Find the rectangular equation for the plane curve defined by the parametric equation

x=t+4, y=t^2

-infinity < t < infinity

Step-by-step explanation:

this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

length² = 9² + 12² = 81 + 144 = 225

length = sqrt(225) = 15 ft

Answer:  x + 8

Step-by-step explanation:

[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]

A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.

In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.

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The mapping of the function f of g(x) will result to 41

A function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.

By mapping of the functions f and g defined as;

f : x » x + 5 and g : x » 8x

then;

f of g(x) = f of 8(4.5)

f of g(x) = f of 36

f of g(x) = 36 + 5

f of g(x) = 41

Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.

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to be honest ion even know

Answer: 200 Meters

Step-by-step explanation:

Answer:

Domain: {0 \leq x} Range {0 \leq y}

Step-by-step explanation:

btw \leq means less than or equal to

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

What is the similarity test of two triangles?

If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.

In the given figures,  the length of side AB is equal to the length of side DE.

                        Side AB = Side DE ----------(I)

Similarly, the length of side BC is equal to the length of side EF.

                        Side BC = Side EF ----------(II)

And the measure of angle  ABC is equal to the measure of angle DEF.

                              ∠ ABC = ∠ DEF -------(III)

From (I), (II), and (III), and by using the SAS test we can say that

                               ΔABC ~ ΔDEF    ----------- SAS test

Hence,

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

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a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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The 10 forms 1/8 can be written is as follows;

A fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction.

A denominator is the lower value of a fraction.

1 over 8 can be written in the following ways;

1/8

1 ÷ 8

1/2³

= 1 / 2×2×2

= 1/8

1/√64

= 1/8

[tex]{8}^{ - 1} [/tex]

= 1/8

1 : 8

= 1/8

[tex]{√64}^{ - 1} [/tex]

= 1/√64

= 1/8

[tex]{2}^{ - 3} [/tex]

= 1/2³

= 1/8

2/16

= 1/8

4 : 32

= 4/32

= 1/8

In conclusion, 1/8 can be written in different forms including using square root and ratios.

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Answer:

12.85

Step-by-step explanation:

hope it helps, pls lmk if it is wrong in comments!

Answer:

12.85

Step-by-step explanation:

64.25÷5

Answer:

Mr. Carson drove 39 more miles in April than in May

Step-by-step explanation:

1027-988=39

Answer:

The cat is at at  8 north 6 west

Step-by-step explanation:

The cat ran a total of 14 meters

Answer:

x = 2

Step-by-step explanation:

For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.

Hope this helps!

The linear function for the situation is :-

Amount at the end of 3 years = Original investment + original investment*Rate*Time/100

It is given in the question that:-

Investment of George's friend in startup company = $ 500.

Interest percent = 8 %

Time period of investment = 3 years

We have to find the linear function for this situation.

As this interest is on original investment, the interest will be simple.

Hence,

The linear function for the situation will be :-

Amount at the end of 3 years= Original investment + original investment*Rate*Time/100

Amount at the end of 3 years = 500 +  500*8*3/100 = 500 + 120 = $ 620

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Answer: hours

Step-by-step explanation:

minutes would be way too many

seconds - just self explanatory

days- would be less than one

hours is the only possible solution

Answer:4/5 : 1/3=4/5 x 3/1=12/5

Step-by-step explanation:

Answer:

12/5

Step-by-step explanation:

If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5

was it helpful?

The equation of line q is  y = x/10 - 9/10.

What is equation of straight line?

   A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.

Here the given line P,

=> y+5=-10(x+2)

=> y+5=-10x-20

=> y = -10x-25

Here in the given line y=mx+c , where m=slope. Then,

=> Slope of line P = -10.

Here line P is perpendicular to line q.

Then, slope of line q = -1/ slope of line p = -1/-10 = 1/10

Now the line passes through the point [tex](x_1,y_1)=(-1,-1)[/tex] then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+1 = 1/10 (x+1)

=> 10y+10 = x+1

=> 10y=x-9

=> y = x/10 - 9/10.

Hence the equation of the line q is  y = x/10 - 9/10.

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Answer:

Given

Distributive Property

Addition Property of Equality

Division Property of Equality

Step-by-step explanation:

Frist you distribute the -2 by multiplying it to everything in the parentheses.  Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4

Answer:

6/7

Step-by-step explanation:

2÷3/7=2*3/7

6/7

The sale price including tax for the refrigerator is $520.

From the information, the following can be deduced:

Refrigerator = $595

Discount = 20%

Tax = 9.25%

The sales price will be:

= Refrigerator price + Tax - Discount

= $595 + (9.25% × $595) - (20% × 650)

= $595 + $55 - $130

= $520

The price is $520.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]

[tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]

[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]

Similarly,

[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]

[tex] \textsf{GCD = 2 × 3 = 6 } [/tex]

[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]

[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]

[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]

[tex] \textsf{GCD = 2 × 2 = 4 } [/tex]

[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]

Answer:

Numbers are : 36, 3, 12

36 = 2 × 2 × 2 × 2 × 2 × 1

3 = 3 × 1

12 = 2 × 2 × 3

HCF = product of total common factors of all three numbers, i.e : 2

LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96

Similarly,

2. Numbers are : 6, 54, 12

6 = 2 × 3

54 = 2 × 3 × 3 × 3

12 = 2 × 2 × 3

GCD = 2 × 3 = 6

[ 2 and 3 are the only ones common among all three ]

LCM = 2² × 3³ = 4 × 27 = 108

3. Numbers are : 16, 8, 12

16 = 2 × 2 × 2 × 2

8 = 2 × 2 × 2

12 = 2 × 2 × 3

GCD = 2 × 2 = 4

LCM = 2⁴ × 3 = 16 × 3 = 48

The rate of change of the linear functions given in tabular form and equations are found as follows;

1. a. The rate of change of the function is 5

b. The rate of change of the function is 7

c. The rate of then function is 0.75

d. The function has a rate of change of -8

2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values

b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days

c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day

The rate of change of a function is a measure of how much the output changes per unit change in the input.

1. The rate of change of the functions are as follows;

a. The first difference of the y-values is constant, therefore the function is a linear function

The formula for the rate of change of the linear function is presented as follows;

[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]

The rate of change of the function is therefore;

b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]

c. The function is a linear function, as the first difference is constant and equal to 0.75

The rate of change of the function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]

d. The first difference is constant and equal to -8

The rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]

2. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function

The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4

The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units

b. When the number of antibodies is 360, we have;

360 = 20·d + 100

20·d = 360 - 100 = 260

d = 260 ÷ 20 = 13

c. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.

3. The function that gives the amount of antibodies in the body is a = 20·d + 100

d = The number of days

a = The number of antibodies

a. The table is completed as follows;

Data for Medicine A

d    [tex]{}[/tex]                  a

0    [tex]{}[/tex]                  100

1    [tex]{}[/tex]                   120

2    [tex]{}[/tex]                  140

3    [tex]{}[/tex]                  160

4    [tex]{}[/tex]                  180

5    [tex]{}[/tex]                  200

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The number of touchdowns is 4.

The number of extra-point kicks is 4.

and the number of field goals is 2.

What are linear equations in three variables?

If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.

How to solve the system of linear equations in three variables?

Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.

Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".

Total points scored in game = 20+14 =34

Now,

According to the given question,

                                6x + y + 3z = 34 -----------(I)

                                x = y ----------(II)

                                x = 2z

                                z = [tex]\frac{x}{2}[/tex] -----------(III)

Putting the values of "y" and "z" in equation (I), we get

                              6x + x + 3×[tex]\frac{x}{2}[/tex] = 34

                               [tex]\frac{17x}{2}[/tex] = 34

                               x = 4

Now, putting the value of "x" in equations (II) and (III), we get

                               y = 4.

                               z = 2.

Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.

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The 98% confidence interval limits are given by 1.6 < μ < 33.7.

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain confidence level, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

Given data: 10, 32, 24, 0, 5, 27, 5, 50, 6.

Sample mean = ∑x/n = 159/9 = 17.66

Sample variance = s² = ∑(x - sample mean)²/n-1

                                   = 2206/8

                                   =  275.75

Sample standard deviation = s = [tex]\sqrt{s^2}[/tex]

                                                    = [tex]\sqrt{275.75}[/tex]

                                                    = 16.60

Significance level = α = 1 - 0.98 = 0.02

Degree of freedom (d.f.) = n - 1 = 9 - 1 = 8

Critical value = [tex]t_{{\frac{\alpha}{2}},d.f}[/tex]

                      = 2.896

Margin of error = E = critical value * [tex]\frac{s}{\sqrt{n} }[/tex]

                                = 16.03

Limits of 98% confidence level are given by:

Lower limit = sample mean - E = 17.66 - 16.03 ≈ 1.6

Upper limit = sample mean + E = 17.66 + 16.03 ≈ 33.7.

Hence, the 98% confidence interval limits are given by 1.6 < μ < 33.7.

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Answer: a.) 397.5 b.) 1.3333

Step-by-step explanation:

1 cent = £0.75

530 x 0.75 = 397.5

530 / 397.5 = 1.3333

Hope this helped please thank and rate!!

It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.

a) Given equation

h(t) = v₀t - 16t^2

Substitute v₀ = 40, h(t) = 0 in the given equation

40t - 16t^2 = 0

Solve for t

⇒ 16t^2 = 40t

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Hence, water will take 2.5 seconds to hit the nozzle on the way down.

b) The function that represents the given condition

h(t) = -16t^2 + 40t + 5

The maximum value of the function is the y-coordinate of the vertex.

The x-coordinate of the vertex

= -40/2(-16) = 5/4

Find the y-coordinate of the vertex by substituting t = 5/4

⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5

⇒ h(5/4) = -25 + 50 + 5

⇒ h(5/4) = 30

Hence, the maximum height of the water is 30 ft.

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Answer:

x is 70°

hopefully this will help u

By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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