[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]
[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]
As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.
The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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tìm số hữu tỉ
(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
I need help, please. I don’t understand
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
Karen needs to make a total of 60 deliveries this week. So far she has completed 33 of them What percentage of her total deliveries has Karen completed?
Answer:
55%
Step-by-step explanation:
(33/60) * 100
leave a comment if u need further explanation
I need help on this please
Answer:
-22
Step-by-step explanation:
each mark decreases by three, two marks down from 16 would be 16+3+3; which equals 22, and it has to be negative
hope this helped!
Is 0.2775 a rational number
Answer:
yes it is
Step-by-step explanation:
It is a rational number, as it can be written as a fraction.
If cos θ= 12 /13 and θ is located in the Quadrant I, find sin (2 θ ), cos(2 θ ), tan(2 θ )
Answers: sin(2∅) = 120/169, cos(2∅) = 119/169, tan(2∅) = 120/119
What are trigonometric functions?Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.
Analysis:
If cos∅ = adjacent/hypotenuse = 12/13,
Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5
sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12
sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169
cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169
tan(2∅) = sin(2∅) / cos(2∅) = 120/169 ÷ 119/169 = 120/119
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Solve number 8 please
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3
this is shown in graph b
A helicopter flies 125 miles west and 20 miles north and lands.
The helicopter flies back on a direct course.
What is its bearing?
Find A and B if Cos(A - B) = (sqrt(3))/2 ; Sin(A + B) = 1
Expand the expression to yield a trinomial of the form
ax² + bx + c.
(2x + 3)²
Step-by-step explanation:
(2x + 3)(2x + 3)
4x² + 6x + 6x + 9
4x² + 12x + 9
Write this percentage as a fraction in its simplest form. 96 %
(pls)
Answer:
24/25
Step-by-step explanation:
96%=0.96. 96/100=48/50=24/25
Jenny wants to start an after-school club, so she decides to survey the student body to determine which club would be the most popular: French Club, Architecture Club, or Anime Club. She decides (with Mrs. Howell's permission) to survey the first 25 students who show up to her class one day.
Does her survey comprise an accurate representation of the Reach student body? Why or why not?
Answer:
no because it just reaches one class, not the student body
Step-by-step explanation:
The diagram shows a convex polygon.
What is the sum of the interior angle measures of this polygon?
This is an equilateral triangle, therefore, all the angles are 60 degrees.
3 times 60 is 180.
180 is the answer
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
Imagine that you are given two linear equations in slope-intercept form. You
notice that the slopes are the same, but the y-intercepts are different. How
many solutions would you expect for this system of equations?
O A. 1
OB. cannot be determined
OC. infinitely many
O D.O
Answer:
No solution.
Step-by-step explanation:
When two lines have the same slope but different y-intercepts, they are parallel. Parallel lines never intersect, and therefore there is no solution.
a number, n is multiplied by -5/8 the product is -0.4 how would you set this up to solve
The value of n in the mathematical statement is 0.64
How to solve the equation?The statement is given as:
n multiplied by -5/8 equals -0.4
Rewrite properly as:
n * -5/8 = -0.4
Multiply both sides by -1
n * 5/8 = 0.4
Multiply both sides by 8/5
n = 0.64
Hence, the value of n in the mathematical statement is 0.64
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37:28
Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and
a quart is 32 ounces. The number of pints he canned is represented by p, and the number of quarts he canned is
represented by q. Which equation models the scenario if Chin canned a total of 1,280 ounces?
1,280+16p=32q
1,280+32q=16p
32q-16p=1,280
16p+32q = 1,280
The equation that models the scenario is 16p+32q = 1,280.
Which equation models the scenario?Addition is the mathematical operation that is used to determine the sum of two or more numbers.
The equation that would model the scenario can be determined by adding the total pints and total quarts Chin has :
Total pint + total quart = total ounces
16p+32q = 1,280.
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Sun cover manufactures umbrellas for a monthly fixed cost of $675,921.00 and a
variable cost per umbrella of $42.15. determine the break-even sales price per umbrella if sun cover manufactures 8,573 umbrellas per month
$109.95
$114.50
$120.99
$131.25
The break-even sales price per umbrella if sun cover manufactures the units is $120.99.
How to calculate the sales price?This can be done by using the formula:
Break even units = Total fixed cost / (Price - Variable cost)
8573 = 675921/(Price - 42.15)
8573(P - 42.15) = 675921
8573P - 361351.95 = 675921
8573P = 675921 + 361351.95
8573P = 1037273.4
P = 1037273.4/8574
P = $120.99
Therefore, the price is $120.99.
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For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10
Answer:
a) 13
b) 1/3
c) -2
d) 1
Step-by-step explanation:
This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:
For example:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
________
f(-3) = 3x + 7
f(-3) = 3(-3) + 7
f(-3) = -9 + 7
f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.
f(-3) = -2
The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:
For example:
f(x) = 8
f(x) = 3x + 7
8 = 3x + 7
8 - 7 = 3x
1 = 3x
x = 1/3
f(x)= 10
f(x) = 3x + 7
10 = 3x + 7
10 - 7 = 3x
3 = 3x
3/3 = x
1 = x
I hope this helps!
What is the value of the underline digit?
119.65
any help is great find the missing length?
Answer:
3Step-by-step explanation:
Similar = proportional
solve with an equation
12 : 9 = 4 : x
x = 4 * 9 : 12
x = 3
4x what = 364
please put the calculation
Answer:
91
Step-by-step explanation:
4 x 91 = 364
To work this out, we must do the inverse operation. The inverse (opposite) of x (times or multiply) is ÷ (divide).
So, we do 364 ÷ 4 = 91
Hope this helps!
- profparis
A line has a slope of -3 and passes through the point
passes through the point (-2, -3/2)
By substituting into the equation y = mx + b, find the value of b for this line
Answer:
If I am not mistaking it should be -7.5
Step-by-step explanation:
Answer:
b = -15/2
y = -3x -15/2
Step-by-step explanation:
The value of the y-intercept can be found from a point and the slope of the line by solving the slope-intercept equation for the intercept.
__
intercepty = mx + b . . . . . . . equation of a line with slope m and y-intercept b
y -mx = b . . . . . . . . subtract mx from both sides
For the point (x, y) = (-2, -3/2) and slope m = -3, the value of b is ...
b = -3/2 -(-3)(-2) = -3/2 -6
b = -15/2 . . . . . the value of b for this line
__
equation of the lineThen the equation for the line is ...
y = mx +b
y = -3x -15/2
Question 7(Multiple Choice Worth 1 points)
(02.05 LC)
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5.
−4
−5
4
5
The value of k based on the information given will be k = 2.
How to calculate the value?It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).
The slope of x will be:
= (4 - 0)/(0 + 4)
= 4/4
= 1
By using slope point form, y = kx + 4.
Substitute x = 2.
g(-2) = -2k + 4 = 0
2k = 4
k = 4/2 = 2
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If f(x)=2(3x-5) when f(x) =74,what is the value of x??
Answer:
x = 14
Step-by-step explanation:
given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives
2(3x - 5) = 74 ( divide both sides by 2 )
3x - 5 = 37 ( add 5 to both sides )
3x = 42 ( divide both sides by 3 )
x = 14
The graph of an absolute value function contains the points (–3, 5), (0, 2) and (3, 5). Which could be the function represented by this graph? Check all that apply.
f(x) = |x| + 2
f(x) = –|x| + 2
f(x) = |x| – 2
f(x) = |–x + 2|
f(x) = |–x| + 2
f(x) = –|x| – 2
f(x) = |x + 2|
The absolute value functions that contains the points are:
f(x) = |x| + 2f(x) = |-x| + 2Which could be the function represented by this graph?Here we have the points (-3, 5), (0, 2), and (3, 5). We want to see which ones of the given functions have that points.
To check that, we need to evaluate the functions in the first value of each point and see if the outcome is the second value of the correspondent point.
For example, for the first equation:
f(-3) = |-3| + 2 = 5 so it has the point (-3, 5)f(0) = |0| + 2 = 2 so it has the point (0, 2)f(3) = |3| + 2 = 5 so it has the point (3, 5).The other option that also contains these 3 points is:
f(x) = |-x| + 2
f(-3) = |3| + 2 = 5 so it has the point (-3, 5)f(0) = |-0| + 2 = 2 so it has the point (0, 2)f(3) = |-3| + 2 = 5 so it has the point (3, 5).And all the other options can be trivially discarded (by evaluating them).
So the two correct options are:
f(x) = |x| + 2f(x) = |-x| + 2If you want to learn more about absolute value functions:
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Is y=2x-3 a funtion?
Answer:
yes
Step-by-step explanation:
Yes.
The graph of y = 2x - 2 is a straight line sloping up to the right.
It passes the vertical line test, so it is a function.
28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
Quadrilateral RUST has a vertex at R (1,5).
T
S
What are the coordinates of R'after the translation (x, y) → (x+1, y-1),
Answer:
R'(2,4)
Step-by-step explanation:
When doing translations you subtract or add within the coordinates like a normal problem.
If it helps you, write it as seperate equations like:
1-1 and 5-1
Hope that helps ✓
Jill jogs 3/4 of a mile in 1/10 of an hour at this rate how fast does she run one mile.
10 minutes
6 minutes
8 minutes
Answer:
8 minutes
Step-by-step explanation:
Jill jogs 3/4 of a mile in 1/10 hour.
⇒ 3/4 of a mile takes 6 minutes
For one mile :
3/4 mile x 4/3 : 6 x 4/3 minutes1 mile : 2 x 4 minutes1 mile takes 8 minutes1 mile she can run
1/10÷3/44/3(1/10)4/302/15hour8/60hour8 mins