Answers
Answer:
x = 33
Step-by-step explanation:
Creating an equation
The angles shown are corresponding angles
Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.
Corresponding angles are congruent ( equal to each other )
This means that 124 = 4x - 8
Solving for x
124 = 4x - 8
==> add 8 to both sides
132 = 4x
==> divide both sides by 4
33 = x
Related Questions
Quadratic Functions in Standard FormCaroline wrote these steps to graph f(x) = 2x2 + 4x + 5 on note cards, but they gotmixed up. Help Caroline by re-writing the steps in the correct order. Use the notecards to complete the steps below.
Answers
1.- Determine the vertex...
2.- The axis of symmetry...
3.- The y-intercept...
4.- Plot a point...
5.- Plot another point...
The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.
In ACDE, mZC = (4x – 16), m D = (6x - 1)", and mZE = (4x - 13). Find mZC.
Answers
Explanation:
We can do a diagram of triangle CDE:
The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:
[tex]\begin{gathered} m\angle C+m\angle D+m\angle E=180º \\ (4x-16)+(6x-1)+(4x-13)=180 \\ (4x+6x+4x)+(-16-1-13)=180 \\ 14x-30=180 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 14x=180+30 \\ 14x=210 \\ x=\frac{210}{14} \\ x=15 \end{gathered}[/tex]And with x = 15, replace into the expression for the measure of angle C to find it:
[tex]m\angle C=4x-16=4\cdot15-16=60-16=44º[/tex]Answer:
m
Ignore c. I only need help with a and b
Answers
Part A.
The composition of f ang g is given by
[tex](f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}[/tex]where we have inserted 3x-7 in the place of x in function f. Then, we have
[tex](f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x[/tex]Therefore, the answer is
[tex](f\circ g)(x))=x[/tex]Part B
Similarly to the previous case, we have
[tex](g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7[/tex]which gives
[tex](g\circ f)(x))=g(f(x))=x+7-7=x[/tex]then, the answer is
[tex](g\circ f)(x))=x[/tex]Part C.
In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.
Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).
Use diagram to find the following 1. m angle RVS = 2. M angle TVU =
Answers
The pie chart provides the following information;
[tex]\begin{gathered} m\angle RVS=(10x-10)^o \\ m\angle RVU=(8x-14)^o \\ m\angle UVT=8x^o \\ m\angle TVS=(5x+12)^o \end{gathered}[/tex]The sum of angles in a circle is 360 degrees.
Thus, we have;
[tex]\begin{gathered} (10x-10)^o+(8x-14)^o+8x^o+(5x+12)^o=360^o \\ 31x^o-12^o=360^o \\ 31x^o=360^o+12^o \\ 31x^o=372^o \\ x^o=\frac{372^o}{31} \\ x^o=12^o \end{gathered}[/tex]Then;
(a)
[tex]\begin{gathered} m\angle RVS=(10x-10)^o_{} \\ m\angle RVS=10(12)-10 \\ m\angle RVS=110^o \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle TVU=8x^o \\ m\angle TVU=8(12) \\ m\angle TVU=96^o \end{gathered}[/tex]Find -7/8 - 2 1/6. Write your answer as a mixed number in simplest form.
Answers
Answer:
3 1/24
Step-by-step explanation:
Find the measure of Z CFD.СF5m + 116T3m + 80D
Answers
solve the equation -8y + 8 = 37y - 7
Answers
you must first get the variables on the same side of the equal sign. It yields,
[tex]-8y-37y+8=-7[/tex]if we also pass the constant 8 to the right hand side, we have
[tex]-8y-37y=-7-8[/tex]Hence, the left and right hand sides are equal to
[tex]-45y=-15[/tex]hence, we have
[tex]y=\frac{-15}{-45}[/tex]since minus times minus is plus, we obtain
[tex]y=\frac{15}{45}[/tex]and it can be reduced to
[tex]\begin{gathered} y=\frac{15}{15\cdot3} \\ y=\frac{1}{3} \end{gathered}[/tex]Finally, the answer is
[tex]y=\frac{1}{3}[/tex]Answer:
y= 1/3
Step-by-step explanation:
1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1.2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5?3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel.(Needs exterior angles)4. Is the bottom shelf parallel to the top shelf? Explain.5. Is the bottom shelf parallel to the middle shelf? Explain.
Answers
1.
The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:
[tex]m\angle2+m\angle1=180\degree[/tex]We know the value of m∠2. Thus, we can replace it and solve for m∠1:
[tex]120\degree+m\angle1=180\degree[/tex][tex]m\angle1=180\degree-120\degree[/tex][tex]m\angle1=60\degree[/tex]2.
If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.
3.
When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:
[tex]m\angle1=m\angle5=60\degree[/tex]Then we can say that the top and middle shelves are parallel.
4.
As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.
5.
Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.
how do you solve 0.27÷0.9?
Answers
Given:
[tex]0.27\div0.9[/tex]To divide the decimals, we must take care of the decimal points
So, we will divide it as follows:
[tex]0.27\div0.9=\frac{27}{100}\div\frac{9}{10}=\frac{27}{100}\times\frac{10}{9}=\frac{27}{9}\times\frac{10}{100}=3\times\frac{1}{10}=0.3[/tex]So, the answer will be 0.27 ÷ 0.9 = 0.3
what is 5.8x10² in standard notation?
Answers
Answer:
[tex]5.8\text{ }\times\text{ 10}^2[/tex]Explanation:
Here, we want to write the given number in standard notation
The form we have given, is the scientific notation
To write in the standard form, we consider the scientific notation as they are the same
We have the standard notation as:
[tex]5.8\text{ }\times\text{ 10}^2\text{ = 5.8 }\times\text{ 10}^2[/tex]Identify the slope and the y-intercept of each line and use them to write an equation of the graph
Answers
Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:
[tex]\begin{gathered} y-\text{intercept: (0,1)} \\ \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-1-0}{3-0}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]now we can find the equation of the line using the slope and the y-intercept:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-\frac{1}{3}(x-0) \\ \Rightarrow y=-\frac{1}{3}x+1 \end{gathered}[/tex]therefore, the equation of the line is y=-1/3x+1
Construct a 95% confidence interval of the population proportion using the given information x=180, n = 300 the lower bound is the upper bound isRound to three decimal places as needed
Answers
Given;
[tex]x=180,n=300[/tex]Then, we can find the point estimation as;
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{180}{360}=0.60 \end{gathered}[/tex][tex]Z_{\frac{\alpha}{2}}=Z_{0.05}=1.96[/tex]Thus, the margin of error E is;
[tex]\begin{gathered} E=Z_{\frac{\alpha}{2}}\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}} \\ E=1.96\sqrt[]{\frac{0.60(0.40)}{300}} \\ E=1.96\sqrt[]{0.0008} \\ E=0.055 \end{gathered}[/tex]A 95% confidence interval for population proportion p is;
[tex]\hat{p}\pm E=0.60\pm0.055[/tex]The lower bound is;
[tex]0.60-0.055=0.545[/tex]The upper bound is;
[tex]0.60+0.055=0.655[/tex]use the elimination to solve each system of equations exercise number 4)
Answers
To solve this system of linear equations using the elimination method, first, add both equations:
[tex]\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}[/tex][tex]\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}[/tex]Now solve for y dividing by 7 on both sides of the equation:
[tex]\begin{gathered} \frac{7y}{7}=\frac{42}{7} \\ y=6 \end{gathered}[/tex]Finally, replace the value of y in any of the initial equations, for example in equation 1
[tex]\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ \frac{8x}{8}=\frac{8}{8} \\ x=1 \end{gathered}[/tex]Therefore, the solution of the system of equations is
[tex]\begin{cases}x=1 \\ y=6\end{cases}[/tex]One thermos of hot chocolate uses 2/3 cup of cocoa powder. How many thermoses can nalli make with 3 cups of cocoa powder?
Answers
In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
In professor Johnson's literature class there are 267 students. At a random check Prof.Johnson notices that 22 students among 59 students did not complete their essays.Can you estimate how many students in Prof. Johnson's class did not finish theiressay?Question 71 pts
Answers
We have a class of a total of 267 students.
The professor has a sample of 59 students, where 22 of them did not complete their essays.
This equals a proportion of:
[tex]p=\frac{22}{59}\approx0.373[/tex]If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.
To do that we multiply the total number of students by the proportion we have just calculated:
[tex]X=N\cdot p=267\cdot0.373\approx99.59\approx100[/tex]Answer: it can be estimated that approximately 100 students did not finish their essay.
which of the following graphs represents the equation Y -4 equals 3(x-1)?
Answers
Answer:
Explanation:
Given the equation:
[tex]y-4=3(x-1)[/tex]To determine its graph, check the graph that corresponds to the x and y-intercepts of this line.
When x=0
[tex]undefined[/tex]The point (-3, - 5) is on the graph of a function. Which equation must be true regarding the function? A. f(-3) = -5B. f(-3, -5) = -8C. f(-5) = -3D. f(-5, -3) = -2
Answers
SOLUTION
The correct option is A
Points with coordinates (x,y) on a graph can also be expressed thus:
[tex]f(x)=y[/tex]So with the above explanation, we can answer the question.
The point (-3,-5) on the graph means that x=-3 and y=-5
So it can be expressed as a function in the form:
[tex]\begin{gathered} f(x)=y \\ x=-3\text{ and y=-5} \\ f(-3)\text{ =-5} \end{gathered}[/tex]The correct option is A
The board of directors of a company must have select a president, a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board
Answers
Given
Total number of members = 22
Find
Possible ways of selection of president, a secretary and a treasurer
Explanation
As we know , the number of possible ways of selection is given by
[tex]N=^nP_r[/tex]there are three members required so , r = 3
now , substitute the values in above equation
[tex]\begin{gathered} N=^{22}P_3 \\ N=\frac{22!}{(22-3)!} \\ \\ N=\frac{22!}{19!} \\ \\ N=22\times21\times20 \\ N=9240 \end{gathered}[/tex]Final Answer
Possible ways of selection of president, a secretary and a treasurer = 9240
What is the measurement of DC? How do you know ?
Answers
The vertices B, C and D form a right triangle.
Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.
[tex]DC^2+BC^2=BD^2[/tex]Replacing with the values, we can calculate DC:
[tex]\begin{gathered} DC^2+60^2=100^2 \\ DC^2+3600=10000 \\ DC^2=10000-3600 \\ DC^2=6400 \\ DC=\sqrt[]{6400} \\ DC=80 \end{gathered}[/tex]Answer:
The correct options are
A: 80
B: Pythagorean theorem
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. Snowfall Summary 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Number of inches (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
Answers
a)
The minimum happens at the end of the left whisker of the box plot, from the graph we notice that his happens at five. Therefore, the minium amount of snow in any of the cities was 5.
b)
The data is more concenrtated in the second quarter (from the median to the third quartile) this comes from the fact that the length of this part of the block is smaller compared to the second quarter.
c)
The data is more spread out in the second quarter (from the second quartile to the median); this comes from the fact that the length of that part of the box is larger than any other part of the plot
What is the sum of 7/8 and 11/8
Answers
From the table above what is the probability that the respondent chosen at random answers something other than somewhat likely
Answers
Find the probability that the respondent will choose "somewhat likely". Divide the number of respondents who chose the option by the total number of respondents.
[tex]\begin{gathered} P(SL)=\frac{290}{\~likely)=\frac{290}{210+290+340+80+80}} \\ =\frac{290}{1000} \\ =0.29 \end{gathered}[/tex]Since we need to find the probability of the complement of "somewhat likely", subtract the obtained probability from 1.
[tex]\begin{gathered} P(notSL)_{}=1-0.29 \\ =0.71 \end{gathered}[/tex]I need help with this practice problem solving Make sure to read the instructions, answer by filling in the three boxes
Answers
Solution
[tex](-2\sqrt{3}-2i)^4[/tex]Therefore the correct answer is
The polar form of a complex number
[tex]128\text{ cis }\frac{2\pi}{3}[/tex]The rectangular form of a complex number
[tex]-128+128\sqrt{3}i[/tex]Question 2You buy a house for $299,000. If you make a 20% down payment, how much will your principal and interest payment be per month if you take out a 30 year loan with an interest rate of 4.25%.
Answers
The price of the house is $29900
At first you paid 20% of that price, to calculate how much the down payment was you have to do as follows:
[tex]299000\cdot0.2=59800[/tex]The down payment was $59800 and there are $299000-$59800=$239200 left to pay.
From this $239200 you have to calculate the interest rate:
$239200*0.0425= $10166 → this represents the total interest rate you'll pay
This is a 30 year loan, which means you'll pay
30*12=360
for 360 months
Divide the principal payment $239200 by 360 to calculate the monthly fee:
[tex]\frac{239200}{360}=664.44[/tex]Do the same with the total interest rate:
[tex]\frac{10166}{360}=28.24[/tex]Monthly you'll pay $664.44 plus $28.24 of interest, that adds up for a total of $692.68
see, I got an answer but my teacher showed us the websites answer and I'm confused.
Answers
First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator.
Integers include negative numbers and, positive numbers and zero. For example, these are Integers:
[tex]4,2,-3,-8[/tex]An Integer is always a Rational number, because it can be written as a fraction with denominator 1:
[tex]\frac{4}{1},\frac{2}{1},\frac{-3}{1},\text{ }\frac{-8}{1}[/tex]Then:
A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:
[tex]\frac{1}{2}[/tex]but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):
[tex]4=\frac{4}{1}[/tex]Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.
Jalen measured a bookcase to be 8.4 ft the actual measurement is 5.6 ft what is Gary percent error
Answers
We start by calculating the difference between the expected measured value and the value measured by Gary:
8.4 ft - 5.6 ft = 2.8 ft
Now we estimate what 2.8 ft is of the actual measurement 8.4 ft. That is:
2.8 / 8.4 = 0.33333... this is written in percent form as: 33.33%
This is the percent error.
The area of the parallelogram below is square meters. 9 m 7 m 2m
Answers
Answer:
63 square meter
Explanation:
Area of the parallelogram = Base * Height
From the given diagram;
Base = 9m
Height = 7m
Area of the parallelogram = 9m * 7m
Area of the parallelogram = 63 square meter
(statistics) urgently need help with question 32, is it valid or not valid & is the argument sound or not?
Answers
From the Venn diagram shown above we notice that the conclusion is false. This comes from the fact that even if all queens are women not all women are quenss.
In NOP, PNOP and m2O = 32. Find m P.
Answers
Solving Angle Problems.
[tex]PN\cong\text{ OP implies congruency, that is, length PN is the same as length OP.}[/tex]It follows therefore that
[tex]\begin{gathered} \angle NPO=\angle NOP=32^o\ldots.(\operatorname{Re}ason\colon\text{ Base angles of the isosceles triangle)} \\ \text{Hence}, \\ m\angle P=32^o \end{gathered}[/tex]The correct answer is the measure of angle P is 32 degrees
I need help with my math
Answers
SOLUTION:
Step 1:
An adult's ticket costs $11
A child's ticket costs $6
The number of Adult's tickets sold is x
The number of Children's tickets sold is y
The total number of tickets sold is 60
The total amount of sales made is $460
Step 2:
We need to form two equations based on the information given in the question;
[tex]undefined[/tex]