The proof can be completed with the concept of the slope formula, which shows that two line segments with identical slopes equate to parallel lines. This fits perfectly in the context of the given two-column proof.
Explanation:In the provided incomplete two-column proof, the statement in question infers that the segment DE is parallel to segment AC because they have the same slope. The reason for this, which completes the proof, would be the slope formula. The slope formula allows us to calculate the steepness, incline, or gradient of a line segment defined by two points in a 2D space. When applied to segments DE and AC, it gives us identical values, indicating that the two line segments are parallel as per the theorem stating that parallel lines have equal slopes.
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To complete the proof, the correct answer is 'By the slope formula'
Explanation:To complete the proof, we need to show that the slopes of segment DE and segment AC are equal. By calculating the slopes using the slope formula, we can determine if they are indeed equal. Therefore, the correct answer is 'By the slope formula'.
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Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.
DE = 1.5 cm, EF = 2.25 cm, FD = 3 cm
Step-by-step explanation:Side DE corresponds to side AB and is (1.5 cm)/(2 cm) = 3/4 the length of it.
Because the triangles are similar, all pairs of corresponding sides have the same ratio. That is, the side lengths in ΔDEF are 3/4 of those in ΔABC.
... EF = (3/4)×BC = (3/4)×(3 cm)
... EF = 2.25 cm
... FD = (3/4)×CA = (3/4)×(4 cm)
... FD = 3 cm
The lengths of the sides of triangle △DEF, given that AB=2 cm, BC=3 cm, CA=4 cm, and DE=1.5 cm, would be EF = 2.25 cm and DF = 3 cm.
Explanation:If triangles △ABC and △DEF are similar, then the ratio of the corresponding sides is the same. We know AB = 2 cm which corresponds to DE = 1.5 cm in the triangle △DEF. The ratio of AB to DE is 2cm:1.5cm or 4:3. Let's compute the sides of the triangle △DEF using this ratio:
EF corresponds to BC in triangle △ABC. Using the ratio 4:3, EF = BC * (3/4) = 3cm * 3/4 = 2.25 cm DF corresponds to CA in triangle △ABC. Using the ratio 4:3, DF = CA * (3/4) = 4cm * 3/4 = 3 cmLearn more about Similar Triangles here:https://brainly.com/question/32489731
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What is the result of isolating x^2 in the equation below? y^2-3x^2=6
A. x^2 = y^2/3 -2
B. x^2 = -y^2/3 -2
C. x^2 = y^2/3 + 2
D. x^2 = -y^2/3 + 2
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
Add 3x^2 to both sides of the equation. We do this so that the coefficient of x^2 is positive. It can be less confusing that way.
... y^2 = 3x^2 +6
Divide by 3.
... y^2/3 = x^2 +2
Subtract 2.
... y^2/3 -2 = x^2 . . . . . matches selection A.
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
According to the diagram which of the following statement is true?
Cos x =4/5
Sin x = 5/3
Tan x = 5/4
Cos x = 3/5
We know that :
✿ [tex]\mathsf{Cos\theta = \frac{Adjacent\;Side}{Hypotenuse}}[/tex]
✿ [tex]\mathsf{Sin\theta = \frac{Opposite\;Side}{Hypotenuse}}[/tex]
✿ [tex]\mathsf{Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}}[/tex]
From the Figure :
✿ [tex]\mathsf{Cosx = \frac{4}{5}}[/tex]
✿ [tex]\mathsf{Sinx = \frac{3}{5}}[/tex]
✿ [tex]\mathsf{Tanx = \frac{3}{4}}[/tex]
Only 1st Statement is True
1st Option is the Answer
Which number(s) below would NOT in scientific notation and why? 4.5 x 10^4 6 x 10^7 12.5 x 10^3 4.2 x 10^-8 2.355 x 10^6 0.45 x 10^3
Scientific notation has exactly one non-zero digit to the left of the decimal point in the mantissa. The numbers listed above do not.
_____
Comment on these numbers
There may be good reasons for writing the numbers in this form. For example, in engineering, it is often useful to have the exponent be a multiple of 3. In other instances, writing the number in these forms may facilitate arithmetic. However good the reasons may be, these numbers are not in in the form defined as "scientific notation."
Solve for u: u/p + u/q =m, if , p≠−q
Answer:
The solution for u is:
[tex]u = \frac{mpq}{q+p}[/tex]
Step-by-step explanation:
The first step to solve this problem is finding the least common multiplicator between p and q, that is pq, so:
[tex]\frac{u}{p} + \frac{u}{q} = m[/tex]
[tex]\frac{uq + up}{pq} = m[/tex]
[tex]uq + up = mpq[/tex]
[tex]u(q + p) = mpq[/tex]
[tex]u = \frac{mpq}{q+p}[/tex]
The required solution of the given equation for u is equal to
(m(p × q)) / (q + p).
Given that:
Equation: u/p + u/q = m, if p ≠ -q
To solve for u in the equation u/p + u/q = m, use the method of finding a common denominator and simplifying the expression.
First, need to find a common denominator for the fractions u/p and u/q. The common denominator in this case would be (p × q).
Multiplying the equation by (p × q) to get,
u(q) + u(p) = m(p × q)
Next, combine the terms with u as:
u × q + u × p = m(p × q)
Now, factor out u as:
u(q + p) = m(p × q)
To solve for u, divide both sides of the equation by (q + p):
u = (m(p × q)) / (q + p)
Therefore, the solution for u is u = (m(p × q)) / (q + p).
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Which piece of additional information can be used to prove △CEA ~ △CDB?
∠BDC and ∠AED are right angles
AE ≅ ED
△BDC is a right triangle
∠DBC ≅ ∠DCB
∠BDC and ∠AED are right angles
Step-by-step explanation:Because ∠C ≅ ∠C, the additional bit of information above can be used to show AA similarity.
____
None of the other offered choices says anything about both triangles. In order to show similarity, you need information about corresponding parts of the two triangles. Information about one triangle alone is not sufficient.
Answer:
I think it's A. ∠BDC and ∠AED are right angles
Step-by-step explanation:
I hope this helps.
The sum of two numbers is 65 . One number is 4 times as large as the other. What are the numbers?
Answer:
13
Step-by-step explanation:
65=5x(because number A is four times number B therefore, it is really B five times)
Then divide both sides by 5.
13=x
To find two numbers when their sum is 65 and one number is 4 times the other, the smaller number is 13, and the larger number is 52.
number, and 4x be the larger number.
Write an equation: x + 4x = 65.
Solve the equation: 5x = 65, x = 13.
The smaller number is 13, and the larger number is 4 times 13, which is 52.
need help pls. I try many ways of this answer
Answer:
3(t+2)
Step-by-step explanation:
As with any problem involving division of fractions, you can invert the denominator and multiply.
Your knowledge of the factoring of the difference of squares helps. If that doesn't work for you, you can always use synthetic division or polynomial long division to find the quotient of (t^2-4) and (t-2).
[tex]\displaystyle\frac{\frac{4t^2-16}{8}}{\frac{t-2}{6}}=\frac{4(t^2-4)}{8}\cdot\frac{6}{t-2}\\\\=\frac{3(t+2)(t-2)}{t-2}=3(t+2)[/tex]
surveying crew located three points on a map that formed the vertices of a triangular area. A coordinate grid in which on unit equals 20 miles is place over the map so that the vertices are located at (0, -1), (-3, -9), and (3, -2). Find the area of the triangle using determinants?
Answer:
5400 mi²
Step-by-step explanation:
The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.
... Area = (1/2)|D|
where D = ...
[tex]\left|\begin{array}{ccc}0&-1&1\\-3&-9&1\\3&-2&1\end{array}\right|=\left|\begin{array}{cc}0&-1\\-3&-9\end{array}\right|+\left|\begin{array}{cc}-3&-9\\3&-2\end{array}\right|+\left|\begin{array}{cc}3&-2\\0&-1\end{array}\right|\\\\=-3+33-3=27[/tex]
Then the area is (in grid squares) ...
... Area = (1/2)|27| = 13.5 . . . . grid squares
Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...
... 13.5 × 400 mi² = 5400 mi²
will mark braniest 2 left also add me i help
Answer:
-9
Step-by-step explanation:
(x-2) is 3 more than (x-5), because -2 is 3 more than -5.
3 more than -12 is -9.
_____
If you like, you can solve for x.
... x -5 = -12
... x = -7 . . . . . add 5
Now find the value of x-2
... x -2 = -7 -2 = -9
Sarah bikes 4/5 km in 2 min. What is the unit rate and what does it mean?
Answer:
The unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
Step-by-step explanation:
It is given that Sarah bikes [tex]\frac{4}{5}[/tex] km in 2 min. It means Sarah covers [tex]\frac{4}{5}[/tex] km in 2 min.
The units rate is defined as
[tex]\text{Unit rate}=\frac{\text{Distance covered}}{\text{Time Taken}}[/tex]
[tex]\text{Unit rate}=\frac{(\frac{4}{5})}{2}[/tex]
[tex]\text{Unit rate}=\frac{4}{5}\times \frac{1}{2}[/tex]
[tex]\text{Unit rate}=\frac{2}{5}[/tex]
Therefore the unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
HELP ASAP PLEASE you make $20 an hour and work fro 40 hours a week, you are paid biweekly and have $185 total deducted from your paycheck, what is your gross annual earnings?
Answer:
615
Step-by-step explanation:u make $20 a week and u worked 40 hours u jus do 40*20=$800
800-185=615 im pretty sure hope this helps
Answer:
Weekly net pay is $36790
Weekly gross pay is $41600
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - taxes
Gross pay = hours worked * hourly rate
Net pay = hours worked * hourly rate - taxes
We know the
hours worked = 40
Hourly rate = 20
tax rate = 185 bi weekly = 185/2 = 92.5 weekly
Net pay = 40 * 20 - 92.5
Net pay = 800-92.5
Net pay = 707.5
This is the weekly net pay
Assuming we work 52 weeks a year
Weekly net pay is 52* 707.5 = 36790
Weekly gross pay is 40*20 * 52 = 41600
PLEASE HELP (Screenshot)
C. 75°
Step-by-step explanation:The sum of the three angles is 180°, as it is for the angles in any triangle.
35° + 70° + x° = 180° . . . . an equation expressing the relationship of the angles
x° = 180° -35° -70° . . . . . subtract 35° and 70°
x° = 75°
Find the reference angle, theta prime, when theta=5 radians. Write your answer in radians.
(2π-5) radians ≈ 1.2831853 radians
Step-by-step explanation:The reference angle is the magnitude of the acute angle made with the x-axis. The value of θ is greater than 3π/2, so the reference angle is ...
... θ' = abs(θ -2π) = 2π-5 . . . . radians
Find approximations for the input where the functions share a solution.
Answer:
x ≈ 0, x ≈ 2.5
Step-by-step explanation:
The left point of intersection is very near the y-axis, where x=0.
The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.
_____
If we knew the actual function definitions, we could solve for the points of intersection.
how do I solve this (not looking for answer
Answer:
Add 78 to 54 to get 132 total patrons, then divide the number of females into the total number of patrons. Therefore, 78/132 = .5909 = 59%
Step-by-step explanation:
Answer:
Thats simple!
Step-by-step explanation:
G.o.o.g.l.e.
PLEASE HELP ASAP!!!!
System
p + m = 100.8m = 0.4·10Solution
p = m = 5 — 5 lb peanuts and 5 lb mixtureStep-by-step explanation:(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
p + m = 100.8m = 0.4·10___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
Please help me with this question I took a picture of it
Answer:
40
Step-by-step explanation:
36 = 90% × (number of questions)
36/0.90 = (number of questions) = 40 . . . . . divide by the coefficient of the variable
There were 40 questions on the test.
The length of each side of a cube is increased by a factor of 4. What is the effect on the volume of the cube?
Answer:
When dealing with VOLUME, an increase in a linear quantity, produces a third power result in the volume.
Increase the sides of a cube by 2 produces an 8 times effect in the volume.
Increasing each side of a cube by 4 produces a chnage of 4 * 4 * 4 or
64 times in the volume.
Step-by-step explanation:
Increasing the length of each side of a cube by a factor of 4 results in the volume increasing by a factor of 64, since volume is proportional to the cube of the linear dimensions.
When the length of each side of a cube is increased by a factor of 4, the effect on the volume of the cube is that it increases by a factor of [tex]4^3[/tex], or 64. This is because volume is a three-dimensional measure, and when each dimension (length, width, height) of a cube is multiplied by a factor, the volume is multiplied by the factor raised to the third power (since volume is calculated by length *width * height).
Therefore, if the original length of one side of the cube is L, the original volume is L3. After increasing each side by a factor of 4, the new length becomes 4L, making the new volume [tex](4L)^3 = 4^3 \times L^3 = 64L^3[/tex]. Hence, the new volume is 64 times the original volume, not simply 4 times because the increase happens in each of the three dimensions.
What is the decimal value of sin S?
(Round your answer to the nearest thousandth if necessary.)
Answer:
0.471
Step-by-step explanation:
The mnemoic SOH CAH TOA reminds you that ...
... Sin = Opposite/Hypotenuse
... sin(S) = 32/68 ≈ 0.471
Solve log x2 + 1 = 5. Round to the nearest thousandth if necessary.
Answer:
x = 100
Step-by-step explanation:
Answer:
the solutions are x = -100,100
Step-by-step explanation:
The given logarithmic equation is [tex]\log x^2 +1=5[/tex]
Subtract 1 to both sides
[tex]\log x^2=4[/tex]
Remove logarithm, we get
[tex]x^2=10^4[/tex]
Take square root both sides
[tex]\sqrt{x^2}=\pm\sqrt{10^4}\\\\x=\pm10^2\\\\x=\pm100[/tex]
Therefore, the solutions are x = -100,100
Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference: ∗ +56a+49
Answer:
[tex]\ast=16a^2[/tex]
Step-by-step explanation:
Use formula for a square of a sum:
[tex](x+y)^2=x^2+2xy+y^2.[/tex]
Note that
[tex]49=7^2;[/tex][tex]56a=2\cdot 28a=2\cdot 7\cdot 4a.[/tex]Then instead of * should be the square of the term 4a that is [tex](4a)^2=16a^2.[/tex]
Then
[tex]16a^2+56a+49=(4a+7)^2.[/tex]
To complete the pattern in the expression ∗ +56a+49 to make it a square of a sum or a difference, we can use the formula for (a+b)² as a guide. If 49 is b² and 56a is 2ab, the missing part would be a². On solving, we find that the value of a² is 16a².
Explanation:The subject of this question is finding a monomial such that the given expression can be rewritten as a square of a sum or a difference. The expression is ∗ +56a+49. We can think of the square of a sum or a difference as the result of the formula (a+b)² = a² + 2ab + b² which gives a hint that we can structure our expression in a similar way.
Let's rearrange the given expression a bit using this hint. If we look at 49, it is equal to 7². This could be our b². Additionally, 56a can be written as 2*7*a or 2ab. So the missing part would be a² which completes the pattern of the formula.
To find the value of a², we need to know the value of a. Here's where 56a comes into play. It is 2ab (or in this case, 2*7*a). Solving this equation for a, we get a=4. So, a²=16. Therefore, the monomial that completes the pattern in the expression is 16a².
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A triangle is 3 inches wide and 1 inch tall. If its enlarged to a height of 4 inched, how wide will it be?
12 in
Step-by-step explanation:If the dilation is uniform, both height and width will be multiplied by 4.
New height = (1 in) × 4 = 4 in
New width = (3 in) × 4 = 12 in
What numbers are in between 1 and 1.01 on a number line?
There is an infinite number of numbers between 1 and 1.01 on the number line. The correct answer should theoretically be: 1 < n < 1.01.
Two similar pyramids A and B have surface areas of 135cm^2 and 60cm^2 respectively . The volume of pyramid A is 405 cm^3 work out the volume of pyramid B
Answer:
120 cm^3
Step-by-step explanation:
The surface areas are in the ratio 60 to 135 so the single dimensions are in the ratio √60 to √135.
Therefore the volumes are in the ratio (√60)^3 to (√135)^3 or 60^3/2 to 135^3/2.
So Volume of Pyramid B / Volume of Pyramid A
= 60^3/2 / 135^3/2.
Therefore we have the equation 60^3/2 / 135^3/2 = V / 405 where V is the volume of pyramid B.
V = (60^3/2 * 405) / 135^3/2
= 120 cm^3
Answer:
120cm³
Step-by-step explanation:
√135/√60=3/2
3/2=1.5
1.5³=3.375
405/3.375=120
120cm³
two angles are congruent. one angle is represented by the expression (4x-2) and the other angle is (5x-3). write an equation and solve for each angle.
Answer:
4x-2=0
5x-3=0
Step-by-step explanation:
polynomial are given:P
[tex] p |x | = {x}^{3} - 3 {x}^{2} + 2x - 1[/tex]
show if
[tex]x = 1[/tex]
is the root of the polynomial.
Erpress the polynomial
[tex]p |x| [/tex]
in the tratment
[tex]p |x| = (x - 1)( {x}^{2} + ax + b) + c[/tex]
Answer:
x = 1 is not a rootp(x) = (x -1)(x^2 -2x +0) -1Step-by-step explanation:
a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero
b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...
... p(x) = (x -1)(x² -2x +0) -1
_____
Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.
From 1994 to 1995 the sales of a book decreased by 80%. If the sales in 1996 were the same as in 1994, by what percent did they increase from 1995 to 1996?
400%
Step-by-step explanation:Suppose sales in 1994 were 100 of some unit. Then in 1995, they were ...
... 100 - 80% × 100 = 100 × (1 - 0.80) = 100 × 0.20 = 20 . . . . units
Then the percent increase to sales of 100 units in 1996 can be found from ...
... percent change = ((new value) - (old value))/(old value) × 100%
... = (100 -20)/20 × 100%
... = 80/20 × 100%
... = 400%
The increase from 1995 to 1996 was 400%.
PLEASE HELP ASAP!
How do I solve and simplify these problems using distributive property?
2x + 10
2(3x + 5)
2x + 10 can be simplified using the distributive property by factoring a 2 out of each term.
2(x + 5)
2(3x + 5) can be solved by applying the distributive property, by multiplying each term inside the parentheses by 2.
6x + 10