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3 years ago

14

The area of the banner is 144 square feet. The width of the banner is 1/4 the length of the banner. What are the dimensions of

the banner?

2 answers:

Galina-37 [17]3 years ago

5 0

Answer:

The width is 6 and the length is 24.

Step-by-step explanation:

You need to create an equation using the area, because we know that the width is 1/4 of the length we can use x for both values:

$x(4x)=144$

$4x^{2} =144$

$x^{2} =36\\$

$x=6\\$

Then you can use this to find the width and the length.

TiliK225 [7]3 years ago

4 0

The width is 6 ft. The length is 24 ft!

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Rewrite the form In exponential form:<br> Log100 = x

andrey2020 [161]

Answer:

$10^x=100$

Step-by-step explanation:

You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that $3^2=9$ ; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this: $\log_3{9}=2$ , which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like $\log1000$ uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression $\log100=x$ means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is $10^x=100$ .

(If we wanted to, we could also solve this: $10^2=100$ , so $\log100=2$ )

6 0

2 years ago

Arie ran an equal number of miles each day for 12 days. He ran 60 miles in total.

Nezavi [6.7K]

Answer:

5 miles/day

Step-by-step explanation:

This is a division problem.

(60 miles)/(12 days) = 5 miles/day

7 0

3 years ago

Read 2 more answers

Help fill in the blanks no

DerKrebs [107]

Answer:

Here is the full proof:

AC bisects ∠BCD Given

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DC ⊥ AD Given

∠ADC = 90° Definition of perpendicular lines

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∠ABC = 90° Definition of perpendicular lines

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3 years ago

One factor of 7x2 + 33x – 10 is

stiv31 [10]

$7x^{2} +33x-10=0$

$\implies 7x^{2} +35x-2x-10=0\\\implies7x(x+5)-2(x+5)=0\\\implies (7x-2)(x+5)=0$

$7x - 2 = 0\\\implies \boxed{\bold{x = \frac{2}{7} }}$

$x+5=0\\\implies \boxed{\bold{x=-5}}$

6 0

3 years ago

Determine the equation of the line that goes through points (1.1) and (3.7).

ValentinkaMS [17]

Answer:

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

Step-by-step explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form $y=mx+b$ where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=1, y_1=1, x_2=3, y_2=7$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3$

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

$y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2$

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

$y=mx+b\\y=3x-2$

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

4 0

3 years ago