Answer:
5/7
Step-by-step explanation:
5x-7y=14
-7y=14-5x
y=-2+5/7x
y=5/7x-2
This slope is 5/7. This is because in the standard form of a line (y=mx + b), m represents the slope. In the equation above, 5/7 is the slope.
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
What is 1/4 0.75 1/3 0.5 greatest to least
Answer:
1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.50.75 → 0.5 → 1/3(0.33) → 1/4(0.25)
Need help please need it quick
Answer:
Choice A
Step-by-step explanation:
An arithmetic sequence is one which has an incremental change.
for our answer, our change is +5
3. A rectangle has a length of 2x – 9 and a width of x2 + 3x – 4. What is the polynomial that models the area
of the rectangle?
Answer:
(C) 2x^3 - 3x^2 - 35x + 36
Step-by-step explanation:
First multiply 2x by x^2 + 3x - 4:
(2x)(x^2 + 3x - 4)
2x^3 + 6x^2 - 8x
Next multiply -9 by x^2 + 3x - 4:
(-9)(x^2 + 3x - 4)
-9x^2 - 27x +36
Now add the two polynomials by adding like terms:
(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)
2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36
2x^3 - 3x^2 - 35x + 36
Hope this helps (●'◡'●)
Help me to prove it
Answer:
see explanation
Step-by-step explanation:
Using the identities
cotA = [tex]\frac{1}{tanA}[/tex]
cot²A = cosec²A - 1
tan²A = sec²A - 1
Consider the left side
(cotA + tanA)² ← expand using FOIL
= cot²A + 2cotAtanA + tan²A
= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1
= cosec²A - 1 + 2 + sec²A - 1
= sec²A + cosec²A - 2 + 2
= sec²A + cosec²A
= right side, thus proven
if a=(p+q),b=(p-q)and c=qsquare -psquare, show that ab+c=0
Answer:
I think this is the ans
Step-by-step explanation:
ab+c=0
(p+q)(p-q)=0
p Square-q Square =0
0=p Square-q Square
Question 5.
Given that cos(O) = 4/5, find:
a) sin(0)
b) tan (0)
Step-by-step explanation:
here's the answer to your question
Plz help me asap !!!
Answer:
all I know is sin square A +cos square A =1
According to the synthetic division below, which of the following statements are true?
Answer:
Step-by-step explanation:
That 3 sitting outside there in that little "box" thing is a root/solution/zero of the polynomial. The numbers underneath the line are the coefficients of the depressed polynomial, which means that the polynomial is 1 degree lower than the degree with which we started. If we started with an x-squared, this degree is a single x, better known as linear (a line). Anyway, (x - 3) is a zero of the polynomial, which also means that it's a factor. So A applies. x = 3 is a root, so C applies. And F also because the depressed polynomial, the remainder, is 2x + 4.
Which of the following lines is parallel to the line
y = 1/2x -6
Select one:
a) y=-1/2x-6
b) y=2x+1
c) y=-1/2x+5
d) y=1/2x-3
Answer:
y = 1/2x - 3 (option - d)
Step-by-step explanation:
The lines are parallel if they have the same slope/gradient. So by comparing with y = mx + c (where 'm' is the slope and 'c' is the y-intercept).
Line y = 1/2 x - 6 has the slope m = 1/2
and the line in option 'd'
y = 1/2 x -3 has the slope m = 1/2
Slopes are equal and lines are parallel.
Thank-you.
#Muhib
Two boys together have $12. One of them has $10 more than the other. How much money does each of them have
The graph f(x) shown below has the same shape as the graph of g(x)=x^2 which of the following is the equation of f(x)
Answer:
Choice D. [tex]F(x)=x^2-4[/tex]
Step-by-step explanation:
Since the graph is translated down 4, it cannot be choice A. or C.Since the graph is concave up, choice B. is ruled out.Leaving choice D. the correct answer.first answer gets marked brainliest!!
QUESTION 2
In A XYZ, X = 18 cm, y = 14 cm, and z= 17 cm.
Determine the measure of Z to the nearest degree.
a. 66°
b. 63°
c. 57°
d. 60°
Answer:
B: 63
Step-by-step explanation:
(3.1 x 10^10) X (4.6 x 10^4) divided by (9.4 x 10^-3)
(This is scientific notation)
Answer:
1.5×10^17
Step-by-step explanation:
it would be better to first multiply the two then divide the answer by 9.4×10^-3
I hope this helps
You are filling a bookcase with books. The bookcase is 3 feet wide. Your hardcover books are 1 1/2 inches wide and your paperback books are 3⁄4 inches wide. If you have already placed 8 hardcover books on the shelf, what is the maximum number of paperback books you can also fit on the shelf?
Answer:
32 paperback books
Step-by-step explanation:
Given that :
Width of hardcover books = 1 1/2 inches
Width of paperback books = 3/4 inches
Number of hardcover books already on shelf = 8
Total width of shelf = 3 feets
1 foot = 12 inches
Hence, total shelf width in inches = (12 * 3) = 36 inches
Total width of hardcover books = (8 * 1 1/2) = 12 inches
Total shelf width left = (36 - 12) inches = 24 inches
Maximum number of paperback books :
Total shelf width left / paperback width
24 inches / (3/4)inches = 32 paperback books
solve x
solve x
solve x
Answer:
x = 25
Step-by-step explanation:
When you combine both angles, you can get a supplementary angle which means that when they are both added, it should add up to be 180 degrees. With that being said, we can create an equation and solve for x.
5x - 5 + 2x + 10 = 180
~Combine like terms
7x + 5 = 180
~Subtract 5 to both sides
7x = 175
~Divide 7 to both sides
x = 25
Best of Luck!
Answer: x = 25
Step-by-Step Explanation:
We are given a line, hence it is a straight angle being 180°
Therefore,
=> 5x - 5 + 2x + 10 = 180
= 5x - 5 + 2x = 180 - 10 = 170
= 5x + 2x = 170 + 5 = 175
= 7x = 175
=> x = 175/7 = 25
Therefore, x = 25
Additionally, finding the values of each angle :-
=> 5x - 5
= 5(25) - 5
= 125 - 5
=> 120°
=> 2x + 10
= 2(25) + 10
= 50 + 10
=> 60°
Therefore, one angle is 120° and the other is 60°
Please help with question thank you
Answer:
The answer is 3x=50-10y
the least common multiple of ½,⅓,⅘ and ³/¹⁰ is a)90 b)50 c)30 d)15 e)10
Answer:
Step-by-step explanation:
Please hurry I will mark you brainliest
Answer:
12500
Step-by-step explanation:
11830 - 10464 = 1366 (difference 1995 to 96)
10464 - 8958 = 1506 (94 to 95)
8958 - 8135 = 823
8135 - 7537 = 598
7537 - 6642 = 895
6642 - 5942 = 700
5942 - 3579 = 2363 (5 years)
so, we have the annual differences over 11 years.
the expectation for the following year would be based on the mean value of growth rate and not on the mean value of the absolute numbers, as we know the number of transactions for 1997 will be higher than for 1996.
so, the mean value of growth over these 11 years is 750.
so, based on this we would estimate for 1997
11830 + 750 = 12580 (12500 being the closest answer option).
but if the business environment has changed over the most recent years, we should not bring in earlier years into that calculation (or at least not with the same weight).
we could argue that the last 2 years had a totally different behavior than the years before.
so, just creating a mean value of the last 2 years' changes would be
(1366 + 1506) / 2 = 2872 / 2 = 1436.
now, or prediction would be
11830 + 1436 = 13266, which would be closer to the 13500 answer option.
Whats the correct answer?
Answer:
Actually the answer is "A"
this is a very strange way to present a problem...
this issue her is that [tex](x^{a}) ^{b} = x^{a*b}[/tex]
so you need 1/3 * 3 in the answer... none of them have 1/3 * 3
BUT !!!!! 1/3 + 1/3 + 1/3 is the same as 1/3 * 3 So "A" is the solution
Step-by-step explanation:
a parabola has x-intercepts at x = 1/2 and x=5. what is the equation of the parabola
Answer:
y = 2x²-11x +5
Step-by-step explanation:
We know that a polynomial of degree n with roots (x-intercepts) {x₁, x₂, ..., xₙ} and a leading coefficient A can be written as:
p(x) = A×(x - x₁)×...×(x - x₂)
Here we will find:
P(x) = (x - 1/2)×(x - 5)
Let's see how we found that:
Here we know that is a parabola, so n = 2, and the x-intercepts are:
x₁ = 1/2
x₂ = 5
And we do not know the leading coefficient, so we can assume A = 1.
Then the polynomial is just:
P(x) = (x - 1/2)×(x - 5)
The graph of this polynomial can be seen below.
If you want to learn more, you can read:
https://brainly.com/question/24371640
Marcus plans to spend $72 at a local clothing store that sells t-shirts for $8 each and jeans for $12 each, sales tax included. This scenario is modeled by 8x + 12y = 72, where X represents the number of t-shirts purchased and y represents the number of jeans purchased.
What point on the graph represents Marcus' purchase if it consisted of only t-shirts?
Option
A. The x intercept (9,0)
B. The y intercept (0,6)
C. The x intercept (6,0)
D. The y intercept of (0,9)
Answer:
a. the x intercept (9,0)
Find x round your answer to the nearest integer.
Answer:
C
Step-by-step explanation:
Note that x is opposite to the given angle and we are also given the hypotenuse.
Since we have an angle and the side opposite to it and the hypotenuse, we can use the sine ratio. Recall that:
[tex]\displaystyle \sin \theta =\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
The opposite side is x, the hypotenuse is 15, and the angle is 53. Substitute:
[tex]\displaystyle \sin 53^\circ = \frac{x}{15}[/tex]
Solve for x:
[tex]x=15\sin 53^\circ[/tex]
Use a calculator (make sure you're in Degrees Mode!). Hence:
[tex]x=11.9795...\approx 12[/tex]
Our answer is C.
Answer:
C. 12
Step-by-step explanation:
Pythagoras Theorem
Find the average (mean) of the given set of data.
22,15,31,40,27
Answer:
27
Step-by-step explanation:
Hi there!
We are given this set of data:
22, 15, 31, 40, 27
And we want to find the average (or the mean) of the set
To find the mean, we add up all of the values of the data set and then divide it by how many pieces of data we have
So first, add 22, 15, 31, 40 and 27 together
22+15+31+40+27=135
We have 5 pieces of data, so divide 135 by 5
135/5=27
The mean is 27
Hope this helps!
[tex]\boxed{\large{\mathbf{\blue{ANSWER~:) }}}}[/tex]
Data=22,15,31,40,27no of data=5sum of data=22+15+31+40+27=135we know that,
[tex]\boxed{\sf{mean=\dfrac{sum ~of~ data}{no~ of~ data } }}[/tex]
According to the question,
[tex]{\sf{mean=\dfrac{135}{5 } }}[/tex] [tex]\sf{ mean=27 }[/tex]Therefore,
the average (mean) of the given set of data.(22,15,31,40,27) is 27.
What's the maximum area you can get for a rectangle with two sides along the x and y axes, and the opposite vertex in the first quadrant along the line y = 20 – 4x?
Answer:
Remember that a triangle rectangle of length L and width W has an area:
A = W*L
In our rectangle, we have two sides along the x and y axes.
So one of the vertices of our triangle rectangle is the point (0, 0)
And the other vertex, is along the line:
y = -4x + 20
So, if the opposite vertex is at the point:
(x₁, y₁)
We can define the length as the difference between the x-values of each vertex.
L = (x₁ - 0) = x₁
And the width, similarly, as:
W = (y₁ - 0) = y₁
Such that the point (x₁, y₁) is a solution for the equation y = -4x + 20, then we have:
y₁ = -4x₁ + 20
Then we can rewrite the width as:
W = -4x₁ + 20
Now, we can write the area of our rectangle as:
A = (x₁)*(-4x₁ + 20)
A = -4*x₁^2 + 20*x₁
Now we want to maximize the area, notice that the area is given by a quadratic equation with a negative leading coefficient.
Thus, the maximum will be at the vertex of that quadratic equation.
Remember that for a general quadratic equation:
y = a*x^2 + b*x + c
The x-value of the vertex is:
x = -b/(2*a)
so, in our case, the x-value of the vertex will be:
x₁ = -20/(-4*2) = 20/8 = 5/2
Now we can evaluate this in our area equation:
A = -4*(5/2)^2 + 20*(5/2) = 49.36
This is the maximum area of the rectangle.
∛3x+7=∛2x+1
solve it please
Answer:
x = -6
Step-by-step explanation:
cube each side :
3x + 7 = 2x + 1
solve for x:
x = -6
The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent? the number of seconds after the rocket is released the initial height of the rocket the initial velocity of the rocket the height of the rocket after t seconds The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
Answers:
t is the number of seconds after the rocket is released
V(r) is the volume of the ball with radius r.
====================================================
Explanation:
There isn't much to say in terms of explanation. These variables are simply definitions.
out of 500 bulbs, 0.2 are defective. how many are defctive
Answer:
100
Step-by-step explanation:
0.2*500=100
A hundred chickadees can eat 100 kg of seeds in 100 days. How many kg of seeds can 10 chickadees eat in 10 days?
Answer:
1 kg
Step-by-step explanation:
Number of chickadees = 100
Quantity of seed eaten = 100 kg
Number of days = 100
Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days
= 100 ÷ 100 ÷ 100
= 1 ÷ 100
= 0.01 kg of seed
How many kg of seeds can 10 chickadees eat in 10 days?
= Quantity of seeds each chickadee eats per day × number of chickadee × number of days
= 0.01 kg × 10 × 10
= 1 kg
10 chickadees eat 1 kg of seeds in 10 days
