–5x+4

constant
coefficient:
variable:

Given:

The figure of a triangle.

To find:

The missing length.

Solution:

Let x be the missing length.

Basic proportionality theorem(BPT): According to this theorem, if a line is parallel to the one side of a triangle then that the line intersects the other two sides of the triangle in the same ratio.

Using Basic proportionality theorem, we get

[tex]\dfrac{6}{8-6}=\dfrac{12-x}{x}[/tex]

[tex]\dfrac{6}{2}=\dfrac{12-x}{x}[/tex]

[tex]3=\dfrac{12-x}{x}[/tex]

[tex]3x=12-x[/tex]

Adding x on both sides, we get

[tex]3x+x=12[/tex]

[tex]4x=12[/tex]

[tex]x=\dfrac{12}{4}[/tex]

[tex]x=3[/tex]

The missing length is 3 Therefore, the correct option is D.

Answer:

[tex]f^{-1}(6) = 50[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \sqrt{2x} - 4[/tex]

Required

Find [tex]f^{-1}(6)[/tex]

First, we calculate the inverse function

[tex]f(x) = \sqrt{2x} - 4[/tex]

Express f(x) as y

[tex]y = \sqrt{2x} - 4[/tex]

Swap the positions of x and y

[tex]x = \sqrt{2y} - 4[/tex]

Solve for y: Add 4 to both sides

[tex]4 + x = \sqrt{2y} - 4+4[/tex]

[tex]4 + x = \sqrt{2y}[/tex]

Square both sides

[tex](4 + x)^2 = 2y[/tex]

Divide both sides by 2

[tex]y = \frac{(4 + x)^2}{2}[/tex]

Express y as an inverse function

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

Next, solve for: [tex]f^{-1}(6)[/tex]

Substitute 6 for x

[tex]f^{-1}(6) = \frac{(4 + 6)^2}{2}[/tex]

[tex]f^{-1}(6) = \frac{(10)^2}{2}[/tex]

[tex]f^{-1}(6) = \frac{100}{2}[/tex]

[tex]f^{-1}(6) = 50[/tex]

Answer:

x>3

Step-by-step explanation:

2x+3>9

2x>6

x>3

So all values of x must be greater than 3 in order for the inequality to be true.

Answer:

[tex](-2,8)[/tex]    [tex](7,5)[/tex]      [tex](1,7)[/tex]

Step-by-step explanation:

Given

[tex]x + 3y = 22[/tex]

Solving (a): The possible coordinates

We have:

[tex](x,y) = (-2,8)[/tex]

This gives:

[tex]x + 3y = 22 \to -2 + 3 * 8[/tex]

[tex]x + 3y = 22 \to -2 + 24[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(-2,8) is a point on the grid

[tex](x,y) = (7,5)[/tex]

This gives:

[tex]x + 3y = 22 \to 7 + 3 * 5[/tex]

[tex]x + 3y = 22 \to 7 + 15[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(7,5) is a point on the grid

[tex](x,y) = (-5,5)[/tex]

This gives:

[tex]x + 3y = 22 \to -5 + 3 * 5[/tex]

[tex]x + 3y = 22 \to -5 + 15[/tex]

[tex]x + 3y = 22 \to 10[/tex]

(-5,5) is a not point on the grid

[tex](x,y) = (1,3)[/tex]

This gives:

[tex]x + 3y = 22 \to 1 + 3 * 3[/tex]

[tex]x + 3y = 22 \to 1 + 9[/tex]

[tex]x + 3y = 22 \to 10[/tex]

(1,3) is a not point on the grid

[tex](x,y) = (1,7)[/tex]

This gives:

[tex]x + 3y = 22 \to 1 + 3 * 7[/tex]

[tex]x + 3y = 22 \to 1 + 21[/tex]

[tex]x + 3y = 22 \to 22[/tex]

(1,7) is a point on the grid

So, we plot the following on the grid

[tex](-2,8)[/tex]    [tex](7,5)[/tex]      [tex](1,7)[/tex]

See attachment

Answer:

x = 40 degrees

Step-by-step explanation:

Triangle angle sum is 180 so 180 = 65 + 75 + x.

180 = 65 + 75 + x

180 = 140 + x

40 = x

Answer:

Step-by-step explanation:

subtrct 2 from every x co-ordinate and add 7 to every y co-ordinate.

Answer:

a - they should be large and sturdy

Step-by-step explanation:

The article states that artificial reefs can be made from materials such as concrete, or large pieces of waste such as subway cars, takes, and aircraft carriers. All of these items are large and sturdy.

Hope this helps, have a wonderful day :))

Answer:

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

Answer:

95

Step-by-step explanation:

a cardinal number is anything that is to 70 and the rest of the numbers above 70 are counting by 10s

Answer: B. 183 cm^3

V = pi r^2 h/3

V = pi (5^2) (7/3)

V = pi (25) (2.33)

V = 183

Answer:

B.183 [tex]cm^{3}[/tex]

Step-by-step explanation:

Volume of cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]

where h=7 and r=5 (because r=d/2, where d=10)

V=[tex]5^{2}\frac{7}{3}\pi[/tex]

V=25·[tex]\frac{7}{3} \pi[/tex]

V=175/3[tex]\pi[/tex]

V=183.2595715 or 183 [tex]cm^{3}[/tex]

Answer:

Harper's age = 18

Miguel age = 16

Step-by-step explanation:

Given:

Miguel age = [2/3][Harper's age] + 4

Sum of their age = 34

Computation:

Assume;

Harper's age = a

So,

Miguel age = [2/3][a] + 4

Sum of their age = 34

So,

Miguel age + Harper's age = 34

[2/3][a] + 4 + a = 34

[2a / 3] + a = 34 - 4

[2a + 3a] / 3 = 30

5a / 3 = 30

5a = 90

a = 18

So,

Harper's age = 18

Miguel age = [2/3][a] + 4

Miguel age = 16

Answer:

She needs a time of 61 min on her 8th ride

in order to average 51 min for the 8 rides

Step-by-step explanation:

+%28+46+%2B+48+%2B+50+%2B+43+%2B+54+%2B+54+%2B+52+%2B+t+%29+%2F+8+=+51+

+347+%2B+t+%29+%2F+8+=+51+

+347+%2B+t+=+408+

+t+=+61+

Answer:

(2,14)

Step-by-step explanation:

Since y=5x+4, you can plug that into the other y in the other equation which would give you x+12=5x+4

Now subtract 12 from both sides

x=5x-8

Subtract 5x from both sides

-4x=-8

Now you divide them both by -4 which gives you x=2

Now plug x in to any of the equations

y=5(2)+4

y=10+4

y=14

Your final answer is (2,14)

Answer: B

Step-by-step explanation: So that you know you are only getting the best for what YOU PAID for.

Answer:

.8

Step-by-step explanation:

.8 is the largest

Answer:

B: g=5

C: g=6

Step-by-step explanation:

Given

[tex]7 \ge 12 - g[/tex]

Required

All possible values of g

We have:

[tex]7 \ge 12 - g[/tex]

Collect like terms

[tex]7 - 12\ge - g[/tex]

[tex]-5\ge - g[/tex]

Divide both sides by -1 [The inequality changes because of negative division]

[tex]5\le g[/tex]

Swap both terms

[tex]g \ge 5[/tex]

This implies that g is greater than of equal to 5

i.e.

[tex]g= \{5,6,7.....\}[/tex]

Hence:

(b) and (c) are correct

Answer:

sure

Step-by-step explanation:

but you gotta post the question...

Yes I think you are correct. The domain appears to be the set of x values such that -4 < x < 3 meaning that x is between -4 and 3, excluding each endpoint. In interval notation, that translates to (-4, 3). This of course assumes that we have two vertical asymptotes bookending the left and right sides of the curve, and these vertical asymptotes are at x = -4 and x = 3. If the curve extends beyond these boundaries, then the domain would instead be the set of all real numbers.

Answer:

Step-by-step explanation:

Number of possible combinations:

Answer:

Solution given:

Number of possible combinations:

4×6×8×12×20 = 46080 faces

Answer:

[tex]{\huge\pink{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]

The speed of light (c) is considered a fundamental constant of nature. In the famous relativity equation, E = mc², the speed of light (c) serves as a constant of proportionality, linking the formerly disparate concepts of mass (m) and energy (E).

Answer:

$15.03

Step-by-step explanation:

  50.00

-  34.97

_______

  15.03

Answer:

The answer is $15.03.

Step-by-step explanation:

Just subtract.

Answer:

Answer B.

Because we know He's checking the experiment every 5 minutes.

Answer:

x = 20

Step-by-step explanation:

60 = x+40

subtract 40 from both sides and you get

20 = x

so x = 20

The big orange cooler will hold 14 pitchers of iced tea. The response is C.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Since a pitcher of iced tea holds 128 ounces, we can find the number of pitchers required to fill the large orange cooler by dividing the total volume of the cooler by the volume of one pitcher:

1792 / 128 = 14

Therefore, it will take 14 pitchers of iced tea to fill the large orange cooler. The answer is C.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ2

Answer:

H0 : P = 0.72

H1 : P > 0.72

Step-by-step explanation:

Claim is to test that percentage of customers who leave a review is greater than 72%

From the information given :

P0 = 72/100 = 0.72

The null hypothesis, H0 : P = 0.72

Alternative hypothesis claims the proportion is greater than 0.72 and from the sampling result obtained, phat = 0.90

Hence,

Alternative hypothesis, H1 : P > 0.72