If M is the midpoint of AB and AM = 3x -1 and AB =5 x + 2, find x, AM, MB, and AB.

Answer:

56.077

Step-by-step explanation:

Answer:

56.077

Step-by-step explanation:

i did it in my caculator lol :)

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).

The length of the  rectangle is:

l = 3.5 - (-3.5)

l = 3.5 + 3.5

l = 7

The width of the rectangle is:

w = 3-(-3)

w = 3 + 3

w = 6

The perimeter of the rectangle is given by:

P = 2 (l +w)

P = 2(7 + 6)

P = 26

The area of the rectangle is:
A = l × w

A = 7 × 6

A = 42

Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

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Answer:

The Domain of g (x) = x2 is all the Real Numbers.

Step-by-step explanation:

The composed function is: (g º f) (x) = g (f (x)) = (√x)2. = x. Now, "x" normally has the Domain of all Real Numbers ... ... but because it is a composed function we must also consider f (x), So the Domain is all non-negative Real Numbers.

Hi there,

I hope you and your family are staying safe and healthy!

For this problem, we need to find the domain and the range (if you don't know their meaning and differences, I would recommend you study them).

In order to find the domain and range, we need to start by finding the first two points of the graph.

So by looking at the attached graph, we can find (-2,-2) as well as (-1,2)

Now we need to make an inequality using our first and second X values

Thus, we get: \(-2 \leq x \leq -1\)

Then, we gonna do the same thing for Y values

Thus, we get: \(-2 \leq y \leq 2\) which is our range

In conclusion,

The Domain is \(-2 \leq x \leq -1\)

The range is \(-2 \leq y \leq 2\)

The relation is a function because the vertical line in the graph doesn't intersect the graph more than once.

Happy to help! Let me know if you have more questions

Answer:

Step-by-step explanation:

Given function:

This is a third degree function with negative leading coefficient.

This is therefore decreasing function and can have one local maximum and one local minimum.

From the given graphs we can see only bottom left one can be a matching one.

Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.

1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.

2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.

3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.

4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.

5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.

6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.

7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.

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Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A = (-3, 3 + 3) = (-3, 6)

B = (0, 7 + 3) = (0, 10)

C = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A(-3, 6), B'(0, 10), and C(-3, 3).

So the correct answer is: A(−3, 6), B(0, 10), C(−3, 3).

The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

Answer:

$0.90 per pound.

Step-by-step explanation:

4.50:5

5/5=1

4.50/5=0.90

This Question can be easily solved on the basis of concept knowledge of Alternate Angles

What are Alternate Angles?

Whenever we draw a transversal between 2 parallel lines the opposite angles inside the parallel lines are alternate angles and they are equal

Solution:

As we are given that FA II DE

Hence AD is the transversal and hence

∡A = ∡D because they are alternate angles

similarly

∡B = ∡C because they are also alternate angles

Now we know that sum of angles in a triangle is equal to 180 degree

therefore in triangle AFC

∡A + ∡F + ∡C = 180 degree

and similarly in triangle BED

∡B + ∡E + ∡D = 180 degree

Hence both equations RHS = 180 degree hence i can equate LHS of both

∡A + ∡F + ∡C = ∡B + ∡E + ∡D

∡A + ∡F  + ∡C = ∡C + ∡E + ∡A

∡F =  ∡E

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Answer:

the angle between u=(8, -2) and v=(9,3) is 32.5°

Step-by-step explanation:

u=(8,-2)=(u1,u2)→u1=8, u2=-2

v=(9,3)=(v1,v2)→v1=9, v2=3

We can find the angle between two vectors using the formula of dot product:

u . v =║u║║v║cos α   (1)

And the dot product is:

u . v = u1 v1 + u2 v2

u . v = (8)(9)+(-2)(3)

u . v = 72-6

u . v = 66

║u║=√(u1²+u2²)

║u║=√((8)²+(-2)²)

║u║=√(64+4)

║u║=√(68)

║u║=√((4)(17))

║u║=√(4)√(17)

║u║=2√(17)

║v║=√(v1²+v2²)

║v║=√((9)²+(3)²)

║v║=√(81+9)

║v║=√(90)

║v║=√((9)(10))

║v║=√(9)√(10)

║v║=3√(10)

Replacing the known values in the formula of dot product (1):

u . v =║u║║v║cos α

66 = 2√(17) 3√(10) cos α

Multiplying:

66 = 6√((17)(10)) cos α

66 = 6√(170) cos α

Solving first for cos α: Dividing both sides of the equation by 6√(170):

Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:

(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170

cosα=11/13.03840481→cosα=0.84366149

]

Answer:

The angle is in the third quadrant

Answer:

4-2(16x+8)^1/3=-8

-2(16x+8)^1/3=-12

(16x+8)^1/3=6

16x+8=216

16x=208

x=13

Checking if x=13 is an extraneous solution:

4-2[16(13)+8]^1/3=-8
4-2(208+8]^1/3=-8

4-2(216)^1/3=-8

4-2(6)=-8

4-12=-8

-8=-8

Not an extraneous solution.

The graph in which point are plotted is given below and Point D and F lie on Y axis and X axis respectively other lie on the different quadrant

What does a math quadrant mean?

The term "quadrant" refers to each of the four divisions of the coordinate plane. Furthermore, when we speak of the sections, we also mean the sections as the coordinate axes split them. This is where the x-axis is, and this is where the y-axis is on the up-down axis. On a coordinate plane, it divides the space into four parts, as you can see.

Point A (-5,4)

Lies in 2 quadrant of the graph

Point B (-3,-2)

Lies in 3 quadrant of the graph

Point C (4,6)

Lies in 1 quadrant of the graph

Point D (0,-4)

Lies on negative y axis of the graph

Point E (2,-1)

Lies in 4 quadrant of the graph

Point F (1,0)

Lies on positive x axis of the graph

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Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

The radius of the circle, marked p on the diagram, is approximately 5.8 cm.

Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.

The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.

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Answer:

Step-by-step explanation:

If 11 flights were sampled with an 85% on-time arrival rate, the number of flights from the sample that arrived on time would be estimated to be 9.35, which would round to 9 flights.

This can be solved by:

(0.85x11)= 9.35

Since there can't be .35 of a flight, we would round to the nearest whole number, which would just be 9.

The final answer= 9 flights

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Answer:

148

Step-by-step explanation:

59.2/100x250

9514 1404 393

Answer:

  a) S(p) = -97.78p +2977.78

  b) about 98 fewer shirts per week will be sold for each $1 increase in price

  c) 533 shirts per week

  d) $15.63

Step-by-step explanation:

a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  s = (1120 -2000)/(19 -10)(p -10) +2000

  s = -97.78(p -10) +2000

  S(p) = -97.78p +2977.78

__

b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.

__

c) S(25) ≈ 533

At a price of $25, the store would sell about 533 shirts per week.

__

d) 1450 = S(p) = -97.78p +2977.78

  -1527.78 = -97.78p

  15.625 = p ≈ 15.63

The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

C

Step-by-step explanation:

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

The number under the fraction line tells how many equal parts the whole was broken into

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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The two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

To determine which expressions are less than 7/8, we can compare them individually to 7/8 and evaluate their values.

Let's consider each expression one by one:

7/8 x 9/19:

To compare this expression to 7/8, we multiply the fractions:

(7/8) x (9/19) = 63/152.

Since 63/152 is less than 7/8, this expression is less than 7/8.

7/8 x 3/4:

Multiplying the fractions:

(7/8) x (3/4) = 21/32.

Since 21/32 is less than 7/8, this expression is less than 7/8.

7/8 x 9/9:

The fraction 9/9 simplifies to 1, so the expression becomes:

(7/8) x 1 = 7/8.

Since 7/8 is equal to 7/8 (not less than), this expression is not less than 7/8.

7/8 x 4/3:

Multiplying the fractions:

(7/8) x (4/3) = 28/24.

We can simplify 28/24 to 7/6.

Since 7/6 is greater than 7/8, this expression is not less than 7/8.

Therefore, the two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

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Answer:

-10.8

Step-by-step explanation:

-8.1 + 1.3 = -6.8 + -4 = -10.8

Hope this helps mate

Complete question :

Assume that both populations are normally distributed. ​a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of significance for the given sample data. ​b) Construct a 95​% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1

Answer:

(-0.445 ; 4.645)

Null:

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 ≠ 0

Step-by-step explanation:

__________Sample 1 ____ Sample 2

n ___________19 _________19

x overbar ____16.2 ________14.1

s __________ 4.5 _________3.1

The confidence interval : (2 independent means)

(x1 - x2) ± Tcritical * √(s1²/n1) + (s2²/n2)

T(1 - α/2), 36 = 2.03

(16.2 - 14.1) ± 2.03 * √(4.5²/19) + (3.1²/19)

2.1 ± 2.545

Lower boundary = (2.1 - 2.545) = - 0.445

Upper boundary = (2.1 + 2.545) = 4.645

(-0.445 ; 4.645)