If DH = 4x - 2 and FH = x + 28, find the value of x for which DEFG must be a parallelogram.

6

10

7

8

Answer:

[tex]\large\boxed{y=2\pm\sqrt{28+4x}}[/tex]

Step-by-step explanation:

[tex]2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}[/tex]

Answer:

y is inverse:  2 ±[tex]\sqrt{28+ 4x}[/tex] .

Step-by-step explanation:

Given: 2(x - 2)²=8(7+y)​.

To find: Find inverse.

Solution : We have given

2(x - 2)²=8(7+y)​.

Step 1: inter change the x and y.

2(y - 2)²=8(7+x)​.

Step 2:

Solve for y

On dividing both sides by 2

(y - 2)² = 4 (7+x)​.

Distributes 4 over ( 7 + x)

(y - 2)² =  28 + 4x

Taking square root both sides.

[tex]\sqrt{(y-2)^{2} } = ±\sqrt{28+ 4x}[/tex].

y - 2 =  ±[tex]\sqrt{28+ 4x}[/tex].

On adding both sides by 2

y =  + 2 ±[tex]\sqrt{28+ 4x}[/tex] .

Therefore, y is inverse : 2 ± [tex]\sqrt{28+ 4x}[/tex].

Final answer:

Kevin can safely take sacks weighing up to 308.33 pounds each in the elevator, provided he takes six sacks at a time and the elevator's capacity is 2,000 pounds with Kevin weighing 150 pounds.

Explanation:

The student's question is asking for the maximum weight of each sack of grain that Kevin can deliver on the elevator, given the elevator's weight capacity and the additional weight of Kevin himself. To answer this question, we need to consider the weight that the elevator can hold minus Kevin's weight, and then determine how much weight is left for the sacks of grain.

The elevator has a capacity of 2,000 pounds, and Kevin weighs 150 pounds. This means the total weight that the elevator can carry in addition to Kevin is:

2000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1850 pounds (available for sacks)

If Kevin needs to deliver six sacks at a time, we can divide the total available weight by six to find the maximum weight for each sack:

1850 pounds / 6 sacks = approximately 308.33 pounds per sack

Therefore, the weight of each sack must be 308.33 pounds or less for Kevin to safely use the elevator without exceeding its capacity.

Answer:

y=2

x=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since it's a division we need to look for a common factor to cancel

so first we try to break the numbers to there prime factors

[tex]\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }[/tex]

So , now we try to factors that are common in top and bottom

[tex]= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }[/tex]

common factor is sqrt 2 so lets cancel it

we get

[tex]\frac{\sqrt{5} }{4\sqrt{4} }[/tex]

[tex]\frac{\sqrt{5} }{8}[/tex]

Step-by-step explanation:

All three sides are equal, so this is an equilateral triangle.

Answer:

This is an equilateral triangle

Step-by-step explanation:

All three sides are equal, making it equilateral

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=\cfrac{2}{5}[x-(-3)]\implies y+1=\cfrac{2}{5}(x+3) \\\\\\ y+1=\cfrac{2}{5}x+\cfrac{6}{5}\implies y=\cfrac{2}{5}x+\cfrac{6}{5}-1\implies y=\cfrac{2}{5}x+\cfrac{1}{5}[/tex]

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{2x}{3}-17\to y=\dfrac{2x}{3}-17\\\\\text{exchange x to y and vice versa:}\\\\x=\dfrac{2y}{3}-17\\\\\text{solve fro y:}\\\\\dfrac{2y}{3}-17=x\qquad\text{add 17 to both sides}\\\\\dfrac{2y}{3}=x+17\qquad\text{multiply both sides by 3}\\\\2y=3x+51\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}[/tex]

Answer:

Center of the circle= (-9,6)

Radius = 5 units

Step-by-step explanation:

Once the equation of the circle has been written in the format

(x-h)²+(y-k)²=r² , (h,k) is the center while r is the radius of the circle.

From the given equation, -h=9 therefore h= -9.

-k = -6 therefore k = 6. r² = 25 therefore r= √25=5

Center of the circle= (-9,6) radius = 5 units

Answer:

AAS

Step-by-step explanation:

Given one pair of congruent angles and one pair of congruent sides.

When two lines intersect they form a pair of congruent angles (vertical angles are equal)

So the two triangles are congruent by AAS.

Answer: AAS

Step-by-step explanation:

By the figure we can say that the have one side equal. Now for the angles we have that in the part of the triangles are touching we have an oposite angles then these two angles have to be equals. Finally the two triangles have two equal angles and ones equal side. we can conclude that the correct method is AAS.

Answer:B

f(0)=0

Step-by-step explanation:

when 0 is squared it’s just 0

Answer: option b.

Step-by-step explanation:

Given the function f(x):

[tex]f(x)=x^2[/tex]

In order to find [tex](fof)(x)[/tex], the first thing you must do is to substitute the function f(x) into the same  function f(x). Observe the procedure:

[tex](fof)(x)=(x^2)^2[/tex]

Now, you need to simplify:

[tex](fof)(x)=x^4[/tex]

Finally, to find  [tex](fof)(0)[/tex] you need to substitute  [tex]x=0[/tex] into  [tex](fof)(x)=x^4[/tex], then you get:

 [tex](fof)(0)=(0)^4[/tex]

 [tex](fof)(0)=0[/tex]

Answer:

The fifth term is 620

Step-by-step explanation:

y=40×(-2)^(n-1)​

The 5th terms means n=5

y = 40 * (-2) ^ (5-1)

  = 40 * (-2) ^4

  = 40 * (16)

  = 640

[tex]a_n=3n-10[/tex]

Answer:

an = -7 + (n - 1) 3

Step-by-step explanation:

Step-by-step explanation:

75.99 ×.0625=4.749

75.99+4.75(because I rounded)=

$80.74 total cost incase you have another step

75.99 ×.0625 = 4.749

I rounded to get 4.75.

75.99 + 4.75 = $80.74

$80.74 - $75.99 = $4.75

Answer: $4.75

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=-\left|x\right|+2[/tex]

we know that

The graph is inverted V-shaped.

The x-intercepts are the points (-2,0) and (2,0)

The vertex is the point (0,2)

The domain is all real numbers

The range is all real numbers less than or equal to 2

using a graphing tool

The graph in the attached figure

Answer:

32

Step-by-step explanation:

Substitute n = 4 into the formula

[tex]a_{4}[/tex] = 2 × [tex]4^{4-2}[/tex] = 2 × 4² = 2 × 16 = 32

The answer is [tex]\( 24xy^2 \)[/tex].

To solve the expression [tex]\( 3x \cdot 8y^4 \)[/tex], we first multiply the coefficients and the variables separately. The coefficients are 3 and 8, and when multiplied, they give us 24. For the variables, we multiply x by [tex]\( y^4 \)[/tex], keeping in mind that when multiplying exponents with the same base, we add the exponents. Therefore, [tex]\( x \cdot y^4 \)[/tex] remains [tex]\( xy^4 \)[/tex].

Combining the coefficient and the variables, we get \( 24xy^4 \). However, we can simplify this further by recognizing that any variable raised to the power of 1 is simply the variable itself. Thus, [tex]\( xy^4 \)[/tex] is equivalent to [tex]\( xy^2 \)[/tex] because [tex]\( y^1 \)[/tex] is just [tex]\( y \)[/tex].

So the final simplified expression is [tex]\( 24xy^2 \)[/tex].

Answer:

-2 + i

Step-by-step explanation:

v = -3i

w = 2 - 4i

v - w =

= -3i - (2 - 4i)

= -3i - 2 + 4i

= -2 + i

The given value of  v = -3i and w = 2-4i, so v-w = -2 + i.

Given: v = -3i, w = 2-4i

To find: v - w

Solution:

Substitute the values of v and w into the expression v - w.

v - w = -3i - (2-4i)

v - w = -3i - 2 + 4i

v - w = -2 + i

Answer:

The coordinates of the point in question is (1, 3).

Step-by-step explanation:

Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).

What will be the horizontal distance between the point (-1, 7) and the point in question?

The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be [tex]a[/tex]. Let the horizontal distance between the point in question and point (4, -3) be [tex]b[/tex].  

[tex]\displaystyle \frac{a}{b} = \frac{2}{3}[/tex].

[tex]\displaystyle a = \frac{2}{3} \; b[/tex].

[tex]\displaystyle b = \frac{3}{2}\; a[/tex].

However,

[tex]a + b = 5[/tex].

[tex]\displaystyle a + \frac{3}{2}\; a = 5[/tex].

[tex]\displaystyle \frac{5}{2}\; x= 5[/tex].

[tex]a = 2[/tex].

In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be [tex]-1 + 2 = 1[/tex].

The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is [tex](2/5) \times 10 = 4[/tex] units below the point (-1, 7). The y-coordinate of this point will be [tex]7 - 4 = 3[/tex].

Thus, the point in question is (1, 3).

Answer:

To solve our given problem we will use section formula :]

Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\ [/tex]

Let

(-1 , 7) = (x₁ , y₁)

(4 , -3) = (x₂ , y₂)

m = 2

n = 3

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\ [/tex]

[tex]x+40=3x\\2x=40\\x=20[/tex]

For this case we have by definition of angles between secant lines that:

[tex]x + 40 = 3x[/tex]

Also, the angle between T and V is equal to the angle between S and W.

Returning to the question, we have to:

[tex]x + 40 = 3x[/tex]

We must know the value of "x":

Subtracting 3x on both sides of the equation we have:

[tex]x-3x + 40 = 0[/tex]

Subtracting 40 from both sides of the equation:

[tex]-2x = -40[/tex]

Dividing between -2 on both sides of the equation:

[tex]x = \frac {-40} {- 2}\\x = 20[/tex]

So, the value of x is 20

Answer:

[tex]x = 20[/tex]

Answer:

Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]

Step-by-step explanation:

We need to divide

[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]

For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]

The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]

Solving

[tex]=\frac{2}{\sqrt{13}+\sqrt{11}} *\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}} \\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]

So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]

Answer:

The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]

Step-by-step explanation:

Answer:

- 768

Step-by-step explanation:

Substitute n = 8 into the explicit formula, that is

[tex]a_{8}[/tex] = 6 × [tex](-2)^{7}[/tex] = 6 × - 128 = - 768

Answer:

An average of 661 people per day.

Step-by-step explanation:

1. 365-7= 358

2. 236,758/ 358= 661.3351

3. Round to 661

Answer:

a) $2248.75

Step-by-step explanation:

Susan pays $0.3 per $100

For $483000, she pays $1449 insurance annually : Calculation shown below

483000/100 x 0.3 = $1449

Monthly instalments of the insurance premium for 12 months :

annual insurance premium/ 12 months

1449/12 = $120.75

Monthly mortgage payments = $2128

Monthly total payments = monthly mortgage payments + monthly insurance premium instalment.

                                       = 1449 + 120.75

                                       = $2248.75

!!

Answer:

0.50

Step-by-step explanation:

we know that

Observing the graph

we have the following points

(1,3),(2,4),(3,9),(4,7),(5,2),(6,18)

Using a Excel tool (Correl function)

The correlation coefficient is equal to r=0.605639

see the attached table

therefore

The correlation coefficient that best matches the data plotted on the graph is 0.50

Answer:

Step-by-step explanation:

y - 3 = -4(x - 5)

Add 3 to both sides to isolate y

y = -4 ( x - 5 ) + 3

Distribute

y = -4x +20 + 3

Combine like terms

y = -4x + 23

y = mx + b is standard form for which m is slope

m = -4

Please mark for brainliest!! :D Thanks!!

If you have any questions or need more information, please comment below and I'll respond asap!!

Answer:

-4

Step-by-step explanation:

Distribute -4 into the parenthesis and get -4x + 20. The number paired with x is the slope, usually represented by m in y = mx + b. So, the slope is -4. For the full slope intercept format, move the -3 on left side to the right by adding 3. The new equation is y = -4x + 23.

Answer:

[tex]24\sqrt{5}\ yards[/tex]

Step-by-step explanation:

Let A1 be the area of one square and A2 be the area of second square

So,

A1 = s^2

where s is side of square

[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]

So side of one square is [tex]5\sqrt{5}[/tex]

To calculate the length of fence we need to find the perimeter of the square

So,

P1 = 4 * s

[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]

For second square:

[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]

The perimeter will be:

[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]

So the total fence will be: P1+P2

[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]

Answer:

-9

Step-by-step explanation:

find the value of i2, which is -9, find the value of i7, which is 6

Then, add them together and multiply by the number of terms in the sequence divided by 2 (6/2=3)

Answer:

The area is 0.015m²

Step-by-step explanation:

Step one

Given that the expression for area of the circle is A = π r²

Step two

Now our raduis r= 7cm - - - meter =7/100= 0.07

And Pi = 3.142

Step three

Substituting r in the formula for area we have

A= 3.142*(0.07)²

A=3.142*0.0049

A= 0.015m²

Answer:

x =3

Step-by-step explanation:

5(x + 1) = 4x + 8

Distribute the 5

5x+5 = 4x+8

Subtract 4x from each side

5x-4x+5 = 4x-4x+8

x+5 =8

Subtract 5 from each side

x+5-5 = 8-5

x =3

Answer:

One globe costs $60.79

Step-by-step explanation:

The area of the globe is

A = 4.π.r^2

Since the radius is 11 inches

A = 4*(3.14)*(11 in)^2 = 1519.76 in^2

We apply a rule of three

1 in^2  --------------------------------- $0.04

1519.76 in^2 ------------------------- x

x = (1519.76 in^2/ 1 in^2)*$0.04

x = (1519.76)*$0.04

x = $60.79

x ≈ $60.8

Answer: Second Option

$60.79

Step-by-step explanation:

To solve this problem let's suppose that the balloons are spherical

Then the surface area of a sphere is given by the formula:

[tex]SA=4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that the radius of each globes is 11 inches, then:

[tex]SA=4(3.14) (11)^2[/tex]

[tex]SA=4(3.14)(121)[/tex]

[tex]SA=1519.76\ in^2[/tex]

If the material to make globes costs $ 0.04 per square inch then the cost of a globes is:

[tex]C=1519.76*0.04[/tex]

[tex]C=\$60.79[/tex]