Solve the following system of equations algebraically:

y=x^2-x-22
y=x-7

Answer:

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Since the triangle is isosceles, the two angles opposite to equal sides are congruent:

The sum of the three angles is 180°:

The angle measures are:

Answer: The distributive property is a property where there is a coefficient/number, that is being multiplied to a group of numbers enclosed in parentheses. The coefficient can be distributed/multiplied to the numbers in the parentheses individually or after solving the expression in it.

Step-by-step explanation:

You can spot when the distributive property is used when you see a number in front of a group of numbers, such as these examples (in bold):

1. 4(5 + 6) = 46 , in this problem you can solve 5+6 before multiplying it by 4, or multiply 4*5 and 4*6 and then add it.

2. 2(x-3) = 12 , in this situation x is the unknown variable so you must distribute the 2 individually, so the result would look like: (2*x) + (2*-3) -> 2x - 6 = 12

Answer: 21x + 21

Step-by-step explanation:

Simply multiply 7 to 3x and 3 respectively.

The linear function f with the given values is f(x) = 2x + 2

From the question, we have the following parameters that can be used in our computation:

f(0) = 2 , f(-2) = -2

A linear equation can be represented as

f(x) = mx + c

Substitute the known values in the above equation, so, we have the following representation

m * 0 + c = 2

m * -2  + c = -2

Solving 0 * x + c = 2, we have

c = 2

So, we have

m * -2 + c = -2

This gives

-2 * m + 2 = -2

Evaluate

-2m = -4

Evaluate

m = 2

So, we have

f(x) = 2x + 2

Hence, the function is f(x) = 2x + 2

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We need to assume the sample was randomly selected because we are making inferences about parameters.

In mathematics, the parameter is a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx+b, in which m and b are parameters, is an example of a parametric equation.

In statistics, the parameter in a function is a variable whose value is sought by means of evidence from samples. The resulting assigned value is the estimate or statistic.

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Solving given algebra problem, value of x is equal to -1. It is the area of mathematics that uses arithmetic to manipulate or operate abstract symbols rather than actual numbers.

Isolate the squared term and the constant term on the opposite sides of the equation to solve quadratic equations using the square root method. After that, take the square root of both sides, plus or minus the side with the constant term.

Given equation,

[tex]12+\sqrt{1-5x} =18\\\sqrt{1-5x}=18-12\\ \sqrt{1-5x}=6\\\\square\\ case1\\1-5x=64x=-1\\case2\\1-5x=-6\\x=7/5[/tex]

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The product of -22/5 × - 1/3 is 12/15

A product in math is defined as the result of two or more numbers when multiplied together. For example if 5 is multiplied by 2 , the product is 10 i.e 5 × 2 = 10 , 10 is the product where 5 and 2 are the factors. Also 5×4 = 20, 20 is the product and the 5 and 4 are the products.

The division of this of the product with any of the factors will give the other factors.

To solve -2 2/5 × -1/3

we first change the mixed fraction to improper fraction.

We then multiply -12/5 with -1/3

-2 2/5 = -12/5

-12/5 × -1/3

= 12/15

therefore the value of -2 2/5 × -1/3 is 12/15

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Answer: 5.75pi(yards)

Step-by-step explanation: We know the radius is 3 so the area is 9pi. The shaded area has an angle of 230 and the total angle of a circle is 360. We multiply the area by the fraction of the angle which is 230/360(9pi).

Answer:

The length would be 29.

Step-by-step explanation:

Follow the distance formula in the image.

-Hope this Helped

In this problem the statement that the mean is greater than the median is true. So, the correct answer is option(a).

We have a histogram which shows the distribution of the annual hours of commuting delay per traveler for 46 small, medium and urban areas, fewer than one million in population. See the diagram carefully and try to draw the conclusion. The shape of the histogram showing that positive skewed or right skewed distribution since Curve increases fastly and decreases slowly. A positive skewed distribution is a type of distribution where most of the values are concentrated in the left tail of the distribution and the right tail of the distribution is longer. In positive skewed distribution,

i) Mean > Median

ii) (Q₃ - Q₂) > (Q₂ - Q₁)

iii) Sqrt(β₁) >0

Hence, The mean is greater than the median is true.

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Match the word to its definition or symbol.

1. ∈                                            element

2. { }                                           braces representing a set with no elements

3. C                                            subset

4. {whole numbers]                  finite set

5. ∅                                           symbol for the empty set or null set

6. A set limited by definition - infinite set

7. ∉                                            not an element

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form.

Curly brackets are typically used to represent sets.

Sets with a finite/countable number of members are referred to as finite sets. Due to their ability to count, finite sets are often referred to as countable sets.

A set with an infinite number of elements is one that cannot be numbered. Any set that has no last element is said to be infinite Set

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The given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.

So, None of the above will be the correct answer.

A×(B∩C)=(A×B)∩(A×C)

We have B∩C={1,2,3,4}∩{5,6}=ϕ

∴ L.H.S = A×(B∩C)=A×ϕ=ϕ

A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}

A×C={(1,5),(1,6),(2,5),(2,6)}

∴R.H.S.=(A×B)∩(A×C)=ϕ

∴L.H.S=R.H.S

Hence A×(B∩C)=(A×B)∩(A×C)

To verify: A×C is a subset of B×D

A×C={(1,5),(1,6),(2,5),(2,6)}

B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),

(3,8),(4,5),(4,6),(4,7),(4,8)}

which is 13.

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The first quadrant starts on (12,11)

If the quadrant moves 8 units left it will be located at (12-8, 11) = (4,11)

and if it moves 7 units down it will be located at (4,11-7) = (4,4)

So the new location of the quadrant is (4,4)

It's important to notice that the first quadrant starts on (12,11) and the coordinates are (x,y) where x is on the horizontal axis and y is on the vertical axis. So when it moves left it's decreasing the x value and when it moves down it's decreasing the y value

8. The ratio of the adjacent over the hypotenuse is 8:17

10. The ratio of the adjacent over the hypotenuse is 1:√2

From the question, we are to calculate the ratio of the adjacent over the hypotenuse in the given triangles

8.

Using angle A as the reference angle

Adjacent = 16

Hypotenuse = 34

Thus,

The ratio of the adjacent over the hypotenuse = 16/34

The ratio of the adjacent over the hypotenuse =  8/17

Hence, the ratio is 8:17

10.

First,

We will calculate the hypotenuse, H

From the Pythagorean theorem, we can write that

H² = 4² + 4²

H² = 16 + 16

H² = 32

H = √32

H = 4√2

Now,

Using angle A as the reference angle

Adjacent = 4

Hypotenuse = 4√2

Thus,

The ratio of the adjacent over the hypotenuse = 4/4√2

The ratio of the adjacent over the hypotenuse =  1/√2

Hence, the ratio is 1:√2

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The derivative of f at (a, b) is the gradient vector [4a - b, -a].

From the question, we have the following parameters that can be used in our computation:

f(x, y) = 2x^2 − xy

The two-variable function f(x, y) = 2x^2 - xy is differentiable at any point (a, b) if its partial derivatives exist and are continuous at that point.

This is represented as

∂f/∂x = 4x - y

∂f/∂y = -x

The derivative of f at (a, b) can be calculated by evaluating the partial derivatives of f at (a, b):

∂f/∂x(a, b) = 4a - b

∂f/∂y(a, b) = -a

Hence, the derivative of f is [4a - b, -a].

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Answer:

-40 17/40

Step-by-step explanation:

Answer: -40 7/40

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator
40.425=40.4251/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
40.4251×1000/1000=40425/1000
Find the Greatest Common Factor (GCF) of 40425 and 1000 and reduce the fraction by dividing both numerator and denominator by GCF = 25
40425÷25
1000÷25
=1617/40

Simplify the improper fraction
in conclusion
-40 17/40
you must not forget the minus/negative sign :)

The vertex form of parabola y = x² + 9 · x + 8 is the quadratic equation y + 49 / 4 = (x + 9 / 2)².

Herein we find the equation of a parabola in standard form, that is, a quadratic equation of the form:

y = a · x² + b · x + c

Where:

And we are asked to transform this expression into vertex form, that is, a quadratic equation of the form:

y - k = C · (x - h)²

Where:

This can be done by means of algebra properties. First, write the quadratic equation:

y = x² + 9 · x + 8

Second, use algebra properties until a perfect square trinomial is found:

y = x² + 9 · x + 8

y + 49 / 4 = x² + 9 · x + 81 / 4

Third, factor the perfect square trinomial:

y + 49 / 4 = (x + 9 / 2)²

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The correct linear equation which shows a proportional relationship is,

⇒ y equals two thirds times x.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Now,

We know that;

The proportion relationship is,

⇒ y = kx

Where, k is constant of proportional.

By option 1;

The expression is,

⇒ y = 2/3 × x

⇒ y = 2/3x

Hence, It shows the linear equation.

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The sum of all possible values of b is 124 in the given question.

If two or more objects have a common centre, they are said to be concentric in geometry.

Concentric shapes include spheres, circles, regular polyhedral, and regular polygons because they all share a central axis. In Euclidean geometry, concentric circles always have different radii but the same centre.

The difference between the areas is [tex]$ \frac{\pi(b^2 - a^2)}{4} = 48 \pi[/tex]

Therefore  b² = a² +1 92

We can write the equation as  (b−a)(b+a)=192

So b−a and b+a are factors of 192

Here are the possibilities:  

 b−a=1, b+a=192 ;

 b−a=2, b+a=96 ;

 b−a=3, b+a=64 ;

 b−a=4, b+a=48 ;

 b−a=6, b+a=32 ;

 b−a=8, b+a=24 ;

and

 b−a=12, b+a=16

Add the pairs of equations and divide by 2 (as long as the sum is even): b=49; b=26; b=19; b=16; and b=14.

49 + 26 + 19 + 16 + 14 = 124

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Answer:

One can use the formula for a compound annuity

A = (1 - (1 + i)^-n) / i

n = payments = 360 (12/yr * 30 yr)

i - interest rate = .075 / 12 = .00625

The formula tells you what $1 / mo will be worth after 360 mos

A = (1 - 1.00625^-360) / .00625 = (1 - .10362) / .00625

A = 143.02

To have 150,000 after 30 yrs the monthly payment needs to be

150000 / 143.02 = 1048.82

a) The 95​% confidence interval about μ with n = 26 is given as follows: (109, 117).

b) The 95​% confidence interval about μ with n = 15 is given as follows: (107.5, 118.5).

c) The 90​% confidence interval about μ with n = 26 is given as follows: (109.7, 116.3).

d) The intervals could not have been computed if the population was not normally distributed, as the sample size is less than 30.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample mean and standard deviation for this problem are given as follows:

[tex]\overline{x} = 113, s = 10[/tex]

The critical values are given as follows:

The bounds of the interval for item a are given as follows:

The bounds of the interval for item b are given as follows:

The bounds of the interval for item c are given as follows:

The Central Limit Theorem states that the intervals can only be calculated for non-normal populations if the sample size is greater than 30.

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Answer:

Step-by-step explanation: Multiply 20 by 12 and divied 8 that should give u your answer

Answer: x > -11

Step-by-step explanation:

3x + 7 > 2x - 4

First, we can simplify the right side of the equation by combining like terms:

3x + 7 > 2x - 4

then we can subtract 2x from both sides of the equation:

3x + 7 - 2x > -4

This gives us:

x+7 > -4

then we can add 4 to both sides of the equation:

x + 7 + 4 > 0

This gives us:

x + 11 > 0

then we can subtract 11 from both sides of the equation:

x + 11 - 11 > 0 - 11

This gives us:

x > -11

so the number is greater than -11.

Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

Answer:

Step-by-step explanation: i can't see the lab top

The team loses 20 people/audience with each loss.

The slope formula defines to the formula used to calculate the steepness of a line and determines how much it's inclined. To calculate the slope of the lines, the x and y coordinates of the points lying on the line can be used.

The formula to calculate slope is:

m = (y2 - y1)/(x2 - x1) = Δy/Δx

When the team lost eight games, 295 people attended the next game.

When the team lost 13 games, 199 people attended the next game.

Slope = 295-199/8-13

slope=100/-5

slope=-20

Therefore, the team loses 20 people/audience with each loss.

And the attendance loss is 20 times as great as the number of games lost/losses

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There are times when I use or calculate percentages in my personal life or at work. This is true.

The benefits that result from using percentages in this application is that it gives one an idea of the value to be paid as tax. The drawback is that it can be complicated for large number.

A word problem that can Illustrate percentage is that "An income is $1000 and there's a tax of 10%, how much will be paid?"

A number or ratio expressed as a fraction of 100 is called a percentage. Divide the value by the total value to get the percentage, then multiply that number by 100.

For instance, many statistics in the media, bank interest rates, retail discounts, and inflation rates are all expressed as percentages. For understanding the financial aspects of daily life, percentages are crucial.

For example, an income is $1000 and there's a tax of 10%, the tax will be:

= 10% × $1000

= $100

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By analytic geometry, the equations for lines represented by figure are:

In this problem we find the representation of five lines (red - yellow - green - blue - black). There is a horizontal line (green), a vertical line (blue) and three oblique lines (red - yellow - black). According to analytic geometry, we find the following definitions:

The slope for oblique lines is determined by secant line formula:

m = Δy / Δx

Where:

From picture we get the following hints:

Finally, we proceed to find the equations for each line:

Red line

Slope

m = 5 / 2.5

m = 2

Intercept

b = y - m · x

b = 5  - 2 · 0

b = 5

The equation for the red line is y = 2 · x + 5.

Yellow line

Slope

m = - 5 / 1.5

m = - 3.333

Intercept

b = y - m · x

b = 5 - (- 3.333) · 0

b = 5

The equation for the yellow line is y = - 3.333 · x + 5.

Black line

Slope

m = 6 / 3

m = 2

Intercept

b = y - m · x

b = - 6 - 2 · 0

b = - 6

The equation for the black line is y = 2 · x - 6.

Green line

The equation for the green line is y = - 2.

Blue line

The equation for blue line is x = 5.

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Answer:

I have graphed it and attached an image in the explanation.

Step-by-step explanation: