mike is looking at the roof of a new house from the front. he notices that the roof is triangular in shape with a base 11.2m. the left side is 6.7m long and makes an angle of 72 degree with the base of the roof. if this is the only known information, determine the angle the right side of the roof makes with the base of the roof to the nearest degree. be sure to first make a sketch

Answer:

Step-by-step explanation:

The formula to find the angle between 2 vectors is

[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is

u·v = (2×(-6)) + (a×8) so

u·v = -12 + 8a. Then we need the magnitudes of both u and v:

[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and

[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]

Putting all of together looks like this:

[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get

[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is

[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:

100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get

800 + 200a² = 256a² -768a + 576. Combine like terms to come up with

0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.

Therefore, the value for a is 14. I checked it...it works

Answer:

a = 14, U = (2, 14)

Step-by-step explanation:

the other answer is correct.

just to add the solution path for the quadratic equation

0 = 56a² - 768a - 224

in general, a quadratic equation usually expressed in x

0 = ax² + bx + c

has its solution as

x = (-b ± sqrt(b² - 4ac))/(2a)

for us here this looks like this then

a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =

= (768 ± sqrt(589824 + 4×56×224))/112 =

= (768 ± sqrt(589824 + 50176))/112 =

= (768 ± sqrt(640000))/112 = (768 ± 800)/112

a1 = (768 + 800)/112 = 1568/112 = 14

a2 = (768 - 800)/112 = -32/112 = -0.29

and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.

so, 14 is the solution for U.

Answer:

24 per day

Step-by-step explanation:

'x' = days, so since 24 is with x, the rate of change is 24

Answer:

1960 dancers

Step-by-step explanation:

your are on "ace" level and need help here ?

a pair is 2 people

4 pairs is therefore 4×2 people = 8

245 teams of 4 pairs or 8 people each means

245×8 = 1960 people

Answer:

Step-by-step explanation:

The element decay percentage rate of change 2.22% per minute.

Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.

Here, mass decreases by 73% every hour.

Weight of element X is 680 grams.

According to question,

f(t) = 680 (1 - 73%)ⁿ

f(t) = 680 (1 - 0.73)ⁿ

f(t) = 680 X 0.27ⁿ

f(t) = 680 X 0.9778ⁿ

f(t) = 680 X (1 - 0.02322)ⁿ

Thus, the element decay percentage rate of change 2.22% per minute.

Learn more about radioactive isotope from:

https://brainly.com/question/1907960

#SPJ2

Answer:

42g

Step-by-step explanation:

70% of 60 = 42

right triangle

Hope this helps! :)

Answer:

No entiendo

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

are you in elementary school

Answer:

8 staff

Step-by-step explanation:

6 +2 = 8 There are 8 staff working there.

If this is done a different way explain or lmk? Hope you are having a wonderful day!! Of not it'll get better I promisee! <33 :))

Answer:

Step-by-step explanation:

[tex]81^{1/2}[/tex]

[tex]3^4*{1/2}[/tex]

[tex]3^{4/2}[/tex]

[tex]3^{2}[/tex]

9

[tex]-16^{3/4}[/tex]

[tex](-2)^{4 *3/4}[/tex]

[tex](-2)^{12/4}[/tex]

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

-8

Answer:

Step-by-step explanation:

A customer satisfaction survey refers to a questionnaire that's designed by a company in order for businesses to know what customers think about their products.

Since the manager of a local car dealership wants to conduct a customer satisfaction survey, then the group of people should make up a sample of the population will be the people who bought cars from the dealership

Answer:

c

Step-by-step explanation:

Answer:

(-3,2)

Step-by-step explanation: The bottom most point of the graph is 3 back from 0 and 2 up from 0

Answer: 0.973

Step-by-step explanation:

The probability mass function of geometric distribution is

[tex]f(x)=(1-p)^{x-1}p,\ \ \ x=1,2,3,...[/tex], p= probability of success on a trial.

As per given, we have

p=0.7

The probability that we'll have at most 3 orders [tex]P(X\leq3)=P(x=1)+P(x=2)+P(x=3)[/tex]

[tex]=(1-0.7)^{1-1}(0.7)+(1-0.7)^{2-1}(0.7)+(1-0.7)^{3-1}(0.7)\\\\=0.7+0.21+0.063\\\\=0.973[/tex]

hence, the required probability = 0.973

The probability that we'll have at most 3 orders will be "0.973".

According to the question,

→ [tex]x \sim Geometric (p)[/tex]

here,

p = 0.7

then,

→ [tex]P(X=x) = (1-p)^{x-1}\times p[/tex]

By putting the given values, we get

                   [tex]= (1-0.7)^{x-1}\times 0.7[/tex]

hence,

The probability that we'll have at most 3 orders will be:

→ [tex]P(X \leq 3)=P(X=1)+P(X=2)+P(X=3)[/tex]

                   [tex]=0.7+0.21+0.063[/tex]

                   [tex]=0.973[/tex]

Thus the above response is correct.

Learn more about probability here:

https://brainly.com/question/6981569

Answer:

334.4 m²

Step-by-step explanation:

The formula for the area of a sector is given as:

1/2 × r² × θ

Where θ = Central angle

Area of a Circle = 700 m²

The formula for the area of a circle = πr²

r = Radius of a circle

r² = Area / π

r = √Area / π

r = √700/π

r = 14.927053304 m

Approximately, r = 14.93 m

Therefore, the area of the sector

= 1/2 × r² × θ

= 1/2 × 14.93² × 3 rad

= 334.35735 m²

Approximately, Area of the sector = 334.4 m²

Answer:

11

Step-by-step explanation:

3/7*14=6

5/8*8=5

6+5=11

Answer:

31/5 as a mixed number: 6 and 1/5

-73/8 as a mixed number:-9 and 1/8

Step-by-step explanation:

Rewriting each mixed number as a sum of two signed numbers 3 1/5  and -7 3/8 are 3 and 1/5  and -8 and 5/8 respectively

The mixed number to rewrite as a sum of two signed numbers are as follows:

Rewriting as a sum of the two signed numbers can be represented as follows;

3 1/5 = 16 / 5

-7 3/ 8 = - 59 / 8

Therefore,

3 1/5  will be 3 and 1/5

-7 3/ 8 will be -8 and 5/8

Note

3 + 1/5 = 3 1/5

-8 + 5/8 = -7 3/8

learn more on fraction here: https://brainly.com/question/24645582

Answer:

3/10.

Step-by-step explanation:

The 3 men will be on the numerator, to signify they're the group we're focusing on.

Then you add all of the people together (7 + 3 = 10) and put that on the denominator.

therefore, you get 3/10.

The probability of a man getting the job for the post of HR Manager is 3/10.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

We know, The ratio of favorable events to unfavorable events for a given event is known as the odds in favor.

Given, Three men and seven women have been shortlisted for the post of HR Manager.

Therefore, The probability  of a man getting the job is,

= (3/(3 + 7)).

= 3/10.

learn more about probability here :

https://brainly.com/question/743546

#SPJ2

Answer:

B

Step-by-step explanation:

Slope Formula

6 - (-2) / 3 - 1

8 / 2 = 4

The slope of the graph is 4.

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The coordinates from the graph are:

(1, -2), and (3, 6)

Now,

Slope.

= (6 -(-2)) / (3 - 1)

= (6 + 2) / 2

= 8/2

= 4

Thus,

The slope of the graph is 4.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ5

Answer:

Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%

Step-by-step explanation:

We are given that

Population was Caucasian=64%

Population was African-American=11%

Population was Hispanic=10%

Let the population of U.S=10000

Now,

Population was Caucasian=[tex]\frac{64}{100}\times10000=6400[/tex]

Population was African-American=[tex]\frac{11}{100}\times 10000=1100[/tex]

Population was Hispanic=[tex]\frac{10}{100}\times 10000=1000[/tex]

Population of others=10000-(6400+1100+1000)=1500

Population of Caucasians used the Internet for e-mail=86% of 6400

Population of Caucasians used the Internet for e-mail=[tex]\frac{86}{100}\times 6400[/tex]

Population of Caucasians used the Internet for e-mail=5504

Population of African-American used the Internet for e-mail=77% of 1100

Population of African-American used the Internet for e-mail=[tex]\frac{77}{100}\times 1100=847[/tex]

Population of Hispanics used the Internet for e-mail=77% of 1000

Population of Hispanics used the Internet for e-mail=[tex]\frac{77}{100}\times 1000=770[/tex]

Population of others used the Internet for e-mail=84% of 1500

Population of others used the Internet for e-mail=[tex]\frac{84}{100}\times 1500=1260[/tex]

Total population used the Internet for e-mail=5504+847+770+1260

Total population used the Internet for e-mail=8381

Percentage of U.S resident who used the Internet for e-mail were Hispanic

=[tex]\frac{Population \;of \;Hispanics \;used \;the \;Internet \;for \;e-mail}{total\;population\; used \;the \;Internet \;for\; e-mail}\times 100[/tex]

Percentage of U.S resident who used the Internet for e-mail were Hispanic=[tex]\frac{770}{8381}\times 100[/tex]

Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%

Answer:

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Step-by-step explanation:

[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]

[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]

[tex] {x}^{2} (x+2)+12(x+2)[/tex]

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Answer:

its c my dude

Step-by-step explanation:

....................

answer is c because that is right plz brainliest and like plz

Answer:

x = 6.9

Step-by-step explanation:

[tex]\frac{sin(90)}{12} = \frac{sin(35)}{x} \\\\x = 6.9[/tex]solve for x

Answer:

She must buy more than 5 lbs

Step-by-step explanation:

First write the inequality

cost per pound * number of pounds >  total cost

8 * lbs > 40

Divide each side by 8

8 lbs /8 > 40/8

lbs > 5

She must buy more than 5 lbs

Answer:

Cannot be factored

Step-by-step explanation:

Given

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]

Required

Factorize

Take LCM

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]

The expression cannot be factored

Y = 20

X = 70

We know Y is 20 because both triangles are the same size. 20 is in the opposite corner to Y. The right corner is 90 degrees. There are 180 degrees in a triangle. To get your answer you are going to add 20 and 90 to get 110 then you will subtract 110 from 180.

[tex]\longrightarrow{\green{A.\:-8}}[/tex] ✔

Step-by-step explanation:

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

Plugging in the value "[tex]x\:=\:-3[/tex]" in the above expression, we have

[tex]f( - 3) = - ({ - 3})^{2} + 1 \\ \\ = - ( - 3 \times - 3) + 1 \\ \\ = - (9) + 1 \\ \\ = - 9 + 1 \\ \\ = - 8[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

[tex] \quad \quad \quad \quad \tt{f(x) = { - x}^{2} + 1} \: \: when \: \: x = - 3[/tex]

[tex] \quad \quad \quad \quad \tt{ ⟶f(x) = { - x}^{2} + 1}[/tex]

[tex] \quad \quad \quad \quad \tt{⟶f(-3) = {- (-3)}^{2} + 1}[/tex]

[tex] \quad \quad \quad \quad \tt{⟶ f( - 3) = { - (9) + 1}}[/tex]

[tex]\quad \quad \quad \quad \tt{⟶ f( - 3) = { - 9 + 1}}[/tex]

[tex]\quad \quad \quad \quad \tt{ ⟶f( - 3) = { -8}}[/tex]

[tex]\quad \quad \quad \quad \boxed{\tt{ \color{green}f( - 3) = { - 8}}}[/tex]

_________

#LetsStudy

Answer:

both apply

Step-by-step explanation:

i guessed just do it

Answer:

[tex]V_c=452.16\ mm^3[/tex]

Step-by-step explanation:

Given that,

The volume of a sphere is 904.32 mm³.

The volume of a cone that has the same height and circular base with the same diameter is:

[tex]V_c=\dfrac{1}{3}\pi r^2 \times 2r=\dfrac{2}{3}\pi r^3[/tex]

The volume of a sphere with the same radius is:

[tex]V_s=\dfrac{4}{3}\pi r^3=2\times \dfrac{2}{3}\pi r^3[/tex]

So, the volume of sphere is :

[tex]V_c=\dfrac{V_s}{2}\\\\V_c=\dfrac{904.32 }{2}\\\\V_c=452.16\ mm^3[/tex]

So, the volume of the cone is [tex]452.16\ mm^3[/tex].

Answer:

0.5

Step-by-step explanation:

Wanted outcome / possible outcomes = 0.5 in this case.

Answer:

44.94

Step-by-step explanation:

Answer:

C) 5.66

Step-by-step explanation:

For a 45-45-90 triangle, the length of each leg length (not including the hypotenuse) is congruent to each other. If 8=y√2, then y=8/√2=4√2=5.66

Answer:

5.66

Step-by-step explanation:

take 45 degree as reference angle

using cos rule

cos 45 =adjacent /hypotenuse

[tex]\frac{1}{\sqrt{2} }[/tex] =y/8

[tex]\frac{1}{\sqrt{2} } *8=y[/tex]

[tex]\frac{8}{\sqrt{2} }=y[/tex]

[tex]4\sqrt{2} =y[/tex]

5.66=y