solve 49x^2+64=0 by using square roots

Answer:

Ashley is faster.

Step-by-step explanation:

I find it is easiest to convert into decimals.

Ashley ran 5/8 mile in 4 1/2 minutes.

5/8  is 0.625

Josh ran 3/4 mile in 5 minutes 15 seconds.

3/4 is 0.75

It looks like Josh won because his number is closer to 100, but, Ashley ran 0.625 mile faster than he ran 0.75 mile.

But then again, Josh ran more than her. Who won? Here is the answer.

Josh can run 0.75 mile in 5 minutes 15 seconds.

Ashley can run 0.625 miles in 4 1/2 minutes.

(4 + 1/2) ÷ 0.625 = 7.2

(5 + .15)  ÷ 0.75 = 6.8

7.2 is more & closer to 10.

So to sum it up, Ashley is faster.

To determine who's the faster runner, we calculate the speed of each runner by dividing the distance they run by the time it takes. Josh is slightly faster than Ashley because he covers more distance per minute.

In this problem, we are comparing the speeds of Ashley and Josh. Speed is calculated by dividing the distance traveled by the time it took to travel that distance. In Ashley's case, she runs 5/8 miles in 4 minutes and 30 seconds, or 4.5 minutes. So, her speed is (5/8) / 4.5 = 0.139 miles per minute.

Josh runs 3/4 miles in 5 minutes and 15 seconds, or 5.25 minutes. His speed is then (3/4) / 5.25 = 0.143 miles per minute.

We can see that Josh is slightly faster than Ashley because his speed (0.143 miles per minute) is higher than Ashley's speed (0.139 miles per minute).

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Answer:

true, false, true, false

Step-by-step explanation:

On a graph, you can see wether or not you have a function by doing the VLT, or vertical line test. Hold a pen or pencil vertically on the paper on move it from left to right. If no 2 points touch the pencil at once, it's a function.

Another way to find out is if any two different points have the same x coordinate. If there is a match, this is not a function. For example, 3,4 and 3,9 cause the graph to not be a function.

Answer: 3 ft

Step-by-step explanation: It is a ratio, the shadows are half the length of the original object .

Answer:

$7,650.00

Step-by-step explanation:

5.5 x 5 = 27.5

turn 27.5 into a percent

6000 x 0.275 = $7,650.00

Final answer:

There are two portions of two-fifths in four-fifths; this is determined by dividing four-fifths by two-fifths, which simplifies to 2.

Explanation:

The student is asking how many portions of two-fifths fit into four-fifths. This is a basic division problem, which we can solve by dividing four-fifths [tex](\frac{4}{5})[/tex] by two-fifths ([tex]\frac{2}{5}[/tex]). The division of fractions is performed by multiplying the first fraction by the reciprocal of the second fraction.

To find the reciprocal of two-fifths ([tex]\frac{2}{5}[/tex]), we flip the numerator and denominator, resulting in five-halves ([tex]\frac{5}{2}[/tex]). Next, we multiply four-fifths ([tex](\frac{4}{5})[/tex]) by five-halves ([tex]\frac{5}{2}[/tex]).

 [tex]\frac{4}{5} \times \frac{5}{2}[/tex] =  [tex]\frac{4 \times 5}{5 \times 2}[/tex] = [tex]\frac{20}{10}[/tex] = 2

Therefore, there are two two-fifths in four-fifths.

Answer:

2 out of 20 chance you will roll a 1 or a 2.

Answer:

Step-by-step explanation:

*It's an isosceles triangle so 2 of the angles are going to be the same degrees

*Every triangle is 180 degrees

(48)+(48)=96 then 180-96=84

Answer:

It would be the third one

Answer:

The third one.

Step-by-step explanation:

Answer:

B= 36cm squared

h = 4 cm

V = 48 cm cubed

Step-by-step explanation:

A square pyramid has a square base. The edge length are all equal.

Given that:

base length (b) = 6 cm and slant height (l) = 5 cm.

The height and the slant height form a right triangle i.e the slant height is the hypotenuse, the base of the triangle is the distance from the center of the square to the edge which is half of the base length (b/2). The height of the pyramid (h) is given as:

l² = h² + (b/2)²

h² = l² - (b/2)²

h² = 5² - (6/2)²

h² = 25 - 9

h = √16 = 4 cm

The area of the base = b² = 6² = 36 cm²

The volume of the pyramid (V) = 1/3 × b² × h = 1/3 × 6² × 4 = 48 cm³

Answer:

(26,65)

Step-by-step explanation:

We know that each package has 5 sheets of paper and 2 staples. So, to know how many sheets of paper and staples that will be used in 13 packages, we just need to multiply each quantity of material used by 13.

So, we have that:

Total sheets of paper = 13 * 5 = 65

Total staples = 13 * 2 = 26

So the ordered pair (x,y), where x is staples and y is sheets of paper is:

(26,65)

Answer:

The ordered pair is (26, 65).

Step-by-step explanation:

From the given information, a package has 5 sheets of paper and is held together with 2 staples.

13 packets contains 13 packages, so that:

Number of sheet of paper required = 13 × 5

                                                           = 65

Number of staples required = 13 × 2

                                              = 26

Therefore, the ordered pair is; staples (26) and sheets of paper (65) i.e (26, 65).

Answer:

[tex] - (x - 4 {)}^{2} [/tex]

Step-by-step explanation:

The given expresion is

[tex] - {x}^{2} + 8x - 16[/tex]

Factor -1;

[tex] - ( {x}^{2} - 8x + 16)[/tex]

Split the middle term with -4x-4x

[tex] - ( {x}^{2} - 4x - 4x + 16)[/tex]

Factor by grouping within the parenthesis:

[tex] - ( x({x} - 4)- 4(x - 4) )[/tex]

Factor further:

[tex] - (x - 4)(x -4 )[/tex]

[tex] - (x - 4 {)}^{2} [/tex]

This the opposite of the square of (x-4)

Answer:

e

Step-by-step explanation:

you do math

3 + 1.75m

This represents 1.75 per mile plus a one time 3 charge.

Another way this can be written is

(1.75m + 6) - 3

This is a less efficient way, but represents the same. It is 1.75 per mile, this is plus 6, therefore we add the -3 outside the parenthesis so it evens out to +3 as the base charge.

Example: Lets say its 3 miles.

3 + 1.75 (3) = 8.25

(1.75 (3) + 6) - 3 = 8.25

Answer:

When m= 0,25

(8m-m ) + 3

3+ 8m-1/4m

With the first one you can add any number of miles infront of the brackets; ie) 4 miles

4(8m-m) +3 = 0.25t

32m-4m /28 (+3) = 0.25t x 28

28m +3 = 0.25t x 28

28m + 3 = 7t + 3t

31m = 10t

Step-by-step explanation:

Answer:

60.4

Step-by-step explanation:

75.5-15.1=60.4

Answer:

60.4*F.

Step-by-step explanation:

75.5-15.1=60.4

Answer:

30. [tex]x=5\\y=5\sqrt{3}[/tex]

31.  [tex]x=4\\y=4\sqrt{3}[/tex]

32. [tex]x=6\\y=6\sqrt{3}[/tex]

33. [tex]x=4.5\\y=\frac{9\sqrt{3} }{2}[/tex]

34. [tex]x=40\\y=40\sqrt{3}[/tex]

35. [tex]x=7.5\\y=\frac{15\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Use SOHCAHTOA to find one of the missing sides, then use the pythagorean theorem ([tex]x^{2}+ y^{2} =z^{2}[/tex]) to find the other one

[tex]sin=\frac{opposite}{hypotenuse}[/tex]

[tex]cos=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan=\frac{opposite}{adjacent}[/tex]

30.

First find [tex]x[/tex] using Sin

[tex]sin(30)=\frac{x}{10}[/tex]

[tex]10*sin(30)=x[/tex]

[tex]x=5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]5^{2}+ y^{2} =10^{2}[/tex]

[tex]25+y^{2} =100[/tex]

[tex]y^{2} =75[/tex]

[tex]\sqrt{y^{2}} =\sqrt{75}[/tex]

[tex]y=5\sqrt{3}[/tex]

32.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{8}[/tex]

[tex]8*sin(30)=x[/tex]

[tex]x=4[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]4^{2}+ y^{2} =8^{2}[/tex]

[tex]16+y^{2} =64[/tex]

[tex]y^{2} =48[/tex]

[tex]\sqrt{y^{2} } =\sqrt{48}[/tex]

[tex]y=4\sqrt{3}[/tex]

32.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{12}[/tex]

[tex]12*sin(30)=x[/tex]

[tex]x=6[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]6^{2}+ y^{2} =12^{2}[/tex]

[tex]36+y^{2} =144[/tex]

[tex]y^{2} =108[/tex]

[tex]\sqrt{y^{2} } =\sqrt{108}[/tex]

[tex]y=6\sqrt{3}[/tex]

33.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{9}[/tex]

[tex]9*sin(30)=x[/tex]

[tex]x=4.5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]4.5^{2}+ y^{2} =9^{2}[/tex]

[tex]20.25+y^{2} =81[/tex]

[tex]y^{2} =60.75[/tex]

[tex]\sqrt{y^{2} } =\sqrt{60.75}[/tex]

[tex]y=\frac{9\sqrt{3} }{2}[/tex]

34.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{80}[/tex]

[tex]80*sin(30)=x[/tex]

[tex]x=40[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]40^{2}+ y^{2} =80^{2}[/tex]

[tex]1600+y^{2} =6400[/tex]

[tex]y^{2} =4800[/tex]

[tex]\sqrt{y^{2} } =\sqrt{4800}[/tex]

[tex]y=40\sqrt{3}[/tex]

35.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{15}[/tex]

[tex]15*sin(30)=x[/tex]

[tex]x=7.5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]7.5^{2}+ y^{2} =15^{2}[/tex]

[tex]56.25+y^{2} =225[/tex]

[tex]y^{2} =168.75[/tex]

[tex]\sqrt{y^{2} }=\sqrt{168.75}[/tex]

[tex]y=\frac{15\sqrt{3} }{2}[/tex]

Answer:

12x/(4+x)

Step-by-step explanation:

The algebraic expression for 'the product of 12 and x divided by the sum of 4 and x' is written as (12  imes x) / (4 + x). This expression follows the order of operations and uses parentheses to ensure clarity.

The algebraic expression for 'the product of 12 and x divided by the sum of 4 and x' can be written as:
(12 x x) / (4 + x).

To write this expression, first, recognize the terms that signify mathematical operations. 'Product' signifies multiplication and a 'sum' signifies addition. The given statement involves both these operations, with 12 being multiplied by the variable x and then divided by the sum of 4 and x.

Using parentheses clarifies that the division applies to the entire sum of 4 and x, rather than just 4 or x. Without parentheses, it may lead to confusion about the order of operations. To represent division, we use the '/' symbol.

The correct algebraic expression (12  imes x) / (4 + x) follows the order of operations and ensures accurate representation of the mathematical relationship described in the problem.

Answer:

11.5

Step-by-step explanation:

3 x  3 5/6

3 x 23/6

=69/6

=11.5

To find out how many pepperoni pizzas Patsy's Pizzeria sold, we need to multiply the number of vegetable pizzas by 3. They sold 11 1/2 pepperoni pizzas.

To find out how many pepperoni pizzas Patsy's Pizzeria sold, we need to multiply the number of vegetable pizzas by 3. If they sold 3 5/6 vegetable pizzas, we can represent this as a mixed number of 3 + 5/6. To multiply this by 3, we first convert the mixed number to an improper fraction: 3 + 5/6 = (3 * 6 + 5) / 6 = 23/6. Next, multiply the improper fraction by 3 to get: (23/6) * 3 = 69/6 = 11 1/2. Therefore, Patsy's Pizzeria sold 11 1/2 pepperoni pizzas.

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Answer:

B) 24

Step-by-step explanation:

3 x 8 = 24

4 x 6 = 24

Answer:

24

Step-by-step explanation:

Answer: 36 in²

Step-by-step explanation:

A=length times width

4.5 times 8 = 36

Answer:

[tex] 36.0 \: {inches}^{2} [/tex]

Step-by-step explanation:

[tex]area = l \times w = 8 \times 4.5 \\\hspace {65 pt} = 36.0 \: {inches}^{2} \\ [/tex]

Answer:

Y = 10/5x

10 divided by 5 = 2

Step-by-step explanation:

Answer:

The function is linear; therefore, the slope of the line joining any two points is the same. We take any two points from the table and compute the slope or rise/ run between them— let is take points (-4, -2) and (-2, -10).

Answer:

1/7

i took the quiz already

Answer:

f(x) = 3x -5 is your answer

Step-by-step explanation:

f(x)=3x-5 is the function notation of the equation  y=3x-5.

The equation y=3x−5 can be written in function notation as: f(x)=3x−5.

In function notation, we use f(x) to represent the dependent variable (usually y), and  x remains the independent variable.

So, the function f(x) takes an input x, multiplies it by 3, and then subtracts 5 to determine the corresponding output y.

Hence, the equation y=3x-5 in function notation is f(x)=3x-5.

To learn more on Equation:

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Answer:

The legs are 12 cm each, so the hypotenuse is

√(144+144)=12√2

So it would be the last one

Answer:

12√2

Step-by-step explanation:

To calculate the probability of a spinner landing on a yellow section, specific information about the spinner is required. For instance, with 5 sections where 1 is yellow, the probability would be 20%. Without such information, however, the correct percentage cannot be determined from the choices provided.

To determine the probability of the spinner stopping on a yellow section, we need specific information about the spinner such as the number of sections and the number of yellow sections. Without this information, we are unable to calculate the exact percentage. Assuming a student is given this type of probability question, they would typically be provided with a diagram or description of the spinner. For example, if there are 5 equal sections and 1 of those is yellow, then the probability (in percentage) would be 20%, calculated as (1 yellow section / 5 total sections) × 100%. However, since we do not have this information here, the correct option cannot be determined from the choices provided (A. 20%, B. 30%, C. 40%, D. 80%).

As for the probability of a randomly chosen student not living within five miles of the campus, this would typically be based on specific data provided in the context of the problem. Without the data, we cannot determine the correct percentage for this scenario as well, thus the correct answer is "Cannot be determined."

Given that the crazy coaster has 3 trains each holding 27 people and runs 9 times in 1 hour, and also operates for 13 hours a day, it can carry a total of 9,477 people in a day.

To figure out how many people can ride the crazy coaster each day, we need to multiply all the related factors together. First, we consider the passengers each train can carry. Each of the 3 trains can hold 27 people which makes 81 people (3 trains multiplied by 27 people each). Then, each of these trains runs 9 times in 1 hour, so that's 81 people multiplied by 9 runs, which makes 729 people per hour. Since the crazy coaster operates for 13 hours a day, that's 729 people multiplied by 13 hours, which equals 9,477 people. Therefore, a total of 9,477 people can ride the crazy coaster each day, assuming every train is full on every run.

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Slope formula: y2-y1/x2-x1

Question 1:

= 14-(-15)/1-(-11)

= 29/12

= 2 5/12

Therefore, the slope is 2 5/12 or 29/12.

Question 2:

= 12-(-19)/-9-16

= 31/-25

= -31/25

= 1 6/25

Therefore, the slope is 1 6/25 or -31/25.

Question 3:

= -3-(-3)/8-(-18)

= 0/26

Therefore, the slope is 0.

Best of Luck!

Answer:

As the number of hours spent on homework increases, the tests scores increase.

Step-by-step explanation:

because the independent variable and dependent variable are both increasing.

Final answer:

The statement "As the number of hours spent on homework increases, the test scores increase" best describes a positive correlation, where two variables increase together.

Explanation:

A positive correlation is described as a relationship in which the increase in one variable leads to the increase in another variable. Looking at the situations you provided, the scenario, "As the number of hours spent on homework increases, the test scores increase," clearly illustrates a positive correlation. More hours of homework tend to result in higher test scores, suggesting that the two variables change in the same direction.

A negative correlation involves an inverse relationship where an increase in one variable leads to a decrease in the other. For example, "As the number of times going to bed early increases, the number of times waking up late decreases," is a negative correlation because the variables move in opposite directions.

No correlation occurs when the changes in one variable do not relate to changes in another variable, such as "As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same." Here, there is no consistent pattern of increase or decrease between apple consumption and doctor visits.

Final answer:

The rate 6 + 4 2/3 in lowest terms is 32/3 or, as a mixed number, it is 10 2/3.

Explanation:

The student asked to express the rate 6 + 4 2/3 in lowest terms. To do this, we will first convert the mixed number 4 2/3 into an improper fraction. The mixed number 4 2/3 can be converted by multiplying the whole number 4 by the denominator 3 and then adding the numerator 2, which gives us 14/3. So now we have the expression 6 + 14/3.

To add the whole number and the fraction, we can convert the whole number 6 into a fraction with the same denominator as 14/3. This means converting 6 to 18/3 (since 6 times 3 equals 18). Now we can add the fractions directly: 18/3 + 14/3 equals 32/3. Therefore, the rate 6 + 4 2/3 expressed in lowest terms is 32/3 or 10 2/3 when represented as a mixed number.