Johhny earns $2,334.50 from his job each month. He pays $1,437 for monthly expenses. Johnny is planning a vacation in 3 months' time that he estimates will cost $1,750 total. How much will Johnny have leftover from three months of saving once he pays for his vacation?

The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.

The slope of the line through the given points :

m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

Then, The slope of the required bisector:   m = -1/(1/2) = -2

The midpoint of the given segment:

((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

Then the point-slope form of the equation of the bisector:

y -y1 = m(x -x1)

y -2 = -2(x -(-2))

y = -2x -4 +2

y = -2x -2 . . . . . . . slope-intercept form equation

2x +y = -2 . . . . . . .standard form equation

Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

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if r(x) = x² and r(x) = 4, then the value of x = ± 2

Equal means same in all aspects, whereas equivalent means similar but not identical. For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

For example y = x+5 and the same y = 2x+7

then we can say that x+5 Is also equal to 2x+7

2x+7 = x+5

then x = -2

similarly r(x) = x²

thesame r(x) = 4

this means that x² = 4

solving for x

we find the square root of both sides

√x² = √4

x= ±2

It is ± because square root value as two possible values of either both positive or both negative.

Therefore the value of x is ±2

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Answer:

Roots x = -1 and x =5

k(x) = (x + 1)(x - 5)

m(x) = 1/2(x + 1 )(2x - 10)

Roots x = 1 and x = -5

n(x) = (3x + 15)(x - 1)

f(x) = (x - 1)(x + 5)

q(x) = (2x - 2)(3x + 15)

Neither

h(x) = 1/2(x + 1)(2x - 20)

Step-by-step explanation:

We have given that ,the quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.

1. Write root as factor changing the sign and put each factor in paranthesis

2.Multiply paire of roots together using box to find the multiplication

3.Make sure that each factor multiplied by every other factor.

The function has roots x = -1 and x =5

[tex]k(x) = (x + 1)(x - 5)\\\\k(x)=x^2-5x+x-5\\k(x)=x^2-4x-5\\[/tex]

[tex]m(x) = 1/2(x + 1 )(2x - 10)\\m(x)=1/2(2x^2-10x+2x-10)\\m(x)=1/2(2x^2-8x-10)\\m(x)=x^2-4x-5[/tex]

The function k(x) and m(x) has root x=-5 and x=5

The function has roots x = 1 and x = -5

[tex]n(x) = (3x + 15)(x - 1)\\n(x)=3x^2-3x+15x-15\\n(x)=3x^2+12x-15\\n(x)=1/3(x^2+4x-5)[/tex]

[tex]f(x) = (x - 1)(x + 5)\\f(x)=x^2+5x-x-5\\f(x)=x^2+4x-5[/tex]

[tex]q(x) = (2x - 2)(3x + 15)\\q(x)=6x^2+30x-6x-30\\q(x)=6x^2+24x-30\\q(x)=1/6(x^2+4x-5)[/tex]

The function n(x),q(x) and f(x) has roots x=1 and x=-5

h(x) = 1/2(x + 1)(2x - 20)

h(x) has no roots from roots at x=−1 and x=5, and x=1 and x=−5.

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Answer:

Step-by-step explanation:

line given is x-y+1= 0

you can rewrite it in slope intercept y=mx+b where m is the slope, and b is the y-intercept where the line meets the y-axis

x-y+1 =0 subtract x and 1 from both sides of the equation

-y = -x-1 multiply both sides by -1

y = x+1 so the slope of this line is 1 and the y-intercept is 1

If you draw this line you can see that there are actually 2 lines that form 45° angles with y=x+1 and pass through (-1, 2), one is vertical x= -1 and one horizontal y =2

Answer:

∠T≈44.1

Step-by-step explanation:

Please see the attached image.

Relative to ∠T, we know the adjacent side and the hypotenuse, 28 and 39 respectively.

We can use a trig function to solve for ∠T. When given the adjacent side and hypotenuse, we can use cosine.

The cosine of an angle is the adjacent side to that angle over the hypotenuse.

cos(T)=28/39

T=[tex]cos^-1[/tex](28/39)

T≈44.1

Convert from number format to standard form as a decimal multiplied by a power of 10.

step 1

convert 1.5806*10rais to 4

Convert to decimal notation

1.5806*10^4

The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)

1.5806 ->15806

step 2

final result

15806

Simplify the expression

1.581*10^4

Simplify exponents and square roots

1.581*10^4

10 ^4 = 10 × 10 × 10 × 10 = 10,000

1.581*10000

Perform any multiplication or division, from left to right:

1.581*10000

15806

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The given algebraic equation can be written in many ways as shown.

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

Solution:-

-5x-15+25x-30

it can be written as

-5(x+3-5x+6)

20x-45

5(4x-9)

and also

-5(9-4x)

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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].

First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]

*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up

[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]

Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].

Both have the same factor is [tex]-5[/tex].

Use the distributive property to find the equation that is equivalent.

[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]

So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]

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Answer:

9(8d + 9)

Step-by-step explanation:

Since 72 and 81 are both divisible by 9, we can factor out a 9 from the expression:

72d + 81

9(8d + 9)

So, the factored expression is 9(8d + 9)

Answer:

12.5%

Step-by-step explanation:

He scored [tex]168-147=21[/tex] points in the playoff game.

This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].

Answer:

a) 35/8

b) 7/3

c) 27/5

Step-by-step explanation:

Answer:

a) 35/8

b) 7/3

c) 27/5

Step-by-step explanation:

*to solve multiply the whole number by the denominater and add that total with the numerator, keep the denominater the same

a)

[tex]4 \frac{3}{8} [/tex]

[tex] \frac{32 + 3}{8} = \frac{35}{8} [/tex]

b)

[tex]2 \frac{1}{3} [/tex]

[tex] \frac{6 + 1}{3} = \frac{7}{3} [/tex]

c)

[tex]5 \frac{2}{5} [/tex]

[tex] \frac{25+ 2}{5} = \frac{27}{5} [/tex]

The given set of ordered pairs does not satisfy a linear function.

A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.

Given:

The given set of ordered pairs is:

{(3, 2), (4, 3), (5, 4), (6, 5)}

To find:

Whether the given set of ordered pairs satisfies a linear function or not.

Explanation:

The slope of a linear function is:

m = (y₂ - y₁)/ (x₂ -x₁)

The slope of the linear function passes through the points  and  is:

m₁ = (3-1)/(3-1)

m₁ = 2/2

m₁ = 1

The slope of the linear function passes through the points  and  is:

m₂ = (9-3)/(5-3)

m₂ = 6/2

m₂ = 3

Therefore m₁ ≠ m₂ therefore the given set of ordered pairs does not satisfy a linear function.

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Answer:

117

Step-by-step explanation:

The figure is five sided, therefore the sum of the angles = (5-2)180

                                                                                             = 3*180

                                                                                             = 540

113 + 123+97+90(since its right angles)+y(unknown) = 540

423 + y = 540

y = 540 - 423

y = 117

Let the angle vertically opposite to y be z

y = z (vertically opposite angles)

z = 117

x = 117 (Corresponding angles are equal)

Hope u understand.

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Answer:

AC ≈ 10.3

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{9.3}[/tex] ( multiply both sides by 9.3 )

9.3 × tan48° = AC , then

AC ≈ 10.3 ( to 3 sf )

Answer:

I think the third option

Step-by-step explanation:

Have a nice day! Hope this helps! Owa Owa!!!!

So x = 2.1 is the only possible value of x that makes the equation true.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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Answer:

-2, 4

-1, -2

0, 0

1, 2

2, 4

Step-by-step explanation:

X. Y

-2 = 4

-1 = 2

0 = 0

1 = -2

2 = -4

Answer:

  25%

Step-by-step explanation:

Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.

The percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.

  percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%

  percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%

25% of the students in Mr. Johnson's class wear glasses.

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The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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Answer:

The answer is x=-6, x=8

Step-by-step explanation:

I recommend using the quadratic formula to solve this problem.

x^2=a

-2x=b

-48=c

Plug it into the quadratic formula.

New equation:[tex]\frac{2+-\sqrt{(-2)^2-4(1)(-48)}}{2(1)}[/tex]

Simplify

Equation: [tex]\frac{2+-\sqrt{4+192}}{2}[/tex]

Add 4 and 192.

Equation: [tex]\frac{2+-\sqrt{196}}{2}[/tex]

Do the square root of 196.

Equation: [tex]\frac{2+-14}{2}[/tex]

Make into two different equations.

Equation 1: [tex]\frac{2+14}{2}[/tex]

Equation 2: [tex]\frac{2-14}{2}[/tex]

Solve the two equations and you will get -6 and 8.  Hope this helps!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

[tex] \large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}[/tex]

[tex] \sf \: x ^ { 2 } - 2 x - 48 = 0[/tex]

All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula: [tex]\sf \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

[tex] \sf \: x^{2}-2x-48=0 [/tex]

This equation is in standard form: ax² + bx + c = 0 Substitute 1 for a, -2 for b and -48 for c in the quadratic formula.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-48\right)}}{2} \\ [/tex]

Square -2.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4-4\left(-48\right)}}{2} \\ [/tex]

Multiply -4 times -48.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4+192}}{2} \\ [/tex]

Add 4 to 192.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{196}}{2} \\ [/tex]

Take the square root of 196.

[tex] \sf \: x=\frac{-\left(-2\right)±14}{2} \\ [/tex]

The opposite of -2 is 2.

[tex] \sf \: x=\frac{2±14}{2} \\ [/tex]

Now solve the equation [tex]\sf\:x=\frac{2±14}{2}[/tex] when ± is plus. Add 2 to 14.

[tex] \sf \: x=\frac{16}{2} \\ [/tex]

Divide 16 by 2.

[tex] \boxed{ \boxed{ \bf \: x=8 }}[/tex]

Now solve the equation [tex]\sf\:x=\frac{2±14}{2} [/tex] when ± is minus. Subtract 14 from 2.

[tex] \sf \: x=\frac{-12}{2} \\ [/tex]

Divide -12 by 2.

[tex] \boxed{\boxed{ \bf \: x=-6 }}[/tex]

The equation is now solved.

[tex] \underline{ \bf \: x=8 }\\ \underline{ \bf \: x=-6 }[/tex]

Answer:

yes

Step-by-step explanation:

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.

Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

Answer:

two hundred fifty and six hundred elensths (i dont remember the end)

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

its needs to be under 90

Answer:

Explanation:

A triangle's three interior angles will add up to

180

∘

. Since it's a right angle, that means one angle is

90

∘

and the other is given as

15

∘

.

Therefore,

90

+

x

+

15

=

180

So

x

=

180

−

90

−

15

x

=

75

The acute angle is

75

∘

.

Answer:

(y-x=1.75)×2

2y-2x=3.5

2y-2x+4x-2y=3.5+4

2x. =7.5

X=3.75

y-x=1.75,

y. =1.75+3.75

y=5.5

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers.

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Answer:

A

Step-by-step explanation:

Radius = 8

Volume = (pi)r^2(h)

Volume = (pi)8^2(7)

Answer:

Positive

Step-by-step explanation:

Positive / positive = positive

positive / negative = negative

negative / negative = positive

negative/ positive = negative

Sign of -4 divided by -8 we get positive expression.

Here we have to find the sing of expression,

When -4 divided by -8

Since we know that,

Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.

We can write it,

-4 divided by -8  = -4/-8

                            = (4/8)x(-1/-1)

                            =  1/2    its a positive number.

Hence,

-4 divided by -8  = 1/2

Hence we get positive expression.  

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