In this figure, DC is parallel to AB. angle DCA is 3x+14, angle ACB is 10x+12, and angle CAB is 5x-2. Find the degrees in angle CBA.
Answers
Answer:
Angle CBA = 50 degrees
Step-by-step explanation:
Known Information:
DC is parallel to ABAngles DCA and CAB are equal (they are alternate interior angles)Angles CAB + ACB + CBA = 180°Calculations:
[tex]3x + 14 = 5x - 2[/tex][tex]16 = 2x[/tex] [tex]x = 8[/tex][tex]180 - CAB - ACB = CBA[/tex][tex]180 - [ 5(8) - 2] - [ 10(8) + 12] = CBA[/tex][tex]100- [38] - [92] = CAB[/tex][tex]CBA = 50[/tex]The measure of the angle CBA is 50 degrees if DC is parallel to AB. angle DCA is 3x+14.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have:
DC is parallel to AB. angle DCA is 3x+14, angle ACB is 10x+12, and angle CAB is 5x-2.
The equation can be framed:
3x + 14 = 5x - 2
x = 8
Angle CBA = 180 - (Angle CAB - Angle ACB)
Angle CBA = 180 - [5(8)-2+10(8)+12]
Angle CBA = 180 - [40-2+80+12]
Angle CBA = 180 - [40-2+80+12]
Angle CBA = 50
Thus, the measure of the angle CBA is 50 degrees if DC is parallel to AB. angle DCA is 3x+14.
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Related Questions
i need help what ones represents numerical data
Select all that apply
A. 1,1.2,1.4,1.5,1.6,1.8,1.9,2,2,2.1,2.5
B. Red,Red,Yellow,Yellow,Blue,Blue,Blue
C.45,60,60,70,75,80,85,90,90,100,100,100
D. -7,-5,-3,-1,-1,-1,0
E. 98.2,98.4,98.4,98.6,98.6,98.6,98.6,98.7,98.8,98.8
F.Yes,Yes,Yes,Yes,Maybe,Maybe,No,No,No
G.A,A,A,B,B,B,C,C,C
Answers
Answer:
A and C?
Step-by-step explanation:
they have numbers innit e.g. 1.2 is a nmuber and so is 45 sooo yea
Answer:
a, c, d, e
Step-by-step explanation:
all numbers rest are words
WHY I HHAVE FAT CHIKIN HE DO NOTHIG HE IS REALLY FAT AND HEVY HE MO LAY WGG EITHER TELL ME WHY HOW I MAKE HIM NO FAT
Answers
what is the slope of (-3,-5) (-2,-2)
Answers
Answer:
m=3
Step-by-step explanation:
entlying
A and B are forces acting on a falling object. Which
force, A or B, represents gravity in the diagram?
Force
is gravity because it attracts the ball
to the ground.
Answers
Answer:
B... Because indicates the direction of gravity because its direction is downward
Answer:b
Step-by-step explanation:
The entrance to a museum in Paris is shaped like a square pyramid the base of the pyramid has a side length of 35 meter and the height of the pyramid is 22 meters which measurement is closest to the volume of the pyramid in cubic meter
Answers
Answer:
Step-by-step explanation:
8,983
Answer:
just to comfirm the answer it is 8,983 m, I got it right on my test
Step-by-step explanation:
i’ll mark brainliest
Answers
Answer:
A
Step-by-step explanation:
ok so pretend the 2.00 was just 2 so whats 8 divided by 2? 4 right so if we test that witht he other problems its the same so its A
Hope this helps!!!! :D
Which table represents the second piece of the function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 3.5 x + 0.5, 2nd column x less-than 1 2nd row 1st column 8 minus 2 x, 2nd column x greater-than-or-equal-to 1 EndLayout?
Answers
Answer:
C
Step-by-step explanation:
Third table represents the second piece of the function f(x)
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given function is given by -3.5x+0.5, x<1 and 8-2x≥1
The second piece of the function f(x) is 8-2x ,x≥1
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
f(1)=8-2(1)=6
f(1)=6
For x = 2
f(2)=8-2(2)=4
f(2)=4
For x = 3
f(3)=8-2(3)=2
f(3)=2
Among the given tables, third tables contains these values.
Hence, Third table represents the second piece of the function f(x)
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Tony and Sam are sharing the driving on a 520-mile trip. If Tony drives 90 more miles than Sam, how far did each of them drive?
Answers
Answer:
miles driven by sam =215 miles
Miles driven by Tony = 305 miles.
Step-by-step explanation:
Let the miles driven by sam is x
given that Tony drove 90 miles more than sam
miles driven by Tony = miles driven by sam + 90 = x + 90
Total miles driven by them together
= miles driven by Tony + miles driven by sam = x + 90 + x = 2x + 90
given
Tony and Sam are sharing the driving on a 520-mile trip
2x + 90 = 520
2x = 520 - 90 = 430
x = 430/2 = 215
Thus,
miles driven by sam = x = 215 miles
Miles driven by Tony = x + 90 = 215 + 90 = 305 miles.
Simplify the ratio 12:8 and write the ratio in all three forms.
Answers
Answer:
Step-by-step explanation:
1. Simplify
greatest common factor = 4
3:2
a. 3 to 2
b. 3:2
c. 3/2
could i please get some help?
Answers
2: slope = 5/-5
3: slope = 3/2
4: slope = 7/-4
5: slope = 3/5
6: slope = 2/-8
7: slope = 6/2 or 3
8: slope = 2/-4
9: slope = 1/6
A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a
predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?
Answers
Step by step explanation:
Now write an equation that represents the situation. You want to find the change in the dolphins depth, so subtract it’s beginning depth from its final depth.
Hope it helps!
What is 30% out of 89
Answers
Answer:
30 percent off 89.00 is 62.30
What is 100000000000000x234500000020000030040040
Answers
Answer:
234500000020000000000000000
Step-by-step explanation:
What is the image of the point (7,-5) after a rotation of 270° counterclockwise
about the origin?
Answers
Answer:
(-5, -7)
Step-by-step explanation:
if you rotate the point by 270 degrees counterclockwise, you get (5,-7) and I'm guessing image is another way to say reflection so after it is reflected then the point would be (-5,-7)
solve for p2. p1v1 = p2v2
Answers
Answer:
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
Step-by-step explanation:
Given expression:
Boyle's law:
P₁ V₁ = P₂ V₂
Problem is to find P₂;
Solution:
P₁ V₁ = P₂ V₂
To solve this problem, multiply both sides by [tex]\frac{1}{V_{2} }[/tex];
P₁ V₁ x [tex]\frac{1}{V_{2} }[/tex]; = P₂ V₂ x [tex]\frac{1}{V_{2} }[/tex];
[tex]\frac{1}{V_{2} }[/tex] cancels out V₂ on the right hand side;
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
Please please help me answer number 14
Answers
Answer:
A and E is base angle.
B and D is leg.
F is base.
C is vertex angle.
Thank you and please rate me as brainliest as it will help me to level up
Answer:
answer below
Step-by-step explanation:
a base angle
b leg
c vertex angle
d leg
e base angle
f base
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes.
Answers
A college information pamphlet provides some statistics about the students and the professors to help high school seniors decide if they want to attend the college. The pamphlet lists the ratio of students to professors as 18 to 1. If there are 702 students at the college, how many professors are there?
Answers
Answer:
39
Step-by-step explanation:
Setting up your problem and solving:
In the question it says the ratio is students to professors right? So 18 to 1.
Write that down: Students to Professors is 18 to 1.
We know that there are 702 students in that college correct?
Write that down: 702 students in the college
We are trying to find how many professors there are so...let's do that.
Number 1:
Set your equation: have your fraction bar and equal sign like this: --- = ---
On the top, we have 1 so... 1/? = ?/?
On the other top we have the x...: 1/? = x/?
Why? Because we do not know the total of professors there are so that is X.
We put the number 1 on the other side because we know that there is only 1 out of 18 professors to students.
Number 2:
On the bottom, we will have 18...: 1/18 = x/?
On the other bottom we have 702...: 1/18 = x/702
Why? Because we know that there is a total number of 18 to 1 students on the ratio and a real total of 702 students.
Number 3.
Now you have your equation set up: 1/18 = x/702
The next step is yours: cross multiple, divide on the bottom or top or find the comparison.
I'm going to divide by the bottom okay? so.. 18/702
Set that up.
(702/18)
702/18 is 39!
SO in the end there is a total of 39 professors!
'x=39'
Hoped this helped! :)
Abby has 96 photos from her vacation. She wants to make a scrapbook that has 24 pages with the same number of photos on each page.
Answers
Answer:
There will be 4 photos on each page
Step-by-step explanation:
96/24=4
if a dog can eat one thirds of a bag of food in 1/2 a week how many bags of food can the dog eat in one week
Answers
Answer:
Two thirds of a bag.
Step-by-step explanation:
1/2 * 2 = 1
1/3 * 2 = 2/3
Hope this helped!
(GR.7MATH)
Can somebody plz answer all these correct in simplify form thanks!
I’m confused on how to write in simplify so can somebody plz write it in that way.
WILL MARK BRAINLIEST
Answers
Answer:
dcc
Step-by-step explanation:
aajajaja
i am in doubt in this task... Thanks
Answers
Answer:
the answer is a
Step-by-step explanation:
Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sister who is two years younger than him. If the product of his sisters' ages is 70, how old is Richard?
Answers
Answer:
7 years
Step-by-step explanation:
Given that:
Let Richard's age = x
Elder sister's age = 2x
Youngwr sister's age = x - 2
Product of sisters ages = 70
2x * (x - 2) = 70
2x² - 4x = 70
2x² - 4x - 70 = 0
x² - 2x - 35 = 0
x² - 7x + 5x - 35 = 0
x(x - 7) +5(x - 7) = 0
(x - 7) or (x + 5) = 0
x = 7 or x = - 5
X can't be negative
Hence, x = 7
Richard is 7 years
6. Spiderman is three times as old as Superman.
The sum of their age is 160. How old are each of
them?
Answers
Superman 40
Answer:
Spiderman is 120, and Superman is 40.
Step-by-step explanation:
40 x 3 = 120
120 + 40 = 160
Educators in Michigan have been trying to raising math achievement scores for several years without success. Results from the state assessment test given in fourth grade show that 52% of all fourth graders cannot subtract when borrowing from zero (regrouping with zero in the subtrahend). Two new techniques for teaching this concept have been developed by teachers who belong to the Michigan Council of Teachers of Mathematics. It is decided that each technique be used in randomly selected classrooms throughout the state. Sixty third-grade classrooms are selected to try each of the techniques. Results from the state assessment test will then be monitored for each of the next two years to see whether either of the two techniques will be effective in teaching subtraction from zero. Sixty-three percent of the students who were taught with first technique passed the objective. Only 32% of students who were taught with the second technique passed the objective.
1. The population is:______.
A. All fourth graders in Michigan.
B. All third graders in Michigan.
C. The students who were in the 60 third-grade classrooms that used each technique.
D. All students in fourth grade who were taught with one of the techniques.
2. The sample is:______.
A. All fourth graders in Michigan.
B. All third graders in Michigan.
C. The students who were in the 60 third-grade classrooms that used each technique.
D. All students in fourth grade who were taught with one of the techniques.
3. An example of a parameter in the study is:______.
A. 63% of the students taught using technique 1 achieved the objective of subtracting from zero.
B. 32% of the students taught using technique 2 passed the state objective test.
C. 52% of all fourth graders in Michigan cannot subtract from zero.
D. 52% of all fourth graders in Michigan cannot pass the fourth-grade mathematics state assessment test.
4. An example of a statistic in the study is:_______.
a. 63% of the students taught using technique 1 achieved the objective of subtracting from zero.
b. 32% of the students taught using technique 2 passed the state objective test.
c. 52% of all fourth graders in Michigan cannot subtract from zero.
d. both a & b.
e. all of the above.
5. The dependent variable is the:______.
A. Results from the fourth-grade state assessment test in mathematics state assessment.
B. Instruction in math in third grade.
C. Two new techniques for teaching subtraction from zero.
D. Percentage of children who passed the objective subtraction from zero.
6. The independent variable is the:______.
A. Results from the fourth-grade state assessment test in mathematics state assessment.
B. Instruction in math in third grade.
C. Two new techniques for teaching subtraction from zero.
D. Percentage of children who passed the objective subtraction from zero.
Answers
Answer:
1. A. All fourth graders in Michigan.
2. C. The students who were in the 60 third-grade classrooms that used each technique.
3. C. 52% of all fourth graders in Michigan cannot subtract from zero.
4. d. both a & b.
5. D. Percentage of children who passed the objective subtraction from zero.
6. C. Two new techniques for teaching subtraction from zero.
Step-by-step explanation:
1. We can make this conclusion since an assessment test often comes after students undergo the required lessons (that is using taught the new techniques, so when they entered the fourth grade the assessment would be taken to determine their performance. Hence, the population of the study is the entire fourth-graders in Michigan.
2. The sample includes only students who made up the "60 third-grade classrooms that used each technique". In other words, they were the subject of the study.
3. Remember, a parameter often refers to numbers that summarize the entire data of a particular population. So we could say, that 52% of all fourth graders in Michigan that cannot subtract from zero make up the parameter.
4. A statistic is usually any resulting values gotten from a sample. Hence, both statements a and b are statistics from the sample.
5. Remember, the dependent variable is a variable that can be influenced by another variable; the independent variable. In other words, the percentage of children who passed the objective subtraction from zero could be affected by the independent variable.
6. The independent variable is the variable that could influence the dependent variable. In other words, the two new techniques for teaching subtraction from zero could influence "the percentage of children who passed the objective subtraction from zero."
Mario tracks his heart rate after throwing warm-up pitches before a game. In 1/4 minutes, Mario's heart beats 28 times
Answers
Answer:112
Step-by-step explanation: 1/4 divided by 28/1 = 1/112
Answer:
112 and very light
Step-by-step explanation:
What is the solution set for |x/2|=8?
Answers
Answer:
D) x=16 and x=-16
Step-by-step explanation:
D) x=16 and x=-16
If you replace x with either one of them and then take the absolute value, you would have 8.
a baker can bake 20 cakes per hour how long will it take him to bake 400 cakes
Answers
Answer:
20 hours
Step-by-step explanation:
400/20 is 20 which means to bake 400 cakes, he needs 20 hrs
1.find the domain,range and function.
{(-6, 4), (5, -1), (0, 3), (-2,4)}
Domain:
Range:
Function
Answers
Answer: domain: {-6, 5, 0, -2}
Range: { 4, -1, 3, 4}
Function: Yes it is a function
Select the correct locations on the graph. Select the lines that represent functions.
Answers
Answer:
SECOND QOURDANT
Step-by-step explanation:
The graph lying in first quadrant and graph of horizontal line lying in the fourth quadrant are representing functions.
A function is such type of mapping which strictly has one and only one value corresponding to each input given to the function.
The graph of first quadrant satisfies the condition of a mapping being a function.
The second quadrant contains a graph of parabola but as it is visible, the graph has two values for each input x it takes from -3 to -6. Example: At x = -6, the function outputs y = 2 and y = 5 two values. Thus it is NOT a function.
The third quadrant contains similar graph which also doesn't satisfy the single output constraint. Example, at x = -1, it outputs y = -2 and y = -6 both. Thus its NOT a function.
The fourth quadrant has a graph of two lines. First line is horizontal and has only one value to each x it allows as valid input. Thus it represents a function.
In the same fourth quadrant lies another line but that is vertical. For value x=4. it has several values of y. Thus its NOT a function either.
Thus the graph lying in first quadrant and graph of horizontal line lying in the fourth quadrant are representing functions.
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