Grant is painting a rectangular board that has a width of 1/3 foot. He has enough paint to cover 3 square feet. If he is able to cover the whole board by using all of his paint, what is the length of the board in feet?

Answer:

2x + 6 = 90

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees, so the sum of the angles is 90 degrees. We could let x be the measure of the angle. The other angle is x + 6, so the answer is x + x + 6 = 90, or 2x + 6 = 90

From the given measure whose angle is 6° less than the measure of its complement.

The measure of the two angles is 47° and 43° respectively.

Complementary angles are angles whose sum is equal to 90°. It is usually composed of two angles complementing themselves.  

Mathematically;

Let the first angle be a and the second angle be b

∴

a + b = 90°   (complemntary angles)

If one of the angles is 6° less than  its complement;

i.e.

Let a = 6

SO, the algebraic equation for the value of a is:

a = b - 6

 Replacing the value of a to solve the equation, we have:

(b - 6) + b = 90

2b - 6 = 90

2b = 90 - 6

2b = 86

b = 86/2

b = 43°

From a + b = 90°

a = 90° - 43°

a = 47°

Therefore, we can conclude that the measure of each angle is 47° and 43°.

Learn more about complementary angles here:

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Answer:

yes it is rational

Step-by-step explanation:

it is rational because if 62 can be expressed as a ratio, then a quotient is the result you get when you divide one number by another number. For 62 to be a rational number, the quotient of two integers must equal 62. it can be expressed as a fraction in the form 62/1

Answer:

[tex]\huge\boxed{xy = 2}[/tex]

Step-by-step explanation:

=> [tex]\sf (x+y)^2 = x^2 + y^2 + 2xy[/tex]

Given that [tex]\sf x + y = 3 , x^2 + y^2 = 5[/tex]

=> [tex]\sf (3)^2 = 5 + 2xy[/tex]

=> [tex]9 = 5 + 2xy[/tex]

=> [tex]9-5 = 2xy[/tex]

=> [tex]4 = 2xy[/tex]

Dividing both sides by 2

=> 2 = xy

OR

=> xy = 2

Answer:

536 cm is equal to 53.6 dm

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

Answer:

nq = -3/5

Step-by-step explanation:

2nq = 3 + 7nq

5nq = -3

nq = -3/5

Answer:

y=1/2x+0

Step-by-step explanation:

Since the slope is 1/2 and it starts at the origin, the b value is 0.

Answer:

1/2x

Step-by-step explanation:

Answer:

10 √10

Step-by-step explanation:

Answer:

[tex]10\sqrt{10}[/tex]

Step-by-step explanation:

The largest perfect square of the factors of 1000 is 100. We can therefore convert √1000 like this:

√100 × 10

Next, we separate the numbers inside the √ as such:

√100 × √10

√100 is a perfect square that equals 10. We can therefore put 10 outside the radical and get the final answer to square root of 1000 in simplest radical form as follows:

10√10

Answer:

x = 1

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ÷)

Answer:

D

Explanation:

I'm just typing this part to get to 20 characters

Answer:

(h+9)⋅(h+2)

Step-by-step explanation:

1.1     Factoring  h2+11h+18  

The first term is,  h2  its coefficient is  1 .

The middle term is,  +11h  its coefficient is  11 .

The last term, "the constant", is  +18  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18  

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   11 . -18    +    -1    =    -19  

     -9    +    -2    =    -11  

     -6    +    -3    =    -9  

     -3    +    -6    =    -9  

     -2    +    -9    =    -11  

     -1    +    -18    =    -19  

     1    +    18    =    19  

     2    +    9    =    11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  9  

                    h2 + 2h + 9h + 18

Step-4 : Add up the first 2 terms, pulling out like factors :

                   h • (h+2)

             Add up the last 2 terms, pulling out common factors :

                   9 • (h+2)

Step-5 : Add up the four terms of step 4 :

                   (h+9)  •  (h+2)

            Which is the desired factorization

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{(h + 9)(h + 2)}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ {h}^{2} + 11h + 18}[/tex]

Here, we have to find out two numbers that adds to 11 and multiplies to 18

[tex] \dashrightarrow{ \sf{ {h}^{2} + (9 + 2)h + 18}}[/tex]

Distribute h through the parentheses

[tex] \dashrightarrow{ \sf{ {h}^{2} + 9h + 2h + 18}}[/tex]

Take h as common. Similarly, take 2 as common

[tex] \dashrightarrow{ \sf{h(h + 9) + 2(h + 9)}}[/tex]

[tex] \dashrightarrow{ \sf{(h + 9)(h + 2)}}[/tex]

Hope I helped!

Best regards! :F

Answer:

they did not meet their goal

Step-by-step explanation:

Answer:

B) Irrational numbers

Step-by-step explanation:

The given number is [tex]70[/tex].

We know the number which doesn't have any fractional part or decimal part is an integer. Here, there is no fractional part with the number 70, so this is an integer.

This is one of counting numbers from the set of [tex]\{ 1,2,3,4,5,...\}[/tex], so this is a natural number.

Also, this belongs to the set of whole numbers [tex]\{0,1,2,3,...\}[/tex].

But, [tex]70[/tex] can be written in the form of  [tex]\frac {p}{q}[/tex] as [tex]70= \frac {70}{1}[/tex] where [tex]p=70[/tex] , [tex]q=1[/tex] are integers and [tex]q \neq 0[/tex], so this is a rational number.

We know that any number that belongs to the rational number is not an irrational number.

Hence, [tex]70[/tex] does not belong to the set of irrational numbers.

So, option [tex](B)[/tex] is correct.

Answer:

the correct answer is b

Step-by-step explanation:

i took the test

Answer:

2835x^5.

Step-by-step explanation:

By Binomial Theorem, T(r+1) = nCr * a^(r+1) * b^r.

Term 5 = 7C4 * x^5 * 3^4

= 35 * x^5 * 3^4

= 2835x^5.

Answer:

y=1/5x+7/5

Step-by-step explanation:

X AND Y INTERCEPTS

1st Answer:

x = 9

Step-by-step explanation:

first you want to substitute the y

move the expression to the left

divide both sides

move the constant to the right

calculate

change the signs

2nd Answer:

x = -65/9  OR x = - 7 2/9, x = - 7.2

Step-by-step explanation:

first you want to substitute the y

move the expression to the left

divide both sides

move the constant to the right

calculate

Answer:

x=39/2 or 19.5

Step-by-step explanation:

Answer:

MY=80

Step-by-step explanation:

MX=MY ( since M is the midpoint)

2x+10=3x-5

10+5=3x-2x

15=x

MX+MY=MX

2x+10+3x-5=MY

2(15)+10+3(15)-5=MY

MY=80

Answer:

18 dish soaps

Step-by-step explanation:

Answer:

it's 18 dish soap dish bottle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question lacks appropriate diagram. Find the diagram in the attachment.

From the diagram, it can be seen that the triangle is an isosceles triangle because two of its sides are parallel (i.e the same). Since two of the sides are the same, hence the two base angles will be the same.

From the diagram, <EFG = <EGF

Since  <EFG  = 55° hence  <EGF = y = 55°

Hence the va;ue of y is 55°

Answer:

30 liters of 30% solution and 30 liters of 70% of solution should be mixed by the researcher to get 60 liters of 50% solution.

Step-by-step explanation:

Let 'x' liters of 30% solution and 'y' liters of 70% solution are added together to get the required 60 liters of 50% of the solution.

According to the question, 30% solution and 70% solution are mixed and so, we get

[tex]0.3x+0.7y=0.5 \cdot 60\\\Rightarrow 0.3x+0.7y=30----(1)[/tex]

Also, sum of the final solution should be 60 liters only so, we get

[tex]x+y=60----(2)[/tex]

Solving equations (1) and (2), we get

[tex]x=30 liters\\ y=30 liters[/tex]

Hence, we can say that 30 liters of 30% solution and 30 liters of 70% of solution should be mixed by the researcher to get 60 liters of 50% solution.

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Divide total cost by quantity.

$36 / 4 = $9 per basketball

Answer:

800 different sets of digits.

Step-by-step explanation:

Since the first digit is a factor of 20, the factors of 20 are 1,2,4,5,10,20. We only need the single digit factors which are 1,2,4 and 5. These 4 numbers can be permuted in 1 way for the first digit, so we have ⁴P₁.

For the second digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and also for the third digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and for the last digit, which is divisible by 5, it is either a 0 or 5, so we have two digits permuted in 1 way, ²P₁.

So, the number of different 4 digit number that Zara'2 4-digit PIN code could be is ⁴P₁ × ¹⁰P₁ × ¹⁰P₁ × ²P₁ = 4 × 10 × 10 × 2 = 800 different sets of digits

800 different sets of 4 digit PIN could be made.

So, ways of choosing 1 out of 4 digits = 4 P 1 = 4

So, ways of choosing 1 out of 10 digits = 10 P 1 = 10

So, ways of choosing 1 out of 10 digits = 10 P 1 = 10

So, ways of choosing 1 out of 2 digits = 2 P 1 = 2

Hence, total number of ways = 4 x 10 x 10 x 2 = 800 ways

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Answer:

In general, a relationship f (x) = y is a function only if, for each value of x that you plug into it, you get only one value for y.

Step-by-step explanation:

Sometimes the only way to tell if a given relationship is a function or not is to try various values for x to see if they yield unique values for y.

Answer:

Option (1)

Step-by-step explanation:

Lines given in the graph represent the piecewise function,

We will find the domain of the given pieces in each quadrant of the graph.

For a line in quadrant 2,

Domain (set of x-values) → [-4, -2]

For second line in the same quadrant,

Domain : [-1, 0]

For a line in quadrant 4,

Domain : [1, 3]

Therefore, Option (1) is the correct option,

Option (1). 1 ≤ x ≤ 3

Answer:

When we have a rectangle of width W and length L, the area of this rectangle can be calculated as:

A = W*L

In this case we have:

W = x

L = 10/x.

Then the area of the rectangle will be:

A = W*L = x*(10/x) = 10

So the value of x cancels in the equation, which means that we can not find the value of x.

Now, as L = 10/x we can find some restrictions:

if x = 0, we would have L = 10/0

So we can not have x = 0.

And as W = x, this represents a positive measure, we also have that x can not be a negative number.

So the relation:

W = x

L = 10/x

Gives us all the possible combinations of width and length such that the area of the rectangle is exactly 10 square units.

Answer:

third graph

Step-by-step explanation:

Answer: Same will get $4800

Step-by-step explanation:

If Sam will get 4 times the amount of money they will give Max then we can come up with the equation  s = 4m    where s is the amount that same get and m is the amount that Max will get.

And we know that if they combine their money they will have $6000 in total so we can also come up the equation s + m = 6000  

So using the equation

s= 4m  and s+m=6000  substitute the value of x into the second equation and sole for m ..

4m + m = 6000

5m = 6000

m =  1200

So we know that Max will get $1200 and Sam will get 4 times as much as that.

s= 4(1200)

s = 4800