Answers
IF (x - 30) + (x + 50) = 180 then, line line n || m.
x - 30 + x + 50 = 180
2x + 20 = 180
subtract 20 from both sides
2x = 160
divide both sides by 2
x = 80
IF (x - 30) + y = 180, then k || j.
(80 - 30) + y = 180
50 + y = 180
subtract 50 from both sides
y = 130
The values of x and y are 80 and 70 respectively which make k parallel to j and m parallel to n.
Geometrically, parallel means two or more lines, line segments, or rays that never intersect or cross each other, it doesn't matter how far they are extended. Parallel lines always maintain the same distance between them and remain equidistant at every point.
The sum of two adjacent angles is [tex]180^o[/tex],
therefore,
[tex](x-30)^o+(x+50)^o= 180^o[/tex]
2x +20 = 180
2x = 180 - 20
2x = 160
[tex]\frac{2x}{2} = \frac{160}{2}[/tex]
x = 80.
Again, as the sum of two adjacent angles is [tex]180^o[/tex],
[tex](x-30)^o+y^o= 180^o[/tex]
x + y = 180 + 30
Substitute value of x,
80 + y = 150
y = 150 - 80
y = 70.
Thus, x = 80 and y = 70 are the values for which k is parallel to j and m is parallel to n.
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Related Questions
A net can be folded to form a cube. The numbers on the three faces meeting at any vertex can be multiplied together. What is the smallest such product for the vertices of this cube
Answers
the square with number 5 will face the square with number 10 = 5×10 = 50
the square with number 7 will face the square with number 6 = 7×6 = 42
the square with number 8 will face the square with number 9 = 8×9 = 72
The smallest product is 42
A triangle has squares on its three sides as shown below. What is the value of x?
FIRST ONE GETS BRAINLIEST AND 12 PTS!!
Answers
Here's how!
Use Pythagorean theorem, which is a^2+b^2=c^2, and only applies to right triangles.
Rules: 'c' is always your hypotenuse! (Longest side) Your 'a' and 'b' are your legs (the other two sides.)
Plug in your information-
a^2+b^2=c^2
8^2+6^2=x^2
Solve!
64+36=x^2
100=x^2
(square root of 100)=(square root of x^2)
10=x
☺☺☺☺☺
A city planner designs a park that is a quadrilateral with vertices at J(-3, 1), K(1, 3), L(5,-1), and M(-1,-3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 m, what is the total length of the path to the nearest meter?
Answers
Our first solution is to find the midpoint of each sides. This is done by taking the average of each coordinate. The equation would be:
x,midpoint = (x₁+x₂)/2
y,midpoint = (y₁+y₂)/2
So, applying the equation:
midpoint jk = (-3+1/2, 1+3/2) = (-1,2)
midpoint kl = (1+5/2, 3+⁻1/2) = (3,1)
midpoint ml = (5+⁻1/2, ⁻1+⁻3/2) = (2,-2)
midpoint jm = (⁻3+⁻1/2, 1+⁻3/2) = (-2,-1)
Next, we find the lengths of the paths by using the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Distance between jk and ml = √(⁻1-2)² + (2 - ⁻2)² = 5
Distance between jm and kl = √(3-⁻2)² + (1-⁻1)² = √29
Total distance = 5 + √29 = 10.385 units
Since the scale is 1 unit = 10 meters, the actual total length of paths is equal to:
Actual Total Distance = 10.385*10
Actual Total Distance = 103.85 meters
Express without negative exponents
Answers
1/5^-1 = 5
.4^-2 = 6.25
so it would be 5 x 6.25
Which planet is 10 times as far as earth is from the Sun
Answers
An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom
Answers
Answer:
The measure of the bedroom is 14 by 21
Step-by-step explanation:
This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.
So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4
The real measures of the beadroom are:
(3 1/2 * 4, 5 1/4 * 4)
(14,21)
The measure of the bedroom is 14 by 21
how to write unit form for (2 tens 1 one) x 10
Answers
So for this problem, all you have to do is multiply the number of units of each place value, then multiple them all by 10.
(2(10) + 1(1))×10
21 × 10 = 210
Therefore, the number is equivalent and written as 210.
what is the value of D to the nearest tenth ?
Answers
26(26 + d) = 22(22 + 40)
676 + 26d = 22 * 62
26d = 1364 - 676
26d = 688
d = 688/26
d = 26.5 ← to the nearest tenth
Which graph represents the solution to the system of inequalities?
x + y ≤ 4
y – x ≥ 1
Answers
The correct answer is C.
EXPLANATION
To find which set represents the solution set of the system of inequalities, the best thing is to graph the inequalities and locate the intersection of the solution region of the two graphs.
The given inequalities are,
[tex]x + y \leqslant 4 \: \: and \: \: y - x \geqslant 1[/tex]
Let us start with,
[tex]x + y \leqslant 4[/tex]
To graph this inequality, we first of all graph the corresponding linear equation,
[tex]x + y = 4[/tex]
using the intercepts,
[tex](0,4) \: and \: (4,0)[/tex]
We plot the above points and draw a solid straight line through them.
We test for the origin to determine which half plane should be shaded.
[tex]0 + 0 \leqslant 4[/tex]
[tex]0 \leqslant 4[/tex]
This statement is true, so we shade the lower half plane.
We repeat the same process to graph,
[tex]y - x \geqslant 1[/tex]
So we graph the corresponding straight line,
[tex]y - x = 1[/tex]
using the intercepts,
[tex](0,1) \: and \: (-1,0)[/tex]
We plot the intercepts and draw a solid line through them.
We test for the origin again to see which half plane to be shaded.
[tex]0 - 0 \geqslant 1[/tex]
[tex]0 \geqslant 1[/tex]
This statement is false, so we shade the
upper half plane.
The intersection of the two region is the region in option C of the graphs provided.
A triangle has angles that measure 30, 60, 90. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle?
Answers
10sin60=8.66
since you have the measure of the hypotenuse, add 10+5+8.66
=23.66
Which of the following best describes the expression 6(y + 3)?
1.)The product of two constant factors six and three plus a variable
2.)The sum of two constant factors six and three plus a variable
3.)The product of a constant factor of six and a factor with the sum of two terms
4.)The sum of a constant factor of three and a factor with the product of two terms
Answers
The product of a constant factor of 6 and a factor with the sum of 2 terms
Answer: Hence, option '3' is correct.
Step-by-step explanation:
Since we have given that
[tex]6(y+3)[/tex]
This expression can be written in statement.
Here, we can see that there are two terms:
1) A constant factor of 6
2) Sum of two terms
So, according to options it can be written as :
The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.
Hence, option '3' is correct.
K+3d=8c-8d
solve for d
Answers
So we will get 3d = 8c - 8d - k
Now divide both sides by 3 to isolate d.
So d = 8/3c - 8/3d - k/3
The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.
(a) Write a system of equations for the situation. Use r for the amount charged for a refill and b for the amount charged for the egg breakfast.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each item cost.
Answers
Answer:
(1) Egg Breakfast $6.50
(2) Egg Breakfast $6.50
(3) Refill #1 $0.95
(4) Refill #2 $0.95
(5) Refill #3 $0.95
(6) Refill #4 $0.95
(7) Refill #5 $0.95
Check answer: $6.50+$6.50=$13.00
$0.95+$0.95=$1.90
$0.95+$0.95=$1.90
$1.90+$1.90=$3.80
$3.80+$0.95=$4.75
$13.00+$4.75=$17.75
Total: $17.75
Nick has two more than twice as many quarters as dimes.. one fewer than three times as many nickels as dimes, and eight more pennies than dimes.. he has $7.37. How many of each coin does he have?
Thank you so much :)
Answers
This would mean we have:
(2x + 2) quarters,
(3x - 1) nickels and
(x + 8) pennies
The total value is 737 cents ($7.37)
We can thus say that if we multiply the number of each type of coin by the value of that coin and add it all, we will get 737, so we can write an equation:
10x + 25(2x + 2) + 5(3x - 1) + x+8 = 737
And if we tidy this up by multiplying out the brackets and collecting like terms, we get:
76x + 53 = 737
Now, solve for x:
76x = 684
x = 9
So by subbing into the expressions constructed at the start, we find how many of each coin we have:
9 dimes,
(2(9) + 2) quarters,
(3(9) - 1) nickels and
((9) + 8) pennies.
so... 9 dimes, 20 quarters, 26 nickels and 17 pennies.
Reduce the rate 210 miles per 3 hours to it's unit rate and write the miles portion of your answer
Answers
unit rate would be miles per hour
so divide 210/3 = 70
Which factor does the width of the peak of a normal curve depend on?
Answers
Answer: The width of the peak depends on the Standard Deviation. The standard deviation is a measure used to quantify the variation or dispersion in the data set. If the standard deviation is low, this means that the set of data tends to be closer to the mean, then the width of the peak in the normal curve is small, for other part if the standard deviation is big, this means that the variation is big and the data set is more spread, this causes that the width of peak to be larger.
An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?
Answers
so
x + x + 20 = 90
2x = 70
x = 35
35 + 20 = 55
answer
the measure of each angle: 55 and 35
Haley and Samuel can each make one gift box in two hours. Rachael takes three hours to make the gift box alone. If Haley, Samuel, and Rachael work together, how long will it take them to make one gift box?
Answers
It will take 40 minutes for them to make one gift box.
Combined ratesGiven that Haley and Samuel can each make one gift box in two hours, while Rachael takes three hours to make the gift box alone, to determine, if Haley, Samuel, and Rachael work together, how long will it take them to make one gift box, the following calculation must be performed, using combined rates:
1/2 + 1/2 + 1/3 = X3/6 + 3/6 + 2/6 = X8/6 = X6/6 = 1 hour8/6 = 40 minutesTherefore, it will take 40 minutes for them to make one gift box.
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Answer:It will take 40 minutes for them to make one gift box
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPP
Answers
the y intercept is where x=0
x represents the number of months
when the number of months is 0, that is the initial number of games won
that looks to be a little below y=2, so maybe y=1.8?
the y intercept is y≈1.8
it represents the number of games won with 0 months of practice
B.
we can use y=mx+b
m=slope
b=y intercept
we know the y intercept
find the slope
slope=rise/run
the I'm going from x=0 to x=10
the rise is about 18.95 (from 1.8 to 20.75)
the run is 10
so slope would be 18.95/10=1.895
the equation would be y=1.895x+1.8
the points were (0,1.8) and (10,20.75)
If the APY of a savings account is 2.4% and if the principal in the savings account is $2200 for an entire year, what will be the balance of the savings account after all the interest is paid for the year? A. $2200 B. $2252.80 C. $2300 D. $2205.28
Answers
To solve this problem, we must recall that the formula for money with compound interest is calculated as:
Total = Principal × ( 1 + Rate ) ^ n
Total = $2,200 × ( 1 + 0.024 ) ^ 1
Total = $2,252.80
Therefore the answer is letter B.
For the equation x^2+3x+j=0 , find all the values of j such that the equation has two real number solutions. Show your work.
Answers
The solution is j<2.25, meaning all values of j less than 2.25 will provide two real solutions.
For the equation [tex]x^2+3x+j=0,[/tex] to have two real number solutions, the discriminant must be greater than 0. The discriminant, D, of a quadratic equation [tex]ax^2+bx+c=0[/tex] is given by [tex]D=b^2-4ac[/tex].
In this case, a=1, b=3, and c=j. Applying the values, we get:
[tex]D=3^2-4(1)(j)[/tex]
D=9-4j
For two real solutions, D>0. Therefore:
9-4j>0
To find the values of j, solve the inequality:
9>4j
j<9/4
Thus, all the values of j that satisfy j<2.25 will ensure that the equation x^2+3x+j=0 has two real number solutions.
If n = 8 and 16 • 2m = 4n – 8, then m = ?
Answers
First, let's examine the question, and proceed to evaluate once we understand what we're dealing with.
"If n = 8, and 16 • 2m = 4n - 8, then m = ?"
This question is requesting for us to input the value for n, and then solve for m.
Here is our equation:
16 • 2m = 4n - 8
Let's plug in 8 for n.
Our equation should look like this now:
16 • 2m = 4(8) -8
First, let's get 4(8) by itself; Add 8 to both sides.
16 + 8 = 24
-8 + 8 = 0
Our equation is now:
24 • 2m = 4(8)
Multiply 4 by 8 to simplify the right side of the equation.
4 • 8 = 32
Now we have:
24 • 2m = 32
To solve for m, we need to isolate 2m and then divide both sides by 2.
Subtract 24 from both sides to isolate 2m.
24 - 24 = 0
32 - 24 = 8
Our equation is now:
2m = 8
Divide both sides by 2 to solve for m.
2m / 2 = m
8 / 2 = 4
Our final equation and solution is:
m = 4.
The value for m is 4.
I hope this helps!
Final answer:
The value of m is 0.75 when n = 8 and the equation 16 • 2m = 4n – 8 is satisfied, by performing simple algebraic operations to isolate and solve for m.
Explanation:
To find the value of m when n = 8 and 16 • 2m = 4n – 8, we first replace n with 8 in the second equation:
16 • 2m = 4(8) – 8
16 • 2m = 32 – 8
16 • 2m = 24
Now we divide both sides of the equation by 16 to isolate 2m:
2m = 24 / 16
2m = 1.5
Finally, to find m, we divide both sides of the equation by 2:
m = 1.5 / 2
m = 0.75
So the value of m that satisfies the given conditions is 0.75.
Write an equation ten times the sum of half a number and 6 is 8.
Answers
Is the equation. Hope this helped!
the x/2 means x over two
Help me plz so bad I don't want to get bad grade on this
Answers
Answer:
1. 16666666666667 2. .72727272727 3. .25
Step-by-step explanation:
all you do is divide the top number by the bottom number to get it in decimal form
A restaurant did a survey among 100 customers to find their food preferences. The customers were asked about their preferences for beef or chicken. Out of the total 75 people who liked beef, 60 also liked chicken. There were 80 people who liked chicken.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like beef Do not like beef Total
Like chicken A D G
Do not like chicken B E H
Total C F I
Part B: What percentage of the survey respondents did not like either beef or chicken? (3 points)
Part C: Do the survey results reveal a greater dislike for beef or chicken? Justify your answer. (2 points)
Answers
like chicken 60 20 80
do not like c 15 5 20
-------------------------------------------------------------------------
total 75 25 100
B. did not like beef or chicken.....5/100 = 0.05 = 5%
C. the survey reveals a greater dislike for beef...because 15% like just beef, but 20% like just chicken
Answer:
A:
like beef do not like beef total
like chicken 60 20 80
do not like chicken 15 5 20
total 75 25 100
B: 5%
C: Beef. 20% of the people do not like chicken. 25% do not like beef ( 5% from each dislike both.)
Step-by-step explanation:
The net of a square pyramid is shown below: What is the surface area of the solid?What is the surface area of the solid?
32 square inches 14 square inches 20 square inches 24 square inches 32 square inches
Answers
ANSWER BOTH QUESTIONS IF U CANT SEE THE CHOICES ITS FINE! ALL U NEED IS THE QUESTION
Answers
Area of a triangle = (bh)/2
Counting the squares in the figure, the base (bottom) of the triangle looks to be about 8. The height looks like 5.
b = 8
h = 5
A = (8*5)/2
A = (40)/2
A = 20
So the closest answer would be
A. 21.5 square units
13.
Area of a trapezoid = [(b₁ + b₂)/2]h
b₁ = 3
b₂ = 9
h = 6
A = [(3 + 9)/2]6
A = [12/2]6
A = (6)6
A = 36
Since I can't see the answer choices, it would be the closest number to 36.
Answer:
12 and 13
Step-by-step explanation:
A car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. What was the mean for the profits of the sales?
Answers
Answer:
$9819.4
Step-by-step explanation:
We have been given that a car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. We are asked to find the mean for the profits of the sales.
Since mean is the average of numbers. So let us add all the profits and divide the sum of profits by number of cars.
[tex]\text{Mean for the profits of the sales}=\frac{10126+9999+12398+12007+4567}{5}[/tex]
[tex]\text{Mean for the profits of the sales}=\frac{49097}{5}[/tex]
[tex]\text{Mean for the profits of the sales}=9819.4[/tex]
Therefore, the mean for the profits of sales is $9819.4.
Which is an obtuse angle?
∠CAB
∠BAC
∠BCA
∠ABC
Answers
∠BCA ← answer
If p-1 is a factor of p^4+p^2+p-k the value of k is
Answers
p^4+p^2+p-k=0
1+1+1-k=0 k=3
The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
How to determine the value of k?The expression is given as:
[tex]p^4+p^2+p-k[/tex]
The factor is given as:
p - 1
Set the factor to 0
p - 1 = 0
Add to both sides
p = 1
Substitute 1 for p in the expression and equate it to 0
[tex]1^4+1^2+1-k = 0[/tex]
Evaluate the exponents
1+1+1-k = 0
Evaluate the sum
3-k = 0
Add k to both sides
k = 3
Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
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