Solve the problems. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it. In isosceles triangle ∆ABC, BM is the median to the base AC . Point D is on BM . Prove the following triangle congruencies: b ∆AMD ≅ ∆CMD △ AM D≅△CMD by rule ______

Answer:

14

Step-by-step explanation:

5x-7=3x+21

2x=28

x=14

Answer:

14

Step-by-step explanation:

Subtracting 3x and adding 7 to both sides we get 2x = 28. Dividing the equation by 2 gets us x = 14.

Answer:

The width of the garden is 99 feet.

Step-by-step explanation:

Given: The perimeter is 306 ft.

Given: the length of the garden is 99 ft.

Step 1: Because the garden is rectangular and so 2 of its sides are the lengths, we must multiply 99 by 2. 99x2=108.

Step 2: To find out the 2 remaining sides of the garden (the widths), we must subtract the perimeter by the lengths. 306-108=198.

Step 3: Because there are 2 sides which are the widths, we know that they are each equal and add up to 198. To find out how long the width is, we must divide the 2 widths by 2. 198/2=99.

So, the width of the garden is 99 feet.

Make two shapes out of it.

The bottom is a rectangle 14 x 5 = 70 square cm

The top is a triangle 1/2 x 12 x 5 = 30 square cm

Total area = 70 + 30 = 100 square cm

Answer:

100 cm²

Step-by-step explanation:

The composite shape can be cut into two shapes. One triangle and one rectangle. The sum of their areas is the area of the whole composite shape.

The area of the triangle:

b × h × 1/2

(14 - 2) × 5 × 1/2

60 × 1/2

= 30 cm²

The area of the rectangle:

l × w

14 × 5

= 70 cm²

Add the areas of the two shapes.

30 cm² + 70 cm²

= 100 cm²

The area of the composite shape is 100 cm².

Answer:

[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Step-by-step explanation:

We are given that in 1995, the USPS approximated that they handled  [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex]  pieces.

To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.

Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]

Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]  

As it is clear that more pieces of mail were handled in 1995.

So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]

=  [tex]10^{11} \times (1.8 -1.7)[/tex]

=  [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]

Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Answer:

(9,6)

Step-by-step explanation:

So, if we're thinking about a (fair in amount, related to something else/properly sized compared to something else) relationship, or the graph of a (fair in amount, related to something else/properly sized compared to something else) relationship, there should be two things that we're looking for. One, it should be a line. It should be a linear relationship between the two (numbers that change/things that change). Y should be some constant, some (fair in amount, related to something else/properly sized compared to something else)ity constant, times X.

rise/run

2/3 is the proportionality

(6,4) is the last point so if we apply the proportionality the next point should be located at (9,6)

please mark me brainliest :)

Step-by-step explanation:

Overtime rate= r+50%= 1.5r

Regular hours= 800/r

Overtime hours= 240/1.5r

Total hours worked

Answer:

A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.

Step-by-step explanation:

The measures of the angles of in a triangle should correspond to the length size of the side opposite each angle in a triangle.

In simple terms, this means that the larger the measure of an angle, the longer the length of the side opposite that angle. Therefore, the smallest measure of an the 3 angles in the triangle should correspond with the shortest length.

Therefore, the triangle with the correct side length would be "A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees." Check the attachment below to see how each side length corresponds with each angle opposite them.

Answer:

D

Step-by-step explanation:

your welcome

The correct pairs of equivalent expressions are given below.

We have given that,

(5 + 2b)+(2b + 3/2)

(-14 + 3/2b)-(1 + 8/2b)

(-10 + b)+(7b -5)

(7/2b - 3)-(8 + 6b)

We have to determine the equivalent expression

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

(5 + 2b)+(2b + 3/2) <--> 4b + 13/2

(-10 + b)+(7b - 5) <---> 8b - 15

(-14 + 3/2b)-(1 + 8/2b) <----> -15 - 5/2b

(7/2b - 3)-(8 + 6b) <-----> -5/2b - 11

To learn more about the expression visit:

https://brainly.com/question/723406

#SPJ2

Answer:

what i know for sure is 10/19 is rational

Answer:

=> All of the options are correct.

Step-by-step explanation:

a rational number is a number that can be shown as the quotient of two integers a and b(the denominator b must not be equal to zero).

10/19 => a = 10, b = 19 (correct)

85/74 => a = 85, b = 74 (correct)

-48 => a = -48, b = 1 (correct)

-57 =>a = -57, b = 1 (correct)

=> All of the options are correct.

Hope this helps!

Answer:

x and y = 66.5

Step-by-step explanation:

180-47=133

133/2=66.5

Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

Answer:

u^2 +7u -8=0  where u = 3x+2

Step-by-step explanation:

(3x+2)^2 + 7(3x+2) - 8=0

Let 3x+2 = u

u^2 +7u -8=0

Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]

[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

Answer:x=7/5 or 1 2/5

Step-by-step explanation:

x + 3/5=2

Step 1: Subtract 3/5 from both sides.

X+3/5-3/5=2-3/5

X=7/5

Answer:

7/5 or 1 2/5

Step-by-step explanation:

[tex]x+\dfrac{3}{5}=2 \\\\\\x=2-\dfrac{3}{5} \\\\\\x=\dfrac{10}{5}-\dfrac{3}{5} \\\\\\x=\dfrac{7}{5}= 1\dfrac{2}{5}[/tex]

Hope this helps!

Answer:

its y = |x| + 2

Step-by-step explanation:

Answer:

A) Quadrant I

(Both X and Y are positive)

B) Quadrant III

(Both X and Y are negative)

C) Quadrant IV

(X is positive and Y is negative)

D) Quadrant II

(X is negative and Y is positive)

Answer: -11/2

Step-by-step explanation:

First, find the reciprocal of -16/121. Which is -121/16 (you can put the negative sign anywhere). Now, you must multiply the two fractions:

[tex]\frac{8}{11} *-\frac{121}{16}[/tex]      

You can cross out the terms 8 and 16 because they can be simplified into 1 and 2. And you can cross out 11 and -121 because they can be simplified into 1 and -11:

= [tex]\frac{1}{1} * -\frac{11}{2}[/tex]

Now multiply the numerators together, and multiply the denominators:

= [tex]-\frac{11}{2}[/tex]

Answer:

1) 5.9

2) 8.1

3) 54

Step-by-step explanation:

A is opposite, so we have sine 36=a/10

sine 36(10)=a

a=5.9

B is adjacent, so we have cosine 36=b/10

cosine 36(20)=b

b=8.1

Angles of a triangle add to 180

we have a angle of 36 and a right angle which is 90

36+90=126

180-126=54

Answer:

D. ("24.")

Step-by-step explanation:

it is D

Answer:

19) x=-3, 20) a=1, 21) b=3, 22) x=8

Step-by-step explanation:

hope that helps, those are the answeres to each question. :)))

Answer:

Step-by-step explanation:

Answer:

x = -5/2

x = 1

Step-by-step explanation:

(x-1) (2x+5) = 0​

Divide both sides by (x-1)

2x+5 = 0​

Subtract 5 on both sides.

2x = -5

Divide 2 into both sides.

x = -5/2

(x-1) (2x+5) = 0​

Divide both sides by (2x+5).

x - 1 = 0

Add 1 to both sides.

x = 1

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1. So,

1 x 1 = 1

Answer:

1

Step-by-step explanation:

Any base with an exponent of 0 is equal to 1.

4^0 × 16^0

1 × 1

= 1

The answer is 1.

Answer: The cost to make 400 baseball caps is $3,200

Step-by-step explanation:

The answer they gave you is a set of coords, x and y coords to be exact. That means that x value is inputed into the equation and that y value is the asnwer.

You put in 400, you get 3200.

They also gave us that x equals the number of baseball caps. Then y equals the cost of making those baseball caps

Answer:

The cost to produce 400 caps is the same as the income made from selling 400 caps.

The company will break even when it sells 400 caps; it will not make a profit.

Step-by-step explanation:

EDGE 2021

Answer:

L= 12170  ft

Step-by-step explanation:

The runaway at the airport has the shape of a rectangle and the area of 2,312,300 ft².  The rectangular runaway is 190 ft wide . The length is what we are asked to find.

area of a rectangle = LW

Where

L = length

W = width

area of a rectangle = LW

area of the rectangular runaway = 2,312,300 ft²

W = 190 ft

L = ?

2,312,300 = L × 190

2,312,300 = 190L

divide both sides by 190

L = 2,312,300/190

L= 12170  ft

Answer:

D

Step-by-step explanation:

The angle between the vertical and horizontal line is 90°, thus

75° + x = 90° ( subtract 75 from both sides )

x = 15° → D

Answer:

⅑

Step-by-step explanation:

Let m represents number of males, and f represents number of females taking the maths course.

Given that number of males (m) taking the maths course is 8 times as much as number of females (f), total number of students taking the maths course (T).

Thus we can represent the information above with the following:

m = no. of males

f = no. of females

T = Total

m = 8f

T = m + f

Thus,

Total = 8f + f = 9f

==>The fraction of the course that are females = No. of females (f) ÷ Total no. of students (T)

= f/9f

Fraction of females in simplified form would be ⅑

Answer:

11 is the answer

Step-by-step explanation: i hope so cuz my calculations gives this answer

Answer:

it's answer is

125+25+5+1

Answer:

A. q = 39

Step-by-step explanation:

Since the lines are parallel, their sides will be proportional,

So,

Taking their proportion

=> [tex]\frac{60}{40} = \frac{q}{26}[/tex]

Cross Multiplying

q × 40 = 26 × 60

q = [tex]\frac{1560}{40}[/tex]

q = 39

Answer:

11

Step-by-step explanation:

g(x) = 2x + 7

Put x as 2 and evaluate.

g(2) = 2(2) + 7

Multiply.

g(2) = 4 + 7

Add the terms.

g(2) = 11

Answer:

80 = x

Step-by-step explanation:

The base angles are the same if the side lengths are the same

The unmarked angle is 50 degrees

The sum of the angles is a triangle is 180 degrees

180= 50+50+x

180 = 100 +x

180 -100 = 100+x-100

80 = x

Answer:

80°

Step-by-step explanation:

In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.

The other angle on the base line is also equal to 50°.

Angles in a triangle add up to 180°.

x° + 50° + 50° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°