50 points please with explanation​

Answer:15

Step-by-step explanation:

Answer:  The radius of the given circle is 4 units.

Step-by-step explanation:  We are given to find the radius of the circle with the following equation :

[tex]x^2+y^2-10x+6y+18=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the standard equation of a circle with center at the point (h, k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex]x^2+y^2-10x+6y+18=0\\\\\Rightarrow (x^2-10x+25)+(y^2+6y+9)-25-9+18=0\\\\\Rightarrow (x-5)^2+(y+3)^2-16=0\\\\\Rightarrow (x-5)^2+(y-(-3))^2=4^2.[/tex]

Comparing it with the standard equation, the radius of the circle is given by

[tex]r=4.[/tex]

Thus, the radius of the given circle is 4 units.

Answer:

0.5

Step-by-step explanation:

The required simplified value of a is 1/2 .

Given that,
3 +0.5(4a + 8) = 9 – 2a
The simplified value of a is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3 +0.5(4a + 8) = 9 – 2a
3 + 0.5*4a + 0.5*8 =9 - 2a
3 + 2a + 4 = 9 - 2a
7 - 9 = - 4a
a = 1 / 2

Thus, the required simplified value of a is 1/2.

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Answer:

[tex]\frac{30}{3x}[/tex]

Step-by-step explanation:

Let

x ----> the number

we know that

The phrase " The quotient of 30 and three times a number" is equal to divide the number 30 by the number x multiplied by 3

so

The algebraic expression is equal to

[tex]\frac{30}{3x}[/tex]

Answer:

- 5x² - 11x + 2

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= - 4x² - 6x - 1 + (- x² - 5x + 3)

= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms

= - 5x² - 11x + 2

Answer:

   -5x^2 -11x +2

Step-by-step explanation:

f(x) = -4x^2 - 6x-1

g(x) = – x^2 - 5x + 3,

Add them together

f(x) =     -4x^2 - 6x-1

+ g(x) = – x^2 - 5x + 3,

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

        -5x^2 -11x +2

Answer:

The correct answer will be "588 square centimeters"

Step-by-step explanation:

The answer would be 588 squared cm because the area of a triangle is 1/2(base*height).

and The base is 42 cm and the height is 28 cm.

588 square centimeters is the correct answer !

Answer:

C) 588

Step-by-step explanation:

A= 1/2 b*h

First you need to find the base and height

Which is 42 and 28

42*28=1176

1176/2= 588

Answer:

The correct answer option is D. [tex]10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex].

Step-by-step explanation:

We are given the following expression:

[tex] \left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right ) [/tex]

Assuming that [tex]x\geq 0[/tex], we are to find its simplified product.

[tex] \left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right ) [/tex]

[tex]\\\\ = 2 \sqrt { 150 x ^ 8 } + \sqrt { 3 0 x ^ 7 }-2x\sqrt{75x^6}-x\sqrt{15x^5} \\\\ =2\sqrt{25\times6x^8}+x^3\sqrt{30x}-2x\sqrt{25\times3x^6}-x^3\sqrt{15x} \\\\ =10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

The simplified product is:

       [tex]10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

The expression is given by:

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]

Now we know that:

[tex]\sqrt{x^2}=x\\\\and\\\\\sqrt{x^4}=\sqrt{(x^2)^2}=x^2[/tex]

Hence, we get the expression as follows:

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})=(x^2\sqrt{10}-x\cdot x\sqrt{5})(2x^2\sqrt{15}+x\sqrt{3x})[/tex]

Now, we will use the property that:

[tex](a+b)(c+d)=a(c+d)+b(c+d)[/tex]

Hence, we have the expression as:

[tex]=x^2\sqrt{10}(2x^2\sqrt{15}+x\sqrt{3x})-x^2\sqrt{5}(2x^2\sqrt{15}+x\sqrt{3x})[/tex]

[tex]=2x^4\sqrt{10}\sqrt{15}+x^3\sqrt{10}\sqrt{3x}-2x^4\sqrt{5}\sqrt{15}-x^3\sqrt{5}\sqrt{3x}[/tex]

Now we know that:

[tex]\sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

i.e. we have:

[tex]=2x^4\sqrt{150}+x^3\sqrt{30x}-2x^4\sqrt{75}-x^3\sqrt{15x}\\\\=2x^4\sqrt{5^2\cdot 6}+x^3\sqrt{30x}-2x^4\sqrt{5^2\cdot 3}-x^3\sqrt{15x}\\\\=10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

B 1/3

Ratio of AB:BC

3 : 9

1 : 3

Answer:

The Answer is 9

Step-by-step explanation:

To find the answer you divide 63 by 7.

[tex]7m=63\\m=9[/tex]

Answer:

The missing number (i.e. the coefficient of x) is 5.

Step-by-step explanation:

5x - 8 - 9x = -4x + 8

-4x - 8 = -4x + 8

-8 ≠ 8

Answer:

60

Step-by-step explanation:

There are 5 different ways to choose the first class.

There are 4 classes left to choose from.

There are 4 different ways to choose the second class.

There are 3 classes left to choose from.

There are 3 different ways to chooses the third class.

5*4*3 = 60

Answer:

l = [tex]\frac{P}{2}[/tex] - w

Step-by-step explanation:

P = 2l + 2w

2l = P - 2w

l = [tex]\frac{P}{2}[/tex] - w

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{2}x-\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]f(x)=2x+1\to y=2x+1\\\\\text{exchange x to y and vice versa:}\\\\x=2y+1\\\\\text{solve for y:}\\\\2y+1=x\qquad\text{subtract 1 from both sides}\\\\2y=x-1\qquad\text{divide both sides by 2}\\\\y=\dfrac{x-1}{2}=\dfrac{1}{2}x-\dfrac{1}{2}[/tex]

Answer:

Minimum = 50

First Quartile = 80

Median = 135

Third Quartile = 165

Maximum = 200

Step-by-step explanation:

First, it is important to reorder our values into ascending order:

50, 60, 100, 130, 140, 150, 180, 200

You've correctly identified the minimum, median and maximum values, however the quartiles are where the mistakes lie.

1. In order to calculate the first quartile, you need to look at where the median of the first half of the values is, ie. 50, 60, 100, 130

The median will be the value between (or the average of) 60 and 100:

(60 + 100)/2 = 80

Thus, the first quartile is 80.

2. In order to calculate the third quartile, we must find the median of the second half of the data set, ie. 140, 150, 180, 200

The median will be the value between (or the average of) 150 and 180:

(150 + 180)/2 = 165

Thus the third quartile is 165.

I find it's always a good idea to just draw this out and label the different values on paper to make it a bit easier.

Hope that helped! If you find anything confusing just ask :)

The minimum, first quartile, median, third quartile, and maximum of the data set are:

Minimum = 50

First quartile = 115

Median = 145

Third quartile = 190

Maximum = 200

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

To find the minimum, first quartile, median, third quartile, and maximum of the given data set, we need to arrange the data in order from smallest to largest:

50, 60, 100, 130, 140, 150, 180, 200

The minimum is the smallest number in the set, which is 50.

To find the first quartile, we need to find the median of the lower half of the data set.

Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers in the set:

First quartile = (100 + 130)/2 = 115

The median is the middle number in the set.

Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers in the set:

Median = (140 + 150)/2 = 145

To find the third quartile, we need to find the median of the upper half of the data set.

Since there are 8 numbers in the set, the median is the average of the 6th and 7th numbers in the set:

Third quartile = (180 + 200)/2 = 190

The maximum is the largest number in the set, which is 200.

Therefore,

The minimum, first quartile, median, third quartile, and the maximum of the data set are:

Minimum = 50

First quartile = 115

Median = 145

Third quartile = 190

Maximum = 200

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Answer:

58%

Step-by-step explanation:

The change between 12 to 19 is 7

The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%

7/12*100

=58.3333333%

=58%(rounded to nearest percent)

58% increase

Percent change = 19 - 1212 × 100 = 58.333333333333 % (increase) Where: 12 and 19 is the new value. In this case we have % of increase because the new value is greater than the old value.

Percent change differs by the percent increase or percent decrease of the sense that we could see both directions of the change. For example, the percent increase calculator calculates amount of increase, in which we shall say, "x percent increase".

The change between 12 to 19 is 7

The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%

7/12*100

=58.3333333%

=58%(rounded to nearest percent)

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Answer:

The value of x=6 and y=4.

Answer:

(6, 4 )

Step-by-step explanation:

Given the 2 equations

4x - 3y = 12 → (1)

x + 2y = 14 → (2)

Multiplying (2) by - 4 and adding to (1) will eliminate the y- term

- 4x - 8y = - 56 → (3)

Add (1) and (3) term by term

(4x - 4x) + (- 3y - 8y) = (12 - 56) ← simplify

- 11y = - 44 ( divide both sides by - 11 )

y = 4

Substitute y = 4 into either (1) or (2)

(2 ) : x + 8 = 14 ( subtract 8 from both sides )

x = 6

Solution is (6, 4 )

Answer:

[tex]\$158,400[/tex]

Step-by-step explanation:

step 1

Find the area of the warehouse

[tex]A=(40)(22)=880\ ft^{2}[/tex]

step 2

Remember that one year is equal to 12 months

step 3

Find the cost to rent the warehouse for a year

Multiply the area by $15 per square foot per month and then multiply by 12 months

so

[tex]880(15)(12)=\$158,400[/tex]

Answer:

158,400

Step-by-step explanation:

Answer:

Sample Response: The goal is to get x alone on one side of the equals sign. First, isolate the variable by applying the subtraction property of equality to subtract 1/2x from both sides. Next, find a common denominator to combine like terms. Then use inverse operations to multiply both sides by the reciprocal of the fraction coefficient. The result will be x = 16. Finally, check the solution by substituting 16 for x in the original equation.

Step-by-step explanation:

58x = 12x + 2

58x -12x = 2

46x = 2

x = 2/46 = 0.434

There are many situations in which equations can be used. Whenever an unknown quantity has to be found, an equation can be formed and solved.

An equality relationship between two expressions written on both sides of the equal to sign.

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Answer:

- 5 < x < 10

Step-by-step explanation:

Given

- 6 < x - 1 < 9 ( add 1 to each of the 3 intervals )

- 5 < x < 10

The value of x ranges from -5 to 10 as this inequality - 5 < x < 10.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given inequality is -6 < x-1 < 9. The value of x will be calculated as,

x- 1 < 9

x < 10

x- 1 > -6

x > 1 - 6

x > -5

Therefore, the value of x ranges from -5 to 10 as this inequality - 5 < x < 10.

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Answer:

4(x-7)^2 - 19

Step-by-step explanation:

Shifting 7 units to the right:  4(x-7)^2 - 16.

3 units down:                         4(x-7)^2 - 16 - 3, or    4(x-7)^2 - 19

Answer: C is correct, No solution

Step-by-step explanation:

Let’s simplify the second equation,

8x-4y=-20

We can divide the whole equation by 4...

8x/4-4y/4=-20/4

Which becomes....

2x-y=-5

Now let’s move things around to see if it’s the same equation as the one on top...

-y=-2x-5

y=2x+5

Now we need to solve the systems...

y=2x-5

y=2x+5

Since their slopes are both 2 and their y-intercepts are not identical, the answer is no solution. The two lines will continue on without ever crossing because they have the same slope.

The solution set for the given system of linear equations is -

(2.5, 0).

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the number of solutions that the given linear system of equations have -

y = 2x - 5

- 8x - 4y = -20

We will solve the given system of equations using the method of substitution. We can write -

y = 2x - 5

- 8x - 4y = - 20

- 8x + 20 = 4y

y = - 2x + 5

Now -

2x - 5 = - 2x + 5

4x = 10

x = 2.5

and -

y = 2 x 2.5 - 5

y = 0

Therefore, the solution set for the given system of linear equations is -

(2.5, 0).

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Answer:

97.79

Step-by-step explanation:

1062.98 * 0.092 = 97.79416

To the nearest hundredth would be to the second 9. Since 4 is less than 5 just drop the 4 and anything after it.

Answer:

B.

As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions. TRUE (Exponential functions increase faster than linear or quadratic)

Step-by-step explanation:

We can easily solve this problem if we plot each graph by using a graphing calculator or any plotting tool.

1st function

f(x) = 10x

2nd function

g(x) = 5^x

3rd function

h(x) = 4x^2 + 5x

Please, see attached graph.

A.

As x approaches positive infinity, the quadratic function will exceed both the linear and exponential functions. FALSE

B.

As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions. TRUE (Exponential functions increase faster than linear or quadratic)

C.

As x approaches positive infinity, the linear function will exceed both the quadratic and exponential functions.FALSE

D.

As x approaches positive infinity, it cannot be determined which function will exceed the other two.FALSE

Answer:

b

Step-by-step explanation:

just look up

Answer:

ill just cut to the chase it is c

Step-by-step explanation:

Answer:

b.Yes, because if you substitute 10 for r in the equation and simplify, you find that the equation is true.

Step-by-step explanation:

did the test

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (10, 14) and (x₂, y₂ ) = (2, - 2)

m = [tex]\frac{-2-14}{2-10}[/tex] = [tex]\frac{-16}{-8}[/tex] = 2

Answer:

slope =2

Step-by-step explanation:

To find the slope, we use the formula

m = (y2-y1)/(x2-x1)

    = (-2-14)/(2-10)

    = -16/-8

    =2

Answer:

[tex]2\frac{2}{9} hrs[/tex]

Step-by-step explanation:

At a speed of 50m/h time taken is 2hours

At a speed of 45m/h time take is 2.5 hours

You can find the distance between A and B

Distance=speed × time

[tex]D=50*2=100\\[/tex]

But time y varies inversely with speed x , hence

[tex]y=\frac{k}{x}[/tex]

where k is a constant of proportionality and D is distance.

To find k

[tex]2=\frac{k}{50} \\\\2*50=k\\\\100=k\\\\y=\frac{100}{x}[/tex]

where y is time and x is speed

Given

x=45m/h  you should find time y. Apply the expression above

[tex]y=\frac{100}{x} \\\\\\y=\frac{100}{45} =\frac{20}{9} =2\frac{2}{9} hrs[/tex]

Answer: 22

Step-by-step explanation:

28 + 7 + 6 + 3 = 44

then multiply it and you end up with 44 over 2 and then you divide it, which is 22!

your answer would be 22.

-- first, do what is in the parenthesis

28 plus 7 is 35; 35 plus 6 is 41; 41 plus 3 is 44.

-- second, 1/2 is another word for splitting in half or dividing by 2. SO, do 44 divided by 2. you get 22.

i hope this helps! please mark brainliest x

Answer:

x = 19

Step-by-step explanation:

YZ || XW, so ∠Y = ∠W

if ∠Y = ∠W, then ∠W = 2x

since the sum of the angles of a triangle is 180 degrees:

(3x-5) + 2x + 90 = 180

x = 19

Plug in values.

xy=

6(3) =

18 = Answer

Answer:

False

Step-by-step explanation:

Vertical angles are a pair of opposite angles created by intersecting lines. The Vertical Angles Theorem states that if two angles are vertical, then they are congruent.

Answer:

False.

Step-by-step explanation:

Supplementary angles always equal up to 180 degrees.