Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}x\leq\dfrac{20}{a}&\text{for}\ a>0\\\\x\geq\dfrac{20}{a}&\text{for}\ a<0\end{array}\right }[/tex]
Step-by-step explanation:
[tex]ax-8\leq12\qquad\text{add 8 to both sides}\\\\ax-8+8\leq12+8\\\\ax\leq20\qquad\text{divide both sides by}\ a\neq0\\\\(1)\ \text{if}\ a>0,\ \text{then:}\\\\x\leq\dfrac{20}{a}\\\\(2)\ \text{if}\ a<0,\ \text{then you must flip the sign of inequality:}\\\\x\geq\dfrac{20}{a}[/tex]
Final answer:
To solve the inequality Ax - 8 ≤ 12 for x in terms of a, add 8 to both sides to get Ax ≤ 20, and then divide by A (assuming A > 0) to find x ≤ 20/A.
Explanation:
To solve the inequality for x in terms of a, we start with the given inequality:
Ax - 8 ≤ 12.
First, we add 8 to both sides to isolate the term with x on one side:
Ax ≤ 20
Next, assuming A is not zero, we divide both sides by A to solve for x:
x ≤ 20 / A
This is the solution to the inequality, with the understanding that it only applies if A is positive, because if A were negative, we would need to reverse the inequality sign when dividing by A.
Please select the best answer.
Answer:
C; The left end goes up; the right end goes down
Step-by-step explanation:
If you expand the function, you end up with a polynomial with a negative coefficient and it has an odd power. According to polynomial behaviors of a function that is odd negative, the graph will rise to the left (y → ∞ and x → -∞) and falls to the right (y → -∞ and x → ∞).
ANSWER
C. The left end goes up; the right end goes down.
EXPLANATION
The given function is
[tex]f(x) = - 2( {x - 2)}^{5} [/tex]
We analyze the end behavior of this function using the leading term.
The leading term of this function is:
[tex] - 2 {x}^{5} [/tex]
Since the degree(5) is odd and the leading coefficient (-2) is negative, the graph rises on the left and falls on the right.
In other words, the left end of the graph goes up and the right end goes down.
The correct option is C.
A given line has the equation 10x - 2y=-2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
y= -5x+12
5x+y=12
y- 12 = 5(x - 1)
5x+y=-1
Answer:
y= -5x+12
Step-by-step explanation:
slope int form ; y=mx+b
that is the only option in that form.
Answer:
the equation is y = 5x + 12
Step-by-step explanation:
The equation of line is 10x - 2y=-2
Write this equation in slope intercept form of line y = mx + b
[tex]10x-2y=-2\\\\2y=10x+2\\\\y=5x+1[/tex]
Therefore, the slope of the line is m = 5
Now, we know that parallel lines have same slope.
Hence, slope of the required line is also 5.
Thus, the equation of line is in the form y = 5x + b
Now, use the point (0,12) to find b
12= 5(0) + b
b = 12
Hence, the equation is y = 5x + 12
Determine the slant asymptote for the function f(x) = 3x^3-4x +5 divided x-3
Answer:
don´t exist
Step-by-step explanation:
The slant asymptote only exist under two condition:
1) Don't exist horizontal asymptote
2) If the degree of the denominator is n, the degree of the numerator should be n+1
In this case, the degree of the numerator is n+2, for that the slant asymptote don´t exist
The length of a rectangle is equal to triple the width.
Find the width of the rectangle if the perimeter is 80 centimeters.
Answer:
10 cm
Step-by-step explanation:
If the length of a rectangle is equal to triple the width, the width of the rectangle is 10 cm if the perimeter is 80 centimeters.
L = 3w
P = 80
Formula: a = l × w
8W = 80 cm
W = 80 / 8 = 10 cm
Therefore, the width of the rectangle is 10 centimeters.
The width of the rectangle is found to be 10 centimeters, obtained by solving the equation created based on the fact that the perimeter of a rectangle is 2(length + width) and the given data that length is thrice the width and perimeter is 80 cm.
Explanation:To figure out the width of the rectangle, we first need to understand the relationship between the length and width, and how they relate to the perimeter. The length of the rectangle is triple the width. Let's define the width as 'w'. Therefore, the length would be '3w'.
The formula for the perimeter of a rectangle is 2(length + width).
Given that the perimeter is 80 centimeters, we can set up the equation 2(3w + w) = 80. Simplifying this gives 8w = 80. To find the width 'w', we divide both sides of the equation by 8, giving us w = 10 centimeters.
Therefore, the width of the rectangle is 10 centimeters.
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Need help now!!!!!!!
Answer:
I got you.Use pemdas to solve this expression. First, evaluate the exponets, then multiply them together. Finally, divide that by 100.
Answer:
256
Step-by-step explanation:
First evaluate the exponents
100 ÷ 25 × 64
Division and multiplication are of equal precedence
When they appear together in a mixed calculation then evaluate from left to right, that is
100 ÷ 25 × 64
= 4 × 64
= 256
Do you guys know the answer for number 1 and 2
If f(x) = 2x + 4, what is the value of the function
when x = 5?
O 14
O 10
oo
Submit
Answer:
14
Step-by-step explanation:
Plug the 5 into the equation
2(5) + 4 = 14
Answer:
f(5)= 2(5) + 4 = 10 + 4 = 14
Which expression is equivalent to the expression below?(6c^2+3c/-4c+2)/(2c+1/4c-2)
Answer:
-3c
Step-by-step explanation:
The given expression is:
[tex]\frac{\frac{6c^{2}+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]
We need to simplify this expression. The rational expression in the denominator can be multiplied to numerator by taking its reciprocal as shown below:
[tex]\frac{\frac{6c^{2}+3c}{-4c+2}}{\frac{2c+1}{4c-2}} \\\\ =\frac{6c^{2}+3c}{-4c+2} \times \frac{4c-2}{2c+1}\\\\=\frac{3c(2c+1)}{-(4c-2)} \times \frac{4c-2}{2c+1}\\\\ =-3c[/tex]
Thus, the given expression in simplified form is equal to -3c
Answer:
-3c
Step-by-step explanation:
We are given that an expression
[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]
We have to find an expression which is equal to given expression
Taking common 3c from nominator and -2 from denominator in dividened and 2 common in divisor then we get
[tex]\frac{\frac{3c(2c+1)}{-2(c-2)}}{\frac{2c+1}{2(2c-1)}}[/tex]
[tex]\frac{3c(2c+1)}{-2(2c-1)}\times \frac{2(2c-1)}{(2c+1)}[/tex]
By reciprocal divisor
By canceling same factor
Then ,we get
[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]
=-3c
If the probability of an event is 0.3, what is the probability of its complement?
The probability of an event and its complement add up to 1. If the probability of an event is 0.3, the probability of its complement is 0.7.
Explanation:The probability of an event and its complement always add up to 1. So, if the probability of an event is 0.3, the probability of its complement can be calculated by subtracting the probability of the event from 1. In this case, the probability of the complement would be 1 - 0.3 = 0.7. Therefore, the probability of the complement is 0.7.
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6 times a certain number is added to 8, the result is 32
Which of the following equations could be used to solve the problem?
6x +32
6x5)= 32
6x=8 - 32
6x-8= 32
Answer:
6x + 8 = 32
Step-by-step explanation:
Let the number be= x
So 6 times a certain number is added to 8 which gives the answer 32.
6( x ) + 8 = 32
6x + 8 = 32
Hence this is the equational form.
On further solving we get,
6x = 32 - 8
6x = 24
x = 24 / 6
x = 4....
Answer:
The required equation is 6x+8=32
Step-by-step explanation:
Consider the provided information.
6 times a certain number is added to 8, the result is 32
Let the number is represents by x.
6 times of a number can be written as: 6x
Add 8 to the above expression.
6x+8
The expression is equal to 32.
Thus, the required equation is 6x+8=32
what is the slope of the line with equation y-3=-1/2(x-2)?
Answer:
slope = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = - [tex]\frac{1}{2}[/tex](x - 2) ← is in point- slope form
with slope m = - [tex]\frac{1}{2}[/tex]
can someone help me pliz
Answer:
The correct option is C
Step-by-step explanation:
81x²+72x+16
We have to break the middle term:
If we multiply 81 by 16 we get 1296:
The same answer we get when we multiply 36 by 36:
36*36=1296
And if we add 36+36 then we get the middle term which is 72.
So,
=81x²+72x+16
=81x²+36x+36x+16
=9x(9x+4)+4(9x+4)
=(9x+4)(9x+4)
Thus the correct option is C ....
Name 3 ways that a parabola changes with different types of "a" values.
Answer:
Up down and side to side on the graph
Step-by-step explanation:
If a is 1, since it is positive the parabola moves up. If a is -1, since it is negative the parabola moves down. (not sure about side to side because I can't back that one up but I'm 100% sure about up and down)
When a is between 0 and 1, the parabola gets wider.
What is the parabola?A parabola is a mathematical curve that is defined by a point and a line. The point is known as the focus, and the line is called the directrix. The parabola has the property that all points on it are equidistant from the focus and the directrix.
Here,
When a is negative, the parabola flips 180°.
When |a| is less than 1, the parabola opens wider.
When |a| is greater than 1, the parabola opens more narrow.
When a is between 0 and 1, the parabola gets wider, when it is greater than 1, it gets narrower, and when it is less than 0 it is reflected across the x-axis.
Therefore, when a is between 0 and 1, the parabola gets wider.
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Find the value of x and y.
A) x=12, y=10
B) x=14, y=11
C) x=14, y=10
D) x=12, y=11
This is for Geometry.
Answer:
The correct answer is first option
x = 12, y = 10
Step-by-step explanation:
From the figure we can see that a triangle ADC, and EB is parallel to side DC.
To find the value pf x
From the given figure we get,
<ABC = <BCD [ corresponding angles are equal]
3x + 9 = 4x - 3
4x - 3x = 9 + 3
x = 12
To find the value of y
<ABE and <EBC are linear pairs.
Therefore, <ABE + <EBC = 180
(3x + 9) + (14y - 5) = 180
(3 * 12 + 9) + 14y - 5 = 180
45 + 14y - 5 = 180
14y = 180 -40
14y = 140
y = 140/14 = 10
y = 10
Therefore x = 12 and y = 10
The correct answer is first option
If a circle has diameter endpoints at (-1,7) and (6,2), what is its center and radius
Answer:
The radius is [tex]\frac{\sqrt{74}}{2}[/tex].
The center is (5/2 , 9/2).
Step-by-step explanation:
The radius is half the diameter. We aren't given the length of the diameter but we are given endpoints to one of them.
So let's find the length of that diameter using the distance formula.
The distance formula is
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].
I just do big x minus small x or big y minus small y.
Anyways the points are (-1,7) and (6,2).
The x distance is 6-(-1)=7.
The y distance is 7-2=5.
So we have this using the distance formula so far:
[tex]d=\sqrt{(6-(-1))^2{(7-2)^2}[/tex]
[tex]d=\sqrt{7^2+5^2}[/tex]
[tex]d=\sqrt{49+25}[/tex]
[tex]d=\sqrt{74}[/tex]
So the radius is half that much because that was the distance between the endpoints of a diameter.
So the radius is [tex]\frac{\sqrt{74}}{2}[/tex].
Now the center of a circle will lie on the midpoint of a diameter, any given diameter.
We have the endpoints of one, so we just need to use midpoint formula.
Midpoint formula says the midpoint is (average of x, average y).
Midpoint formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].
So average of x's is (-1+6)/2=5/2.
The average of y's is (7+2)/2=9/2.
So the midpoint of the diameter or the center of the circle is at (5/2 , 9/2).
A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many per hour? There are 5,280 feet in one mile
Answer:
American Bison
Step-by-step explanation:
First find out how many feet the bison runs in an hour.
To find that out you have to multiply 3520 by 60 minutes because there are 60 minutes in an hour.
So 3520*60 = 211,200 feet
Then you have to convert 211,200 feet into miles and since there are 5,280 feet in an a mile you have to divide.
So 211,200 divided by 5,280 = 40
So the American Bison runs 40 miles per hour which is faster than the White Tailed Deer who only runs 30 miles per hour.
So the answer is the American Bison.
music band came to town. The amphitheater filled all 50,000 seats at two-level pricing. Level 1 tickets are $150 each, and level 2 tickets are $250 each. The amphitheater made $125,000 in ticket sales. The system of equations that models this scenario is: x + y = 50,000 150x + 250y = 125,000 What do the x and y represent in the system?
In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.
Given to us,
system of equations,
Equation 1, 150x + 250y = 125,000,
Equation 2, x + y = 50,000,
Total number of seats = 50,000 seats,
Total number of sales = $125,000,
Level 1 tickets price = $150,
Level 2 tickets price = $250,
Let us assume, Number of tickets of Level 1 is [tex]\bold x[/tex], and, Number of tickets of Level 2 is [tex]\bold y[/tex],
Total sales = (Number of tickets of Level 1 x Level 1 tickets price ) + (Number of tickets of Level 2 x Level 2 tickets price )
125,000 = ([tex]\bold x[/tex] x 150) + ([tex]\bold y[/tex] x 250)
125,000 = 150x + 250y
Now,
Total number of seats = Number of tickets of Level 1 + Number of tickets of Level 2
50,000 = x + y
Therefore, In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.
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The variables x and y represent the number of Level 1 and Level 2 tickets sold, respectively. These variables show how many of each type of ticket were sold at their respective prices ($150 and $250) to achieve a total sale of $125,000.
The problem presents a linear system of equations that models the pricing of tickets sold at a concert.
The equations are:
x + y = 50,000150x + 250y = 125,000In this system:
x represents the number of Level 1 tickets sold at $150 each.y represents the number of Level 2 tickets sold at $250 each.Therefore, these equations together show the total number of tickets sold and the total revenue from these tickets.
What is the value of x?
A. 75º
B. 95
c. 35°
D 105
The answer is A.75°
The sum of all the angles of a triangle is 180°
75+35+x = 180.
x = 180-75-35
x = 75
What is a triangle and explain it?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle.
The sum of all three angles of the triangle is equal to 180 degrees.
Why triangle sum is 180?
The angles of a triangle always add up to 1800 degrees because one exterior angle of the triangle is equal to the sum of the other two angles in the triangle. When all the angles are added up, the sum obtained should be 180 degrees.
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Suppose that the functions g and h are defined for all real numbers x as follows.
g(x) = 4x– 4
h(x) = x-5
Write the expressions for (g+h)(x) and (g-h)(x) and evaluate (g.h)(1).
Answer:
See below in bold.
Step-by-step explanation:
(g + h)(x) = 4x - 4 + x - 5
= 5x - 9.
(g - h)(x) = 4x - 4 - (x - 5) ( Note we put the x - 5 in parentheses)
= 4x - 4 - x + 5
= 3x + 1.
(g.h)(x) = (4x - 4)(x - 5)
so (g.h)(1) = (4(1) - 4)(1 - 5)
= 0 * -4
= 0.
The product of the functions will be (g·h)(x) = 4x² – 24x + 20. At x = 1, the product of the functions is zero.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The functions are given below.
g(x) = 4x – 4
h(x) = x – 5
Then the sum of the functions will be
(g + h)(x) = (4x – 4) + (x – 5)
(g + h)(x) = 4x – 4 + x – 5
(g + h)(x) = 5x – 9
Then the difference in the functions will be
(g – h)(x) = (4x – 4) – (x – 5)
(g – h)(x) = 4x – 4 – x + 5
(g – h)(x) = 3x + 1
Then the product of the functions will be
(g·h)(x) = (4x – 4)(x – 5)
(g·h)(x) = 4x² – 4x – 20x + 20
(g·h)(x) = 4x² – 24x + 20
At x = 1, then we have
(g·h)(x) = 4(1)² – 24(1) + 20
(g·h)(x) = 4 - 24 + 20
(g·h)(x) = 0
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write 1-2log7x as a single logarithm
Answer:
[tex]log_{7} \frac{7}{x^{2} }[/tex]
Step-by-step explanation:
We need to write [tex]1 - 2log_{7}x[/tex] as a single logarithm.
We know that
[tex]log_{7}7 = 1[/tex]
Therefore we have:
[tex]log_{7}7 - 2log_{7}x[/tex]
→ [tex]log_{7}7 - log_{7}x^{2}[/tex]
→ [tex]log_{7} \frac{7}{x^{2} }[/tex]
The solution is: [tex]log_{7} \frac{7}{x^{2} }[/tex]
Could you guys help me answer this question.
Answer:
9
Step-by-step explanation:
8.5*9(h)=76.5
76.5+15=91.5
A triangular field has sides 218.5 and 213.3 and the angle between them measures 58.96°. Find the area of the field.
Answer:
The area of the field = 19966.21 units²
Step-by-step explanation:
* Lets explain how to find area of a triangle by trigonometry rule
- In any triangle if you have the lengths of two sides and the measure
of the including angle between these two sides, then the area of the
triangle is A = [tex]\frac{1}{2}s_{1}s_{2}sin\alpha[/tex] , wher α is the
including angle between them
* Lets solve the problem
∵ The field is shaped triangle
∵ The lengths of two sides of the field are 218.5 and 213.3
∴ s1 = 218.5
∴ s2 = 213.3
∵ The measure of the angle between the two sides is 58.96°
∴ α = 58.96°
- Lets find the area using the rule of trigonometry
∴ [tex]A=\frac{1}{2}(218.5)(213.3)sin(58.96)=19966.21[/tex]
∴ The area of the field = 19966.21 units²
2. If the radius of a circle is 12.5 meters, the diameter is
o a) 6.25 meters
I b) 125 meters
O c) 25 meters
od) 50 meters
[tex]\huge{\boxed{25}}[/tex]
The radius is the distance from the center of the circle to its edge.
The diameter is the distance from one point on the edge to the opposite point on the edge, so it is twice as much as the radius.
This means we just need to multiply the radius by two to get the diameter. [tex]2r=d[/tex]
[tex]2(12.5)=d[/tex]
[tex]\boxed{25}=d[/tex]
the larger of two consecutive integers is 7 greater than twice the smaller. Find the integers. A. 4,5 B. -8, -9 C. -5, -6
Answer:
The integers are -5 , -6 ⇒ answer C
Step-by-step explanation:
* Lets explain the meaning of consecutive numbers
- Consecutive numbers are numbers that follow each other in order.
- They have a difference of 1 between every two numbers
- Consider that the smaller of two consecutive integer is n, then the
larger one will be n + 1
* In the problem
∵ The larger of the two consecutive integers is 7 greater than twice
the smaller
- That means the larger one is 7 plus twice the smaller
∵ The smaller one is n
∵ The larger one is n + 1
∴ n + 1 = 2(n) + 7
∴ n + 1 = 2n + 7
- Subtract n from both sides
∴ 1 = n + 7
- Subtract 7 from both sides
∴ -6 = n
∴ The smaller number is -6
∵ The greater number is n + 1
∴ The greater number = -6 + 1 = -5
* The integers are -6 , -5
whats 85 percent of 250
Answer:212.5
Step-by-step explanation:85/100×250
=212.5
85 percent of 250 results in 212.5.
To find 85 percent of 250, follow these steps:
Change the percentage to a decimal by dividing by 100: 85% = 85 / 100 = 0.85
Multiply the decimal by the number: 0.85 x 250
Calculate the product: 0.85 x 250 = 212.5
Therefore, 85 percent of 250 is 212.5.
For example, if 250 students are surveyed, then 212.5 students would represent 85 percent of the surveyed group.
Mr. Wilson is building a swimming pool in his backyard. The width of the pool is twice the depth and the length of the pool is 3 feet
longer than the width.
Which of the following statements is true?
The monomial 3d represents the length of the swimming pool.
The trinomial 2d3 +3d2+1 represents the volume of the swimming pool.
The binomial 6d3 + 4d2 represents the volume of the swimming pool.
The binomial 2d + 3 represents the length of the swimming pool.
Answer:
The binomial 2d + 3 represents the length of the swimming pool
Step-by-step explanation:
Let
l ----> the length of the swimming pool
w ---> the with of the swimming pool
d ---> the depth of the swimming pool
we know that
[tex]w=2d[/tex] -----> equation A
[tex]l=w+3[/tex] ----> equation B
substitute equation A in equation B
[tex]l=2d+3[/tex] -----> equation C
The volume of the swimming pool is equal to
[tex]V=lwd[/tex]
Substitute equation A and equation C in the formula of Volume
[tex]V=(2d+3)(2d)d\\ \\ V=4d^{3}+6d^{2}[/tex]
therefore
The binomial 2d + 3 represents the length of the swimming pool (equation C)
What is the range of the function y= e4x?
Answer:
Range is y > 0
Step-by-step explanation:
We need to find the range of y = e^4x
The range is defined as a set of values of dependent variable for which the function is defined.
The exponential function of form c. n^x + k has range f(x) > k
in the given function y = e^4x ,k =0
so Range is y > 0
What are the coordinates of the vertices of the image of
rectangle WXYZ after the transformation Ro 90°(x, y)?
W'(-4,-1)
X'
Y'
Z'(-4, 2)
Answer:
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
Step-by-step explanation:
We are given the graph with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.
We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).
So,
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
Answer
W'
✔(-4,1)
X'
✔ (-2, -1)
Y'
✔ (-2, 2)
✔Z'(–4, 2)
Step-by-step explanation:
What is Three is less than one-third the number p.
Write it out as an equation:
3 < 1/3P
Rewrite so P is on the left side:
1/3P >3
Multiply each side by 3:
1/3P x 3 > 3 x 3
Simplify:
P > 9
A ball travels on a straight surface at 20 ft/sec it begins to decrease at 6 ft/sec How far will it travel ?
Answer:
14 ft/sec
so 14 feet in one second.
Hope this helps you :)
Good Luck :)))
Answer:
14 feet per second
Step-by-step explanation:
If a ball travels on a straight surface at 20 ft/sec and begins to decrease at 6 ft/sec, it will travel 14 feet per second.