1.5 x 10 9
8.9 x 10 7

The resulting coordinate of △ D'E'F' is translated by the vector is

(-1, -2),  (3,-4), and (1, -7)

Given the vertices of ∆DEF are D(2,5), E(6,3), and F(4,0).

we are asked to graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7)​.

If the coordinate of the vertices is translated by the vector (-3, -7), the resulting coordinates of △ D'E'F' will be expressed as:

D'= (2-3, 5 - 7) = (-1,-2)

E' = (6 - 3, 3 - 7) = (3, -4)

F' = (4 -3 , 0 - 7) = (1, -7)

Hence we get the required coordinates of the translated image.

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Check the picture below.

[tex]tan(x )=\cfrac{\stackrel{opposite}{13}}{\underset{adjacent}{6}}\implies tan^{-1}[tan(x)]~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right) \\\\\\ x~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right)\implies x\approx 65^o[/tex]

Make sure your calculator is in Degree mode.

4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

If four people use all three facilities,

then 16 - 4 = 12 of them use the gym and the track but not the pool, and 9 - 4 = 5 of them use the pool and the track but not the gym.

The pool and gym are used by 19 - 4 = 15 individuals, however the track is not used.

4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

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Remember that to model this kind of problems, we can use the equation of a straight line

Where:

• b, are the fixed costs

• x ,represents what varies

• m, is the cost of what varies

1. Therefore, using the data provided, we can model the cost of production with a function where:

• x ,is the numbers of CD's produced

• C, is the cost of producing those CD's

2. To model the revenue, we'll have to take into account that every CD sells at $68. Therefore, the money collected by selling the x CD's produced is:

Where:

• x ,its the number of CD's produced and sold

• R, is the total revenue

3. To get the profit, we'll have to substract the production cost to the money collected by the sale. Remember we already have two expressions, in terms of x, that describe both situations. Therefore,

Where:

• x ,its the number of CD's produced and sold

• P, is the total revenue

4. In order to break even, the revenue (R) has to be equal to the cost of production (C), Thus,

Therefore, 546 CD's would have to be produced to break even.

Answer:

A) y = 23°

B) ∠A = 67°, ∠C = 113°, ∠D = 113°

Step-by-step explanation:

Hello!

Angle A and B are vertical angles, meaning they are equal in measure. We can solve for y by setting the two equations equal to each other.

Vertical angles are the opposite angles formed by the intersection of 2 lines.

Supplementary angles are angles that add up to 180°.

The value of y is 23°.

Measure of Angle A is 67°, as Angle A and B are vertical and equal in measure

Measure of Angle C is 113°, because the sum of angles on a line are equal to 180°, and are supplementary.

Measure of Angle D is also 113°, because it is vertical to Angle C.

There are [tex]700[/tex] children and [tex]1300[/tex] adults.

What is system of linear equations?

A System of Linear Equations is when we have two or more linear equations working together.

Let [tex]x[/tex] be number of children and [tex]y[/tex] be number of adults.

Since [tex]2000[/tex] people enter the zoo then [tex]x+y=2000.[/tex]

The admission fee at a local zoo is $ [tex]1.50[/tex] for children and $ [tex]5.00[/tex] for adults and $[tex]7550.00[/tex] collected then [tex]1.5x+5y=7550[/tex].

Thus there are two linear equations to solve.

Substitute [tex]x=2000-y[/tex]  in  [tex]1.5x+5y=7550.[/tex]

[tex]1.5(2000-y)+5y=7550[/tex]

[tex]3000-1.5y+5y=7550[/tex]

[tex]3000+3.5y=7550[/tex]

[tex]3.5y=7550-3000[/tex]

[tex]3.5y=4550[/tex]

[tex]y=\frac{4550}{3.5}[/tex]

[tex]y=1300[/tex]

So [tex]x=2000-y=2000-1300=700.[/tex]

Therefore there are [tex]700[/tex] children and [tex]1300[/tex] adults.

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Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

Answer:

area = l×b

= 6×4

. = 24 cm²

Step-by-step explanation:

this is the answer

The probability that one or more of them tests negative is 0.85.

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

If Marv and Patricia will each take a Covid test, then the events that will occur are : both will test positive, both will test negative, or one of them will test negative.

Based on the given information, the probability that both will test positive is 0.15. Subtract it from 1 to and get the probability that one or more of them tests negative.

probability = 1 - 0.15

probability = 0.85

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Answer:

15/8 for exact form

1.875 for decimal form

And

1 and 7/8 for mixed number form

hope this helps you!

(also already in the simplest form :)

Answer:

0.5

Step-by-step explanation:

0.5 x 0.5 = 0.25

Answer:

x=0.5

Step-by-step explanation:

x=±√0.25

x=±0.5

x=0.5,−0.5

Answer:

7/5

Step-by-step explanation:

1/2 + 1/5

probability that at least one of the two students fail is 7/5

Option C gives the graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Choice C provides a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

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Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer:

A. k ≥ 8.14

Step-by-step explanation:

Hope this helps! :))

The image of the point (-4, -1) after the translation is:

(-3, 1)

A translation:

Tᵃ'ᵇ applied to a point (x, y) gives:

Tᵃ'ᵇ(x, y) = (x + a, y + b).

In this case, we know that:

Tᵃᵇ(1, 1) = (1 + a, 1 + b) = (0, 3)

Then:

1 + a = 0

1 + b = 3

Solving these we get:

a = 1

b = 3 - 1 = 2

The translation is:

T¹'²

Applying this to the point (-4, -1) gives:

T¹'²(-4, -1) = (-4 + 1, -1 + 2) = (-3, 1)

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4.8% of voters with annual incomes over $50,000 will be polled, or at least 1,450 of them when an opinion poll of 4,000 (randomly selected) voters is con.ducted

What is probabilty ?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

We have,

n = 4000

p = 0.35 , q=1-p=0.65

= E(X) = np= 4000 (0.35) 600 1400

6 = SE(X) = √npq √ 4000 (0-35)(0.65) = 30.1662

Consider

P(X[tex]\geq[/tex]1450) = p 7

X-U

1450 1400

30.1662

=P(z>1,66)

=0.048457

from standard normal table,

Hence, 4.845% chance that 1,450 or more of the voters with annual incomes above $50,000 will be polled

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Answer:

X=11

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

Because, [tex](8*18+14)=(9*18-4)[/tex] is true

The original equation is:

5 x^2 + (10 x^2 + 10) = 3 x^2 - 5

The first step the person did was:

15 x^2 + 10 = 3 x^2 - 5

so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.

Please check if there is an option that states such among your options.

for the square root you must look for a number that multiplied with itself gives you the indicated value

for this case a number that multiplied by itself gives you 100

sothe square root of 100 is:

Answer:

30

Step-by-step explanation:

it doesn't seem to be correct question

x=3

You have the following vertices of a triangle:

A(1,1)

B(4,1)

C(4,5)

For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:

A(1,1) => A'(1+4,1) = A'(5,1)

B(4,1) => B'(8,1)

C(4,5) => C'(8,5)

Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':

A'(5,1) => A''(5,1+3) = A''(5,4)

B'(8,1) => B''(8,4)

C'(8,5) => C''(8,8)

Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:

for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:

A''(5,4) => A'''(5,-1-5)=A'''(5,-6)

for the point B''(8,4), the distance is again 5 units, then, you have:

B''(8,4) => B'''(8,-1-5) = B'''(8,-6)

for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:

C''(8,8) => C'''(8,-1-9) = C'''(8,-10)

Hence, the final points are:

A'''(5,6)

B'''(8,-6)

C'''(8,-10)

Answer:

Whats the question?

The formula to calculate the missing arc is,

where,

Therefore,

Hence, the answer is

In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .

Taking 4 as LCM from the above equation.

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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Answer: The answer is 0.

X = 0 when evaluated.

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

STEP 2: Find the value of x

Cross multiply the equation

Divide both sides by 4

Hence, the value of x is -18

The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.

From the question, we have the following;

Hypotenuse=17 foot

Height(y)=13 feet

Base(x)=(17^2-13^2)^1/2

        =120^1/2 or sqrt(120)

The ladder against the wall is a right angle triangle, so we have:

x^2+y^2=17^2

x^2+y^2=289

Top slips down at 2ft/s

dy/dt=-2 ft/s, where height (y)=13ft

The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt

Now, we take the derivative with respect to time:

=x^2+y^2=17^2

=2x(dx/dt)+2y(dy/dt)=0

Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s

2(sqrt(120))(dx/dt)+2(13)(-2)=0

2(sqrt(120))(dx/dt)-52=0

We solve for dx/dt:

dx/dt=52/(2sqrt(120))

dx/dt=52/21.9089

dx/dt=2.373 ft/s

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The rate at which the sloth travels as required in the task content is; -22ft/min.

It follows from the task content that the rate at which the sloth travels is to be determined.

Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;

(98, 1) , (76, 2) , (54, 3), (32, 4).

Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;

Rate = ∆Distance/∆time.

Rate, R = (98 - 76)/(1 - 2)

Rate, R = 22/-1

R = -22 ft/min.

Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.

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x is each friend

3x + 28 > 200

3x > 172

x > $57.33

if right can a i get brainliest pls

Answer:

Step-by-step explanation: $200-$28= $172

                                                $172÷3=$57.33