Given: ∆FGH~∆JKH. List all congruent angles and write a proportion that relates the corresponding sides.

Answer:

To find the solutions of the equation x^2+4x+3=0, you can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 4, and c = 3. Plugging these values into the formula gives:

x = (-4 +/- sqrt(16 - 413)) / (2*1)

x = (-4 +/- sqrt(4)) / 2

x = (-4 +/- 2) / 2

This means the two solutions for x are (-4 - 2) / 2 = -3 and (-4 + 2) / 2 = -1.

So the biggest and lowest numbers you can get with the number x^2+4x+3=0 are -3 and -1, respectively.

Answer: The biggest number is  x= -1 and

                   the lowest number is    x= -3 .

Step-by-step explanation: Solution

or, x^2+4x+3=0

or, x^2+ ( 3+1 )x+3=0

or, x^2+3x + x +3=0

or, x (x + 3)+ 1(x + 3)=0

or, (x + 3) (x + 1)=0

Either,

        (x + 3)= 0  ,    (x + 1)= 0

     or, x= -3       ,    x= -1

Therefore, The biggest number is  x= -1 and

                   the lowest number is    x= -3 .

The equation y = 3/5 x is graphed on a coordinate plane and attached

The equation is graphed using some points for the input which is x values and solving to get the y values

This is called the table of values used to plot on the coordinate plane

The table of values for y = 3/5 x is formed as follows

For x = -10, y = 3/5 * -10 = -6

For x = -5, y = 3/5 * -5 = -3

For x = 0, y = 3/5 * 0 = 0

For x = 5, y = 3/5 * 5 = 3

For x = 10, y = 3/5 * 10 = 6

table of values

x     y

-10  -6

-5   -3

0     0

5     3

6     6

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Answer: 2nd option

Step-by-step explanation:

If m stands for miles, we know it must be $0.85m. Since there is a $0.75 and $0.10 charge, we add those together to get $0.85. Then, we must add the tourist charge of $2.50. So, the equation. 0.85m+ 2.50

Answer:

0.85m + 2.50

Step-by-step explanation:

mileage charge is equal to 0.75 dollars each mile

city gas tax is equal to 0.10 dollars each mile

mileage charge plus city gas tax is equal to 0.85

plus the tourist charge , so the answer is

0.85m + 2.50

Answer:

The answer is D

Step-by-step explanation:

Trust me on this, its hard to explain but Im 100% sure.

The monthly payment of loan is $180.26.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Given principal = $4,000

APR = 4%

time = 2 years

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A =[tex]P(1 + r/n)^{nt}[/tex]

A = 4,000.00(1 + 0.04/1)¹ˣ²

A = 4,000.00(1 + 0.04)²

A = $4,326.40

amount for 2 years = $4,326.40

monthly payment  = 4326.40/24

monthly payment  =  $180.26

Hence the monthly payment is $180.26

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The cost of the 12 units sold is, $224 - $144 = $80

Using the FIFO periodic inventory method, the cost of the 12 units that are sold is $120. This is because the first 12 units sold were the ones that were purchased on February 3 for $12 each. The total cost of these units is 12 units * $12/unit = $12*12=144. The remaining 8 units in the inventory were purchased on February 1 for $10 each, for a total cost of 8 units * $10/unit = $8*10=80. The total cost of the inventory is therefore $144 + $80 = $224. The cost of the 12 units sold is, therefore, $224 - $144 =$80.

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The total would be 25 + (0.06 x 350) = $51. So my friend's charge for last month will be $51.

My friend's charge for last month will be calculated by adding the monthly customer fee of $25 and the minutes spent price of 0.06 for the 350 minutes spent. The total would be 25 + (0.06 x 350) = $51. So my friend's charge for last month will be $51.

Monthly customer fee = $25

Price per minute = $0.06

Total minutes spent = 350

Total cost = $25 + (0.06 x 350)

Total cost = $25 + 21

Total cost = $51

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The area of triangle E is 144 square inches

Since the isosceles triangles D and E are similar. The ratio of their perimeters and areas will be equal.

 Let Pd, Pe, Ad and Ae respresent the perimeter of D, perimeter E, area of D and area of E respectively

We can write that:

Pd / Pe = Ad / Ae

where Pd =  64 inches, Pe =  72 inches and Ad = 128 square inches. Substituting these value will give:

64 / 72 = 128 / Ae

Ae = (128×72)/64

Ae = 144 square inches

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Difference in miles travelled by Bus X and Y is  12.8 miles in distance

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, velocity is a vector, whereas speed is a scalar number.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to go from one point to another is the distance traveled. Travel distance is not a vector.

Bus X travels 40 miles in 1 hour

Distance travelled in 2 hrs = 40*2 = 80 miles

Bus Y travels 60 miles per hour

Distance travelled in 1.12 hrs = 60*1.12 = 67.2 miles

Difference in miles travelled by Bus X and Y is = 80 - 67.2 = 12.8 miles

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By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:

(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4

Here we want to add two polynomials:

6x^2 - 3

And

8x^2 - 5x - 1

To make that addition, we just need to group like terms and take common factors.

We start with:

(6x^2 - 3) + (8x^2 - 5x - 1)

Grouping like terms we will get:

(6x^2 + 8x^2) + (-5x) + (-3 - 1)

Now we can simplify that, so we will get:

(6 + 8)*x^2 - 5x - 4

14x^2 - 5x - 4

That is the addition of the polynomials.

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The area of the parallelogram is 500 in squared

A parallelogram is a four sided polygon that has opposite sides parallel to each other.

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

A= bh

From the figure, b = 20 in, h= 25 in

Area = 20*25 = 500 in square

Conclusively, taking into consideration the height of the parallelogram as 25 in and the base as 20 in, the area is given as 500 in square

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The cost price of an article is Rs.600 and the profit of dealer is Rs.200

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given;

An article marked at Rs.800 sold at a discount of 10%.

That means,

selling price = 800 - 10% 0f 800

                 =  800 - (10 x 800 / 100)

                 = 800 - 80

                 = 720

The dealer makes a profit of 20% means is selling the article at 120%.

120%=720

1%=6

Hence, 100% = 600

Thus, the cost price of article = 600

Profit= SP-CP = 800-600 = 200

Therefore, Rs.600 is the cost price and the profit is Rs.200

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Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.

The formula for the n-th term of an arithmetic sequence is given by:

a(n) = a(1) + (n - 1) d

Where:

a(1): the first term

d = common difference

The consecutive terms of an arithmetic sequence can be obtained as:

a(n) = a(n - 1) + d

Information available in the problem:

first term = a(1) = -6

common difference = d = -7

Hence,

a(1) = -6

a(2) = -6 - 7 = -13

a(3) = -13 - 7 = -20

a(4) = -20 - 7 = -27

a(5) = -27 - 7 = -34

Therefore the first five terms are: -6, -13, -20, -27, -34

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The correct option is option a) The critical value depends on the number of categories, not the sample size.

The critical value for a chi-square test is determined by the level of significance (alpha) and the degrees of freedom (df). The degree of freedom is a function of the number of categories in the test, not the sample size. Therefore, increasing the sample size does not affect the critical value for a chi-square test.

The chi-square test is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It is used to test the independence of two categorical variables.

Therefore, The correct option is option a) critical value depends on the number of categories, not the sample size.

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The angle of elevation 80.537°.

Although it may not directly address fixing real-world problems, it is employed in many different fields. In order to create computer music, for instance, trigonometry is utilised. As you are likely aware, sound travels in the shape of waves, and this wave pattern is achieved using a sine or cosine function. Here are several situations in which trigonometry and its operations are useful.

Given height of airplane from ground is 12 km,

and distance from plane to airport tower is 2 km,

to find the angle of elevation

angle of elevation = tanФ = p/b

where p = perpendicular = height = 12 km

b = base = distance from airplane to tower = 2 km

tanФ = p/b = 12/2

tanФ = 6

Ф =  [tex]tan^{-1} (6)[/tex]

Ф = 80.537°

Hence the  angle of elevation is 80.537°.

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The line could pass through any of the following points: (1, 0),(2, 1),(3, 2),(4, 3), and (5, 4).

A line with a positive slope passes through points that are higher and to the right of the starting point. The line could also pass through points with higher y-values and smaller x-values, such as (1, 2) or (0, 5), but it could not pass through points with lower y-values or larger x-values. For example, the line could not pass through the point (-1, 0) because it has a larger x-value than the starting point (0, -1) and a positive slope. Similarly, the line could not pass through the point (1, -2) because it has a lower y-value than the starting point and a positive slope.

Therefore, the line could pass through any of the following points:

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For a line with a positive slope that passes through (0, 1), the points that can't be on the line are:

(-3, 1) and (5, -2)

Now, According to the question:

Given a line with

To find:

The point from the list that is not on the same line

Slope formula is m = (y2 - y1)/(x2 - x1)

Using one given point, we get the slope:

m = (y - 1)/(x - 0)

m = (y - 1)/x and m > 0

Let's verify the answer choices:

Point (12, 3)

m = (3- 1)/12 = 2/12 > 0, yes, on the line

Point (-2,-5)

m = (-5 - 1)/( -2) = 3 > 0, yes, on the line

Point (-3, 1)

m = (1 - 1)/(-3) = 0, no, not on the line

Point (1, 15)

m = (15 - 1)/1 = 14 > 0, yes, on the line

Point (5,-2)​

m = (-2 - 1)/5 = -3/5 < 0, no, not on the line

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The complete question is this:

A line passes through the point (0, –1) and has a positive slope. Which of these points could that line pass through? Check all that apply.

(12, 3)

(–2, –5)

(–3, 1)

(1, 15)

(5, –2)

k≤8 is the solution of inequality 16 ≥ 2k

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 16 ≥ 2k

Sixteen greater than or equal to two time of k.

16 ≥ 2k

Divide both sides by 2

8 ≥ k

Eight is greater than or equal to k

k≤8

k is less than or equal to eight

Hence, k≤8 is the solution of inequality 16 ≥ 2k

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Answer:

Below

Step-by-step explanation:

To find the number of games g that the team could lose and still be eligible for the playoffs, we can write the inequality:

g / 18 ≤ 40%

g / 18 ≤ 0.4

g ≤ 7.2

We can round down to 7 to get the maximum number of games the team could lose and still be eligible for the playoffs.

If the baseball team loses 8 of its remaining games, they will not advance to the playoffs. This is because 8 is greater than the maximum number of games they could lose and still be eligible for the playoffs, which is 7.

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The radius of convergence,R, of the series [tex]\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \][/tex] is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series [tex]\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \][/tex]

We need find the radius of convergence.

We use ratio test.

We know for [tex]$\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L[/tex]

if L < 1, then the series converges

and If [tex]$\lim_{x\to\infty}~a_n \neq 0[/tex] then [tex]\sum a_n[/tex] diverges.

Using ratio test for given series,

[tex]$\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\[/tex]

= [tex]$\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|[/tex]

= [tex]$\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|[/tex]

[tex]=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|[/tex]

= |x|

This means, the series is convergent for |x| < 1.

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Part (i)

[tex]a^6 \times a^3=a^{6+3}=\boxed{a^9}[/tex]

Part (ii)

[tex]\frac{24}{6} \times \frac{b^{16}}{b^4}=4b^{16-4}=\boxed{4b^{12}}[/tex]

Answer: Not linear

Step-by-step explanation:

Use the slope-intercept form

y

=

m

x

+

b

to find the slope

m

.

The proper answer from each drop-down menu in the system depicted by the graph. Reset In the Next'system of Inequalities, the graph stands for 4x-y.

The system of inequality is depicted in the graph. 1. 4x-y less than or equal to 4 and 2x-2y less than or equal to 3, 2. 4x-y greater than or equal to 4 and 2x-2y less than or equal to 3, 3. 4x-y less than or equal to 4 and 2x-2y larger than or equal to 3, 4. 4x-y greater than or equal to 4 and 2x-2y greater than or equal to 3. In the graph-representation of the system, the test point fulfils both of the inequalities.

Pick the appropriate response from each drop-down menu in the system shown by the graph. Reset The graph represents 4x-y in the Next'system of Inequalities.. Equations simultaneously, or a system of equations Multiple equations must be solved simultaneously in algebra. There must be an equal number of equations and unknowns for a system to have a singular solution.

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Answer:

Green = 18.84

Blue =24

Orange = 20

Total outer perimeter = 18.84 + 24 + 20 = 62.84

Answer:

18.84 m, 24m, 20m

Step-by-step explanation:

Green:

We need the radius of this circle, is can be calculated by 12 ÷ 2 = 6

2π6 / 2 = 37.68 / 2 = 18.84 m

Blue:

12 + 12 = 24 m

Orange:

10 + 10 = 20 m

Using the same-side exterior angles theorem, the value of y is: 92°.

The same-side exterior angles theorem states that if two lines are cut by a transversal, and the alternate interior angles are congruent (equal in measure), then the same-side exterior angles are supplementary (add up to 180 degrees).

The image shows two angles that are same-side interior angles, which are (x + 1) and (x - 3) degrees. Therefore, their sum would be equal to 180 degrees. This means that:

(x + 1) + (x - 3) = 180 [based on the same-side exterior angles theorem]

x + 1 + x - 3 = 180

2x - 2 = 180

2x = 180 + 2

2x = 182

2x/2 = 182/2

x = 91

Thus, based on the alternate interior angles, we also have:

x + 1 = y

Plug in the value of x:

91 + 1 = y

92 = y

y = 92°

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By applying partial derivative rule, we can obtain the answer as follows:

A. 321312 pounds

B. [tex]f_{x}[/tex] = 13000 + 14xy - 39x²

C. [tex]f_{y}[/tex] = 3500 + 7x²

D. 15211 weekly pounds per skilled worker

E. 4347 weekly pounds per unskilled worker

Partial derivative is the derivative of a function that has several independent variables, to one of the independent variables by holding the other independent variables as constants.

Now we take a look at the given problem. The production function is:

z = f(x, y) = 13000x + 3500y + 7x²y - 13x³, where

z = the weekly number of pounds of acetate fiber

x = the number of skilled workers at the plant

y = the number of unskilled workers at the plant

Weekly fiber that can be produced with 11 skilled workers and 45 unskilled workers:

z = f(x, y) = 13000x + 3500y + 7x²y - 13x³

  f(11,45) = 13000*11 + 3500*45 + 7*11²*45 - 13*11³

              = 143000 + 157500 + 7*121*45 - 13*1331

              = 143000 + 157500 + 38115 - 17,303

              = 321312 pounds

Rate of change of output with respect to the number of skilled workers:

[tex]f_{x}[/tex] = dz / dx

   = d(13000x + 3500y + 7x²y - 13x³) / dx

   = 13000 + 7*2xy - 13*3x²

   = 13000 + 14xy - 39x²

Rate of change of output with respect to the number of unskilled workers

[tex]f_{y}[/tex] = dz / dy

  = d(13000x + 3500y + 7x²y - 13x³) / dy

  = 3500 + 7x²

Rate of change of output with respect to skilled workers when 11 skilled workers and 45 unskilled workers are employed:

[tex]f_{x}[/tex] = 13000 + 14xy - 39x²

   = 13000 + 14*11*45 - 39*11²

   = 13000 + 6930 - 4719

   = 15211 weekly pounds per skilled worker

Rate of change of output with respect to unskilled workers when 11 skilled workers and 45 unskilled workers are employed:

[tex]f_{y}[/tex] = 3500 + 7x²

   = 3500 + 7*11²

   = 3500 + 847

   = 4347 weekly pounds per unskilled worker

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WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

If quadrilateral WXYZ is a parallelogram, the opposite sides will be equal, in length from which the value of x will satisfy the two equations.

Given,

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

The length of the opposite sides of a parallelogram are equal, which gives;

2x - 5 = x + 2

2x - x = 2 + 5

x = 7

Similarly, we have;

x + 8 = 15

x = 15 - 8 = 7

The lengths of the opposite sides are therefore;

2·x - 5 = 2 × 7 - 5 = 9 and x + 8 = 15

The option that indicates if WXYZ is a parallelogram is therefore;

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

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WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent best explains that WXYZ is not a parallelogram.

Therefore the answer is d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that the sides of the quadrilateral are arranged such that opposite sides are parallel and have the same length. In other words, if you draw a line through one pair of opposite sides, the other pair of opposite sides will also be parallel to that line and have the same length.

So, to determine if a quadrilateral can be a parallelogram, we need to check if it has two pairs of parallel and congruent sides. It does not matter what the lengths of the sides are.

In this case, option (d) is the correct answer because it states that one pair of sides can be congruent, but the other pair of sides is not congruent, which means that the quadrilateral cannot be a parallelogram

--The question is incomplete, complete question is given below--

"Which best explains if quadrilateral WXYZ can be a parallelogram?

a) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

b) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.

c) WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.

d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent."

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Rounded to the nearest ten-thousandth, the solution is x of the logarithmic equation is 2.000.

To solve this equation, we can begin by isolating the logarithmic expression on one side of the equation. To do this, we can divide both sides of the equation by 3:

3 log 2x / 3 = 4 / 3

This simplifies to:

log 2x = 4/3

Now, we can use the property of logarithms that states that "log [tex]a^b[/tex] = b × log a" to rewrite the logarithmic expression on the left side of the equation:

log 2x = 4/3

log [tex]2^{(4/3)}[/tex] = 4/3

4/3 × log 2 = 4/3

This simplifies to:

log 2 = 1

Since "log [tex]a^1[/tex] = 1" for any value of "a," this means that [tex]2^1[/tex] = 2. Therefore, the solution to the equation is x = 2.

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Answer: x=27 y=25

Step-by-step explanation: the question is (x+2)+y=52

we can move subtract 2 from both sides leaving x+y=50

then we can divide 50 by 2 because they are now equaled to eachother

that means hannah is 25 but we will add back to Ms. Johnsons 2 years that she is older so Ms. Johnson is 27

x=Ms. Johnson so x=27 amd y=Hannah so y=25

Answer: If event A and event B cannot occur at the same time, then events A and B are said to be _________

Answer:  a) mutually exclusive

Mutually exclusive events are those events that do not occur at the same time. For example, when a coin is tossed, the result will be either head or tail, but we cannot get both effects. Such events are also called disjoint events since they do not happen simultaneously.

If event A and event B cannot occur at the same time, then events A and B are said to be mutually exclusive

Step-by-step explanation: