Answer:
The lines represent the inequalities .
Further explanation:
The linear equation with slope m and intercept c is given as follows.
The formula for slope of line with points and can be expressed as,
Given:
The inequalities are as follows.
a. x – 5y < –5 and y < –2x – 4
b. x + 5y > 5 and y < 2x + 4
c. x – 5y < –5 and y < –2x + 4
d. x + 5y > 5 and y < 2x – 4
Step-by-step explanation:
The blue line intersects y-axis at , therefore the y-intercept is 4.
The blue line intersect the points that are and .
The slope of the line can be obtained as follows.
The slope of the line is m = 2.
Now check whether the inequality included origin or not.
Substitute in equation y=x+1.
0 is not greater than 1 which means that the inequality doesn’t include origin.
Therefore, the blue line is y < 2x + 4.
The orange line intersects y-axis at , therefore the y-intercept is 1.
The orange line intersect the points that are and .
The slope of the line can be obtained as follows.
The slope of the line is m = .
Now check whether the inequality included origin or not.
Substitute in equation y > .
0 is not greater than 1 which means that the inequality doesn’t include origin.
Therefore, the orange line is y > .
Solve the equation y > .
The equation of orange line is 5y + x > 5.
Option (a) is not correct as it satisfy the inequalities of the graph.
Option (b) is correct as it satisfy the inequalities of the graph.
Option (c) is not correct as it satisfy the inequalities of the graph.
Option (d) is is not correct as it satisfy the inequalities of the graph.
Hence, is correct.
Answer:
b
Step-by-step explanation:
For the parrallelogram, if measure of angle 2= 5x-28 and measure of angle 4= 3x-10, Find x.
Answer:
x = 9
Step-by-step explanation:
Unfortunately you didn’t provide the figure however we can use the picture below to work on:
from a property of the parallelogram (opposit angles) we know that angle 2 and 4 are equal in measure
then
5x - 28 = 3x - 10
then
5x - 3x = 28 - 10
then
2x = 18
then
x = 18/2
= 9
What is the slope of the line parallel to y= 5x+2.
A. -1/5
B. -5
C. 5
D. 1/5
. You deposit $600 in an account that earns simple interest. The difference between the total interest earned after 5 years and the total interest earned after 3 years is $24. What is the annual interest rate?
Answer:
The answer is .007874989
Step-by-step explanation:
PLZ HELP! WILL MARK BRAINLIEST
Tell what whole number you can substitute for x in the following list so the numbers are ordered from least to greatest.
1/x , x/8, 65%
x=
Answer:
4
Step-by-step explanation:
If you add 4 it would be 1/4, 4/8, 65% which goes from least to greatest!
Answer:
x= 3
Step-by-step explanation:
1/3 = 33.3%. 3/8 = 37.5%. 65%
Hope this helps.
The position of a ball after it is kicked can be determined by using the function f left parenthesis x right parenthesis equals negative 0.11 x squared plus 2.2 x plus 1f(x)=−0.11x2+2.2x+1, where f(x) is the height, in feet, above the ground and x is the horizontal distance, in feet, of the ball from the point at which it was kicked. What is the height of the ball when it is kicked? What is the highest point of the ball in the air?
Answer:
When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.
Step-by-step explanation:
We are given that the height is given by [tex]f(x)=-0.11x^2+2.2x+1[/tex]. The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1 = 1.
To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that
[tex] x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}[/tex].
In this scenario, the highest/lowest points is [tex]c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise).
Then, we can proceed as follows.
[tex] f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1[/tex]
We will complete the square for [tex]x^2-20x[/tex]. In this case b=-20, so
[tex] f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1[/tex]
We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then
[tex] f(x) = -0.11(x^2-20x+100)+1+100*0.11 = -0.11(x^2-20x+100)+1+11 = -0.11(x-10)^2+12[/tex]
So, the highest point in the ball's trajectory is 12 feet.
Answer:
Initial height = 1ft
Heighest height = 12ft
Step-by-step explanation:
In order to solve this problem, we can start by graphing the given height function. This will help us visualize the problem better and even directly finding the answers, since if you graph it correctly, you can directly find the desired values on the graph. (See attached picture)
So, the initical height happens when the x-value is equal to zero (starting point) so all we need to do there is substitute every x for zero so we get:
[tex]f(x)=-0.11x^{2}+2.2x+1[/tex]
[tex]f(0)=-0.11(0)^{2}+2.2(0)+1[/tex]
which yields:
[tex]f(0)=1 [/tex]
so the height of the ball when it is kicked is 1 ft.
In order to find the highest point of the ball in the air, we must determine the x-value where this will happen and that can be found by calculating the vertex of the parabola. (see the graph)
the vertex is found by using the following formula:
[tex]x=-\frac{b}{2a}[/tex]
in order to find "a" and "b" we must compare the given function with the standard form of a quadratic function:
[tex]f(x)=ax^{2}+bx+c[/tex]
[tex]f(x)=-0.11x^{2}+2.2x+1[/tex]
so:
a=-0.11
b=2.2
c=1
so the vertex formula will be:
[tex]x=-\frac{b}{2a}[/tex]
[tex]x=-\frac{2.2}{2(-0.11)}[/tex]
so we get that the highest point will happen when x=10ft
so the highest point will be:
[tex]f(10)=-0.11(10)^{2}+2.2(10)+1[/tex]
f(10)=12ft
so the highes point of the ball in the air will be (10,12) which means that the highest the ball will get is 12 ft.
John’s rectangular backyard is (10x+4) feet long and (3x+2) feet wide. What is the area of his backyard?
A. (30x^2+8) ft^2
B. (13x^2+19x+8) ft^2
C. (30x^2+32x+8) ft^2
D. (13x+6) ft^2
Answer:
Areas = (10x+4)(3x+2)
Area = 30x^2 + 20x +12x +8
Area = 30X^2 +32x +8 sq. ft.
Step-by-step explanation:
Which expression is equivalent to - 4(m - 3)?
Answer:
12 - 4 m
Simplify: -4(m -3)
Step-by-step explanation:
1: Solve the expression by using the distribute property
2: Simplify -4(m -3)
3: Done
Answer: 12 - 4 m
Hope this helps.
What
are the quotient and remainder of (5x^4+5x^2 +5)/(x^2-x+1)?
Answer:
Quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
Step-by-step explanation:
Given: [tex]\frac{5x^4+5x^2+5}{x^2-x+1}[/tex]
To find: quotient and remainder
Solution:
In the given question,
Dividend = [tex]5x^4+5x^2+5[/tex]
Divisor = [tex]x^2-x+1[/tex]
[tex]\frac{5x^4+5x^2+5}{x^2-x+1}\\=\frac{5(x^4+x^2+1)}{x^2-x+1}\\=\frac{5[x^2(x^2+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+x+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x^3+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1+x-1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1)+(x^2-x+1)]}{x^2-x+1}\\=\frac{5[(x^2-x+1)(x^2+x+1)}{x^2-x+1} \\=5(x^2+x+1)[/tex]
So, quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
Help im failing miserably
Answer:
UTR and UTW, hope this helped!
Step-by-step explanation:
Idk what to explain here...
Answer:
XWY and VWT
Step-by-step explanation:
Vertical angles are formed from the same lines but are opposite each other
XWY and VWT are formed by the same lines but are opposite each other
I'm not really looking for an exact answer, I'm more so looking for an explanation on how to do this.
I would have each block be 1/6 of a yard
You could technically have any value you want, but for me 1/6 is easiest because 1/2 and 1/3 will scale up to this like so
1/2 = (1/2)*(3/3) = 3/6
1/3 = (1/3)*(2/2) = 2/6
The diagram below might help if you're still stuck on why I picked 1/6.
what's 7×2/3×5(2×6)
Answer: your answer is 11.2 plz rate fairly im only 14
Step-by-step explanation:
7x2= 14 ÷15 = 0.93x12= 11.2
A family has three children. The oldest child is 4 years older than the
middle child, and the youngest child is 2 years younger than the
middle child. The sum of the ages of the children is 26.
R
How many years old is the youngest child?
years old
Q
Answer:6 years
Step-by-step explanation:
Given
A family has 3 children
Suppose the age of middle child is [tex]x[/tex]
According to the question, Age of oldest child is [tex]=x+4[/tex]
Eldest child age [tex]=x-2[/tex]
Sum of the ages of children is [tex]26[/tex]
[tex]x+4+x+x-2=26[/tex]
[tex]3x+2=26[/tex]
[tex]3x=24[/tex]
[tex]x=8[/tex]
Therefore age of youngest child is [tex]x-2=8-2=6\ years[/tex]
what is the volume of the solid
Answer:
204 cubic feet
Step-by-step explanation:
The formula for the volume of a rectangular prism is simply to multiply together the length, width, and height. In this case, 6*17*2=204 cubic feet. Hope this helps!
Answer:
do 16x17 divided by 2
Step-by-step explanation:
:)
329,444,000,777,234 in words
Step-by-step explanation:
Three hundred and twenty nine trillion four hundred and fourty four billion seven hundred and seventy seven thousand two hundred and thrity four
Answer:
Look at the attachment
What is the missing exponent in the equation 2? = 16?
Answer:
4
Step-by-step explanation:
2x2x2x2 = 16
Answer:
2^4 =16
Step-by-step explanation:
Rewriting 16
2^n = 2*2*2*2
2^n = 2^4
2^4 = 16
Unit 5. 10) Please help. A rectangle with a width of 9 ft. and a length of 13 ft. is the base of a 30 ft. tall pyramid. What is the volume of the pyramid?
Answer:
Volume of that pyramid:
V = Base area x Height
= (9 x 13) x 30
= 3510 ft3
Hope this helps!
:)
Answer:
Yes they're right, the correct answer is option 3.
what is the answer to i^{2n+1}
Answer:
(no solutions)
Step-by-step explanation:
Solve for n:
(0 + i)^(2 n + 1) = 0
Since i^z is never zero for any z element C, no solution exists for i^(2 n + 1) = 0:
Answer: (no solutions)
what is the answer to factorise 10x - 15
Answer:
5(2x-3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
hello :
10x-15 = 5(2x-3) ...the factor is : 5
Angle c is inscribed in circle O. AB is a diameter of circle O. what is the radius of circle.
Answer:
The value of radius is 7.5 units
Step-by-step explanation:
Given that a line that pass through the origin and form a triangle is a right-angle triangle. So in order to find the diameter/hypotenuse, you have to use Pythogaras Theorem :
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
Let a = 12 units,
Let b = 9 units,
Let c = hypo.,
[tex] {hypo.}^{2} = {12}^{2} + {9}^{2} [/tex]
[tex] {hypo.}^{2} = 225[/tex]
[tex]hypo. = \sqrt{225} [/tex]
[tex]hypo. = 15 \: \: units[/tex]
We have found out that the hypotenuse of the triangle is the diameter of circle. So in order to find radius, you have to divide it by 2 :
[tex]radius = diameter \div 2[/tex]
[tex]radius = 15 \div 2[/tex]
[tex]radius = 7.5 \: \: units[/tex]
Answer: 7.5
Step-by-step explanation: Khan academy
The expression (x2 - 5x - 2) - (-6x2 - 7x - 3) is
equivalent to
Answer:
7x² + 2x + 1
Step-by-step explanation:
(x² - 5x - 2) - (-6x² - 7x - 3)
Now, combine your like-terms together...
(x² - (-6x²)) + (- 5x - (-7x)) + (- 2 - (-3))
7x² + 2x + 1
PLEASE HELP!! Which diagram best models 2x3 + x2 + 3x + 4?
Answer:
O lol top right still
Step-by-step explanation:
Tabitha's Time Spent on Homework
Which best explains who spends more time on homework?
Ayana, because she has a higher maximum time spent
Ayana, because she has more variability in her time spent
Tabitha, because she has a higher median time spent
Tabitha, because she has more variability in her time spent
Answer:c Tabitha, because she has a higher median time spent
Step-by-step explanation:
Answer:
CStep-by-step explanation:
help plsssssssssssssssssssssss again
Answer:
35 degrees
Step-by-step explanation:
The lower quartile is the most left point of the box but not all the way to the whiskers
1) Find the volume of the triangular prism.
5 yd
5 yd
3 yd
6 yd
8 yd
27 yd
72 yd
240 yd
360 yd
Answer:
I am not completely sure but I believe that it is C) 240 yd^3
Step-by-step explanation:
A store buys shirts from a distributor for $10 each and marks them up 50%. After selling them for 3 weeks, they put them on sale for 50% off. Is the discounted price $10?
Answer:
No, it’s 7.50
Step-by-step explanation:
The discounted price is 7.5, but according to question the discounted price is $10. Therefore given statement is wrong.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
Cost price of one shirt = $10.
Also, Shopkeeper marks up 50 % on shirts.
Marked up price = 10 x 50% = 10 x 50 / 100 = $15
Since, shopkeeper gives discount as put the shirts on sale for 50% off.
So the price after giving discount = 15 x 50 / 100 = 7.5
The discounted price of shirt is 7.5.
Hence, the given statement that is discount price is $10 is incorrect.
To learn more on Percentage:
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Unit 5. 8) Please help. Which of the two-dimensional cross sections listed below could be created by cutting a cube with a plane?
Select all that apply.
Answer:
hexagonrectanglesquaretrianglepentagonStep-by-step explanation:
Only a straight line can be formed at the intersection of a plane with another plane. The faces of a cube are planes, so a 2-dimensional (planar) cross section of a cube cannot be a curve. It cannot be an ellipse or circle.
What polygons are possible?The intersection of a plane with a cube can be a polygon with 3, 4, 5, or 6 sides. That is, the 2-D cross section of a cube can be ...
triangle, rectangle, square, pentagon, hexagon
__
The attachment shows some possibilities.
Which expression is equivalent to mn+z
solution of 4y - 2x < 8
a. (0,2)
b. (-4,0)
c. (1,2)
d. (10,7)
Answer:
A
Step-by-step explanation:
Find the lowest common denominator for the fractions shown.
8/51
19/85
a. 255
b. 17
c. 4,335
Answer:
A.
Step-by-step explanation:
Just find the lowest common multiple of 51 and 85.
51 = 3 * 17
85 = 5 * 17
3 * 5 * 17 = 255
The lowest common denominator for the fractions is 17.
What are Fractions?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
fraction = 8/51 and 19/ 85
Now, LCM of 51 and 85.
51 = 17 x 3
85= 17 x 5
So, the least common multiple is 17.
Hence, the lowest common denominator for the fractions is 17.
Learn more about Fraction here:
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what is the slope of the line below? If necessary, enter your answer as a fraction in lowest terms, using the slash as the fraction bar. Do not enter your answer as a decimal number or an equation. (6, 9) (0, -5)
Answer:
-7/-3
Step-by-step explanation:
The point (6,9) should be labeled as x1 and y1 and the point (0,-5) should be labeled as x2 and y2, so the slope equation ends up as -5-9 / 0-6, which turns out to be -14 / -6, but when you simplify it, it becomes -7 / -3. :)
The slope of line given below is 7/3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have the points as (6, 9) and (0, -5)
So, the slope of line
slope = (-5 - 9)/ (0-6)
slope = -14 / (-6)
slope = 7/3
Thus, the required slope is 7/3.
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