6. Let the measurement of ZBAC be 86° & ZBAD be 52°. What is the measurement of ZDAC? 1380 24° 52° 340
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Related Questions
The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?(1 Point)a) 84b) 21c) 42d) 32
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SOLUTION:
Step 1:
In this question, we are given the following:
The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?
(1 Point)
a) 84
b) 21
c) 42
d) 32
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Le\text{t the two numbers be x and y , such that:} \\ \text{x + y = 106 --- equation 1} \\ x\text{ + \lparen x+ 22 \rparen = 106} \\ 2x\text{ + 22 = 106} \\ \text{2x = 106 - 22} \\ 2x=84 \\ Divide\text{ both sides by 2, we have that:} \\ \text{ x =}\frac{84}{2} \\ \text{x = 42} \\ This\text{ means that the smaller number is 42 and} \\ The\text{ larger number is \lparen 42 + 22 \rparen = 64} \\ Then,\text{ Half of the smaller number = }\frac{42}{2}\text{ = 21 \lparen OPTION B \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer = 21 ( OPTION B )
Allison spent $7.80 on lunch. That represents 6% of her daily net income. What is Allison's daily net income? Round your answer to the nearest penny if needed.
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we get that the net income of Alison is:
[tex]\frac{7.8}{6}\cdot100=130[/tex]so her net income is $130
A house is on a 60,000-squarefoot lot. Rounded to the nearest tenth, approximately how many acres are inthe lot?Note: There are 43,560 square feet in an acre.A 1.3 acresB 1.0 acres1.7 acres1.4 acres
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Given:-
[tex]60,000\text{sqfeet}[/tex]To find the given area in acre.
So now we use the formula,
[tex]1\text{acre}=43560[/tex]So now we get,
[tex]\frac{60000}{43560}=1.3774[/tex]So rounding to the nearest tenth we get,
[tex]1.4[/tex]So the required solution is 1.4acres.
Two letters are chosen at random from the word MATHEMATICS, with replacement. What is the probability that the first letter is a consonant and the second letter is a vowel?
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We want to know the probability of choosing two letters at random, and the first letter is a consonant and the second one is a vowel. The word we are given is
MATHEMATICS
We see that it has 7 consonants and 4 vowels. We will denote by E to the event:
[tex]E=\text{"Getting as a first letter a consonant and second letter a vowel"}[/tex]As the events: "Obtaining a consonant" and "Obtaining a vowel" are independent, we get:
[tex]P(E)=\frac{7}{11}\cdot\frac{4}{10}=\frac{28}{110}=\frac{14}{55}=0.25\bar{45}[/tex]This means that the probability that the first letter is a consonant and the second letter is a vowel is (approximately) 25.45%.
Consider the data regarding car costs. The mean is $22,000 and the standard deviation is $2,000.a) Not everyone pays the same price for the same model of car. Use the 68-95-99.7% Rule to find what percentage ofbuyers paid between $18,000 and $26,000.b) The middle 99.7% of car costs are between what values?c) What is the probability a car will cost less than $24,000?d) What is the probability a car will cost more than $26,000?
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Answer:
a) 95%
b) $16,000 to $28,000
c) 84%
d) 2.5%
Step-by-step explanation:
Given the mean of car costs is $22,000 with a standard deviation of $2,000, you want to use the empirical rule to find ...
percentage of buyers paying $18–26 thousandrange of values for middle 99.7% of costsprobability of cost less than $24,000probability of cost more than $26,000Empirical ruleThe empirical rule tells you that the center 68% of costs will be between -1 and +1 standard deviations from the mean: $20,000 to $24,000.
95% of costs will lie within 2 standard deviations: $18,000 to $26,000.
The "tails" of the distribution are split equally between the upper values of these ranges and the lower values.
a) 18-26These values are ±2 standard deviations from the mean.
95% of buyers will pay between $18 and 26 thousand.
b) 99.7%The middle 99.7% of the distribution lies between ±3 standard deviations from the mean:
22,000 ± 3(2000) = 22,000 ± 6,000 = {16000, 28000}
The middle 99.7% of costs are between $16,000 and $28,000.
c) < 24We know that 68% of costs are between $20,000 and $24,000, and 50% of costs are below $22,000. The distribution is symmetrical, so 68%/2 = 34% of costs are between $22,000 and $24,000..
The fraction below $24,000 is ...
P(<24) = P(<22) +P(22 to 24) = 0.5 + 0.34 = 0.84
The probability a car will cost less than $24,000 is about 84%.
d) > 26The empirical rule tells us 95% of the distribution is between 18 and 26 thousand. Half the remaining amount is above 26 thousand.
P(> 26) = (1 -0.95)/2 = 2.5%
The probability a car will cost more than $26,000 is about 2.5%.
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Danny uses an app that shows him how many kilometers he has ran to prepare for a marathon. The app said he ran 8.045 kil. He wants to post online how many miles he ran. Danny ran _____ miles.
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1 kilometer is equivalent to 0.62 miles. To find how many miles are 8.045 kilometers, we can use the next proportion:
[tex]\frac{1\text{ km}}{8.045\text{ km}}=\frac{0.62\text{ mi}}{x\text{ mi}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=0.62\cdot8.045 \\ x=5\text{ miles} \end{gathered}[/tex]Another way to solve this, is the next one:
[tex]8.045\text{ km}\cdot\frac{0.62\text{ miles}}{1\text{ km}}=5\text{ miles}[/tex]Danny ran 5 miles.
on the beach boardwalk there are 20 different places to get food this year the World War II Saturday of 25% more places to get food how many total places to get food this year
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Originally 20 places
Now there are 25% more
25% of 20 = 25(20)/100 = 500/100 = 5
25% of 20 = 25 times 20 and divided by 100 = 500/100 = 5
[tex]\frac{25\cdot20}{100}\text{ = 5}[/tex]Original quantity = 20
25% of 20 is 5
Ttotal quantity = original quantity + 25% = 20 + 5 = 25
Answer:
There are 25 places to get food this year
20 old plus 5 new
Which expression below is an equivalent expression to this one: (8x- 4x^4 + 8x^3) - (6 - 2x + 6x^4) Select one: 1) -10x^4 + 13x^3+ 10x - 6 2) - 10x^4 + 13x^3 + 15x - 13) -10x^4 + 8x^3 + 10x – 6 4) -10x^4 + 13x^3 + 15x - 6
Answers
Which is an equation of the line perpendicular to y+5X=7and passes through (10,-4)[A] y = 1/5x +7[B] y = 5x + 25/4[C] y = 1/5x - 6[D] y = 5x + 7
Answers
Given the equation:
[tex]y+5x=7[/tex]we can find its slope if we write it in the y=mx+b form:
[tex]\begin{gathered} y+5x=7 \\ \Rightarrow y=-5x+7 \end{gathered}[/tex]Now, we know as a general rule, that the slope of the perpendicular of the line that has slope m, is -1/m, more clearly:
[tex]\begin{gathered} \text{if m is the slope of the line} \\ \Rightarrow m_p=-\frac{1}{m}\text{ is the slope of the perpendicular line} \end{gathered}[/tex]So, in this case we have:
[tex]\begin{gathered} m=-5 \\ \Rightarrow m_p=-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5} \\ m_p=\frac{1}{5} \end{gathered}[/tex]now we use the slope-point formula to find the equation of the perpendicular line:
[tex]\begin{gathered} (x_0,y_0)=(10,-4) \\ m_p=\frac{1}{5}_{} \\ y-y_0=m(x-x_0)_{} \\ \Rightarrow y-(-4)=\frac{1}{5}(x-10) \\ \Rightarrow y+4=\frac{1}{5}x-\frac{10}{5} \\ \Rightarrow y=\frac{1}{5}x-2-4=\frac{1}{5}x-6 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]therefore, the line perpendicular to y+5x=7 that passes through (10,-4) is y=1/5x-6
I need help with my math
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Given the equation:
[tex]y=\frac{2}{3}x-3[/tex]We will graph the equation using the intercepts
The X-intercept is the value of x when y = 0
so,
[tex]\begin{gathered} y=0\rightarrow0=\frac{2}{3}x-3 \\ \frac{2}{3}x=3 \\ x=\frac{9}{2}=4.5 \end{gathered}[/tex]The y-intercept is the value of y when x = 0
so,
[tex]x=0\rightarrow y=-3[/tex]So, the graph of the line passes through the points (0, -3) and (4.5, 0)
The graph of the equation is as shown in the following picture:
The correct option is:
2x = 5(2-y)y = 3(-x + 5)Solve system of equation using elimination method
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The given system of equations is:
[tex]2x=5(2-y);y=3(-x+5)[/tex]Simplify to get:
[tex]\begin{gathered} 2x=10-5y \\ 2x+5y=10\ldots(i) \\ y=-3x+15 \\ 3x+y=15\ldots(ii) \end{gathered}[/tex]Multiply (ii) by 5 to get:
[tex]15x+5y=75\ldots(iii)[/tex]Subtract (i) from (iii) to get:
[tex]\begin{gathered} 15x+5y=75 \\ -2x-5y=-10 \\ 13x=65 \\ x=\frac{65}{13}=5 \end{gathered}[/tex]Substitute x=5 in (ii) to get:
[tex]\begin{gathered} 3(5)+y=15 \\ y=0 \end{gathered}[/tex]Solution set {5,0}.
3x – 2y= 12Find the x- and y-intercepts from the equation in standard form above. Explain how you got each intercept.
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To find the y-intercept, we have to make x=0 and solve for y:
[tex]\begin{gathered} 3x-2y=12 \\ x=0 \\ \Rightarrow3\cdot0-2y=12 \\ \Rightarrow-2y=12 \\ \Rightarrow y=\frac{12}{-2}=-6 \\ y=-6 \end{gathered}[/tex]Now, to find the x-intercept, we make y=0 and do the same as the previous case:
[tex]\begin{gathered} y=0 \\ \Rightarrow3x-2\cdot0=12 \\ \Rightarrow3x=12 \\ \Rightarrow x=\frac{12}{3}=4 \\ x=4 \end{gathered}[/tex]therefore, the y-intercept is the point (0,-6) and the x-intercept is the point (4,0)
i do not know how to get the stuff it is asking me for
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We can check in the graph the the parabola touches the x-axis in only one point, which is (5,0). Therefore, the quadratic function has 1 solution.
Solution: x = 5 and x = 5
Explain how I know the vertex of m(x)=x(x+6)
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Answer: a lot of 5
Step-by-step explanation:
yes
Answer:
Rewrite in vertex form and use this form to find the vertex (h,k)(h,k).(12,−254)
Step-by-step explanation:
Hope this helps ;)
on Core Math 6 A What is the greatest common factor of 16 and 24? O4 X 6 O 8 O 10
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The Greatest Common Factor
The greatest common factor (or divisor) (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers of that set.
For example, we have the numbers 16 and 24. One common divisor is 2 because 16/2=8 and 24/2=12. Both divisions are exact.
But 2 is not the greatest common divisor. To find the GCF, the procedure is:
* Write the prime factor of each number:
16 = 2*2*2*2
24 = 2*2*2*3
Select the maximum number of common prime factors from the numbers, even if they repeat.
We can select the product of 2*2*2 = 8 as the GCF, thus:
Answer = 8
how would you find the absolute value of 5.23? i do not know how. my child is using a number line.
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The absolute value is to write the nubmer as a positive number
For example:
|-4| = 4
|-2.5| = 2.5
| 6| = 6
So, the number if was negative, we will make it positive
And the number if positive, will remain as it is
There is no need to use the number lines
So, the absolute value of 5.23 = | 5.23 | = 5.23
1. Patty is arranging the chairs for an awards ceremony. She wants to put the 36 chairs into a rectangular array. Choose the ways that Patty can arrange the chalrs. 1. Select all the expressions that have a product of 640. 16 x 40 (4 x 4) * (4 x 10) 40 = 16 (4 x 4) * (8 x 6) (2 x 5) * (8 x 2) x (2 x 2)
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The pieces of construction paper ordered can be determined as,
[tex]\begin{gathered} N=22\times64 \\ =1408 \end{gathered}[/tex]Thus, the required pieces of construction paper is 1408.
What are the coordinates of point F? 5 4 F 3 2 1 E 4 2 3 -5 -4 -3 -2 -1 0 4 -2 -3 4 -5
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According to the graph, point F is on the first quadrant. Its coordinates are (1,3). Remember that the first value is x, adn the
Hence, the coordinates of point F are (1,3).Can I get help on 22. I don’t understand what I did wrong
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From the problem, we have an inequality :
[tex]-6x+1<7[/tex]Subtract 1 to both sides of the equation :
[tex]\begin{gathered} -6x+1-1<7-1 \\ -6x<6 \end{gathered}[/tex]Divide both sides by -6 :
[tex]\begin{gathered} -6x<6 \\ x<\frac{6}{-6} \\ x<-1 \end{gathered}[/tex]The solution is x < -1
AREA AND VOLUMEInvestigating the effects on the area for non-proportiona
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(a)
Let:
w1 = Original width
l1 = Original length
w2 = New width
l2 = New length
A1 = Original area
A2 = New Area
so:
[tex]\begin{gathered} w2=3w1=3\cdot10=30ft \\ l2=2l1=2\cdot50=100ft \\ A2=w2\cdot l2=3000ft^2 \end{gathered}[/tex]Answer:
New length: 100ft
New width: 30 ft
New Area: 3000ft²
-------------------------------------------
(b)
[tex]\frac{A2}{A1}=\frac{3000}{500}=6[/tex]Answer:
The area of the new walkway will be 6 times the area of the current walkway
---------------------------------------
(c)
[tex]\begin{gathered} 8\cdot500=x\cdot50\cdot4\cdot10 \\ 4000=2000x \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{2000} \\ x=2 \end{gathered}[/tex]Answer:
Make the new length 2 times the current length.
Hi I’ve been struggling with these two problems for sometime now
Answers
Answer
The answer is Distributive property
SOLUTION
Problem Statement
We are given the mathematical statement below:
[tex]5(x-3)=5x-15[/tex]We are asked to find the property that justifies the above statement.
Solution
To solve this problem, we need to understand what the distributive property is.
The distributive property states:
[tex]A(B+C)=AB+AC[/tex]If A = 5, B = x and C = -3
Thus, applying the Distributive property on the left-hand side of the mathematical equation given:
[tex]\begin{gathered} A(B+C)=AB+BC \\ 5(x-3)=5(x)+5(-3)_{} \\ =5x-15 \end{gathered}[/tex]This conforms to the Distributive property
Final Answer
The answer is Distributive property
Which of the following is the following measure of angle BOC
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The tangent of a circle always form 90 degree angle with the radius. So measure of angle ABO and angle ACO is 90 degrees each.
The sum of angles of a quadilateral is 360 degrees. So,
[tex]\angle BOC+\angle ABO+\angle ACO+\angle BAC=360[/tex]Substitute the measures of angles in the equation to obtain the measure of angle BOC.
[tex]\begin{gathered} \angle BOC+90+90+90=360 \\ \angle BOC=360-270 \\ =90 \end{gathered}[/tex]Thus, measure of angle BOC is 90 degrees.
What is the equation of the line passing through the points( 29 ) and 2) in slope-intercept form?O y-zx-3O y-3x+o y = 2 x - 22O x- x+Mark this and retumSave and ExitNexSubmit
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The slope-intercept form is
[tex]y=mx+b[/tex]First we find m which is defined as rise / run
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{y_1-y_2}{x_1-x_2}[/tex][tex]\Rightarrow m=\frac{(\frac{11}{12})-(\frac{19}{20})}{(\frac{1}{3})-(\frac{2}{5})}[/tex][tex]m=\frac{1}{2}[/tex]And finally, we find the y-intercept b from one of the points given.
Let us use the point (1/3, 11/12).
[tex]\frac{11}{12}=\frac{1}{2}(\frac{1}{3})+b[/tex][tex]\frac{11}{12}=\frac{1}{6}+b[/tex][tex]b=\frac{11}{12}-\frac{1}{6}[/tex][tex]b=\frac{3}{4}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]y=\frac{1}{2}x+\frac{3}{4}[/tex]which is the second choice in the column.
-2.5 (-3 +4n + 8) how can i expand the expression
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SOLUTION:
Step 1:
In this question, we are given the following:
[tex]-2.\text{ 5( -3 + 4n + 8 )}[/tex]Step 2:
Expanding the expression, we have that:
[tex]\begin{gathered} -2.\text{ 5 ( -3 + 4n + 8 )} \\ \text{solving the bracket first, we have that:} \\ -2.\text{ 5( 4n + 5)} \\ -10n\text{ - 12. 5} \end{gathered}[/tex]Which number is divisible by both 2, 5, and 10?1. 9002. 8023. 9624. 745
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Given:
The numbers are 2,5 &10.
900 is divisible by 2,5 &10.
Therefore, Option 1. 900 is the correct answer.
I need help with math
Answers
Answer:
w = 52
Step-by-step explanation:
We have supplementary angles.
[tex]3w - 28 + w = 180[/tex]
[tex]4w - 28 = 180[/tex]
[tex]4w = 208[/tex]
[tex]w = 52[/tex]
Question: Ramona wrote down an expression that was equivalent to... 3 . 15 + 10 (8 - 1) -82.(please look at the photo the numbers are different.)
Answers
ANSWER
[tex]45+70-64[/tex]EXPLANATION
We want to find the equivalent expression to:
[tex]3\cdot15+10(8-1)-8^2[/tex]To do this, first simplify the bracket:
[tex]\begin{gathered} 3\cdot15+10(7)-8^2 \\ 3\cdot15+70-8^2^{} \end{gathered}[/tex]Now, simplify the exponent:
[tex]3\cdot15+70-64[/tex]Finally, simplify the muiltiplication:
[tex]45+70-64[/tex]That is the answer.
Mayra bought x grams of rice.Anika boughtmore than Mayra bought.Select ALL of the equations that represent therelationship between the amount of rice that Mayrabought, x, and the amount of rice that Anika bought, y.#1. y=4/3x #2.Y=2/3x 3#.Y=1/3x #4.y=x+1/3x #5.Y=X-1/3x
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Given that the amount of rice Anika bought is
more than Mayra bought and Mayra bought x grams while Anika bought y grams then considering the options
#1. y=4/3x - this is true
#2.Y=2/3x - this is not true as this means that the value of y is less than that of x
3#.Y=1/3x - this is not true as this means that the value of y is less than that of x #4.y=x+1/3x - this is same as #1
#5.Y=X-1/3x - this is same as #2
Hence th
x is inversely proportional to y, and x = 18 when y = 4. a. Write an equation relating x and y b. Find x when y = 30
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Here, we want to solve a proportional relationship problem
a) We have the proportion as follows;
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \\ k\text{ as constant} \\ \\ k\text{ = xy} \\ \\ \text{for x = 18 and y = 4} \\ \\ k\text{ = 18}\times4\text{ = 72} \\ xy\text{ = 72} \end{gathered}[/tex]b) X, when y = 30
[tex]\begin{gathered} xy\text{ = 72} \\ x\text{ = }\frac{72}{y} \\ x\text{ = }\frac{72}{30} \\ x\text{ = 2.4} \end{gathered}[/tex]5. The picture below showsthe number of pages in 3textbooks.424 pages 290 pages286 pagesMarc has 10 days to finish allthree before exams. He plansto read an equal amounteach day. How many pagesshould he read the first day?
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The number of pages in 3 textbooks are ; 424 pages, 290 pages, and 286 pages.
The total number of pages in the three books is;
[tex]N=424+290+286=1000\text{ pages}[/tex]To complete the three books in ten days ( before the exam), Marc must read one-tenth of the total pages daily.
Since, He plans to read an equal amount each day.
The number of pages P he should read in the first day is;
[tex]P=\frac{1000}{10}=100\text{ pages}[/tex]He should read 100 pages in the first day.