In the figure, is a median. If = 6 + 10 and = 2 + 12, find the length of . Show your work.

Answer:

x=62

Step-by-step explanation:

all angles should add to 180

180-56=124

124÷2=62

Answer:

Step-by-step explanation:

1st notice that two of the sides are the same length?   ( isosceles ) that mean the two angles at the "base" which is the side that both of the same size legs tie into... that's the side that is 4.5 in the picture.  soooo if both of those angles are the same.. and we know that the angles are going to add to 180 then....  we can say    the the 56° is the same as the one at the other end of the 4.5 side (base) so  2*56°=112°

and then 112° + x = 180°

x = 180-112

x = 68°

:)

Answer:

C)  µ = 8000.

Step-by-step explanation:

Explanation:-

Given data A grocery store has an average sales of $8000 per day

mean of the Population μ = $ 8000

sample size 'n' = 64

mean of the sample x⁻ = $ 8300

Null Hypothesis : H₀ : μ = $ 8000

Alternative Hypothesis : H₁: μ > $ 8000

Test statistic

\(Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }\)

\(Z = \frac{8300 -8000}{\frac{1200}{\sqrt{64} } }\)

Z = 2

Level of significance : ∝ = 0.05

Z₀.₀₅ = 1.96

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted at 0.05 level of significance

Conclusion :-

The advertising campaigns have been effective in increasing sales

Answer:

= y + x - 4 = 0

Step-by-step explanation:

a slope or -1

The point = (0,4).

the equation =

\( \frac{y - y1}{x - x1} = m\)

y - 4 = -1

x - 0

note: Perform close multiplication

remember every whole number is over 1

y - 4 = - ( x - 0)

y - 4 = - x + 0

y + x - 4 = 0.

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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Answer:

Initial balance 500, compounds 4 times at an interest rate of 15%

Step-by-step explanation:

Initial balance 500, compounds 4 times at an interest rate of 15%

Given the expression:

The angle of the sine and the cosine is the same angle = 67.5°

The given expression is the same as the rule of the sine of the double angle

Where:

so, we will use the sine double-angle to solve the question

So, the answer will be:

So, the answer will be option B) sin 135°

The marginal rate of substitution (MRS) is a measure of how much of one good an individual is willing to give up in exchange for another good. In other words, it represents the slope of the indifference curve at a given point.

If Victoria's indifference curves are bowed outward, it means that as she moves from right to left along the horizontal axis, the MRS will decrease. This is because as she consumes more of one good, she becomes less willing to give up units of the other good in exchange. The MRS will continue to decrease until it reaches its minimum value at the point where the indifference curve is tangent to the budget line.

It's important to note that the MRS will only decrease if Victoria's indifference curves satisfy the other three properties of indifference curves:

If Victoria's indifference curves do not satisfy these properties, it is not possible to accurately determine the behavior of her MRS as she moves from right to left along the horizontal axis.

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The function that we want to get is:

t(h) = √(-h + 500)/4

And the height is 250 ft after 3.95 seconds.

Here we have the height function defined as:

h(t) = 500 - 16t²

And we want to write t as a function of h, so we just need to isolate the variable t.

h - 500 = -16*t²

(-h + 500)/16 = t²

√((-h + 500)/16) = t

√(-h + 500)/4 = t

This is the function that defines h as a function of t. Notice that we only care for the positive solution of the square root.

The time at which the height is 250ft is given by:

√(-250 + 500)/4 = t

√(250)/4 = 3.95

So the height after 3.95 seconds is 250ft.

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The width of the garden with an area of 70 square feet is 10 feet

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

The area of a field the amount of space occupied by the field. The area is the product of its length and width. It is given by:

Area = length * width

Let w represent the width. The length is 3 feet longer, hence:

Length = w + 3

Area = length * width

Area = (w + 3)(w)

But the area is 70 ft², hence:

70 = (w + 3)(w)

w² + 3w = 70

w² + 3w - 70 = 0

w = 7 feet

Length = w + 3 = 7 + 3 = 10 feet

The width is 10 feet

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Answer:

40hsbdkankahjwdjbdifbcud

Answer:

If she divided 6 of a pound into equal portions of 3/4 of a pound, how many portions did she make?

Step-by-step explanation:

6 ÷ 3/4

Answer:

D

Step-by-step explanation:

The answer is D because when you look at an ordered pair it is (x , y) the x stands for x-axis and y for y-axis. The x numbers are the ones on the bottom line going horizontally across your screen and the y numbers are the ones on the left side of the graph going up and down. Therefore when you are looking at (1.5 , 9) you start on the bottom line and go to 1.5 then go strait up to 9 on the line on the left and thats where the point is! Hope this helps, let me know if somthing doesn't make sense!

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

m∠KML = 35°

Step-by-step explanation:

This is an isosceles triangle because 2 of the sides are equal so we know the 2 unknown angles are equal. The 3 angles of any triangle always add up to 180° so since we know 1 angle is 110° then the 2 unknown angles must add up to 70° (because 180° minus the known 110° leaves us with 70°). Since we know the 2 unknown sides are equal 70° ÷ 2 = 35°. So, m∠KML = 35°

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

20

Step-by-step explanation:

10 + 8 + 2 = 20

Answer:

20 calls before 6 pm

10 + 2 +8 = 20

Step-by-step explanation:

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)

The inverse of a function that maps x into y, maps y into x.

The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)

To determine the domain of

\( {f}^{ - 1}( x)\)

The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x

The reflection of the point (x, y) across the line y = x, gives the point (y, x)

The points on the graph of the inverse of the function, f(x), \( {f}^{ - 1} (x)\) are therefore;

\(( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)\)

\(( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)\)

( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)

The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)

Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, \( {f}^{ - 1}( x)\), which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;

The domain of the inverse of the function, \( {f}^{ - 1}( x)\), using interval notation is; [-2, ∞)

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Answer:

-7/3

Step-by-step explanation:

Rise/Run = -4-3/1--2

= -7/3

Answer:

where is the whole question

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

y = -2/3x + 4

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.

59 is much closer to 60 than to 50.

42 is much closer to 40 than to 50.

of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.

and the sum of the differences of the factors should be as close to 0 as possible.

so, 60×40 is the closest and therefore best estimation.

the sum of the factor differences is (+1 - 2) = -1.

compare to the real result :

59×42 = 2,478

answer a and b are by the way not correct :

50×40 = 2000 (and not 2500)

60×50 = 3000 (and not 3500)

FYI - in this case 50×50 = 2500 would be the closest estimation.

and the sum of the factor differences would be (-9 + 8) = -1.

normally, this wide "jumping" (-9 to +8) would make it only second choice.

1. Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M°

Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter. This means that she ate 100% of the pizza. Andy's wife ate 2/6 of the small pizza, which is 12 inches in diameter. This means that she ate 1/3 of the pizza. Andy's younger daughter ate 1/8 of the medium pizza, which is 14 inches in diameter.

This means that she ate 12.5% of the pizza. Andy cut himself a piece that had a central angle of 180° from the large pizza, which is 16 inches in diameter. This means that he ate 50% of the pizza.

The least amount of pizza was eaten by Andy's younger daughter. She only ate 1/8 of the medium pizza.

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M° by using the following formula:

Percentage of pizza eaten = (M° / 360°) * 100%

For example, if a person cut themselves a piece of an extra large pizza with a central angle of 180°, they would have eaten 50% of the pizza.

Percentage of pizza eaten = (180° / 360°) * 100% = 50%

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Triangle ABC and triangle XYZ are not congruent because they do not have the same side lengths or angles. To be congruent, two triangles must have the same side lengths and the same angles.

To determine if two triangles are congruent, we first need to check if they have the same side lengths. If the two triangles have the same side lengths, then we can move on to check if the angles of the two triangles are the same. If the two triangles have the same side lengths and the same angles, then we can conclude that the two triangles are congruent. If the two triangles do not have the same side lengths and the same angles, then we can conclude that the two triangles are not congruent. In the case of triangle ABC and triangle XYZ, they do not have the same side lengths or angles, so they are not congruent. To be congruent, two triangles must have the same side lengths and the same angles.

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