PLEASE HELP EASY MATH

Tomas needs lumber to make corner braces for a piece of furniture he is building. He cuts 4 feet from a board that is 8 feet long. With the wood he has left, Tomas makes 18 corner braces of equal size.
How many inches of wood does each brace use? - in​

Answer(s):

[tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2 \\ y = 3cos\: 1\frac{1}{2}x - 2[/tex]

Explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{3}} \hookrightarrow \frac{-\frac{\pi}{2}}{1\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\: 1\frac{1}{2}x - 2,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{pi}{3}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle \frac{\pi}{3}\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{3}} = \frac{-\frac{\pi}{2}}{1\frac{1}{2}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 1],[/tex] from there to [tex]\displaystyle [1\frac{1}{3}\pi, 1],[/tex] they are obviously [tex]\displaystyle 1\frac{1}{3}\pi\:unit[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 1\frac{1}{3}\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -2,[/tex] in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts horisontally, the midline will ALWAYS follow.

I am delighted to assist you at any time.

9514 1404 393

Answer:

  3x^4 +x^3 +3x^2 -18x +4

Step-by-step explanation:

The multiplication is done the same way as "long multiplication" with numbers. Each partial product is placed in the column corresponding to its "place value" (the degree of the variable). The only difference from numerical multiplication is that the sums of the partial products have no carry into any column with a different "place value".

Answer:

29

Step-by-step explanation:

plug in 5 where x is.

so

4(5)^2-16(5)+9=

which equals 29

SEE IMAGE BELOW:)

1.) The answers:

A) BME

B) MER

C) Mm

D) xBy

E) Straight

F) REB

G) MEB and BER

H) xBy

Answer:

circumference= 32.56

area= 44.18

Step-by-step explanation:

for area: (A=pi×r^2) your diameter is 7.5 so you divide that by 2 to get your radius. and the radius is 3.75. then you are going to do 3.75^2 to get 14.1 then you are going to multiply 14.1 by pi to get 44.18

for circumference: (2×pi×r) you are going to take the same radius for the area and simply multiply that by pi (3.14) to get 11.78, then you are going to multiply 11.78×2 and that equals 23.56

Answer:

[tex]Varianve = 3.842[/tex]

[tex]SD = 1.960[/tex]

Step-by-step explanation:

Given

See attachment for data

First, calculate [tex]\sum x^2[/tex]

[tex]\sum x^2 = 18^2 + 17^2 +20^2 + 19^2 + 20^2 + 16^2 + 16^2 + 15^2 + 18^2+14^2 +19^2 + 19^2+18^2+17^2 + 16^2+20^2+16^2+18^2+14^2+20^2[/tex]

[tex]\sum x^2 = 6198[/tex]

Calculate [tex]\sum x[/tex]

[tex]\sum x = 18 + 17 +20 + 19 + 20 + 16 + 16 + 15 + 18+14 +19 + 19+18+17 + 16+20+16+18+14+20[/tex]

[tex]\sum x = 350[/tex]

So, we have:

[tex]SS_x = \sum x^2 -\frac{(\sum x)^2}{n}[/tex]

[tex]SS_x = 6198 -\frac{350^2}{20}[/tex]

[tex]SS_x = 6198 -\frac{122500}{20}[/tex]

[tex]SS_x = 6198 -6125[/tex]

[tex]SS_x = 73[/tex]

Solving (a): The variance

[tex]Varianve = \frac{SS_x}{n-1}[/tex]

[tex]Varianve = \frac{73}{20-1}[/tex]

[tex]Varianve = \frac{73}{19}[/tex]

[tex]Varianve = 3.842[/tex]

Solving (b): The standard deviation

[tex]SD = \sqrt{Variance}[/tex]

[tex]SD = \sqrt{3.842}[/tex]

[tex]SD = 1.960[/tex]

Answer:

21 cookies

Step-by-step explanation:

First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28

So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.

Chris ate 21 cookies.

Hope this helped!

Answer:

21 cookies

Step-by-step explanation:

1/3 × 84 = 28

3/4 × 28 = 21

Answer:system of linear equalities in one variable .

Step-by-step explanation:

Answer:

x = 29

Step-by-step explanation:

[tex]x+(-21)=8[/tex]

[tex]29+(-21)=8[/tex]      

[tex]29-21=8[/tex]

[tex]x=29[/tex]

9514 1404 393

Answer:

  35

Step-by-step explanation:

The 16 onion bagels are twice as many as plain bagels, so there were 8 plain bagels.

There were 4 more sesame bagels than plain bagels, so there were 12 sesame bagels.

Adam has 8 plain, 12 sesame, and 15 onion bagels left, for a total of 35 bagels left.

Answer:

Line 3 is incorrect; we don't know anything about the lengths of HG, FG, HE, and EF, so this line is not valid based on the given information.

Step-by-step explanation:

In the Noah's poof of the construction, segment EG would divide angle FGH into two equal parts, which makes line 2 to be valid. i.e <EGH ≅ <EGF. And it can also be observed that line 4 is a valid theorem in proving the congruent nature of triangles.

But line 3 is not valid because of the condition of the statement. Furthermore, segments FG, EG, HG, HE and FE may not be congruent. Thus, the condition of the statement in line 3 is incorrect.

i don't think this is complete question there isn't value for x

Answer:

85x−12

Step-by-step explanation:

y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)

Step-by-step explanation:

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {A. \:-39}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \sqrt[5]{x + 7} = - 2[/tex]

➺[tex] \: x + 7 =( { - 2})^{5} [/tex]

➺[tex] \: x + 7 = ( - 2 \times - 2 \times - 2 \times - 2 \times - 2)[/tex]

➺[tex] \: x + 7 = - 32[/tex]

➺[tex] \: x = - 32 - 7[/tex]

➺[tex] \: x = - 39[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex] \sqrt[5]{x + 7} = - 2 \\\\ ➼ \: \sqrt[5]{ - 39 + 7} = - 2 \\ \\➼ \: \sqrt[5]{ - 32} = - 2 \\\\ ➼ \: \sqrt[5]{ - 2 \times - 2 \times - 2 \times - 2 \times - 2} = - 2\\ \\ ➼ \: \sqrt[5]{( { - 2})^{5} } = - 2\\ \\ ➼ \: - 2 = - 2 \\\\ ➼ \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning. }}{\orange{❦}}}}}[/tex]

The solution of the given equation would be; x = -39.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

WE have been given an equation as,

[tex]\sqrt[5]{x+7} = -2[/tex]

WE need to find the solution of the given equation which can be calculated as;

[tex]\sqrt[5]{x+7} = -2[/tex]

First raise both sides to the power 5;

[tex](\sqrt[5]{x+7} )^5= -2^5[/tex]

Now x + 7 = - 32

subtract 7 from both sides, we get;

x = - 39  

Hence, the  solution of the given equation would be; x = -39.

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Answer:

1. [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. 18

b. -12

2. nth = a + (n - 1)d

ii. k = 103

3. [tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume = 25.025 [tex]m^{3}[/tex]

Step-by-step explanation:

1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

                                       = [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. [tex]\sqrt[3]{5832}[/tex] = 18

b. 2[tex]a^{2}[/tex] - 3[tex]b^{2}[/tex] + 3abc

a = 3, b = 2, c = -1

Thus,

2[tex](3)^{2}[/tex] - 3[tex](2)^{2}[/tex] + 3(3 x 2 x -1)

= 18 - 12 - 18

= -12

2. The required formula is;

nth = a + (n - 1)d

where: a is the first term, n is the number of terms in the sequence and d is the common difference.

b. kth term = 304, then

304 = -2 + (k - 1) 3

      = -2 + 3k -3

      = 3k - 5

3k = 304 + 5

3k =  309

k = [tex]\frac{309}{3}[/tex]

  = 103

k = 103

3. Comparing <DAB and < EBC;

<DAB ≅ <EBC = [tex]x^{o}[/tex]

<BEC = [tex]90^{o}[/tex] (right angle property)

<C = [tex]63^{o}[/tex]

Thus,

<B + <C + <E = [tex]180^{o}[/tex] (sum of angles in a triangle)

[tex]x^{o}[/tex] + [tex]63^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] + 153 = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] = 180 - 153

   = 27

[tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius and h is the height of the cylinder.

Diameter = 3.5 m, h = 2.6 m

r = [tex]\frac{3.5}{2}[/tex]

r = [tex]\frac{7}{4}[/tex] m

So that,

Volume = [tex]\frac{22}{7}[/tex] x [tex](\frac{7}{4}) ^{2}[/tex] x 2.6

             = [tex]\frac{22}{7}[/tex] x [tex]\frac{49}{16}[/tex] x [tex]\frac{13}{5}[/tex]

             = 25[tex]\frac{1}{40}[/tex]

Volume = 25.025 [tex]m^{3}[/tex]

Answer:

It's on the negative side, so make sure you put -2.25. But yes, it's right.

Answer:

The distance of the run was 27 miles and the distance of the bicycle race was 88 miles.

Step-by-step explanation:

Since I have entered 115-mile biathlon that consists of a run and a bicycle race, and during my run, my average velocity is 9 miles per hour, and during my bicycle race, my average velocity is 22 miles per hour , and I finish the race in 7 hours, to determine what is the distance of the run and what is the distance of the bicycle race, the following calculations must be performed:

7 x 22 + 0 x 9 = 154

5 x 22 + 2 x 9 = 128

4 x 22 + 3 x 9 = 115

Therefore, the distance of the run was 27 miles and the distance of the bicycle race was 88 miles.

The fourth term of the given expansion is [tex]-280x^{3}[/tex].

The binomial expansion is used to expand and write the terms which are equals to the natural number exponent of the sum or differences of two terms.

[tex]T_{r+1} =nC_{r} x^{n-r} y^{r}[/tex]

According to the given question

We have,

A binomial expression, [tex](1-2x)^{n}[/tex]

and, the binomial coefficients are taken from the row of Pascal's triangle 1  6  15  20  15  6  1

⇒ n = 7

Therefore,

The fourth term of the expansion of [tex](1-2x)^{n}[/tex] is given by

[tex]T_{3+1} = 7C_{3} 1^{7-3} (-2x)^{3}[/tex]

[tex]T_{4} =\frac{(7)(6)(5)(4)(3!)}{3!(4)(3)(2)} (1)(-2x)^{3}[/tex]

[tex]T{4} = -280x^{3}[/tex]

Hence, the fourth term of the given expansion [tex](1-2x)^{3}[/tex] is [tex]-280x^{3}[/tex].

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Answer:

[tex]2/3[/tex]

Step-by-step explanation:

The total number of sums (not distinct) is [tex]4\cdot 3=12[/tex], because we're removing without replacement.

Count the sums that fit the stipulation (sum [tex]\leq[/tex] 5):

[tex]1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2[/tex]

There are 8 sums that work. Therefore, the desired answer is [tex]\frac{8}{12}=\boxed{\frac{2}{3}}[/tex]

Answer:

Step-by-step explanation:

17.

18.

f(x)=6x^2+7x-4

(a)

f(3)=6(3)^2+7(3)-4

=54+21-4

=71

(b)

f(m)=6m^2+7m-4

(c)

f(x+1)=6(x+1)²+7(x+1)-4

=6(x²+2x+1)+7x+7-4

=12x²+12x+6+7x+7-4

=12x²+19x+9

19.

(fg)(x)=f(g(x)=f(2x²+3)=2x²+3+5=2x²+8

20.

(a)

f(x)=x²+3x+4

domain:all real values

(b)

domain:all real values≥-2

(c)f(x)=log(x+7)

Domain:x≥-7

21.

x²+6x+y²-7=0

(x²+6x+6/2)²)-(6/2)²+y²=7

(x+3)²+y²=7+9

(x+3)²+y²=4²

center=(-3,0)

radius=4

22.

(x-3)²+(y-5)²=3²

or

x²-6x+9+y²-10y+25=9

x²+y²-6x-10y+25=0

Graph is for 17th question.

Answer:

Scuse me what the flip

Answer:

Step-by-step explanation:

Soooo, angle 1 is 157 degrees

That means:

Angle 2 is 23 degrees                                   Supplementary Angles

Angle 3 is 157 degrees                                  Vertical Angle to Angle 1

Angle 4 is 23 degrees                                   Vertical angle to Angle 2

Answers:

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

Explanation:

Angles 1 and 2 are supplementary as they form a straight line. So the angles add to 180

(angle1)+(angle2) = 180

angle2 = 180-(angle1)

angle2 = 180-157

angle2 = 23 degrees

Angle 4 is congruent to this because angles 2 and 4 are vertical angles. Vertical angles are always congruent. Note how angles 1 and 4 are supplementary.  

Since angles 1 and 3 are the other pair of vertical angles, this must mean angle 3 is 157 degrees.

Answer:

The pie chart is best because pie charts are a good way to portray percentage based data.

Step-by-step explanation:

Pie charts are used for graphical representation of data. The data can be shown in percentages or numbers. It is easy for the user to understand the data in the pie chart because it clearly represents the data in circular graphical form.

Answer:

291870 kilotons

Step-by-step explanation:

Since the country cuts its carbon content by 1.1% each year. The initial value at the first year is 50000. Therefore this can be represented by the exponential function:

y = a(b)ˣ ⁻ ¹

where y is the amount of carbon emission in kilotons in x years.

a = 50000, b = 100% - 1.1% = 98.9% = 0.989

y = 50000(0.989)ˣ ⁻ ¹

In the first year: y = 50000(0.989)¹ ⁻ ¹ = 50000

In the second year: y = 50000(0.989)² ⁻ ¹ = 49450

In the third year: y = 50000(0.989)³ ⁻ ¹ = 48906

In the fourth year: y = 50000(0.989)⁴ ⁻ ¹ = 48368

In the fifth year: y = 50000(0.989)⁵ ⁻ ¹ = 47836

In the sixth year: y = 50000(0.989)¹ ⁻ ¹ = 47310

The total emission in 6 years = 50000 + 49450 + 48906 + 48368 + 47836 + 47310 = 291870 kilotons

Answer:

The second answer

Y=X³-4X²+2X

Y=0

The system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation.

Given is an equation, 4x² = x³+2x, we need to identify the system of equations can be used to find the roots of this,

An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.

See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.

The attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.

The intersection point is (0,0) meaning that the solution is x = 0, y = 0.

Hence, the system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x

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Answer:

a = 14

b = 24

c = 24.9

A = 33.2 degrees

B = 70 degrees

C = 76.8 degrees

Step-by-step explanation:

a/sin(A) = b/sin(B) = c/sin(C)

14/sin(A) = 24/sin(70)

sin(A)×24 = sin(70)×14

sin(A) = sin(70)× 14/24 = sin(70) × 7/12 = 0.548154029...

A = asin(0.548154029...) = 33.240464... degrees

the sum of all angles in a triangle is airways 180 degrees.

C = 180 - 70 - 33.240464... = 76.75954... degrees

24/sin(70) = c/sin(76.75954...)

c = 24×sin(76.75954...)/sin(70) = 24.86133969...