Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC
According to the midsegment theorem, the midsegments are parallel to
and half the length of the opposite side.
The completed statement are as follows;
Because the slopes of [tex]\overline{EF}[/tex] and [tex]\overline{AC}[/tex] are both -4, [tex]\overline{EF}[/tex] ║ [tex]\overline{AC}[/tex]EF = [tex]\underline{\sqrt{17}}[/tex] and AC = [tex]\underline{2 \cdot \sqrt{17} }[/tex]Because [tex]\underline{\sqrt{17} }[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }[/tex], [tex]EF = \frac{1}{2} \cdot AC[/tex]Reasons:
From the given graph of ΔABC, we have;
Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)
The coordinates of the point D and E on [tex]\mathbf{\overline{DE}}[/tex] are; D(-4, -2), and E(-2, 0)
The coordinates of the point F is; F(-1, -4)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4[/tex]
[tex]Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]Length of EF = √((-1 - (-2))² + (-4 - 0)²) = √(17)
Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)
Therefore, we have;
Because the slope of [tex]\mathbf{\overline {EF}}[/tex] and [tex]\mathbf{\overline {AC}}[/tex] are both , -4, [tex]\overline {EF}[/tex] ║ [tex]\overline {AC}[/tex]. EF = [tex]\underline{\sqrt{17}}[/tex], and AC
= [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex],. Because [tex]\underline{\sqrt{17}}[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex], [tex]EF =\mathbf{ \frac{1}{2} AC}[/tex]
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What is?..
1. 8 4/7 divided by 15?
2. How many 1/4-pound hamburgers can you make from 3 1/2 pounds of ground beef ?(In simplest form)
3. 3 divided by 1 1/5 plus 1/3? (Evaluate the expression. Write the answer in simplest form.)
4. 2/5 plus 2 1/6 divided by 5/6? (Evaluate the expression. Write the answer in simplest form.)
5. 6 1/2 - 7/8 divided by 5 11/16? (Evaluate the expression. Write the answer in simplest form.)
HURRYYYYYY PLEASEEEE.
Answers:
1. 4/7
2. DIVIDE – 3 ½ ÷ ¼ = 14 hamburgers
3. 2 5/6
4. 3
5. 6 9/26
Given the set of domain D = {-3, -2, -1, 0, 1, 2, 3}
Construct /Do the following:
1. Set of ordered pairs such that the range is one less than the domain.
2. Construct table of values such that the range is 2 more than the domain.
3. Write the equation for numbers 1 and 2.
4. Graph numbers 1 and 2 on separate coordinate plane.
Given the domain of values D = {-3, -2, -1, 0, 1, 2, 3}
1) If the set of range is one less than the domain, the required range will be:
Range = {-4, -3, -2, -1, 0, 1, 2}
2) If the set of range is 2 more than the domain, the required range will be:
Range = {-1, 0, 1, 2, 3, 4, 5}
The table of values is given as:
x y
-3 | -1
-2 | 0
-1 | 1
0 | 2
1 | 3
2 | 4
3 | 5
2) For equation 1, we will use the coordinate points (0. -1) and (1, 0)
The equation in slope-intercept form is given as y = mx + b
m = 0-(-1)/1-0
m = 1/1 = 1
Since the y-intercept is at (0, -1), hence b = -1
Substitute the given value into the formula:
Recall that y = mx + b
y = 1x + (-1)
y = x - 1
Hence the equation 1 will be y = x - 1
For equation 2, we will use the coordinate points (-1, 1) and (0, 2)
The equation in slope-intercept form is given as y = mx + b
m = 2-1/0-(-1)
m = 1/1 = 1
Since the y-intercept is at (0, 2), hence b = 2
Substitute the given value into the formula:
Recall that y = mx + b
y = 1x + 2
y = x + 2
Hence the equation 2 will be y = x + 2
4) The graph of each equation on a different coordinate plane is attached.
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I’ll give 100 points
Answer:
2055 is the answer.
Step-by-step explanation:
If x represents the number of minutes and y represents the hiker elevation in feet.
y = 8.19x + 663
y = 8.19(170) + 663
y = 1392.3 + 663
y = 2055.3
Hope it helps:)
Answer:
:)
Step-by-step explanation:
Bobby and Sue Ellan both ride their bikes to the library. Bobby’s home is 6.5 blocks from the library and Sue Ellan’s home is 1 ½ times farther from the library than Bobby’s home. How much farther must Sue Ellan ride her bike to get to the library than Bobby does?
Answer:
3.25 blocks
Step-by-step explanation:
6.5 * 1.5 = 9.75 blocks
9.75 - 6.5 = 3.25blocks
Farther 3.25 blocks sue ellan need to ride than Bobby ride
Josh went to a restaurant for dinner. The cost of the
meal was $24 with a discount of $2. If the total bill includes
an 8% sales tax and a 14% tip, what is the discount
percent? What was the total bill including the tax and the
tip?
Answer:
17.41 Dollars
Step-by-step explanation:
First, you take the discount, which is 2 dollars, so now the cost without any additional costs is 22 dollars. Next, find 8 percent of 22 by multipling 22*0.08 and then you get 1.76. Subtract that from 22 and 20.24. Then take 14 percent of 20.24 by multiplying it by 0.14, which you get 2.8336. Round that down and you get 2.83. Subtract that from that and you get 17.41.
Write an expression that represents 42 is the product of 6 and y
No explanation needed, just tell me the answer :)
Answer:
[tex]6y = 42\\y = 7[/tex]
Step-by-step explanation:
Will Give Brainliest
Answer:
x = 19
Step-by-step explanation:
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60 Use dist property
Subtract 3x from both sides
-3 = 3x - 60
Add 60 to both sides
57 = 3x
Divide both sides by 3
19 = x
37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
Solve the equation for x.
2(2) + x = 4
[tex]2(2) +x =4\\\\\implies 4 +x =4\\\\\implies 4 +x -4 = 4-4\\\\\implies x = 0[/tex]
Answer:
x = 0
Solve solution:
Question:
2(2) + x = 4
Multiply:
2 x 2 + x 4
Cancel equal terms:
4 + x = 4
Answer: x = 0
What is the range of this graph?
The range is the y value of where the dots are located.
Answer: (3,4,5,6)
A function is defined as k(x)=2x^2 - 5x + 3 The value of k(-3) is
Answer:
36
Step-by-step explanation:
k(-3) = 2(-3)² - 5(-3) + 3
= 18 - (-15) + 3
= 33 + 3
= 36
The conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period. A 4-column table with 3 rows titled television programming. The first column has no label with entries adult, children, total. The second column is labeled live with entries 0. 625, 0. 5, nearly equal to 0. 583. The third column is labeled recorded with entries 0. 375, 0. 5, nearly equal to 0. 417. The fourth column is labeled total with entries 1. 0, 1. 0, 1. 0. Which is the best description of the value 0. 375 in the table? Given that the program was targeted at adults, there is a 37. 5% chance that it was recorded. Given that the program was recorded, there is a 37. 5% chance that it was targeted at adults. 37. 5% of the programs are targeted at adults. 37. 5% of the programs are recorded.
The conditional relative frequency presents the result of the survey that conveys information about the programming and the audience.
The best description of the value 0.357 in the table is; Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.Reasons:
The table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&Live&Recorded&Total\\Adult&0.625&0.375&1.0\\Children&0.5&0.5&1.0\\Total&\approx 0.583&\approx 0.417&1.0\end{array}\right][/tex]
Based on the given table, we have that the programs are categorized based on the intended audience.
Therefore, the 0.375, indicates that 37.5% of the program targeted at adults are recorded.
Therefore, the correct option is;
Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
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https://brainly.com/question/3712144
Answer:
A
Step-by-step explanation:
its a
Someone helppppppp. I swear I will cry for the rest of my life ;-;
3
Pentagon PQRST is 1/2 the size of ABCDE therefore, x = 3
Answer: there is no x so i can't answer it
Step-by-step explanation:
A quadrilateral regular pyramid, the area of any of its lateral faces equal the area of its base, if the side
length of the base of the pyramid is = 6 cm, then the volume of the pyramid =..........cm3
a) 36
b) 673
c) 36/15
d) 216V15
Answer:
c) 36√15 cm³
Step-by-step explanation:
We can compute the volume of the pyramid if we know the area of its base, and its height.
__
A regular quadrilateral is a square. If one side of the square is 6 cm, its area will be ...
A = s² = (6 cm)² = 36 cm² . . . . area of the pyramid base
__
Each triangular face will have a slant height that makes its area the same as that of the base.
A = 1/2bh
36 cm² = (1/2)(6 cm)h
(36 cm²)/(3 cm) = h = 12 cm . . . . . divide by the coefficient of h
The slant height of a face is the hypotenuse of a right triangle whose short leg is half the side length, and whose long leg is the height of the pyramid. If that height is represented by h, the Pythagorean theorem tells us ...
(6 cm/2)² +h² = (12 cm)²
h² = (144 -9) cm²
h = 3√15 cm . . . . . height of the pyramid
__
The volume of the pyramid is given by ...
V = 1/3Bh . . . . . . base area B, height h
Using the values we found above, we compute the volume to be ...
V = (1/3)(36 cm²)(3√15 cm) = 36√15 cm³
Help!!
Question in picture!!
Step-by-step explanation:
A. monomial
B. polonomial
hope it helps.
stay safe healthy and happy.
Answer:
A= monomial
B= trinomial
When r= 1 , h=2.4 find r in terms of h
Answer:
r= 5/12 h
Step-by-step explanation:
r/h = 1/2.4
r =[tex]\frac{10}{24}[/tex]h
r=[tex]\frac{5}{12}[/tex]h
Use the translation rule (x, y) --> (x -10, y + 6) to find the image of A(5, - 10).
Answer:
(-5, -4)
Step-by-step explanation:
Plugin the values:
(x, y) ⇒ (x -10, y + 6)
= x - 10, y + 6
= (5 - 10, -10 +6)
= (-5, -4)
Therefore, A prime is (-5, -4).
If there are 30 boys and 12 girls in a room, fill out all of the possible ratios of boys to girls that could be made
Answer:
30:12
Step-by-step explanation:
if each quadrilateral below is a rectangle, find the missing measures.
Answer:
Recall each angle in a rectangle is 90 degrees. So to find the other portion, subtract the given angle from the 90 degrees.
Step-by-step explanation:
The missing measures of the angles are as follows:
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
What is a rectangle?A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
here, we have,
to determine the measures of the angles:
The figure that completes the question is added as an attachment
From the figure of the rectangle, we have:
m∠BDC = 16°
A rectangle has four (4) interior angles that are 90 degrees each.
This means that
m∠ADE = 90 - 16
m∠ADE = 74°
Also, we have:
m∠ABD = m∠BDC = 16° by the alternate interior angles
By the complementary angle, we have:
m∠CBE = 90 - 16 = 74°
By the alternate interior angles, we have
m∠ADE = m∠CBE = 74°
Solving further, we have the following equations:
m∠AEB = 180 - 2(16)
m∠AEB = 148°
m∠DEA = 180 - m∠AEB
m∠DEA = 180 - 148
m∠DEA = 32°
Hence, the measure of the angle DEA is 32 degrees
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
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mr polaski bought a variety pack of muffins that has 9 apple muffins. the ratio of apple muffins to blueberry muffins in variety pack is 3:5 . how many blueberry muffins are in ms polaski's variety pack?
Answer:
He has 15 Blueberry Muffins
Step-by-step explanation:
If the ratio is 3 to 5, and he has 9 apples, that means that he has 3 times the normal ratio. So, multiply 5 by 3 and you get 15 blueberries.
1. The price of one share of a stock fell 4 dollars each day for 8 days. How
much value did one share of the stock lose after 8 days?
2. A credit card company charges a late fee of 25 dollars each time a customer
fails to pay on time. A customer missed the payment 4 times last year. At
the customer's request and out of courtesy, the credit card company
decides to cancel all late fees for that year. Write a numerical expression to
show how much money was return.
Step-by-step explanation:
1.
$4 for 8 days. that means $4 on each and every day, 8 times.
so, in total that is 4 × 8 = $32
that is how multiplications work.
m×n means that m is added n times (or vice versa and n is added m times).
2.
similar here.
$25 each time the customer missed a payment. and he missed 4 times that year.
the bank returned the fees for all 4 occasions. so,
returned money = 25 × 4 = $100
find the distance between find the distance between following points: a) M(5,4) and N(2, 3)
Answer:
sqrt(10)
Step-by-step explanation:
[tex] \sqrt[2]{ x_{2} - x_{1}) + ( y_{2} - y_{1})} [/tex]
Solve the set of simultaneous equations graphically. Use a scale of 1cm = 1 unit on both axes.
y=4+x
y=1+3x ; 0≤x≤6
Graphs attached
(x,y)=(1.5,5.5)You can retry this question below
The sum of two numbers is 71. The difference of the two numbers is 41. What are the two numbers.
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 71."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 41."
Solve the system you have written above.
The larger number, x is
The smaller number, y is
Calculator
Answer:
x = 56
y = 15
Step-by-step explanation:
"The sum of two numbers is 71."
x + y = 71
"The difference of the two numbers is 41."
x - y = 41
Solve the system:
From the first eq.
x = 71 - y
Replacing this value in the second eq.
(71-y) - y = 41
71 - 2y = 41
71 - 41 = 2y
30 = 2y
y = 30/2
y = 15
From the second eq.
x - y = 41
x - 15 = 41
x = 41 + 15
x = 56
Check:
from the first eq.
x + y = 71
56 + 15 = 71
What number comes in the blank?
20 x 47 x 5 = ____ x 100
Answer:
47
Step-by-step explanation:
20*47= 940
940*5=4,700
47*100=4,700
Solve the system of equations
{y= 15x+9
{y= 1/2x–20
What is the solution to the system?
[tex]y = 15x +9~~~~.....(i)\\\\y = \dfrac 12 x -20~~~ ....(ii)\\\\\\\text{Substitute equation (i) in equation (ii):}\\\\15x +9 = \dfrac 12 x -20\\\\\ \implies 9 +20 = \dfrac x2 - 15 x\\\\\implies 29 = -\dfrac{29 x}2\\\\\ \implies 1 = -\dfrac x 2\\\\\implies x= -2\\\\\text{Substitute}~ x=-2~ \text{in equation (i):}\\\\y = 15(-2) +9 = -30 +9 = -21\\\\\text{Hence}~ (x,y) = (-2,-21)[/tex]
Answer plz answer !!!
Answer:
B
Step-by-step explanation:
1/4 yard long, area is 1/3 and we have to find the width so:
1/3(area) divided by 1/49(length) would get you your width
what is the equation
Answer:
y = -2x+9
Step-by-step explanation:
To figure out equations of tile patterns simply count the initial value and the rate of change, then convert it into (slope intercept form) which is
y = mx+b
In this case the rate of change is -2x because each figure loses 2 blocks as it goes.
You can also see the the initial figure 1 has 9 blocks so this is our constant
With this information we can create the equation y = -2x+9
m = -2
x = x
b = 9
If more aid is needed a simple search of (Visual Pattern - Writing an Equation and Creating a Table) will help you with a video easily.
A rock is thrown into a pool 72 inches deep. The rock sinks at a rate of 4 inches per
second (s). The rock's height (h) above the bottom of the pool is given by the
equation: h = 72 – 4s. After how many seconds will the rock be half way to the
bottom?
Half of 72 is 36. If you divided 36 by 4, you would get 9. So, s = 9 and means that it takes 9 seconds for the rock to be sunk half way.