What number can be subtracted from both the numerator and the denominator of this fraction to produce the fraction on the right? 34/53 -?=1/2

Answers

Answer 1

Answer: $(34-x)/(53-x)= (1)/(2) \ \ \ \Leftrightarrow\ \ \ 53-x=2(34-x)\ \ \wedge\ \ \ x \neq 53\n \n53-x=68-2x\n \n-x+2x=68-53\n \nx=15\n \ncheck\ result:\n \n (34-15)/(53-15) = (19)/(38) =(1)/(2)$

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How many factors in the expression 8(x +4) (y +4) (z 2 + 4z + 7) have exactly two terms?

Answers

From the expression 8(x +4) (y +4) (z 2 + 4z + 7),
the factors are 8, (x+4), (y+4), (z^2 + 4z + 7) since each of these factors, when you divide that to the whole expression won't give a remainder.

Answer:

Only 2 factors have exactly two terms i.e, (x+4)(y+4)

Step-by-step explanation:

Given : Expression $8(x+4)(y+4)(z^2+4z+7)$

To find : How many factors in the expression have exactly two terms?

Solution :

Expression $8(x+4)(y+4)(z^2+4z+7)$ cannot be further factorized.

Now, We count the terms in each factor.

1) Factor- 8

Only 1 term i.e, 8 itself.

2) Factor- x+4

Two terms .i.e., x and 4

3) Factor- y+4

Two terms .i.e., y and 4

4) Factor- $z^2+4z+7$

Three terms .i.e., $z^2$ , 4z and 7.

Therefore, Only 2 factors have exactly two terms i.e, (x+4)(y+4).

A two-way frequency table is shown below that displays the relationship between pizza type and pizza crust choices. We took a sample of 110 people and recorded the following results:Thin Crust Thick Crust Stuffed Crust Total
Cheese Pizza 3 9 13 25
All-Meat Pizza 5 15 25 45
Hawaiian Pizza 2 6 32 40
Total 10 30 70 110

The restaurant is about to prepare pizza for a children's birthday party. Knowing that the party planner only wants cheese pizza, what percentage (rounded to the nearest whole percent) of the order will be for stuffed-crust pizza?

Answers

  Thin Crust Thick Crust    Stuffed Crust   Total
Cheese Pizza   3   9 13 25
All-Meat Pizza 5 15   25   45
Hawaiian Pizza   2 6   32 40
Total    10 30   70 110

Cheese Pizza : 100%
Stuffed Crust: 70/110 = 0.636 x 100% = 63.6% or 64%

Boyd charges a $3.50 fee for setting up and taking down the umbrellas. He also charges $2.50 for each hour of use. Suppose h stands for the number of hours you rent. How much will it cost to rent an umbrella for h hours

Answers

2.5h + 3.5

This is because it will cost $2.50 for every hour you use, plus an additionally fee for set up

what is the length of the diagonal of a non-regulation tennis court with length 20 feet and width 15 feet?

Answers

Answer:

25 feet

Step-by-step explanation:

Basically that non-regulation tennis court is a rectangle. You want to know the length of the diagonal. If you draw it on paper, you'll see that this then become 2 triangles... of which you have 2 sides, and are seeking the hypotenuse. So....

H² = A² + B²

H² = 20² + 15² = 400 + 225 = 625

H = 25 feet.

Answer:

The diagonal of a non-regulation tennis court = 25 feet

Step-by-step explanation:

Pythagorean theorem

Hypotenuse² = Base² + Height²

The tennis court is like a rectangle.

We can consider the court as made of two right angled triangle

To find the length of diagonal of court

Here base = 15 feet and height = 20 feet

Diagonal or hypotenuse can be written as,

Diagonal ² = Base² + Height²

= 15² + 20²

= 225 + 400

= 625

Diagonal = √625 = 25 feet

Therefore the diagonal of a non-regulation tennis court = 25 feet

Write an equation that is perpendicular to the line y = 2x + 13?

Answers

An equation can't be perpendicular to a line, but the graph of the equation can.

When that happens, we recall that the slopes of perpendicular lines are negative reciprocals.

One line is the graph of [ y = 2x + 13 ]. The slope of the line is 2 .
So the slope of a line perpendicular to it must be -1/2 .

The equation of a line perpendicular to it is: y = (-1/2 x) plus (any number).

The y-intercept of the perpendicular line doesn't matter. Only its slope does.

$k:\ y=m_1x+b_1\ \ \ and\ \ \ l:\ y=m_2x+b_2\n\nk\perp l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\n------------------------\n\nk:\ y=2x+13\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\n\n2\cdot m_2=-1\ \ \ \Leftrightarrow\ \ \ m_2=- (1)/(2) \n\nl:\ y=- (1)/(2) x+b_2\ \ \ and\ \ \ b_2\ \in\ R\n\nfor\ example:\n\ny=- (1)/(2) x,\ \ \ y=- (1)/(2) x+5 (1)/(7) ,\ \ \ y=- (1)/(2)x - √(13)\ ,\ ...$

Seven tenths of a number plus fourteen is less than forty-nine

Answers

I'm going to assume you need this inequality solved.

First, write it as numbers, not words.

7/10n + 14 < 49

where "n" is the unknown number.

Second, if I were you, I'd change that fraction into a decimal, as it'll make life easier later on.

7/10 = 0.7

Now, solve it like you would any other equation.

0.7n + 14 < 49

0.7n +14 - 14 < 49 - 14

0.7n < 35

0.7n ÷ 0.7 < 35 ÷ 0.7

n < 50

The answer is n < 50

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