Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.(2x - 20)INNISmaller angle:Larger angle:O0UNSFANA(4x - 10)
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define complementary angles
When the sum of two angles is 90°, then the angles are known as complementary angles.
STEP 2: Write the pairs of the angles formed
[tex]\begin{gathered} (2x-20)\degree \\ (4x-10)\degree \end{gathered}[/tex]STEP 3: find the value of x
Following the definition in step 1, this goes that;
[tex]\begin{gathered} (2x-20)+(4x-10)=90\degree \\ 2x-20+4x-10=90\degree \\ 6x-30=90 \\ 6x=90+30 \\ 6x=120 \\ x=\frac{120}{6}=20 \end{gathered}[/tex]STEP 4: Find the two pair of angles
[tex]\begin{gathered} (2x-20)=2(20)-20=40-20=20\degree \\ 4x-10=4(20)-10=80-10=70\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} smaller\text{ }angle=20\degree \\ Larger\text{ }angle=70\degree \end{gathered}[/tex]Related Questions
in a popular restaurant on a Saturday night three out of every four customers are female. how many customers y are there for x number of total customers
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Let y be the number of female customers in the restaurant. Since we know that 3 out of 4 customers are females and that x is the total number of customers, this means that:
[tex]y=\frac{3}{4}x[/tex]Find WX.Write your answer as an integer or as a decimal rounded to the nearest tenth.WX = ____
Answers
The give figure is of a triangle WXY right angled at X.
From the figure, WY=10 and
Using trigonometric property in the triangle,
[tex]\cos \theta=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos Find WX by solving the above equation.[tex]\begin{gathered} WX=10\times\cos 44^{\circ} \\ =7.2 \end{gathered}[/tex]Therefore, WX=7.2.
Marcus hikes at a rate of 2 1/9 miles per hour. If he hikes for 6 hours, how many miles will he hike?
Answers
We have the following:
let s is speed, d is distance and t is time, therefore:
[tex]\begin{gathered} s=\frac{d}{t} \\ d=s\cdot t \\ d=2\frac{1}{9}\cdot6 \\ d=\frac{18+1}{9}\cdot6=\frac{19}{9}\cdot6 \\ d=\frac{114}{9}=\frac{38}{3} \\ d=12\frac{2}{3} \end{gathered}[/tex]Therefore, the answer is the third option 12 2/3 miles
what is 6 3/8 written as a demcimal
Answers
Explanation using the division method:
As a result, you get 6.38 as your answer when you convert 6 3/8 (or 51/8) to a decimal.
Answer:
The solution is 6,375
Step-by-step explanation:
[tex] \sf 6 \frac{3}{8} \\ \\ = \sf \frac{6 \times 8 + 3}{8} \\ \\ \sf \frac{48 + 3}{8} \\ \\ = \sf \frac{51}{8} \\ \\ = \sf 51 \div 8 \\ \\ = \sf6.375[/tex]
write the equation for each sentence below.a) (p) is the product of 7 to the sum of 3 and 9 b) The difference of (T) and 24 is 9 more than 34
Answers
(p) is the product of 7 to the sum of 3 and 9
This means we take the sum of "3" and "9" and multiply it with the variable "p". The expression is shown below
[tex]\begin{gathered} p\times(3+9) \\ =p\times12 \\ =12p \end{gathered}[/tex](b)The difference of (T) and 24 is 9 more than 34
The difference of T and 24 means T - 24
is 9 more than 34 means 34 + 9
Writing it together:
[tex]\begin{gathered} T-24=34+9 \\ T-24=43 \end{gathered}[/tex]Which set of graphs can be used to find the solution to the equation?
Answers
Given
The inequality,
[tex]3e^x>-\frac{1}{2}x[/tex]To find:
Which set of graphs can be used to find the solution to the equation?
Explanation:
It is given that,
[tex]3e^x>-\frac{1}{2}x[/tex]That implies,
The graph representing 3e^x is,
Also, the graph representing y> - ( 1/2) x is,
By combining these two we get,
[tex]3e^x>-\frac{1}{2}x[/tex]A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an openbox. If the volume of the box is 1530 in. What were the original dimensions of the piece of metal?What is the original width? ____in
Answers
Given:-
A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1530 in.
To find the original width.
The formula for volume of the box is,
[tex]v=l\times b\times h[/tex]The volume given is 1530.
Also we have,
[tex]L=W+25,H=5[/tex]Substiutiting the values. we get,
[tex]\left(W+15\right)*W-10*5=1530[/tex]Divide both sides by 5,
[tex]\left(W+15\right)*W-10=306[/tex]So,
[tex]w^2+5w-150=306[/tex]So now we get,
[tex]w^2+5w-456=0[/tex]Now we solve the quadratic equation,
[tex]\begin{gathered} w=\frac{-5\pm\sqrt{5^2-4\cdot\:1\cdot\left(-456\right)}}{2\cdot\:1} \\ w=\frac{-5\pm\:43}{2\cdot\:1} \\ w=19,-24 \end{gathered}[/tex]So now we skip the negative value and take the positve value 19.
So the required value is 19.
The recycling center processed 36,000 pounds of recyclable materials. How many tons of recyclable materials are processed? A 18 TonC 72,000 TonB 38,000 TonD 180 Ton
Answers
We were told that the recycling center processed 36,000 pounds of recyclable materials. We would convert from pounds to tonnes. Recall,
1 tonne = 2000 pounds
Thus, x tonnes = 36000 pounds
By cross multiplying, we have
2000x = 36000
x = 36000/2000
x = 18
18 tons of recyclable materials were processed
How do you solve an area of a rectangle with fractions
Answers
Given the figure, we can deduce the following information:
Perimeter = 65 in.
length = n
width = 11 2/4 in. = 23/2 in.
To determine the value of n, we use the formula:
[tex]P=2(l+w)[/tex]where:
P= Perimeter
l=length
w=width
We plug in what we know:
[tex]\begin{gathered} P=2(l+w) \\ 65=2(n+11\frac{2}{4}) \\ \text{Simplify and rearrange} \\ 65=2(n+\frac{23}{2}) \\ \frac{65}{2}=n+\frac{23}{2} \\ n=\frac{65}{2}-\frac{23}{2} \\ n=\frac{65-23}{2} \\ n=\frac{42}{2} \\ \text{Calculate} \\ n=21 \end{gathered}[/tex]Therefore, the value of n is 21 in.
7(1 - 6p) need help please
Answers
Find 7•(1-6p)
First eliminate parenthesis
Apply distributive law
a•(b+c) = ab + ac
Then
7•(1-6p) = 7•1 - 7•6p
. = 7 -42p
ANSWER IS
7 - 42p
Which statement describes the product of the expression 5 x 1/2?A, It is less than 1/2B. It is greater than %. C. It is between 5 and 6. D. It is between 1/2 and 5.
Answers
we have the expression
[tex]5\cdot\frac{1}{2}=\frac{5}{2}[/tex]so
Verify each statement
A, It is less than 1/2 -----> is not true
B. It is greater than 5 ----> is not true
C. It is between 5 and 6 ----> is not true
D. It is between 1/2 and 5 ----> is true
because
1/2 < 5/2 < 5
therefore
The answer is option D
which domain restrictions apply to the rational expression? 14-2x / x^2-7x
Answers
The domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
We are given the rational expression:-
[tex]\frac{(14-2x)}{(x^2-7x)}[/tex]
We have to find the domain restrictions that apply on the given expression.
We know that in a fraction, denominator cannot be 0, or else it will make the fraction indefinite.
Hence, by putting the denominator as 0, we will get the domain restrictions of the expression.
[tex]x^2-7x=0[/tex]
x(x - 7) = 0
x = 0 and 7
Hence, the domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
To learn more about fraction, here:-
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Question 8 of 10What should you multiply the first equation (top equation) by in order toeliminate the variable x when the two equations are added together?(3x-y-14-12x+y - 7dar hereISUBMIT
Answers
You can multiply the first equation by 4:
3x - y = 1 (*4)
12x-4y=4
Adding both equations:
12x - 4y = 4
+
-12x + y = 7
__________
0x - 3y = 11
so, you eliminate the X.
In order to eliminate the variable x when the two equations are added together, we needed to multiply the first equation by 4.
To eliminate the variable x when adding the two equations:
First, let's write the equations in a form where the x and y terms have opposite coefficients:
3x - y = 1 (Equation 1)
-12x + y = 7 (Equation 2)
To eliminate the x term, we can multiply Equation 1 by 4:
4 (3x - y) = 4 × 1
12x - 4y = 4 (Equation 3)
Now, we can add Equation 2 and Equation 3 together:
(-12x + y) + (12x - 4y) = 7 + 4
-12x + 12x + y - 4y = 11x - 3y = 11
The x term has been eliminated, and we are left with the equation 11x - 3y = 11.
To learn more about the system of equations;
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if 15 pizza cost $195. how much will 100 pizza cost?
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15 pizza ---> $195
100 pizza --> x
[tex]\begin{gathered} 15\times x=100\times195 \\ 15x=19500 \\ \frac{15x}{15}=\frac{19500}{15} \\ x=13000 \end{gathered}[/tex]answer:
$13000
Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact.Number 11.
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Given the Right Triangle shown in the exercise, you need to use the following Trigonometric Function in order to find the measure of "x":
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]In this case, you can identify that:
[tex]\begin{gathered} \alpha=21° \\ opposite=x \\ adjacent=18 \end{gathered}[/tex]Then, by substituting values and solving for "x", you get:
[tex]\begin{gathered} tan(21\text{\degree})=\frac{x}{18} \\ \\ 18\cdot tan(21\text{\degree})=x \end{gathered}[/tex][tex]x\approx6.9[/tex]Hence, the answer is:
[tex]x\approx6.9[/tex]During a class election the ratio of students who voted for candidate A compared tocandidate B was 7: 4. If candidate A received 21 votes, what is the combined amount ofvotes candidate A and candidate B received?
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Given: Ratio of students that voted for A compared to B is 7:4
A recieved 21 votes so let B recieve x votes.
So as the given ratios,
[tex]\frac{7}{4}=\frac{21}{x}[/tex][tex]x=\frac{21\times4}{7}=12[/tex]Hence, combined votes received by candidate A and B is 12+21=33
Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81
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Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:
[tex]P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)[/tex]Using the values reported on tables for the standardized normal distribution, we know that:
[tex]\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}[/tex]Now, using these results:
[tex]P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507[/tex]A bag of 11 marbles contains 7 marbles with red on them, 6 with blue on them, 6 with green on them, and 3 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
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In the case of two not mutually exclusive events, we have that, given events A and B,
[tex]P(A\lor B)=P(A)+P(B)-P(A\cap B)[/tex]Notice that if we only include the first two contributions, we would count the intersection of the two events twice; therefore, we must subtract the probability of its intersection once.
In our case,
[tex]P(R\lor G)=\frac{7}{11}+\frac{6}{11}-\frac{3}{11}=\frac{10}{11}[/tex]Therefore, the answer is 10/11.
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53. Using the empirical rule, whatpercentage of American women have shoe sizes that are less than 11.1? Please do not round your answer.
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The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So we have
So we can apply the rule to obtain
2/5 x 2/3???????????
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hello
to solve this question, we simpply need to multiply both fractions
[tex]\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]from the calculation above, the value of answer is 4/15
what is 20/5*(3.8)=?
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Given:
[tex]\frac{20}{5}\cdot3.8=\text{?}[/tex]first, we will find the result of dividing 20 by 5, then multiply the result by 3.8
so, the answer will be as follows:
[tex]\begin{gathered} \frac{20}{5}\cdot3.8 \\ \\ =4\cdot3.8=15.2 \end{gathered}[/tex]So, the answer will be 15.2
Jerry and Steve each had 24 candy bars to sell. Jerry sold 50% of his candy bars. Steve sold of his candy 6 bars. What fraction of the total candy bars did Jerry and Steve sell together?
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Jerry and Steve each had 24 candy bars, that is, the total candy bars are 48:
If Jerry sold 50% of his candy bars, it means that he sold one half of the total, then, he sold 12 bars.
Steve sold 6 candy bars.
Then, they both sold 12 + 6 = 18 candy bars together.
The fraction of the total candy bars is then:
18/48 = 9/24 = 3/8
(a) Approximate the population mean and standard deviation of age for males And For females.
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1) Since we have a table for grouped data, we need to place into that table another column with the middle point of each interval to get the mean.
2) Setting that table with another column we've got:
Age Middlepoint Male Female Male*freq Female*fr
0-9 (0+9)/2 =4.5 10 9 10*4.5=45 9*4.5=40.5
10-19 (10+19)/2=14.5 11 5 159.5 72.5
20-29 (20+29)/2= 24.5 12 13 294 318.5
30-39 (30+39)/2= 34.5 16 19 552 655.5
40-49 (40+49)/2= 44.5 25 21 1112.5 934.5
50-59 (50+59)/2= 54.5 20 24 1090 1308
60-69 (60+69)/2=64.5 18 18 1161 1161
70-79 (70+79)/2= 74.5 15 14 117.5 1043
Now, we can pick the absolute frequency of males and females and multiply by the middle point.
Now we can add the number of males multiplied by the frequency and divide them by the sum of the frequencies, this way:
[tex]\mu=\frac{45+159.5+294+552+1112.5+1090+1161+117.5}{10+11+12+16+25+20+18+15}\approx38.68[/tex]3) Now to find the standard deviation of this population, we can write out the following:
[tex]\begin{gathered} \sigma=\frac{\sqrt[]{(45-38.68)^2+(159.5-38.68)^2+(294-38.68)^2+(552-38.68)^2+(1112.5-38.68)^2+(1090-38.68)^2+(1161-38.68)^2+(117.5-38.68)^2}}{8} \\ \\ \sigma=452.6694 \end{gathered}[/tex]Tamara's monthly budget shows$490.00 in fixed expenses, $529.50in variable expenses, and anexpected income of $1,250.00.1. Why doesn't Tamara's budgetbalance?
Answers
She has an expected income of $1250.
The total expenses are $490 + $529.50 = $1019.50.
She has a superavit that she can save. This amount is $1250 - $1019.50 = $230.50.
Answer: the budget balance does not balance because the income is greater than the expenses.
sunscreen is priced at $10 per bottle, +8% tax. If Tonya purchases a bottle of sunscreen with a $20 bill, then what is her change
Answers
Solution
For this case we know that the price is 10$ per bottle with 8% of tax
We can find the tax using this:
[tex]\frac{10}{100}=\frac{x}{8}[/tex]With x= tax value, solving for x we got:
[tex]x=8\cdot\frac{10}{100}=0.8[/tex]Then the total price is: 10+0.8 = 10.8
Then we can find the change like this:
20-10.8= 9.2
Write a sine function that has an amplitude of 5, a midline of 4 and a period of 3/2
Answers
Note that in any sine function :
[tex]y=A\sin (B(x+C))+D[/tex]Amplitude = A
Verical Shift or midline = D
Period = (2π)/B
Horizontal or Phase Shift = C
From the given,
since we dont have any horizontal shift, C = 0.
Amplitude = 5, so A = 5
Midline = 4, so D = 4
and
Period = 3/2, so equating it to (2 π)/B
[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]Now, substituting the values obtained, the sine function will be :
[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]An archaeologist finds dinosaur bones 100 miles East and 200 miles North of his office. He finds whale bones 100 miles East and 300 miles South of his office. Graph and label these two points. How far apart are they?
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Let's draw a picture of our problem:
where the red point (100 East, 200 Norh) represents the place where Archaeologist found the dinosaur. The blue point (100 East, 300 South) represents the place where Arcaeologist found the whale bones. Additionally, the green point (0,0) represents Arcaeologist's offfice.
A sample of 34 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are summarized in the following table. Find the mean price for the sample. Round your answer to the nearest dollar
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To find the mean we will sum the prices (total price, including repeated values) and divide by the total number of computers, then
[tex]m=\frac{14\cdot1400+11\cdot800+3\cdot2600+6\cdot1500}{34}[/tex]Using a calculator
[tex]\begin{gathered} m=\frac{45200}{34} \\ \end{gathered}[/tex]Do the division (use a calculator)
[tex]\begin{gathered} m=\frac{45200}{34} \\ \\ m=1329.41 \end{gathered}[/tex]The mean price is 1329.41
A gift box for a shirt has a length of 45 centimeters, a width of 30 centimeters, anda height of 8 centimeters. Find the surface area of the gift box
Answers
The main values in order to find the surface are the width and the length, therefore, the surface will be the product between them
[tex]45cm\times30cm=1350cm^2[/tex]Because the box cover from a gift box depends on the width and length, the surface area is 1350cm^2.
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. How many milliliters are in 1 quart? Label your answer to the hundredths place and in mL.