The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4 . If there were 6597 total votes, how many yes votes were there?

If the value of a = 5 and c = √21  then the value of b = 2i, b = -2i.

In this problem, we have one leg and the hypotenuse.

Let the equation be a² + b² = c²

substitute the values in the above equation, we get

5² +b² = (√21)²

25+b²=21

Move 25 to the right side

b² = -4

For x² = f(a) the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]

[tex]$$b=\sqrt{-4}, b=-\sqrt{-4}$$[/tex]

simplifying the above equation, we get

[tex]& \sqrt{-4}=2 i \\[/tex]

[tex]& -\sqrt{-4}=-2 i \\[/tex]

b = 2i, b = -2i

Therefore, the value of b = 2i, b = -2i.

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Answer:

  24

Step-by-step explanation:

Given right triangle sides x, 2x-3, and 2x+3, you want to know the length of the side labeled x.

The Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  (2x +3)² = (2x -3)² +x²

  4x² +12x +9 = 4x² -12x +9 +x²

  x² -24x = 0 . . . . . subtract 4x² +12x +9

  x(x -24) = 0   ⇒   x = 0 or 24

The length of the side labeled x is 24 units.

__

Additional comment

The triangle is an 8-15-17 triangle scaled up by a factor of 3.

(x + 6) is the solution for the quadratic equation 5x² + 60x + 187 = 7

Given,

The quadratic equation;

5x² + 60x + 187 = 7

Arrange this in standard form;

5x² + 60x + 187 - 7 = 0

5x² + 60x + 180 = 0

We have to find the solution for this quadratic equation;

Quadratic formula ;

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 5

b = 60

c = 180

Now,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex] = [tex]\frac{-60(+-)\sqrt{60^{2}-4*5*180 } }{2*5}[/tex] = [tex]\frac{-60(+-)\sqrt{3600-3600} }{10}[/tex] = -60±0 / 10 = -60/10 = -6 = (x + 6)

That is,

The solution for the quadratic equation 5x² + 60x + 187 = 7 is (x + 6)

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Answer:

2

Step-by-step explanation:

Slope is Rise/Run

Pick two points and count the number of units up (rise) and sideways (run) between them

Answer: Slope = 2

Step-by-step explanation: The equation for slope is y2 - y1 / x2 - x1

so using points (2,2) and (3,4)

4-2 / 3-2 = 2/1 = 2

The compounded amount earned in Big Sky Bank is $40,365.00.

The compounded amount earned in Valley Bank is $13,248.24.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

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

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = 10% of 60,000

P = 6000

t = 10 years

Big sky Bank:

r = 20%

n = 2 (semiannually)

A = 6000 [tex](1 + 0.1)^{20}[/tex]

A = 6000 x [tex]1.01^{20}[/tex]

A = $40,365.00

Valley Bank:

r = 8%

n = 4 (quarterly)

A = 6000 [tex](1 + 0.02)^{40}[/tex]

A = 6000 x [tex]1.02^{40}[/tex]

A = $13,248.24

Thus,

Big Sky Bank compounded amount is $40,365.00.

Valley Bank compounded amount is $13,248.24.

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The additional amount Ahmad will spend if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

Ahmad will spend at most $34 on gifts,

He spent = $21,

c = additional amount

The total amount he can spend now = total amount - he spent

c = 34 - 21

c = 13

Therefore, the additional amount Ahmad will spend, if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.

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Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is a function as it passes the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Answer:

25)  Domain:  (-6, 6)      

       Range:  [-5, 3)

26)  Domain:   [-3, 7]

       Range:  [-1, 5]

Step-by-step explanation:

Definitions

Interval notation

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the endpoints of the continuous curve are:

As the endpoints are open circles, the values are excluded from the domain and range.

Therefore, the domain in interval notation is:

The smallest y-value is y = -5 and the greatest y-value is y = 3.

Therefore, the range in interval notation is:

The graph is a conic section (ellipse) and therefore it is not a function.

The smallest x-value is x = -3 and the greatest x-value is x = 7.

The smallest y-value is y = -1 and the greatest y-value is y = 5.

Therefore, the domain and range in interval notation are:

The amount of money that she needs to buy a video game will be $21.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Alex gets $5.00 consistently she does CVS her tasks. She tackled errands for a long time. Presently, she needs to purchase a computer game for $36.00.

The amount of money is given as,

⇒ $36 - $5 x 3

⇒ $36 - $15

⇒ $21

The amount of money that she needs to buy a video game will be $21.

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The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The function is given below.

f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)

Factorize the expression, then we have

f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)

f(x) = x⁴ - 2x³ + 4x³ - 8x² + 5x² - 10x + 6x - 12

f(x) = x³(x - 2) + 4x²(x - 2) + 5x(x - 2) + 6(x - 2)

f(x) = (x - 2)(x³ + 4x² + 5x + 6)

f(x) = (x - 2) (x³ + 3x² + x² + 3x + 2x + 6)

f(x) = (x - 2)[x²(x + 3) + x(x + 3) + 2(x + 3)]

f(x) = (x - 2)(x + 6)(x² + x + 2)

The zeroes of the function are given as,

f(x) = 0

(x - 2)(x + 3)(x² + x + 2) = 0

x = 2, -3, - 1/2 + (√7/2)i, - 1/2 - (√7/2)i

The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.

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Step-by-step explanation:

(-1.5)x × -0.25x = 0.375x²

remember, -×- = +

Answer:

The Answer is B/2/middle option

Step-by-step explanation:  im great at math

Answer:

Originally $600.

Step-by-step explanation:

[tex]\frac{528}{88} =\frac{y}{100}[/tex]

88 · y = 528 · 100

88y = 52800

y = 600

Originally $600.

The congruent reason for 5 is (c) ASA

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

Triangles = VWX and ZYX

The ASA similarity theorem implies that the corresponding angles of the triangles in question are similar and the sides between these angles are congruent

From the question, we can see that the following corresponding angles on the triangles:

Angles W and Y

Angles X and X

This implies that these angles are congruent angles

For the triangle to be congruent by ASA, the following sides must also be congruent

WX must be congruent to YX

This is indicated in the table of values at (3)

Hence, the additional information on the similarity of the triangles is (d) ASA

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Answer:

Step-by-step explanation:

I got 196/90

I got this by plugging in 47 for y so I got 4(2+47) and got 196 when I solved it. The bottom one I did 2(47-2) and got 90...( I don't know if it's right though, if wrong I'm sorry)

The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

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The graph of the inequality is attached below.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

      K/2 - 20 ≥ -18

Add 20 on both sides,

K/2 - 20 + 20 ≥ -18 + 20

               K/2 ≥ 2

Multiply both sides by 2,

        K/2 x 2 ≥ 2 x 2

                  K ≥ 4

Now to graph the inequality.

The graph of the inequality is attached below.

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The expression that shows the situation where x is the number of strings of lights Farah will need to decorate the perimeter of the room = X = 70/5

Perimeter is defined as the total area of an object which is measured or calculated by addition of the whole sides.

The perimeter of the given room = 70feet

The area covered by 1string of light = 5 feet

The number of spring of light needed would be calculated using X = 70/5 =14

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The Integral value of  (2x+11)/(x²-x-2) is[tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

The given integral is [tex]\int\dx \frac{2x+11}{x^{2} -x-2} dx[/tex]

By partial fractions we divide the integral

Apply the sum rule:

∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx+\int\dx \frac{11}{x^{2} -x-2} dx[/tex]

Let  us calculate the first integral part

[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx[/tex]

Let us use the partial fraction of [tex]\frac{x}{x^{2} -x-2} dx:\frac{1}{3(x+1)} +\frac{2}{3(x-2)}[/tex]

[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2\int\dx \frac{1}{3(x+1)} dx+ \frac{2}{3(x-2)} dx[/tex]

[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)[/tex]

Now let us integrate second term.

[tex]\int\dx \frac{11}{x^{2} -x-2} dx=11\int\dx \frac{1}{x^{2} -x-2} dx[/tex]

We can write denominator as x²-x-2= (x-1/2)²-9/4

[tex]=11\int\dx \frac{1}{(x-\frac{1}{2}) ^{2} -\frac{9}{4}} dx[/tex]

We apply u substitution method

[tex]\int\dx \frac{11}{x^{2} -x-2} dx=-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)[/tex]

[tex]=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]

Hence, [tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex] is the integral value of of (2x+11)/(x²-x-2).

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As a result, the area of an equilateral triangle represented across one side of a square is equal to half the area (1/2)of something like the triangle described on one of its diagonals.

A square is a compact, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides. A rectangle with equal length and breadth is also comparable to a square.

a rectangle with two adjacent sides that is the same length. a quadrilateral with four equal sides and four straight angles. a parallelogram having one right angle and sides that are evenly spaced apart. a right-angled rhombus's form.

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(a). The alternative to the null hypothesis, H₀ = μ₁= μ₂ = μ₃=μ₄= μ₅ is Hₐ: At least two 1s are unequal. (b). Refuse H₀  If p-value is less than 0.05, the 5% presumed threshold of significance is exceeded.

In mathematics, the middle value—which is determined by dividing the sum of each of the values by the total number of values—is the approximate amount in a collection of numbers. To determine the median of a collection of data, add all of the values and divide the result by the total number of values.

a). The study's goal is to determine if there is discernible variation in the typical quantity of time spent on childcare services across levels of educational achievement.

Null hypothesis, H₀ = μ₁= μ₂ = μ₃=μ₄= μ₅

(The average quantity of time spent on child rearing across educational levels does not change much.)

Alternative hypothesis, Hₐ : At least two μ₁s are unequal.

(The mean number of hours on child care varies significantly depending on the degree of education).

b). Let the level of significance be, ∝ = 0.05

Decision rule: Reject H₀ if p-value ≤ 0.05

The result statistic F has a value of 1.26 and a p-value of 0.2846 based on the provided ANOVA table. Keep in mind that the p-value exceeds the 5% expected level of significance. Therefore, don't reject H₀.

There is insufficient data to draw the conclusion that the average quantity of time spent with child care throughout education level differs significantly.

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Multiplication expression equivalent to 5/8 ÷ 1/16  is 5/8 × 16.

What do you mean by fractionol expression?

Fractions with a variable in the denominator are called fractional expressions. They frequently also include variables in the numerator. Since fractions can also be conceived of as ratios, these expressions are often called rational expressions. In algebra, we most frequently refer to fractional expressions as expressions that are the ratio of two polynomials.

Given expression:

5/8 divided by 1/16

⇒ 5/8 ÷ 1/16

= 5/8 × 16

= 10

Therefore, multiplication expression equivalent to 5/8 ÷ 1/16  is 5/8 × 16.

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Answer:

d = 3.2

Step-by-step explanation:

1 * 3.2 = 3.2

Hence,

d = 3.2

the value of x is 5 feets and p = 2, q = 6 and r = 16.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,

Area of rectangle is A = a*b

Perimeter = 2(a+b)

given in the question that the perimeter is 16 feet.

p= 2(3+x)

p = 6+2x

p = 2

q = 6

r = 16

2x = 10

x =5 feet.

Hence, the value of x is 5 feets.

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Answer:

-------------------------------

Apply the rules to point T.

Translation:

Dilation:

The matching choice is A.

Mr. Rooks would receive $2,040 in interest in 3 years.

The interest rate is given as 4%, which means that for every $100 Mr. Rooks has in the bank, he will receive $4 in interest per year.

To find the total interest Mr. Rooks will receive in 3 years, we need to multiply the annual interest rate by the number of years, and then multiply that result by the amount of money Mr. Rooks has in the bank.

In this case, the calculation would be as follows:

Annual interest rate × number of years × amount in the bank = total interest

(4 / 100) × 3 × $17,000 = $2,040

Therefore, Mr. Rooks would receive $2,040 in interest in 3 years.

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Answer:

Step-by-step explanation:

if a person is not a hockey player, they are not a prof athlete

if a person is a hockey player, they are a prof athlete

if a person is not a prof athlete, then they r not a hockey player

Answer:

12 hours

Step-by-step explanation:

4 / 2

2/2

1

4 = 2²

2² x 3 = 4 x 3 = 12

The coordinates of point y after the transformation is (-6,5).

Firstly , we need to get the coordinates of the point y before the transformation

The coordinates are

(-6,-5)

By reflecting over the y-axis, we have the following change;

(x,y) becomes (-x,y)

So we have;

(6,-5)

Then we are to rotate at an angle of 180 degrees counterclockwise

The operation here will be;

(x,y) to (-x,-y)

So we have;

(6,-5) to (-6,5)

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