Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg.

Which equation can be used to find x, the length of the shorter leg?

x(x + 7) = 13
x(x + 7) = 169
x2 + (x + 7)2 = 13
x2 + (x + 7)2 = 169

Answer: x = -2

Step-by-step explanation:

[tex]x=4+(4x-4)\frac{1}{2} \\x=4+\frac{4x}{2}-\frac{4}{2}\\x=4+2x-2\\x=2+2x\\x-2x=2\\-x=2\\x=-2[/tex]

4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound

Step-by-step explanation:

 the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .

Answer:

therefore the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .........

Answer:

D = 51, other = 30

Step-by-step explanation:

d = | 5  1 |

     |-1  10|

D = (5 x 10) - ( 1 x -1) = 50 + 1 = 51

| 2   4|

|-3   9|

(2 x 9) - (4 x -3) = 18 + 12 = 30

Answer:

32, 34

Step-by-step explanation:

The answer must be grater than 30 so 30 is not an option the integers in the range are 31, 32, 33, and 34 the only even integers in this set are 32, and 34. Hope this helps. :)

Answer:

y=3x-8

Step-by-step explanation:

Answer:

10 kilometer/hour

Step-by-step explanation:

Average speed = Total distance travelled / Total time taken

Ardi:

Total distance travelled = 70 km

Total time taken = 35 minutes = 35/60 hour

Average speed = Total distance travelled / Total time taken

= 70 km ÷ 35/60 hr

= 70 × 60/35

= 4,200/35

= 120 kilometer/hour

Lei:

Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes

= 4.5 hours

Average speed = Total distance travelled / Total time taken

= 585 km / 4.5 hours

= 130 kilometer/hour

Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train

= 130 kilometer/hour - 120 kilometer/hour

= 10 kilometer/hour

Answer:

0.410714

Step-by-step explanation:

Dividend ÷ Divisor = Quotient

B. 63

some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite

Answer:

you need to learn how to "prime factor" numbers....

primes are 2,3,5,7,11,13,17....

they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.

take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...

15 = 3 * 5

24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6

thus   [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex]  now just cancel all the SAME numbers from to to bottom

"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top

result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]

~~~~~~~~~~~~~~~~~~~~

[tex]\frac{21}{35}[/tex]

21= 3 * 7

35= 5* 7

[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]

Step-by-step explanation:

With ASA, we need two angles and an included side. An included side is one that is between the two angles.

But, we need to make sure the sides match up. So, triangle KJI is congruent to triangle ZYX.

Therefore, we need to know that side JI is congruent to YX.

Hope this helps!

Answer:

The cube root of a number x is the length of the side of a cube whose volume is x cubic units.

The square root of a number x is the length of the side of a square whose area is x square units.

Hence the words ‘cube’ and ‘square’.

Mathematicians have then generalized these two concepts for when x is not necessarily a volume of a cube or an area of a square

Answer:

A. 35 square centimeters

Step-by-step explanation:

The area of a triangle is (b*h)/2.

7 * 10 = 70

70/2 = 35

Answer:

x = 140

Step-by-step explanation:

Given the equations

[tex]\frac{2}{5}[/tex] x - [tex]\frac{1}{5}[/tex] y = 98 ( multiply through by 5 to clear the fractions )

2x - y = 490 → (1)

[tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{14}[/tex] y = 55 ( multiply through by 14 to clear the fractions )

4x - y = 770 → (2)

Subtract (1) from (2) term by term to eliminate y

2x + 0 = 280

2x = 280 ( divide both sides by 2 )

x = 140

The first one because there is only one y value for every x value. The correct option is first.

To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.

In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.

Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.

Learn more about Function here:

https://brainly.com/question/31062578

#SPJ6

Answer:

8.42

Step-by-step explanation:

* means multiply

31.65/5.45 = x/1.45

5.45x = 31.65 * 1.45

5.45x = 45.8925

x = 45.8925/5.45

x = 8.42064220183

Answer:

g(x) = |x-7|+4

Step-by-step explanation:

If we imagine trying to find the vertex of f(x) or the lowest part, we can always input x and y into each equation and see if they equal on either side.

The vertex is at points (7,4)

4=|7-7|+4 : 4=4.

Answer:

c

Step-by-step explanation:

just took it

Answer:

D. 1

Step-by-step explanation:

CA = 17

ZA = 16

CZ + ZA = CA

CZ + 16 = 17

CZ = 1

D. 1

Answer:

1/2

Step-by-step explanation:

3/4 x 2/3

= 1/2

Step-by-step explanation:

sorry I wanted to help you but my calculator is take out decimals sorry I don't know what to do

Answer:

(a) [tex]x\³ - 6x - 6[/tex]

(b) Proved

Step-by-step explanation:

Given

[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root

Solving (a): The polynomial

A cubic function is represented as:

[tex]f = (a + b)^3[/tex]

Expand

[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]

Rewrite as:

[tex]f = a^3 + 3ab(a + b) + b^3[/tex]

The root is represented as:

[tex]r=a+b[/tex]

By comparison:

[tex]a = $\sqrt[3]{2}[/tex]

[tex]b = \sqrt[3]{4}$[/tex]

So, we have:

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

Expand

[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

Evaluate like terms

[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]

Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = 6 + 6r[/tex]

Equate to 0

[tex]f - 6 - 6r = 0[/tex]

Rewrite as:

[tex]f - 6r - 6 = 0[/tex]

Express as a cubic function

[tex]x^3 - 6x - 6 = 0[/tex]

Hence, the cubic polynomial is:

[tex]f(x) = x^3 - 6x - 6[/tex]

Solving (b): Prove that r is irrational

The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]

[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]

[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]

[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]

[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]

[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]

[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]

[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

Answer:

-(cos α)/(sin α)

= -cot α

Step-by-step explanation:

use trigonometric identities

Answer: Choice D

Explanation:

The increase of 9.8% rounds to 10% when rounding to the nearest ten

An increase of 10% would use the multiplier 1.1

Think of it like saying 1 + 0.10 = 100% + 10%

Similarly, the 5.1% rounds to 5% and an increase of this amount will use the multiplier 1.05

So if we started with 20 items, then 20(1.1)(1.05) is the expression that estimates an increase of 10% followed by an increase of 5%. The order doesn't matter (so you could increase by 5% first, then 10% later).

Answer:

24 meters

Step-by-step explanation:

Use the pythagorean theorem

18² + x² = (x + 6)²

Expand

324 + x² = x² + 12x + 36

Subtract x² from both sides

324 = 12x + 36

Subtract 36 from both sides

288 = 12x

Divide both sides by 12

24 = x

24 meters

Answer:

33 jóvenes prefieren el basquetbol.

Step-by-step explanation:

Hay 165 jóvenes.

De estos, 20% prefieren el basquetbol.

¿cuantos prefieren el basquetbol?

20% de 165, entonces:

[tex]20\% = \frac{20}{100} = 0.2[/tex]

[tex]0.2*165 = 33[/tex]

33 jóvenes prefieren el basquetbol.