Factor the expression.

4r^2 – 64

1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)

The solution is x = (7 - r) / a.

To solve the equation ax + r = 7 for x, follow these steps:

Subtract r from both sides of the equation:

ax + r - r = 7 - r

This simplifies to:

ax = 7 - r

Divide both sides by a:

x = (7 - r) / a

Substitute the value of x back into the original equation to ensure it is correct.

To solve the problem, denote the number of brown shoes as x, and the black shoes as 2x, as the store has twice as many black shoes. The total number of shoes is x + 2x = 66. Solving this gives us x (brown shoes) as 22.

The subject is concerning a mathematical problem involving ratios. In the given problem, it is stated that the shoe store has twice as many black shoes as brown shoes, and the total number of shoes is 66. Here's a step-by-step process to solve it:

Therefore, there are 22 brown shoes in the store.

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Answer:

True

Step-by-step explanation:

By the distance formula,

The distance between two points [tex](a_1, b_1)[/tex] and [tex](a_2, b_2)[/tex] is,

[tex]d=\sqrt{(a_2-a_1)^2+(b_2-b_1)^2}[/tex]

Here, [tex]a_1=3[/tex], [tex]b_1=7[/tex], [tex]a_2=x_1[/tex] and [tex]b_2=y_1[/tex]

Thus, the distance would be,

[tex]d=\sqrt{(x_1-3)^2+(y_1-7)^2}[/tex]

= the square root of [tex](x_1 - 3)^2 + (y_1 - 7)^2[/tex]

Answer:

Area is 2√3 ft².

Step-by-step explanation:

Given,

A right triangle having sides,

a = 2√3 ft,

c = 4 ft,

Where, c is the hypotenuse of the triangle,

If b is the other leg of the triangle,

By the pythagorean theorem,

[tex]c^2=a^2+b^2[/tex]

[tex]4^2=(2\sqrt{3})^2+b^2[/tex]

[tex]16=12+b^2[/tex]

[tex]4=b^2[/tex]

[tex]\implies b = 2[/tex]

Hence, the area of the given triangle is,

[tex]A=\frac{1}{2}\times a\times b[/tex]

[tex]=\frac{1}{2}\times 2\sqrt{3}\times 2[/tex]

[tex]=\frac{4\sqrt{3}}{2}[/tex]

[tex]=2\sqrt{3}\text{ square ft}[/tex]

Answer:

he made an error, the probability that his homeruns traveled at least 380 feet is 65.54%

Step-by-step explanation:

let´s see the Robinson's calculation:

using the formula for normal distribution:

Z = (x-μ)(σ/[tex]\sqrt{n}[/tex]) [1]

where:

x is raw measurement

μ is the mean

σ is the standar deviation

n is the size of sample

in this case x = 380, μ = 394, σ = 35, n = 1.

then using the equation [1] he calculated the Z score:

[tex]Z = \frac{380-394}{\frac{35}{\sqrt{1}}}\\\\Z = -\frac{14}{35}\\\\Z = -0.4\\\\[/tex]

and it's correct but his answer is wrong because he confuse the term at least.

at least means that the probability be greater than 380 feet, not less than 380 feet.

so he looked the Z score in a table of normal distribution (this table has been attached) and effectively this value is 0.3446. but as I told you this probability is for x < 380.

therefore, the probability that his homeruns traveled at least 380 feet is:

[tex]P(x > 380) = 1 - P(x < 380)\\\\P(x > 380) = 1 - 0.3446\\\\P(x > 380) = 0.6554 \ or \ 65.54 \%[/tex]

please see the table attached.

Answer:

[tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]

Step-by-step explanation:

we have to write the sum using summation notation of the following series:

2-12+72-432+...

which could also be written as:

2+(-12)+72+(-432)+...

We observe that first term=2

second term=2×-6

Third term=2×-6×-6

Fourth term=2×-6×-6×-6

nth term=[tex]2\times (-6)^{n-1}[/tex]

Hence, the series sum=   [tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]

The measure of the angle will be;

⇒ 60°

The sum of two or more angle is 180 degree then the angle is called the Supplementary angle.

Given that;

The statement is,

''The measure of an angle is 60° less than nineteen times the measure of its supplement.''

Let measure of an angle = x

So, The measure of its supplement = 180° - x

Hence, We can formulate;

⇒ x = (180 - x) - 60°

Solve for x as;

⇒ x = 180 - x - 60

⇒ x + x = 120

⇒ 2x = 120

⇒ x = 120/2

⇒ x = 60°

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Answer:

14 units

Step-by-step explanation:

both points have the same y-coordinate, so therefore, the line is horizontal from x = -9 and x = 5 9        (plus I did the 5.05 math quiz segment two 6th grade)

Answer:

133  degrees

Step-by-step explanation:

Given is a picture of a kite DCFE inscribed in circle A

The vertices of the kite D, C, E and F lie on the circle.

A is the centre.

Arc DEF = 266 degrees

This means the subtended angle of arc DEF at the centre = Angle DAF = 266

By theorem on circles, we have central angle of any arc is twice the angle subtended by the arc on the remaining part of the circumference

Hence

Angle DEF = 1/2 angle DAF

i.e. DEF =[tex]\frac{266}{2} =133[/tex]

133 degrees

The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:

∑4i = 0(5)(1/3)i

= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵

= 364/243

To rank the company sales by smallest to largest percent of increase, calculate the percent of increase for each company, which in this case is 0% for all companies.

To rank the company sales by smallest to largest percent of increase, we need to calculate the percent of increase for each company. The percent of increase can be found by subtracting the initial value from the final value, dividing that number by the initial value, and then multiplying by 100.

Since all the percent of increase values are 0%, the company sales can be ranked in any order, as there is no change in sales for any of the companies.