Question
1
Graph the line passing through (-2, 4) whose slope is m =—1/4

Answer:

[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]

[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given equation:

[tex]x^2+y^2-12x+4y-24=0[/tex]

Move the constant to the right side of the equation and collect like variables on the left side of the equation:

[tex]\implies x^2-12x+y^2+4y=24[/tex]

Create perfect square trinomials for the both variables by adding the square of the half the coefficient of x and y to both sides:

[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2+y^2+4y+\left(\dfrac{4}{2}\right)^2=24+\left(\dfrac{-12}{2}\right)^2+\left(\dfrac{4}{2}\right)^2[/tex]

[tex]\implies x^2-12x+\left(-6\right)^2+y^2+4y+\left(2\right)^2=24+\left(-6\right)^2+\left(2\right)^2[/tex]

[tex]\implies x^2-12x+36+y^2+4y+4=24+36+4[/tex]

[tex]\implies x^2-12x+36+y^2+4y+4=64[/tex]

Factor the two perfect trinomials:

[tex]\implies (x-6)^2+(y+2)^2=64[/tex]

Therefore:

[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]

[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]

Answer

Infinite solutions

Step-by-step explanation:

try any example you want it keeps going on and on.

According to the law of exponent, the value of positive exponent is greater than the negative exponent, this defines that they are not equal.

Exponent

Exponent refers the number of times a number is multiplied by itself.

Given,

Here we need to verify that, if  two expressions with exponents are a perfect match except one has a negative exponent and the other has a positive exponent, like 5³ and 5⁻³, then how does the exponent change the meaning of the expression.

According to the following law of the exponent, the positive exponent can be written as,

5³ = 5 x 5 x 5 = 125

Similarly, the negative exponent is written as,

5⁻³ = 1/5³

Which can be simplified as,

1/125 = 0.008

Therefore, when we compare these values, the value of positive exponent is greater than the negative exponent.

Thus, defines that the value of positive and negative exponent are not same.

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Answer:

Step-by-step explanation:

there are 6 numbers, but 3 and 6 take up double the space, so the probabilities are not 6 but 8

1/8 is your answer

Answer:

x = 4.5

Step-by-step explanation:

5(2x + 1) = 50  Distribute the 5

5(2x) + (5) (1) = 50

10x +5 = 50  Subtract 5 from both sides

10x = 45  Divide both sdies by 10

x = 4.5

Answer:

F-1(x) = 4x2 - 3 x<0

The present age of Tom is 12 years old

Jan is five years older than Tom

The age of Tom = x

The age of Jan = x + 5

After 3 years

The age of Tom = x + 3

The age of Jan = x + 5 + 3

= x + 8

The Tom's age is 3/4 of Jan's age

Then the equation will be

x + 3 = 3/4(x + 8)

Apply distributive property

x + 3 = (3/4)x + 6

x - (3/4)x = 6 - 3

Subtract the terms

1/4 x = 3

Move 1/4 to the right hand side of the equation

x = 3 ÷ 1/4

x = 3 × 4

Multiply the terms

x = 12 years old

Hence, the present age of Tom is 12 years old

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Considering the given scatter plot, it is found that:

a. The line of best fit is: y = -0.245x + 5.59.

b. The correlation coefficient is: r = -0.57.

c. The interpretation of the correlation coefficient is of: There is a negative association between y and x.

d. The estimate of y when x = 12 is of: 2.65

A scatter plot is a set of points of a data-set, and these points are used to calculate both the correlation coefficient and the line of best fit.

For this problem, the points are given as follows:

(0,5), (1,7), (2, 6), (3, 4), (4, 3), (5,5), (6,4), (7,2), (8,5), (9,3), (10,4).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = -0.245x + 5.59.

Hence the estimate of y when x = 12 is obtained as follows:

y = -0.245(12) + 5.59 = 2.65.

Inserting these points into a correlation coefficient calculator, the correlation coefficient is given as follows:

r = -0.57.

The interpretation is that there is a negative association between y and x, which is neither strong neither weak, as the absolute value of the coefficient is close to the threshold of 0.6.

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Triangle ONM is congruent to Triangle CBA

The area of the garden with a base of [tex]6\frac{1}{2}[/tex] feet and a height [tex]2\frac{5}{8}[/tex] feet is equal to 17.06 square feet.

What is a Parallelogram?

In the given question, it is said that the garden decided to be created by the Johnson family is in the shape of a parallelogram.

The base and height of the parallelogram are given as  [tex]6\frac{1}{2}[/tex] feet and [tex]2\frac{5}{8}[/tex] feet respectively.

[tex]\implies b=6\frac{1}{2} =\frac{13}{2}[/tex], and

[tex]h=2\frac{5}{8} =\frac{21}{8}[/tex]

The area of a parallelogram is calculated using the formula,

[tex]A=b \times h[/tex]

Substituting the values in the given formula, we get

[tex]A=\frac{13}{2} \times \frac{21}{8} \\\implies A=\frac{273}{16}\\ \implies A=17.06 ft^{2}[/tex]

Therefore, the required area of the garden is equal to 17.06 square feet.

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Answer: The minimum is 13.5

Step-by-step explanation:

But if I got to multiply the 12 also it will be 162

For the given equation (x/4)+3= 1/5, the value of x which will make the given equation valid is lies between the numbers of ( -10 and -15).

As given in the question,

Given equation is equal to :

(x/4)+3= 1/5

Simplify the given equation (x/4)+3= 1/5 to get the value of x we have,

(x/4)+3= 1/5

Take least common multiple of 4 and 1 we get,

( x + 12) / 4 = 1/5

⇒5( x +12 )  =  4

⇒ 5x + 60 = 4

⇒ 5x = -56

⇒ x= -11.2

-11.2 lies between (-10 and -15).

Therefore, for the given equation (x/4)+3=1/5, the value of x which will make the given equation valid is lies between the numbers of

(-10 and -15).

The complete question is:

Consider the following equation:

(x/4)+3= 1/5

The value of x that will make the equation above valid lies between

which of the following numbers?

A) 10 and 15

B) -1 and -5

C) 1 and 5

D) -10 and -15

E) -5 and -10

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Answer:

Step-by-step explanation:

This is about the LCM of the numbers 20 and 36.

First find the prime factors of both numbers:

Now find the LCM:

They will both inspect every 180 cartons.

Answer:

They will both inspect every 180 cartons.

Step-by-step explanation:

Firstly you could find the LCM of 20 and 36.

Multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, 180, etc...

Multiples of 36 are: 36, 72, 108, 144, 180, 216, 252, 288, etc...

Therefore 180 is the answer, all they were asking was what was the LCM. Hope this helped you !!

The mean of the probability distribution of X is 0.9375.

Given that,

From the given

We have to find the probability distribution of X and mean of X.

Now, We know,

X --                               0         1          2        3        4

Probability of X--        1/2     1/4       1/8      1/16     1/16

The mean is average of the distribution

Statistics refers to deviation as the difference between the observed value of a data point and the expected value. The average deviation of a data point from the mean, median, or mode of the data collection is known as the mean deviation, sometimes known as the mean absolute deviation. 

μₓ=0×1/2+1×1/4+2×1/8+3×1/16+4×1/16

μₓ=1/4+1/4+3/16+1/4

μₓ=15/16

μₓ=0.9375

Therefore, The mean distribution of X is 0.9375.

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Answer: 260 calories

Step-by-step explanation:

    If one serving has 80 calories, we will multiply 80 by 3 1/4 to find the total number of calories in 3 1/4 servings.

80 calories * (3 1/4) servings = 260 calories

Answer:

EDC = 56 degrees

Step-by-step explanation:

triangle OED is isosceles : base angles are congruent

2 * EDC + 68 = 180

2 * EDC = 180 - 68

2 * EDC = 112

2/2 EDC = 112/2

EDC = 56 degrees

Step-by-step explanation:

Triangle DOE is isosceles. So OED and ODE has same angle.

Total angle for isosceles triangle is 180.

ODE + OED = 180 - 68 = 112

OED = ODE = 112 /2 = 56

Answer:

5/4

Step-by-step explanation:  

(2/3)/(8/15)

= (2/3)(15/8)

= (2*15)/(3*8)

= 30/24

= 5/4

The correct answer is:  " [tex]\frac{5}{4}[/tex] " ; {written as an improper fraction} ;

                                 or:  " 1.25 " ; {written as a decimal value} ;
                                 or:  " [tex]1\frac{1}{4}[/tex] " ;  {written as a mixed number fraction}.
__________________

Step-by-step explanation:

Given:   [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{8}{15}[/tex] = ? {for which we shall solve}.

Note:  'Dividing by' a value; results in the same value as 'multiplying by' its reciprocal value [that is: 'multiplying by its inverted form'].

This is especially noteworthy in problems that involve 'dividing by fractions'.

So, to solve and simply our given problem:
[tex]\frac{2}{3} * \frac{15}{8}[/tex]  =  ? ;
Note:  The 2 cancels out to 1 ; and the 8 cancels out to 4 ;
         The 3 cancels out to 1 ; and the 15 cancels out to 5 ;
→ since:  {8 ÷ 4 =  2 } ;  &  {2 ÷ 2 = 1} ;
        and :

→ since:   {15 ÷ 3 = 5 } ;  & {3 ÷ 3 = 1 } .
______
We can rewrite our "further simplified" expression as:
→   [tex]\frac{1}{1}[/tex] * [tex]\frac{5}{4}[/tex]  ;

=  "  1 *   [tex]\frac{5}{4}[/tex]  " ;

=  "  [tex]\frac{5}{4}[/tex] " .

Further explanations:
1)  Note:  Re:  the "commutative property" of multiplication:
         " a * b = b * a " ;  or, write as:   " ab = ba " ;    
As such:      "  1  *   \frac{5}{4}  " ;  is the same as:
              ↔  "   [tex]\frac{5}{4}[/tex]  * 1 " .

2)  Note:  Re:  the identity property of multiplication:
 Any value, multiplied by "1", results in/ retains its same value}.  
As such;  our calculated value:
        "   [tex]\frac{5}{4}[/tex]   *  1  "   =    \frac{5}{4}  " .

3)  Note:  Re: the division of one (1) property of division:
Any value, divided by "1" ; results in that same initial value.
As such:  our calculated value:  " [tex]\frac{1}{1}[/tex]  = (1 ÷ 1) = 1 " ;

4)  Note:  Re:  the division by itself property of division:
Any value (except "0"), divided by itself, is equal to "1 " ;
As such:  our calculated value:  " [tex]\frac{1}{1}[/tex]  = (1 ÷ 1) = 1 " ;
______  

So, this answer—which is the most simplified, improper fraction—
is: " [tex]\frac{5}{4}[/tex] " .

Or, to write as a mixed fraction:
   Use the mnemonic:

     [tex]\frac{n}{d}[/tex]  = M [tex]\frac{a}{d}[/tex] ;

That is: "numerator/denominator =  M( [tex]\frac{a}{d}[/tex] )"  ; {"M a/d" !} l

⇒ in which M is the [calculated singular whole number portion within the mixed number equivalent] ;
⇒ followed by " [tex]\frac{a}{d}[/tex] "  ; in which d is the same denominator as that of the improper fraction ;
⇒ & in which a is the calculated numerator value for the fraction portion for this number ;

So:  " \frac{5}{4}} "  =  (5 ÷ 4)  = 1.25 =   1 [tex]\frac{1}{4}[/tex]  " .
______

Long division method:
__________________________________________
              1 R 1 ; ⇒    1 + (1/4) ;  that is;  " 1 + (remainder) / (divisor)";
          4⟌5                                           →  1  +  ( 1 / 4)  ;
          −  4                                           =   "  1 [tex]\frac{1}{4}[/tex]  ".            
               1       ;               So, " [tex]1\frac{1}{4}[/tex]  " ;  as a mixed number fraction.

or:  Use a fraction calculator to convert improper fractions into mixed number fractions.

________________________
or:  Use a calculator:  " {5 ÷ 4} = 1.25 " .

____
The correct answer is:  " [tex]\frac{5}{4}[/tex] " ; {written as an improper fraction} ;

                                 or:  " 1.25 " ; {written as a decimal value} ;
                                 or:  "  [tex]1\frac{1}{4}[/tex]  " ;  {written as a mixed number fraction}.
____

Hope this answer is helpful!

Wishing you the best!

____

Answer:

900 meters long

Step-by-step explanation:

Toby is riding his bicycle at 15 m/s. If it takes him 60 seconds to get to the end of the street. What was the length of the street?

at 15 meters per second for 60 seconds:

= time * speed

60* 15= 900 meters traveled,

so the street is 900 meters long.

Answer:

320,000.00

Step-by-step explanation:

The solution with a pH of 3.3 has a hydronium ion of 0.000501

The pH of a solution is a measure of hydrogen ion concentration, which in turn is a measure of its acidity. Pure water dissociates slightly into equal concentrations of hydrogen and hydroxyl (OH−) ions.

Applying the formula of pH which is given as

pH = -log[H₃O⁺]

But the fruit juice has a pH = 3.3

3.3 = -log[H₃O⁺]

This becomes 10⁻³.³

[H₃O⁺] = 0.000501

The concentration of hydronium ion is 0.000501

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Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}[/tex]

Answer:

Option 4

Step-by-step explanation:

In integer division or multiplication,

1) If a < 0  and b < 0 means a and b are both negative numbers.

Then a/b will be positive. But it is given that a/b < 0. So, it is wrong.

2) If a< 0 and b > 0 means a is negative & b is positive. So, a/b will be negative. But it is given a/b is positive. So, it is wrong.

3) a and b are positive (as a >0 and as b > 0), then a/b > 0  (a\b will be positive). So, it is wrong.

4) a is positive (as a>0) & b is negative (as b < 0), then a/b will be negative So, this is correct.

Answer:

31

Step-by-step explanation:

2⋅5+5⋅3+2⋅3

10+15+6

31

Answer:

The Board of Governors of the Federal Reserve System is responsible for the discount rate and reserve requirements, and the Federal Open Market Committee is responsible for open market operations.

Step-by-step explanation:

Answer: 60 pages

Step-by-step explanation: 24 pages time 2 would be 48 pages, which is 80% of the pages. Since 12 pages is 20%, you would add 12 pages, which equals 60 pages.

Answer: b ≈ 74.605 meters

Step-by-step explanation:

    Let b be the length of the blue rope, r be the length of the red rope, and g be the length of the green rope. We will write different equations to show the situation given.

         b =  2r

         g = 8b

         b + r + g = 708.75 meters

    Next, we will substitute expressions into the last equation for the variables r and g so we can solve for b.

b + r + g = 708.75 meters

b + ([tex]\frac{b}{2}[/tex]) + (8b) = 708.75 meters

9.5b = 708.75 meters

b ≈ 74.61 meters

    b ≈ 74.605 meters

Answer:

Belle has 25 apples she shares them equally with her 5 friends, how many apples does each friend get? 25/5=5

Step-by-step explanation:

Answer:

The answer is 35 children and 105 adults

Step-by-step explanation:

we don't know the number of kids or adults in the theater , so they are unknown.

x: adults

y: kids

we know that y=3x (1)

we also know that all the people in the theater are 140.

so we also know that x+y= 140 (2)

And now you need to take (1) and put it in (2):

y=3x

x+y= 140 x+3x=140 =} 4x=140=} x=140/4=} x=35 kids. so if we put on (1) the number of the kids we have the number of adults: y=3*35=}y=105 adults

I hope I helped !