Solve the right triangle

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[tex]b. {b}^{m} = {b}^{1 + m} [/tex]

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Answer:

Step-by-step explanation:

The  statement "The expression contains 2 terms." is false because the expression contains 3 terms:  7f, 15 and -2g

The given statement "expression contains 2 terms" is false, Because it contains three terms of which two are the variable and one is a constant.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

The expression is,

7f + 15 - 2g

The given expression contains 2 terms.

A term is a single expression, a single integer (positive or negative), and a  single variable (a letter), or a number of variables that have been multiplied but never added or canceled are all acceptable.

The given statement is false because it reported only two terms but there are more than two terms.

Thus, the given statement "expression contains 2 terms" is false Because it contains three terms of which two are the variable and one is a constant.

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Answer:

x = 2

Step-by-step explanation:

Answer:

49

Step-by-step

step 1 subtract 10 -3

step 2 multiply 7 x 7

that's your answer

Answer:

49

Step-by-step explanation:

Step 1:

a = 3; b = 2; c = 10         Given

Step 2:

[tex](c-a)^{b}[/tex]         Equation

Step 3:

[tex]( 10 - 3)^{2}[/tex]        Input values

Step 4:

( 7 ) ²           Parentheses

Answer:

49

Hope This Helps :)

Answer:  

(−2,2)

Hope it helps!

Step-by-step explanation:

A binomial expression has two terms. For example, 4x + 5,

The degree of any polynomial refers to the term with the highest exponent on its variable. For example, In expression 4x + 5, the exponent of x is 1 so it is 1st degree polynomial and in the same way, for  since the variable y has the highest exponent i.e., 2 therefore it is 2nd degree polynomial.

Now, third degree binomial with constant term 8 =

As it has two terms where first term is  and second term is 8. Therefore, it is called binomial and since the highest exponent with variable x is 3, therefore it is third degree binomial with constant term of 8.

Answer: $6828

Step-by-step explanation:

James annual income = $85350

Income tax = 8%

The amount of income tax in dollars and cents that James has to pay will be calculated by multiplying the income tax by his annual income. This will be:

= 8% × $85350

= 8/100 × $85350

= 0.08 × $85350

= $6828

Answer: 105 degrees

Step-by-step explanation:

Both angles equal 180 so if we subtract 75 from 180 we get 105.

Answer:

105º

Step-by-step explanation:

<ONC and <BNJ are a linear pair, the angles are supplementary (eqauls 180º).

Answer:

i cant see image

Step-by-step explanation:

oof

Answer:

first pic, 2.5 pounds of peanuts cost $1, 17.5 pounds of peanuts cost $7, and the point (4,10) is also on the line. second pic, G.

Step-by-step explanation:

2.5 goes into 17.5, 7 times. then $7/7 means $1 for 2.5 pounds. that is true. second one they state the graph. the last one, if you calculate knowing 2.5 pounds is $1, then it is correct. for the second pic, i dont know but ill give you this im really sorry. draw a triangle from the two points getting a slope of 3. but this is negative so it's -3. the slope for the equation if it's perpendicular is 1/3 tho. wait i got it i think it's G since it's going to be perpendicular so if you draw it on, it would be positive.

Answer:

oml not u making me do math

Step-by-step explanation:

not u making me do math

Answer:

I am sorry

Step-by-step explanation:

I am new

Answer:

a

Step-by-step explanation:

im 100% sure

Answer:

Step-by-step explanation:

The explicit formula for a GP is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is the common ratio

a) If a3 = 36 and r = 6

a3 = ar^3-1

a3 = ar^2 = 36

ar^2 = 36

a(6)^2 = 36

36a = 36

a = 1

Get the nth term

Tn = 1(6)^{n-1}

Tn = 6^{n-1}

b)  If a6 = 64 and r = 2

a6 = ar^6-1

a6 = ar^5 = 64

ar^5 = 64

a(2)^2 = 64

4a = 64

a = 16

Get the nth term

Tn = 16(2)^{n-1}

Tn = 16*(2^n/2)

Tn = 8(2^n)

Answer:

Step-by-step explanation:

Step one:

the unit rate is the amount of water per unit of time

Given data

4/5 gallon to decimal= 0.8gallon

1/5 minute decimal= 0.2 minute

We are told that 0.8 gallons run in 0.2 minute

                      then x gallon will run in 1 minute

cross muliply we have

x=0.8/0.2

x=4

this means that in one minutes 4gallons will run in the faucet

The unit rate is 4gallons per minute

Answer:

The total budget is $1260

Step-by-step explanation:

Given

[tex]Props = \$693[/tex]

[tex]Costumes = 45\%[/tex]

Required

Determine the total budget

Since all budgets was spent on Props and Costumes only.

We have that.

[tex]\%Props + \%Costumes = 100\%[/tex]

[tex]\%Props + 45\%= 100\%[/tex]

[tex]\%Props= 100\% -45\%[/tex]

[tex]\%Props= 55\%[/tex]

In other words, 55% was spent on Props

Let the total budget be x, we have:

[tex]55\% * x = \$693[/tex]

Make x the subject

[tex]x = \$693/55\%[/tex]

[tex]x = \$1260[/tex]

Hence, the total budget is $1260

Answer:

10.65 inches

Step-by-step explanation:

You simply add Saturday's and Sunday's total together

6.14+4.71=10.85

The slope of a line is [tex]\frac{dy}{dx}[/tex]

where [tex]d[/tex] is the difference and [tex]y[/tex] and [tex]x[/tex] are the values.

In this case, the difference in [tex]y[/tex] is 10 and the difference in [tex]x[/tex] is 0

And division where the denominator being 0 leads to the answer being Undefined or Infinity as the line is directly on the [tex]y[/tex] axis.

In other words, everything but choice B

==========================================================

Explanation:

You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division

There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

------------------------------------------------

Here's a fairly short proof:

Consider a polynomial q(x) such that

p(x) = (x-k)q(x)

which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.

If we plug x = k into the p(x) function, we get

p(x) = (x-k)q(x)

p(k) = (k-k)q(k)

p(k) = 0*q(k)

p(k) = 0

------------------------------------------------

How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.

So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.

-------------------------------------------------

Plug x = 3 into the first function

A(x) = x^3 - 2x^2 - 4x + 3

A(3) = 3^3 - 2(3)^2 - 4(3) + 3

A(3) = 0

This shows (x-3) is a factor of the function A(x)

------------------------------------------------

Repeat for the second function

B(x) = x^3 + 3x^2 - 2x - 6

B(3) = 3^3 + 3(3)^2 - 2(3) - 6

B(3) = 42

We don't get an output of 0, so (x-3) cannot be a factor of B(x)

-----------------------------------------------

Now onto the third function

C(x) = x^4 - 2x^3 - 27

C(3) = 3^4 - 2(3)^3 - 27

C(3) = 0

So (x-3) is a factor of C(x)

----------------------------------------------

Finally the last function

D(x) = x^4 - 20x - 21

D(3) = 3^4 - 20(3) - 21

D(3) = 0

Therefore (x-3) is a factor of D(x) as well.

The remainder theorem will be used to identify the polynomial that has a remainder of zero when divided by (x - 3)

The polynomials that have 0 as a factor are;

Reason:

According to the remainder theorem, we have;

The remainder following the division of a polynomial, by (x - a) is P(a)

Therefore, (x - 3) is a factor of the polynomial P(x) where P(3) = 0

For option (A), we have; A(x) = x³ - 2·x² - 4·x + 3

The remainder when (x³ - 2·x² - 4·x + 3) is divided by (x - 3) is therefore;

A(3) = 3³ - 2 × 2² - 4 × 2 + 3 = 14

Therefore, (x - 3) is not a factor of A(x) = x³ - 2·x² - 4·x + 3

For option (B), we have;

B(x) = x³ + 3·x² - 2·x - 6

The remainder when B(x) is divided by (x - 3) is therefore;

B(3) = 3³ + 3×3² - 2×3 - 6 42

Therefore, (x - 3) is not a factor of B(x) = x³ + 3·x² - 2·x - 6

For option (C), we have;

C(x) = x⁴ - 2·x³ - 27

The remainder when C(x) is divided by (x - 3) is therefore;

C(3) = 3⁴ - 2×3³ - 27 = 0

Therefore;

For option (D), we have;

D(x) = x⁴ - 20·x - 21

The remainder when D(x) is divided by (x - 3) is given as follows;

D(3) = 3⁴ - 20×3 - 21 = 0

Therefore;

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Answer:

14

Step-by-step explanation:

14

Answer:

it's a

Step-by-step explanation:

its a on edge

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

The slope would be 4 (because in y=mx+b form, m = slope)

The y-intercept would be zero (0,0) since b = y-intercept, and there is no b in this equation.

From (0,0) you would rise four to get (0,4) and go over to the right one (1,4)

To make another point, you could go down 4 from (0,0) to get (0,-4) and to the left one to get (-1,-4)

Hope this helps.

Answer:

I suppose that each number is repeated 3 times, the actual question is:

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

Now, remember the relation:

Distance = Speed*Time

Let's define:

D1 = distance between Courtney's house and the beach.

D2 = distance between the beach and the park.

T1 = time that it took the first walk.

T2 = time that it took the second walk.

We know that the total distance Courtney walked is 8km, then:

D1 + D2 = 8km.

And we also know that the entire walk took 2 hours, then:

T1 + T2 = 2h.

We also have the equations:

D1 = 4km/h*T1

D2 = 5km/h*T2.

Then we have a system of equations:

D1 + D2 = 8km

T1 + T2 = 2h

D1 = 4km/h*T1

D2 = 5km/h*T2.

To solve this, first let's replace equations 3 and 4 in the first equation:

4km/h*T1 + 5km/h*T2 = 8km

Now we have only two equations left:

4km/h*T1 + 5km/h*T2 = 8km

T1 + T2 = 2h

Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:

T1 = 2h - T2.

Replacing this in the first equation gives:

4km/h*(2h - T2) + 5km/h*T2 = 8km

Now let's solve this for T2.

8km - 4km/h*T2 + 5km/h*T2 =  8km

8km + 1km/h*T2 = 8km

1km/h*T2 = 0

from this, we have T2 = 0

This would mean that T1 = 2h.

Then:

D1 = 4km/h*2h = 8km.

T2 = 0

D2 = 5km/h*0 = 0.

This happens because the numbers in the problem were not well thought.

You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.

Given:

A student says that the graph of the equation [tex]y = 3(x + 8)[/tex] is the same as the graph of [tex]y = 3x[/tex], only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

[tex]y=3x[/tex]

[tex]f(x)=3x[/tex]

Equation of after transformation is

[tex]y=3(x+8)[/tex]

[tex]g(x)=3(x+8)[/tex]

Now,

[tex]g(x)=f(x+8)[/tex]      ...(i)

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

[tex]a=8\text{ and }b=0[/tex]

Therefore, the graph of [tex]y=3x[/tex] translated left by 8 units. Hence, the student is wrong.

Answer:

second quadrant

Step-by-step explanation:

(x, y ) → (x - 5, y + 3 ) means subtract 3 from the original x- coordinate and add 3 to the original y- coordinate.

(- 3, - 2 ) ← in third quadrant

→ (- 3 - 5, - 2 + 3) → (- 8, 1 ) ← in second quadrant

Answer:

13.5 miles or 13 1/2

Step-by-step explanation: because 27 divided by 27 is 13.5 or 13 1/2.

Answer: -3 1/2 and -6