Let $ABCD$ be a parallelogram. Extend $\overline{DA}$ through $A$ to a point $P,$ and let $\overline{PC}$ meet $\overline{AB}$ at $Q$ and $\overline{DB}$ at $R.$ Given that $PQ = 735$ and $QR = 112,$ find $RC.$

The difference in the values of the two cars when they are each 7 years old is equal to $6,000.

In order to determine the difference in the values of the two cars, we would have to write an equation that models the price of the cars after a length of time, by using the data points shown in the graph above.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For Car A, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (9 - 12)/(4 - 2)

Slope, m = -3/2

Slope, m = -1.5

At point (4, 9), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 9 = -1.5(x - 4)

y = -1.5x + 15

In 7 seven years, the value of Car A is given by:

y = -1.5x + 15

y = -1.5(7) + 15

y = $4,500

Note: The negative sign indicates that the value of the car is depreciating.

For Car B, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (10 - 18)/(5 - 1)

Slope, m = -8/4

Slope, m = -2

At point (5, 1), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 5)

y = -2x + 11

In 7 seven years, the value of Car B is given by:

y = -2x + 11

y = -2(7) + 3.5

y = $10,500

Now, we can determine the difference as follows:

Difference = $10,500 - $4,500

Difference = $6,000.

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Answer:72

Step-by-step explanation:

115+115=230

230-158=72

If you add the 115 a month that she earns from babysitting, then add both the months pay together, than subtract 158(cost of the bicycle) by the total pay, you should get 72$

Answer:  D. $72

Step-by-step explanation:

If she earns $115 a month and June and July is a combination of two months then we will have to find the amount she earn toegther in June and July by multiplying 2 by $115.

2(115) = 230

She earned $230 in those months, and if the bicycle cost $158 , then we will have to subtract $158 from $230 to find her remaining amount.

$230 - $158 = $72  

The band boosters had custom t-shirts made for homecoming and need to sell a certain number of shirts to cover their expenses. An equation, 10x = 25.90 + 8.15x, can be used to determine the number of shirts they need to sell to break even.

Let's break down the given information and formulate an equation to represent the situation.

The band boosters paid a setup fee of $25.90 and an additional cost of $8.15 per shirt to have the custom t-shirts made. They plan to sell each shirt for $10.

Let's represent the number of shirts they need to sell as 'x'. The cost to produce 'x' shirts would be the sum of the setup fee and the cost per shirt multiplied by the number of shirts:

Cost to produce 'x' shirts = Setup fee + (Cost per shirt × Number of shirts)

Using the given values, the equation becomes:

Cost to produce 'x' shirts = $25.90 + ($8.15 × x)

To break even, the revenue from selling the shirts should equal the cost to produce them. The revenue can be calculated by multiplying the selling price per shirt ($10) by the number of shirts sold:

Revenue from selling 'x' shirts = Selling price per shirt × Number of shirts sold

The equation representing the situation can be written as:

$10x = $25.90 + ($8.15 × x)

Simplifying the equation, we have:

10x = 25.90 + 8.15x

Now we have the equation that represents the situation.

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Binary integer variables are variables whose values consist of two values, 0 and 1.

Correct answer will be :- b. Variables with values 0 and 1.

These values are also known as bits, which are represented as 0 and 1 in computers. Binary integer variables are used in computing as a way to represent numbers, characters, and instructions. Binary integer variables are used to represent information in digital systems, because they can be used to represent any value with a single bit.

For example, a single bit can represent a number, letter, or instruction. Binary integer variables are also used in computer programming, as they can be used to represent boolean values, such as true and false. Additionally, they can be used to represent various types of data, such as numbers, characters, and images.

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Answer:

30 students

Step-by-step explanation:

The 15 students that came were 30% of the class:

30% = 15 students

To find 100%, we can first find 10% by dividing both sides by 3

10% = 3 students

(30% ÷ 3 = 10%, 15 ÷ 3 = 5)

Then, multiply both sides by 10 to get 100%

100% = 30 students

(10% × 10 = 100, 3 × 10 = 30)

\( \large{\red{\underline{\bf{Required \: Solution \: : }}}} \)

Here we have been provided with two equations and we have to solve them by substitution method and get the value of x and y.

Here we have been already provided a temporary value of y in first equation so let us substitute in the second equation.

\(: \implies \: \sf{y \: = \: 4x \: - \: 10}\)

\(: \implies \: \sf{x \: - \: 4 \: = \: 4x \: - \: 10}\)

\(: \implies \: \sf{x \: = \: 4x \: - \: 10 \: + \: 4}\)

\(: \implies \: \sf{x \: = \: 4x \: - 6}\)

\(: \implies \: \sf{x \: - 4x \: = \: - 6}\)

\(: \implies \: \sf{ - 3x \: = \: - 6}\)

\(: \implies \: \sf{ \cancel - \: 3x \: = \: \cancel- \: 6}\)

\(: \implies \: \sf{ 3x \: = \: 6}\)

\(: \implies \: \sf{ x \: = \: \dfrac{6}{3} }\)

\(: \implies \: \sf{ x \: = \: \cancel\dfrac{6}{3} }\)

\(: \implies \: \boxed{\bf{ x \: = \:2 }} \pink\bigstar\)

Therefore, value of x is 2..!!

Finding out value of y :

Here we would substitute the value of x which we got as 2 in the first equation inorder to get the value of y.

\(: \implies \: \sf{ y \: = \: x \: - \: 4 }\)

\(: \implies \: \sf{ y \: = \: 2 \: - \: 4 }\)

\(: \implies \: \boxed{\bf{ y \: = \:-2 }} \pink\bigstar\)

Therefore, value of y is -2.

Answer:

14.6mm

Step-by-step explanation:

The formula for finding the circumference of a circle is 2πr.

The circumference is 91.688 millimeters inorder to find the radius we have to do the opposite or inverse of multiplication which is division.

So we divide the circumference by 2 and pi which is 3.14 which will give us the radius

r = radius = 91.668 ÷ 3.14 ÷ 2 = 14.6

Answer: its c

Step-by-step explanation:

The distance between Donny and Leo is approximately 117.56 feet.

In this problem, we have two right triangles. One has a base of d1 (the distance between Michael and Donny), a height of h1 (the height Donny paints), and an angle of elevation of 23.1 degrees.

The second triangle has a base of d2 (the distance between Michael and Leo), a height of h2 (the height Leo paints), and an angle of elevation of 25.9 degrees.

The angle of elevation for Donny is 23.1° and for Leo, it is 25.9°.

We can use tangent functions to find the values of h1 and h2.In general, for a right triangle, we have the trigonometric relationship;

Tanθ = opposite / adjacen

tWe can say that the opposite side is the height of the triangles, and the adjacent side is the distance from Michael to each of the painters (d1 for Donny and d2 for Leo).

Therefore, for Donny; Tan23.1° = h1 / d1

and for Leo; Tan25.9° = h2 / d2

Rearranging, we can solve for h1 and h2;

h1 = d1 × Tan23.1°

h2 = d2 × Tan25.9°

We also know that Michael stands 205 feet away, so;

d1 + d2 = 205

We can substitute the expressions for h1 and h2 into the previous equation;

d1 × Tan23.1° + d2 × Tan25.9° = 205

We can solve for d2, as that is what the question is asking;

d2 = (205 - d1)

Rearranging;

Tan25.9° × d2 = 205 - d1

d1 =  Tan23.1° × d1Tan25.9° × d2

Substituting for d2 in terms of d1;

Tan25.9° × (205 - d1)

= 205 - Tan23.1° × d1Tan25.9° × 205 - Tan25.9° × d1

= 205 - Tan23.1° × d1(205 × Tan25.9° - 205)

= (Tan23.1° - Tan25.9°) × d1

d1 = (205 × Tan25.9° - 205) / (Tan23.1° - Tan25.9°)

d1 = (205 × Tan25.9° - 205) / (- Tan23.1° + Tan25.9°)

Therefore, d1 ≈ 87.44 feet

Substituting back into the original equation;

d1 + d2 = 205

d2 = 205 - d1

87.44 + d2 = 205

d2 ≈ 117.56 feet

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Using trigonometry and the angle of elevation, the distance between Leo and Donny is 87.44ft

To find the distance between Donny and Leo, we can use trigonometry. Let's consider the triangle formed by Michael, Donny, and Leo.

Let the distance between Michael and Donny be represented by "x," and the distance between Michael and Leo be represented by "y."

In this triangle, we have two right angles (at Donny and Leo) and two known angles of elevation: 23.1° and 25.9°. The angles of depression from Donny and Leo to Michael will be equal to these angles of elevation.

Using trigonometry, we can establish the following relationships:

tan(23.1°) = x / 205   ...(1)

x = 205 * tan(23.1°)

x ≈ 87.44 ft

Therefore, the distance between Leo and Donny is approximately 87.44 ft.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Answer:

h < 46

  --

hope it help

Inequalities are used to represent unequal expressions.

The inequality is:

⇒ H ≤ 46

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The height (h) is said to be no greater than 46 inches.

Here, The text "no greater than" means less than or equal to.

Hence, the inequality is:

⇒ H ≤ 46

Thus, The correct inequality is:

⇒ H ≤ 46

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The solution of the given system of equations is (-2, -4).

The given system of equations is:x² + 6x + 8 = 0x + 4 = 0To solve the system using graphing, follow the given steps below:Step 1: Graph both the equations on the same coordinate axes. For this, rewrite the given quadratic equation as y = x² + 6x + 8. Then, draw the graphs of y = x² + 6x + 8 and y = -4 on the same coordinate plane. The graphs of both equations intersect at x = -2. Therefore, the solution of the system is (-2, -4).

The graph of y = x² + 6x + 8 is given below: The graph of y = -4 is a straight horizontal line passing through the point (-4, 0).The graph of both the equations on the same coordinate axes is given below: Step 2: Identify the point of intersection of the graphs. The point of intersection of the graphs is the solution of the system. Therefore, the solution of the system is (-2, -4).

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To calculate MAP, you will need to know both the systolic and diastolic blood pressures.

MAP, or mean arterial pressure, is a measure of the average blood pressure in the arterial system. It is calculated by taking into account both the systolic and diastolic blood pressures. BP, or blood pressure, is the measure of the force of blood against the walls of the arteries as it is pumped by the heart. Blood pressure is measured in millimeters of mercury (mmHg) and is expressed as two numbers, with the systolic pressure (the higher number) measured first and the diastolic pressure (the lower number) measured second. For example, a blood pressure reading of 120/80 mmHg would be expressed as "120 over 80."

The formula for MAP is: MAP = (2 x diastolic blood pressure) + systolic blood pressure / 3

For example, if the systolic blood pressure is 120 mmHg and the diastolic blood pressure is 80 mmHg, the MAP would be calculated as: MAP = (2 x 80) + 120 / 3 = 80 + 40 + 120 / 3 = 100 mmHg

It's important to note that the MAP is not an actual measurement that is taken directly but it is calculated from the systolic and diastolic pressure.

It's also important to note that MAP is not the only parameter to evaluate the cardiovascular function, other parameters like heart rate, cardiac output, and others are also important. In addition, the normal MAP values vary based on different factors such as age, sex, and other health conditions.

In summary, Mean arterial pressure (MAP) is a measure of the average blood pressure in the arterial system, which is calculated by taking into account both the systolic and diastolic blood pressures. The formula for MAP is: MAP = (2 x diastolic blood pressure) + systolic blood pressure / 3. It's important to note that the MAP is not an actual measurement that is taken directly but it is calculated from the systolic and diastolic pressure and MAP is not the only parameter to evaluate the cardiovascular function.

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Answer:fixed cost=10

Independent variable=months paid

Dependent=hours on support

month=x,h=hour,10x+35h=total cost

97.50=10+35h

87.50=35h

h=2.5 hours

Step-by-step explanation:

showed work

The number of ways to roll a total of 24 with four 10-sided dice is 2925.

To solve this problem using inclusion-exclusion, we need to consider all possible ways to roll a total of 24 with the four 10-sided dice, and then subtract the number of cases where at least one die rolls a number greater than 10.

However, we also need to add back the number of cases where at least two dice roll a number greater than 10, since they were subtracted twice.

Let A be the event that at least one die rolls a number greater than 10, and let B be the event that at least two dice roll a number greater than 10. Then we can use the inclusion-exclusion principle:

N(A) = total number of ways to roll 24 with four 10-sided dice = (number of solutions to x1 + x2 + x3 + x4 = 24) = C(24 + 4 - 1, 4 - 1) = C(27, 3) = 2925

N(B) = total number of ways to roll 24 with at least two dice greater than 10

If two dice are greater than 10, then their sum can be 11, 12, ..., 18, for a total of 8 possibilities. For each of these cases, we need to find the number of ways to distribute the remaining 16 points among the four dice, where each die can have any value from 1 to 10. This can be done using stars and bars:

For 11, the remaining 16 points can be distributed among 4 dice in C(16 + 4 - 1, 4 - 1) = C(19, 3) = 969 ways.

For 12, the remaining 16 points can be distributed among 4 dice in C(14 + 4 - 1, 4 - 1) = C(17, 3) = 680 ways.

For 13, the remaining 16 points can be distributed among 4 dice in C(12 + 4 - 1, 4 - 1) = C(15, 3) = 455 ways.

For 14, the remaining 16 points can be distributed among 4 dice in C(10 + 4 - 1, 4 - 1) = C(13, 3) = 286 ways.

For 15, the remaining 16 points can be distributed among 4 dice in C(8 + 4 - 1, 4 - 1) = C(11, 3) = 165 ways.

For 16, the remaining 16 points can be distributed among 4 dice in C(6 + 4 - 1, 4 - 1) = C(9, 3) = 84 ways.

For 17, the remaining 16 points can be distributed among 4 dice in C(4 + 4 - 1, 4 - 1) = C(7, 3) = 35 ways.

For 18, the remaining 16 points can be distributed among 4 dice in C(2 + 4 - 1, 4 - 1) = C(5, 3) = 10 ways.

So, the total number of ways to roll 24 with at least two dice greater than 10 is:

N(B) = 8*(969 + 680 + 455 + 286 + 165 + 84 + 35 + 10) = 38304

By the inclusion-exclusion principle, the number of ways to roll a total of 24 with four 10-sided dice is:

N = N(A) - N(B)

N = 2925

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Answer:

3x16

Answer to the equation:

48

Step-by-step explanation:

Answer:

≅ 0.76 or 76%

Step-by-step explanation:

To find the probability that at least one copy machine is out of order, we can use the complement rule. That is, we can find the probability that none of the copy machines are out of order, and then subtract that from 1.

The probability that a particular copy machine is working is 1 - 0.3 = 0.7. Since we have four copy machines that work independently of each other, the probability that all four machines are working is:

0.7 x 0.7 x 0.7 x 0.7 = 0.2401

So the probability that none of the copy machines are out of order is 0.2401.

Therefore, the probability that at least one machine is out of order is:

1 - 0.2401 = 0.7599

So the probability that at least one copy machine is out of order is approximately [0.76, or 76%.]

The statement are matched with their reasons as;

∠5 and ∠7 are supplementary; Definition of supplementary angles

m∠1 = m∠5;  If lines are ||, corresponding angles are equal

m∠1 + m∠7 = 180°; Exterior sides in opposite rays.

To determine the proofs, we need to know the following;

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The correct answer i.e. the total area is A. (3 × 13^2) + (2 × 15^2).

The edge of a shape's area is measured. You must divide the length and breadth of a rectangles or square in order to determine its area. A is x times y in size.

The area of a square is composed of (Side) (Side) square units. Once the diagonally, d, is known, the surface of a square is equal to d22 square units. For instance, 8 8, or 64 sq ft is the size of a cube with sides that are each 8 feet long (ft2).

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Answer:

40 quarts

Step-by-step explanation:

one gallon is 4 quarts, so ten gallons would be 40.

4(quarts) x 10(gallons) = 40(number of quarts in the 10 gallons)

Answer:

1: 5.83

2: 4.12

3: 3.61

4: 5

5: 6.32

6: 5.10

Step-by-step explanation:

The Pythagorean theorem is a^2 + b^2 = c^2

For all of these you can count the number of blocks over to find two sides of the triangle.

For example: the first one has two sides, one is 3 units, the other is 5. To find the missing angle you square 3 and 5, then add that together. That is equal to 34. 34 = c^2. To get the c by itself, you then take the square root of 34. So the missing side (c) is equal to 5.83.

Answer:

One way streets make it harder to turn into business, also one way streets often are long and they can throw you off your course

Step-by-step explanation:

I hope this helps

The number of permutations of 8 objects taken 3 at a time is 336.

To calculate the number of permutations, we use the formula for permutations of n objects taken r at a time, which is given by P(n, r) = n! / (n - r)!. In this case, we have 8 objects and we want to take 3 objects at a time. Therefore, the number of permutations is P(8, 3) = 8! / (8 - 3)! = 8! / 5!.

Simplifying further, we have 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 and 5! = 5 x 4 x 3 x 2 x 1. Canceling out common factors, we get (8 x 7 x 6) / (3 x 2 x 1) = 336.

Therefore, the number of permutations of 8 objects taken 3 at a time is 336.


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Answer:

$14

Step-by-step explanation:

Make the variables:

x

x + 3

2x + 3 = 25

2x = 22

x = 11

11, 14

Answer:

$14

Step-by-step explanation:

price of cheaper scarf → x

price of more expensive scarf → x + 3

x + x + 3 = 25

2x + 3 = 25

2x = 22

x = 11

The cheaper scarf costs $11 so the more expensive scarf costs $14.

Answer:

A) Given that the figure is a rectangle, it has a rotational symmetry and by rotating the figure 180° about the center of the figure, the preimage and image will coincide

The figure also has a line symmetry for the vertical line x = 5, and a line symmetry for the horizontal line y = 5

Therefore the figure has both symmetry

B) The transformation that maps the figure unto itself are therefore;

1) Rotating the figure 180° about the point (5, 5) which is the center of the figure

2) Reflection of the figure across the line x = 5 and also reflection of the figure across the line y = 5

Step-by-step explanation:

Answer:G=3/7

Step-by-step explanation:

The solution is in the attached file belowyhetheyhethe

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Internal angles of a triangle = 180 degrees

So knowing this we can form the following equation

(x + 26) + (x + 14) + (4x - 10) = 180

Simplify

(x + x + 4x) + (26 + 14 - 10) = 180

6x + 30 = 180

Rearrange for x

6x = 180 - 30

6x = 150

x = 25

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According to angle sum property of the triangle, we can say that :

Answer:

A. Positive

Step-by-step explanation:

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Brainliest please! I am so close to getting my next ranking! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer: False

Step-by-step explanation: Let's review the idea of graphs.

For a graph to be linear, it must be a straight line.

To determine whether a given graph is a function,

we use the vertical line test.

The vertical line test tells us that if a vertical line is drawn on a graph,

and hits the graph in more than one place, the graph is not a function.

In fact, this definition tells us the only type of linear graph

that will fail the vertical line test, and that's a vertical line.

Any vertical line that we draw will be both linear and not a function.

One possible graph could be x = 2.

Any vertical line will fit this description.