Answers
Answer:
EF = 22 , AB = 1
Step-by-step explanation:
the midsegment of a trapezoid is equal to half the sum of the parallel bases
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values
x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction
2x + 12 = 3x - 4 ( subtract 3x from both sides )
- x + 12 = - 4 ( subtract 12 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
Then
EF = x + 6 = 16 + 6 = 22
Similarly
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is
x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction
2x + 6 = 6x + 2 ( subtract 6x from both sides )
- 4x + 6 = 2 ( subtract 6 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
Then
AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1
Related Questions
Solve for t 16−2t=t+9+4t
Answers
Answer:
Step-by-step explanation:
16-2t=t+9+4t
7=7t
t=1
The endpoints of FG are F(3.75,9) and G (2,-12).
If point E divides FG in the ratio 3:4, the coordinates of point E are what?
If point H divides FE in the ratio 2:3, the coordinates of point H are what?
Answers
Using proportions, it is found that:
The coordinates of point E are (3,0).The coordinates of point H are (3.45, 5.4).What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point E divides FG in the ratio 3:4, hence:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]x - 3.75 = \frac{3}{7}(2 - 3.75)[/tex]
x - 3.75 = -0.75.
x = 3.
For the y-coordinate:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]y - 9 = \frac{3}{7}(-12 - 9)[/tex]
y - 9 = -9
y = 0.
The coordinates of point E are (3,0).
Point H divides FE in the ratio 2:3, hence:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]x - 3.75 = \frac{2}{5}(3 - 3.75)[/tex]
x - 3.75 = -0.3.
x = 3.45.
For the y-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]y - 9 = \frac{2}{5}(0 - 9)[/tex]
y - 9 = -3.6
y = 5.4.
The coordinates of point H are (3.45,5.4).
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Answer:
The coordinates of point E are (3,0).
The coordinates of point H are (3.45, 5.4).
Step-by-step explanation:
I just got it right on the test
An inequality is shown below:
−np − 3 ≥ 7(c − 4)
Which of the following solves for n?
Answers
The solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
How to solve for n?The inequality is given as:
−np − 3 ≥ 7(c − 4)
Add 3 to both sides
−np ≥ 7(c − 4) + 3
Divide through by -p;
This changes the inequality sign.
So, we have:
[tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
Hence, the solution of n is [tex]n \le -\frac 1p(7(c - 4) + 3)[/tex]
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The French army stayed behind in Egypt—and so did the scholars. In late August, shortly after Napoleon's departure, a large, heavy package arrived at the scholars' palace in Cairo. When they opened it, they found it contained a black stone slab covered with writing in three different scripts.
A note from a French army officer accompanied the package. He told the scholars that the stone had been unearthed in an old fort near the town of Rosetta, thirty-five miles north of Alexandria. French soldiers were tearing down a ruined wall in the fort when they came upon the slab.
Which statement accurately describes a cause-and-effect relationship described in this excerpt?
Because Napoleon departs for France, the French army and scholars decide to stay in Egypt.
Because the French army and scholars decide to stay in Egypt, Napoleon decides to depart for France.
Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
Because the French soldiers are searching for the Rosetta Stone, they tear down a ruined wall in a fort.
Answers
The statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
What is a cause-and-effect relationship?A cause-and-effect relationship occurs when:
Two events occur at the same time and in the same place.One event immediately precedes the other.The second event appears unlikely to have happened without the first event occurring.Thus, the statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.
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A sum of Rs. 500 is in the form of denominations of Rs. 10 and Rs. 20. If total number of notes are 35, find the number of notes of each denomination.
Answers
Answer: 20 of banknotes, denomination of Rs. 10 and 15 of banknotes, denomination of Rs. 20.
Step-by-step explanation:
Let the number of banknotes, denomination of Rs. 10 will be equal to x,
and the number of banknotes, denomination of Rs. 20 will be equal to y.
Hence; [tex]\left \{ {{x+y=35\ \ \ \ } \atop {10*x+20*y=500\ |:10 \ \ }} \right. \ \ \ \ \left \{ {{x+y=35\ \ (1)} \atop {x+2y=50\ \ (2)}} \right. \\[/tex]
From (2) subtract (1):
[tex]y=15\ \ \ \ \ \Rightarrow\\x+15=35\\x=20.[/tex]
Identify each of the following as rational or irrational.
Answers
Answer:A rational number can be written as a fraction of two integers. √23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction. 104.42 is rational because it can be expressed as 10442/100 . We can express it as this because.
Step-by-step explanation:
PLEASE HELP!!!!
Use the following set of data:
78, 78, 83, 85, 89, 91, 95, 98
What is the median for the set of data?
(A) 85
(B) 89
(C) 87
(D) 98
Answers
Answer:
87
Step-by-step explanation:
The median of a data set is the value that is exactly in the middle of all other values.
To find the median of a data set, we typically list the values in order of greatest to least, and we look for the number in the middle.
Here, the list-maker has already provided the list in this order!
78, 78, 83, 85, 89, 91, 95, 98
we can see two numbers exactly in the middle here--when this happens, we take the mean/average of the two:
85 + 89 = 174
174 / 2 = 87
So, the median of this data set is 87
hope this helps! have a lovely day :)
To get 697, then divide by amount on numbers (8)
To get 87.125 then round to the nearest whole number
To get 87
Trini rode her bike 12 miles on Friday. She rode 14 miles on Saturday and 15 miles on Sunday. How many miles did she ride in all?
Answers
Answer: 41
Step-by-step explanation:
12+14+15= 41
Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was 2.5, and the standard deviation was 0.5. What is the margin of error, assuming a 95% confidence level
Answers
The margin of error is ±0.1706
What is the margin of error?The margin of error is a statistical solution for the amount of random sampling error in the survey results.
What is 95% of a confidence level?The 95% confidence interval means from 100 different samples computing a 95% of confidence for each sample. From this, we get the approximate value 95 of the 100 confidence intervals will contain the true mean value.
We have a sample size of n=33
The critical value of the significance level is [tex]\alpha =0.05\\z_{\frac{\alpha }{2} }=1.96[/tex]
Then our sample mean will be 2.5
then the standard deviation is 0.5
from this, we can assume that this is a normal distribution.
then our margin of error will be
[tex]E=[/tex]±[tex]z_{\frac{\alpha }{2} }\frac{deviation}{\sqrt{n} }[/tex]
⇒[tex]E=[/tex]±[tex](1.96)\frac{0.5}{\sqrt{33} }\\[/tex]
≅±0.1706 is the margin of error.
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PLEASE HELP ASAP. I WILL MARK AS BRAINLIEST
Answers
You must go 45 miles per hour to reach the longest distance.
Number of hours the car can runThe given parameters are:
Speed = 60 miles per hourTime = 5 hoursWhen the speed increases by 1 mile per hour, the time reduces by 10 minutes.
This means that:
When
Speed = (60 + x) miles per hour
The time is:
Time = 5 hours - 10 minutes * x
Convert minutes to hour
Time = 5 hours - 1/6 * x hour
This gives
Time = 5 - x/6 hour
Hence, the car can run for (5 - x/6) hours
The distance for 1 tank of gasWe have:
Speed = (60 + x) miles per hour Time = (5 - x/6) hoursThe distance is calculated using
Distance = Speed * Time
This gives
Distance = (60 + x)(5 - x/6)
Expand
Distance = 300 - 10x + 5x - x^2/6
Evaluate the like terms
Distance = 300 - 5x - x^2/6
Hence, the distance for 1 tank of gas is 300 - 5x - x^2/6 miles
The longest distanceWe have:
D = 300 - 5x - x^2/6
Differentiate
D' = -5 - x/3
Set to 0
-x/3 = 5
Solve for x
x = -15
Substitute x = -15 in D = 300 - 5x - x^2/6
D = 300 - 5(-15) - (-15)^2/6
Evaluate
D = 337.5
Hence, the longest distance is 337.5 miles
The speed for the longest distanceWe have:
x = -15
Substitute x = -15 in Time = (5 - x/6) hours
Time = (5 + 15/6) hours
Evaluate
Time = 7.5 hours
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 337.5/7.5
Evaluate
Speed = 45
Hence, you must go 45 miles per hour to reach the longest distance.
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Simplify 4a - 2a + a
Answers
Answer:
=> 3a
Step-by-step explanation:
=> 4a - 2a + a
=> 2a + a
=> 3a
Answer:
[tex]\boxed{\bf 3a}[/tex]
Step-by-step explanation:
[tex]\bf 4a - 2a + a[/tex]
Combine 4a and -2a = 2a.
[tex]\bf 2a+a[/tex]Combine 2a and a = 3a
[tex]\bf 3a[/tex]---------------------------------------
Which number is equal to –906,060? –9.0606 times. 105 –9.06 times. 105 9.06 times. 10–5 9.0606 times. 10–5
Answers
Answer:
I don't understand the formatting of the possible answers. Below is a solution.
Step-by-step explanation:
906,060 is the same as 9.0606 x 10^5
The given number is equal to [tex]-9.0606 * 10^5[/tex]
What is Scientific notation ?Scientific notation is a way to write numbers in an abbreviated way, making it easier to work with these numbers.
Why should we use Scientific notation ?The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant.
A widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10
Converting –906,060 into scientific notation, we get
-906060/100000
= - 9.06060*10^5
Thus, The given number is equal to -9.06060*10^5
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PLEASE HELP URGENT
B Pick the inequality that matches the graph shown. Show all of your work to explain the
choice you selected. (See Ex. 1)
Answers
Answer:
B. y > 3x -7
Step-by-step explanation:
We can choose the correct inequality based on the y-intercept and the shading.
Y-interceptThe dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.
ShadingThe shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...
y > ( ) . . . . eliminates choice A
and
x < ( ) or ( ) > x . . . . eliminates choice C, confirms choice B
The inequality that matches the graph is y > 3x -7.
__
Additional comment
For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a positive coefficient. If the coefficient is negative, you can do either of ...
add the opposite of that variable term to both sides of the equationreverse the inequality symbolThat is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.
what is 2,104.50 divided by 122
Answers
2104.50 ÷ 122 = 17.25
...
I need answer quickly
Answers
Answer:
√85
Step-by-step explanation:
a² + b² = c²
6² + b² = 11²
36 + b² = 121
b² = 121 - 36
b² = 85
b = √85
Answer:
Hello! The answer is [tex]b = \sqrt{85}[/tex].
Step-by-step explanation:
To solve this question, we have to use the Pythagorean theorem. We are given one of the legs and the hypotenuse. (The hypotenuse is opposite the right angle).
a^2 and b^2 represent our legs while c^2 represents the hypotenuse.
We have to substitute our values in for a^2 and c^2:
6^2 + b^2 = 11^2
This leaves us with 36 + b^2 = 121
To get b^2 by itself, we have to subtract 36 from both sides:
36 + b^2 = 121
-36 -36
This leaves us with b^2 = 85
To get just b, we have to take the square root:
√b^2 = √85
This leaves us with [tex]b = \sqrt{85}[/tex].
In the parallelogram below, solve for x and y.
I have y but i can’t figure out x
Answers
Step-by-step explanation:
how did you get y, when you don't know how to get x ?
the easiest way to solve this is to base on the fact that the opposite angles must be identical.
so,
2x + 32 = 4x - 12
32 = 2x - 12
44 = 2x
x = 22
and the to be sure
-8y - 14 = -5y + 4
-3y = 18
y = -18/3 = -6
or, the sum of 2 consecutive angles must be 180°.
2x + 32 - 5y + 4 = 180
2x - 5y + 36 = 180
2x - 5y = 144
-8y - 14 + 4x - 12 = 180
-8y + 4x = 206
-4y + 2x = 103
-5y + 2x = 144
- -4y + 2x = 103
------------------------
- y 0 = 41
y = -41
-4×-41 + 2x = 103
164 + 2x = 103
2x = -61
x = -30.5
ha, your teacher either set a trap or made a mistake.
these given angles do not belong to a parallelogram.
there is no solution for x and y with these angle expressions to create a parallelogram.
every condition that has to be true creates a different and inconsistent set of solutions (and implausible ones at that creating single angles larger than 200° and even 300°, or smaller than 0°).
Miss Goh bought 6 blouses, 2 skirts and 2 dresses for $560. A blouse and a skirt cost $107. A blouse and a dress cost $134. What was the cost of a dress?
Answers
Answer:
$95 FOR A DRESS
Step-by-step explanation:
Let's rearrange the given:
She bought a blouse and skirt for two, a blouse and a dress for two, and a blouse for two.
A blouse and a skirt cost $107
A blouse and a dress cost $134
blouse cost x dollars
The equation:
2($107) + 2($134) + 2x = $560
SOLUTION:
$214 + $268 + 2x = $560
2x = $560 - $214 - $268
2x = $78
x = $39 for a single blouse
FIND THE COST OF DRESS:
A blouse and a dress cost $134 - $39 for a single blouse
$134 - $39 = $95
$95 IS THE COST OF DRESS
find the values of x work 10% of my grade
Answers
Answer:
x = 35
Step-by-step explanation:
1. Add all angles
[tex]115+(x+36)+24+(2x+10)+2x[/tex]
= [tex]5x+185[/tex]
2. Match 360 and fix
[tex]5x+185=360[/tex]
[tex]5x=360-185[/tex]
[tex]5x=175[/tex]
[tex]x=175/5[/tex]
[tex]x=35[/tex]
Hope this helps
Answer:
[tex]\boxed{\sf x = 35^o}[/tex]
Step-by-step explanation:
Let's find the value of x :-
[tex]\sf 115 + x + 36 + 24 + 2x + 10 + 2x = 360^o[/tex]
Add the numbers.
[tex]\sf 185 + x + 2x + 2x = 360[/tex]Combine like terms.
[tex]\sf 5x + 185 = 360[/tex]Subtract 185 from both sides.
[tex]\sf 5x = 175[/tex]Divide both sides by 5.
[tex]\sf x = 35^o[/tex]--------------------------------------
60 POINTS PLEASEEEEEEEEEEEE
Answers
Answer:
A.) Two
Step-by-step explanation:
You can determine the amount of solutions the functions have by counting the number of intersections they have. Since the functions cross each other at two different points, there are two solutions.
Which is the graph of f(x) = 4( 1 /2)x
Answers
Answer:
I don't see any option to choose from.
Step-by-step explanation:
See attached graph.
f(x) = 4( 1 /2)x can be rewritten as y = 2x. This is a straight line with slope 2 and a y-intercept of 0.
-2x
10. What is the least common denominator of 21+2+³=1?
+3
O(x - 1)(x+1)
Ox(x - 1)2(x + 1)
O(x-1)2(x + 1)
Ox(x - 1)(x + 1)
Answers
Answer:
O(x-1)2(x + 1)
Step-by-step explanation:
35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
35. Passes through (-2, 8) and (4, 6)
Answers
Answer:
The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as [tex]$y=-\frac{1}{3} x-\frac{26}{3}$[/tex].
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 3
Determine the slope of the line.
The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute [tex]$6 \& 8$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 4&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows, [tex]$m=\frac{6-8}{4-(-2)}$[/tex]
[tex]$$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$$[/tex]
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute [tex]$-\frac{1}{3}$[/tex] for m,-2 for [tex]$x_{1}$[/tex], and 8 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows, [tex]y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex]
Step 3 of 3
Simplify the equation further.
Add 8 on each side of the equation [tex]$y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex], and simplify as follows, [tex]$y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$[/tex]
[tex]$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$[/tex]
This is the required linear equation.
Can someone help me out on this problem
Answers
The correlation is a strong negative correlation, because as the weights increases the city MPG decreases
The graph of the table of valuesTo do this, we plot the weights on the x-axis, and the city MPG on the y-axis
See attachment for graph
Type of correlationThe correlation is a strong negative correlation, because as the weights increases the city MPG decreases
The equation of the line of best fitTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 463Sum of Y = 388Mean X = 28.9375Mean Y = 24.25Sum of squares (SSX) = 862.9375Sum of products (SP) = -857.75The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -857.75/862.94 = -0.99399
a = MY - bMX = 24.25 - (-0.99*28.94) = 53.01354
So, we have:
y = -0.99399x + 53.01354
Approximate
y = -0.99x + 53
Hence, the equation of the line of best fit is y = -0.99x + 53
The weight for 30 MPGThis means that y = 30
So, we have:
-0.99x + 53 = 30
Subtract 53 from both sides
-0.99x = -23
Divide by -0.99
x = 23.23
Approximate
x =23
Hence, the predicted weight is 23 pounds
The city MPG for 1500 poundsThis means that x = 1500
So, we have:
y = -0.99 * 1500 + 53
Evaluate
y = -1432
Hence, the city MPG for 1500 pounds is -1432
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2. Find four consecutive integers such that six times the sum of the first and third is 12
greater than 9 times the fourth.
Answers
Answer:
9
Step-by-step explanation:
a,a+1,a+2,a+3,...
6(a+(a+2))=12+9(a+3)
6(2a+2)=12+9a+27
12a+12=12+9a+27
12a-9a=27
3a=27
a=9
How many sandwiches do
you think would be supplied by this
market if the price were $3.50?
Answers
=========================================================
Explanation:
Start at $3.50 on the vertical y axis. Draw a horizontal line until you reach the supply curve. Then drop straight down to land somewhere between 650 and 700 units supplied per day. Check out the diagram below.
A good estimate may be to use the midpoint. Add up those values and divide in half.
(650+700)/2 = 1350/2 = 675
Therefore, we estimate that 675 sandwiches per day would be supplied if the price was $3.50 per sandwich.
The interior angle of a regular polygon is twice the exterior angle how many sides has the polygon
Answers
Answer:
6 sides
Step-by-step explanation:
the interior angle + the exterior angle = 180°
let x be the exterior angle then 2x is the interior angle and
x + 2x = 180
3x = 180 ( divide both sides by 3 )
x = 60
the exterior angle = 60°
the sum of the exterior angles of a polygon = 360°
since the polygon is regular the the exterior angles are congruent, then
number of sides = 360° ÷ 60° = 6
I need to find the restrictions for this equation:
Answers
Answer:
Simplify 2x^2-5x-3/x^2-9
The answer is 2x+1 / x+3
Step-by-step explanation:
Simplify the expression.
Which expressions are equivalent to 12r-5
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
6(2r+(-1))+1
(Choice B)
B
-4(2+(-3r))+3
(Choice C)
C
None of the above
Answers
The expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= 12r - 5
A) 6(2r+(-1))+1
= 12r + 6(-1) + 1
= 12r -5
B) -4(2+(-3r))+3
= -8 -4(-3r) + 3
= -5 + 12r
or
= 12r - 5
Thus, the expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.
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You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answers
Answer: the answer is 28
Step-by-step explanation:
Y=
Help me please thank u
Answers
Answer:
Y≈4.6
Step-by-step explanation:
Because the hypotenuse is 9rad2 and the angle opposite of it is a 90. You can deduce it is a 90-45-45. From this you can tell the legs are 9. You then do 9 tan 26 to get about 4.4, and after this you subtract it from 9.