WILL GIVE BRAINIEST IF ANSWER ALL QUESTIONS

The solution to the given system of equations is:

x = 4, y = -3, z = 4.

To solve the given system of equations:

5x - 3y - 4z = 13

2y - 4z = -22

-2z = -8

We can start by solving equation (3) for z:

-2z = -8

Dividing both sides by -2:

z = (-8) / (-2)

z = 4

Now, substitute z = 4 into equations (2) and (1) to solve for y and x, respectively:

2y - 4z = -22

2y - 4(4) = -22

2y - 16 = -22

2y = -22 + 16

2y = -6

Dividing both sides by 2:

y = -6 / 2

y = -3

5x - 3y - 4z = 13

5x - 3(-3) - 4(4) = 13

5x + 9 - 16 = 13

5x - 7 = 13

5x = 13 + 7

5x = 20

Dividing both sides by 5:

x = 20 / 5

x = 4

Therefore, the solution to the given system of equations is:

x = 4, y = -3, z = 4.

Learn more about equation  from

https://brainly.com/question/29174899

#SPJ11

The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus \(\frac{UV}{VW} = \frac{6}{21}\)

this is further equal to \(\frac{2}{7}\)

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = \(\frac{y}{28 }\) which on equation will give y as 8

because \(\frac{8}{28}\) when divided by 4 will give us the required ratio that is 2 : 7

To know more about similar triangles or related problems you may visit the link which is mentioned below:

https://brainly.com/question/25882965

#SPJ1

The percentage of the total hours did Andrea work is,

⇒ 27.1%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Total number of hours to work is,

⇒ 5.8 + 8.1 + 7.3 + 8.7 hours

⇒ 29.9 hours

Here, Andre work 8.1 hours.

Hence, The percentage of the total hours did Andrea work is,

⇒ 8.1 / 29.9 × 100

⇒ 27.1%

Thus, The percentage of the total hours did Andrea work is,

⇒ 27.1%

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

Answer:

Brainliest

Step-by-step explanation:

35,423 ÷ 15= 2361 R 8

An orthonormal basis for the orthogonal complement W of V is {(2/√5)(1, -1/2, 0, 0)}. The problem asks us to find an orthonormal basis for the orthogonal complement of a subspace in R₄.

We are given two vectors, v₁ and v₂, which span the subspace V. We need to find the orthogonal complement W of V and determine an orthonormal basis for W using the standard inner product in R₄.

To find the orthogonal complement of a subspace, we need to find all vectors in R₄ that are orthogonal to every vector in the subspace V. In this case, V is spanned by v₁ and v₂. We can find the orthogonal complement W of V by finding the null space of the matrix whose columns are v₁ and v₂.

Constructing the augmented matrix [v₁ | v₂] and performing row reduction, we find that the matrix reduces to [1 -1 2 3 | 0 0 0 0]. The solution to this system gives us the basis for W.

Solving the system of equations, we obtain the vector [1 -1/2 0 0]. Since W is the orthogonal complement of V, this vector is orthogonal to both v₁ and v₂. To obtain an orthonormal basis for W, we normalize the vector by dividing it by its length.

Normalizing the vector [1 -1/2 0 0], we find that its length is √(1 + (1/2)²) = √(5/4) = √5/2. Dividing the vector by its length, we get the normalized vector (2/√5)(1, -1/2, 0, 0).

Therefore, an orthonormal basis for the orthogonal complement W of V is {(2/√5)(1, -1/2, 0, 0)}.

To learn more about augmented matrix, click here:

brainly.com/question/30403694

#SPJ11

The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

Learn more about circular cylinder here : brainly.com/question/2963891

#SPJ1

Answer:

70

Step-by-step explanation:

The real values of "a" that make (x - a) a factor of the given polynomial are: a = 3, a = 2, and a = 3/14.

To find the values of "a" for which (x - a) is a factor of the given polynomial x⁴ + 3x³ - 6x² - 28x - 24, we can use the Remainder Theorem.

So, let's divide the given polynomial by (x - a) and set the remainder to zero to find the values of "a".

Using long division or synthetic division, we get:

       x³ + (a - 3)x² + (3a - 6)x + (6 - 28a)

   __________________________________________

x - a | x⁴ + 3x³ - 6x² - 28x - 24

Since the remainder is zero, we have;

x³ + (a - 3)x² + (3a - 6)x + (6 - 28a) = 0

Now, for (x - a) to be a factor of the given polynomial, the coefficients of x², x, and the constant term must be zero, because these are the coefficients of (a - 3)x², (3a - 6)x, and (6 - 28a), respectively.

So, we can set them to zero and solve for "a":

a - 3 = 0 (Coefficient of x²)

3a - 6 = 0 (Coefficient of x)

6 - 28a = 0 (Constant term)

Solving these equations, we get:

a - 3 = 0 => a = 3

3a - 6 = 0 => 3a = 6 => a = 2

6 - 28a = 0 => 28a = 6 => a = 6/28 => a = 3/14

Learn more about factors of polynomial here: https://brainly.com/question/24351176

#SPJ1

Step-by-step explanation:

In geometry, we have many formal definitions using defined words or terms. However, I can think of three words that are not formally defined. These words are point, line and plane. Even though these words are undefined we can describes them as follows:

1. Point. A point is an exact position or location in space.

It is important to understand that a point has no dimension (that is, actual size). So, it has no length, no width, and no height (thickness).

We usually named a point with a capital letter. In the coordinate plane, a point is named by an ordered pair, x,y .

Even though we represent a point with a dot, the dot can be very tiny or very large. Recall that a point has no size.

2. Line (Straight line)

A line has no thickness.

So, its length extends in one dimension.

The line extends in both directions without end (infinitely). A line has infinite length and has no width, no height.

We assume the line to be straight.

and can be drawn with arrowheads on both ends.

3. Plane

A plane is a flat surface with no thickness extending indefinitely in all directions and having two dimensions. So, it has infinite length, infinite width and has no height (thickness). Moreover, a plane is drawn as a four-sided figure resembling a parallelogram.

The representation of each concept is shown in the Figure below.

a. Z-score formula

where,

• x: observed value

• μ: mean

• σ: standard deviation

Substituting with x = $275, μ = $280, and σ = $20, we get:

In terms of the z-score, we need to find

From the table:

Then, the percentage of customers that has daily balances of more than $275 is:

b. Substituting with x = $243, μ = $280, and σ = $20 into the z-score formula, we get:

In terms of the z-score, we need to find:

From the table, the percentage of customers that has daily balances of less than $243 is:

c. Substituting with x₁ = $241 and x₂ = $301.60, μ = $280, and σ = $20 into the z-score formula, we get:

In terms of the z-score, we need to find:

From the first table:

From the second table:

Therefore, the percentage of its customers' balances between $241 and $301.60 is:

on solving the provided question we can say that  the selling price of the fiction novel series is $61.56.

Cost: The cost price is the amount paid for an item at the time of purchase or the cost for producing it. Costs are identified by the notation C.P. Selling price: The selling price is the price at which a thing is sold. The amount that the seller really receives when the sale is complete is known as the selling price. The price a seller pays for a good or service is really called the cost. A profit percentage is then added.

markup rate is 62%,

t the seller is adding 62% of the cost to the price to make a profit.

Markup = 62% of Cost = \(0.62 * $38 = $23.56\)

Selling price = \(Cost + Markup = $38 + $23.56 = $61.56\)

the selling price of the fiction novel series is $61.56.

To know more about selling price visit:

https://brainly.com/question/29109312

#SPJ1

(A) The differential equation that represents the spring oscillating most quickly is s" + 9s = 0

(B) The spring oscillating with the largest amplitude is represented by equation 36s" + s = 0

(C)The spring oscillating most slowly (with the longest period) is described by equation 98" + s = 0

(D)The spring oscillating with the largest maximum velocity is represented by equation s" + 36s = 0

(a) The differential equation that represents the spring oscillating most quickly (with the shortest period) is (iv) s" + 9s = 0. This is because the coefficient of s" is the largest among the given equations, which indicates a higher frequency of oscillation and shorter period.

(b) The spring oscillating with the largest amplitude is represented by equation (iii) 36s" + s = 0. This is because the coefficient of s is the largest among the given equations, which indicates a stronger restoring force and thus a larger amplitude of oscillation.

(c) The spring oscillating most slowly (with the longest period) is described by equation (ii) 98" + s = 0. This is because the coefficient of s" is the smallest among the given equations, which indicates a lower frequency of oscillation and longer period.

(d) The spring oscillating with the largest maximum velocity is represented by equation (i) s" + 36s = 0. This is because the coefficient of s is the largest among the given equations, which indicates a higher velocity during oscillation and thus the largest maximum velocity.

To know more about differential equation click here :

https://brainly.com/question/30773776

#SPJ4

Answer:

x = 8

Step-by-step explanation:

I hope this helps!

Answer:

its either b or d

Answer:

-4.2

Step-by-step explanation:

-2 4/5 - 1 .4

-2.8 -1.4

-4.2

Answer:

-21/5

-4.2- decimal form

-4 1/5- mixed number form

Step-by-step explanation:

Therefore, the present value of the perpetuity that pays $1,800 per year forever, assuming a 5% interest rate, is $36,000. To find the present value of a perpetuity that pays $1,800 per year forever, we can use the formula:
Present Value = Cash Flow / Interest Rate

In this case, the cash flow is $1,800 and the interest rate is 5%. Plugging these values into the formula, we get:
Present Value = $1,800 / 0.05. Simplifying this equation, we find that:
Present Value = $36,000

To know more about perpetuity visit:

https://brainly.com/question/28205403

#SPJ11

(c) 494 buses will have more than 46 passengers.

On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is approximately normally distributed. If 660 buses are selected, approximately how many buses will have

For this question, Mean= 48

Standard deviation= 3

We have to find how many buses have more than 46 passengers, i.e we have to find the value of P(X > 46)We need to standardize the distribution to use the Z table

Z = (X - μ)/σ  where μ is the mean and σ is the standard deviation

So for the given distribution,

P(X > 46) = P(Z > (46 - 48)/3) = P(Z > -0.67) = 1 - P(Z < -0.67)

From the Z table, the value for P(Z < -0.67) is 0.2514So P(Z > -0.67) = 1 - 0.2514 = 0.7486Hence, approximately 0.7486 * 660 = 494 buses will have more than 46 passengers.

Answer: (c) 494 buses will have more than 46 passengers.
Learn more about Statistics: https://brainly.com/question/31538429

#SPJ11

Answer:

y=-2x-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

Answer:

20 - b

Step-by-step explanation:

5a - b

substitute a for 4 because a = 4

5(4) - b

20 - b

By the SAS congruence theorem, we can conclude that the triangle △MLQ ≅ △NPQ.

Congruent triangles are those that have the same size and shape. There are several congruence theorems that we can use to prove two triangles are congruent.

The given information tells us that MQ = NQ, and Q is the midpoint of LP. This means that Q is equidistant from M and N, which implies that MQN is an isosceles triangle. We also know that LM ≅ PN. Since Q is the midpoint of LP, we can conclude that MQ and NQ bisect angles LMP and PNL, respectively.

This is because the angle bisector of a triangle divides the opposite side into two segments that are proportional to the adjacent sides. Therefore, we have two triangles that share a common side MQN and have two pairs of congruent sides, LM ≅ PN and MQ = NQ.

The congruence theorem that we can use to prove △MLQ ≅ △NPQ is the SAS (Side-Angle-Side) congruence theorem. The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, we can see that the sides MQN and LM ≅ PN are congruent, and the included angles QML and QNP are congruent because they are vertical angles.

To know more about triangle here

https://brainly.com/question/8587906

#SPJ4

Complete Question:

Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN Triangles M L Q and N P Q are connected at point Q. A line is drawn from points M to N to form triangle M N Q. Which congruence theorem can be used to prove △MLQ ≅ △NPQ?

Answer:

The false statement is D) All kites are rectangles.

A kite is a quadrilateral with two pairs of adjacent sides that are congruent. A rectangle is a quadrilateral with four right angles and opposite sides that are parallel and congruent. While some kites can be rectangles (when the two pairs of congruent adjacent sides are also perpendicular), not all kites are rectangles. Therefore, statement D is false. Statements A, B, and C are true.

Step-by-step explanation:

The relationship between the central angle and interior angle is Central angle = 2 * Interior angle.

The internal angle is the angle created by two adjacent sides of a polygon within the circle, whereas the central angle is the angle formed by two radii of a circle that intersect at its centre. Since one of the sides of the polygon opposing the interior angle is opposite the central angle, the two angles are connected by the following formula:

central angle = 2 * Interior angle.

As the number of sides in a polygon increases, the measure of each interior angle decreases while the measure of each central angle remains constant.

Learn more about central angle here:

https://brainly.com/question/15698342

#SPJ1

Answer: can you help me i cant put a q     i have to points

Step-by-step explanation: plssssssssssssssss      

A customer wanted to purchase a video game and realized that they were short $4.28 to be able to pay. Which value is the opposite of being short $4.28

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

Learn more about sinusoidal function here

https://brainly.com/question/29529184

#SPJ11

In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.

The previous births do not affect the probability of the next birth since each birth is an independent event.

The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.

Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.

In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.

Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.

To learn more about independent event visit:

brainly.com/question/32716243

#SPJ11

Answer:

LN and NK

Step-by-step explanation:

trust

Answer: c

Step-by-step explanation:

Its correct

Answer:

7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³

Step-by-step explanation:

Dimensions of the cube = (x+7y),(7x-y) and (xy-5)

Volume of the cube = (x+7y) (7x-y) (xy-5)

= (7x² - xy + 49xy - 7y²)(xy - 5)

= 7x³y - 35x² - x²y² + 5xy + 49x²y² - 245xy - 7xy³ + 35y²

= 7x³y - 35x² + 35y² + 49x²y² - x²y² + 5xy - 245xy - 7xy³

= 7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³

Volume of the cube = 7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³