Answer:
So the line that is a perpendicular bisector of AB is [tex]y=\frac{3}{8}x+\frac{11}{16}[/tex].
Step-by-step explanation:
If we are looking for a line such that is is perpendicular bisector of AB, then we first need to find the midpoint of AB.
The midpoint of AB is going to be the "average" point.
What I mean by this, to find the x-coordinate of the midpoint we need to average our x-coordinates of our endpoints and we also need to do the same for the y-coordinate part.
Let's begin this.
The average of the x-coordinates of the endpoints are:
[tex]\frac{2+5}{2}=\frac{7}{2}[/tex]
The average of the y-coordinates of the endpoints are:
[tex]\frac{6+(-2)}{2}=\frac{4}{2}=2[/tex]
This concludes the midpoint of AB is [tex](\frac{7}{2},2)[/tex].
Now we also need to calculate the slope of [tex]AB[/tex] so we can find the slope of the line perpendicular to it.
To do this we could use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Without using the formula directly, I like to line the points up vertically and subtract. I then put the 2nd difference over the first difference. Like so,
[tex](5,-2)[/tex]
-[tex](2,6)[/tex]
----------------------
[tex]3 , -8[/tex]
So the slope is [tex]\frac{-8}{3}[/tex].
The line that is perpendicular to the line AB will have an opposite reciprocal slope.
So the line we are looking for has slope [tex]\frac{3}{8}[/tex].
So we are looking for a line going through the midpoint [tex](\frac{7}{2},2)[/tex] and has slope [tex]\frac{3}{8}[/tex].
A line in slope-intercept form is [tex]y=mx+b[/tex].
We know [tex]m=\frac{3}{8}{/tex] and we know a point [tex](x,y)=(\frac{7}{2},2)[/tex]. We could plug this in to find [tex]b[/tex].
Let's do that now.
[tex]2=\frac{3}{8}(\frac{7}{2})+b[/tex]
Simplify:
[tex]2=\frac{21}{16}+b[/tex]
Subtract 21/16 on both sides:
[tex]2-\frac{21}{16}=b[/tex]
Find a common denominator:
[tex]\frac{32}{16}-\frac{21}{16}[/tex]
[tex]\frac{11}{16}[/tex]
So the line that is a perpendicular bisector of AB is [tex]y=\frac{3}{8}x+\frac{11}{16}[/tex]. This is so because the line we found will be perpendicular to AB while also cutting AB into two equal halves.
What is the next fraction in this sequence? Simplify your answer.
2/3 1/3 1/6 1/12
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.
What is six lots of five
Answer:
6 lots of 5 means 6×5=30
Step-by-step explanation:
Answer:
Multiplication - When we multiply we find 'lots of'
6 lots of 5 = 30
6×5=30
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.
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?
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
Fill in the blanks to make the solution correct.
3 3/4-_* _/8=2
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
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.
a rabbit can move 1 2/3 miles every hour, then how many hours would it take for a rabbit to go 5miles?
Answer: 5 hours
Step-by-step explanation: 5 hours because 7/5 *5/1=35/5 and 35 divided by 5 equals 7
Is 1/8 -10(3/4-3/8x) + 5/8x equivalent to -1/8(59 -35X)
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]
What is the mean of the data below?
43,38,37,57,57,58,45
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
HELP ! PLEASE
examine the system of equations.
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].
8m²n³-24m²n²+4m³n
how do I factor out the GCF
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]
Solve this -2 (v + 3) + 6v
Answer:4v+3
Step-by-step explanation:
-2v+3+6v
-2+6=4
What two numbers multiplies to -4 and adds to 3?
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 :)
A dozen eggs cost $3.84. At this rate, how much would 50 eggs cost?
(8x+5)+(4x-3) what is that equal to
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
6(8x^2-25x-28)
Please factor fully
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.
When graphed, which function would appear to be shifted 5 units up from the graph of f(x)=x^2+3?
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!
If possible, factor 100 − 121y2.
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 :)
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
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
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
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?
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]
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.
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:
Solve f(-7) for f(x) = 17 – X
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
write an equation in point-slope form for the line throught the given slope (8,3);m=6
Answer: [tex]y - 3 = 6 (x - 8 )[/tex]
Step-by-step explanation:
The equation of line in point slope form is given as :
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]x_{1}[/tex] = 8
[tex]y_{1}[/tex] = 3
[tex]m = 6[/tex]
substituting into the formula , we have :
[tex]y - 3 = 6 (x - 8 )[/tex]
Let f(x)=2x-8 and g(x)=x+9. Find f(g(x)) and g(f(x))
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
Please show work for both problems
Answer:
1) x = 25 2) x = 23; m∠CBD = 80 degrees
Step-by-step explanation:
1) 5x + 15 = 6x - 10 Set both equations equal to each other
- 5x - 5x Subtract 5x from both sides
15 = x - 10
+ 10 + 10 Add 10 to both sides
25 = x
2) 2x + 14 + x + 7 = 90 Set the equations equal to 90
3x + 21 = 90 Combine like terms
- 21 - 21 Subtract 21 on both sides
3x = 69 Divide both sides by 3
x = 23
Plug 23 into the equation
2(23) + 14 = 60
Roxy is multiplying 18
1
8
by 43
4
3
.
Use the drop-down menu to complete the statement.
CLEAR
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].
At grocery store, the price of a watermelon is determined by how many pounds the watermelon weighs. The price of the watermelon that weighs 7.3 pounds is $4.38. Write an equation that can be used to determine the price, p. in dollars, of any watermelon based on the number of pounds, w, the watermelon weighs.
Determine the cost of a watermelon that weighs 8.5 pounds.
please help with this question
Answer:
7.3 divided by 4.38
Step-by-step explanation:
What is 5 x 4/5 = and how did you get that answer
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.
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.
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!