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3 years ago

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Mathematics

1 answer:

ZanzabumX [31]3 years ago

7 0

Answer:

x = 4 is the solution

Step-by-step explanation:

given = x ( square both sides )

x + 12 = x² ( rearrange into standard form )

x² - x - 12 = 0 ← in standard form

(x - 4 )(x + 3 ) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

Insert these values into the original equation, and if both sides are equal, and those are the solutions.

x = 4 : = = 4 = x ← correct

x = - 3 : = = 3 ≠ - 3 ← false

the answer is x = 4

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Which expression is equivalent to 5^10 • 5^5

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Answer:

5^15

Step-by-step explanation:

5^10•5^5

When bases are same powers are to be added

5^10+5

5^15

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4 years ago

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3 years ago

A baseball team played 32 games and lost 8. Katy was the catcher in 5/8 of the winning games and 1/4 of nthe losing games.

kaheart [24]

Answer:

fraction of the games did the team win is = $\frac{3}{4}$

Katy play game = 17

Step-by-step explanation:

given data

baseball team played = 32 games

lost = 8

Katy catcher = 5/8 of winning

Katy catcher = 1/4 of losing

to find out

What fraction of the games did the team win and how many games did Katy play

solution

we know total game = 32 and lost 8

so win is total - lost = 32 - 8 = 24

fraction of the games did the team win is = $\frac{\frac{24}{8} }{\frac{32}{8} }$

fraction of the games did the team win is = $\frac{3}{4}$

and

so total game 24 winning is $\frac{5}{8}$

so katy winning is $24*\frac{5}{8}$

katy winning = 3 × 5 = 15

and

losing $\frac{1}{4}$

total lose game 8

so Katy lose = 8 × $\frac{1}{4}$ = 2

Katy play game = 15 + 2 = 17

5 0

3 years ago

Miriam is going to the county fair. Each ride ticket costs $2 and admission costs $7. Miriam has $25 to spend at the fair.

Talja [164]

Answer:

Step-by-step explanation:

Given data

Ride ticket= $2

Admission= $7

Amount= $25

We want to find the greatest number of rides

let the number of rides be x

The expression to describe how she spends the amount is given as

y=7+2x

for y= 25, let us find x

25= 7+2x

25-7= 2x

18=3x

x= 18/2

x= 9

Hence the number of rides is 9

6 0

3 years ago

A liner function of x is graphed on a coordinate grid. the points 6,34 and 18,26 lie on the graph of the function what are the r

Lynna [10]

Answer:

Rate of change: m = -2/3

Value of the function at x = 24: y = 22

Step-by-step explanation:

You can write linear functions in <u>slope-intercept form</u>: y = mx + b

"x" and "y" are points on the line

"m" is the slope, how steep the line is, also known as <u>rate of change</u>

"b" is the y-intercept, when the graph hits the y-axis

Find the rate of change of the function by finding the slope between the two given points.

The formula for slope: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Label point 1 and point 2. Label each coordinate; remembered ordered pairs are (x, y).

Point 1 (6, 34) x₁= 6 y₁ = 34

Point 2 (18, 26) x₂ = 18 y₂ = 26

Substitute the points into your equation using the bolded information.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{26-34}{18-6}$ Subtract

$=\frac{-8}{12}$ Reduce the fraction. Top and bottom divide by 4

$=\frac{-2}3}$ Slope of the line, "m"

Substitute the slope and any point you want into slope-intercept form. I choose point (6, 34). x = 6 y = 34 m = -2/3

y = mx + b

34 = (-2/3)(6) + b Multiply to simplify

34 = (-12/3) + b

Start isolating "b"

34 + 12/3 = (-12/3) + 12/3 + b Add 12/3 on both sides

34 + 12/3 = b

Add fractions by combining the whole number into the numerator. Multiply the whole number by the denominator and add to the numerator.

b = (34*3 + 12) / 3 Solve numerator

b = 114/3 Value of "b"

Substitute the values "m" and "b" into slope-intercept form.

y = -2/3 x + 114/3 Equation of the line

To find the x = 24, take the equation of the line and substitute "x" for 24. Then solve for "y".

y = -2/3 x + 114/3 Equation of the line

y = (-2/3)(24) + 114/3

y = (-2*24)/3 + 114/3 Multiply into the numerator

y = (-48)/3 + 114/3 Combine under the same denominator

y = (-48 + 114) / 3 Add

y = 66/3 Divide

y = 22 Value of function

Therefore the rate of change, or slope "m", is -2/3. When "x" is 24, the value of the entire function is 22.

4 0

3 years ago