n the blanks below.
Find the slope of the line passing through the points (8, -4) and (8, -7).
slope:
Find the slope of the line passing through the points (-3, -9) and (-3, 9).
slope:

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

Solving For #7

We will use the Angle Bisector Theorem

The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS

According to the angle bisector theorem:

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]

Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]

If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]

From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.

Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.

Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.

Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.

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The common factor is  6[tex]e^{6x}[/tex]  (2x - 5)⁸.

What is a common factor?

These are the "common factors" when we determine the factors of two or more numbers and discover some of those factors are the same (or "common").

Given that

d/dx[[tex]e^{6x}[/tex](2x - 5)⁹]

The formula of the product rule is d/dx(uv) = uv' + vu'.

=(2x - 5)⁹d/dx([tex]e^{6x}[/tex]) +  [tex]e^{6x}[/tex]d/dx(2x - 5)⁹

Now applying the formula d/dx(x^n) = nx^(n-1), d/dx e^(mx) = m e^(mx)

=(2x - 5)⁹ 6[tex]e^{6x}[/tex] + [tex]e^{6x}[/tex]×2×9 × (2x - 5)⁸

= 6[tex]e^{6x}[/tex]  (2x - 5)⁹ + 18[tex]e^{6x}[/tex](2x - 5)⁸

Now taking common 6[tex]e^{6x}[/tex]  (2x - 5)⁸

= 6[tex]e^{6x}[/tex]  (2x - 5)⁸ [(2x - 5) + 3]

= 6[tex]e^{6x}[/tex]  (2x - 5)⁸ [2x - 5 + 3]

= 6[tex]e^{6x}[/tex]  (2x - 5)⁸(2x - 2)

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Given the information that the average of the ages of 5 women is 47 years and that their ages are 48, y, 52, 50, and (2y-5), we can set up the following equation:

(48 + y + 52 + 50 + 2y - 5) / 5 = 47

Expanding the equation and simplifying, we get:

5y = 244

y = 48.8

So the age of the woman whose age is represented by the variable y is 48.8 years.

The oldest woman is represented by the age of 52 years, which is the largest of all the ages.

Therefore, the age of the oldest woman is 52 years.

Answer: 25 per child

Step-by-step explanation:

20 x 10 = 200

200/8 = 25

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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The probability that the sum of the ticket is 5, expressed as a percentage is 30%

The probability that an event will occur can be found by the ratio of the number of times the event occurs to the number of all possible events.

The five tickets in the box = 1, 2, 3, 4, 3

The tickets that sum to 5 are; 1 and 4, 2 and 3

The probability that the first ticket picked is 1 = 1/5

The probability that the next ticket picked is a 4 = 1/(5-1) = 1/4

Therefore, the probability of picking a 1 and 4 = (1/5) × (1/4) = 1/20

Similarly, the probability of picking a 4 and then a 1 is 1/20

The probability of picking tickets with numbers 1 and 4 in either order therefore = 2 × 1/20 = 1/10

The probability that the first ticket drawn is 2 = 1/5

The probability that the next ticket picked is a 3 = 2/(5-1) = 1/2

Therefore, the probability to draw a 2 and 3 = (1/5) × (1/2) = 1/10

The probability that the first ticket picked is 3 = 2/5

The probability that the next ticket picked is a 2 = 1/(5-1) = 1/4

Therefore, the probability of picking a 3 and 2 = (2/5) × (1/4) = 2/20 = 1/10

The probability of picking a 2 and a 3 in either order is therefore;

1/10 + 1/10 = 2/10 = 1/5

The probability that the sum of the ticket is 5, is the sum of the probabilities of picking a 1 and a 4 and the probability of picking a 2 and a 3, which is; 1/10 + 1/5 = 3/10 = 0.3

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Answer:

Step-by-step explanation:

To prove that sin(51) + sin(81) - cos(21) = 0, we can use the trigonometric identity:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We can rewrite 51 and 81 as the sum of two angles:

51 = 45 + 6

81 = 90 - 9

Using the above identity, we can write:

sin(51) = sin(45 + 6) = sin(45)cos(6) + cos(45)sin(6) = (2/2)sin(6) + (2/2)cos(6) = sin(6) + cos(6)

and

sin(81) = sin(90 - 9) = sin(90)cos(9) - cos(90)sin(9) = 0 + (-1)sin(9) = -sin(9)

Finally,

sin(51) + sin(81) - cos(21) = sin(6) + cos(6) - sin(9) - cos(21) = (sin(6) + cos(6)) - (sin(9) + cos(21))

We know that sin(90 - x) = cos(x) and cos(90 - x) = sin(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(90 - 9) + sin(90 - 21)) = (sin(6) + cos(6)) - (cos(9) + sin(69))

We also know that sin(180 - x) = -sin(x) and cos(180 - x) = -cos(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(9) + -sin(111)) = (sin(6) + cos(6)) - (-sin(111) + cos(9))

Since sin(6) + cos(6) = sin(6 + 90) = sin(96) and -sin(111) + cos(9) = sin(69 - 180) = -sin(111), we can simplify the expression further to:

sin(6) + cos(6) - (-sin(111)) + cos(9) = sin(96) + cos(9)

Since sin(x + y) = sin(x)cos(y) + cos(x)sin(y), we can write:

sin(96) + cos(9) = sin(60)cos(36) + cos(60)sin(36) = (2/2)sin(36) + (√3/2)cos(36) = sin(36) + (√3/2)cos(36)

Finally, since sin(2x) = 2sin(x)cos(x), we can write:

sin(36) + (√3/2)cos(36) = 2sin(18)cos(18) + (√3/2)cos(36) = 2(√2/2)(√2/2) + (√3/2)(√2/2) = (√2 + √6)/2 + (√6/2) = (√2 + √6)

So, sin(51) + sin(81) - cos(21) = (√2 + √6) ≠ 0.

Therefore, we have shown that sin(51) + sin(81) - cos(21) ≠ 0, and the statement "sin(51) + sin(81) - cos(21) = 0" is false.

The values of f(-1) , f(0) and f(2) are 0, 8 , 16 .

What is a function ?

Function can be defined in which it relates an input to output.

Given function ,

f ( x ) =  4x + 4 when x < 0

= 4x + 8 when x >= 0

f(-1) = 4x + 4

= 4 ( -1 ) + 4

= 0

f(0) = 4x + 8

= 4*0 + 8

= 8

f(2) = 4x + 8

= 4*2 + 8

= 8 + 8

= 16

Therefore, The value of f(-1) , f(0) and f(2) are 0, 8 , 16 .

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The value of expression after change its measurement as;

⇒ 3.4 × 10⁻⁴ kg . m²/ s²

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

The expression is,

⇒ 3.4 × 10⁵ g . cm² / s²

Now, We know that;

⇒ 1 cm = 1/1000 m

⇒ 1 cm = 1/10³ m

⇒ 1 g = 1/1000 kg

⇒ 1 g = 1/10³ kg

Hence, We get;

⇒ 3.4 × 10⁵ g . cm² / s²

⇒ 3.4 × 10⁵ (1/10³) kg . (1/10³)² m²/ s²

⇒ 3.4 × 10⁵ × 10⁻³ × 10⁻⁶ kg . m²/ s²

⇒ 3.4 × 10⁻⁴ kg . m²/ s²

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Answer:

(a) highest number of groups  = 5

(b) out how many, of each color marble, will be in each group.
5 red

3 blue

2 yellow

Step-by-step explanation:

The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers

GCF of 25, 15 and 10 can be found as follows by finding factors of each number:

25 = 5 x5

15 = 5 x 3

10 = 5 x 2

Choose the highest number that is common in each group and this is 5

So John can make a maximum number of 5 groups

Divide each number by the GCF to find how may in each group

25/ 5 = 5 red marbles
15/5 = 3 blue marbles

10/5 = 2 yellow marbles

So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles

The quotient and remainder, written as partial fractions, of 15x²+52x+43/3x²+5x-8 would be  A/(3x + 8) + B/(x - 1) where A is -8/3 and B is 1.

What in mathematics is a partial fraction?

The fractions that are utilized to break down a rational expression are called partial fractions.

                     Any component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.

15x²+ 52x + 43/3x²+5x-8

15x²+52x +43/3x² + ( 8 -3)x - 8

15x²+52x +43/3x² + 8x -3x - 8

15x²+52x +43/3x(x - 1) +8(x - 1 )

15x²+52x +43/(3x + 8)(x -1 )

A/(3x + 8) + B/(x - 1)

To find the value of A;

3x + 8 = 0

x = -8/3

To find the value of B;

x - 1 = 0

x = 1

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By proving the two triangles as similar triangles , the value of x in the triangles is x = 5 cm .

By using the proportions, for the two triangles which are similar because they contain three equal angles ;

The One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and

the third angle one has to be same because of the sum of the three internal angles of a triangle must equal 180 degrees.

So , the proportions of the sides are written as :

⇒ 4/32 = x/40  ;

Cross multiplying , and solving for "x" ,

we get ;

⇒ x = (4 × 40)/32 ;

⇒ x = 5 .

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The given question is incomplete , the complete question is

What is the value of x in the polygon given below ?

Answer:

3rd choice  (x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - -8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = -8

k = 11

r = 2

(x + 8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

The answer is C. (x+8)² + (y-11)² = 4

The next two terms of the number sequence 2,3,5,9,17,33,65 are given as follows:

129, 257.

This is a recursive number sequence, as each term is obtained multiplying the previous term by 2 and then subtracting one.

Then the term after 65 is given as follows:

65 x 2 - 1 = 130 - 1 = 129.

The term after 129 is given as follows:

2 x 129 - 1 = 257.

Then the next two terms are 129 and 257.

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A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

First, we need to know the conversion rate between the two units (pounds lb and kilograms kg)

Now, we can convert 90 pounds.

So, 90lb ≈ 41kg

(If you were to round)

The equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p at x = -1, -2

A polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

Given that:

(p+1)x² + (2p+3)x + (p+2) = 0

Open brackets;

px² + x² + 2px + 3x + p + 2 = 0

Move all terms not containing p to the right side of the equation.

px² +  2px + p = −x² − 3x − 2

Factor p out of px² + 2px + p.

p(x² + 2x + 1) = −x² − 3x − 2

Factor using the perfect square rule.

p(x+1)² = −x² − 3x − 2

Divide each term in p( x + 1 )² = −x² − 3x − 2 by (x + 1)² and simplify.

[tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex]

Set [tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex] to be equal to zero;

[tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex]

Solve for x;

-x² - 3x - 2 = 0

Factor the left side of the equation.

-(x + 1) (x + 2) = 0

x = -1

x = -2

The final solution is all the values that make -(x + 1) (x + 2) = 0 true

x = -1, - 2

Exclude the solutions that do not make  [tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex] true.

Therefore, x  = -2

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On solving the provided question, we can say that Frequency Percentage is equal to the relative frequency times one hundred.

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9.

25–29 is listed as the First Class Group.

Class size is 4 (29-25).

Maintain the same class size for reminders from 89 through 93.

Count the values and record the frequency next to the appropriate class.

Midpoint equals (higher class limit plus lower class limit) / 2.

Relative Frequency is equal to Frequency/total Values.

Cumulative Frequency equals the sum of the past and current frequencies.

Frequency Percentage is equal to the relative frequency times one hundred.

Class Recurrence Point Midway Frequency relative Frequency Added Up percentage of frequency 25-29 0 27 0 0 0.00% 1.25% 1 31 0.0125

%ile Rank for 48 = 12.5

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The correlation coefficient r of the data given is 0.938  

The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables.

Given that a set of data showing the values of variables x and y, we are asked to find the correlation coefficient r of the data given,

We know that,

The correlation coefficient r is a number between and calculated to represent the linear dependence of two variables or sets of data.

Using an Excel tool :- (CORREL function) = CORREL(B3:B10,C3:C10)

We get, r = 0.938

Hence, the correlation coefficient r of the data given is 0.938  

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The value of b is given as follows:

b = 8.4.

The value of b is obtained solving the definite integral in this problem.

The integral of the function 2x - 6 is given as follows:

x² - 6x.

At x = b, the numeric value of the integral is given as follows:

b² - 6b.

At x = -1, the numeric value of the integral is given as follows:

(-1)² - 6(-1) = 1 + 6 = 7.

Applying the Fundamental Theorem of Calculus, the equation to obtain the value of b is given as follows:

b² - 6b - 7 = 13.

b² - 6b - 20 = 0.

Which is a quadratic function with the coefficients given as follows:

a = 1, b = -6 and c = -20.

The discriminant is given as follows:

D = b² - 4ac

D = (-6)² - 4(1)(-20)

D = 116.

Hence the positive solution is given as follows:

b = (-b + sqrt(D))/2a

b = (6 + sqrt(116))/2

b = 8.4.

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The complete question:

Which inequality's solution is graphed here?

A) x + 8 < 5

B) x - 5 < 8

C) x + 5 < 8

D) x - 8 < 5

The given graph represents on the number line is represented by inequality  x - 5 < 8. So option B is correct.

Real numbers are represented by a straight line known as a number line. The distance between the dots on the line, which correlates to the magnitude of the numbers, is how the numbers are typically represented. Positive or negative numerals can be used, and they are normally marked at regular intervals.

Given that,

A graph,

which has values less than 13,

In form of inequality it can be written as,

x < 13

And inequality x - 5 < 8,

can be written as  x < 13

Hence, the option b is correct inequality.

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Answer:

3 paintbrushes

Step-by-step explanation:

15 divided by 5 is 3.

So, Mrs. Hamada will put 3 paintbrushes in each cup.

Answer: A) $725

Step-by-step explanation:

The value of the asset that the business bought with $300 cash and $425 on credit is $725. The total amount that the business spent on the equipment is equal to the sum of the cash and the credit, which is $300 + $425 = $725.

The error is 20 and absolute error for the pen sets is also 20. Absolute error is the difference between a quantity's observed or inferred value and its actual value.

Absolute error is the difference between such a quantity's observed or assumed value and its real value. Because it doesn't indicate the error's magnitude, the absolute inaccuracy is insufficient.

The difference between a quantity's measured value and its actual value is known as absolute error. The difference between the measurement's absolute error and the quantity's actual value is referred to as relative error.

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Answer:

15%

Step-by-step explanation:

flip edge

Answer:

s = 13.6

m∠T = 35.7°

m∠U = 61.3°

Step-by-step explanation:

• Solving for side s:

To find the length of side s, we have to use the cosine rule:

[tex]\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}[/tex],

where:

In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,

[tex]s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^{\circ})[/tex]

⇒ [tex]s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^{\circ})}[/tex]

⇒ [tex]s = \bf 13.6[/tex]

• Solving for m∠T:

In order to find m∠T, we can use the sine rule:

[tex]\boxed{\frac{sinA}{a}= \frac{sinB}{b} =\frac{sinC}{c}}[/tex],

which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.

The side opposite to ∠T is US = 8. Therefore:

[tex]{\frac{sinT}{8} = \frac{sin(83^{\circ})}{13.6}}[/tex]

⇒ [tex]sinT= \frac{sin(83^{\circ})}{13.6} \times 8[/tex]

⇒ [tex]T = sin^{-1}( \frac{sin(83^{\circ})}{13.6} \times 8)[/tex]

⇒ [tex]T = \bf 35.7^{\circ}[/tex]

• Solving for m∠U:

Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:

∠U + ∠S ∠T = 180°

⇒ ∠U + 83° + 35.7° = 180°

⇒ ∠U = 180° - 83° - 35.7°

⇒ ∠U = 61.3°

The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).

By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.

Given function is xy²= 4. The given expression will be different as below,

dy / dx ( xy² ) - 4 = 0

2xy( dy / dx) + y² = 0

dy / dx = -y / 2x

Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).

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Answer:

To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.

Discount = $365 × 0.20 = $73

So, the discount on a $365 purchase is $73.

The price after the discount would be $365 - $73 = $292.

To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:

1. Calculate the discount amount:

Discount = 20% x $365 = $73

2. Subtract the discount from the original price:

Final price = $365 - $73 = $292

Therefore, the final price of the $365 purchase with a 20% discount is $292.

Answer:

$560

Step-by-step explanation:

The formula for simple interest is:

I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).

Plugging in the values, we get:

I = $7,000 * 2% * 4 years = $560

So, Marsha earned $560 in interest.

Answer

[tex] - 95.783[/tex]