Answers
Answer:
a= 63 ⁰; z= 80⁰; x= 30⁰; N= 102⁰;M = 66⁰
Step-by-step explanation:
Example 1 : the angle opposite to angle 2a is 54 degrees because it is the opposite exterior angle of 54 degrees angle so
2a+54⁰= 180⁰
2a= 180⁰-54⁰
2a= 126⁰
a= 126/2= 63⁰
EXAMPLE 2: Opposite exterior angles are equal so
z+25⁰= 105⁰-------A
z= 105⁰-25⁰
z=80⁰
It is making a straight angle so
105⁰+ 3x-15= 180⁰
3x-15=180-105
3x-15=75⁰
3(x-5)=75⁰
x-5⁰=75/3
x-5⁰=25⁰
x= 25⁰+5⁰
x=30⁰
EXAMPLE 3:
114⁰= N+12⁰ (exterior opposite angles are equal)
N= 114⁰-12⁰
N= 102⁰
114⁰+M= 180⁰ (straight angles)
M= 180⁰- 114⁰
M= 66⁰
Related Questions
86.4 is what percent of 192
Answers
Answer:45%
Step-by-step explanation:
I believe it’s 45%
Divide 86.4 by 192 and multiply the result by 100 to get the percentage, hence it is 45%.
A figure or ratio that may be stated as a fraction of 100 is a percentage.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Here we have to find:
86.4 is what percent of 192
Divide 86.4 by 192:
86.4 / 192 = 0.45
Multiply the result by 100 to convert it into a percentage,
Therefore,
0.45 x 100 = 45%
Hence,
86.4 is 45 percent of 192.
Learn more about the percentage visit:
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the zeros of f(x) algebraically
Answers
Answer:
The zeros are 4, -6, and 1.
Step-by-step explanation:
Given f(x) = x³ + x² - 26x + 24
(x - 4) is a factor of f(x). That means it is a zero of f(x).
To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).
That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]
[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]
Taking [tex]$ x^2 $[/tex] out, we have:
[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]
Taking (x - 4) common out, we have:
[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]
[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]
[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]
[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]
This means the zeros are 4, -6, & 1.
At a farm ,Justin picks 3 bushels of fruits, the bushel weigh 8 1/4 pounds,6 1/2 pounds, and 6 5/8 pounds. What is the average weight per bushel
Answers
Answer:
7.125
Step-by-step explanation:
The average weight per bushel of fruits that Justin picked is calculated as the sum of all weights divided by the number of bushels, which comes out to be 7.125 pounds per bushel.
To calculate the average weight per bushel when Justin picks 3 bushels of fruits weighing 8 1/4 pounds, 6 1/2 pounds, and 6 5/8 pounds, we need to add up the weights of the bushels and then divide by the number of bushels. Here are the steps:
First, convert all fractions to decimals or common denominators for easier addition:
8 1/4 = 8.25 pounds
6 1/2 = 6.5 pounds
6 5/8 = 6.625 pounds
Add up the weights of the three bushels:
8.25 + 6.5 + 6.625 = 21.375 pounds
Finally, divide the total weight by the number of bushels to find the average:
21.375 pounds \/ 3 bushels = 7.125 pounds per bushel
The average weight per bushel that Justin picks is 7.125 pounds.
Aiden has three 20$ bills and two 10$ bills he wants to save a total of 95$ how much more money does he need what bills could they be
Answers
Answer:
$15.00
A $10.00 and a $5.00 dollar bill
Step-by-step explanation:
Answer:$80
Step-by-step explanation:
3 times 20=60
2 times 10=20
either 1, $10 and 1, $5, or 3, $5 or 15, $1
The two-way table represents data from a survey asking teachers whether they teach English, math, or both. A 4-column table with 3 rows. The first column has no label with entries math, not math, total. The second column is labeled English with entries 34, 40, 74. The third column is labeled not English with entries 22, 8, 30. The fourth column is labeled total with entries 56, 48, 104. Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent. 8% 21% 33% 38%
Answers
Answer:
b 21%
Step-by-step explanation:
good luck and hurry :)
The given 22 teachers from the total of 104 teachers in the survey gives
the teachers who teach math and not English as approximately; 21%
How can the joint relative frequency be obtained?
The relative frequency table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&English&Not english & Total\\Math&34&22&56\\Not math&40&8&48\\Total&74&30&104\end{array}\right][/tex]
Required:
The joint relative frequency for teachers teaching math and not English
Solution:
The joint relative frequency is the ratio of the frequency of a given category to the total number of data points within the category.
The number of teachers that teach math but not English = 22
Total number of teachers in the survey = 104
Therefore;
[tex]The \ joint \ relative \ frequency = \dfrac{22}{104} \times 100\approx \mathbf{21\%}[/tex]
Therefore;
The joint relative frequency for the teachers that teach math and not English is approximately 21%Learn more about joint relative frequency here:
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PLZ HELP I REALLY NEED IT
Answers
Answer:
Angle = 64 Degrees
Supplement of Angle = 116 Degrees
Step-by-step explanation:
Let the angle be "x"
We know
The complement of the angle is "90 - x"
and
The supplement of the angle is "180 - x"
From the statement given, we can write:
supplement is 12 LESS THAN twice the angle
The equation would be:
180 - x = 2x - 12
Now, we solve this for x:
[tex]180 - x = 2x - 12\\180+12=2x+x\\192=3x\\x-\frac{192}{3}\\x=64[/tex]
The angle is 64 degrees
The supplement of the angle is 180 - 64 = 116 degrees
if a rectangle is 95 meters long and 65 meters wide what is the diagonal
Answers
Answer:
115.1
Step-by-step explanation:
Which of the following matrix addition problems are possible?
Answers
Answer:
Option A
Step-by-step explanation:
When adding two matrices, they should be of the same sizes.
Option A:
Matrix [tex]\left[\begin{array}{c}2&3\end{array}\right][/tex] has 2 rows and 1 column.
Matrix [tex]\left[\begin{array}{c}3&4\end{array}\right][/tex] has 2 rows and 1 column too.
So, these matrices can be added.
The result will be
[tex]\left[\begin{array}{c}2+3&3+4\end{array}\right]=\left[\begin{array}{c}5&7\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
E2020
plz hurry!!!! thank you!!!!
Answers
Step-by-step explanation:
Since SP=TR, the differnce of PR and ST 24-15 divided by 2 is the length of PD (4.5)
Try to understand the rest from the attached picture
a pancake recipe asks for one and one half times ad much milk as flour. if two and one quarter cups of milk is used what quantity of flour would then be needed
Answers
Answer:
x = 4/3
Step-by-step explanation:
x = amount of flour
x = amount of milk / 2.5
x =(3 1/3) / 2.5
change both to improper fractions
x = 10/3 / (5/2)
invert and mutiply
x = 10/3 * 2/5
George invested a total of $5,000 at the beginning of the year in two different funds. At the end of the year, his investment had grown to $5,531. The money in the first fund earned 9%, while the money in the second fund earned 13.5%. Write a system of equations, then solve it to find out how much of the $5,000 was invested into each fund at the beginning of the year
Answers
Answer:
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested at 9% (first fund)
5,000-x ----> the amount invested at 13.5% (second fund)
Remember that
[tex]9\%=9/100=0.09[/tex]
[tex]13.5\%=13.5/100=0.135[/tex]
The total interest earned is equal to
[tex]\$5,531-\$5,000=\$531[/tex]
we know that
The amount earned by the first fund at 9% plus the amount earned by the second fund at 13.5% must be equal to $531
so
the linear equation that represent this situation is equal to
[tex]0.09x+0.135(5,000-x)=531[/tex]
solve for x
[tex]0.09x+675-0.135x=531[/tex]
[tex]0.135x-0.09x=675-531[/tex]
[tex]0.045x=144[/tex]
[tex]x=\$3,200[/tex]
so
[tex]\$5,000-x=\$5,000-\$3,200=\$1,800[/tex]
therefore
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
Convert Зcis 180° to rectangular form.
А. -3
в. -3i
с. з
D. Зі.
Answers
Answer:
-3
Step-by-step explanation:
[tex]3 cis(180^\circ)[/tex] means [tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
What is the [tex]x[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is -1.
What is the [tex]y[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is 0.
So this implies [tex]\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0[/tex].
[tex]3 cis(180^\circ)[/tex]
[tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
[tex]3(-1+i (0))[/tex]
[tex]3(-1+0)[/tex]
[tex]3(-1)[/tex]
[tex]-3[/tex]
Which pair of ratios does not
form a true proportion?
A) 6:16 and 21:56
B) 2 to 10 and 15 to 75 C) 9/11=27/15
D) y = 5x
Answers
Answer:
C
Step-by-step explanation:
Triangle ABC has vertices at A(-3,4)B(4,-2)C(8,3).The triangle is translated 4 units down and 3 units left . Which rule represents the translation? After the translation, what are the coordinates of vertex C
Answers
Answer:
see explanation
Step-by-step explanation:
A translation of 4 units down means subtract 4 from the y- coordinate of the original point and a translation of 3 units left means subtract 3 from the original x- coordinate, thus translation rule is
(x, y ) → (x - 3, y - 4 )
Thus
C(8, 3 ) → C'(8 - 3, 3 - 4 ) → C'(5, - 1 )
what does a midpoint of a line segment create? Choose All The Apply.
(in pic below)
Answers
Answer: Two lines of equal length
A point equidistant from two end points
Step-by-step explanation:
The mid - point of a line segment is the point on the segment that is equidistant from the endpoints.
It is not equidistant to all point on the segment , it is only equidistant from the endpoints.
With this , the first option is out.
The midpoint of a line divides the line into two equal part , so the second option holds and the third option holds too.
An airplane takes 3 hours to travel a distance of 2250 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
Answers
Answer:
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
Step-by-step explanation:
The distance equation is D = RT
Where
D is the distance
R is the rate
T is the time
Let rate of airplane be "x" and rate of wind be "c"
Also, note: rate with wind is airplane's and wind's, so that would be "x + c"
and rate against the wind is airplane's minus the wind's, so that would be "x - c"
Now,
2250 miles with wind takes 3 hours, so we can write:
D = RT
2250 = (x + c)(3)
and
2250 miles against the wind takes 5 hours, we can write:
D = RT
2250 = (x - c)(5)
Simplifying 1st equation:
[tex]2250 = (x + c)(3)\\3x+3c=2250[/tex]
Simplifying 2nd equation:
[tex]2250 = (x - c)(5)\\5x -5c=2250[/tex]
Multiplying the 1st equation by 5, gives us:
[tex]5*[3x+3c]=2250\\15x+15c=11250[/tex]
Multiplying the 2nd equation by 3 gives us:
[tex]3*[5x -5c=2250]\\15x-15c=6750[/tex]
Adding up these 2 equations, we solve for x. Shown below:
[tex]15x+15c=11250\\15x-15c=6750\\---------\\30x=18000\\x=600[/tex]
Now putting this value of x into original 1st equation, we solve for c:
[tex]3x+3c=2250\\3(600)+3c=2250\\1800+3c=2250\\3c=450\\c=150[/tex]
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
17 divided by 768 in long Division
Answers
Answer:
45 remainder 3.
Step-by-step explanation:
Find the equation of a line that has the same slope ask why equals 10-4x and the same Y intercept is why equals -9x-8
Answers
Answer:
[tex]y=-4x-8[/tex]
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
1) Find the slope of the given line [tex]y=10-4x[/tex]
The slope is [tex]m=-4[/tex]
2) Find the y-intercept of the given line [tex]y=-9x-8[/tex]
The y-intercept is [tex]b=-8[/tex]
therefore
The equation of the line with
[tex]m=-4[/tex]
[tex]b=-8[/tex]
is equal to
[tex]y=-4x-8[/tex]
graph a line with a slope of -5 that contains the point -3,-4
Answers
Answer:
The equation of the line is 5x + y + 19 = 0
Step-by-step explanation:
The equation of the line with slope 'm' and given a point (x₁, y₁) passing through it we use the Slope - one - point form which is given by:
y - y₁ = m(x - x₁)
The point given is: (-3, -4) and the slope is -5.
We get the equation of the line to be:
y - (-4) = -5(x - (-3))
⇒ y + 4 = -5(x + 3)
⇒ y + 4 = -5x - 15
⇒ 5x + y + 19 = 0. is the required equation of the line.
According to the theorem, which statement, about Parallelogram ABCD is true?
Answers
bisect = to cut into two equal halves.
so from that theorem Juan used we can derive that once both diagonals bisect each other, the halves of AO = OC and DO = OB.
Simplify the square root of 30/20
Answers
Answer:
√6/2
Step-by-step explanation:
Which ordered pair is a solution of the equation?
y=-3x-4y=
Answers
To find the solution to the given equation y = -3x - 4 from the provided pairs, substitute the values and solve, giving the solution as (0,-2).
The given equation is y = -3x - 4.
To find which ordered pair is a solution, substitute the given pairs into the equation and check:
(1,0): y = -3(1) - 4 = -3 - 4 = -7
(0,-2): y = -3(0) - 4 = -4
(13,-3): y = -3(13) - 4 = -39 - 4 = -43
Therefore, the ordered pair that is a solution of the equation is (0,-2).
please help thanks ❗
Answers
Answer:
see the explanation
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent
In this problem
PO≅SO ----> given problem
NO≅TO ----> because O is the midpoint NT
∠PON≅∠SOT -----> by vertical angles
so
two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT
therefore
Triangles PON and SOT are congruent by SAS
hence
∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)
plz someone help me 7(2m−1)−35m=65(4−3m)
Solve for m.
Enter your answer in the space provided. Enter only your answer.
Answers
Answer:
Step-by-step explanation:
1. m = -1/5
2. c = -9.75
3. q = 0
Answer:
m = 89/56 = 1 33/56
(Can be simplified to 1.58)
will can jump rope at a rate of 8 jumps for every 10 seconds. find the unit rate
Answers
Answer:
The unit rate is 1.25 seconds per jump.
Step-by-step explanation:
Given:
Will can jump rope at a rate of 8 jumps for every 10 seconds.
Now, to find the unit rate:
So, by dividing we get the unit rate.
At the rate of 8 jumps Will takes 10 seconds.
Thus, for the rate of 1 jump he will take = [tex]10\div 8=1.25\ seconds.[/tex]
Therefore, the unit rate is 1.25 seconds per jump.
Given f(x) = x - 7 and g(x) = x2.
Find g(f(4)).
g(f(4)) =
Answers
Answer:
Step-by-step explanation:
If we are looking to find the composition of g(f(4)), we start at the innermost part of the problem which is to evaluate f(4).
If f(x) = x - 7, then f(4) = 4 - 7. f(4) = -3.
Now take that -3 and evaluate the g(-3).
If g(x) = x^2, then g(-3) = (-3)^2 which is 9.
Therefore, f(g(4)) = 9
Answer:
9
Step-by-step explanation:
edg 2020
What is the equation of the line that has a slope of -1/3 and a y intercept of 5/2
Answers
Answer:
y=-1/3x+5/2
Step-by-step explanation:
Slope intercept form makes this a breeze. Essentially, just plug these values into the following formula:
y = [SLOPE]x + [Y-INTERCEPT]
Answer:
y=-1/3x+5/2
Hope this helps
HELP/ANSWER PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answers
Answer:
Step-by-step explanation:
An artist is making a mural by reproducing a painting at a different scale. The original painting is 12 1/2 inches long and 5 inches wide. The mural will cover an entire wall that is 52.5 feet long and 20 feet wide. What will be the scale that relates the original painting to the mural?
Answers
Answer:
The scale is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
The correct question is
An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?
we know that
To find out the scale divide the measure of the original painting by the measure of the mural
so
Long
[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
Verify the scale with the wide (both scale must be equals)
wide
[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?
Answers
Answer:
z = x^3 +1
Step-by-step explanation:
Noting the squared term, it makes sense to substitute for that term:
z = x^3 +1
gives ...
16z^2 -22z -3 = 0 . . . . the quadratic you want
_____
Solutions derived from that substitution
Factoring gives ...
16z^2 -24z +2z -3 = 0
8z(2z -3) +1(2z -3) = 0
(8z +1)(2z -3) = 0
z = -1/8 or 3/2
Then we can find x:
x^3 +1 = -1/8
x^3 = -9/8 . . . . . subtract 1
x = (-1/2)∛9 . . . . . one of the real solutions
__
x^3 +1 = 3/2
x^3 = 1/2 = 4/8 . . . . . . subtract 1
x = (1/2)∛4 . . . . . . the other real solution
The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.
Answer:
x^3 +1
Step-by-step explanation: