Answers
opposite angels = 180
so 6m+13 +4m+7 =180
combine like terms
10m+20=180
10m =160
m=160/10 = 16
Angle M = 6m = 6(16) = 96 degrees
Related Questions
If M is the midpoint of FG and MG = 7x-15, FG = 33, X = ?
Answers
The given expression gives x = 4.5.
If M is the midpoint of FG, this means that M divides FG into two equal segments. Therefore, FM = MG. We are given that MG = 7x - 15 and the total length of FG = 33. Hence, FM = MG = (1/2) * (FG).
Step-by-step solution:
Set up the equation for FM: FM = MG = (1/2) * 33.
This simplifies to FM = MG = 16.5.
Since MG = 7x - 15, we set 7x - 15 equal to 16.5.
Solve for x: 7x - 15 = 16.5.
First, add 15 to both sides: 7x = 31.5.
Finally, divide both sides by 7: x = 4.5.
Therefore, the value of x is 4.5.
It takes 113 pounds of seed to completely plant a 12 -acre field. how many acres can be planted per pound of seed?
Answers
It takes about 9lbs of seed to plant 1-acre, so to find the answer divide 12/113 and you get how many acres 1lb of seed could cover.
Hope this helps :-)
What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?
Answers
The measure of a base angle in an isosceles triangle with a vertex angle of 38° is 71°, as isosceles triangles have two equal base angles and the total sum of angles in any triangle is 180°.
Explanation:To calculate the measure of a base angle in an isosceles triangle, we need to remember that the sum of angles in a triangle is always 180°. Given that we have a vertex angle of 38°, we subtract that from 180° to find the sum of the two base angles. Since it's an isosceles triangle, these angles are equal:
180° - 38° = 142° (sum of both base angles)142° / 2 = 71° (measure of one base angle)Therefore, the measure of one base angle in this isosceles triangle is 71°.
The measure of each base angle of an isosceles triangle is 71°.
Explanation:An isosceles triangle has two congruent sides and two congruent base angles. In this case, the vertex angle measures 38° and the congruent sides each measure 21 units. To find the measure of a base angle, we can use the fact that the sum of the angles in a triangle is 180°. Since the vertex angle is 38°, the sum of the base angles is 180° - 38° = 142°. Since the base angles are congruent, we can divide 142° by 2 to find the measure of each base angle.
142° / 2 = 71°
Therefore, the measure of each base angle is 71°.
Simplify 8 − (14)
1. −22
2. −6
3. 6
4. 22
Answers
Answer:
2
Step-by-step explanation:
-6
How do you use the slope to prove lines are parallel or perpendicular?
How do you write an equation of a line so that it is parallel or perpendicular to a given point?
Answers
Final answer:
To prove lines are parallel, their slopes must be equal, and to prove they are perpendicular, their slopes must be negative reciprocals. To write an equation for a parallel line, use the same slope as the original; for a perpendicular line, use the negative reciprocal of the original line's slope. Manipulating a line involves changing either its slope or intercept.
Explanation:
To use slope to prove that lines are parallel or perpendicular, you need to compare their slopes. Two lines are parallel if their slopes are equal. Conversely, two lines are perpendicular if their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other (e.g., the slope of one line is 2 and the other is -1/2).
To write an equation of a line so that it is parallel to a given line, you must use the same slope as the given line. If the equation of the given line is y = mx + b, then the equation of a parallel line will be y = mx + c, where c is a different y-intercept. To write an equation of a line so that it is perpendicular to a given line, you use the negative reciprocal of the slope of the given line. If the slope of the given line is m, then the slope of the perpendicular line will be -1/m.
For example, consider a line with the equation y = 3x + 9, which signifies a slope of 3 and a y-intercept of 9 based on Figure A1. A parallel line would have a slope of 3 but could have a different y-intercept, such as y = 3x + 4. A perpendicular line would have a slope of -1/3, so it could be something like y = -1/3x + 5.
Manipulating a line involves changing its slope (m) or intercept (b). Changing the slope will tilt the line, while changing the intercept will shift the line up or down on the graph. Understanding how to read and manipulate a graph is crucial for visualizing these changes.
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
Answers
For the first part:
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.
[tex]\begin{center} \begin{tabular} {|c|c|c|c|c|} & Cats & Dogs & Other & Total \\ [1ex] Male & 42 & 58 & 6 & 106 \\ Female & 52 & 48 & 2 & 102 \\ [1ex] Total & 94 & 106 & 8 & 208 \end{tabular} \end{center}[/tex]
Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male.
Find P(B| NOT A).
P(A) = P(choosing cat) + P(choosing dog) = [tex] \frac{94}{208} + \frac{106}{208} = \frac{200}{208} = \frac{25}{26}[/tex]
P(NOT A) = [tex]1- \frac{25}{26} = \frac{1}{26} [/tex]
P(B and NOT A) = P(males that did not choose cat or dog) = [tex] \frac{6}{208} = \frac{3}{104} [/tex]
P(B | NOT A) = [tex] \frac{P(B \, and \, NOT \, A)}{P(NOT \, A)} = \frac{ \frac{3}{104} }{ \frac{1}{26} } =\frac{3}{104}\times26= \frac{3}{4} [/tex]
For the second part of the question.
Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
If his investment increases by 10%, the value of the investment will be 1.1 x $19 = $20.90 with a probability of 30% or 0.3
The expected value of the investment is given by
[tex]\$20.90\times0.3+(-\$19\times0.7)=\$6.27-\$13.30=-\$7.03[/tex]
Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.
Find 3 consecutive integers if the sum of the first and third is 128
Answers
2x + 2 = 128
2x = 126
x = 63
numbers are: 63, 64, 65
Question 25. How do you do it?
Answers
One person rents for $6 plus the green fee for one person. Let g = the green fee for a person. The total cost, club rental plus green fee, was $76.
6 + g = 76
g = 70
PLEASE HELP I WILL RATE YOU BRAINLIEST!!
Write -5.8 as a mixed number in simplest form. Show your work
Answers
16x+9=9y−2x
solve for y
I am confused on how to solve for y, I learned it but I forgot how to can some one please help me?
Answers
16x + 9 = 9y - 2x
Add 2x to both sides to isolate y (get it by itself on one side of the equation).
16x + 2x = 18x
-2x + 2x = 0
18x + 9 = 9y
Divide both sides by 9 to solve for y.
18x / 9 = 2x
9 / 9 = 1
9y / 9 = y
We are now left with:
2x + 1 = y
I hope this helps!
What is the area of the triangle?
Answers
answer
first one.
24 square units
In one baseball season, Peter hit twice the difference of the number of homeruns Alice hit and 6. Altogether, they hit 18 homeruns. how many homeruns did each player hit that
season?
Answers
x = 2(y - 6)
This is the equation for the relationship between Peter's and Alice's hits. The second equation would be the sum of their hits:
x + y = 18
These are the two independent equations in order to solve the two unknowns, x and y. Substituting the first equation into the second equation,
2(y - 6) + y = 18
2y - 12 + y = 18
3y = 18 + 12
3y = 30
y = 10
Using y=10 to the first equation:
x = 2(10 - 6)
x = 8
Therefore, Peter made 8 homeruns, while Alice made 10 homeruns for a total of 18.
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B"C"D"?
Answers
a 270-degree rotation about point B
If 3 is added to a number and the sum is tripledtripled, the result is 27 more than the number. find the number.
Answers
To solve this problem, let us say that the number is called x and let us do this step by step.
1st step: 3 is added to the number, therefore:
x + 3
2nd step: the sum is tripled, therefore:
3 (x + 3)
3rd step: the result in the 2nd step is equal to 27 more than the original number, therefore:
3 (x + 3) = x + 27
4th step: find for the value of x using the equation
3 x + 9 = x + 27
3 x – x = 27 – 9
2 x = 18
x = 9
Answer:
The number is 9
Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. what is the number of centimeters in the length of the longer leg of the smaller triangle?
Answers
The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the shorter leg is x.
- The length of the longer leg is x[tex]\sqrt{3}[/tex].
- The length of the hypotenuse is 2x.
Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:
2x = 16
Solving for x:
x = [tex]\frac{16}{2}[/tex] = 8
Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.
Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
The question is:
There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?
A gardener has 27 pansies and 36 daisies he ants an equal number of each type of flower in each row what is the greatest possible number of pansies in each row
Answers
The possible rows that will contain equal numbers of pansies are
1 row, 27 pansies in the row, or
3 rows, 9 pansies per row, or
9 rows, 3 pansies per row.
There are 36 daisies.
The possible rows that will contain equal numbers of daisies are
1 row, 36 daisies in the row,
2 rows, 18 daisies per row, or
3 rows, 12 daisies per row, or
4 rows, 9 daisies per row, or
6 rows, 6 daisies per row, or
9 rows, 4 daisies per row, or
12 rows, 3 daisies per row, or
18 rows, 2 daisies per row.
The only common row combination is 3 rows, with 9 pansies and 12 daisies per row.
Answer: 9 pansies in each row.
In the past ten years, the population of a city decreased from 90,000 to 75,000 Find the percent decrease.
Answers
((75,000−90,000)÷90,000)×100
=−16.7%
Ten is no more than 4 times the sum of twice a number and 3? Equation?
Answers
[tex]Ten: 10 \\ NoMore: less \\ 4times: 4 And Multiply \\ sum: + (add) \\ twice: 2 \\ number: a \\ 3: 3 \\ \\ \\ \\ \\ \\ Answer: 10 \leq 4 (2a + 3) \\ \\ \\ \\ Good\\ luck\\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ MeIsKaitlyn :)[/tex]
I need help finding ac, cb, and ab
Answers
CB is 3x-4
AB= 2x+1+3x-4
For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. What number of pieces of checked luggage is 3 standard deviations above the mean?
Answers
Answer:
The answer is 440 pieces of checked luggage
Step-by-step explanation:
Mean = 380
Standard deviation = 20
No. of pieces of checked luggage for 1 standard deviation = 20 pieces
Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60
Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean
⇒ 380 + 60 = 440 pieces
A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (5x + 2) wide by (3x + 1) long. The dimensions of the spa are (2x + 3) wide by (x + 2) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
Find the area of the new deck if x = 2 feet.
Answers
The area of the deck is
A₁ = (5x + 2)(3x + 1)
= 15x² + 5x + 6x + 2
= 15x² + 11x + 2
Answer: 15x² + 11x + 2
The dimensions of the spa are (2x + 3) wide by (x + 2) long.
The area of the spa is
A₂ = (2x + 3)(x + 2)
= 2x² + 4x + 3x + 6
= 2x² + 7x + 6
Answer: 2x² + 7x + 6
The area remaining after the hole for the spa has been cut from the deck(the area of the new deck) is
A = A₁ - A₂
= 15x² + 11x + 2 - (2x² + 7x + 6)
= 15x² - 2x² + 11x - 7x + 2 - 6
= 13x² + 9x - 4
Answer: 13x² + 9x - 4
If x = 2 feet, the area of the new deck is
A(2) = 13*2² + 9*2 - 4 = 78 ft²
Answer: 78 ft²
A store manager is looking at past jewelry sales to determine what sizes of rings to keep in stock. The list shows the ring sizes purchased by the last ten jewelry customers.
9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8
What is the variance of the data? Round to the nearest hundredths.
Answers
Mean = 9 + 7 + 6.5 + 7.5 + 7 + 8 + 5 + 6 + 7.5 + 8 / 10
Mean = 6.4
Squared of the sum of the differences = (9-6.4)^2 + (7-6.4)^2 + (6.5-6.4)^2 + (7.5-6.4)^2 + (7-6.4)^2 + (8-6.4)^2 + (5-6.4)^2 + (6-6.4)^2 + (7.5-6.4)^2 + (8-6.4)^2 = 17.15
Variance = 17.15 / 10 = 1.715
Identify the property that justifies the statement: If 4x-3=7, then 4x=10
Answers
The equation shown above is showing the Addition Property of Equation where the number “3” is added to both of its sides. This is shown below,
4x - 3 = 7
4x - 3 + 3 = 7 + 3
4x = 10
f(x)=11x-5, then f^-1(x)=
Answers
y=11x-5
x=11y-5
11y=5+x
divide each term by 11 to get:
y= 5/11 + x/11
so f^-1(x) = 5/11 + x/11
Sasha sets a goal to read 5 minutes longer than each previous day for 30 days. On the first day, Sasha reads for 20 minutes. The expression mc018-1.jpg represents the total number of minutes Sasha reads during the 30 days. How many total minutes does she read?
Answers
Final answer:
Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.
Explanation:
To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.
We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).
Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).
Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.
Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.
How tall would a stack of 1000 pennies be in centimeters?
Answers
Diameter: 19 mm
Thickness: 1.52 mm ( according to the US mint )
1000 * 1.52 = 1,520 mm = 1.52 m = 1 m 52 cm
Answer:
A stack of 1000 pennies would be 1 m 52 cm tall.
To calculate the height of a stack of 1000 pennies, multiply the thickness of one penny (0.1524 cm) by 1000. The total height would be 152.4 cm.
Explanation:Calculating the Height of a Stack of 1000 Pennies
To calculate the height of a stack of 1000 pennies, we first need to know the thickness of one penny. Unfortunately, the data provided talks about the volume of a stack of 100 bills, which is not directly relevant to our problem. However, by using the correct information, we find that a US penny is approximately 0.0598 inches (or 0.1524 cm) in thickness. So the calculation for the height of 1000 pennies stacked would be as follows:
Thickness of one penny = 0.1524 cmTotal height = 0.1524 cm/penny × 1000 penniesTotal height = 152.4 cmThus, the height of a stack of 1000 pennies would be 152.4 centimeters.
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Please HELP. Thank you
Answers
I would go with A because the lengths of the sides don't abide by the pythagorean theorem rule: A^2 + B^2 = C^2
Point C to Point B appears to have a slope of 2/3, 3 blocks apart (in width) and 2 blocks apart (in height). Using a^2 + b^2 = c^2 will help where ^2 means (squared).
(2 x 2) + (3 x 3) = 13
Line CB is (square root) of 13.
Point A and B are 2 blocks apart (width) and 3 blocks apart (height), so using what we did in the last step...
(3 x 3) + (2 x 2) = 13
Line AB is (square root) of 13.
So now... With Line AB and Line CB being the square root of 13, the line AC should be (square root) (13 + 13), so (square root) 26. If it does equal this, then it is a right-triangle.
Point C and A are 1 block apart (width) and 5 blocks apart (height) so...
(1 x 1) + (5 x 5) = 26
Square root of 26...
In conclusion, the Triangle IS a Right-angle and you should pick "D"
(02.06 MC)
What is the measure of angle x?
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 40 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 40 degree angle, is labeled as x.
40 degrees
80 degrees
130 degrees
140 degrees
Answers
A brick patio measures 18 ft by 16 ft by 6 in. find the volume of the bricks. if the density of the bricks is 130 pounds per cubic foot, what is the weight of the patio in pounds?
Answers
18 x 16 = 288
6 inches = 0.5 ft
288*0.5 = 144
patio = 144 cubic feet
144*130 = 18,720 total pounds
The formula a = 118e^0.024t models the population of a particular city, in thousands, t years after 1998. when will the population of the city reach 140 thousand?
Answers
So, substituting the values:
140 = 118 e^0.024t
140/118 = e^0.024t
Taking the natural logarithm, ln, on both sides,
ln (140/118) = lne^0.024t
ln(140/118) = 0.024t
t = ln(140/118) ÷ 0.024
t = 7.12 years
So, that would be approximately 7 years after 1998. The population would reach 140 thousand in year 2005.
Final answer:
To find when the population of the city will reach 140 thousand, the formula a = 118e⁰.⁰²⁴t must be solved, resulting in approximately 3.52 years after 1998.
Explanation:
The formula a = 118e^0.024t models the population of a city, in thousands, t years after 1998. To find when the population reaches 140 thousand, set the formula equal to 140 and solve for t:
a = 118e⁰.⁰²⁴t
140 = 118e⁰.⁰²⁴t
t = (ln(140/118)) / 0.024 ≈ 3.52 years after 1998.