The hypotenuse of a right triangle is 6 feet long. One leg is 2 feet longer than the other. Find the length of each leg to the nearest hundredth of a foot.

Answer:

50% of 60 is 30

Step-by-step explanation:

The sum of the square of the constants is 3/4

Given the equation [tex]\frac{1}{a+1} +\frac{1}{b+1} +\frac{1}{c+1} =2[/tex]

The partial form of the equation is given as:

Solve for the constant "a"

[tex]\frac{1}{a +1} = 2\\a+1 = \frac{1}{2} \\a = \frac{1}{2} - 1\\a =-\frac{1}{2}[/tex]

Hence [tex]a=b=c=-\frac{1}{2} \\[/tex]

Taking the square of the constant, we will have:

[tex]a^2 + b^2 + c^2 =(-1/2)^2 +(-1/2)^2+(-1/2)^2\\a^2 + b^2 + c^2 =1/4 + 1/4 + 1/4\\a^2 + b^2 + c^2 =3/4[/tex]

Hence the sum of the square of the constants is 3/4

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Answer -the sum of the square of the consonants is 3/4

Answer:

-16

Step-by-step explanation:

start with brackets

-5-3 = -8

2(-8)

= -16

Answer:

5

Step-by-step explanation:

plug in the numbers (-15x9/5)+35 PEMDAS.

Answer:

2520cm²

Step-by-step explanation:

Surface area = sum of the area of all the bases.

Area of bottom base = 28 * 30 = 840

Area of right base = 25 * 30 = 750

Area of left base = 17 * 30 = 510

Area of two triangles = ( 15 * 28 ) / 2 = 210 * 2 = 420

Then add all the areas together to find surface area

Surface area = 840 + 750 + 510 + 420 = 2520cm²

Relevant Formulas:

Area of a rectangle = length * width. This formula was used to find the area of the bottom base, the right base and the left base

Area of a triangle = ( height * base length ) / 2 . This formula was used to find the area of the sides which are triangles.

Answer:

D) 8

Step-by-step explanation:

What the problem is asking you to do is multiply the two expressions and substitute x=3 into the product.

[tex]f(x)=2^x[/tex]

[tex]g(x)=2x-5[/tex]

[tex](f*g)(x)=f(x)g(x)=(2^x)(2x-5)[/tex]

[tex](f*g)(3)=f(3)g(3)=(2^3)(2(3)-5)=(8)(6-5)=(8)(1)=8[/tex]

Therefore, the correct answer is D

Using the normal distribution, it is found that the correct option is:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{117 - 100}{17}[/tex]

[tex]Z = 1[/tex]

Hence, the option d is correct.

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Answer:

X=4

Step-by-step explanation:

28−(3x+4)=2(x+6)+x

28+−1(3x+4)=2(x+6)+x(Distribute the Negative Sign)

28+−1(3x)+(−1)(4)=2(x+6)+x

28+−3x+−4=2(x+6)+x

28+−3x+−4=(2)(x)+(2)(6)+x(Distribute)

28+−3x+−4=2x+12+x

(−3x)+(28+−4)=(2x+x)+(12)(Combine Like Terms)

−3x+24=3x+12

−3x+24=3x+12

Step 2: Subtract 3x from both sides.

−3x+24−3x=3x+12−3x

−6x+24=12

Step 3: Subtract 24 from both sides.

−6x+24−24=12−24

−6x=−12

Step 4: Divide both sides by -6.

−6x

−6

=

−12

−6

x=2

Answer:

x = 2

Step-by-step explanation:

28 - 3x + 4 = 2x + 12 + x

24 - 3x = 3x + 12

     + 3x   +3x

24 = 6x + 12

-12          -12

12 = 6x

x = 2

Answer:

5

Step-by-step explanation:

Answer:

if you mean [tex]\frac{\sqrt{-1} }{8}[/tex] then the answer[tex](1/8)i[/tex]

and if you mean:[tex]\sqrt{\frac{-1}{8}}[/tex] then the answer is[tex]\frac{i\sqrt{2} }{4}[/tex]

Hence, the answer value of [tex]\sqrt\frac{-1}{8}[/tex] is [tex]i\frac{\sqrt2}{4}[/tex].

What is the fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts

As per the given information

i.e.,

[tex]\sqrt\frac{-1}{8}=i\frac{\sqrt2}{4}[/tex]

Hence, the answer value of [tex]\sqrt\frac{-1}{8}[/tex] is [tex]i\frac{\sqrt2}{4}[/tex].

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Answer:

D

Step-by-step explanation:

Answer:

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Prime Factorization of 80: 80 = 24 × 5.

Step-by-step explanation:

Answer:

This is true

Step-by-step explanation:

This is true because of the communitive property that makes the numbers you multiply the same product in different orders

Answer:

Step-by-step explanation:

[tex]\sf 4+4\div 5[/tex]

[tex]\sf 4\div 5 =0.8[/tex]

[tex]\sf 4+0.8[/tex]

[tex]\sf 4.8[/tex]

* Hope it helps, ty 4 pts!

* Have a good day!

Answer:

Step-by-step explanation:

C is right.

5(a + b + c + d)

when you express it it's gonna be 5a + 5b + 5c + 5d

Answer:

8:10

Step-by-step explanation:

8 parts for brown sugar and 10 parts flour.

In simplest, 4:5 (divide 8 and 10 by 2)

Answer:

0.8 km per day

Step-by-step explanation:

5 3/5 is the same as 5.6, so

5.6/7

= 0.8 km per day

Answer:

7: (3,9) 8:(-2,1) 6: (2,10)

Step-by-step explanation:

7) 2x+3=-2x+15

x=3

y=2(3)+3

y=6+3

y=9

8)x= -1(1+2y)/3

-4-2y=-6

y=1

x=-2(1+2(1))/3

x=-2

6)2x-16=-12

x=2

y=2+8

y=10

Answer:

g=6

Step-by-step explanation:

6.4×6-1.4×6=

38.4-8.4=30

its true if it is not the result is incorrect

Answer:

the ranger will need 6 signs

Step-by-step explanation:

Answer:

[tex]5\frac{1}{4}[/tex]

Step-by-step explanation:

Catherine walks her dog 3/4 a mile everyday.

We want to find how far she walks each week.

There are 7 days a week and she walks 3/4 a mile everyday so weekly she walks 3/4 * 7 = 5  1/4 mile a week.

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

[tex]\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}[/tex]

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

[tex]\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}[/tex]

Another identity is:

[tex]\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}[/tex]

Therefore:

[tex]\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}[/tex]

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

[tex]\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}[/tex]

Another identity:

[tex]\displaystyle \large{\sin^2x+\cos^2x=1}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}[/tex]

Hence proved, this is proof by using identity helping to find the specific identity.

Answer:

w = 2.5

Step-by-step explanation:

Write these 2 equations to represent the problem:

[tex]l=w+5\\2w+2l=20[/tex]

where w is width and l is length. This can then be solved as a system of equatios. I'll solve by substitution, and as the [tex]l[/tex] is already solved for at the top:

[tex]2w+2l=20\\2w+2(w+5)=20\\2w+2w+10=20\\4w+10=20\\4w=10\\w=2.5[/tex]

If you just need the width, then you're already done there. I'll find  the other variable too, and then check it to be sure it's correct.

[tex]l=w+5\\l=(2.5)+5\\l=7.5[/tex]

Now, confirm that with the second equation:

[tex]2w+2l=20\\2(2.5)+2(7.5)=20\\5+15=20\\20=20[/tex]

The perimeter of a rectangle is the sum of its side lengths.

The width of the rectangle is 2.5 units

Represent the length with l and the width with w.

So, we have:

[tex]P =2 \times (l + w)[/tex] --- the formula of perimeter

The perimeter is 20 units.

So, we have:

[tex]20 =2 \times (l + w)[/tex]

Divide both sides of the equation by 2

[tex]10 =l + w[/tex]

The length is said to be 5 more than its width.

So, we have:

[tex]l =5 + w[/tex]

Substitute 5 + w for l in [tex]10 =l + w[/tex]

[tex]10 = 5 + w + w[/tex]

[tex]10 = 5 + 2w[/tex]

Subtract 5 from both sides

[tex]5 = 2w[/tex]

Divide both sides by 2

[tex]2.5 = w[/tex]

Rewrite as:

[tex]w =2.5[/tex]

Hence, the width of the rectangle is 2.5 units

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Answer:

Slope = 3/2

y-intercept = -4

x  |  y

0  -4

2   -1

Step-by-step explanation:

Answer:

48 ÷12 will help you 48 is cost divided by total cost which means cost of one adult and one child

Answer:4

Step-by-step explanation: each quarter of an hour is 1.5 miles they both can go into 12 so if you multiply 2*4 and 3*4 you get 8/12 and if you multiply 3*3 and 4*3 you get 9/12 then you subtract 9/12 by 8/12 to get so 1/12=1/2 miles so you would subtract 4 1/2 by 1/2 to get 4

ANSWER:

9m is the answer

Answer:

b

Step-by-step explanation:

Remove full rotations of  

2

π

until the angle is between  

0

and  

2

π

.

sin

(

5

π

6

)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

sin

(

π

6

)

The exact value of  

sin

(

π

6

)

is  

1

2

.

1

2

The result can be shown in multiple forms.

Exact Form:

1

2

Decimal Form:

0.5

"This is an example of a combination. There are 148,995 possible arrangements of first through fourth place winners. ​

Combination has to do with selection. Since we are to select thee first four positions from the 45 runners. To get the possible number of arrangements, we will use the combination formula;

45C4 = 45!/(45-4)!4!

45C4 = 45!/41!4!

45C4 = 45*44*43*42*41!/41!*4!

45C4 = 45*44*43*42/4*3*2

45C4 = 3,575,880/24

45C4 = 148,995

Therefore the correct statement is that "this is an example of a combination. There are 148,995 possible arrangements of first through fourth place winners. ​

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answer: permutation and 3,575,880 (plato/edmentum)

Answer:

7/8 yards

Step-by-step explanation:

converting each fraction to match 1/8 would be

1/4=2/8

1/8

1/2=4/8

add them together and get 7/8