Answer/Step-by-step explanation:
Part A:
(6x + 2)° + (8x + 6)° + (7x + 4)° = 180° (angles in a straight line)
Solve for x
6x + 2 + 8x + 6 + 7x + 4 = 180
Add like terms
21x + 12 = 180
21x + 12 - 12 = 180 - 12
21x = 168
21x/21 = 168/21
x = 8
Part B:
Method 1:
m<CFD + m<CFB + m<BFA = 180° (Angles in a straight line)
m<CFD + (6x + 2)° + (8x + 6)° = 180° (substitution)
Plug in the value of x
m<CFD + 6(8) + 2 + 8(8) + 6 = 180
m<CFD + 48 + 2 + 64 + 6 = 180
m<CFD + 120 = 180
m<CFD + 120 - 120 = 180 - 120
m<CFD = 60°
Method 2:
m<CFD = m<AFE (vertical angles are congruent)
m<CFD = (7x + 4)° (substitution)
Plug in the value of x
m<CFD = 7(8) + 4
m<CFD = 60°
What is the equation of the line that is the perpendicular bisector of the segment
with (10,-15) and (-10, 25) as endpoints?
y= kx + 10
y= kx + 5
y= -x + 10
y = 2x + 5
Answer:
y= kx + 5Step-by-step explanation:
Perpendicular bisector passes through the midpoint of the line.
The midpoint is:
x = (10 - 10)/2 = 0y = (-15 + 25)/2 = 5Slope of the line:
m = (25 - (-15))/(-10 - 10) = -2The line perpendicular to this has to have a slope of 1/2 as perpendicular lines have opposite-reciprocal slopes.
Use point-slope form and point (0, 5) to find the equation of the line:
y - 5 = 1/2(x - 0)y = 1/2x + 5Correct option seem B as others don't match ours
h(x) = 3x + 5
g(x) = 4x – 2
Find h(x) – g(x)
Answer:
6
Step-by-step explanation:
seshhhhh is that dababy. he valid
convert 320% to an equivalent decimal.
Answer:
Answer is 3.2
Step-by-step explanation: you can take any percent and divide it by 100. So in this example you would divide 320/100 and it will give you 3.2
Hudson is going to invest $320 and leave it in an account for 9 years. Assuming the
interest is compounded monthly, what interest rate, to the nearest tenth of a percent,
would be required in order for Hudson to end up with $540?
Answer:
5.8
Step-by-step explanation:
The interest rate, to the nearest tenth of a percent, will be 0.05828.
How do you determine the amount of compound interest?If the principal amount is P, the interest rate is R percent per unit time, and the compound interest is left for T units of time, the interest amount gained is:
[tex]\rm CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The total is:
[tex]\rm A = CI + PA = P(1 +\dfrac{R}{ 100})T[/tex]
The amount is found as;
[tex]\rm A = P(1+\frac{r}{n})^{nt}\\\\ 540=320 (1+\frac{r}{12} )^{12\times 9}\\\\ (1+\frac{r}{12})^{108}=\frac{540}{320}\\\\ 1+\frac{r}{12}=(\frac{540}{320})^{\frac{14}{108}[/tex]
[tex]\rm 1+ \frac{r}{12}=1.00486\\\\ \frac{r}{12}=0.00486\\\\ r=12 \times 0.0486 \\\\ r=0.05828[/tex]
Hence, the interest rate, to the nearest tenth of a percent, will be 0.05828.
To learn more about compound interest, refer:
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help me please!!!
solve a quadratic equation by factoring
solve for g.
g^2-24g+144=0
9514 1404 393
Answer:
g = 12
Step-by-step explanation:
You recognize that 144 is 12², so you check to see if the x-coefficient is 2·12. It is. The quadratic is a square:
(g -12)² = 0
The only solution is the one that makes the squared term equal to zero:
g -12 = 0
g = 12
_____
The square of a binomial is ...
(a +b)² = a² +2ab +b²
Here, we have a=x, b=-12.
Help me with this question please!
Answer:
84 in²
Step-by-step explanation:
12+9=21
21x0.5=10.5
10.5x8=84
You want to install a 3 yd wide walk around a circular swimming pool. The diameter of the pool is 16 yd. What is
the area of the walk? Use 3.14 for it.
The area of the walk is approximately
i need number 22 PLS AND THANK YOU!
Answer:
For any two given points (x1,y1) and (x2,y2), the slope = (y2-y1)/(x2-x1)
Let's take the points (15,3) and (30, 6):
slope = (y2-y1)/(x2-x1)
= (6-3)/(30-15)
=3/15
=1/5 =0.2
The slope, in general, means the rate of change of y, relative to x. In the context of this question, the slope tells us that the amount of concrete that can be poured (in yards) is a fifth of the time taken (in minutes).
What is the solution of the equation?
Answer:
+8 and -8, 2nd answer from the right.
Rewrite 7^-2 using a positive exponent an evaluate the result.
Mrs.Hilt’s yard is 48 feet long and 39 feet wide . What is the area of Mrs.Hilt’s back yard?
Answer:
1872
Step-by-step explanation
From the equation y = 4 - X, which ordered pair would represent a solution?
A (3,-1)
B (9,5)
C (6,-2)
D (0,-4)
Alice has 5 quarters and 2 nickels. How many cents does Alice have
Answer:
Alice has 135 cents, or $1.35.
Step-by-step explanation:
A quarter is worth 25 cents.A nickel is worth 5 cents.Multiply 25 by 5, since there are 5 quarters. That will give you 125.Multiply 5 by 2, since there are 2 nickels. That will give you 10.Add 125 and 10. That will give you 135, which is your answer!A triangle has side lengths of 6,9, and 17. Is this possible or impossible
Answer:
impossible
Step-by-step explanation:
the formula for triangle sides is a^2 + b^2 = c^2
and these numbers dont equal that
A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 15 greeting cards indicates an average value of $3.00 and a s of $0.40. The critical value for a 99% confidence interval is
Answer:
The critical value for a 99% confidence interval is T = 2.9768
Step-by-step explanation:
We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
Critical value
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.9768
The critical value for a 99% confidence interval is T = 2.9768
6 Melvin and Roberto played football on two different teams last season.
• Melvin's team won w games.
• Roberto's team won 3 fewer games than Melvin's team.
Which expression can be used to represent the number of games Roberto's
team won last season?
Select one answer.
A W + 3
BW-3
CW.3
Dw3
Answer:
B is the answer
Step-by-step explanation:
soup is 3 cans for $0.82, so each can of soup is $0.2733. how much does it cost for each one?
21 students are going on a field trip and 3 students are staying at school what is the ratio of the numbers of students who are going on a field trip to the number of students who are staying at school?
Answer:
21/3 or 7/1
Step-by-step explanation:
Answer:
21/3
Step-by-step explanation:
hope this helps you
3/4+1/2= 2. 5/6+1/2= 3. 3/6+1/2= 4.1/6+4/8= 5.7/8+1/4= 6.3/8+1/2=
Answer:
1.) [tex]\frac{5}{4\\}[/tex]
2.) [tex]\frac{4}{3}[/tex]
3.) 1
4.) [tex]\frac{2}{3}[/tex]
5.) [tex]\frac{9}{8}[/tex]
6.) [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
The 2 steps for all of these is to get common denominators and then add and simplify.
1.) 3/4 + 1/2 (common denominator) 3/4 + 2/4 = 5/4
2.) 5/6 + 1/2 (common denominator) 5/6 + 3/6 = 4/3
3.) 3/6 + 1/2 (common denominator) 3/6 + 3/6 = 6/6 (simplify) = 1
4.) 1/6 + 4/8 (common denominator) 8/48 + 24/48 = 32/48 (simplify) = 2/3
5.) 7/8 + 1/4 (common denominator) 7/8 + 2/8 = 9/8
6.) 3/8 + 1/2 (common denominator) 3/8 + 4/8 = 7/8
Which is the greater decimal?
.721 or .72
Answer:
.721 is bigger because Il earned that the decimal that has a larger number as there last number is the greatest decimal.
Step-by-step explanation:
A large clock in a town square has a minute hand that is 10 feet long. Which value is the best estimate of
how many degrees the minute hand moves from 4:00 - 4:40?
Answer: 240 degrees
Step-by-step explanation: minute hand makes 360 degree circle in hour.
There is no influence for the length of hand in this case.
40 minutes is 2/3 hours. 2/3 ·360 degrees
Della needs fabric that is 12.4 yards long. If the store sells fabric in meters, how much fabric will she need?
The number of students that participated in sports last year was 100. This year there are 140 students participating in sports. What is the percent of increase in the number of students participating in sports from last year to this year? __________%
Answer: 40%
Step-by-step explanation:
HOPE THIS HELPS ^^
Consider the probability that fewer than 46 out of 134 students will not pass their college placement exams. Assume the probability that a given student will not pass their college placement exam is 98%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
a. Yes
b. No
Answer:
b. No
Step-by-step explanation:
Binomial approximation to the normal:
Binomial distribution has n trials, with p probability.
If
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], it can be approximated to the normal distribution.
Assume the probability that a given student will not pass their college placement exam is 98%.
This means that [tex]p = 0.98[/tex]
134 students:
This means that [tex]n = 134[/tex]
Necessary conditions:
[tex]np = 134*0.98 = 131.32 \geq 10[/tex]
[tex]n(1-p) = 134*0.02 = 2.68 < 10[/tex]
Since the necessary condition n(1-p) < 10 is not satisfied, the answer is No, given by option b.
Cynthia says that when you evaluate the expression (21 3/4 + 4 1/2) - 5 3/12 you get a whole number. What whole number do you get?
Answer: 21
Step-by-step explanation:
First, convert the mixed fractions to improper fractions.
(87/4 + 9/2) - 21/4
Next, calculate within the parentheses:
87/4 + 9/2
Next, change the denominator of 9/2 to 4. To do that, multiply the denominator of 9/2 to get 4 to match the denominator of the first fraction. 9/2 * 2/2 = 18/4.
87/4 + 18/4 = 105/4
Then, 105/4 - 21/4 = 84/4
Finally, divide 84 by 4 and you get 21.
The ratio of soccer players to baseball players on two school teams is 4 to 7. Which of the following could be the number of players on each team?
Select one:
16 soccer players and 49 baseball players
16 soccer players and 19 baseball players
12 soccer players and 15 baseball players
12 soccer players and 21 baseball players
Answer:
12 soccer players and 21 baseball players
Step-by-step explanation:
Multiply each ratio by the same number
4x3=12 7x3=21
Jasmine was expected to get $150 for her bonus, but she only got $100. What was the percent error?
Answer:
Jasmine expected to get $150 for her bonus, but she only got $100. What was the percent error?
-----
Amt of error:: $50
----------
% error:: 50/150 = 1/3 = 33 1/3%
Please help me with this question if you can
Answer:
exterior angle = the sum of two remote interior angles
14x + 1 = 89 + 5x - 7
=> 9x = 81
=> x = 9
substitute x = 9 into angle H (5x - 7)
=> 5(9) - 7 = 45 - 7 = 38
Please please help please
Answer: 72 feet
Step-by-step explanation:
24 yards= 72 feet
I need the area can someone help meeee pls?
Answer:
54ft
Step-by-step explanation:
9ft x 6ft