7

Write a Two-Column Proof

Given: m 8-125-

m/3-55°

Prove: pr

3/4

5/6

7/8

2

According the given question the side οf the WY is 25.

Angle-Side-Angle cοngruence rule is referred tο as ASA. Twο triangles are said tο be cοngruent accοrding tο this rule if any twο angles and the side included between them οf οne triangle are equal tο the cοrrespοnding angles and the included side οf the οther triangle.

See if the twο triangles given, ABC and XYZ, are cοngruent accοrding tο the ASA rule by lοοking at the image prοvided belοw. Accοrding tο the ASA cοngruence rule, twο triangles are said tο be cοngruent if twο οf their respective sides and angles are equal tο thοse οf twο οther triangles and their respective sides and angles, respectively.

BC = BD

m< B=13x-35

m < C = 5x-19

m < D = 2x + 14

m< B=13*11 - 35

m< B=143-35

m< B = 108

m<C=5x-19

m<C=511 - 19

m < C = 55-19

m < C = 36

This is sο because the theοrem οf SAS (Side-Angle-Side)

Sο, we have:

9x117x - 3

WY = 7x-3

WY = 7*4-3

WY = 28-3

WY = 25

Hence the side οf the WY is 25.

Learn more about congruent by ASA, by the following link.

brainly.com/question/9513034

#SPJ1

There are 18.75 quarts of apple juice in a case of 24 bottles.

To calculate the number of quarts of apple juice in a case of 24 bottles, we must first calculate the number of ounces in the case. To do this, we can use the formula:

Total Ounces = Number of Bottles x Ounces per Bottle

Total Ounces = 24 x 25

Total Ounces = 600

Now that we have the total ounces of apple juice in the case, we can convert this to quarts using the formula:

Quarts = Ounces ÷ 32

Quarts = 600 ÷ 32

Quarts = 18.75

Therefore, there are 18.75 quarts of apple juice in a case of 24 bottles.

Learn more about total ounces here:

https://brainly.com/question/14827945

#SPJ4

The sets of side lengths that are similar to the triangle that Kendall drew are; A. 16, 30, 35, and D. 8, 15, 17​.

The tangent of a right triangle is given as the opposite side divided by the adjacent side. Now, we are given the value of the tangent to be 1.8750.

To obtain the tangents, we are going to divide the opposite by the adjacent as follows:

30/16 = 1.875

8/6 = 1.333

8/1.875 = 4.266

15/8 = 1.875.

So, the set of side lengths that are similar to the triangle that Kendall drew are 16, 30, 35, and 8, 15, 17​.

Learn more about right triangles here:

https://brainly.com/question/2217700

#SPJ1

Answer:

95ft²

Step-by-step explanation:

2πr = 11π

πr = 11π/2

r = 11/2 = 5.5ft

area = πr²

area = π(5.5)² = 95.0331... ≈ 95ft²

Answer:

SAS proves that these triangles are congruent.

Answer:

x = 17

Step-by-step explanation:

We Know

(6x + 3) + (7x - 44) = 180°

Let's solve

6x + 3 + 7x - 44 = 180

13x - 41 = 180

13x = 221

x = 17°

So, x = 17°

There are 184,756 possible 9 player batting orders for a softball team with 20 players.

The formula to calculate the combination number of possible batting orders for a team with n players is n!/(n-r)! where n = the total number of players, and r = the number of players in the batting order. Therefore, for a softball team with 20 players, the number of possible 9 player batting orders is 20!/(20-9)! = 184,756.

20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

(20-9)! = (20 - 9) × (19 - 9) × (18 - 9) × (17 - 9) × (16 - 9) × (15 - 9) × (14 - 9) × (13 - 9) × (12 - 9) × (11 - 9) × (10 - 9) × (9 - 9)

20!/(20-9)! = 184,756

Therefore, there are 184,756 possible 9 player batting orders for a softball team with 20 players.

Learn more about combination here:

https://brainly.com/question/20211959

#SPJ4

One possible solution is Keshawn has 2 nickels and 12 dimes.

What is inequality equation?

An inequality equation is a mathematical expression that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to)

To solve the system of inequalities graphically, we can plot the two inequalities on the coordinate plane and shade the region that satisfies both inequalities. Let x be the number of nickels and y be the number of dimes.

The first inequality represents the maximum number of coins:

x + y ≤ 14

The second inequality represents the minimum value of the coins:

0.05x + 0.1y ≥ 1

We can rewrite this inequality as:

x + 2y ≥ 20

Now we can plot these two inequalities on the coordinate plane:

Draw a horizontal line for x + y = 14.

Draw a diagonal line with negative slope for x + 2y = 20.

Shade the region below the diagonal line and to the left of the horizontal line.

The shaded region represents the feasible region that satisfies both inequalities. We also know that x ≤ 4 since a maximum of 4 coins are nickels.

One possible solution that lies in the shaded region and satisfies the constraint x ≤ 4 is (x, y) = (2, 12). This means Keshawn has 2 nickels and 12 dimes. We can check that this solution satisfies both inequalities:

2 + 12 = 14 (maximum number of coins)

0.05(2) + 0.1(12) = 1.2 ≥ 1 (minimum value of the coins)

Therefore, one possible solution is Keshawn has 2 nickels and 12 dimes.

To know more about inequality equations visit :

https://brainly.com/question/30238989

#SPJ1

After solving the given numbers with (PEMDAS) 11 - 11 x 11 + 11 = we get the answer of -88.

To solve 11-11x11+11, we need to use the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order of operations, we can simplify the expression as follows:

11 - 11 x 11 + 11

= 11 - 121 + 11 (since multiplication should be done before addition and subtraction)

= -99 + 11

= -88

Therefore, the value of 11-11x11+11 is -88.

In general, when simplifying expressions, it is important to follow the order of operations to ensure that you get the correct answer. Additionally, it is always a good idea to check your work by plugging the answer back into the original expression and making sure that it is correct.

To learn more about Parentheses click here

brainly.com/question/28146414

#SPJ4

The expanded form that can be used to factor the function is 12x² - 18x + 10x - 15.

option C,

To factor 12x² - 8x - 15 by grouping, we need to split the middle term -8x into two terms whose sum is -8x and whose product is -180 (the product of 12 and -15).

We can do this by splitting -8x into -18x and +10x:

12x² - 18x + 10x - 15

Now, we can group the first two terms together and the last two terms together, and factor out the greatest common factor from each group:

6x(2x - 3) + 5(2x - 3)

Notice that we have a common factor of (2x - 3) in both groups, so we can factor it out:

(2x - 3)(6x + 5)

Therefore, the factored form of 12x² - 8x - 15 by grouping is (2x - 3)(6x + 5).

Learn more about factorization here: https://brainly.com/question/25829061

#SPJ1

Answer : The probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

The probability of an accident being caused by aggressive driving is 56%, or 0.56. Therefore, the probability of an accident NOT being caused by aggressive driving is 1 - 0.56 = 0.44. Since the accidents are chosen at random, we can assume that they are independent events. Therefore, we can multiply the probabilities together to find the overall probability.

For part 1, we want to find the probability that none of the 3 accidents are caused by aggressive driving. This means we want the probability of an accident not being caused by aggressive driving (0.44) to happen 3 times in a row:

P(none are caused by aggressive driving) = 0.44 * 0.44 * 0.44 = 0.085184

Round to 3 decimal places:

P(none are caused by aggressive driving) = 0.085

Therefore, the probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

A greater distance if it hits any other part of the bat.

When a ball hits the sweet spot of a bat, it will travel a greater distance than if it hits any other part of the bat. This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

If the ball hits any other part of the bat, the energy transfer is less efficient, resulting in a less powerful hit and a shorter distance travelled by the ball.

Learn more About distance

https://brainly.com/question/15172156

#SPJ1

Answer:

Vol = 120 cm^3

Step-by-step explanation:

The volume of a prism is:

Vol = BaseArea×height

Here, the base is the triangle.

Area_triangle

= 1/2bh

= 1/2•6•4

= 12 cm^2

The height is 10cm (and we don't even need the 5cm measurement given)

Volume

= BaseArea × height

= 12 × 10

= 120 cm^3

Therefore , the solution of the given problem of rectangle comes out to be  DE ≅ BF | Corresponding parts of congruent triangles are congruent

A rectangle is a cube with four perpendicular sides in the Euclidean plane. It is also known as an equal-sided rectangle or an equiangular trapezoid. Additionally, the trapezoid may have a straight border. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides but instead four 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".

Here,

ABCD is a rectangle | Given

=> AE ≅ CF | Given

AEFC is a parallelogram | Definition of parallelogram

=> AC ≅ EF | Opposite sides of a parallelogram are congruent

=> ∠EAF ≅ ∠ACF | Opposite angles of a parallelogram are congruent

=> ∠EAF ≅ ∠CAD | Diagonals of a rectangle bisect each other

=> ∠ACF ≅ ∠CAD | Transitive property of congruence

=> ∆ACF ≅ ∆CAD | ASA (angle-side-angle) congruence

=> DF ≅ DF | Reflexive property of congruence

=> ∆DFC ≅ ∆DFE | SSS (side-side-side) congruence

=> ∠BCF ≅ ∠ADE | Corresponding angles of congruent triangles are congruent

=> ∠BCF ≅ ∠BDF | Diagonals of a rectangle bisect each other

=> ∠ADE ≅ ∠BDF | Transitive property of congruence

=>∆ADE ≅ ∆BDF | ASA congruence

=> DE ≅ BF | Corresponding parts of congruent triangles are congruent

To know more about rectangle visit:

https://brainly.com/question/29123947

#SPJ1

P(female or grade 11) = 31/34

Given that a classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). The teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?The sample space is the total number of students which is given by23 + 11 = 34.There are 13 females in the grade 12 and 7 females in the grade 11. So the total number of female students is 13 + 7 = 20.There are 11 grade 11 students. So the total number of grade 11 students is 11.The total number of students that are female or in grade 11 is obtained by adding the two:20 + 11 = 31.So the probability of choosing a female or grade 11 student is:P(female or grade 11) = 31/34

Learn more about probability

brainly.com/question/29381779

#SPJ4

The amount budgeted for dances is approximately $380.00.

Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:

x/532 = 5/7

We can cross-multiply and simplify to find the answer for "x"

7x = 532 × 5

7x = 2660

x = 2660/7

x ≈ 380.00

The estimated $380.00 planned money for dances is the result.

To know more about Budget visit:

https://brainly.com/question/14196340

#SPJ9

The two solutions to the given quadratic equation are x = (a+b + √(a2 - 6ab + 8b2))/(2(a-b)) and x = (a+b - √(a2 - 6ab + 8b2))/(2(a-b)).

The general form of a quadratic equation is ax2 + bx + c = 0. To solve this equation, we need to use the Quadratic Formula. The Quadratic Formula is [tex]x = [-b ± √(b2 - 4ac)]/ 2a[/tex].

We can plug the values for a, b, and c into this equation. For this equation, a = (a-b), b = -(a+b), and c = 2b.

Therefore, using the Quadratic Formula, we get [tex]x = [-(-(a+b)) ± √((-(a+b))2 - 4(a-b)(2b))]/ 2(a-b)[/tex].

Simplifying this, we get [tex]x = [a+b ± √(a2 + 2ab - 4ab - 8b2)]/(2(a-b))[/tex].

Finally, we can solve for the two values of x by computing the two cases. In the first case, we add the square root, and in the second case, we subtract the square root. This gives us the two solutions [tex]x = [(a+b + √(a2 - 6ab + 8b2))/(2(a-b))][/tex] and [tex]x = [(a+b - √(a2 - 6ab + 8b2))/(2(a-b))][/tex].

Learn more about quadratic equation here:

https://brainly.com/question/30098550

#SPJ4

If the boxes are all stacked on top of each other, what is their combined height is 11/8

Height of large box = 7/8m

Height of medium box = 2/6m shorter than large box

Height of small box = 1/4m shorter than the medium box

Calculating the height of the medium and small boxes.

Medium box height x large box height

= 2/6 × 7/8

= 7/24

Since, the small box is 1/4 of a meter shorter than the medium box, therefore its height -

= 7/24 - 1/4

= 5/24

Calculating the height of three boxes -

7/8 + 7/24 + 5/24

= 21/24 + 7/24 + 5/24

= 33/24

= 11/8

Correct Question:

Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined height?

Read more about height on:

https://brainly.com/question/28122539

#SPJ4

Step-by-step explanation:

she has x money at the beginning.

(3/4)x = dictionary

the remainder is (1/4)x.

1/2 of that (1/4 × 1/2 = 1/8) is the calculator.

that means she has (1/4)x - (1/8)x = (1/8)x left.

the dictionary is $30 more than the calculator.

so,

(3/4)x = (1/8)x + 30

(6/8)x = (1/8)x + 30

(5/8)x = 30

5x = 240

x = 240/5 = $48

so, the dictionary cost

(3/4)x = (3/4)×48 = 3×12 = $36

By answering the presented question, we may conclude that When x equals 7, the equation holds true. As a result, "True" is the correct response.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.

The image's equation is:

2x + 4 = 18

We must solve for x to discover if the equation is true or untrue.

When we subtract 4 from both sides, we get:

2x = 14

When we divide both sides by 2, we get:

x = 7

When x equals 7, the equation holds true. As a result, "True" is the correct response.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

It would take the apprentice alone 11 hours to complete a kitchen island, the same amount of time it took the cabinet maker and apprentice together.

When the cabinet maker and apprentice work together, they are able to complete the kitchen island in 8 hours. This implies that the apprentice is able to do their portion of the work in 3 hours, while the cabinet maker does their portion in 8 hours. Therefore, if the apprentice were to work on the kitchen island alone, it would take them 11 hours to complete it, the same amount of time it took the cabinet maker and apprentice together. This is because the apprentice does not have the same level of experience and expertise as the cabinet maker, so they are not able to complete the same amount of work in the same amount of time as the cabinet maker. The cabinet maker is able to work faster and more efficiently, which is why they are able to complete the kitchen island in 8 hours, while the apprentice would need 11 hours to complete the same task.

Learn more about hours here

https://brainly.com/question/13533620

#SPJ4

a)0.1071

b)0.2857

c) 0.3571`.

a) The probability of observing all successes is `(5/8) × (4/7) × (3/6) × (2/5) = 0.1071`b) The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`c) The probability of at most two successes is equal to `P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)`.The probability of observing zero successes is `(3/8) × (2/7) × (1/6) × (0/5) = 0`.The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`The probability of observing two successes is `(5/8) × (3/7) × (4/6) × (1/5) = 0.0714`.Therefore, `P(X ≤ 2) = 0 + 0.2857 + 0.0714 = 0.3571`.

Learn more about probability

brainly.com/question/14017353

#SPJ4

The total surface area of this figure is 94, rounded to the nearest hundredth.

The figure in question is a rectangular prism. To calculate the total surface area of a rectangular prism, we must use the following formula: Total Surface Area = 2(lw + wh + lh), where l is the length, w is the width, and h is the height.

For this figure, the length is 5, the width is 4, and the height is 3. Thus, we can calculate the total surface area of the figure as follows: 2(5*4 + 4*3 + 5*3) = 2(20 + 12 + 15) = 2(47) = 94. Therefore, the total surface area of this figure is 94, rounded to the nearest hundredth.

Learn more about total surface area here:

https://brainly.com/question/8419462

#SPJ4

Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

Answer:

Step-by-step explanation:

12% of 77 is 10.24 or 10.

Step-by-step explanation:

12/100 * 77

12*77=824

824/100

divide by 2

206/25

use long division method

8.24

Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).

An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.

Here,

By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance

With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:

72 / 3.25 = 22.15 years

In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:

2022 - 22 ≈ 2000

As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).

To know more about average , visit

https://brainly.com/question/24057012

#SPJ1

Answer:

19.8

Step-by-step explanation:

Therefore, the measure of angle 1 is 40°.

Two rays (half-lines) that share a terminal are combined to form an angle. In contrast, the rays are variously referred to as the angle's legs and its arms, with the latter serving as the angle's vertex.

The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we can use this property to find the measure of angle 1.

If mAB = 80°, then arc AB is also 80° because an inscribed angle intercepts an arc with the same measure as the angle. Therefore, the measure of arc AB is 80°.

Since angle 1 is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB. Therefore, we can find the measure of angle 1 as follows:

m∠1 = (1/2) x m arc AB

m∠1 = (1/2) x 80°

m∠1 = 40°

Therefore, the measure of angle 1 is 40°.

To know more about angle visit:

https://brainly.com/question/28451077

#SPJ1

Therefore , the solution of the given problem of expressions comes out to be Sebastian strolled his dog for 4/5 of the allotted time today.

Calculations like arbitrary division, joining, multiplication variable , and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

You can calculate how much of the allotted time Sebastian spent walking his dog today by dividing the time he spent walking him (20 minutes) by the time he was meant to walk him (25 minutes).

Therefore, the division formula that represents this portion is:

=> 20 ÷ 25

The short form of this phrase is:

=>  4/5

As a result, Sebastian strolled his dog for 4/5 of the allotted time today.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The exponential function in the given table is:

y = 0.02*(1/2)^x

This seems to be an exponential function of the form:

y = a*b^x

Using the points in the table we can try to find the values of a and b.

for the first point we can write:

0.02 = a*b^0

0.02 = a

Then the function is:

y = 0.02*b^x

Now the second point, (1, 0.01), replacing that we will get:

0.01 = 0.02*b^1

0.01 = 0.02*b

0.01/0.02 = b

1/2 = b

The function is:

y = 0.02*(1/2)^x

Learn more about exponential functions at:

https://brainly.com/question/2456547

#SPJ1