100 Points! Geometry question. Photo attached. Find x, y, and z. Please show as much work as possible. Thank you!

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

1 and 2 adjacent

5 and 6 are linear pair

Step-by-step explanation:

The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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The inverse of the given statement will be- Option 3, If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

Here, we are given a statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.

According to the statement,

if B bisects AC ⇒ AB = BC

then, B is the midpoint.

The inverse of this will be-

if B is the midpoint of AB ⇒ AB = BC

then, B bisects AB

This can be written as-

If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

Thus, option 3 is the correct answer.

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Your question was incomplete. Check below for full content-

Which statement is the contrapositive of the conditional statement:

Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.

1. If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments.

2. Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.

3. If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

4. If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint.

(a) The sequence formed by the given numbers is: 40, 24, 56, 16, 36, 72, 8, 48, 32.

(b) The sum of the given arithmetic series is 324.

Based on the given table, we can observe the following pattern:

Using these patterns, we can fill in the missing entry in the second row as follows:

So, the completed table looks like this:

40 | 24 | 56 |

16 | 36 | 72 |

8 | 48 | 32 |

The sum of the series is calculated as;

S = n/2(a + l)

Using this formula, we can find the sum of the given arithmetic series. Since there are 9 terms in the series, and the first term is 40, and the last term is 32, we have:

S = 9/2 x (40 + 32)

S = 9/2 x 72

S = 324

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Answer:

$448

Step-by-step explanation:

This can be solved simply by using multiplication:

28 (chairs) x 16 (dollars per each chair) = 448 (dollars total)

Hope it helps! :)

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

suerte espero q te ayude

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.

An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)

If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:

8 : 12

Simplifying this ratio by dividing both numbers by 4, we get:

2 : 3

This means that for every 2 cups of flour, we need 3 cups of sugar.

If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:

2/3 = x/27

Multiplying both sides by 27:

2 × 27 / 3 = x

Simplifying:

x = 18

Therefore, we need 18 cups of flour if we are using 27 cups of sugar.

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definitely missing a number so it's prolly something like

a/20=20

sorry if this doesn't help you didn't give us much to work on

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer:

y = 30200

x = -29950

Step-by-step explanation:

1.)

Let x represent children and y for adults.

200x + 450y = 7,600,000

x + y = 250

2.)

200x + 450y = 7,600,000

x + y = 250

-200(x + y = 250)

-200x + -200 = -50000

200x + 450y = 7,600,000

+ -200x + -200 = -50000

——————————————-

250y = 7550000

y = 30200

x + 30200 = 250

x = -29950

Uhm so I don’t know why for children I got a negative number? The wording for this question is very weird.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

x = sqrt(13) - 4 or x = -4 - sqrt(13)

Step-by-step explanation:

Solve for x:

x^2 + 8 x + 3 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 3 from both sides:

x^2 + 8 x = -3

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 16 to both sides:

x^2 + 8 x + 16 = 13

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 4)^2 = 13

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 4 = sqrt(13) or x + 4 = -sqrt(13)

Hint: | Look at the first equation: Solve for x.

Subtract 4 from both sides:

x = sqrt(13) - 4 or x + 4 = -sqrt(13)

Hint: | Look at the second equation: Solve for x.

Subtract 4 from both sides:

Answer: x = sqrt(13) - 4 or x = -4 - sqrt(13)

Answer:

The bottom right one

Step-by-step explanation:

i did the test

Fourth one or right one at the bottom  rectangular prism has a volume equal to the expression 6 × 3 × 4 cubic unit.

" Volume is total amount of space occupied by any three dimensional body."

Formula used

Volume of rectangular prism = Length × width ×height

According to the question,

Compare the expression of given volume with given diagrams

Given volume = 6 ×3×4

From the diagram we can conclude that right one at the bottom has length = 6 units, width = 3 units and height = 4 units.

Hence, Option(D) or right one at the bottom  is the correct answer.

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Answer:

16.78% probability that exactly 12 of them use their smartphones in meetings or classes.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they use their smartphone in meetings or classes, or they do not. The probability of a person using their phone in meetings or classes is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

64​% use them in meetings or classes.

This means that \(p = 0.64\)

20 adult smartphone users are randomly​ selected

This means that \(n = 20\)

Probability that exactly 12 of them use their smartphones in meetings or classes.

This is P(X = 12).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 12) = C_{20,12}.(0.64)^{12}.(0.36)^{8} = 0.1678\)

16.78% probability that exactly 12 of them use their smartphones in meetings or classes.

Answer: x > 64 and x < 68 is another way of rewriting inequality.

Step-by-step explanation:

To qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches.

⇒The inequality 64 < x < 68, where x represents height,gives the range of height.

⇒In other words range of height can be x > 64 and x < 68 , such that both conditions are applied to single actor.

[with the use of or it will appear to give priority by actor to follow any 1 conditon]

Answer:

t = 19.7

Step-by-step explanation:

24.8 = t + 5.1

-5.1           -5.1

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

19.7 = t

Answer: t = 19.7

Step-by-step explanation:

24.8 = t + 5.1

-t + 24.8 = 5.1

-t = 5.1 - 24.8

-t = -19.7 change both signs and t = 19.7

Answer:759

Step-by-step explanation:

The solution is : the value of y is 7.

Here, we have,

The perimeter of a rectangle is found by

P = 2 (l+w)

P = 2( 3y+3+2y)

Combine like terms

P = 2(5y+3)

We know the perimeter is 76

76 = 2(5y+3)

Divide each side by 2

76/2 = 2/2(5y+3)

38 = 5y+3

Subtract 3 from each side

38-3 = 5y+3-3

35 = 5y

Divide each side by 5

35/5 = 5y/5

7 =y

We want the length of AD = BC = 2y

AD = 2y=2*y = 14

Hence, The solution is : the value of y is 7.

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The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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Answer:

Co-interior angles adds to 180

54+75=129

180-129=51

? Is 51 degrees

Hope this helps!

Answer:

51

Step-by-step explanation:

/_xwv =54

/_vxw = 75

if xwv = 54 then xyv = 54

and if vxw= 75 then xvy = 75

so vxy = 180-(75+54)

= 51

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Brief history of triangle numbers

What is Triangle Number?

An equilateral triangle-shaped group of objects is counted using a triangular number or triangle number. Square and cube numbers are two further examples of figurate numbers, which also include triangle numbers.

Students are typically introduced to triangular numbers through the account of Carl Gauss, a well-known mathematician who used the concept of the triangle number formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.

Triangular numbers were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to triangular, square, pentagonal, and other numbers.

After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for triangle numbers of

n(n+1)/2

Drawing triangle numbers is an exercise that could be helpful in establishing a connection between these two concepts.

The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.

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The heaviest 10% of fruits weigh more than 814.79 grams.

The problem setup implies that the weight of this fruit is a random variable when it says a particular fruit's weights are normally distributed.

Define X = Random Variable of the fruit's weight

\(X \sim N(mean = 760, standard deviation = 39)\)

We want to find the specific gram value for which 8% of the fruits are heavier

The 92nd percentile of X's normal distribution

\(Solve for x: Pr( X < x ) = Normal( 760, 39 ) CDF = .92\)

Standardizing we obtain

\(Pr( [X - 760]/39 < [x - 760]/39 ) = Pr( Z < [x - 760]/39 ) = .92,\)

where Z is a standard normal random variable

\(Pr( Z < [x - 760]/39 ) = Standard \ Normal \ CDF( [x - 760]/39 )\)

==> Set this equal to .92:

\(Standard \ Normal \ CDF( [x - 760]/39 ) = .92\)

Then, from the standard normal table:

\([x - 760]/39 = Inverse Standard Normal\)

\(CDF( .92 ) = 1.405\)

Use algebra to solve for x:

\(x = 39 * 1.405 + 760 = 814.795\)

Therefore the heaviest 10% of fruits weigh more than 814.79 grams.

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).