Answers
AE x BE = DE x CE
6x5 = 30
6 x DE = 30
DE = 30/6 =5
DC = DE +CE = 5+6 =11
Answer is C) 11
Related Questions
George's page contains twice as many typed words as bills page and bills page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on bills page and the number of words on Charlie's page is 210. How many words did bills page contain initially? Use a table to organize the information.
Answers
Let:
x = number of words in George's page
y = number of words in Bill's page
z = number of words in Charlie's page
The equations formulated from the relationships would be:
x = 2y
y = z - 50
2(y - 60) - (z - 60) = 210
Simplifying the third equations:
2y - 120 - z + 60 = 210
2y - z = 210 + 120 - 60
2y - z = 270
Substituting eqn 2 to eqn 3:
2(z - 50) - z = 270
z = 370
y = 370 - 50 = 320
x = 2(320) = 640
Therefore, there are 320 words initially in Bill's page.
Find the sale price when the original price is $37.00 and the discount rate is 44%.
a.
$20.72
c.
$35.37
b.
$16.28
d.
$1.63
Please select the best answer from the choices provided
Answers
37(0.56)
$20.72
37-16.28=20.72 so answer A. Is ur answer
A cylindrical tree trunk is 14 yards high from the ground up to the lowest branch, and it measures 4 yards around. What is the volume of wood in this section of the trunk?
Answers
V=πr^2h
Given that the circumference of the figure is 4 yds, the radius will be:
C=2πr
4=2πr
hence;
r=4/(2π)
r=0.64 yds
Therefore the volume of the cylinder will be:
V=π*0.64^2*14
=17.83 cubic yards
Calculate the hypotenuse
Answers
[tex] 10^{2} + 14^{2} = c^{2} [/tex]
[tex]100+196= c^{2} [/tex]
[tex]296= c^{2} [/tex]
[tex] \sqrt{296} = \sqrt{ c^{2} } [/tex]
[tex]17.205=c[/tex]
A man travelled 3/8 of his journey by a rail 1/4 by a taxi 1/8 by and the remaining 2km on foot what is the length of his total journey?
Answers
Since all of these travels are equal to 1 whole journey, you can express each travel as a fraction. When you add them up, the answer would be 1. So,
3/8 + 1/4 + 1/8 + x = 1
The variable x here denotes the fraction of his travel by foot. We are only given the exact distance travelled on foot which is 2 km. We have to find the fraction of the travel by foot to determine the length of the total distance travelled. Solving for x,
x = 1 - 3/8 - 1/4 - 1/8
x = 1/4
That means that the travel by foot comprises 1/4 of the whole journey. Thus,
Let total distance be D.
1.4*D = 2 km
D = 8 km
Therefore, the man travelled a total of 8 kilometers.
find a positive angle less than one rotation that is coterminal with 750 degrees
Answers
To solve this problem, all you have to do is to subtract 360 degrees (equivalent to 1 rotation) from the given angle until the answer is less than 360 degrees.
1st subtraction: 750 – 360 = 390 degrees
2nd subtraction: 390 – 360 = 30 degrees
Therefore the positive angle less than one rotation that is coterminal with 750 degrees is 30 degrees.
PLEASE help me!!!!! and can you show me how you did it please!?!
Answers
3x + 8 = 7x -24
32 = 4x
x = 8
angle JHK = 52°
Adjacent parallelogram angles are supplementary. (add up to 180°)
So angle HMK = 180° - 52 -20
Angle HMK = 108°
A die is rolled 12 times find the probability of rolling exactly 12 ones
Answers
Answer:
[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
We assume that the die is fair and the probability of obatin a one is 1/6.
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=12, p=1/6)[/tex]
And we want to find this probability:
[tex] P(X=12)[/tex]
And if we replace we got:
[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]
A school typically sells 500 yearbooks each year for $50 each.
The economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Let X represent the number of $5 decreases in price. If the expression that represents the revenue is written in the form R(X)=(500+ax)(50-bx). Find the values of a and b.
Answers
Answer: a=100 and b=5
Step-by-step explanation:
Given: A school typically sells 500 yearbooks each year for $50 each.
The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.
Let x represents the number of $5 decreases in price.
Then the new price (in dollars)=50-5x
Total yearbook sold=500+100x
If the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Then the revenue function will be [tex]R(X)=(500+100x)(50-5x)[/tex]
On comparing this with the given revenue expression we get
a=100 and b=5.
In this exercise we have to calculate the values of A and B, so we have to:
[tex]A=100\\B=5[/tex]
Since the equation is:
[tex]R(X)=(500+ax)(50-bx)[/tex]
And the following information was given:
A school typically sells 500 yearbooks each year for $50 each.The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.So knowing that by increasing 100 more books sold this is equal to A and the decrease in value is going to be equal to b.
[tex]R(X)=(500+100x)(50-5x)[/tex]
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Standard automobile license plates in a country display 1 numbers, followed by 2 letters, followed by 4 numbers. how many different standard plates are possible in this system? (assume repetitions of letters and numbers are allowed.)
Answers
there are 10 numbers ( 0-9)
there are 26 letters ( A-Z)
10 x 26 x 26 x 10 x 10 x 10 x 10 =67,600,000 possible combinations
The number of baseball cards in Neil's collection is 80 percent of the number in Larry's collection. If Neil has 80 fewer baseball cards than Larry, how many do they have altogether
Answers
N=0.8L
....
N=L-80
Since N=N
0.8L=L-80 subtract 0.8L from both sides
0=0.2L-80 add 80 to both sides
80=0.2L divide both sides by 0.2
400=L, and since N=L-80
N=320
N+L=400+320
So they have 720 baseball cards altogether.
The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.
Explanation:This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.
Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.
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What is the awnser to -10x+3(4x-2)=6
Answers
In order to solve that equation, you would need to distribute the 3 inside the parenthesis.
-10x + 3(4x - 2) = 6
-10x + 12x - 6 = 6
Then you would need to keep the variable in the left and everything else to the right - in other words, solving for x.
-10x + 12x - 6 = 6
2x = 12
x = 6
Your answer would be 6.
first, distribute
remember that a(b+c)=ab+ac
so
3(4x-2)=3(4x)+3(-2)=12x-6
so
-10x+3(4x-2)=6
-10x+12x-6=6
2x-6=6
add 6 to both sides
2x=12
divide by 2
x=6
If 5x + x2>100 then x is not
Answers
find the area of a regular hexagon if a side is 20cm
Answers
Area = 1039.23 square units
Round answer as needed. See picture for equation
the equation of line AB is y = 1/5x -1 write an equation of a line perpendicular to line AB in slope intercept form that contains point (1, -2)
Answers
y-(-2) = -5(x-1)
y=-5x + 3
What is #3 step by step?
Answers
(-9) - (-7) × [2 - (-9)]^2 + (-7)
-9 + 7 × [2 + 9]^2 - 7
- 9 + 7 * (11)^2 - 7
-9 + 7*121 - 7
-9 + 847 - 7
831
P = 3^7 x 11^2 and Q = 3^4 x 7^3 x 11. Write as the product of prime factors the LCM of P and Q
Answers
The LCM of P and Q is found by taking the highest powers of the common prime factors from both numbers, which results in LCM(P, Q) = 37 x 73 x 112.
Explanation:To find the Least Common Multiple (LCM) of P and Q when given as products of prime factors, we look for the highest powers of the prime factors that appear in either P or Q. In this case:
P = 37 x 112Q = 34 x 73 x 11For prime factor 3, the highest power in P and Q is 37. For prime factor 11, the highest power is 112 (from P). Since prime factor 7 only appears in Q, we include it in its highest power, which is 73. Combining these, the LCM of P and Q as the product of prime factors is:
LCM(P, Q) = 37 x 73 x 112
write the following inequality in slope intercept form. -6+2y less than or equal to 42
Answers
m=slope, c=y-intercept.
Thus the slope-intercept form of our equation will be:
-6+2y≤42
adding 6 in both sides we get:
-6+6+2y≤42+6
2y≤6
dividing both sides by 2 we get:
(2y)/2≤6/2
y≤3
the answer is y≤3
Answer: The required slpe-intercept form of the given inequality is
[tex]y\leq 0\times x+24.[/tex]
Step-by-step explanation: We are given to write the following inequality in the slope-intercept form :
[tex]-6+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope intercept form of a straight line with slope m and y-intercept c is given by
[tex]y=mx+c.[/tex]
Writing equation (i) in slope-intercept form, we have
[tex]-6+2y\leq 42\\\\\Rightarrow 2y\leq 42+6\\\\\Rightarrow 2y\leq 48\\\\\Rightarrow y\leq 24\\\\\Rightarrow y\leq 0\times x+24,[/tex]
where slope, m = 0 and y-intercept, c = 24.
Thus, the required slpe-intercept form of the given inequality is
[tex]y\leq 0\times x+24.[/tex]
A contractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 What is the variance?
Answers
This can be calculated through the equation,
σ² = summation of X² / N - μ²
where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.
summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
N = 5
μ = (100 + 100 + 120 + 120 + 180) / 5
μ = 124
Substituting these values to the equation for variance,
σ² = (81200/5) - 124² = 864
Thus, the variance is equal to 864.
The variance of the five bedroom house is 864.
The formula varianceσ²
[tex]=\frac{X^2}{N} -u^2[/tex]
To get the value of X²
= 100²+100²+120²+120²+180²
= 81200
The number is N = 5
u = mean
[tex]u = \frac{100+100+120+120+180}{5}[/tex]
u = 124
The values in the variance formula
[tex]\frac{81200}{5} -124^2[/tex]
16240-15376
= 864
The variance is 864
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A rectangle has a length of ∛81 and a width of 3 2/3 inches. Find the area of the rectangle.
A.3 2/3 power inches squared
B.3 8/3 power inches squared
C.9 inches squared
D. 9 2/3 power inches squared
Answers
[tex] \sqrt[3]{81}= 81^{ \frac{1}{3} }= (3^{4}) ^{ \frac{1}{3} }= 3^{ \frac{4}{3} } [/tex]
The area of the rectangle = length*width
=[tex]3^{ \frac{4}{3} } * 3^{ \frac{2}{3} } =3^{(\frac{4}{3} +\frac{2}{3}) }=3^{ \frac{6}{3} }= 3^{2}=9 [/tex] (inches squared).
Answer: 9 inches squared
length = ∛81
width = [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] \sqrt[3]{81} [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 81^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] ( 3^{4}) ^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{4}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{6}{3} } [/tex]
Area = [tex] 3^{2} [/tex]
Area = 9 inches squared
A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
a. 15,504
b. 20,145
c. 23,670
d. 25,890
Answers
[tex]C(n, r)= \frac{n!}{(n-r)!r!} [/tex]
where a! is "a factorial", defined as a!=1*2*3*...*(a-1)*a
We are picking 15 objects (questions) out of 20, so substitute r=15 and n=20 in the formula:
[tex]C(20, 15)= \frac{20!}{(20-15)!15!}= \frac{20!}{15!*5!}= \frac{20*19*18*17*16*15!}{15!*5!}= [/tex]
[tex]\frac{20*19*18*17*16}{5!}= \frac{20*19*18*17*16}{5*4*3*2}= \frac{19*18*17*16}{3*2}=19*3*17*16=15,504[/tex]
Answer: A
Write two ratios that are equivalent to 3:11
Answers
Hopefully, this helps!
Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Check all that apply.
The domain of the function is .
The range of the function is all real numbers.
The vertex of the function is .
The function has two x-intercepts.
The function is increasing over the interval (, ∞).
Answers
we have
[tex] f(x) = 2x^{2}- x -6 [/tex]
using a graph tool
see the attached figure
we know that
1) the domain of the function is all real numbers-------> interval (-∞,∞)
2) The range of the function is the interval [-6.125,∞)
3) The vertex of the function is the point (0.25,-6.125)
4) The function has two x-intercepts-----> ( -1.5,0) and (2,0)
5) The function is increasing over the interval (0.25,∞) and decreasing over the interval (-∞,0.25)
For what values of x and y are the triangles congruent?
a. x=-4. y=-4
b. x=-4, y=4
c. x=4, y=7
d. x=7, y=4
Answers
From the given choices above, it can be seen that only the choice in A will give us this relationship. Thus, the answer is A.
A quadrilateral has two consecutive angles that measure 90° each. Which of the following quadrilaterals could have this property?
i. square
ii. rectangle
iii. parallelogram
iv. kite
v. rhombus
vi. trapezoid
A.
i, ii
B.
i, ii, iii
C.
i, ii, iii, iv
D.
i, ii, iii, v, vi
Answers
Final answer:
A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.
Explanation:
In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.
A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.
A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.
Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.
Given these definitions, the correct answer to the question would be:
D. i, ii, iii, v, vi
Final answer:
The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).
Explanation:
If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. find the number?
Answers
Answer:x equals 12
Step-by-step explanation:
4x+40=100-x
add x to both sides
5x+40=100
Subtract 40 on both sides
5x=60
divide both sides by 5
x=12
The number is 12 from the obtained equation.
Given that, When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number be x.
4 times a number is increased by 40
=4x+40
100 is decreased by the number
= 100-x
So, equation is 4x+40=100-x
4x+x=100-40
⇒ 5x = 60
⇒ x=12
Therefore, the number is 12 from the obtained equation.
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PLEASE HELP! A square piece of paper 144 mm on a side is folded in half along a diagonal. The result is a 45 -45-90 triangle. What is the length of the hypotenuse
A:140 mm
B:12 square root 2
C:280mm
D: 140 square root 2
Answers
:) Answers? Thanks,❤
Answers
6) answer: 12?
8) answer: 8?
10+18+18-12=34
6. the answer is 12
10+10+19-12=27
8. the answer is 12
12-10+19+10=31
What is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane?
Answers
Answer:
The answer is rotational symmetry.
Step-by-step explanation:
The Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane. A shape is said to possess rotational symmetry when it still looks the same after we rotate it.
Which graph shows the solution set for -1.1x+ 6.4> -1.3
Answers
-1.1x > -7.7
x <7
answer
x is less than 7