Determine whether each equation represents a proportional relationship.

Y=2.5x

y= x - 4

Answer:

The area of rectangle BEFD is 180 square units.

Step-by-step explanation:

After checking the figure given, we have the following information:

[tex]AD = 15[/tex], [tex]AB = 12[/tex], [tex]BC = 15[/tex], [tex]CD = 12[/tex]

By Pythagorean Theorem, we determine the length of the line segment BD:

[tex]BD = \sqrt{AB^{2}+AD^{2}}[/tex] (1)

[tex]BD = \sqrt{12^{2}+15^{2}}[/tex]

[tex]BD = 3\sqrt{41}[/tex]

In addition, we know the following characteristics of the rectangle BEFD:

[tex]BD = EF[/tex], [tex]EF = EC + CF[/tex], [tex]BE = FD[/tex] (2), (3), (4)

By Pythagorean Theorem:

[tex]BC^{2} = BE^{2}+EC^{2}[/tex] (5)

[tex]CD^{2} = CF^{2}+DF^{2}[/tex] (6)

By (3), (4), (5) and (6):

[tex]BC^{2} = BE^{2} + EC^{2}[/tex] (7)

[tex]CD^{2} = (EF-EC)^{2} + BE^{2}[/tex] (8)

By (7) in (8):

[tex]CD^{2} = (EF-EC)^{2}+ (BC^{2}-EC^{2})[/tex]

[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC + EC^{2}+BC^{2}-EC^{2}[/tex]

[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC +BC^{2}[/tex]

Then, we clear [tex]EC[/tex]:

[tex]2\cdot EF\cdot EC = EF^{2} + BC^{2} - CD^{2}[/tex]

[tex]EC = \frac{EF^{2}+BC^{2}-CD^{2}}{2\cdot EF}[/tex]

If we know that [tex]EF = 3\sqrt{41}[/tex], [tex]BC = 15[/tex] and [tex]CD = 12[/tex], then the length of the segment [tex]EC[/tex] is:

[tex]EC = \frac{75\sqrt{41}}{41}[/tex]

And the length of the line segment [tex]CF[/tex] is:

[tex]CF = EF - EC[/tex]

[tex]CF = 3\sqrt{41}-\frac{75\sqrt{41}}{41}[/tex]

[tex]CF = \frac{48\sqrt{41}}{41}[/tex]

And the length of the line segment [tex]DF[/tex] is determined by Pythagorean Theorem:

[tex]FD = \sqrt{CD^{2}-CF^{2}}[/tex]

[tex]FD = \sqrt{12^{2}-\left(\frac{48\sqrt{41}}{41} \right)^{2}}[/tex]

[tex]FD = \frac{60\sqrt{41}}{41}[/tex]

And the area of the rectangle is determined by the following formula:

[tex]A = FD\cdot EF[/tex]

[tex]A = \left(\frac{60\sqrt{41}}{41} \right)\cdot (3\sqrt{41})[/tex]

[tex]A = 180[/tex]

The area of rectangle BEFD is 180 square units.

Answer:

(0,8)

Step-by-step explanation:

To get the y-intercept put all x values equal to 0 (because we want to see where y lies on the graph when x is zero.

y=2^0+3

y=2^3

y=8

The y-intercept is (0,8)

As for the rest of the answers.....

1)A) 2[tex]\sqrt{12}[/tex]-5[tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]-5[tex]\sqrt{3}[/tex] so the final answer is -[tex]\sqrt{3}[/tex]

1B) the problem is (3-[tex]\sqrt{7}[/tex])(3+[tex]\sqrt{7}[/tex]) a quick formula to help you solve this type of problem is (a-b)(a+b)= a^2-b^2 so you transform the question to 3^2-[tex]\sqrt{7}[/tex] ^2

to get 9-7 which is 3 therefore the final answer is 3

2) when you transform a function from y=x^2-3 to y=x^2+1 the graph moves 4 units up. So the final answer is b)4 units up

Question 3a and 3b are correct

Answer:

4, 7, 14

Step-by-step explanation:

Because it's were it decreases

Answer:

(2,-7)

Step-by-step explanation:

The point moves down 3 units resulting in (2,-7)

Answer:

The range is the set of possible output values, which are shown on the y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

Step-by-step explanation;

The range of a function is the set of y-coordinates of all the points int he graph of the function.

Look at the graph. The vertex is point (2, -3).

The graph does not go lower than that point.

The lowest y-coordinate is -3.

The graph goes up forever on both sides until infinity.

The range is all numbers greater than or equal to -3.

Answer:

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

Explanation:

Oxford dictionary definition

Step-by-step explanation:

a circle is a shape consisting of all points in a plane that are at a given distance from a given point the center

Answer:

C.

Step-by-step explanation:

C. 3x-2 is the answer .

Answer:

C.3х – 2

Step-by-step explanation:

Explanation is in the attachment

Hope it is helpful to you

Answer:

[tex]\frac{y}{2}[/tex]

Step-by-step explanation:

n is doubled: 2n

y added: 2n + y

divided by 2: n + [tex]\frac{y}{2}[/tex]

n subtracted -> final resutl: [tex]\frac{y}{2}[/tex]

Answer: f(x) = -(x-1)^2+5

Explanation:

f(x) = h(x) + 6

f(x) = -(x-1)^2 - 1 + 6

f(x) = -(x-1)^2+5

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Answer:

hello,

Step-by-step explanation:

a)

In an isocele triangle, base's angles have the measure:

42+2a=180

2a=180-42

a=69(°)

b)

in a triangle, an external angle has for measure the sum of the angles not adjacents.

55+b=132

b=77 (°)

c)

in a quadrilater the sum of the (interior) angles is 2*180=360 degrees.

90+90+68+c=360

c=360-90-90-68

c=112 (°)

Answer:

2

Step-by-step explanation:

[tex](2 * 6x) + (2 * 7x) + (2 * (6 * 7)) = 136[/tex]

[tex]12x + 14x + (2 * 42) = 136[/tex]

[tex]12x + 14x + 84 = 136[/tex]

[tex]12x + 14x = 136 - 84[/tex]

[tex]26x = 52[/tex]

[tex]x = 2[/tex]

Answer:

4 sqrt(3)

Step-by-step explanation:

sqrt(3) * sqrt(16)

sqrt(3) *4

4 sqrt(3)

Answer: d

Step-by-step explanation: I took the test

Hi there!

[tex]\large\boxed{\text{9 quarters}}[/tex]

We can let x = dimes and y = quarters.

We know that one dime = $0.10 and a quarter = $0.25, so:

$3.05 = $0.10x + $0.25y

And:

17 = x + y

Solve the system of equations. We can rearrange the bottom equation to create an expression equal to y:

17 - x = y

Substitute this into the top equation for y:

3.05 = 0.10x + 0.25(17 - x)

Distribute and simplify:

3.05 = 0.10x + 4.25 - 0.25x

3.05 = 4.25 - 0.15x

Solve for x:

-1.2 = -0.15x

x = 8

Find y using the above expression:

17 - 8 = y

y = 9

Answer:

D

Step-by-step explanation:

0.8x-5<=65

0.8x<=70

x<=700/8=87.5

Answer:

D

Step-by-step explanation:

Answer:

The first two.

Step-by-step explanation:

See that L is 600mm MORE than W.

From there, you can note that L = W+600  

or rearrange the formula and get W= L-600

Then, see that the perimeter of a flag is 2L + 2W

(Because there are two four sides to a rectangle, 2 width, 2 length)

It must total to be 5 meters, or 5000mm

Thus,

2L + 2W = 5000

Answer:

no its not a perfect cube, we need to multiply a seven to make it perfect cube

Step-by-step explanation:

answer from GAUTHMATH

Answer:

60 + 12 * g, with g representing the number of extra gigabytes

Step-by-step explanation:

First, we know that Maritza has to pay $60 for 10GB of data, no matter what. Therefore, the base cost of the cell phone plan is 60 dollars, and all extra costs must be added to that. Currently, our expression is therefore 60 + something = cost of cell phone plan.

After that, the plan costs $12 for each gigabyte of data past 10 GB. This means that, for example, if Maritza uses 11 gigabytes, the plan will cost 60 (the base amount) + 12 for each gigabyte past 10 GB. There are 11-10=1 extra gigabytes, so the cost is 60 + 12 * 1 = 72 dollars. For each extra gigabyte, 12 dollars are added, so we can represent this as

60 + 12 * g, with g representing the number of extra gigabytes

Answer:

45

Step-by-step explanation:

(27*27)+(36*36) = 2025

square root 2025 and you get 45

to check 45*45=2025

Answer:

Answer

5.0/5

2

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Virtuoso

133 answers

14.9K people helped

Answer:

): "x2" was replaced by "x^2". 4 more similar replacement(s).

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

x6 - x5 + x4 - x3 + x2 - x =

x • (x5 - x4 + x3 - x2 + x - 1)

2.2 Factor x5 - x4 + x3 - x2 + x - 1

Try to factor this 6-term polynomial into (2-term) • (3-term)

Begin by splitting the 6-term into two 3-term polynomials:

-x2 + x - 1 and x5 - x4 + x3

Next simplify each 3-term polynomial by pulling out like terms:

-1 • (x2 - x + 1) and x3 • (x2 - x + 1)

Note that the two simplified polynomials have x2 - x + 1 in common

Now adding the two simplified polynomials we get

(x3 - 1) • (x2 - x + 1)

Answer:

the graph curve will goes above f(x)=x^2.f(x)=3*x^2 curve will also give higher value same value of x .

Step-by-step explanation:

Answer: 135

Step-by-step explanation: Write 150% as 150/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 150/100 of 90= 150/100 X 90

Therefore, the answer is 135

If you are using a calculator, enter 150÷100×90 which will give you 135 as the answer.

150 percentage of 90 is 135 which we obtained by multiplying 1.5 with 90.

"Percent" means "per hundred," so when we say "150%," it means 150 per hundred or 150 out of 100.

To find 150% of 90, we can use the following formula:

150% of 90 = (150/100) × 90

Convert 150% to a decimal.

To do this, divide 150 by 100:

150/100 = 1.5

Multiply the decimal value by 90:

1.5 × 90

= 135

So, 150% of 90 is 135 which means that 135 is 150% of 90, which is equivalent to saying that 135 is 1.5 times larger than 90.

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Answer:

Here is the detailed answer below

Step-by-step explanation:

Answer:

M ≤ μ (=78)

Here μ denotes the means of the population

And, M denotes the sample mean

Step-by-step explanation:

The computation of the  null hypothesis, in both words and symbols is given below:

Null Hypothesis(H0) is

M ≤ μ (=78)

This means that the study application does not improve the grades

Also

Alternative hypothesis (H1): M> μ

Here μ denotes the means of the population

And, M denotes the sample mean

Answer: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

Concept:

Here, we need to know the concept of the distance formula.

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Find the length of UV, where:

[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance = \sqrt{(1-2)^2+(-9+1)^2}[/tex]

[tex]Distance = \sqrt{(-1)^2+(-8)^2}[/tex]

[tex]Distance = \sqrt{1+64}[/tex]

[tex]Distance = \sqrt{65}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

El área del cuadrado es de 3 centímetros cuadrados.

Dado que se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura, para calcular el área del cuadrado se debe realizar el siguiente cálculo:

Aplicando teorema pitagórico: lado al cuadrado mas lado al cuadrado es igual a hipotenusa al cuadrado.

Por lo tanto, el área del cuadrado es de 3 centímetros cuadrados.

Aprende más en https://brainly.com/question/16405529

El área del cuadrado es de 18 centímetros cuadrados.  

El procedimiento de resolución se basa en conocer que la Medida de la Diagonal de un Cuadrado inscrito es igual a la Medida del Radio del Círculo, lo cual permite determinar el valor de la medida del Cuadrado en función del Radio del Círculo. Finalmente, determinamos el Área del Cuadrado mediante su fórmula conocida.

Dado que existe un cuadrado inscrito en un círculo, la medida de la diagonal del cuadrado es igual a la medida del radio del círculo. Además, conocemos que un cuadrado está formado por 4 triángulos rectángulos con configuración angular 45-45-90. Entonces, la medida del lado del cuadrado se calcula mediante la siguiente relación geométrica:

[tex]l = \sqrt{2}\cdot R[/tex] (1)

Donde:

[tex]R[/tex] - Radio del círculo, en centímetros.

[tex]l[/tex] - Longitud del lado del cuadrado, en centímetros.

Por otra parte, la ecuación de área del cuadrado es igual a:

[tex]A = l^{2}[/tex] (2)

Donde [tex]A[/tex] es el área del cuadrado, en centímetros cuadrados.

Si sabemos que [tex]R = 3\,cm[/tex], entonces el área del cuadrado es:

[tex]l = \sqrt{2}\cdot (3\,cm)[/tex]

[tex]l = 3\sqrt{2}\,cm[/tex]

[tex]A = (3\sqrt{2}\,cm)^{2}[/tex]

[tex]A = 18\,cm^{2}[/tex]

El área del cuadrado es de 18 centímetros cuadrados.  

He aquí una pregunta relacionada sobre el área del cuadrado: https://brainly.com/question/23915250

Answer:

720º

Step-by-step explanation:

To find the total amount of interior angles in any polygon, we have to use the formula, (n-2)*180.

Here, the n is the number of sides the polygon has. In this case, your polygon has 8 sides. Therefore it would be (8-2)*180 --> 4*180 = 720º.

Answer:

the answer is 720. Please give me brainliest

Answer:

x^2+3x+3

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x^2 + 4

f(x) + g(x) = 3x-1+ x^2 +4

                 Combine like terms

                   = x^2+3x+3

Answer:

$44.00 + $85.00 = $129.00

Step-by-step explanation:

The least amount that she needs is $129.00 because we're summing the amount for food and House Rent.

Movies and Shopping are less important.

Answer:

[tex] \bf \: y = 2 {x}^{2} - 6x - 8[/tex]

It is equation of a parabolla.

It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is  y = -12x² - 12x. is attached accordingly.

The graph of y = -12x² - 12x is a downward-opening parabola.

It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.

The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.

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