Answers
x = 11 (or) x = –13
Solution:
Theorem:
If three or more parallel lines are cut by a transversal then they divide the transversals proportionally.
Given lines l, m, n are parallel lines cut by a two transversal lines.
Therefore, they are in proportion by the above theorem.
[tex]$\Rightarrow\frac{x+5}{10}=\frac{12.8}{x-3}[/tex]
Do cross multiplication.
[tex]$\Rightarrow(x+5)\times(x-3)=12.8\times10[/tex]
[tex]$\Rightarrow x^2+5x-3x-15=128[/tex]
[tex]$\Rightarrow x^2+2x-15=128[/tex]
Arrange all terms in one side.
[tex]$\Rightarrow x^2+2x-15-128=0[/tex]
[tex]$\Rightarrow x^2+2x-143=0[/tex]
[tex]$\Rightarrow x^2-11x+13x-143=0[/tex]
Take common terms outside
[tex]$\Rightarrow x(x-11)+13(x-11)=0[/tex]
[tex]$\Rightarrow (x-11)(x+13)=0[/tex]
[tex]$\Rightarrow (x-11)=0\ \text{(or)}\ (x+13)=0[/tex]
⇒ x = 11 (or) x = –13
Hence x = 11 (or) x = –13.
Related Questions
a rabbit can move 1 2/3 miles every hour, then how many hours would it take for a rabbit to go 5miles?
Answers
Answer: 5 hours
Step-by-step explanation: 5 hours because 7/5 *5/1=35/5 and 35 divided by 5 equals 7
The vertex of a parabola can be:
a. Always a minimum
c. Either a minimum or a maximum
b. Always a maximum
d. Both a minimum and a maximus
Answers
Answer:
c. Either a minimum or a maximum
Step-by-step explanation:
considering that a parabola can grow or decrease from its vertex we can note that in the case of a parabola with the branches down the vertex will always be a maximum, and in the case of a parabola with the branches up it will always be a minimum.
Carlon plans to evaporate a number of gallons of water from 90 gallons of a 15% salt solution to make a 25% salt solution. Which equation can he use to find x, the number of gallons that should be evaporated?
Original
(Gallons)
Removed
(Gallons)
New
(Gallons)
Amount of Salt
13.5
0
Amount of Solution
90
x
StartFraction 13.5 Over 90 minus x EndFraction = StartFraction 25 Over 100 EndFraction
StartFraction 13.5 Over x EndFraction = StartFraction 25 Over 100 EndFraction
13.5 (90 minus x) = 0.25
13.5 (90 minus x) = 25
Answers
Answer:
actually the right answer is A
Step-by-step explanation:
if you solve it you get x=36 but remember that x is the amount of water that you need to evaporate so if you want to check it just subtract it from 90 and the salt will be 25%
(8x+5)+(4x-3) what is that equal to
Answers
Answer:
12x + 2
Step-by-step explanation:
To find what the expression equals, you can collect like terms. This means to do the operations (add or subtract) the numbers that have the same variables.
(8x + 5) + (4x - 3) Remove brackets to add a binomial (2-term brackets)
= 8x + 5 + 4x - 3 Collect like terms
= 8x + 4x + 5 - 3 I rearranged so you can see which terms are alike
= 12x + 5 - 3 Collected like terms with "x" (8x + 4x = 12x)
= 12x + 2 Collected like terms with no variables (5 - 3 = 2)
Therefore (8x + 5) + (4x - 3) is equal to 12x + 2.
If you want, you can also find another equal expression by factoring. Since "12x" and "2" are both divisible by the factor 2, you can take it out and put the other numbers in a bracket.
12x + 2
= 2(12x/2 + 2/2)
= 2(6x + 1) This is equal, but in factored form.
Answer:
12x+2
Step-by-step explanation:
8x+4x=12x
5-3=2
12x+2
Mick jogs a total distance of 1/2 mile. He counts 5 marker posts that are equally spaced along his jog. What is the distance, in miles, between each marker post? Write and solve an equation
Answers
Answer: [tex]\frac{1}{10} miles=0.1 miles[/tex]
Step-by-step explanation:
If the total distance [tex]D[/tex] Mick jogged is divided among five posts, we can write the following relation to find the distance [tex]x[/tex] between each post:
[tex]x=\frac{D}{5}[/tex]
Where [tex]D=\frac{1}{2} mile[/tex]
Then:
[tex]x=\frac{\frac{1}{2} mile}{5}[/tex]
[tex]x=\frac{1}{10} miles=0.1 miles[/tex] This is the distance between each marker post.
Help por favor I am having problems
Answers
Answer:
∴ΔGHJ ≅ΔLMK
∴ΔABC≅ΔPQR
Step-by-step explanation:
5.
GH= 3.6 , HJ=2.84 and GJ=2.24
LK= 9 ,KM= 5.6 and LM = 7.1
[tex]\frac{LK}{GH} =\frac{KM}{GJ} =\frac{LM}{HJ}[/tex]
[tex]\frac{9}{3.6} =\frac{5.6}{2.24} =\frac{7.1}{2.84} =2.5[/tex]
Therefore ΔGHJ and ΔLMK satisfy SSS rule(side-side-side)
∴ΔGHJ ≅ΔLMK
6.
ΔABC
Since AB=AC this equivalent to the two angels of the triangle are equal
Then
∠CAB+∠CBA=180°-34°
⇔∠CAB=73° [∵∠CAB=∠CBA]
Similarly for ΔPQR ∴ ∠RPQ=∠RQP=73°
Therefore ΔABC and ΔPQR satisfy AAA rule(angle-angle-angle)
∴ΔABC≅ΔPQR
What is the mean of the data below?
43,38,37,57,57,58,45
Answers
Answer:
You may need to plot them.
Step-by-step explanation:
Looks like your confused, if there is a line plot plot it there. Hope this helps! If it doesn't, phone a friend!
Answer: it would be 47.9 if you rounded to nearest tenth
Step-by-step explanation: Add all numbers together then divide by how many numbers are there
if x:y=5:6 then find the value of 5x-2y:6x+2y
Answers
Step-by-step explanation:
x : y = 5 : 6
[tex] \therefore[/tex]let x = 5k & y = 6k
We need to find: 5x-2y:6x+2y
[tex] \therefore \: \frac{5x - 2y}{6x + 2y} \\ \\ = \frac{5 \times 5k - 2 \times 6k}{6 \times 5k + 2 \times 6k} \\ \\ = \frac{25k - 12 k}{30k + 12k} \\ \\ = \frac{13 k}{42k} \\ \\ =\frac{13 }{42} \\ \\ = 13 : 42 \\ \\ \purple{ \boxed{\therefore \: (5x - 2y) :({6x + 2y}) = 13 : 42}}[/tex]
What is 5 x 4/5 = and how did you get that answer
Answers
Answer:4
Step-by-step explanation:
You only multiple the top or in this case 4 so 4x5= 20/5 simplified would be 20 divided by 5=4
Answer:
4
Step-by-step explanation:
Because all you need to do is multiply-5 times 4 equals 20/5 and 20 divided by 5 equals 4.
8m²n³-24m²n²+4m³n
how do I factor out the GCF
Answers
Answer:
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]
Step-by-step explanation:
The given expresion is
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n[/tex]
Observe that 4 is common to 8,-24, and 4
Observe also that, m²n is common to all the terms.
Hence the GCF is:4m²n
We factor the GCF to get;
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]
6(8x^2-25x-28)
Please factor fully
Answers
Answer:
6(8x +7)(x -4)
Step-by-step explanation:
6(8x^2 -25x -28) = 6(8x^2 -32x +7x -28) . . . . rewrite the middle term
= 6(8x(x -4) +7(x -4)) . . . . factor by grouping
= 6(8x +7)(x -4)
_____
To rewrite the middle term, you are looking for factors of (8)(-28) that have a sum of -25. The sum will be odd only if one of the factors is odd. The only odd factor in the product is 7, so we choose (8)(-28) = (7)(-32). Those two factors, 7 and -32, have a sum of -25, so those are the ones we used.
3014 divided by 63___R___
Answers
Step-by-step explanation:
We have,
3014 divided by 63
To find, the remainder of 3014 divided by 63 = ?
3014 divided by 63
∴ [tex]\dfrac{3014}{63}[/tex]
= 63 × 47 + 53
We know that,
Dividend = Quotient × Divisor + Remainder
∴ Remainder = 53
Thus, when 3014 divided by 63, the remainder is 53.
HELP ! PLEASE
examine the system of equations.
Answers
The solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].
Solution:
Given system of equations are
[tex]-3 x+y=4[/tex] ---------- (1)
[tex]-9 x+5 y=-1[/tex] ---------- (2)
To solve the given system of equations by substitution method.
Let us take the equation (1) and find the value of y.
(1) ⇒ [tex]-3 x+y=4[/tex]
Add 3x on both sides of the equation, we get
⇒ [tex]y=4+3x[/tex]
Substitute y = 4 + 3x in equation (2), we get
[tex]-9 x+5 (4+3x)=-1[/tex]
[tex]-9 x+20+15x=-1[/tex]
Combine like terms together.
[tex]-9 x+15x=-1-20[/tex]
[tex]6x=-21[/tex]
Divide by 6 on both sides of the equation.
[tex]$x=-\frac{21}{6}[/tex]
Divide the numerator and denominator by the common factor 3.
[tex]$x=-\frac{21\div3}{6\div3}[/tex]
[tex]$x=-\frac{7}{2}[/tex]
Now, substitute x value in y = 4 + 3x, we get
[tex]$y=4+3\left(\frac{-7}{2} \right)[/tex]
[tex]$y=4+\left(\frac{-21}{2} \right)[/tex]
Take LCM of the denominators and make the same.
[tex]$y=\frac{8}{2} +\frac{-21}{2}[/tex]
[tex]$y=\frac{-13}{2}[/tex]
Hence the solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].
Solve this -2 (v + 3) + 6v
Answers
Answer:4v+3
Step-by-step explanation:
-2v+3+6v
-2+6=4
Roxy is multiplying 18
1
8
by 43
4
3
.
Use the drop-down menu to complete the statement.
CLEAR
Answers
The given question has some missing information. By googling the information we can find the complete question here:
https://simplyans.com/mathematics/roxy-is-multiplying-18-by-43-use-t-11879138
The product 1/8 times 4/3 is greater than 1/8.
Step-by-step explanation:
The given information is Roxy multiplying two numbers [tex]\frac{1}{8}[/tex] and [tex]\frac{4}{3}[/tex].
We have to find that their product is less then or greater than [tex]\frac{1}{8}[/tex].
Let us find the product first.
=[tex]\frac{1}{8}[/tex]×[tex]\frac{4}{3}[/tex].
=[tex]\frac{1}{6}[/tex].
Let us now compare [tex]\frac{1}{6}[/tex] and [tex]\frac{1}{8}[/tex].
We can compare a fraction when the denominators of the fractions are same. Else we can use LCM to make the denominator same.
Or else we can turn the fraction into decimal to compare.
LCM method:
1) Find the least common denominator(LCM) for the denominators.
⇒ LCM of 6 and 8 is 24.
2) Next let us change the fractions for equal denominators.
For the 1st fraction,
[tex]\frac{1}{6}=\frac{1 \times 4}{6 \times 4}=\frac{4}{24}[/tex].
For the 2nd fraction,
[tex]\frac{1}{8}=\frac{1 \times 3}{8 \times 3}=\frac{3}{24}[/tex].
Now compare the two new numbers.
[tex]\frac{4}{24}>\frac{3}{24}[/tex].
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction.
Thus [tex]\frac{4}{24}[/tex] is the greater number which means [tex]\frac{1}{6}[/tex] .
i.e. [tex]\frac{1}{6}[/tex] is greater than [tex]\frac{1}{8}[/tex].
Decimal Method:
[tex]\frac{1}{6}[/tex] = 0.167.
[tex]\frac{1}{8}[/tex]= 0.125.
By comparing 0.167 and 0.125,
0.167 > 0.125.
0.167 is greater than 0.125.
Thus [tex]\frac{1}{6}[/tex] is greater than [tex]\frac{1}{8}[/tex].
richie has a rug in his bedroom with a perimeter of 42 feet. the length of the rug is 12 feet what is the width of the rug
Answers
The width of the rug is 9 feet.
Step-by-step explanation:
Perimeter of rug = 42 feet
Lengths are same in square and rectangle shapes; therefore;
Length of rug = 12 feet
Width of rug = w
Perimeter = Length + Length + Width + Width
Perimeter = [tex]12+12+w+w[/tex]
[tex]42=24+2w\\42-24=2w\\18=2w\\2w=18[/tex]
Dividing both sides by 2
[tex]\frac{2w}{2}=\frac{18}{2}\\w=9[/tex]
The width of the rug is 9 feet.
Keywords: perimeter, division
Learn more about division at:
brainly.com/question/10879401brainly.com/question/10940255#LearnwithBrainly
A dozen eggs cost $3.84. At this rate, how much would 50 eggs cost?
Answers
First you find how much one egg cost which is 3.84/12 (0.32)
Next multiply 0.32 by 50 which would be 16
A slice is made perpendicular to the base of a right rectangular prism, as shown. What is the area of the resulting two-dimensional cross-section? Drag and drop the answer into the box.
Answers
Answer: [tex]A=280\ in^2[/tex]
Step-by-step explanation:
The missing figure is attached.As you can observe in the figure attached, when the slice is made perpendicular to the base of the right rectangular prism, the resulting two-dimensional cross-section is a Rectangle.
By definition, the area of a rectangle can be calculated with this formula:
[tex]A=lw[/tex]
Where "l" is the length of the rectangle and "w" is the width.
In this case, looking at the figure attached, you can identify that the length and the width of the rectangle are:
[tex]l=20\ in\\w=14\ in[/tex]
Now, knowing these values, you can substitute them into the formula:
[tex]A=(20\ in)(14\ in)[/tex]
Finally, you must evaluate in order to find area of this rectangle. You get that its area is the following:
[tex]A=280\ in^2[/tex]
Answer:
A which is 280mm
Step-by-step explanation:
In a recent election in Hartsdale, the leading candidate captured 78% of total votes for state senator.
If there were a total of 24,082 votes, how many votes did this candidate captured?
Answers
Answer:
[tex]Leading\ candidates\ votes\approx 18784\ votes[/tex]
Step-by-step explanation:
Percentage:[tex]x\%\ of\ y=\frac{x}{100}\times y[/tex]
[tex]Total\ votes=24082\\\\Leading\ candidates\ votes=78\%\ of\ total\ votes\\\\Leading\ candidates\ votes=\frac{78}{100}\times 24082\\\\Leading\ candidates\ votes=0.78\times 24082\\\\Leading\ candidates\ votes=18783.96\\\\Leading\ candidates\ votes\approx 18784\ votes[/tex]
You are going to build a new garage similar to the rectangular one you currently have. The current dimensions are 25 feet wide by 20 feet long. You need to stake and rope off where the concrete will be poured. If the new garage is going to have a width of 30 feet, how much rope are you going to need?
Answers
To find the amount of rope needed for the new garage, calculate the perimeter of the planned structure. If the new garage is similar to the current one, maintaining the same width to length ratio (5:4), and the width is increasing to 30 feet, the length will be 24 feet. The total rope required is the perimeter, which is 108 feet.
Explanation:To calculate the amount of rope needed for the new garage with a width of 30 feet, we must find the length of the rectangle that represents the area to be roped off for the concrete pour. If the garage maintains the same shape, which is similar to the current one, we can assume that the length will increase in the same ratio as the width.
The current dimensions are 25 feet wide by 20 feet long, which gives a width to length ratio of 25:20 or 5:4. If we increase the width to 30 feet, maintaining the same ratio, the length should be 24 feet (as 30:24 or 5:4). So the perimeter of the new rectangular area will be twice the width plus twice the length (2 x width + 2 x length = 2 x 30 ft + 2 x 24 ft = 60 ft + 48 ft = 108 ft). Therefore, you will need 108 feet of rope to stake out the perimeter of the new garage.
Final answer:
To find the amount of rope needed for the new garage, calculate the perimeter of the new garage by summing all the sides of the rectangle. The perimeter of the current garage can be used as a reference point. The result is 100 feet of rope needed.
Explanation:
To find the amount of rope you will need, you need to calculate the perimeter of the new garage. The perimeter is the sum of all the sides of a rectangle.
The current garage has a width of 25 feet and a length of 20 feet, so its perimeter is 2(25) + 2(20) = 90 feet.
The new garage will have a width of 30 feet, so its perimeter will be 2(30) + 2(20) = 100 feet.
Therefore, you will need 100 feet of rope to stake and rope off where the concrete will be poured for the new garage.
Mr. Tram was planning his trip from Dallas, TX to Detroit, MI. He knows that the total distance he needs to cover is 1620 km. He usually drives at a speed of 60 km per hour.
Answers
Answer:
27 hours
Step-by-step explanation:
1620 divided by 60 = 27
Answer:
27 Hours
Step-by-step explanation:
Divide 1620 by 60 and get.. 27 hours.
what is the answer to
feet
=
8.5
meter?
Answers
Answer:
27.8871 feet
Step-by-step explanation:
1 meter ≅ 3.28084
You need to multiply the meters by 3.28084 to get the answer in feet.
So, 8.5 * 3.28084 ≅ 27.8871
What is the next fraction in this sequence? Simplify your answer.
2/3 1/3 1/6 1/12
Answers
Answer:
1/24
Step-by-step explanation:
As you go fraction to the next fraction you divide by 2.
2/3 divided by 2 = 1/3
1/3 divided by 2 = 1/6
the rule is "divide by 2"
Final answer:
The next fraction in the sequence is 1/24, found by continuing the pattern of halving each successive fraction.
Explanation:
To determine the next fraction in the sequence 2/3, 1/3, 1/6, 1/12, we observe a pattern. The second fraction is half of the first, the third is half of the second, and the fourth is half of the third. By continuing this pattern, to find the next fraction, we need to take half of the last fraction in the sequence.
To solve the more difficult problem, multiply the numerator and denominator by a skillfully chosen factor: 1/2. For the fraction 1/12, we multiply both the numerator (1) and the denominator (12) by 1/2 to get our next fraction:
Numerator: 1 imes 1/2 = 1/2Denominator: 12 imes 1/2 = 6Therefore, the next fraction in the sequence is 1/2 divided by 6 which simplifies to 1/24.
Is 1/8 -10(3/4-3/8x) + 5/8x equivalent to -1/8(59 -35X)
Answers
Yes, The expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]
Explanation:
The given expression is [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex]
Solving, we get,
[tex]\frac{1}{8} -\frac{30}{4}+\frac{30}{8}x+\frac{5}{8} x[/tex]
Adding the similar terms, we have,
[tex](\frac{1}{8} -\frac{30}{4})+(\frac{30}{8}x+\frac{5}{8} x)\\[/tex]
[tex]\frac{1-60}{8} +\frac{35}{8}x[/tex]
Adding, we get,
[tex]-\frac{59}{8} +\frac{35}{8}x[/tex]
Taking out the common term [tex]-\frac{1}{8}[/tex] , we have,
[tex]-\frac{1}{8} (59-35x)[/tex]
Thus, the expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]
If possible, factor 100 − 121y2.
Answers
Answer:
(10 + 11y)(10 - 11y)
Step-by-step explanation:
100 - 121y²
This is a special factoring called difference of squares. Since both of the numbers in the subtraction expression are perfect squares, we can use this rule:
a² - b² = (√a² - √b²)(√a² + √b²)
Take the square root of each number. Add them in one bracket, subtract them in the other bracket.
(10 + 11y)(10 - 11y)
100 is a perfect square because its square root is a whole number.
√100 = 10
121y² is a perfect square because its square root is a whole number, and its variable is squared.
√121 = 11
√y² = y
Answer:
(10 + 11y)(10 - 11y)
Step-by-step explanation:
difference of squares :)
Let f(x)=2x-8 and g(x)=x+9. Find f(g(x)) and g(f(x))
Answers
Step-by-step explanation:
Given,
f(x) = 2x - 8 and g(x) = x + 9
To find, the values of f(g(x)) and g(f(x)) = ?
f(x) = 2x - 8
∴ f(g(x)) = 2(g(x)) - 8
= 2(x + 9) - 8
= 2x + 18 - 8
= 2x + 10
Also,
g(x) = x + 9
g(f(x)) = f(x) + 9
= 2x - 8 + 9
= 2x + 1
∴ f(g(x)) = 2x + 10 and g(f(x)) = 2x + 1
When graphed, which function would appear to be shifted 5 units up from the graph of f(x)=x^2+3?
Answers
Answer:
f(x)=x^2+8
Step-by-step explanation:
To move a function upwards, you need to shift the function up the y axis. The function intersects the y axis at 3, so you need to add 5 to 3 to shift the graph up 5 units. I hope this helps you!
ABCD is a rectangle. Two circles are drawn inside ABCD such that the circles are tangent at point G. E is the tangent point of the first circle and AB, and F is the tangent point of the second circle and BC, as shown. Find m∠EGF.
Answers
Answer:135 degrees
Step-by-step explanation: Pretend that the 2 circles are equal, and connect the lines that form the angle. You can draw a right triangle on the circle that is on the right, connecting 2 radii to form it. Then, because the two radii are of equal length, you know that it is a 45-45-90 triangle. Then draw a line that is from the top line and connect in to G. That line is perpendicular, so 45 degrees plus 90 degrees is 135 degrees. I hope this helps!
Solve f(-7) for f(x) = 17 – X
Answers
Answer:
f(-7) = 24
Step-by-step explanation:
Step 1: Identify the Function
f(x) = 17 - x is the function
Step 2: Set x to -7 in the function
f(-7) = 17 - (-7)
f(-7) = 17 + 7
f(-7) = 24
Answer: f(-7) = 24
What two numbers multiplies to -4 and adds to 3?
Answers
Answer:
-1 and 4
Step-by-step explanation:
multiply -1 and 4 to get -4.
-1 x 4 = -4
add 4 to -1 to get (positive) 3.
-1 + 4 = 3
hope this helps :)