Find the value of X. Round to the nearest tenth

Answer:

f(-1)= -3

Step-by-step explanation:

We all know f(x) = y

Since x= -1, y= -3 as per given in the graph, so

f(-1)=-3

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

The answer is 4 1/2

Step-by-step explanation:

Because A to C is 2 1/4 so all you have to do add 2 1/4 + 2 1/4 which will equal 4 1/2

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Answer:

C. (0, -6).

Step-by-step explanation:

In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.

In this instance:

y = 4x - 6

The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).

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The y-intercept can also be solved for by substituting in 0 for x:

y = 4(0) - 6

y = 0 - 6

y = -6.

Answer:

C. (0, –6)

Step-by-step explanation:

y = 4x - 6

The equation is:

y = mx + b

where b is the y-intercept.

In this case, - 6 is the vertical intercept.

Do not confuse from (-6, 0) because that represents an x-intercept.

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Answer:

\(\sf 1. \quad \dfrac{3}{8}\)

\(\sf 2. \quad \dfrac{7}{24}\)

Step-by-step explanation:

Spinner 1 is divided into 6 congruent sections.

There are 3 red sections, 2 blue sections and 1 yellow section.

Therefore, the probability of spinning each of the three colors is:

    \(\bullet \quad \sf P(R_1)=\dfrac{3}{6}=\dfrac{1}{2}\)

    \(\bullet \quad \sf P(B_1)=\dfrac{2}{6}=\dfrac{1}{3}\)

    \(\bullet \quad \sf P(Y_1)=\dfrac{1}{6}\)

Spinner 2 is divided into 3 sections of differing sizes.

The red section is half of the spinner. The blue and yellow sections are quarters of the spinner.

Therefore, the probability of spinning each of the three colors is:

    \(\bullet \quad \sf P(R_2)=\dfrac{1}{2}\)

    \(\bullet \quad \sf P(B_2)=\dfrac{1}{4}\)

    \(\bullet \quad \sf P(Y_2)=\dfrac{1}{4}\)

If each spinner is spun once, then:

The probability that both spinners both show red is:

\(\sf P(R_1)\;and\;P(R_2)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}\)

The probability that both spinners both show blue is:

\(\sf P(B_1)\;and\;P(B_2)=\dfrac{1}{3} \times \dfrac{1}{4}=\dfrac{1}{12}\)

The probability that both spinners both show yellow is:

\(\sf P(Y_1)\;and\;P(Y_2)=\dfrac{1}{6} \times \dfrac{1}{4}=\dfrac{1}{24}\)

Therefore, the probability that both spinners show the same colour is:

\(\sf P(R_1\;\&\;R_2)\;or\;P(B_1\;\&\;B_2)\;or\;P(Y_1\;\&\;Y_2)=\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{24}=\dfrac{9}{24}=\dfrac{3}{8}\)

If each spinner is spun once, the probability of getting a red from spinner 1 and a blue from spinner 2 is:

\(\sf P(R_1)\;and\;P(B_2)=\dfrac{1}{2} \times \dfrac{1}{4}=\dfrac{1}{8}\)

The probability of getting a blue from spinner 1 and a red from spinner 2 is:

\(\sf P(B_1)\;and\;P(R_2)=\dfrac{1}{3} \times \dfrac{1}{2}=\dfrac{1}{6}\)

Therefore, the probability of getting a red-blue combination is:

\(\sf P(R_1\;\&\;B_2)\;or\;P(B_1\;\&\;R_2)=\dfrac{1}{8}+\dfrac{1}{6}=\dfrac{7}{24}\)

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Answer:

b = 3

Step-by-step explanation:

Answer:

The Greatest Common Factor, the GCF, is the biggest ("greatest") number that will divide into (that is, the largest number that is a factor of) both 2940 and 3150. On the other hand, the Least Common Multiple, the LCM, is the smallest ("least") number that both 2940 and 3150 will divide into.

Have a good day

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

Cylinder

Step-by-step explanation:

Area of rectangular prism = base area * height

                                           = 50 * 5

                                           = 250 square cm

Area of cylinder = base area * height

                          = 50 * 5

                           = 250 square cm

Solution:

Given that;

The amount of 5th and 6th graders is normally distributed with a mean of 4 inches and standard deviation of 1 inch.

To find the percentage of 5th and 6th graders that grows between 1 and 3 inches, we will apply the z score formula

Where, x = 1 inch

Where, x = 3 inches

Using the z score table,

For the 6th graders, the percentage is the same as the percentage of the 5th graders.

The percentage of the 6th graders is

The percentage of 5th and 6th graders that grows between 1 and 3 inches will be

Since, they have different peaks, it is not appropriate to use normal distribution.

Hence, the answer is A

The solutions associated with the final matrices representing a system of linear equations are listed below:

First case: x = 3, y = 1, z = 8

Second case: No solution

Third case: No solution

In this problem we find three of final matrices, each of them representing a system of linear equations. There are two rules to be considered:

Now we proceed to determine the solution associated with each matrix:

First matrix:

x = 3, y = 1, z = 8

Second matrix:

No solution

Third matrix:

No solution

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Step-by-step explanation:

For the left matrix, since the matrix is already in reduced row form,

The solutions to the matrix is (3,-1,8)

For the middle matrix, we need to convert the -6 to a zero,

notice how in the third row, every entry except the last one is 0, this implies that

0=-2, which is not the case thus the middle matrix has no solution.

For the last one, notice that we have 3 colums but only two non zero rows, this means that this matrix has infinite solutions.

Answer:

95% = Within two standard deviations from the mean

99.7% = Within three standard deviations from the mean

68% = Within one standard deviation from the mean

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks" to help me out!

Step-by-step explanation:

volume = π · r^2 · h

volume = π · 3^2 · 5

volume = π · 9 · 5

volume = π · 45

Answer : 45π

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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The person who gets to say the last number, 1000, will be Person 6.

Here, we have,

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

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complete question:

10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number

Answer:

No solution

Step-by-step explanation:

3 x + 6 = − 6+ 3 x

Move all terms containing  'x ' to the left side of the equation.

'6 = − 6 ' Since  '6 ≠ − 6' , there are no solutions.

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Work Shown:

9+15 = 24 students total

9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

Answer:

x=112

Step-by-step explanation:

First, let's get all of the fractions to a common denominator.

Based on the numbers given (8,56, and 7), let's make all of the denominators be 56

for \(\frac{-7}{8} x\), multiply the numerator and denominator by 7.

\(\frac{-7x}{8}\)×\(\frac{7}{7}\)= \(\frac{-49}{56} x\)

we can leave \(\frac{-5}{56}x\) as it is

and for \(\frac{1}{7} x\), we cam multiply the numerator and denominator by 8

\(\frac{1x}{7}\)×\(\frac{8}{8}\)=\(\frac{8x}{56}\)

Here's the equation now:

\(\frac{-49x}{56}\)-\(\frac{5x}{56}\)+\(\frac{8x}{56}\)=-92

now simlify the fractions

numerators:

-49x-5x+8x=-46x

here's the fraction now:

\(\frac{-46x}{56}\)=-92

We can simplify the fraction by 2 so it's \(\frac{-23x}{28}\)

\(\frac{-23x}{28}\)=-92

now multiply both sides by \(\frac{28}{-23}\), which is the reciprocal of \(\frac{-23}{28}\) (to isolate the variable)

\(\frac{28}{-23}\)×\(\frac{-23x}{28}\)=-92×\(\frac{28}{-23}\)

\(\frac{-92*28}{-23}\)

x=112

Hope this helps!

Answer:

x = 112

Step-by-step explanation:

The common denominator is 56 because 8*7 is 56

\(-\frac{7*7*x}{8*7} -\frac{5*x}{56}+\frac{8*x}{56} = - 92 \\-\frac{49*x}{56} -\frac{5*x}{56}+\frac{8*x}{56} = - 92 \\\frac{-46*x}{56}=-92\)

Multiply both sides by 56

-46*x = -92 * 56

-46*x = -5152

Divide by - 46

x = -5152/-46

x = 112

Answer:

Let x be the total number of children in the class.

Two–thirds of the children in the fourth–grade class are girls, and there are 12 girls so that

(2/3)x = 12

x = 12/(2/3)

  = 12(3/2)

  = 18.

The total number of children in the class is 18.

Step-by-step explanation:

Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

Answer:

Slope Intercept Form

Step-by-step explanation:

its the basics

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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