Determine which of the lines, if any, are parallel or perpendicular. Explain.
Line A: 4x-3y=2
Line B: y=4/3x+2
Line C: 4y+3x=4

The value of b = 17 and c = 6 makes ΔGHI ≅ ΔZYX.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Here, we have

Given the sides of both the triangle and

we have to find the value of b and c that makes ΔGHI ≅ ΔZYX

b = 17 and,

48 = 8c

c = 6

Hence, the value of b = 17 and c = 6 that makes ΔGHI ≅ ΔZYX.

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Answer:

Below

Step-by-step explanation:

3x+15      <==== factor out '3'

3 * ( x+5)       done !

9 square meters is the area of triangle LMN. Using the concept of Heron's formula.

Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.

According to Heron's formula the area = √s (s - a)(s - b)(s - c)

A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.

a triangle with three sides, a, b, and c.

given data was LM = 7,MN = 6 and perimeter was given by 16m

As we know perimeter is the sum of all the sides  

so, Perimeter=LM + MN + NL

NL=Perimeter-(LM+MN)

NL=16 - 7 - 6

NL= 3

By Heron's formula,

Area = √[(s(s-a)(s-b)(s-c)].  

where s = perimeter/2

so, s = 16/2 = 8

area = √[(8(8-7)(8-6)(8-3)]

area = 8.94427191 ≈ 9 square meters.

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Answer: 9m

Step-by-step explanation:

A typical large recycling tote can hold 10 kilograms of plastic yogurt containers. the  volume is 0.01 m^3

Generally, To determine the volume needed to hold 10 kilograms of plastic yogurt containers, you would need to know the density of the plastic and the size and shape of the containers.

The density of a material is a measure of its mass per unit volume. It is usually expressed in kilograms per cubic meter (kg/m^3). The density of plastic can vary depending on the specific type of plastic and any additives that are present.

Once you know the density of the plastic, you can use the following formula to calculate the volume needed to hold a certain mass of the material:

Volume = Mass / Density

For example, if the density of the plastic is 1000 kg/m^3 and you want to hold 10 kilograms of it, the volume needed would be:

Volume = 10 kg / 1000 kg/m^3

Volume  = 0.01 m^3

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THE COMPLETE QUESTION WAS NOT FOUND

The system of inequalities that matches the graph is defined as follows:

The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.

This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:

y ≤ 3x

he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.

When x increased by 3, y decayed by 6, hence the slope of the line is of:

m = -6/3 = -2.

Then:

y = -2x + b.

When x = 1, y = -3, then the intercept is given as follows:

-3 = -2 + b

b = -1.

Thus the constraint is of:

y > –2x – 1.

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The number of boxes of sugar that Alonso can buy are 4.5 boxes.

Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.

The money remaining after buying 12 eggs : {r} = $(55 -2.75).

Cost of one box of sugar = $11.5

The number of boxes that he can buy are -

n = (55 - 2.75)/11.5

n = 4.5 boxes {approx.}

Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.

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The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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Answer:

3y, 9y²

Step-by-step explanation:

We use laws of binomial

(a+b)²=a²+2ab+b²

From this, we get

15x × * × 2 = 90xy

2×*=6y

*=3y

Now, we square this term to get the last term

3y×3y=9y²

Answer:

-48y+24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠)

=-6(8y+-4)

=-48y+24

Answer:

-48y + 24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠) =

= −6⁢(⁠8y - 4)

= -48y + 24

Answer:

j = - 8

Step-by-step explanation:

1 - j/4 - 3

1 is also 4/4

so

4/4 - j/4 = 3

4 - j/ 4= 3

multiply by 4 on both sides

which gets you

-j  + 4 = 12

minus 4 from both sides

-j = 8

j = -8

Answer:j=-8 I hope this helps

Step-by-step explanation:

1-j/4=3

Multiply both sides of the equation by 4

which gives you

4-j=12

Move the constant to the right-hand side and change its sign
-j=12-4

Subtract the numbers

-j=8

Change the signs on both sides of the equation

j=-8 - This is your answer

Answer:

Step-by-step explanation:

7/8
------
3/10

use the fraction rule: 7x10/8x3- 35/12

try that, im not sure if its fully correct

The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. Since it was first described on the first page of Euclid's Elements, the vocabulary for classifying triangles is more than two thousand years old. Modern categorization names are either literal transliterations of Euclid's Greek or their Latin interpretations.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is used to signify a triangle in the previous illustration.

FD/DC=ED/DG

2x+7/48=5x-2/40

40(2x+7)=48(5x-2)

80x+280=240x-96

160x=376

x=2.35

Therefore, The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

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Answer:

a. -4

b. 1/4

Step-by-step explanation:

a. [tex]\textrm{slope}_{||} = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{-4}{1} = -4[/tex]

b. [tex]\textrm{slope}_\perp = \dfrac{-1}{\textrm{slope}_{||}} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]

We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

What do you mean by  Annexation?

International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.

According to the question,

We have the given data:

A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.

The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.

This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.

Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

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Answer:

A. -2, -5, -8, -11, -14, -17, ...

Step-by-step explanation:

The difference between consecutive terms is constant.

The required probability of getting exactly 3 heads is 0.3.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total sample space = 2×5 = 10
Favorable outcome (3 heads) = 3
Probability is given of getting exactly 3 heads
= favorable outcome / total sample space

Substitute the value in the above equation
= 3 / 10
= 0.3

Thus, getting the 3 heads while tossing a coin 5 times has a probability of 0.3.

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Answer:

50x + 9500 ≤ 27500

x ≤ 360

Step-by-step explanation:

50x + 9500 ≤ 27500  Subtract 9500 from both sides

50x + 9500 - 9500 ≤ 27500 - 9500

50x ≤ 18000  Divide both sides by 50

[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]

x ≤ 360

We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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The measure of angle c is m ∠c = 103°.

What is triangle?

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane.

180 degrees is the sum of the triangle's three angles.

Let Δabc is given with m ∠a = 30° and m ∠b = 37°

We have to find the measure of angle c.

Since the sum of three angles of triangle is 180 degree.

⇒ m ∠a + m b + m ∠c = 180°

30° + 37° + m ∠c = 180°

77° + m ∠c = 180°

m ∠c = 180°- 77°

m ∠c = 103°

Hence, the measure of angle c is m ∠c = 103°.

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Answer:

x = 3[tex]\sqrt{7- x}[/tex]

Step-by-step explanation:

so what you do here is move the x to the other side.

X^2 = 63 - x

then you square root both sides

so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]

so you end up with

x =   [tex]\sqrt{63 - x}[/tex]

so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with

x = 3[tex]\sqrt{7- x}[/tex]

have a good day :)

Answer:0.41

Step-by-step explanation:

987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]

What is scientific notation?

Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.

When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].

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Answer:

-2

Step-by-step explanation:

we use the y2-y1/x2-x1 fomrula to find slope

14-8/7-10

6/-3

-2 is the slope

hopes this helps

Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

Answer:

Step-by-step explanation:

g(x) = (-x)1/2