On a number line, point D is at -6, and point E is at 8. Point F lies between points D and E. If DF: FEis 3: 1, where does point F lie on the
number line?

Answer:

t = -35/8

Step-by-step explanation:

Divide both sides by 2/5.

The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

[tex]\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}[/tex]

Step 2: Replace the value of "y" in the equation (2).

[tex]35 x=-0.05(x-400)^{2}+9492[/tex]

Step 3: Make the equation above simpler.

[tex]35 x=-0.05 x^{2}-8000+40 x+9492[/tex]

Step 4: Write the preceding equation in generalised quadratic form.

[tex]0.05 x^{2}-5 x-1492=0[/tex]

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

Answer:

x=4

Step-by-step explanation:

the proportion between 9 and 3 is 1/3

so u just apply the fraction to the corresponding side

so 1/3 of 12 is 4

so x is 4

Generally speaking, Harriot's notation was clearer than Viète's, which made it simple for him to connect Viète's identities.

Harriot made significant contributions to the theory of equations and developed a more straightforward notation for algebra.

The employment of special notation is algebra's most evident characteristic. Variables are the symbols that are used to represent numbers.

A symbolic system known as notation is used to represent mathematical concepts and objects.

The primary components of notation are letters, symbols, figures, and signs. Notation can be made using symbols, characters, numbers, or a combination of these, such as the factorial symbol.

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Laura's walking speed is 4.50 feet per second.

Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.

Average speed = total distance / total time

54 / 12 = 4.50 feet per second

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Answer:

where is the table?

Step-by-step explanation:

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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For the complete question, refer to the attachment.

If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

Given that the sum of an integer and 7 more than the next consecutive integer is 66.

Integer is a number that is written without a fraction component. It can be positive as well as negative.

let the first integer be x.

Consecutive integer will be x+1.

Sum of integer and 7 more than the next consecutive integer is 66.

Sum according to the given information=x+x+1+7

=2x+8

2x+8=66

2x=66-8

2x=58

x=58/2

x=29

Next integer=29+1-30.

Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

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Carpenter remove [tex]3/16[/tex] inches from the top of the plank to the same thickness of wood from the top and bottom of the plank.

How many inches does the carpenter remove from the top of the plank ?

A wooden plank is [tex]5ft[/tex] long and [tex]1\frac{1}{2}[/tex] inches thick

to make the plank [tex]1\frac{1}{8}[/tex] inches thick

Carpenter needs  to cut off

[tex]=1\frac{1}{2} -1\frac{1}{8} \\=\frac{3}{2} -\frac{9}{8} \\=\frac{3}{8}[/tex]

Carpenter cuts each side

[tex]=\frac{3}{8} /2\\=\frac{3}{16} inches[/tex]

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Answer:

1)  4x + 5y = 20         4x + 5y = 20  

  -2x + 3y = 12  -->  2(-2x + 3y) = 2(12)

2) 4x + 5y = 20  

  -4x + 6y = 24

3) 4x + 5y = 20  

   -4x + 6y = 24

   0x + 11y = 44

4) 11y = 44

5) y = 4

6) 4x + 5y = 20  

   4x + 5(4) = 20  

7) 4x + 20 = 20

8) 4x = 0

9) x = 0

10) The solution is the point (0, 4)

Answer: Choice B is correct.

Find some points

Graph attached

Using translation concepts, the inequality that represents the graph is given as follows:

f(x) > sqrt(1 - x)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent square root function is given by:

y = sqrt(x)

It increases to right starting at x = 0, and in this problem it increases to left starting at x = 1, meaning that it was reflected over the y-axis and shifted right one unit, hence the function is:

sqrt(1 - x)

The part graphed is the values above the function, that is, the values that are greater, as the line is only dashed, hence the inequality is:

f(x) > sqrt(1 - x)

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Answer:

  36 meters

Step-by-step explanation:

You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

The height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:

  Tan = Opposite/Adjacent

  (Adjacent)(Tan) = Opposite

  height of Kim's balcony = (30 m)tan(40°)

  height above Kim's balcony = (30 m)tan(20°)

__

  height of Yuri's balcony = height of Kim's + height above Kim's

  height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)

  height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))

  height of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m

The height of Yuri's balcony is about 36 meters.

The five consecutive integers are -2, -1, 0, 1 and 2.

Given that;

The sum of five consecutive integers equals 5.5 times the middle integer.

Since the integers are consecutive, let the integer be;

x, x+1, x+2, x+3 and x+4.

Now, sum of the integers equals 5.5 times the middle integer.

Middle integer is x+2.

Hence we have;

x + x+1 + x+2 + x+3 + x+4 = 5.5( x+2 )

x + x+1 + x+2 + x+3 + x+4 = 5.5x + 11

We collect like terms

x + x + x + x + x - 5.5x = 11 - 1 - 2 - 3 - 4

5x - 5.5x = 1

-0.5x = 1

x = -( 1 / 0.5 )

x = -2

Since our integers are; x, x+1, x+2, x+3 and x+4.

We substitute in the value of x

x = -2

x+1 = -2 + 1 = -1

x+2 = -2 + 2 = 0

x+3 = -2 + 3 = 1

x+4 = -2 + 4 = 2

Therefore, the five consecutive integers are -2, -1, 0, 1 and 2.

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Answer and Step-by-step explanation:

We are given a triangle, a quadrilateral inside a triangle. and exterior angles of the triangle at linear bisectors.

We can figure out the interior angles of the shape to find a by using the linear bisector theorem, in which a line separated by another line will have two angles that will add to 180 degrees.

For the bisected line with the angle of 60 degrees, the other angle will have to equal 120. We know this by taking 60 from 180.

The perpendicularly bisected line will always have 90 degrees for the angles, so the interior angle will be 90 degrees.

For the bisected line with the angle of 80 degrees, the other angle will have to equal 100. We know this by taking 80 from 180.

Now, we have angles to determine a.

Quadrilaterals consist of 4 interior angles, which, when added together, equals 360 degrees.

360 - 90 - 100 - 120 = a

260 - 90 - 120 = a

140 - 90 = 50 = a

So, angle a is equal to 50 degrees.

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

for the first one, it is x=2

for the second one, it is x=9

Answer:

The answer is 75 and here's why.

Let's figure out the amount of remaining votes to prove this.

250 total votes   -    150 votes for candidate a = 100 votes.

               minus ↑ sign

Candidate B received 25% of the votes, so let's find 25% of 100

100 * 0.25 = 25 votes

Candidate B only got 25 votes (that's kinda sad, poor guy)

100 - 25 votes = the # of votes candidate C got

Candidate C got 75 votes!

Answer:

6x^3 -2x^2-11x + 4

Step-by-step explanation:

(3x - 4)(2x^2 + 2x - 1)

(3x - 4)(2x^2 + 2x - 1)

[(3x)(2x^2 + 2x - 1)]  +  [-4(2x^2 + 2x - 1)]

6x^3 + 6x^2 - 3x           -8x^2 - 8x + 4

6x^3 + [6x^2-8x^2] [- 3x- 8x] + 4

6x^3 -2x^2-11x + 4

Answer:

[tex]6x^3-2x^2-11x+4[/tex]

Step-by-step explanation:

Given expression:

[tex](3x-4)(2x^2+2x-1)[/tex]

Distribute the parentheses:

[tex]\implies 3x(2x^2+2x-1)-4(2x^2+2x-1)[/tex]

[tex]\implies 3x \cdot 2x^2+3x \cdot 2x +3x \cdot -1 -4 \cdot 2x^2-4 \cdot 2x-4 \cdot -1[/tex]

[tex]\implies 6x^3+6x^2 -3x -8x^2-8x+4[/tex]

Collect like terms:

[tex]\implies 6x^3+6x^2-8x^2 -3x -8x+4[/tex]

Combine like terms:

[tex]\implies 6x^3-2x^2-11x+4[/tex]

Answer:

24 % (to the nearest percent)

Step-by-step explanation:

the probability that the student is a graduate is equal to :

[tex]=\frac{\text{the total number of graduates} }{\text{the total number of students} }[/tex]

[tex]=\frac{2610}{10730} \\=0.243243243243[/tex]

Converting to percentage:

0.243243243243×100

= 24.3243243243 %

Answer:

Step-by-step explanation:

The first part tells us that y is, or is anywhere below ½x-3

The second part tells us that above 6-2x

Since we don't know what x is, we cannot actually find y.

The best answer to this question is:

6-2x < y < ½x-3

Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.

Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.

Answer:

  (a)  see attached

Step-by-step explanation:

A table will represent a function if no input (x) values are repeated.

The offered tables can be evaluated as follows:

  (a) x-values {-4, -1, 1, 4}, no repeats. Is a function.

  (b) x-values {2, 2, 3, 3}, both values repeated

  (c) x-values {-5, -5, 5, 5}, both values repeated

  (d) x-values {2, 2, 7, 7}, both values repeated

Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.

Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].

Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].

The baker sells all but 3 cakes, so

[tex]P + D = 117[/tex]

After the sale, the baker earns a total of $991, so

[tex]7P + 11D = 991[/tex]

Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.

(The selected answer is actually the correct one.)

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

In this question we have a graph of a quadratic equation translated to another place of a Cartesian plane, whose form coincides with the vertex form of the equation of the parabola, whose form is:

g(x) = C · (x - h)² - k     (1)

Where:

By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.

x = 2

g(2) = (2 - 5)² + 1

g(2) = 10

x = 8

g(8) = (8 - 5)² + 1

g(8) = 10

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

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Answer: B

Step-by-step explanation:

looked at the points from the dude above, or below, anyway i hope this helps

the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.

It is the height greater than the height of the observer.

The opposite of the angle of elevation is the angle of depression which is formed with an observer

Words associated with the angle of elevation are;

The angle of elevation is the angle between the line of sight and the horizontal line.

Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

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Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

Answer:

x > - 3

Step-by-step explanation:

6(x + 2) > x - 3 ← distribute parenthesis on left side

6x + 12 > x - 3 ( subtract x from both sides )

5x + 12 > - 3 ( subtract 12 from both sides )

5x > - 15 ( divide both sides by 5 )

x > - 3

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏

use the distributive property

[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]

subtract both sides by x and 12

[tex]\sf{\longmapsto{5x < -15}[/tex]

divide both sides by 5

[tex]\sf{\longmapsto x < -3}}[/tex]

`hope it's helpful to u ~

Answer:

20 ft by 14 ft

Step-by-step explanation:

See attached image.

The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

According to the statement

There is a region where the range of values of the independent variables in the data used to estimate the regression model.

AND

Those region is called EXPERIMENTAL REGION

So, Experimental region is called a those region in which the region within which we can make valid predictions and doesn't go outside of the bounds of the data we were provided.

So, The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

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