ZA and B are vertical angles. If mZA = (2x + 7)º and m B = (5x + 16),

then find the measure of ZB.

The dimensions of triangle ΔDEF can be obtained from ΔABC by applying a scale factor of dilation of [tex]\displaystyle \frac{1}{2}[/tex].

Reasons:

The given vertices of the triangles are;

ΔABC: A(1, 5), B(3, 9), C(5, 3)

ΔDEF: D(-3, 3), E(-2, 5), and F(-1, 2)

The lengths of the sides of ΔABC are

AB = √((1 - 3)² + (5 - 9)²) = √20 = 2·√5

BC = √((5 - 3)² + (3 - 9)²) = √40 = 2·√10

AC = √((1 - 5)² + (5 - 3)²) = √20 = 2·√10

The lengths of the sides of ΔDEF are;

DE = √((-3 - (-2))² + (3 - 5)²) = √5

EF = FE = √((-1 - (-2))² + (2 - 5)²) = √10

DF = √((-3 - (-1))² + (3 - 2)²) = √5

Therefore;

[tex]\displaystyle The \ dilation \ that \ gives \ \Delta ABC = \frac{\overline {EF}}{\overline {BC}} = \frac{\overline {DE}}{\overline {AB}} = \frac{\overline {DF}}{\overline {AC}} = \frac{\sqrt{10} }{2\cdot \sqrt{10} } = \frac{1}{2}[/tex]

The ratio of the sides of ΔABC to the corresponding sides of ΔDEF are equal to [tex]\displaystyle \frac{1}{2}[/tex].

Which gives;

ΔDEF is a dilation of ΔABC, and ΔDEF and ΔABC are similar by the

definition of similarity in terms of a dilation.

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Answer:

Step-by-step explanation:

They are congruent by the definition of congruence in terms of rigid motions.

Answer: Let the number be x.

According to the question,

2x-3=13

So, 2x=16

So, x=8.

Thus, the number is 8

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

Answer:

23 gallons per hour

Step-by-step explanation:

5 3/4 * 4 = 23

times the amount drank in 1/4 hours by 4 to get the amount drank in 1 hour

(1/4 * 4 = 1 hour (example))

Answer:

70

Step-by-step explanation:

Answer:

213.5035 or 213.50

Step-by-step explanation:

I did the math lol

Answer:

213.5

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

k/-6 - (-4) = 6

k/-6 + 4 = 6

k/-6 = 6 - 4

k/-6 = 2

k = 2 . -6

k = -12

Answer:

max number of people is 9

Step-by-step explanation:

285 - 7.25 - 28.50p

Mag aral ka po ng ayos pag nag f2f na para di ka naka asa dito

Answer:

7

Step-by-step explanation:

Answer:

Make a line connecting points (0,0) (1,5) and (-1,-5)

Step-by-step explanation:

Okay, so you have to start your first point at (0,0), which is the origin, because there is no y-intercept in the equation.

Next you use slope, Rise/Run to plot your next point. In the equation y=mx+b, the slope is in m. So in y=5x, the slope is 5/1 .

So, you're going to move up 5 from the origin and move to the right once, which will give you the point (1,5).

If you need another point to make a line go the opposite way from the origin. So we would go down 5 and left 1. That would give us the point (-1,-5)

Hopefully this helps! Leave a comment if it does and I suggest asking your teacher to make sure it's correct!

Answer:

y=-6.

Step-by-step explanation:

1) the condition f(-1)=-6 and f(4)=-6 mean points A and B have coordinates (-1;-6) and (4;-6);

2) the points A and B has the same y-coordinate, it means, the required line is parallel to the x-axis and the required function is: y=-6.

P.S. the suggested way is not the only one.

The linear function f is f(x) = -6.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(-1) = -6

f(4) = -6

The linear function f can be in the form of f(x) = mx + c.

Now,

m = (-6 + 6) / (4 - 1)

m = 0/3

m = 0

Now,

f(-1) = -6

x = -1

f(x) = mx + c

f(-1) = 0 x -1 + c

-6 = 0 + c

c = -6

Now,

f(x) = -6

Thus,

The function f is a constant function.

f(x) = -6

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Answer:

- 1/40

Step-by-step explanation:

-0.025 = -0.025/1

we have 3 numbers after the decimal point so we multiply both numerator and denominator by 1000

( -0.025 x 1000)/(1 x 1000) = -25/1000

reduce the above fraction by dividing both numerator and denominator by the greatest common divisor between them. in this case GCD (25,1000) = 25.

(-25/25)/(1000/25) = - 1/40

Answer:  32.50  [No $ sign as per the directions]

Step-by-step explanation:

The graph appears as a straight line.  That means we can pick any two points and calculate the slope, m, for the equation of a straight line:  y = mx + b

We can pick any two points, so I'll pick two that do not require interpretation of the graph.  Points (0,0) and (8,20) look good since we can feel relatively confident that the line crosses those two points since they fall on the graph marking lines.

Slope is Rise/Run, or the change in y per the change in x.  For these two points, we have:

Rise = (20 - 0) or 20

Run =    (8 - 0) or 8

The slope is Rise/Run.  20/8, or 2.5

[The units for the slope are $/lb, but units are to be left out of the answer]

The equation is now y = 2.5x + b

b is the y-intercept, the value of y when x = 0.  We can see that y = o when x = 0, so b is zero.

The final equation is y = 2.5x

Use x = 13 lbs to find the cost of 13 lbs of blueberries.

It is 13*2.5 = 32.50

Answer:

I think it's -35

Step-by-step explanation:

sorry if its wrong

Answer:

Step-by-step explanation:

First divide 1500 by 60 to see how many words he can write in a minute. he can text 25 words a minute. multiply that by five to see how many words he can text in five minutes. he can text 125 words in five minutes, so he can text 85 words in a minute.

Answer:

it is linear because there is no answers on the input side that are the same and there is no numbers on the output that are the same  if it was nonlinear there would have 2 be some numbers that are the same but the answer is linear because there are no numbers that are the same

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

Answer: $63.75

Step-by-step explanation:

85-25%= $63.75

Answer:

45.82

Step-by-step explanation:

The dimensions of the border is 1.5 feet for the garden

A rectangle is a quadrilateral with four sides and four angles in which opposite sides are equal and parallel.

The area of a rectangle = Length * breadth

Given that length of garden = 16 ft., width of garden = 12 ft.

It is surrounded by a mulch of width x, hence:

New length = 16 + x + x = 16 + 2x

New width = 12 + x + x = 12 + 2x

The area of garden = 16 + 2x(12 + 2x) = 192 + 56x + 4x²

Since the maximum area is 285 ft, hence:

192 + 56x + 4x² = 285

4x² + 56x - 93 = 0

x = 1.5 feet

The dimensions of the border is 1.5 feet

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Answer: 0.3

Step-by-step explanation:

because the hundreths place is less than 5 you round down the 0.3. If it was 5 or greater you would round up to 0.4

Step-by-step explanation:

ln(x) + ln(x + 25) = 0

ln(x(x + 25)) = 0

ln(x² + 25x) = 0

ln(x² + 25x) = ln(1) , x ≥ 0

x² + 25x = 1

x² + 25x + 625/4 = 1 + 625/4

(x + 25/2)² = 629/4

x + 25/2 = ±√(629/4)

x = ( -25 ±√629)/2

x = (-25 - √629)/2 atau ( -25 + √629)/2

(-25 - √629)/2 ≥ 0 NOT PROVED

(-25 + √629)/2 ≥ 0 PROVED

Solution → x = (-25 + √629)/2

Answer:

Step-by-step explanation: you would start with a dot on the y-axis at -2, then you would go up 2 and over 5 cuz the slope is 2/5. just keep doing this and you’ll have your graph

Step-by-step explanation:

[tex] = ( - \frac{1}{3} + \frac{1}{9} ). {4}^{2} + \frac{5}{18} [/tex]

[tex] = ( - \frac{3}{9} + \frac{1}{9} ).16 + \frac{5}{18} [/tex]

[tex] = - \frac{2}{9} .16 + \frac{5}{18} [/tex]

[tex] = - \frac{32}{9} + \frac{5}{18} [/tex]

[tex] = - \frac{64}{18} + \frac{5}{18} [/tex]

[tex] = - \frac{59}{18} [/tex]

Option → C

letter c

Step by step Explanation:

(-1/3+1/9)(4²)+5/18

=-2/9(4²)+5/18

=-2/9(16)+5/18

=-32/9+5/18

=-59/18

hope this help you!

Notice that 100 is 20 less than 120, or equivalently 2 standard deviations σ below the mean µ. So

P(x ≥ 100) = P(x ≥ µ - 2σ)

Recall the empirical rule for normal distributions (these are true for any mean µ and s.d. σ):

• P(µ - σ ≤ x ≤ µ + σ) ≈ 0.65

• P(µ - 2σ ≤ x ≤ µ + 2σ) ≈ 0.95

• P(µ - 3σ ≤ x ≤ µ + 3σ) ≈ 0.997

The probability we want is the same as

P(x ≥ µ - 2σ) = P(µ - 2σ ≤ x ≤ µ + 2σ) + P(µ + 2σ ≤ x)

or

P(x ≥ µ - 2σ) ≈ 0.95 + P(µ + 2σ ≤ x)

which is clearly some number larger than 0.95, so A must be correct.

Suppose a normal distribution has a mean of 120 and a standard deviation, P(x >= 100) is 0.975. Option A. This is further explained below.

Generally, normal distribution is simply defined as a function that displays the dispersion of numerous unknown parameters as a symmetrical bell-shaped graph.

In conclusion, based on the function

P(x ≥ µ - 2σ) ≈ 0.95 + P(µ + 2σ ≤ x)

the function P(x >= 100) is 0.975

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Answer:

7. (0, -3) (1,-4) (2,-2)

Answer:

60%

Step-by-step explanation:

1% is 3.5

10% is 35

210 / 35 = 6

Answer:

a) 3 lemons = (0.3)^3 = 0.027

------------------------------------

b) No fruit symbols = (0.5)^3 = 0.125

c) 3 bells (the jackpot) = (0.1)^3 = 1/1000

d) No bells = (999/1000)

e) At least one bar (An automatic loser)= 1 - P(no bars)

= 1 - 3C0(0.4)^0*0.6^3 = 1-0.6^3 = 0.784

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

Cheers,