Answers
By using the fact that the interior angles of a triangle must add up to 180, we will see that the value of x is 15.
How to get the value of x?Here we have 3 expressions for the measures of the interior angles of a triangle.
Now, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write:
(8x - 7)° + (x + 7)° + (2x + 15)° = 180°
Ignoring the degrees and solving this for x, we get:
8x - 7 + x + 7 + 2x + 15 = 180
11x + 15 = 180
11x = 180 - 15 = 165
x = 165/11 =15
The value of x is 15.
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Related Questions
You cut a piece of wood that is 69 inches long. The wood is cut into 3 pieces. The second piece is 8 inches
longer than the first. The third piece is 8 inches longer than the second piece. Find the length of each of
the three pieces.
Answers
The length of piece one will be 15 inch, the length of piece two will be 23 inch and the length of third piece will be 31 inch as per the given conditions of "You cut a piece of wood that is 69 inches long. The wood is cut into 3 pieces. The second piece is 8 inches longer than the first. The third piece is 8 inches longer than the second piece."
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
What is equation?In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated statement that has been mathematically quantified.
Here,
according to the question,
x+y+z=69
y=x+8
z=y+8
z=x+16
3x+24=69
3x=45
x=15
y=23
z=31
According to the conditions specified, piece one will be 15 inches long, piece two will be 23 inches long, and piece three will be 31 inches long. "You chop a 69-inch-long piece of wood. Three pieces of the wood are cut out. Eight inches longer than the first piece is the second one. Eight inches longer than the second piece is the third one."
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The proof below shows that sin theta -sin^3 theta=sin2theta cos^2 theta/2cos theta
Answers
Given:
Given the steps of the proof of the equation
[tex]\sin\theta-\sin^3\theta=\frac{2\sin2\theta\cos^2\theta}{2\cos\theta}[/tex]Required: Expression missing on the thrd step
Explanation:
The second step is
[tex]\sin\theta-\sin^3\theta=\sin\theta(1-\sin^2\theta)\frac{2\cos\theta}{2\cos\theta}[/tex]from which leads to
[tex]\sin\theta-\sin^3\theta=\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]The expression missing on the third step is
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]Option D is correct.
Final Answer:
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]Hey I need help with my homework help me find the points on the graph too please Thankyouu
Answers
Given the function:
g(x) = 3^x + 1
we are asked to plot the graph of the function.
Using the table:
x y
-2 10/9
-1 4/3
0 2
1 4
2 10
The graph:
The expomential functions have a horizontal asymptote.
The equation of the horizontal asymptote is y = 1
Horizontal Asymptote: y = 1
To find the domain is finding where the question is defined.
The range is the set of values that correspond with the domain.
Domain: (-infinity, infinity), {x|x E R}
Range: (1, infinity0, {y|y > 1}.
PLEASE HELP! To prepare for a bike race, Rex rides his bike for 12 miles each day for 3 days. The app he uses only tracks distance in kilometers. If 1 mile = 1.61 kilometers, what is Rex's distance in kilometers? Round the answer to the nearest hundredth. 7.45 kilometers 19.32 kilometers 22.36 kilometers 57.96 kilometers
Answers
Based on the distance that Rex rode every day for three days, Rex's distance in 3 days in kilometers can be found to be 57.96 kilometers.
How to find the distance in miles?First, find the distance that Rex rode in those three days in miles. This can be found as:
= Number of miles rode per day x Number of days
= 12 x 3
= 36 miles
Then convert this to kilometers.
If one mile is 1.61 kilometers, then 36 miles would be:
= Number of miles x Miles per kilometer
= 36 x 1.61
= 57.96 kilometers
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If Rex rides his bike for 12 miles each day for 3 days. Then distance in kilometers is 57.96.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Speed=Distance / Time
Distance=Speed × Time.
Given that Rex rides his bike for 12 miles each day for 3 days
and 1 mile = 1.61 kilometre.
Let us convert 12 miles to kilometres
12×1.61=19.32 km
Now let us calculate the Distance as the speed is 19.32km and time is 3 days.
By the formula to get distance we have to multiply speed and time.
Distance=19.32×3
=57.96
Hence Rex's distance in kilometers is 57.96.
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The residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 5 to 8 if there were 4275 yes both what was the total number of votes
Answers
The ratio of votes has been given as;
[tex]Yes\colon No\Rightarrow5\colon8[/tex]This means the ratios can be expressed mathematically as;
[tex]\begin{gathered} \text{Yes}=\frac{5}{5+8}\Rightarrow\frac{5}{13} \\ No=\frac{8}{5+8}\Rightarrow\frac{8}{13} \end{gathered}[/tex]If there were 4275 YES votes, then this means the number 4275 represents 5/13.
Therefore,
[tex]\frac{5}{13}=\frac{4275}{x}[/tex]Where x represents the total number of votes. Therefore,
[tex]undefined[/tex]find the height of the trapezoidA=80 CM2 7Cm9CM
Answers
The area formula for trapezoids is
[tex]A=\frac{(B+b)h}{2}[/tex]Where B = 9 cm, b = 7 cm, and A = 80 cm2. Let's replace these dimensions to find h
[tex]\begin{gathered} 80=\frac{(9+7)\cdot h}{2} \\ 160=16h \\ h=\frac{160}{16} \\ h=10 \end{gathered}[/tex]Hence, the height is 10 cm.Answer question number 20. The question is in the image.Reference angle is the angle form by the terminal side and the x-axis.
Answers
Answer: We have to sketch the angle and find the reference angle for the 20:
[tex]\frac{8\pi}{3}[/tex]The reference angle is an angle between the terminal side of the angle and the x-axis.
[tex]\theta_R=180^{\circ}-\theta[/tex]The provided angle is:
[tex]\begin{gathered} \theta=\frac{8\pi}{3}=480^{\circ} \\ \\ 480^{\circ}=480^{\circ}-360^{\circ}=120^{\circ} \\ \\ \theta=120^{\circ} \end{gathered}[/tex]Sketch of the angle:
Therefore the reference angle is:
[tex]\begin{gathered} \theta_R=180^{\circ}-\theta \\ \\ \theta_R=180^{\circ}-120^{\circ} \\ \\ \theta_R=60^{\circ} \end{gathered}[/tex]the table shows the number of miles people in the us traveled by car annually from 1975 to 2015
Answers
In the year 2022, the predicted number of miles of travels would be 3.601 trillion miles.
What is a model?
The term model has to do with the way that we can be able to predict the interaction between variables. In this case, we can see that there is a line of best fit as we can see from the complete question which is in the image that have been attached to his answer.
The question is trying to find out the number of miles that people are going to travel in the year 2022 based on the line of best fit that have been given in the question that we have attached here.
We know that; y = 0.048x + 1.345. Recall that x here stands for the number of years that have passed since the year 1975. We now have 47 years passed since 1975 thus;
y = 0.048(47) + 1.345
y = 3.601 trillion miles
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Two containers designed to hold water are side by side, both in the shape of acylinder. Container A has a diameter of 8 feet and a height bf 16 feet. Container B hasa diameter of 10 feet and a height of 8 feet. Container A is full of water and the wateris pumped into Container B until Conainter B is completely full.To the nearest tenth, what is the percent of Container A that is empty after thepumping is complete?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate what is the percent of Container A that is empty after the pumping is complete, so we obtain the following:
First we will calculate the volume of each cylinder using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]Applying:
[tex]\begin{gathered} V_A=\pi\cdot4^2\cdot16 \\ V_A=\pi\cdot16\cdot16 \\ V_A=256\pi \end{gathered}[/tex][tex]\begin{gathered} V_B=\pi\cdot5^2\cdot8 \\ V_B=\pi\cdot25\cdot8 \\ V_B=200\pi \end{gathered}[/tex]After pumping the water from container A to container B, the following amount remains in container A:
Remaining amount of water in A=256π-200π
Remaining amount of water in A=56π
Now, we obtain that the empty percentage that results in A is:
Empty percentage that results in A=200/256*100
Empty percentage that results in A=78.125%
Empty percentage that results in A≈78.1%
1 + 3 4 Solve. 3 A 8 B 2 3 1) 1. Illuminate Education TM, Inc.
Answers
Given:
[tex]\frac{1}{2}+\frac{3}{4}[/tex]Let's add the fractions above.
To perform the addition, find the Lowest Common Multiple (LCM) of the denominators.
LCM of 2 and 4 = 4
Divide each denominator by the LCM and multiply the result with the numerator.
Thus, we have:
[tex]\begin{gathered} \frac{1}{2}+\frac{3}{4} \\ \\ \frac{2+3}{4}=\frac{5}{4} \\ \\ \frac{5}{4} \end{gathered}[/tex]Convert the improper fraction (5/4) to mixed fraction.
We have:
[tex]\frac{5}{4}=1\frac{1}{4}[/tex]ANSWER:
[tex]1\frac{1}{4}[/tex]1. Which fraction equals a repeatingdecimal?530АC503013B.1325D1013
Answers
5/30 = 1/6 = 0.16666667
13/25 = 0.52
30/50 = 3/5 = 0.6
13/10 = 1.3
As you can see the fraction which is equal to a repeating decimal is:
5/30 = 1/6 = 0.16666667
Laney can finish 17 math problems in 51 minutes while Hayden can finish 6 problems in 18 minutes. Is this a proportional relationship.
Answers
Given data:
The 17 maths problem finish by Laney in 51 minutes.
The 6 maths problem finish by Hayden in 18 minutes.
The time taken by Laney to finish 1 problem is,
17 prob=51 minutes
1 prob=3 minute.
Simmiarly, the time taken by Hayden to finish 1 problem is,
6 prob=18 minutes
1 prob=3 minute.
As, the time taken by the Laney and Hayden to solve one problem is same .
Thus, the given relationship is proportional one.
When finding the height of a triangle, you need to find the equation of the lineperpendicular to the base of the triangle that passes through the vertex opposite thebase and then find the point of the intersection of the base and the perpendicular line. True Or False?
Answers
EXPLANATION:
Given;
We are given the step by step procedure to find the height of a triangle.
Required;
We are required to determine if the step by step solution is true or false.
Solution/Explanation;
When finding the height of a triangle, we may use the Pythagoras theorem or we may use trigonometric ratios for right angled triangles.
Note that the Pythagoras' theorem is also used only for right angled triangles and one of the three sides will be the height of the triangle.
When required to calculate the the height of a triangle given a line perpendicular to the base (that is, at a 90 degree angle with the base), and passing through the vertex opposite the base, the triangle can be effectively split into two parts along the perpendicular and the perpendicular line will then become the height. Also depending on the amount of information available, we may use the Pythagoras' theorem (if the other two sides are given). Alternatively we may use the trigonometric ratios if one other side and one of the angles is given.
Therefore,
ANSWER:
FALSE
Determine the rate of change of a line that passes through the coordinates G (-13, -4) andB (7, -12). Reduce when necessary. (Show all work)
Answers
EXPLANATION:
-We must first identify the points that correspond to the x-axis and the points that correspond to the y-axis.
-To calculate the slope, then we apply the formula of the slope or rate of change which is the following:
[tex]\begin{gathered} \text{the rate of change :} \\ m=\frac{y2-y1}{x2-x1}\text{ } \end{gathered}[/tex]-now we must correctly locate the points in the formula.
[tex]\begin{gathered} G\text{ }(-13,-4),\text{ X1}=-13\text{ and y1}=-4 \\ B(7,-12);\text{ X2}=7\text{ and y2}=-12 \\ m=\frac{-12-(-4)}{7-(-13)}\text{ }=\frac{-12+4}{7+13}=\frac{-8}{20}=\frac{-4}{10} \\ simplify;\text{ }\frac{-4}{10}=\frac{-2}{5} \end{gathered}[/tex]-
If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
Answers
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale 5 9 2 16Female 7 11 12 30Total 12 20 14 46If one student is chosen at random from those who took the test, find the probability that the student got a 'C' GIVEN they are female.
Answers
Probability that the student got a 'C' GIVEN they are female = number of females that got a C in the test/number of females
From the information given,
number of females that got a C in the test = 12
number of females = 30
Thus,
Probability that the student got a 'C' GIVEN they are female = 12/30
We would simplify the fraction by dividing the numerator and denominator by 6. Thus,
Probability that the student got a 'C' GIVEN they are female = 2/5
Mean player age Mean Absolute Team Three golf teams wanted to compare the ages of their players. Each team calculated their players' mean age in years and the mean absolute deviation of their ages. They displayed the results in this table. 9.5 45 Appleton Coalvale 31 15.9 Which statements are true? Summerton 43 16.1 Select each correct answer. Team Coalvale's players ages and Team Summerton's players ages vary about the same amount Team Summerton's players ages and Team Appleton's players ages vary about the same amount Team Appleton's players ages vary less than do Team Summerton's players ages. Team Appleton's players ages vary more than do Team Coalvale's players ages. a ? 7+ O i JOTE to search
Answers
Given:
• Appleton: Mean = 45; Mean Absolute deviation = 9.5
,• Coalvale: Mean = 31; Mean Absolute deviation = 15.9
,• Summerton: Mean = 43; Mean Absolute deviation = 16.1
Using the given data, let's select the correct statements.
From the data we can see the difference between the Mean Absolute Deviations of team Coalvale and Summerton is (16.1 - 15.9) = 0.2
This means the ages of team Coalvale and Summerton vary about the same about.
The Mean Absolute deviation of Appleton is far from other mean absolute deviation. This means the players ages for team Appleton vary less than others.
Therefore, the correct statements are:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
ANSWER:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
help meee pleaseeee pleasee
Answers
So, let’s evaluate:
f(0)=-(0)^3+7(0)^2-2(0)+12
All the terms with the variable x are accompanied by a coefficient and exponents, which both, by definition, are forms of multiplication. So, we know that a•0=0, so any term with 0 is canceled to 0. We get:
f(0)=0+12
f(0)=12
The half-life of a radioactive isotope is the time it takes for quantity of the isotope to be reduced to half its initial mass. Starting with 175 grams of a radioactive isotope, how much will be left rafter 5 half-lives? Round your answer to the nearest gram
Answers
Exponential Decay
The model for the exponential decay of a quantity Mo is:
[tex]M=M_o\cdot e^{-\lambda t}[/tex]Where λ is a constant and t is the time.
The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:
[tex]\begin{gathered} \frac{M_o}{2}=M_o\cdot e^{-\lambda t} \\ \text{Simplifying:} \\ e^{-\lambda t}=\frac{1}{2} \\ \text{Taking natural log:} \\ -\lambda t=-\log 2 \\ t=\frac{\log 2}{\lambda} \end{gathered}[/tex]It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.
Substituting in the model:
[tex]M=175gr\cdot e^{-\lambda\cdot\frac{5\log 2}{\lambda}}[/tex]Simplifying (the value of λ cancels out):
[tex]\begin{gathered} M=175gr\cdot e^{-5\log 2} \\ \text{Calculating:} \\ M=175gr\cdot0.03125 \\ M=5.46875gr \end{gathered}[/tex]Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.
find the unit price of a 3 pack of bottle juice for $6.75 fill in the amount per bottle of juice
Answers
EXPLANATION
Let's see the facts:
Unit price = $6.75
Number of packs = 3
The unit price is given by the following relationship:
[tex]\text{Unit price= }\frac{6.75}{3}=2.25\frac{\text{dollars}}{\text{pack}}[/tex]The unit price is 2.25 $/pack
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
Answers
Given
A graph of a polynomial with the real coefficients.
To find:
a) The intervals in which the function is increasing is,
[tex]\begin{gathered} (-\infty,-5) \\ (-2,2) \\ (6,\infty) \end{gathered}[/tex]b) The value of x at which the unction has local minima.
From the graph shown in the figure, there is only one local minimum at x=-2.
c) The sign of the functions leading coefficient is positive.
Since the graph is moving upwards.
d) The degree of the function is 5.
Suppose a normal distribution has a mean of 98 and a standard deviation of6. What is P(x < 110)?A. 0.84B. 0.16C. 0.025O D. 0.975
Answers
We know that
• The mean is 98.
,• The standard deviation is 6.
,• The given x-value is 110.
First, we find the z-value using the following formula
[tex]Z=\frac{x-\mu}{\sigma}_{}[/tex]Replacing the given information, we have
[tex]Z=\frac{110-98}{6}=\frac{12}{6}=2_{}[/tex]The z-value or z-score is 2.
Then, we use a z-table to find the probability when P(x<110), or P(z<2).
We obtain a probability of 0.97, which approximates to D.
Hence, the probability would be D.The measure of side VT is 60 inches. Find the length of side VProunded to the nearest tenth.
Answers
It is important to notice that side VP is the hypothenuse of the triangle, and VT is the adjacent leg to 30°.
To find VP, we just have to use the cosine function
[tex]\begin{gathered} \cos 30=\frac{VT}{VP} \\ \cos 30=\frac{60}{VP} \\ VP=\frac{60}{\cos 30} \\ VP\approx69.3 \end{gathered}[/tex]Hence, VP is 69.3 inches long.the variable w varies inversely as the cube of v. if k is the constant of variation, which equation represents this situation?a: qv^=kb: q^3 v= kc: q/v^3=kd: q^3/v=k picture listed below
Answers
Solution
Given that:
[tex]\begin{gathered} q\propto\frac{1}{v^3} \\ \\ \Rightarrow q=\frac{k}{v^3} \\ \\ \Rightarrow k=qv^3 \end{gathered}[/tex]Option A.
please help need answer asap
Answers
Answer:
x = 34 degrees, y = 73
Step-by-step explanation:
Since the triangle is isosceles, the base angles are congruent (equal). First, find the supplement angle by doing 180-107, which gives you 73 for the base angles, which include y. Now there is a theorem that states the 2 remote interior angles are equivalent to the exterior angle, which means 107 = 73 + x. This gives us x = 34
I hope this helps!
Use the same process for the second one.
Using the Rational Roots Theorem which of the values shown are potential roots of ) = 32-132-3x + 457 Select all that apply. +1/3 +5 +5/3 +9 +1 +15 +3 +45
Answers
To solve this problem, you find the value of x that will make the function to be = 0 by substituting the likely values from the option into the eqaution and checking if after the simplification the value is 0
so checking
[tex]\begin{gathered} \text{The factors betwe}en\text{ }3\text{ and 45 are } \\ 1,3,5,9,15,45 \\ \text{factors of 3 are 1,3} \end{gathered}[/tex]we have
[tex]\begin{gathered} =3x^{^3}-13x^2-3x\text{ +45} \\ \pm1,\text{ 3, 5,9, 15,45} \\ \pm\frac{1}{3},\text{ 1, 5/3, 3, 5 , 15} \\ \text{values that apply are +3 twice and -5/3} \end{gathered}[/tex]I need help with #1 and 2 please I’m struggling
Answers
The slope of a line perpendicular to other line is the negative reciprocal of the slope.
This means, if the slope of a line is x, the slope of a perpendicular line will be:
[tex]-\frac{1}{x}[/tex]Then , the first thing we should do is to find the slope of f(x).
To find the slope of a line that passes two points P and Q we use:
[tex]\begin{gathered} \begin{cases}P=(x_p,y_p) \\ Q=(x_q,y_q)\end{cases} \\ \text{slope}=\frac{y_p-y_q}{x_p-x_q} \end{gathered}[/tex]In this case, we can use P = (1, 4) and Q = (-3, 2)
Then:
[tex]\text{slope}=\frac{4-2}{1-(-3)}=\frac{2}{4}=\frac{1}{2}[/tex]Now, we know that the slope of g(x) is perpendicular to f(x) which has a slope of 1/2
The reciprocal is:
[tex]\frac{1}{2}\Rightarrow\frac{2}{1}=2[/tex]And to make it the negative, we multiply by (-1):
[tex]2\cdot(-1)=-2[/tex]Thus, g(x) has a slope equal to -2
The function f(x) = 5x+3 is one to one. Find an equation for f-1(x) the inverse function.
Answers
Given the function:
[tex]f\mleft(x\mright)=5x+3[/tex]To find the inverse function, we make x the subject of the equation.
[tex]\begin{gathered} 5x=f(x)-3 \\ x=\frac{f(x)-3}{5} \end{gathered}[/tex]Next, we replace x with f-1(x) and f(x) with x.
Therefore, the inverse function is:
[tex]f^{-1}(x)=\frac{x-3}{5}[/tex]Enter an algebraic inequality for the sentence. Use x as your variable. The quotient of five times a number and 9 is no more than 15. The answer is ____ < ____
Answers
Answer:
[tex]\frac{5x}{9}\leq15[/tex]Which of the following are equations for the line shown below? Check all that apply. 5 (1,2) (3-6) I A. y + 6 = -4(x-3) B. y + 3 = -4(X-6) I C. y1 = -4(x-2) D. y - 2 = -4(x - 1)
Answers
We have the next points (1,2) and (3,-6)