Answers
Answer:
x = 27
Step-by-step explanation:
I'm going to use letters to label the parts of the triangle while explaining how to solve for x:
Angle A = x (bottom left angle of the triangle)
Angle B = 4x (top angle of the triangle)
Angle C = empty angle (bottom right angle of the triangle)
Angle D = 3x + 54 (angle outside of the triangle)
A line has a angle measurement of 180 degrees.
Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.
To find Angle C, we would subtract Angle D's equation from 180 like this:
180 - (3x + 54)
Now Angle C equals 180 - (3x + 54)
Now we have all the angles inside the triangle. To find x, we are going to sum up Angle A, B, & C and set it equal to 180.
We set the equation to 180 because a the sum of the interior angles for a triangle is 180.
The equation looks like this:
(180 - (3x + 54)) + 4x + x = 180
Now we use basic algebra to solve it:
(180 - (3x + 54)) + 4x + x = 180
(distribute the - to (3x + 54))
180 - 3x - 54 + 4x + x = 180
(add like terms on the left side of the equation)
126 + 2x = 180
(subtract 126 from both sides)
2x = 54
(divide both sides by 2)
x = 27
To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.
Hope it helps (●'◡'●)
Related Questions
Find the answer to each trigonometric function below.
Answers
Answer:
Sin A = [tex]\frac{opposite}{hypotenuse} =\frac{32}{40} =\frac{4(8)}{5(8)} =\frac{4}{5}[/tex]Cos C = [tex]\frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{2(8)}{2(17)} =\frac{8}{17}[/tex]Tan A = [tex]\frac{opposite}{adjacent} =\frac{21}{20}[/tex]WORTH 25 POINTS!!!!!! PLS PLS PLS PLS PLS PLS PLS HELP I DON'T GET IT!!! Write missing monomials to make an identity:
A) (.....+2a)^2=.....+12ab+4*....
B) (3x+.....)^2=....*x^2+.....+49y^2
Answers
Answer:
(3x + 7y)^2 = 9 x^2 + 42xy + 49y^2
Step-by-step explanation:
el jefe decidió agregar la tabla de frecuencias correspondiente a la edad de sus empleados tal Como se muestra a continuación Cuál es el promedio de edad de los empleados de la empresa
Answers
Answer:
Average employee [Mean] = 43.6
Step-by-step explanation:
Given:
Interval Number of employee
25-35 20
35-45 7
45-55 8
55-65 15
Total 50
Find:
Average employee [Mean]
Computation:
Interval X[u+l]/2 Number of employee fx
25-35 30 20 600
35-45 40 7 280
45-55 50 8 400
55-65 60 15 900
Total 50 2,180
Average employee [Mean] = Sum of fx / Sum of x
Average employee [Mean] = 2,180 / 50
Average employee [Mean] = 43.6
Answer:
aeaaa
Step-by-step explanation:
Two times the difference of a number and ten is forty two
Write an equation to represent the sentence:
Answers
Answer:
let the number be x
representing the equation...
it will be....
2 times (the number- 10)=42
2 times(x-10)= 42
2(x-10)=42
Suppose that the natural rate of unemployment in a particular year is 4 percent and the actual unemployment rate is 13 percent. Instructions: Enter your answers as a whole number. a. Use Okun's law to determine the size of the GDP gap in percentage-point terms. percent b. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment? $ billion
Answers
Answer:
a. 18 percent
b. $90 billion
Step-by-step explanation:
a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.
First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment
Difference=13%-4%
Difference= 9%
Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.
Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).
Therefore the the size of the GDP gap in percentage-point terms is 18 percent
b. Calculation to determine how much output is forgone because of cyclical unemployment
Forgone Output :
By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,
Hence,
Output forgone = (18/100) ×$500 billion
Output forgone=0.18×$500 billion
Output forgone=$90 billion
Therefore the Forgone Output is $90 billion
Which of the following are exterior angles?
Answers
Answer:
3,4
Step-by-step explanation:
Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is
16
inches shorter than
1
1
2
times Theresa’s height. Steve says he is
6
inches shorter than
1
1
3
times Theresa’s height. If they are both right, how tall is Theresa?
Answers
Answer:
From given, we have,
Paul says he is 16 inches shorter than 1 1/2 times Theresa's height.
Steve says he's 6 inches shorter than 1 1/3 times Theresa's height.
Let the height of Theresa be "x" inches.
So, we get,
For Paul, 1 1/2 x - 16 = T
⇒ 3/2 x - 16 = T ......(1)
For Steve, 1 1/3 x - 6 = T
⇒ 4/3 x - 6 = T .........(2)
equating equations (1) and (2), we get,
3/2 x - 16 = 4/3 x - 6
6 - 16 = 4/3 x - 3/2 x
-10 = (8 - 9)/6 x
-60 = -x
x = 60 inches.
Therefore, Theresa is 60 inches tall.
at the farmers market 8 apple cost $5.20 if each apple cost the samw amount what is the price per apple
Answers
[tex]\displaystyle\bf Solve:8\times p=5,2 \$ => p=\frac{5,2}{8} =\frac{5,2:\boxed{8}}{8:\boxed{8}} =0,65\$\quad She \:unit\: cost\:is\:\underline{ 0,65} \\\\Check :\:8\times\underline{0,65} =5,2\$ \\\\0,65=0,65 \\\\\rightarrow The\: price\:per \:apple \:is \: 0,65 \$[/tex]
The center of the circle is at the point
, and its radius is
units. The equation of this circle in standard form is
.
Answers
You sunk my battleship...The hms petticoat and uss junction are being monitored on a tracking screen where each ship is measured in millimeters from the lower left corner. The linear path of the hms petticoat is given by y=2x+50. If x=3t, express y as a function of t minutes
Answers
Answer:
y = f(t) = 6t + 50
Step-by-step explanation:
Given:
y = 2x + 50
Where,
x = 3t
Substitute x = 3t into the equation
y = 2x + 50
y = 2(3t) + 50
Open parenthesis
y = 6t + 50
y = f(t) = 6t + 50
Plz help me.
I WILL GIVE BRAINLY
Answers
Answer:
p = T - a - b
Step-by-step explanation:
T = a + p + b
p = T - a - b
what is the range of this function 6 goes to 5 8 goes to -3 10goes to -8 and 12 goes to 7
a.(-3,7,8,12)
b.(-8,-3,5,6,7,8,10,12)
c.(-8,-3,5,7)
d.(6,8,10,12)
Answers
Answer:
C, {-8, -3, 5, 7}
Step-by-step explanation:
the range = the y-coordinates
i hope this helps you
given the polynomial : (3x+4)^5. find the coefficient of x³ !
Answers
Answer:
[tex] \displaystyle 4320 {x }^{3} [/tex]
Step-by-step explanation:
to solve binomials like this there's a way called binomial theorem given by
[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
but for this question we need the following part
[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]
from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute
[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]
simplify which yields:
[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]
and we are done!
find the volume of the cylinder in terms of pi and to the nearest tenth
Answers
Answer:
100π
Step-by-step explanation:
Before we even begin solving for the volume we should note that the question says to find the volume of the cylinder " in terms of pi". this means that if pi is present we do not apply it to our final answer and we just leave our answer as __pi
Having that being cleared let's find the volume
volume of a cylinder = πr²h
where r = radius and h = height
looking at the figure the cylinder has a known radius of 5in and a given height of 4in
so r = 5 and h = 4
that being said we want to plug in these given variables into the volume of a cylinder formula
V = πr²h
r = 5 and h = 4
V = π5²4
5²=25
25(4)=100
V = 100π
once again we must leave our answer in terms of pi so the final answer would be 100π
3c(p-6)+4(p-6)= write the correct expression in factored form.
Answers
[tex]\tt\displaystyle\ 3c\underline{(p-6)}+4\underline{(p-6)}=(p-6)(3c+4)[/tex]
Heather wants to start a business. She has two products to sell, and knows it takes her a
different amount of time to make each. It takes her 1.5 hours to make each frame (f),
and 2.25 hours to make each canvas (c). She is planning to work for 40 hours on these
projects this week. Write the equation that represents this relationship.
Answers
Answer: 1.5f + 2.25c = 40
Step-by-step explanation:
You'd need to multiply the variables of unknown value (how many she'd make in 40 hours) by the time it takes to make one. This would mean multiplying 1.5 by f and 2.25 by c. you'd add this as together they equal the 40 hours she'd be working for the week.
the ratio of boys to girls is 4:3 .if there are 24boys ,how many are there?
Answers
Answer:
[tex]{ \bf{total \: ratio = 4 + 3 = 7}} \\ { \tt{let \: population \: be \: p}} \\ \frac{4}{7} \times p = 24 \\ 4p = 168 \\ p = 42 \\ { \bf{there \: are \: 42 \: people}}[/tex]
Boys to girls- 4:3
Boys and girls- 24 and x (let the girls be x)
4/3=24/x
=4x= 72
= x= 72/4
= x= 18 girls
Ans: There are 42 children (24+18)
plss answer someone the bottom question qracias
Answers
0.6(180) is the same as asking the question - What is 60% of 180?
To find that answer, we can multiply 0.6 by 180. We use the decimal 0.6 because that is the decimal form of 60%.
0.6 x 180 = 108
Another way we can find this answer is to find 1/10 of 180 and multiply this answer by 6 because 60/100 is the same thing as 6/10.
1/10 of 180 = 18
18 x 6 = 108
Hope this helps!
2.
B. Melody had $25 and withdrew $300 from his bank account. She bought a pair of trousers for $30.00, 2 shirts for
$19.00 each, and 2 pairs of shoes for $40.00 each. Give the final expression, and determine how much money Mel had
at the end of the shopping day.
Answers
Answer:
25 + 300 = 325
trousers: spent 30 (a pair of trousers = one unity of trousers)
shirts: spent 19 x 2 = 38
shoes: spent 40 x 2 = 80
80 + 38 + 30 = 148
325 - 148 = 177
She had $177,00 left.
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Question 2 Multiple Choice Worth 1 points)
(01.06 MC)
If D is the midpoint of AB and AB = 15, what is AD?
Answers
Answer:
If D is the midpoint of the segment AB, then we have to find the measure of segment AD. Therefore, AD = 7.5 units will be the answer.
hElP- please.
:) points!
Answers
what expression is equivalent to 96+18
Answers
Answer:
114
Step-by-step explanation:
114
What is the capacity of a rectangular tank calculated to the nearest litre? Length: 85cm Width: 65cm Height: 30cm
Answers
Answer:
Capacity of the rectangular tank in litres is 165.75l
Step-by-step explanation:
Volume of the tank
[tex] = lbh[/tex]
[tex] = 85 \times 65 \times 30[/tex]
[tex] = 165750 {cm}^{3} [/tex]
Capacity of the tank
[tex] = 165750ml[/tex]
[tex] = 165.75l[/tex]
in an isosceles triangle two sides are equal. the third side is 2 less than twice the length of the sum of the two sides. the perimeter is 40. what are the lengths of the 3 sides
Answers
Answer:
s for length of either equal side
b for the unequal side
b=-2+2*(s+s) and 2s+b=40
b=2*2s-2
b=4s-2
2s+4s-2=40
6s-2=40
6s=42
s=7
b=4*7-2
b=28-2
b=26
Please someone help!
solve for X
Answers
Answer:
x = 9
Step-by-step explanation:
The central angle is equal in measure to the arc that subtends it, that is
9x - 1 = 80 ( add 1 to both sides )
9x = 81 ( divide both sides by 9 )
x = 9
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^ p denote the proportion in the sample who say they support the increase. Suppose that 47% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
Answers
Answer:
The correct response is "0.0129".
Step-by-step explanation:
Given:
[tex]n=1500[/tex]
[tex]p=0.47[/tex]
[tex]np=1500\times 0.47[/tex]
[tex]=705[/tex]
[tex]nq=1500\times (1-0.47)[/tex]
[tex]=795[/tex]
Mean of sampling distribution will be:
[tex]\mu_\hat{p}[/tex] = [tex]0.47[/tex]
hence,
The standard deviation will be:
⇒ [tex]\sigma_\hat{p}[/tex] = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
By putting the values, we get
= [tex]\sqrt{\frac{0.47(1-0.47)}{1500} }[/tex]
= [tex]0.012886686[/tex]
= [tex]0.0129[/tex]
the quantity of the square of the sum of 4 times
x and 3, divided by the difference of x and 10
Answers
Answer:
Step-by-step explanation:
(4x+3)²÷(x-10)
=(16x²+24x+9)÷(x-10)
x-10) 16x²+24x+9 (16x+184
16x²-160x
- +
------------------
184x+9
184x-1840
- +
----------------
1849
----------------
Chứng minh a=(P.sinA/2)/(cosB/2.cosC/2)
Answers
Answer:
I can't understand your question friend.
The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.
Answers
Answer:
Solution given:
Since the given triangle is isosceles and right angled triangle
perpendicular [p]=base[b]=x
hypotenuse [h]=6
we have
by using Pythagoras law
p²+b²=h²
x²+x²=6²
2x²=36
x²=36/2
x²=18
x=[tex]\sqrt{18}[/tex]
x=[tex]\bold{3\sqrt{2}}[/tex]
The length of side x in simplest radical form with a rational denominator is [tex]3\sqrt{2}[/tex]
Let the perpendicular base be x.Given the following data:
Hypotenuse = 6 units.To determine the length of side x in simplest radical form with a rational denominator, we would apply Pythagorean's Theorem:
What is the Pythagorean Theorem?Mathematically, Pythagorean's Theorem is given by this formula:
[tex]c^2 = a^2 + b^2[/tex]
Substituting the given parameters into the formula, we have:
[tex]6^2 = x^2 + x^2\\\\36=2x^2\\\\18=x^2\\\\x=\sqrt{18} \\\\x=3\sqrt{2}[/tex]
Read more on Pythagorean Theorem here: https://brainly.com/question/16176867
If the equation to calculate the time it takes
your account balance to double is 72/6, what
is the interest rate of that investment?
Answers
Answer:
12%
Step-by-step explanation:
well when you get 72/6 and to make it into a easier full number/ (not a fraction) you get 12 then you put the % behind it and now you have 12%
