What is the image of the point (-3 , 14) after a counterclockwise rotation about the origin through an angle of 90 degrees?

the vertex of the quadratic  function is (4,-25).

A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is 2. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree two. It carries out algebraic functions.

examples of quadratic functions are:

f(x)=x²-8x-9

x-coordinate of vertex:

x=-b/2a

Putting the values, we get

x=-(-8)/2=4

Y-coordinate vertex:

y(4)=16-32-9=-16-9=-25

Vertex(4,-25)

Hence, the vertex of the function =(4,-25).

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We are given the following lengths:

We will solve it by using this formula:

[tex]\boxed{\mathfrak{\purple {Median = \frac{1}{2}(lower \: base+upper \: base)}}}[/tex]

[tex]\boxed{\mathcal{\purple { XY = \frac{1}{2}( CO+PY)}}}[/tex]

[tex] \green{ \sf4m + 3 = \frac{1}{2} (2m - 10 + 3m + 37)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{1}{2} (5m+ 27)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{5}{2} m + \frac{27}{2} }[/tex]

[tex] \red \implies \green{ \sf8m + 6 = 5m + 27 }[/tex]

[tex] \red \implies \green{ \sf8m + 6 - 5m = 27 }[/tex]

[tex] \red \implies \green{ \sf8m - 5m= 27 - 6 }[/tex]

[tex] \red \implies \green{ \sf3m = 21 }[/tex]

[tex] \boxed{ \mathfrak{ \red{m = 7}}}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4m + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4(7) + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =28 + 3}[/tex]

[tex] \boxed{ \underline{ \underline{ \blue \longmapsto \orange{ \tt \: XY =31}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2m - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2(7) - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 14 - 10}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:CO=4}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3m + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3(7) + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 21 + 37}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:PY=58}}}}[/tex]

Answer:

[tex]\textsf{16.}\quad m = 7[/tex]

[tex]\textsf{17.} \quad \overline{XY}=31[/tex]

[tex]\textsf{18.} \quad \overline{CO}=4[/tex]

[tex]\textsf{19.} \quad \overline{PY}=58[/tex]

[tex]\textsf{20.} \quad \overline{EV}=80.5\; \sf meters[/tex]

Step-by-step explanation:

The median of a trapezoid is the line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases, and its length is equal to the average of the lengths of the two bases.

Given line segments:

    [tex]\bullet \quad \overline{CO}=2m-10[/tex]

    [tex]\bullet \quad \overline{PY}=3m+37[/tex]

    [tex]\bullet \quad \overline{XY}=4m+3[/tex]

As the length of the median XY is equal to the average of the lengths of the two bases we can set up the following equation:

[tex]\overline{XY}=\dfrac{\overline{CO}+\overline{PY}}{2}[/tex]

Substitute the expressions for each line segment into the equation and solve for m:

[tex]\begin{aligned}4m+3&=\dfrac{(2m-10)+(3m+37)}{2}\\2(4m+3)&=(2m-10)+(3m+37)\\8m+6&=5m+27\\8m+6-5m&=5m+27-5m\\3m+6&=27\\3m+6-6&=27-6\\3m&=21\\3m \div 3&=21 \div 3\\m&=7\end{aligned}[/tex]

Therefore, the value of m is 7.

Now we have calculated the value of m, simply substitute this value into each line segment expression to determine their measures:

[tex]\begin{aligned} \overline{XY}&=4m+3\\&=4(7)+3\\&=28+3\\&=31\end{aligned}[/tex]

[tex]\begin{aligned} \overline{CO}&=2m-10\\&=2(7)-10\\&=14-10\\&=4\end{aligned}[/tex]

[tex]\begin{aligned} \overline{PY}&=3m+37\\&=3(7)+37\\&=21+37\\&=58\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The length of the median of a trapezoid is equal to the average of the lengths of the two bases.  

Given the bases of trapezoid LOVE are LO and EV, and the median is XY, we can set up the following equation:

[tex]\overline{XY}=\dfrac{\overline{LO}+\overline{EV}}{2}[/tex]

Given line segments:

    [tex]\bullet \quad \overline{LO} = 48.5[/tex]

    [tex]\bullet \quad \overline{XY} = 64.5[/tex]

To find the measure of the lower base EV, substitute the given values of the line segments into the equation and solve for EV:

[tex]\begin{aligned}\overline{XY}&=\dfrac{\overline{LO}+\overline{EV}}{2}\\\\64.5&=\dfrac{48.5+\overline{EV}}{2}\\\\2(64.5)&=48.5+\overline{EV}\\\\129&=48.5+\overline{EV}\\\\129-48.5&=48.5+\overline{EV}-48.5\\\\\overline{EV}&=80.5\end{aligned}[/tex]

Therefore, the measure of the lower base EV is 80.5 meters.

The Answer for the given functions are:

i) f(-3) = -14.

ii) g[f(0)] = -16.

iii) f[h(2)] = 13.

iv)  hᴏf(x) = 3x - 1.

v)  h-1(1) = -3.

Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.

i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:

f(-3) = 3(-3) - 5 = -9 - 5 = -14

Therefοre, f(-3) = -14.

ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):

f(0) = 3(0) - 5 = -5

g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16

Therefοre, g[f(0)] = -16.

iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):

h(2) = 2 + 4 = 6

f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13

Therefοre, f[h(2)] = 13.

iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:

hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1

Therefοre, hᴏf(x) = 3x - 1.

v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:

h(x) = x + 4 = 1

Subtracting 4 frοm bοth sides, we get:

x = 1 - 4 = -3

Therefοre, h-1(1) = -3.

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Step-by-step explanation:

the answer will be 1272.7cm3

the formula of the volume of the cylinder is pie×radius squared×height so,

we will get the radius and the radius is half of the diameter and the diameter is 9 so 9÷2=4.5 and then it will be squared so it will be 20.25cm2 and so we will write it this way

3.14×20.25×20=1271.7cm3

hope this helped

xoxo adham

By  inverse proportions, 6.4 is the value of y .

What are some examples of inverse proportions?

In the case of two quantities that are inversely proportional, one quantity falls as the other rises. The number of hours needed to construct a wall serves as an illustration of inverse proportion. The time required to build a wall decreases as more people work on the same project.

 suppose that y =√kx

 enter (0.25,16) to y =√kx

    0.5k = 16

      k = 5

   y = 8√x

  when x = 0.64

  y = 8√0.64

 y = 6.4

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The correct function that expresses the town's population after n decades is: p(n) = 8000 × 2ⁿ. So the initial population of the town is 8,000, which is consistent with the problem statement.

A function is a mathematical concept that describes the relationship between a set of inputs, called the domain, and a set of outputs, called the range.

A function assigns a unique output to each input, meaning that for a given input, there is only one possible output.

Starting with a population of 8,000, the population doubles every decade, which means it multiplies by 2.

After n decades, the population will have doubled n times, so we can express the population as 8,000 multiplied by 2 raised to the power of n:

p(n) = 8000 × 2ⁿ

This function gives us the population of the town after n decades, where n is a non-negative integer. If we substitute n=0 into the function, we get:

p(0) = 8000 × 2⁰ = 8000

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Answer:

In each statement:

The rate is the percentage or ratio that relates the quantity being described to the base.

The base is the total quantity or amount that the rate is applied to.

The percent is the rate expressed as a percentage, or the part of the base that corresponds to the rate.

Answer: 5.6 kilograms.

Step-by-step explanation:

We know that 1,000 paperclips have a mass of 1 kilogram.

Therefore, one paperclip has a mass of 1/1000 kilograms, or 0.001 kilograms.

To find out how many kilograms 5,600 paperclips have, we can multiply the mass of one paperclip (0.001 kilograms) by the number of paperclips:

0.001 kilograms/paperclip * 5,600 paperclips = 5.6 kilograms

Therefore, 5,600 paperclips have a mass of 5.6 kilograms.

Answer: 9 3/10

Step-by-step explanation:

6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1  3/10= 8 + 1 + 3/10= 9 3/10

Answer:

B.......................

The area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

the angle of the sector = 70°

the radius = 8 ft

hence the area of the sector is calculated as follows:

(70°/360°) × 22/7 × 8 in × 8 in

we simplify by division and multiplication

1/36 × 22 × 64 in²

352 in²/9

39.1111 in²

Therefore, the area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.

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As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

Length, which is typically expressed in units like meters, feet, or inches, is a measurement of an object's size or the separation between two locations. It alludes to the measurement of an object's longest dimension or the separation between two ends. The term "length" can also be used to describe the extent of a line or the linear separation between two locations, such as the length of a triangle's side, a road, or a length of rope. In geometry, length is a crucial mathematical notion that is used to gauge an object's size, shape, and location.

given

The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. Here are the facts:

60° sine + (BC/AB)

Using sin 60°, whose value is 3/2, as an example:

√3/2 = (BC/AB)

Multiplying AB by both sides:

BC = AB * √3/2

The hypotenuse's length is determined by adding the squares of the lengths of the other two edges. Here are the facts:

We have the following by substituting the earlier-obtained formulas for AC and BC:

Adding 3 to both sides:

4AB2 + 9AB2 = 12AB2

AB = 3x

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

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Answer: D. $722

Step-by-step explanation:

$2,000 - $375 (initial airfare cost which will only be once)

= 1,625

7 x 129 = 903 (cost of the 7 nights in a hotel)

1,625 - 903 = 722

$722 left for the trip

The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.

An equilateral triangle is a type of triangle where all three sides have the same length, and all three angles are equal to 60 degrees.

The formula for the height of an equilateral triangle is given by

Where 'a' is the equal side of the equilateral  

In the given problem we use the height of the triangle to calculate the side of the triangle tenth.

Here we have  

The height of the tent is 5 ft which is the height of the equilateral triangle  

As we know,

Height of equilateral triangle =  ½(√3a)

Let 'a' be the side of the triangle tent

=> 5 ft = ½(√3a)

Multiply by 2 on both sides

=> 5 × 2 = 2(1/2)√3a

=> √3a = 10

=> (1.732) a = 10    [ ∵ √3  1.732 ]  

=> a = 5.8  

Therefore,

The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.

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Answer:

$6235 1

' 1 . ' 8

Answer:

Step-by-step explanation:

The population in the year 2100 will be approximately 18.8 billion.

Determine exponential equation

The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)[tex]^t[/tex], where P(t) is the population in billions and t is the number of years after 2022.

To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.

We can use the formula for exponential growth, P(t) = P0(1 + r[tex])^t[/tex]where P0 is the initial population, r is the growth rate, and t is the number of years.

Substituting the values for [tex]P_0[/tex]and r into the equation, we get:

P(t) = 8(1.011[tex])^t[/tex]

2100-2022=78

This equation can be used to find the population after t years.

For example, to find the population after 5 years, we can substitute t = 78 into the equation and get:

P(5) = 8(1.011[tex])^78[/tex] ≈ 18.8 billion

Therefore, the population in year  2100 will be approximately 18.8 billion.

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The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

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Answer:

Step-by-step explanation:

The corresponding equal angles must be written in the same order. So the first one is the correct answer.

The binary number 1001100 is equivalent to the decimal number 76.

HOW TO CONVERT BINARY TO DECIMAL?

To convert a number in base 2 (binary) to base 10 (decimal), we need to multiply each digit of the binary number with its corresponding power of 2 and then sum up the results. The rightmost digit corresponds to 2, the next digit to 2 the next to 2², and so on, with each successive digit corresponding to the next higher power of 2.

For example, to convert the binary number 1001100 to decimal, we would start by multiplying the rightmost digit (0) by 2 raise the power 0, which equals 1. We would then multiply the next digit (0) by 2 raise the power 1, which equals 0, and so on, until we reach the leftmost digit (1), which corresponds to 2 raise the power 6. We then add up all of these products to get the decimal equivalent of the binary number.

So, using this method, we have:

1 x 2⁶ + 0 x 2⁵ + 0 x 2⁴ + 1 x 2³+ 1 x 2² + 0 x 2¹ + 0 x 2°= 64 + 0 + 0 + 8 + 4 + 0 + 0 = 76

Therefore, the binary number 1001100 is equivalent to the decimal number 76.

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Answer:

24328.49 cm

Step-by-step explanation:

as (A = π r²). r is 88 so and is 24328.49cm

Answer:

55K+60K+65K=184K

100% - 8.25%=91.75%

184000x91.75%=168820

Ans:168K

Answer:

Step-by-step explanation:

To determine the value of the offer today, we need to calculate the present value of all the cash flows using a discount rate of 8.25%.

First, let's calculate the present value of the salary payments.

PV(year 1 salary) = R55 000 / (1 + 0.0825)^1 = R50 760.87

PV(year 2 salary) = R60 000 / (1 + 0.0825)^2 = R51 423.95

PV(year 3 salary) = R65 000 / (1 + 0.0825)^3 = R52 110.69

Next, let's calculate the present value of the starting bonus.

PV(starting bonus) = R4 500 / (1 + 0.0825)^0 = R4 500

Finally, we can add up all the present values to find the total present value of the offer:

PV(total offer) = PV(year 1 salary) + PV(year 2 salary) + PV(year 3 salary) + PV(starting bonus)

PV(total offer) = R50 760.87 + R51 423.95 + R52 110.69 + R4 500

PV(total offer) = R158 795.51

Therefore, the offer is worth R158 795.51 to you today at a discount rate of 8.25%.

Answer:

Height = 630 / (14 x 0.9) = 47.5 cm

f(x) = [tex]x^{2}[/tex] -> f(x) = [tex]x^2[/tex] - 18 (translation) -> f(x) = [tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x (vertical stretching)

To transform the function f(x) =[tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18, we need to apply a series of transformations. Here are the steps:

Translation: We need to shift the graph of f(x) = [tex]x^{2}[/tex] down by 18 units to obtain f(x) = [tex]x^{2}[/tex] - 18. This can be done by subtracting 18 from the function, which results in f(x) = [tex]x^2[/tex]- 18.

Horizontal translation: Next, we need to shift the graph of f(x) = [tex]x^{2}[/tex] - 18 to the right by 3 units to obtain f(x) =[tex](x-3)^2[/tex] - 18. This can be done by replacing x with (x-3) in the function, which results in f(x) =[tex](x-3)^2[/tex]- 18.

Vertical stretching: Finally, we need to vertically stretch the graph of f(x) = [tex](x-3)^2[/tex] - 18 by a factor of -6 to obtain f(x) = [tex](x-3)^2[/tex] - 6x + 18. This can be done by multiplying the function by -6, which results in f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x.

So, the series of transformations required to transform f(x) = [tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18 is:

f(x) = [tex]x^{2}[/tex] -> f(x) =[tex]x^{2}[/tex] - 18 (translation) -> f(x) =[tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex]+ 18 - 6x (vertical stretching)

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Elijah's total earnings for the week if he made x dollars in sales would be: $500 + 0.3x.

What is sale?

A sale is an event or activity in which goods or services are sold at a reduced or discounted price.

What is discount?

A discount is a reduction in the price of an item or service. It is often offered as a promotion or incentive to encourage customers to buy or use a product or service.

Total sales commission earned by Elijah for selling $775 worth of clothing:

30% of $775 = 0.3 x $775 = $232.50

Therefore, Elijah's total earnings for the week would be:

$500 (guaranteed salary) + $232.50 (commission) = $732.50

For selling x dollars worth of clothing, the commission earned by Elijah would be:

0.3x

Therefore, Elijah's total earnings for the week if he made x dollars in sales would be:

$500 (guaranteed salary) + 0.3x (commission) = $500 + 0.3x

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by simplifying the expression, option d ,sec θ is the correct answer.

how can we solve this expression?

We can simplify the given expression as follows:

(tan θ - [tex]sec^2[/tex] θ) / tan θ

= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,

by diving it by tan θ

= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),

since sec = 1/cos and tan=sin/cos

placing the value in expression and solving it , we get

= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))

= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ

= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)

We can simplify the given expression as follows:

= cos θ ( [tex]cos^2[/tex]θ -  [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)

= cos θ (cos θ / [tex]cos^2[/tex]θ)

= 1/cos θ is equal to sec θ

Therefore, the simplified expression is sec θ.

Hence, the answer is option (d) sec θ.

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Answer:

Step-by-step explanation:

ex  2

        4444

2

 4444

Yes, that's correct I even tried to show you.

The 2 is the bags of candy

4 pieces of candy per bag

equals to 8 in total

With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.

The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.

The correct option is A.

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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?

Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of

no difference between the triglyceride test levels.