If QP bisects ZDQL, m/DQP = 5x - 7, and m/PQL = 11 + 2x, determine
the measure of ZDQL.
m₂DQL =

Answer:

==============================

[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]                                              Given

[tex]3(ax+b)=4(x+c)[/tex]                                     Cross-multiply

[tex]3ax + 3b=4x+4c[/tex]                                       Distribute

[tex]3ax-4x=4c-3b[/tex]                                       Collect terms with x

[tex]x(3a-4)=4c-3b[/tex]                                       Factor out x

[tex]x=\cfrac{4c-3b}{3a-4}[/tex]                                                   Divide both sides by 3a - 4

8+9x+4(11-2x)

As a first step we are going to use distributive property of multiplication:

8+9x+44-8x

Solving ths:

52+x

Answer would be M

First, let's calculate the total amount of balls:

Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.

So the probability is:

Correct option: A

The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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For the given figure, we will prove the triangles BGH and BDH are congruent.

So, the proof will be as follows:

Statement Reason

1) m∠F = m∠FEG = m∠FGE Given

2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ

3) FG = GE from (2), the definition of equilateral Δ

4) FG = ED Given

5) m∠ GEH = m∠DEH Given

6) EH = EH Reflexive property

7) ΔGEH ≅ Δ DEH SAS postulate

8) GH = DH from (7) CPCTC

9) m∠GHE = m∠DHE from (7) CPCTC

10) m∠GHB = m∠DHB Definition of supplementary angles

11) HB = HB Reflexive property

12) ΔBGH ≅ ΔBDH SAS postualte

13) ΔAGB is an isosceles Δ Given

14)AG = AB Definition of isosceles Δ

15) ΔBCD is an isosceles Δ Given

16) CB = CD Definition of isosceles Δ

17) CB = AG Given

18) m∠CDB = m∠CBD Definition of isosceles Δ

19) m∠ABG = m∠AGB Definition of isosceles Δ

20) m∠CDB = m∠AGB Given

21) m∠ABG = m∠CBD Transitive property

22) Δ AGB ≅ ΔCBD AAS postualte

The most appropriate choice for Quadratic equation and discriminant will be given by -

Discriminant = -244

What is Quadratic equation and discriminant?

At first it is important to know about equation.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

If [tex]ax^2 + bx + c = 0[/tex] ([tex]a\neq0[/tex]) is a quadratic equation, discriminant is given by

[tex]D = b^2-4ac[/tex].

Here,

The given equation is

[tex]7x^2+23x+168=6x^2+3x+7[/tex]

[tex]7x^2 - 6x^2 + 23x - 3x + 168 - 7 = 0 \\x^2 + 20x +161 = 0\\[/tex]

Discriminant = [tex]20^2 - 4 \times 1 \times 161[/tex]

                     = [tex]400 - 644[/tex]

                     = -244

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Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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Answer: n=7

Step-by-step explanation:

First distribute the numbers to get 5n+10=3+6n

Next Subtract 6n from both sides to get -n=10=3

Finally divide both sides my -1 to get rid of the -n to get n=7

Hope this helps :)

We are given

Therefore the value of x can be gotten by simplifying the above equation

Given that x is 5, we can proceed to find the value of the expression.

This implies that

Answer: C

Step-by-step explanation:

It the only one that includes both.

We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.

PART 1

Let the probability that the marble is red be P(r).

Therefore,

This gives,

Therefore, the probability that the marble is red is:

ANSWER= 0.297

PART 2:

Let the probability of picking odd-numbered balls be P(o)

Therefore,

We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.

Therefore,

The probability of picking odd-numbered balls is

ANSWER = 0.5

PART 3:

Let the probability of picking a red or odd-numbered ball be P(r U o)

Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).

p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.

Therefore,

This implies that,

Hence, the probability of picking a red or odd-numbered ball is

ANSWER = 0.648

PART 4:

Let the probability of picking a blue or even-numbered ball be P(b U e)

Therefore,

From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,

p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.

p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls

Therefore,

Therefore, the probability of picking a blue or an even ball is:

ANSWER = 0.852

Answer:

176 children and 105 adults.

Explanation:

Let's call x the number of children and y the number of adults.

If 281 people entered the park, we can write the following equation

x + y = 281

If they collected 684 dollars, we can write the following equation

1.5x + 4y = 684

because it cost $1.5 for children and $4 for adults.

Now, we have the following system of equations

x + y = 281

1.5x + 4y = 684

First, we need to solve the first equation for y, so

x + y = 281

x + y - x = 281 - x

y = 281 - x

Then, replace this expression on the second equation

1.5x + 4y = 684

1.5x + 4(281 - x) = 684

1.5x + 4(281) - 4(x) = 684

1.5x + 1124 - 4x = 684

-2.5x + 1124 = 684

Finally, we can solve the equation for x

-2.5x + 1124 - 1124 = 684 - 1124

-2.5x = -440

-2.5x/(-2.5) = -440/(-2.5)

x = 176

So, the value of y is equal to

y = 281 - x

y = 281 - 176

y = 105

Therefore, they admitted 176 children and 105 adults.

Based on the length of the ribbon, and the length of the pieces Janice needs to make, the number of 3/8 foot pieces she can make would be

To find the number of pieces that Janice can get from the 7/8 foot ribbon, you need to divide this length by the length of each piece of ribbon.

The length of each of these pieces is 3/8 so the number of pieces of ribbon that Janice can get from the 7/8 foot ribbon is:

= 7 / 8 ÷ 3 / 8

= 7 / 8 x 8 / 3

= 56 / 24

= 2.33 ribbons

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Janice can make 2 pieces of ribbon from 7/8 feet of ribbon each measuring 3/8 feet.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Janice is cutting the ribbon to decorate a present. She has 7/8 feet of ribbon.

She needs to make pieces that are 3/8 feet each.

To obtain the no. of pieces we have to divide the total length of the ribbon by the length of each piece.

∴ (7/8)/(3/8).

= (7/8)×(8/3).

= 7/3 pieces.

But he can only make 2 pieces as pieces must be in integers.

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Answer:

3 years and 6 months

Step-by-step explanation:

35 × 3= 105 + 17 = 122

2.916 a month × 6 = 17. 496. And round to the nears while number = 17.50 = 105 + 17.50 = 122.5 or 122.50 zero fir place holder.

D

1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial

g (x)= (x+1) (x-2) (x+5)

g(x) =x³+4x²-7x-10

As the coefficient is positive, then we'll have

Examining the options, we have as the roots S={-5,-1,2} So the answer is D

The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.

Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:

y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3

According to the general form of a multiple linear regression model:

-143481.1924 = intercept(c) ; where regression line crosses the origin

10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3

y = predicted variable

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Given the equation:

You need to solve for "x" in order to find its value:

1. Apply the Addition Property of Equality by adding 0.03 to both sides of the equation:

2. Apply the Division Property of Equality by dividing both sides of the equation by 0.005:

Hence, the answer is:

As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.

Area of triangle:

In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,

Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}

As the area is always positive.

Given,

Here we have the triangle VWX,

And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).

Now we have to find the area of the triangle.

To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).

Now, we have to apply the values on the formula, in order to get the area of the triangle,

=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|

When we expand the terms, then we get,

=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|

Further simplify the expression will gives you the following,

=> A = 1/2 |27 - 20 + 12|

=> A = 1/2 |19|

Therefore, the area of the triangle is 9.5 square units.

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The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units , the correct option is (D)  .

If the equation of the circle is x² + y² + 2fx + 2gy + c = 0

then the center is (-f,-g)

and the radius is √(f²+g²-c)

In the question ,

it is given that the

equation of the circle is x² + y² + 14x + 2y + 14 = 0

So , on comparing it with the general form of equation , we get

2f = 14

f = 7

and 2g = 2

g = 1

hence, the center is (-7,-1) .

the radius is √(7² + 1² - 14)

= √(49 + 1 - 14)

= √(50 - 14)

= √36

= 6

Therefore , The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units .

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Answer:

Step-by-step explanation:

area=l*w

(x+4)(x-4)

x^2-16 (use foiling)

Answer:

Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.

Answer 2: 11/100 more marks

Answer 3: Rajesh got an A, while Sita got a B-

Step-by-step explanation:

Put the 93 on top of 100, and do the same for 82.

Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.

The price of the car after 15% markup will be $8,280

How to calculate price after 15% of markup ?

The cost price of car for Hanks = $7200

Marking up of price is done by 15%

To find Markup price = Cost price + 15% of cost price

                                  = 7,200 + 7,200 * 15/100

                                  = 7,200 + 1,080 = $8,280

The 15% of car price is $1,080

The price of the car after 15% markup will be $8,280  

What is percentage ?

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The vertical line's equation is x = -7, and the horizontal line's equation           Is y = 7.

Where the given coordinate is (--7, 7).

Here,

The value of x, is -7, will never change for a vertical line. This holds true for any y value. As a result, x = -7 is the equation for a vertical line passing through this point.

Similarly, the value of y, is 7, will never change for a horizontal line. This holds true for any x value. As a result, the equation for a horizontal line passing through this point is as follows: y =7

As a result, the vertical line's equation is x = -7 and the horizontal line's equation is y = 7.

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Answer:

The slope is undefined

Step-by-step explanation:

The vertical component of the force is 69.28  N and the horizontal component of the force is 40 N.

Resolution of forces is the process of separating a force into two or more pieces so that the combined effect on the body is the same as if it had been a single force. We can analyze motion individually in different directions thanks to the resolution of forces.

Given that a heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope.

The vertical component and the horizontal component will be calculated as:-

Vertical component = 80sin60=69.28 N

Horizontal component = 80cos60 = 40 N

Therefore, the vertical component of the force is 69.28  N and the horizontal component of the force is 40 N.

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Answer:

Between -4 and 0

Step-by-step explanation:

Hey! I saw your most recent and I'm assuming it is this question we're talking about it so let's help you with that!

Let's start by looking at what each of them mean, the first one means that 4 is lower than a but a is lower than 5 (Inequality 1) The second one means 5 is lower than b but b is lower than 8 (Inequality 2). Now, in order to find out [tex]a-b[/tex], we need to find the largest and smallest value of [tex]a-b[/tex]. The reason why we do this is because we want to look for the range of what [tex]a-b[/tex] can give us and in finding the largest and smallest value, if we were to evaluate both inequality 1 and 2 using [tex]a-b[/tex], we know that it can't be beyond the largest value or smaller than the lowest value.

In order to figure out the largest possible value of [tex]a-b[/tex], we need to take the maximum x value of inequality 1 and subtract it by the minimum y value of inequality 2, so we get:

[tex]5-5=0[/tex]

In order to figure out the smallest possible value of [tex]a-b[/tex], we need to take the minimum x value of inequality 1 and subtract it by the maximum y value of inequality 2, so we get:

[tex]4-8=-4[/tex]

So, in this case! The answer is b) between -4 and 0

Answer:

B

Step-by-step explanation:

The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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The values are given as;

1. - 2a - 9 = 6a + 15,  a = -3

2. 14 + 3n = 5n - 6, n = 10

An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;

They are also known to be made up of terms, variables, constants, factors and coefficients.

Given the algebraic expression;

- 2a - 9 = 6a + 15

Let's take the following steps;

collect like terms

- 2a - 6a = 15 + 9

add or subtract like terms

-8a = 24

Make 'a' the subject

a = 24/-8

Find the quotient

a = -3

14 + 3n = 5n - 6

collect like terms

3n - 5n = -6 - 14

-2n = -20

Make 'n' the subject of formula

n = 10

Hence, the values are -3 and 10

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Answer:

I don't know if you can use permutations but

(6P2-6)/6=4 ????

Solution;

y=5x

Explanation;