coordinates of each vertex in the first and second polygons to determine the line of reflection. We notice that reflecting the first polygon across the x-axis negates the y-coordinates of all vertices. Therefore, the line of reflection must be the x-axis.

Therefore, the line of reflection is the x-axis.

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Probability of answering exactly 4 questions correctly = 0.206

P (More than 2) = 0.475

1.

ind P(4): Probability of answering exactly 4 questions correctly.

P(X=4) = (10C4) * (0.25^4) * (0.75^6)

10C4 = 10! / (4! * (10-4)!) = 210

P(X=4) = 210 * (0.25^4) * (0.75^6)

= 0.206

P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056

P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187

P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282

Now, calculate P(X>2):

P(X>2)

= 1 - (P(X=0) + P(X=1) + P(X=2))

= 1 - (0.056 + 0.187 + 0.282)

= 1 - 0.525

= 0.475

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The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7

we know that general term for gp is  [tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where r = common ratio

a = first term

putting values we get

8th term = 8x 64/729

= 0.702

hence the 8th term is 0.702

The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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The values for the composition of functions are:

a. (f o g)(x) = -x³ - x + 1

b. (g o f)(x) = -x³ - x - 1

Here, we have,

to Determine the Value of Composite Functions:

The value of composite functions are determined by first finding the output of the inner function, which would be used as the input of the outer functions to derive the value of the composite functions.

Given the following:

f(x) = x³ + x + 1

g(x) = -x

a. To find (f o g)(x), substitute g(x) as the inner function for x into f(x):

(f o g)(x) = (-x)³ + (-x) + 1

Simplify

(f o g)(x) = -x³ - x + 1

b. To find (g o f)(x), substitute f(x) as the inner function for x into g(x):

(g o f)(x) = -(x³ + x + 1)

Distribute by -1

(g o f)(x) = -x³ - x - 1

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complete question:

If f(x)=x³+x+1 and g(x)=-x, find (f°g)(x) and (g°f)(x).

(f°g)(x)=

The correlation coefficient which best matches the data plotted on the graph is 0.25, the correct option is C.

We are given that;

The graph of different values of x

Now,

we can see that there is a weak positive linear relationship between x and y, as the points are scattered around a slightly upward-sloping line. The closer the points are to the line, the stronger the correlation. The farther the points are from the line, the weaker the correlation. Hence, we can expect the correlation coefficient to be a small positive number, less than 1.

Therefore, by correlation coefficient the answer will be 0.25.

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Answer:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Hence, we use this formula to solve for the missing length:

c^2 = a^2 + b^2

Plugging in the given values, we get:

c^2 = 12^2 + 12^2 c^2 = 144 + 144 c^2 = 288 c ≈ √288

Rounding √288 to the nearest ten gives 17. Therefore, the missing length is approximately 17.

Hence, c ≈ 17 is the answer.

Step-by-step explanation:

The value of solution of the equation is,

⇒ tan x = 1 / 3

We have to given that;

The expression is,

⇒ - 2 tan (-x) = 5 tan (x) - 1

Now,, We can simplify as;

⇒ - 2 tan (-x) = 5 tan (x) - 1

⇒ - 2 (-  tan (x) ) = 5 tan (x) - 1

⇒ 2 tan (x) = 5 tan (x) - 1

⇒ 5 tan x - 2 tan x = 1

⇒ 3 tan x = 1

⇒ tan x = 1 / 3

Thus, The value of solution of the equation is,

⇒ tan x = 1 / 3

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The value of Tan A + B is 6.009.

[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]

We have to solve for Tan B

[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]

[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]

= 6.009.

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The statement "Angle ∠AEC and ∠DEB are complementary angles" is false.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Angle ∠AEC and ∠DEB are supplementary angles because the sum is 180 degrees.

Thus, the given statement is false.

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Answer: G=36

Step-by-step explanation:

Step 1: Write out the equation
1/4g-3=6

Step 2: Add 3 to both sides
1/4g=9

Step 3: Divide both sides by 1/4, or 0.25
G=36

Answer:

x ≤ [tex]\sqrt[2]{2}[/tex]

Step-by-step explanation:

x² ≤ 8

[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]

x ≤ [tex]\sqrt[2]{2}[/tex]

Answer:

8.) is D

9.) is B

10.) is A

Step-by-step explanation:

mark brainliest

Answer: D, B, A

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, your answer will be +

[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]

[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]

If the signs are different, your answer will be -

[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]

[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]

If there is no sign in front of number, it is positive

8.

a. 18 / -9 = -2   negative because signs are diff

b. -35 / -7  +5   signs same so +

c.  -12 / -6 = +2          same signs so +

d. 70 / -10 = -7        diff signs so -

Order from least to greatest:

-7    -2   2   5

Answer: D

9.  Follow rules from above:

Be careful with fractions  1/5  is not the same as 5/1.

With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.

a.  +1/5

b.  -1/5

c.  +1/10

d.  +1/10

Order from least to greatest:

-1/5    1/5   1/10    1/10

Answer: B

10.

a. -2/3

b.  +1/25

c.  +3/25

d.  +1/50

The smallest number is the negative number

Answer A

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

We have,

The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.

From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.

Looking at the answer choices, we need to choose the data set that matches the histogram.

The first step is to check if the data set has the same range as the histogram.

The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.

Now,

The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.

The second answer choice has a range from 4 to 42, which matches the histogram.

We can check if the frequencies in the data set match the heights of the bars in the histogram.

For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.

The second data set has 4 passengers in the 11 to 20 interval, so it matches.

We can do the same for the other intervals and find that the second data set matches the histogram.

Therefore,

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

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The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

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Based on the information, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

standard error will be:

= 0.71 / ✓(195) = 0.051 kilograms

Substituting these values into the formula, we will then get:

Confidence interval = 3.04 ± (1.645) × (0.051)

Confidence interval = 3.04 ± 0.084

Confidence interval = (2.956, 3.124)

Therefore, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

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Answer:

B.

Step-by-step explanation:

We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:

10 = -16t^2 + 22t + 6

Rewriting the equation in standard quadratic form:

16t^2 - 22t + 4 = 0

Using the quadratic formula:

t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))

t = (22 ± sqrt(36))/32

t = 3/4 or 1/4

Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.

well, presumably the best deal is the cheaper one, so let's check how much is it for each

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 45.99}}{\left( \cfrac{15}{100} \right)45.99} ~~ \approx ~~ 6.90\hspace{5em}\underset{ Store~1 }{\stackrel{ 45.99~~ - ~~6.90 }{\approx\text{\LARGE 39.09}}}\checkmark \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em} \stackrel{\textit{20\% of 52.99}}{\left( \cfrac{20}{100} \right)52.99} ~~ \approx ~~ 10.60\hspace{4em}\underset{ Store~2 }{\stackrel{ 52.99~~ - ~~10.60 }{\approx\text{\LARGE 42.39}}}[/tex]

The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).

We have,

Let's assume that the barn wall is located on the south side of the rectangular plot, and the fencing is required on the remaining three sides (east, north, and west).

Let's denote the width of the plot as x and the length of the plot as y.

Then, the length of fencing required can be expressed as:

L = x + y + x/2

where x/2 is the length of the shared fencing with the neighbor.

The cost of fencing can be expressed as:

C = 24L

Substituting the value of L, we get:

C = 24(x + y + x/2)

Since the farmer is not willing to spend more than $6000, we have:

24(x + y + x/2) ≤ 6000

Simplifying this inequality, we get:

3x + 4y ≤ 500

Now, we need to maximize the area of the rectangular plot, which is given by:

A = xy

Using the inequality constraint, we can express y in terms of x as:

y ≤ (500 - 3x)/4

Substituting this value of y in the expression for A, we get:

A = x((500 - 3x)/4)

Simplifying this expression, we get:

A = (125/4)x - (3/4)x^2

To find the value of x that maximizes A, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 125/4 - (3/2)x = 0

Solving for x, we get:

x = 125/6

Substituting this value of x in the expression for y, we get:

y = (500 - 3(125/6))/4 = 125/3

Therefore,

The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).

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Step-by-step explanation:

5 (4x^8) ^(-1/2)    -   2 x^-3

p ^(1/2)

r ^5/3  

The length of each garden side is 4 ft.

Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.

Let s be the length of the side of the gardens,

Since, she need 3 gardens,

So,

3 × side² = 48

3s² = 48

s² = 16

s = 4

Hence, the length of each garden side is 4 ft.

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The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.

Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.

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