The perimeter of the scalene triangle is 60 cm. The length of the longest side is 4 times that of the shortest side.

Which statements about the possible measures of the sides are reasonable? Check all that apply.

The value of x can equal 40.
The longest side can equal 30 cm.
The shortest side can equal 7 cm.
The value of x can equal 25.
The shortest side can equal 5.

Answer:

Step-by-step explanation:

In this question we will find the equation of the dotted line first.

Since this line passes through two pints (0, 2) and (-3, -7)

So slope of the line will be m = [tex]\frac{y-y'}{x-x'}[/tex]

                                                 = [tex]\frac{-7-2}{-3-0}[/tex]

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

                                                 = 3

y-intercept of the line is c = 2

Now we will put these values in the standard form of the equation

y = mx + c

y = 3x + 2

Now we will check the inequality shown by shaded region

we take a point from shaded region and plug in the value of x and y.

For point ( -2, 0) y = (-2)(2)+2

                              = -4 + 2 = -2 and 0>-2

So there should be the sign of greater than.

Therefore, inequality will be y > 3x + 2

Linear inequality represented by the graph is y > 3x +2 and this can be determine by using the slope intercept form.

Given :

Two points - (0 , 2) and (-3 , -7)

Slope of the line can be calculated as follows:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-7-2}{-3-0}=3[/tex]

y intercept is 2.

Now we know that the slope intercept form is given by:

y = mx + c

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

To check the inequality we take a point from the shaded region and plug in the value of x and y.

At Point (-3,0), equation (1) can be given by:

y = -9 + 2 = -7 < 0

Than inequality must be y > 3x + 2.

For more information, refer the link given below

https://brainly.com/question/11824567

Answer:

B; 18

Step-by-step explanation:

9/11 = 18/22

Answer:

the correct answer will be D) 9

Step-by-step explanation:

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{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:

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:

2 ( x ^3 + 2 x^ 2 − 2 )

Step-by-step explanation:

Factor  2  out of  

2 x^ 3 + 4 x^ 2 − 4 .

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

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

[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:

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:

-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:

30 sq. units

Step-by-step explanation:

Multiply the length of the two diagonals together and divide by two

[tex]\frac{d1 * d2}{2}[/tex]

10 * 6 = 60

60/2 = 30

The area of the kite is 30 sq. units

Answer: B

Step-by-step explanation:

How to get the area of a rhombus

( diagonal x the other diagonal )1/2

(6*10)1/2

60*1/2

30

you can't solve this nor find the value of y because its not a full equation

Answer:

You cant solve for y without knowing the end number.

Step-by-step explanation:

maybe your equation y + 30 = 32 then we would know y is = to 2

Answer:

3.4657359...

Step-by-step explanation:

just put into your phone calculator 32 then hit In.

The value of ln 32 is 3.468 .

Logarithm is an inverse of Exponentiation , The power to which a number must be raised in order to obtain another number is known as a logarithm.

It is given that

ln 2 = 0.693

ln 32 = ?

32 = 2⁵

ln 32 = ln 2⁵

ln aⁿ = n ln a

ln 32 = 5 ln 2

ln 32 = 5 * 0.6936

ln 32 = 3.468

Therefore the value of ln 32 is 3.468 .

To know more about logarithm

https://brainly.com/question/20785664

#SPJ2

Answer:

20°

Step-by-step explanation:

One way of doing this is to find the constant of proportionality, k:

8k + 6k + 4k = 90°    Then 18k = 90°, and k turns out to be 90/18, or 5.

Then the angles are 8(5), 6(5) and 4(5).  The smallest of these angles is thus 20°

let's recall that the sum of all interior angles in a triangle is 180°.

we know the angles are in a 8:6:4 ratio, so we simply divide 180 by (8+6+4) and then distribute accordingly.

[tex]\bf 8:6:4\qquad \qquad \left( 8\cdot \cfrac{180}{8+6+4} \right) : \left( 6\cdot \cfrac{180}{8+6+4} \right) : \left( 4\cdot \cfrac{180}{8+6+4} \right) \\\\\\ (8\cdot 10):(6\cdot 10):(4\cdot 10)\implies 80~:~60~:~\stackrel{\textit{smallest}}{40}[/tex]

Answer:

3 pounds

Step-by-step explanation:

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:

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:

200 more on Friday than thursday

Answer:

3(x-2)+x=4x+6

Step-by-step explanation:

case 1) we have

3(x-2)+x=4x-6

Solve for x

3x-6+x=4x-6

4x-6=4x-6

0=0 ----> is true for any value of x

therefore

The equation has infinite solutions

case 2) we have

3(x-2)+x=2x-6

3x-6+x=2x-6

4x-2x=-6+6

2x=0

x=0

case 3) we have

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

3x-6+x=3x-3

4x-3x=-3+6

x=3

case 4) we have

3(x-2)+x=4x+6

3x-6+x=4x+6

4x-4x=6+6

0=12 ------> is not true

therefore

The equation has no solution

Answer:

Step-by-step explanation:

The first equation is the one that doesn't have solution. Let's demonstrate this:

[tex]3(x-2)+x=4x+6\\3x-6+x=4x+6\\4x-6=4x+6\\4x-4x=6+6\\0=12[/tex]

As you can observe, the equation doesn't have any solutions, because it result in a false statement.

If we solve the other equations, we would have:

[tex]3(x-2)+x=2x-6\\3x-6+x=2x-6\\4x-6=2x-6\\4x-2x=-6+6\\2x=0\\x=0[/tex]

[tex]3(x-2)+x=3x-3\\3x-6+x=3x-3\\4x-3x=-3+6\\x=3[/tex]

[tex]3(x-2)+x=4x-6\\3x-6+x=4x-6\\4x-6=4x+6\\6=6[/tex]

The last equation has infinite solutions.

Therefore, the only one that doesn't have any solutions is

Answer:

The measures of two complementary angles are 63° ,  27°

Step-by-step explanation:

The measures of two complementary angles are 6y + 3 and 4y - 13.

Sum of complementary angles = 90°

6y + 3  + 4y - 13 =  90°

10y - 10 =  90°

10y = 90 + 10 = 100

10 y = 100

y    = 100/10 = 10

One angle = 6y + 3 = 6 * 10 + 3 = 60 + 3 = 63

other angle = 4y - 13 = 4 * 10 - 13 = 40 - 13 = 27

The angles are 63° ,  27°

Answer:

[tex]r=180-\frac{7\pi }{12}[/tex]

Step-by-step explanation:

To find the reference angle of a given angle, first of all, the quadrant of the given angle is determined.

So for 7pi/12

The quadrant is 2nd.

For the angle belonging to 2nd quadrant the equation for reference angle will be:

r=180 - theeta

[tex]r=180-\frac{7\pi }{12}[/tex]

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:

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:

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

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:

B hope I helped.

Step-by-step explanation:

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:

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.