What divides a line segment into two congruent segments?

Answer:

infinite solutions

Step-by-step explanation:

y=5/2x+2

2y= 5x +4

Multiply the first equation by 2

y = 5/2 x +2

2y = 5/2 *2 x +2 *2

2y = 5x +4

Since this is identical to the second equation (they are the same), the system of equations has infinite solutions

Answer:

2/3

Step-by-step explanation:

slope = run/rise

rise = vertical distance = difference in y-coordinates

run = horizontal distance = difference in x-coordinates

Find the rise = difference in the y-coordinates: 5 - 9 = -4

Find the run = difference in the x-coordinates in the same order: -2 - 4 = -6

Divide the rise by the run: slope = -4/-6

Reduce the fraction: slope = 2/3

(-2, 5) (4, 9)

Y2 - Y1

-----------

X2 - X1

9-5

------- = 4/6

4+2

4/6 simplifies to 2/3

Slope: 2/3

[tex]|2x-4|>-2\\x\in\mathbb{R}[/tex]

Answer:

that would be 38 degrees

Step-by-step explanation:

Answer:

m∠2 = 38°

Explanation:

m∠2 and 38° are corresponding angles; therefore, they are equivalent.

Answer:

2 quarts

Step-by-step explanation:

We know that an automobile's radiator has a capacity of fifteen quarts and currently carries twelve quarts of a thirty percent antifreeze solution.

We are to find the number of quarts of pure antifreeze that must be added to strengthen the solution to forty percent.

We can write the following equation for this and solve it:

[tex] 12 + x = y \\ 12 (.30) + 1 x = y ( . 4 0 ) [/tex]

[tex]3.6 + x = 0.4y[/tex]

[tex]0.4(12 + x) = 3.6 + x&\\4.8 + 0.4x = 3.6 + x[/tex]

[tex]x-0.4x=4.8-3.6[/tex]

[tex]0.6x=1.2[/tex]

[tex]x=2[/tex]

Therefore, 2 quarts are needed.

Answer:

Option D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

step 1

we know that

The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

In this problem

[tex]\frac{HG}{JK}=\frac{GF}{JL}=\frac{HF}{KL}[/tex]

Verify

substitute the values

[tex]\frac{48}{12}=\frac{32}{8}=\frac{36}{9}[/tex]

[tex]4=4=4[/tex] ---> is true

therefore

The triangles are similar by SSS similarity theorem

step 2

we know that

The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

In this problem

Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

therefore

The triangles are similar by SAS similarity theorem

Answer:

D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

Edge 2020 (2021)

Answer:

5x - 8

Step-by-step explanation:

(2x - 7) + (3x - 1)

We would first solve for whatever is in the parenthesis, but there is a variable with both expressions, so we need to remove it to simplify:

2x - 7 + 3x - 1

Now combine like terms and simplify:

2x + 3x - 7 - 1

So the answer is 5x - 8

Final answer:

To add the expressions (2x-7) and (3x - 1), simply combine the like terms, resulting in 5x - 8.

Explanation:

When you are tasked with adding the expressions (2x-7) and (3x - 1), you combine like terms. This means you add the coefficients of the same powers of x together and combine the constants. To demonstrate:

(2x-7) + (3x - 1) = (2x + 3x) + (-7 - 1)

You combine the x terms:

2x + 3x = 5x

And then combine the constants:

-7 - 1 = -8

Thus, the sum of the expressions is:

5x - 8

Answer:

-3

Step-by-step explanation:

First, solve what's inside the absolute value lines. -5+2=-3

Because it's in absolute value lines, the negative becomes a positive so |-3|=3

The result is -3 (because we still have that negative sign outside the absolute value lines.

Answer:

B hope I helped.

Step-by-step explanation:

Answer: answers 1 and 5 are correct.

Answer:

$299

Step-by-step explanation:

Rent+standard deviation 890+206= $1,096

John's rent: $1,395

Z-score: 1395 - 1096=$299

Answer: 2.4515

Step-by-step explanation:

Given : The mean monthly rent of students at Oxnard University is [tex]\mu=\$890[/tex] with a standard deviation of [tex]\sigma=\$206[/tex]

Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], we have the  standardized z-value for x= 1395 as

[tex]z=\dfrac{1395-890}{206}=2.45145631068\approx2.4515\ \text{ [To the nearest four decimal places.]}[/tex]

Hence, the standardized z-score = 2.4515

Answer: 2.3, 1 3/4, 1.6, 2/5

Step-by-step explanation: Convert each fraction into a decimal (or vise versa), then order.

1 3/4 = 1.75

2/5 = 0.4

Answer:

Answer is 2/5, 1 3/4, 1.6, 2.3

Step-by-step explanation:

Lets see: 1 3/4 = 7/4

2.3 = 23/10 or 2 3/10

2/5 is 2/5

and

1.6 is 8/5

so the least is 2/5, 1 3/4, 1.6, 2.3

Hope my answer has helped you in any way!

Answer:

-1/5x +1/2

ghiybifvcodtgy78

Answer:

b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]

Step-by-step explanation:

We have to find the linear which has same slope  as the slope represented by the table.

Slope formula :m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

By using the formula and substitute [tex]y_1=\frac{1}{5},y_2=\frac{7}{50},x_1=-\frac{1}{2},x_2=-\frac{1}{5}[/tex]

Slope=[tex]\frac{\frac{7}{50}-\frac{1}{5}}{-\frac{1}{5}+\frac{1}{2}}[/tex]

Slope=[tex]\frac{-\frac{3}{50}}{\frac{3}{10}}[/tex]

Slope=[tex]-\frac{3}{50}\times \frac{10}{3}[/tex]

Slope=[tex]-\frac{1}{5}[/tex]

a.[tex]y=-\frac{1}{2}x+\frac{1}{10}[/tex]

Compare with

[tex]y=mx+b[/tex]

we get m=[tex]-\frac{1}{2}[/tex]

Slope=[tex]-\frac{1}{2}[/tex]

Hence, option A is false.

b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]

Slope of given function=[tex]-\frac{1}{5}[/tex]

It is true.

c.[tex]y=\frac{1}{5}x-\frac{1}{2}[/tex]

Slope of given function=[tex]\frac{1}{5}[/tex]

Hence, option is false.

d.[tex]y=\frac{1}{2}x-\frac{1}{10}[/tex]

Slope of given function=[tex]\frac{1}{2}[/tex]

Hence, option is false.

Answer:

5/12

Step-by-step explanation:

First find the probability on the first roll

The possible results are 1,2,3,4,5,6

evens: 2,4,6

not 2 = 1,3,4,5,6

P(even)=  number of evens/total = 3/6 = 1/2

P (not 2) = number of results not 2/ total = 5/6

Since the rolls are independent (do not depend on each other), we can multiply the probabilities

P(even, then not 2) = 1/2 * 5/6 = 5/12

To find the linear form of a point-slope equation, simply solve for y:

y+1=-3(x-5)

*Distribute the -3*

y+1=-3x+15

*Subtract 1 from both sides*

y=-3x+14

Hope this helps!!

Answer:

f(x) = –3x + 14

Step-by-step explanation:

Answer:

[tex]\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have

[tex]m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3[/tex]

Substitute:

[tex]y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

[tex]y-3=-\dfrac{1}{3}(x+6)[/tex]           use the distributive property

[tex]y-3=-\dfrac{1}{3}x-2[/tex]           add 3 to both sides

[tex]y=-\dfrac{1}{3}x+1[/tex]

Convert to the standard form

[tex]Ax+By=C[/tex]

[tex]y=-\dfrac{1}{3}x+1[/tex]           multiply both sides by 3

[tex]3y=-x+3[/tex]             add x to both sides

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

Answer:

f(2) = -6

Step-by-step explanation:

f(x) = 3x - 12

Plug in 2 for x & solve:

f(2) = 3(2) - 12

Remember to follow PEMDAS. First multiply, then subtract:

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

f(2) = -6 is your answer.

~

Answer:

Step-by-step explanation:

<, ≤ - line to the left

>, ≥ - line to the right

<, > - open circle

≤, ≥ - closed circle

==================================

We have the line to the left and open circle.

The circle is on -7.

Therefore is x < -7

Answer:

512

Step-by-step explanation:

Solve the parenthesis first. Note that:

2^3 = 2 * 2 * 2 = (4) * 2 = 8

4^3 = 4 * 4 * 4 = (16) * 4 = 64

Multiply:

8 * 64 = 512

512 is your equivalent expression.

~

Answer:

(2³)(4³) = 2³ x [tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512

Answer:

[tex]\large\boxed{x=0\ \vee\ x=1}[/tex]

Step-by-step explanation:

[tex]Domain:\\\\x-2\neq0\ \wedge\ x+1\neq0\\\\x\neq2\ \wedge\ x\neq-1\\\\\boxed{D:\ x\in\mathbb{R}-\{-1,\ 2\}}\\\\=============================[/tex]

[tex]\dfrac{x}{x-2}+\dfrac{x-1}{x+1}=-1\qquad\text{subtract}\ \dfrac{x-1}{x+1}\ \text{from both sides}\\\\\dfrac{x}{x-2}=-1-\dfrac{x-1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)}{x+1}+\dfrac{-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-x-1-x+1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-2x}{x+1}\qquad\text{cross multiply}[/tex]

[tex]x(x+1)=-2x(x-2)\qquad\text{use the distributive property}\\\\(x)(x)+(x)(1)=(-2x)(x)+(-2x)(-2)\\\\x^2+x=-2x^2+4x\qquad\text{add}\ 2x^2\ \text{to both sides}\\\\3x^2+x=4x\qquad\text{subtract 4x from both sides}\\\\3x^2-3x=0\qquad\text{distributive}\\\\3x(x-1)=0\iff 3x=0\ \vee\ x-1=0\\\\x=0\in D\ \vee\ x=1\in D[/tex]

Answer:

Step-by-step explanation:

I'm taking this to mean

x/(x-2) + (x-1)/(x+1)  =  -1

Multiply through by (x - 2)*(x + 1) to get rid of the denominator on the left.

x(x + 1) + (x - 1)(x - 2) = -1 * (x - 2)(x + 1)

Remove the brackets on the left and right.

Be careful about the right side. Do it in two steps (or three)

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

2x^2 - 2x + 2 = - (x^2 - x - 2)

2x^2 - 2x + 2 = - x^2 + x + 2

Bring the right side to the left

2x^2 - 2x + 2 + x^2 - x - 2 = 0

3x^2 - 3x = 0

Factor this

x*(3x - 3) =0

x = 0

3x - 3 = 0

Add 3 to both sides.

3x = 3

Divide by 3

x = 3/3

So either x = 0

or

x = 1

Just to confirm that that is correct, a graph is included which shows the x roots are 0 and 1

Answer:

f(- 1) = 14

Step-by-step explanation:

To evaluate f(- 1) substitute x = - 1 into f(x)

f(- 1) = (- 1)² - 8(- 1) + 5 = 1 + 8 + 5 = 14

Answer:

f(-1)=14

14-4=25

13=70

Step-by-step explanation:

Answer:

58 meters

Step-by-step explanation:

We are looking for the length of the base of a triangle, given the height and area. The formula for the area of a triangle  

A=1/2 bh

relates A= the area, b= length of the base, and h= the height of a triangle, so this is the formula we should use.

We are given that the area of the triangle is A=493 and the height h=17. Substitute this information into the formula and solve for b to find

A=493

493=1/2⋅b⋅17

493=17/2b

58=b

The length of the base is 58 meters.

The length of the base of the triangle is 58 meters.

Given,

A triangular flag has an area of 493 square meters and a height of 17 meters.

We need to find what is the length of the base.

The area is given by:

= 1/2 x base x height

Find the area of the triangle.

Area = 493 square meters

Height = 17 meters

Area = 1/2 x base x height

493 square meters = 1/2 x base x 17 meters

Multiply 2 on both sides.

2 x 493 = 2 x 1/2 x base x 17

986  = base x 17

Dividing both sides by 17.

986 / 17 = base

Base = 58 meters.

Thus the length of the base of the triangle is 58 meters.

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Change f(x) to y , switch x and y , and solve for y.

                   [tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]

We know that while finding the inverse of a function the following steps are to be followed:

We are given a function f(x) by:

[tex]f(x)=e^{2x}-4[/tex]

Now, we put

[tex]f(x)=y[/tex]

i.e.

[tex]e^{2x}-4=y[/tex]

Now, we interchange x and y as follows:

[tex]e^{2y}-4=x[/tex]

and finally we solve for y

i.e.

[tex]e^{2y}=x+4[/tex]

Taking logarithmic function both the side of the equation we get:

[tex]2y=\ln (x+4)\\\\i.e.\\\\y=\dfrac{\ln (x+4)}{2}[/tex]

i.e.

[tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]

Answer:

[tex]x=\frac{34z-r}{n}-17[/tex]

Step-by-step explanation:

Given

[tex]n(17+x)=34z-r[/tex]

We have to isolate x on one side of the equation

Dividing both sides by n

[tex]\frac{n(17+x)}{n} =\frac{34z}{n}-\frac{r}{n}[/tex]

Taking LCM on left side

[tex]17+x = \frac{34z-r}{n}[/tex]

Subtracting 17 from both sides

[tex]17+x-17 = \frac{34z-r}{n}-17[/tex]

So, the value of x will be:

[tex]x=\frac{34z-r}{n}-17[/tex] ..

The answer is:

[tex]x=\frac{34z-r}{n}-17[/tex]

To solve for "x" , we just need to isolate it from the equation.

So, we are given the equation:

[tex]n(17+x)=34z-r[/tex]

Then, isolating we have:

[tex]n(17+x)=34z-r\\\\17+x=\frac{34z-r}{n}\\\\x=\frac{34z-r}{n}-17[/tex]

Hence, the answer is:

[tex]x=\frac{34z-r}{n}-17[/tex]

Have a nice day!

ANSWER

[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]

EXPLANATION

The given function is

[tex] \frac{ - 12x}{ \sqrt{x} - 10 } [/tex]

In the denominator we have

[tex] \sqrt{x} - 10[/tex]

The conjugate of this surd is

[tex] \sqrt{x} + 10[/tex]

To rationalize this function, we multiply both the numerator and the denominator by the conjugate surd.

[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x} - 10)(\sqrt{x} + 1)} [/tex]

We apply the identity

[tex] (a + b)(a - b) = {a}^{2} - {b}^{2}[/tex]

in the denominator.

This implies that,

[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x})^{2} - {10}^{2} } [/tex]

[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]

Answer:

2 ( x ^3 + 2 x^ 2 − 2 )

Step-by-step explanation:

Factor  2  out of  

2 x^ 3 + 4 x^ 2 − 4 .

Answer:

B; 18

Step-by-step explanation:

9/11 = 18/22

Answer:

the correct answer will be D) 9

Step-by-step explanation:

Answer:

3 pounds

Step-by-step explanation:

Answer:

The values are a = 5 , b = 3 , h = 0 , k = 3

The equation is x²/9 + (y - 3)²/25 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where  

-The length of the major axis is 2a  

- The coordinates of the vertices are (h , k ± a)  

- The length of the minor axis is 2b  

- The coordinates of the co-vertices are (h ± b , k)  

- The coordinates of the foci are (h , k ± c), where c² = a² - b²  

* Now lets solve the problem

∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)

∴ The major axis is the y-axis

∴ The vertices are (h , k + a) and (h , k - a)

∴ h = 0

∴ k + a = 8 ⇒ (1)

∴ k - a = -2 ⇒ (2)

∵ The foci of it located at (0 , 7) , (0 , -1)

∵ The coordinates of the foci are (h , k + c) and (h , k - c)

∴ h = 0

∴ k + c = 7 ⇒ (3)

∴ k - c = -1 ⇒ (4)

- To find k and a add equations (1) and (2)

∴ (k + k) + (a + - a) = (8 + -2)

∴ 2k = 6 ⇒ divide both sides by 2

∴ k = 3

- Substitute the value of k in equation (1) or (2) to find a

∴ 3 + a = 8 ⇒ subtract 3 from both sides

∴ a = 5

- To find the value of c substitute the value of k in equation (3) or (4)

∴ 3 + c = 7 ⇒ subtract 3 from both sides

∴ c = 4

- To find b use the equation c² = a² - b²

∵ a = 5 and c = 4

∴ (4)² = (5)² - a²

∴ 16 = 25 - b² ⇒ subtract 25 from both sides

∴ -9 = -b² ⇒ multiply both sides by -1

∴ b² = 9 ⇒ take √ for both sides

∴ b = 3

* The values are a = 5 , b = 3 , h = 0 , k = 3

* The equation is x²/9 + (y - 3)²/25 = 1

Answer:

a=5, b=3, h=0, k=3

Step-by-step explanation:

The center of the circle is (0,3) therefore h is 0 and k is 3. If you use a graphing calculator and plot the points given you should find that a=5. Then try to c and use the equation c^2=a^2-b^2 to find b.

Answer:

Step-by-step explanation:

We have quadratic functions f(x) = ax² + bx + c.

c - y-intercept

If a > 0, then a parabola opens up and has a minimum in a vertex.

If a < 0, then a parabola opens down and has a maximum in a vertex.

The function has maximum and y-intercept of 4:

a < 0 and c = 4

The graph of the function which will have a maximum and a y-intercept of 4 is C. f(x) = x² + 2x + 4.

y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.

Given are four functions.

We have to find the function which has a y intercept of 4.

This means that substitute x = 0 and then find the value of f(x).

A. f(x) = 4x² + 6x - 1

When x = 0, f(x) = -1 ≠ 4

B. f(x) = -4x² + 8x - 5

When x = 0, f(x) = -5 ≠ 4

C. f(x) = x² + 2x + 4

When x = 0, f(x) = 4

D. f(x) = x² + 4x - 4

When x = 0, f(x) = -4

Hence the function which has a y intercept of 4 is C. f(x) = x² + 2x + 4.

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