Two lines are parallel if they are equidistant from one another. The following proves [tex]a || m[/tex]
[tex]Ratio = 1:3[/tex] means that:
[tex]BP=3PA[/tex]
[tex]BQ=3QC[/tex]
To prove that [tex]a || m[/tex] is to prove that side length SR and side length PQ are parallel because:
[tex]SR = a\\ PQ = m[/tex] --------- See attachment for quadrilateral
Considering [tex]\triangle ABC[/tex], we have: [tex]BP=3PA[/tex]
Divide both sides by PA
[tex]\frac{BP}{PA} = \frac{3PA}{PA}[/tex]
[tex]\frac{BP}{PA} = 3[/tex]
Similarly: [tex]BQ=3QC[/tex]
Divide both sides by QC
[tex]\frac{BQ}{QC} = \frac{3BQ}{QC}[/tex]
[tex]\frac{BQ}{QC} = 3[/tex]
So, we have:
[tex]\frac{BP}{PA} = \frac{BQ}{QC} = 3[/tex]
Express as ratios
[tex]BP:PA = BQ:QC = 3[/tex]
[tex]BP:PA \to[/tex] means point P divided side length BA into 3:1
[tex]BQ:QC \to[/tex] means point Q divided side length BC into 3:1
Thales Theorem states that: A line that divides any two sides of a triangle in the same ratio is parallel to the third side.
The third side of [tex]\triangle ABC[/tex] is [tex]AC[/tex].
This means that: [tex]PQ[/tex] is parallel to [tex]AC[/tex]
Since [tex]AC[/tex] is parallel to [tex]SR[/tex], then [tex]PQ[/tex] is parallel to [tex]SR[/tex]
i.e. [tex]SR || PQ[/tex]
Recall that:
[tex]SR = a\\ PQ = m[/tex]
Hence:
[tex]a || m[/tex] has been proved.
Read more about proof of parallel sides at:
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What type of function is represented by the following graph:
(a) Linear
(b) Quadratic
(c) Absolute Value
(d) Exponential
Answer:
b) quadratic
Step-by-step explanation:
Answer:
b. quadratic
Step-by-step explanation:
it makes the shape of a parabola
hope this helps
Quadruple of a number is decreased by twenty gives four.
answer it pls pls
Answer:
[tex]4x - 20 = 4[/tex]
Step-by-step explanation:
Let the missing number be x
Quadruple means 4 times
So According to the question,
4x - 20 = 4 is your answer
Hope this helps
what is 8/9 divided 2/3
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Copy dot flip
8/9 * 3/2
Rewriting
8/2 * 3/9
4 * 1/3
4/3
Can someone help me solve this please!
I am willing to give brainliest too the person who helps the most
Part A
The function y = -16x^2 + c represents the height of the ball at time x
We're told the building is 64 ft tall (roughly 6 stories), so c = 64
That means the function updates to y = -16x^2 + 64
The graph is shown below. Some points of interest on the graph are
(0, 64) ... y intercept(0.5, 60) (1, 48)(1.5, 28)(2, 0) ... x interceptPlot these points, and others if you wish, and draw a parabolic curve through them to complete the graph. To generate any (x,y) point, you simply plug in a given value for x to find its corresponding y value.
For example, if you plugged in say x = 1, then,
y = -16x^2 + 64
y = -16*1^2 + 64
y = -16 + 64
y = 48
Do the same for other x values to get the points mentioned earlier. The more points you plot, the more accurate the curve.
=========================================================
Part B
From the graph made in part A, we see that the parabola crosses the x axis at (2,0). This is the x intercept marked as point E in the diagram. This is when the ball hits the ground because y = 0, aka the height is 0.
The ball hits the ground at 2 seconds (ie the ball is in the air for 2 seconds).
There's not much in terms of steps or explanation here because much of that was already done.
A tanker company has
transported 3.788 x 107 tons
of pineapples during its first
ten years of operation and
expects that total amount to
increase by 25% during the
next ten years.
Which measure
represents the total number of
tons of pineapples that the
company expects to transport
during the next ten years?
A 28.788 X 107 tons
B 9.47 x 106 tons
C 4.735 X 107 tons
D 4.038 X 107 tons
Answer:
c
Step-by-step explanation:
107 x 3.778 x 125/100 = 4.735 x 1-7
Find the solutions to the equation below.
Check all that apply.
2x^2 + 1-1x + 5 = 0
Answer:
Step-by-step explanation:
The trick here is that the equation factors.
y= 2x^2 + 11x + 5
y = (2x + 1)(x + 5)
So either
2x + 1 = 0 subtract 1 from both sides
2x = - 1 divide by 2
2x = -1/2
or
x + 5 = 0 Subtract 5 from both sides
x = - 5
Answer: B and D
Which of the following statements is false?(N=natural numbers)
Answer:
yes N = natural number it's correct what I need to ask
Prove that the circumcenter of a triangle is equidistant from its vertices.
Answer:
Step-by-step explanation:
The circumcenter is equidistant from the three vertices of the triangle. From the figure shown, we will prove DA = DB = DC. 2) DA = DB, DC = DB(If a point is on the perp. bisector of a segment, it is equidistant from each endpoint of the segment.)
Plzzzz help its urgent i will mark u as brainiest i cant find it help
here
Answer:
28.24
Step-by-step explanation:
25 + 32/10 + 4/100
25 + 3.2+ .04
28.24
[tex] \sf25 + \frac{32}{10} + \frac{4}{100} \\ \sf = 25 + 3.2 + 0.04 \\ \sf \: = 28.24[/tex]
Answer:
C. 28.24
Hope you could get an idea from here.
Doubt clarification - use comment section.
Find the product of 3 1/5 and 7 1/4. Express your answer in simplest form.
Answer the question based on the data in the two-way table.
Gender Grades
Below
Average Above
Average Total
Boy 14 23 37
Girl 16 22 38
Total 30 45 75
Which statement is true?
A.
P(boy|above average grades) = P(boy)
B.
P(above average grades|boy) = P(above average grades)
C.
P(boy|above average grades) P(above average grades)
D.
P(above average grades|boy) = P(boy)
Acellus Find the expected value of a random variable x having the following probability distribution. 0 1 2 3 4 5 Probability 1/8 1/4 3/16 1/4 1/16 1/8
Answer:
"2.25" is the right answer.
Step-by-step explanation:
According to the question,
The expected value will be:
= [tex]\sum_{i=1}^{n} x_i P(X = x_i)[/tex]
= [tex]0\times \frac{1}{8}+1\times \frac{1}{4}+2\times \frac{3}{16}+3\times \frac{1}{4}+4\times \frac{1}{6}+5\times \frac{1}{8}[/tex]
= [tex]0+\frac{1}{4}+\frac{3}{8} +\frac{3}{4}+\frac{1}{4} +\frac{5}{8}[/tex]
= [tex]\frac{1}{4} +\frac{8}{8} +\frac{4}{4}[/tex]
= [tex]\frac{1}{4} +1+1[/tex]
= [tex]0.25+2[/tex]
= [tex]2.25[/tex]
Thus the above is the right approach.
Answer:
The answer is 9/4 in fraction form
Step-by-step explanation:
Rate the answer you welcome.
This is a graph of the function g(x) =-3x+2. Determine the domain value when th
range value is -4.
Range = -4= g(x)
Therefore, g(x) = -3x+2
or, -4=3x +2
or, 3x= -4-2
or, 3x= -6
or, x= -6/3 = -2
OPTION A is the correct answer.
When the range value is -4 for the function g(x) = -3x + 2, the corresponding domain value is x = 2.
To find the domain value when the range value is -4 for the function
g(x) = -3x + 2, we need to solve for x when g(x) = -4.
Given: g(x) = -3x + 2
When the range value is -4, we have:
-3x + 2 = -4
Now, isolate x:
-3x = -4 - 2
-3x = -6
Now, divide by -3 to solve for x:
x = -6 / -3
x = 2
So, when the range value is -4 for the function g(x) = -3x + 2, the corresponding domain value is x = 2.
To know more about range:
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the function y=-2(x-3)^2+4 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the 0's of this function.
Find the value of 3 √ 512
Answer:
48√2
Step-by-step explanation:
3√(512)
= 3√(256×2)
= 3√(256)×√(2)
→ we know that 16² = 256 then √(256) = 16
Then
3√(512)
= 3 × 16 ×√(2)
= 48√(2)
Brainly to fastest and correct answer,
Answer:
0.02625
2.1 tenths
2.1
Step-by-step explanation:
Are shape I and shape II similar? If so, give the dilation that proves they are similar. If not, explain why the shapes are not similar.
Answer:
The answer is "They are similar".
Step-by-step explanation:
They were comparable in this respect because both aspect ratios of the top triangle are one square more. The top triangle is equal to the base triangles if you remove one square away from the height and width.
Otherwise, we can say that it forms all different. The dilation factor which translates that bottom left point of shape I to form II is 2. But this does not map the other shape I vertices onto form II. There's, therefore, no dilation in form I of maps on form II.
write the square root of 4√53/169
[tex] \sqrt{4 \frac{53}{169} } [/tex]
[tex] \sqrt{ \frac{729}{169} } [/tex]
[tex] \sqrt{ \frac{27}{13} } [/tex]
▪▪▪ Cutest Ghost ▪▪▪How many pounds of water must be evaporated from 50 pounds of a 3% salt solution so that the the remaining solution will be 5 % salt
Answer:
Step-by-step explanation:
This is kinda tricky, but not nearly as bad as d = rt problems. Those are a nightmare!
We will make a table for this:
#lbs solution * % salt = lbs. salt
3% solution
- Water
New solution
And we will now fill in what we know. The 3% solution part is easy. The number of pounds of that is 50 and the percent salt in 3% salt is....well, 3%. As a decimal, it is .03:
#lbs solution * %salt = lbs salt
3% solution 50 * .03 = 1.5
- Water
New solution
The last column there with a 1.5 in it is the product of 50 times .03, since that is what the formula at the top of the table tells us we have to use. Now for the water. That's easy, too, since the amount of water we are evaporating (notice the subtraction sign out front of the word "water"; that indicates we are removing water) is our unknown, and we also know that water has 0% salt in it:
#lbs solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution
Now all we have left is the new solution row and the equation. Finding the equation from a mixture table is as easy as it can be! Super easy!
The new solution will be 50 - x since, going down column 1, we are subtracting the water from the 3% solution, the % salt is to be 5%:
#lbs. solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution 50 - x * .05 = 2.5 - .05x
Now we're ready for our equation. I got the 2.5 - .05x from multiplying
.05(50 - x), just so you know.
if we had to subtract the water from the salt solution and set it equal to the new solution in the first column, we also have to do it in the third column:
1.5 - 0 = 2.5 - .05x and solve for x:
-1 = -.05x so
x = 20 pounds of water
Find the remainder when f(x)=2x3+2x2−3x−3 is divided by x−2.
Given:
The function is:
[tex]f(x)=2x^3+2x^2-3x-3[/tex]
To find:
The remainder when the given function is divided by [tex]x-2[/tex].
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
We have,
[tex]f(x)=2x^3+2x^2-3x-3[/tex]
This function is divided by [tex]x-2[/tex]. By using the remainder theorem, the remainder is f(2).
Putting [tex]x=2[/tex] in the given function, we get
[tex]f(2)=2(2)^3+2(2)^2-3(2)-3[/tex]
[tex]f(2)=2(8)+2(4)-6-3[/tex]
[tex]f(2)=16+8-9[/tex]
[tex]f(2)=15[/tex]
Therefore, the remainder is 15.
A model of the Pythagorean Theorem is shown below.
If a = 6 and c = 10 , which of the following could NOT be used to find the value of b?
A. 102 = 62 + b2
B. 102 + 62 = b2,
C. 100 = 36 + b2,
D. 100−36=b2
Answer:
D can others can't..............
Find question attached.
a.x=50°
b.x=22°
Answer:
Solution given:
a:
3x=2*75°[inscribed angle is half of central angle]
3x=150°
x=150°/3=50°
x=50°
b.
<BDC=34°+x[exterior angle is equal to the sum of two opposite interior angle of triangle]
again
<DCB=34°+x[base angle of isosceles triangle]
again
<ABC=90°[inscribed angle on a semi circle is 90°]
Now.
In triangle
ABC
<A+ <B+<C=180°[sum of interior angle of a triangle is 180°]
34°+90°+34°+x=180°
x=180°-90°-68°
x=90°-68°
x=22°
a) Solution
By using the inscribed angle is half of central angle,
→ 3x = 2 × 75
→ 3x = 150
→ x = 150/3
→ x = 50°
Thus, 50° is the value of x.
b) Solution
By using the exterior angle is equal to sum of two opposite interior angle of triangle,
→ <BDC = 34+x
→ <DCB = 34+x
(base angle of isosceles triangle)
→ <ABC = 90°
(inscribed angle on a semi circle is 90°)
Then in ∆ ABC,
By sum of interior angle of a triangle is 180°,
→ <A+<B+<C = 180°
→ 34+90+34+x=180°
→ x = 180°-90°-68°
→ x = 90°-68°
→ x = 22°
Thus, 22° is the value of x.
The population of a town is 24,000 and is
increasing at a rate of 6% per year for 3 years
Which digit is in the thousandths place?
98.327
A. 7
B. 2
C. 3
D. 9
Answer:
A.
Step-by-step explanation:
it is A.
Answer: A. 7
Step-by-step explanation:
Given the number 98.327, then we are going to title each digit with a name
9 = tens
8 = ones
3 = tenths
2 = hundredths
7 = thousandths
Therefore, 7 is in the thousandths place
Hope this helps!! :)
Please let me know if you have any questions
Select the true statement about triangle ABC.
A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C
Answer:
B
Step-by-step explanation:
We know that cosθ= adjacent/hypotenuse, sinθ=opposite/hypotenuse, and tanθ=opposite/adjacent.
Using this, we can first try between cos and sin for A-C. We know that two different angles will not have the same side adjacent to both of them. However, one angle might have an adjacent side that is opposite to another angle. Using this knowledge, we can say that A is incorrect, as two different angles in the same triangle cannot have the same cos value (unless the triangle is isosceles).
For B, we can say that cos A = adjacent/hypotenuse = 12/13, and sin C= opposite/hypotenuse = 12/13. These are equal, but we can double check by making sure the other answers are wrong.
For C, we can tell that B is a right angle, signified by the small square representing the angle. sin(90°) = 1, and cosA = 12/13. These are not equal.
Finally, for D, sin A = opposite/hypotenuse = 5/13, while tan C = opposite/adjacent = 12/5. These are not equal
What are the x and y-intercepts of the line described by the equation?
2x + 4y = 12.4
Enter your answers, in decimal form, in the boxes.
x=
y=
Step-by-step explanation:
x intercept is at y=0
2x= 12.4
x = 6.2
y intervept is at x=0
4y= 12.4
y = 3.1
Solve for y in terms of x. 2/3 y - 4 = x
Answer:
y = 3/2x + 6
Step-by-step explanation:
2/3 y - 4 = x
2/3y = x + 4
y = 3/2 * (x + 4)
y = 3/2x + 6
Answer:y=(3x/2)+6
Step-by-step explanation:
(2/3)y-4=x
2y-12=3x
2y=3x+12
y=(3x/2)+6
help please summer school sucks!!!
Answer:
X =30
Step-by-step explanation:
= 60+90
=150
angle sum property
x+150=180
x=180- 150
x= 30
Answer:
Step-by-step explanation:
90 + 60 = 150
(right angles = 90)
There is 180 degrees in a triangle, therefore,
180 - 150 = 30
Therefore, x = 30
p.s. Are you good at history?
p.p.s I dont like summer school either =)
Solve the equation 3(2x+9)=30
Answer:
x=1/2
Step-by-step explanation:
3(2x+9) = 30
Multiply out the 3
6x + 27 = 30
Subtract 27 on both sides
6x = 3
Divide by 6 on both sides
x = 1/2
Answer:
x=1/2
Step-by-step explanation
Find IG in the image below .
Step-by-step explanation:
[tex]ig =2 \times yx = 2 \times 11 = 22[/tex]
