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Part 1
A car moving at a constant speed passed a timing device at tequals
0.
After 9

​seconds, the car has traveled 828

ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.

A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts.

Image search results for The x-intercepts of two parabolas are the same (one positive and one negative). The maximum or minimum of the first is twice the maximum or minimum of the other. Draw these parabolas using the same coordinate grid (with at least 3 points) “-15” “-10” “-10” “-15” 10

The x-intercepts are the spots where the parabola contacts the x-axis. A parabola can have two, one, or no real x intercepts. A parabola might have two x-intercepts, one x-intercept, or none at all.

X-intercepts, or zeros, are the places where a parabola (or any curve) crosses/touches the x-axis. As we’ll see later, the amount that determined

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Answer:

VU = 15, SU = 21.21 or 15[tex]\sqrt{2}[/tex], TV = 21.21 or 15[tex]\sqrt{2}[/tex], and SW = 10.6 or [tex]\frac{15\sqrt{2} }{2}[/tex].

Step-by-step explanation:

VU = 15 by the properties of a square.

To find SU and TV we need to use the rule: the diagonal for a square of side length s is: (√2)s

Then the diagonals for our square are: TV = SU = (√2)*15 = 21.2

SW is just the diagonal divided by 2, so SW = 10.6

The other answers are in radical form, but you can put either the number or radical version.

The range is the set of all real numbers greater than zero.

It is clear that from the figure the exponential function never become zero and it is always positive.

The range is the set of all real numbers greater than zero.  


Real numbers are used to measure quantities that change over time, such as size and time.. They are distinguished from imaginary numbers by the word real, which involves the symbol I or Square root of 1.

Complex numbers. Positive and negative integers are included in the real numbers. an exponential function is a relationship of the form
y = axes, with the independent variable x ranging across the entire real  number line as the exponent of a positive number.

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20 number of students are interested in sports in the class.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. The number is multiplied by 80 and then divided by 100. To demonstrate, consider the following formula:

(Number 80) 100 = Solution

Method No. 2

You shift the decimal point in 80.00 two places to the left, then multiply by your number. As a result, the formula is:

Number 0.8 = Solution

25×0.8= 20

The first approach is useful for learning how to get 80% of a number. When you understand how, the second technique is faster to implement.

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The differentiation of the given function is [tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function, [tex]y = \left(\frac{e^{4x}}{x^7}\right)[/tex], we need to differentiate the given function,

[tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)[/tex]

Applying quotient rule,

[tex]\quad \left(\frac{f}{g}\right)^'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]

[tex]=\frac{\frac{d}{dx}\left(e^{4x}\right)x^7-\frac{d}{dx}\left(x^7\right)e^{4x}}{\left(x^7\right)^2}[/tex]

[tex]=\frac{e^{4x}\cdot \:4x^7-7x^6e^{4x}}{\left(x^7\right)^2}[/tex]

[tex]=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

Hence, the differentiation of the given function is [tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

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When a number is divided by 4, the available remainders are 0, 1, 2, and 3. A number divided by 4 has a residue as a result.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

It may exceed or fall short of the quotient. For instance, the result of 41 divided by 7 is 5 and the remaining is 6.

Division of Euclid Given positive integers a and b, the lemma or Euclid division procedure claims that there are unique integers q and r satisfying

a = bq + r, 0 ≤ r < b.

By Euclid's division lemma

If we divide any number a by 4 we get

a= 4q + r where 0 ≤ r < 4

So, the value of r can be  0, 1, 2, 3

So, when a number is divided by 4, the available remainders are 0, 1, 2, and 3.

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Answer:

Step-by-step explanation:

P(x) is a statement about the square root of x squared equaling the absolute value of x.

Q(x) is a statement about x minus 1 equaling 3. Solving this equation for x we get x = 4.

R(x, y) is a statement about x plus y equaling 0. This is a linear equation and it has infinitely many solutions for x and y as long as x + y = 0.

T(x, y) is a statement about x + y equaling y. This equation is not possible because it will always result in x = 0, y = 0 and thus no solution.

It is important to note that the statement T(x, y) is not a valid equation, it is a contradiction and therefore it has no solution.

Answer:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

The equations that are not equivalent to "6x = 20" are "6x ÷ 6 = 20 ÷ 6," "6x + 5 = 20 + 5," "6x − 1 = 20 − 1," and "6x × 6 = 20 × 20."

Let's evaluate each equation to see if they are equivalent to "6x = 20":

6x ÷ 6 = 20 ÷ 6:

Dividing both sides of the equation by 6 gives us "x = 20/6" or "x = 10/3." This equation is not equivalent to "6x = 20."

6x ÷ 6 = 20 ÷ 20:

Dividing both sides of the equation by 6 gives us "x = 20/6" or "x = 10/3." Then, dividing both sides of the equation by 20 gives us "x = 1."

This equation is equivalent to "6x = 20" since both sides simplify to the same value.

6x + 5 = 20 + 5:

Adding 5 to both sides of the equation gives us "6x + 5 = 25." This equation is not equivalent to "6x = 20."

6x − 1 = 20 − 1:

Subtracting 1 from both sides of the equation gives us "6x − 1 = 19."

This equation is not equivalent to "6x = 20."

6x × 6 = 20 × 20:

Multiplying both sides of the equation by 6 gives us "36x = 400." This equation is not equivalent to "6x = 20."

Therefore, the equations that are not equivalent to "6x = 20" are "6x ÷ 6 = 20 ÷ 6," "6x + 5 = 20 + 5," "6x − 1 = 20 − 1," and "6x × 6 = 20 × 20."

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The solid formed by a given net is cylinder.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The net has two circles and one rectangle.

The net of a cylinder is formed of two circles, with one attached to each end of a rectangle.

A cylinder is a 3D shape with a circular cross section and a curved surface. It has no straight edges

Hence, the solid formed by a given net is cylinder.

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everyboby

Step-by-step explanation:

because it is talking about how much people love her

To form an isosceles triangle Jefferson should plot the third point at (4,2).

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given, Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph.

the given points are,

(-2,-4) (4,-4)

Let, x₁ = -2, y₁ = -4

x₂ = 4, y₂ = -4

distance between (-2,-4) (4,-4) is given as,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - -2)² + (-4 - -4)²]

= √[(4 + 2)² + (-4+ 4)²]

= √[(6)² + (0)²]

= √[(6)²

= 6

now verifying with other options,

1). For points (-2, -9),

Distance between (-2, -4) and (-2, -9) = √[(-2 + 2)² + (-4 + 9)²] = √5

Similarly, distance between (4, -4) and (-2, -9) = √[(4 +2)² + (-4 + 9)²] = √61

side is not equal. So the triangle is not isosceles.

2). For a point (3, 1),

Distance between (3, 1) and (-2, -4) = √[(3 + 2)² + (1 +  4)²] = 5√2

Distance between (3, 1) and (4, -4) = √[(3 - 4)² + (1 +  4)²] = 26

side is not equal. So the triangle is not isosceles.

3). For a point (-2,0),

Distance between (-2, 0) and (-2, -4) = √[(-2 + 2)² + (-4 + 0)²] = 4

Distance between (-2, 0) and (4, -4) = √[(-2 - 4)² + (0 + 4)²] = 2√13

side is not equal. So the triangle is not isosceles.

4). For a point (4, 2),

Distance between (4, 2) and (-2, -4) = √[(4 + 2)² + (2 + 4)²] = 6√2

Distance between (4, 2) and (4, -4) = √[(4 - 2)² + (2 + 4)²] = 6

Sides are equal so the triangle formed is an isosceles triangle.

Therefore, the third coordinate is (4, 2).

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The complete question is,

Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. He has plotted the two points shown. Where should he plot the third point?

The point is on the graph is (-2,-4) (4,-4)

The options is

(-2,-9)

(3,1)

(-2,0)

(4,2)

Answer:

here

let ABC is triangle

SO

Answer:

the answer to this question is 12

The value of C is; 1/3 for the probability density function f(x)=cx , 0<x<2.

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that the function

f(x)={cx} ,at 0, 0≤x≤2

Here, we can see that the value of x is varies as 0,1,2

So, at 0,1,2 the value of the function is;

f(1) = c

f(2) = 2c

Thus, the probability density function is given as:

Summition f(x) = f(1) + f(2)

f(x) =c + 2c = 1

3c = 1

c = 1/3

Therefore, the value of C is 1/3

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The monthly payment on the principal is $33.22

A monthly payment is a regular installment made by a borrower to a lender in order to pay off a debt over a period of time. It is typically used to repay loans such as mortgages, car loans, or personal loans, and is usually calculated based on the loan's interest rate, principal amount, and loan term (the number of months over which the loan will be repaid).

The formula of monthly payment is given as;

The formula for calculating the monthly payment on a loan is:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:

M = monthly payment

P = the principal amount of the loan = $1500

r = the monthly interest rate (expressed as a decimal) = 11.8%

n = the number of payments (in months) = 60 months

Substituting the values into the formula;

Monthly Payment = $ 33.22

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Complete Question:

A music company offers a loan to buy a drum set for $1500. The simple interest is 11.8% and the loan will be paid in equal monthly payments for 5

years. What is the monthly payment?

There are 3d + 6 seeds is going to​ plant.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Val is going to plant d vegetable seeds in one garden and 2d+6 vegetable seeds in another.

Hence, The total vegetable seeds to plant is,

⇒ d + (2d + 6)

⇒ d + 2d + 6

⇒ 3d + 6

Thus, The total vegetable seeds to plant is, (3d + 6)

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The corresponding point for the transformed function are:

Ordered pair (-4, -9).

Ordered pair (-2, 0).

Ordered pair (1, 12).

Ordered pair (3, 36).

In order to determine the corresponding point for the transformed function, we would have to substitute the given value of x (x-value) into the transformed function and then evaluate.

When the x-value = -4, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(-4 + 2)

y = -3f(-2)

y = -3(3)

y = -9.

When the x-value = -2, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(-2 + 2)

y = -3f(0)

y = 0

When the x-value = 1, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(1 + 2)

y = -3f(3)

y = -3(-4)

y = 12.

When the x-value = 3, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(3 + 2)

y = -3f(5)

y = 36

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Answer: the answer is c

Step-by-step explanation:

Answer:

120 inches

Step-by-step explanation:

5 x 8 x 3 = 120

Answer: 30inches

Step-by-step explanation:

P=5a

a=side length

P=5(6)

5*6=30

Looking at the asymptotes  graph, it crosses the y-axis at y = h(x) = -1

Thus, the y-intercept is -1. The graph also crossed x-axis at..

How do you find the asymptotes on a graph?

Set the denominator to 0 and solve for x to discover the vertical asymptotes. Given that this has already been factored, solve by setting each component to zero. They are expressed as equations of lines because the asymptotes are lines.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

As soon as the denominator equals 0, the vertical asymptotes appear. Accordingly, (2x)(x-4)=0. Vertical asymptotes are thus defined as x=0 and x=4.

Given that the degrees are identical, the horizontal asymptote in this situation corresponds to the ratio of a leading coefficients. y = [(1)(1)/(2)(1)] = 1/2.

Simply changing x = 0 makes finding the y-intercept simpler. On the other hand, because x = 0 is indeed a vertical asymptote,

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The point ranges 65-69, includes the median reading test score for ninth grade students in school district x for 1993. So, the correct choice is option (b).

The median class is defined as the class interval whose cumulative frequency is greater than (and nearest to) n/2. We have a pair chart of reading test score for ninth grade students in school district x for 1993. Total number of students in ninth grade in school district x for 1993

= 1200. We have determine the point ranges includes the median reading test for ninth grade. Now, see the pie- chart carefully.

The above figure contains a cumulative frequency table of students points.

Also, n/2 = 1200/ 2 = 600 and we see the class 65-69, consists cumulative frequency value, 636 > 600. So, it is the median class. Hence, the required point ranges is 65-69.

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Complete question:

Which of the following point ranges includes the median reading test score for ninth grade students in school district x for 1993 ?

a) Below 65 points

b) 65 - 69 points

c) 70- 79 points

d) 80 - 90 points

e) 90- 100 points

The expression, which expresses the value of v in terms of x is:

V = x * $2,750 + $825,000

Let's call the value of each acre of property v_a = $2,750.

Then the total value of the real estate firm can be expressed as:

V = x * v_a + other assets

Where x is the number of acres of property owned.

Now, plugging in the given value for other assets,

we will get it as:

V = x * $2,750 + $825,000

So the value of the real estate firm,

V, is a function of the number of acres of property owned, x, and is equal to the product of the number of acres and the value per acre plus the value of the other assets.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

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Two right triangles are similar by angle-angle similarity if they share an acute angle measure. The triangles' corresponding side length ratios will be equal.

The triangle's characteristics are: A triangle's (of all varieties) total sum of angles is 180°. The length of a triangle's two longest sides added together is longer than the third side. Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

Given,

[tex]\frac{AC'}{AC}=\frac{AB'}{AB} \\\\\frac{6}{AC}=\frac{10}{4}\\\\ AC= 8.4[/tex]

The measure of AC is 6 cm.

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The first derivative of y with respect to x is d(y)/dx = 4t² + 10t, and the second derivative of y with respect to x is d(2y)/dx² = 8t + 10.

Differential equations are mathematical equations that describe how a function changes over time or with respect to its inputs.

Let x = t² + 3 and y = t² + 5t. We want to find the derivatives of y with respect to x, which means we need to use the chain rule.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by

=> d(y)/dx = d(y)/du * du/dx.

First, we will find the derivative of y with respect to t, which is given by

=> d(y)/dt = 2t + 5.

Next, we will find the derivative of x with respect to t, which is given by

=> d(x)/dt = 2t.

Finally, we will multiply these two derivatives to find the derivative of y with respect to x, which is given by

=> d(y)/dx = (2t + 5)(2t) = 4t² + 10t.

Next, we will find the second derivative of y with respect to x, which is given by

=> d(2y)/dx² = d((4t² + 10t))/dt = 8t + 10.

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In the given plot, the graph of y=x⁴ is  g, the graph of y = x⁷ is  f and the graph of y=x¹⁰ is the h.

While plotting graphs with power to x values, it usually depends on two things. For example, lets take an equation, y = kxⁿ

As the value of coefficient of x, that is k increases the graph becomes narrower and as the value of k decreases the graph becomes wider. Here in the questions given all have the same coefficients for x, k=1.

So here the graph only depend on the power of x.

As the power increases the graph gets gets narrower. So the graph of x¹⁰ will be narrower than x⁴. As both 10 and 4 are even numbers, for all values of x, y will be positive and parabolas are formed.

In the case of x⁷,  as 7 is odd the value of y can be both positive and negative.

If x=1, y=1⁷ = 1

  x= -1, y = (-1)⁷ = -1

So the graph will be like f as shown in the figure.

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The complete question is included in the image.

Answer:

Step-by-step explanation:

In the diagram there are two vertex A & B

Let us assume the 3rd vertex  to be C

AB is the hypotenuse which is 8

AC is the adjacent side which is 6

CB is the opposite side. Let us assume it to be x for now

[tex]hypotenuse^{2} = opposite^{2} +adjacent^{2}[/tex]

[tex]8^{2} =x^{2}+6^{2} \\64=x^{2} +36\\x^{2} =64-36=28\\x=2 \sqrt{7}[/tex]

sinA=CB/AB = 2[tex]\sqrt{7[/tex] /8

CosA=AC/AB=6/8

TanA=sinA/CosA=CB/AC=2[tex]\sqrt{7}[/tex]/6

Similarly,

CosecA=1/SinA

SecA=1/CosA

CotA=1/TanA