Domain: [tex](-\infty, \infty)[/tex]
Range: [tex](-\infty, \infty)[/tex]
Explanation:
The function is [tex]y=-\frac{1}{4} x[/tex]
The domain of a function is the set of all input values for which the function is well defined. Generally, domain consists of all x-values of the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].
The range of a function is the set of output values obtained by substituting the value of x in the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].
which of the statements is true for the two equations below?
Equation A: 6+3x=3x-3
Equation B: 2(4x-1)=8x-2
A.Equation A has no solution and Equation B has an infinite number of solutions.
B.Equation A has an infinite number of solutions and Equation B has no solution.
C.Equation A and Equation B have an infinite number of solutions.
D. Equation A and Equation B have no solution.
Equation A:
6 + 3x = 3x - 3
This equation has no solution, no matter what number you plug into the equation, it will never = each other
[if you tried simplifying more]
9 + 3x = 3x (added 3 on both sides, then subtracted 3x on both sides)
9 = 0
Equation B:
2(4x - 1) = 8x - 2 Distribute/multiply 2 into (4x - 1)
(2)4x - (2)1 = 8x - 2
8x - 2 = 8x - 2
This will have an infinite number of solutions because whatever number you plugged in, they would always = each other since they are the same on both sides of the equation
[simplified]
8x = 8x (add 2 on both sides, then divide 8 on both sides)
x = x
Your answer is A
Equation A has no solution and Equation B has an infinite number of solutions.
Explanation:The correct answer is D. Equation A and Equation B have no solution. Let's analyze each equation:
For Equation A, we can combine like terms and simplify it to:
6 + 3x = 3x - 3
6 = -3
Since 6 is not equal to -3, Equation A has no solution.
For Equation B, we distribute 2 to the terms inside the parentheses:
2(4x - 1) = 8x - 2
8x - 2 = 8x - 2
Both sides of the equation have the same expression, so Equation B is an identity. It means that for any value of x, both sides will always be equal. Therefore, Equation B has an infinite number of solutions.
Hence, the correct answer is D. Equation A and Equation B have no solution.
Learn more about Equation solutions here:https://brainly.com/question/28741857
#SPJ2
if (x+8) is a factor of f(x), which of the following must be true?
A. both x= -8 are roots of f(x)
B. neither X = -8 nor x equal 8 is a root of f(x)
C. f(-8)=0
D.f(8)=0
Answer:
C
Step-by-step explanation:
Given that (x + 8) is a factor of f(x), then x = - 8 is a root and thus
f(- 8) = 0
If (x+8) is a factor of f(x) then f(-8) =0 is the true statement.
What is factor?" Factor is defined as an algebraic expression or a number when divided by another algebraic expression or a number without leaving remainder."
According to the question,
Given function = f(x)
Factor of f(x) = (x+ 8)
For example [tex]f(x) = x^{2} + 12x+32[/tex]
[tex]= x^{2}+8x+4x+32 \\\\= (x+8) (x+4)[/tex]
(x+ 8) is a factor of f(x).
[tex]f(-8) = (-8)^{2} -64[/tex]
[tex]= 64-64\\\\=0[/tex]
Hence, if (x+8) is a factor of f(x) then f(-8) =0 is the true statement.
Learn more about factor here
https://brainly.com/question/24182713
#SPJ3
Part A: Create a system of linear equations with no solution. In two or more complete sentences, explain the specific characteristics that you included in each equation to ensure that the system would not have a solution.
Part B: Using one of the equations that you created in Part A, create a system of linear equations that has one solution (x, y). Use substitution to solve the system.
So I chose y = 4x + 4 and y = 4x - 4
And I wanna use y = 4x + 4 for part B. For my other part I will use y = -4x - 4
So far I have 4x + 4 = -4x - 4
What do I do next?
Answer:
sbf fb
Step-by-step explanation:
step step step
Answer:
sorry this was a year ago
Step-by-step explanation:
Meredith lives 24 blocks from her friends house if she travels on block every minute how many minutes will it take her to reach her friends house show how you calculate each answer
Meredinth takes 24 minutes to reach her friend house
Solution:
Given that, Meredith lives 24 blocks from her friends house
She travels one block every minute
To find: time taken by Meredith to reach friend house
From given,
Number of blocks between Meredith house and her friedn house = 24
She travels one block every minute
Thus she takes 1 minute for 1 block
One block = 1 minute
So, for 24 blocks, we have to multiply by 24
[tex]24\ block = 1 \times 24\ minute\\\\24\ block = 24\ minute[/tex]
Thus Meredinth takes 24 minutes to reach her friend house
19. A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
a. Write and solve an absolute value inequality to represent this situation
b. A life guard measures the chlorine level in the pool and finds it is 1.0ppm. Should he add more chlorine? Explain.
To ensure safe chlorine levels in the pool, the inequality |Cl - 3.25| ≤ 1.75 must be met, representing levels between 1.50 ppm and 5.00 ppm. The lifeguard found the level at 1.0 ppm, which is below the safe range, so more chlorine needs to be added.
Explanation:Absolute Value Inequality for Chlorine Levels:
The county government specifies that a safe level of chlorine is within 1.75 ppm of 3.25 ppm. We can express this using an absolute value inequality to represent the acceptable range for the chlorine levels: |Cl - 3.25| ≤ 1.75. This represents that the chlorine level (Cl) can be at most 1.75 ppm above or below 3.25 ppm.
To solve this inequality, we consider both the upper and lower bounds:
Therefore, the chlorine level must be between 1.50 ppm and 5.00 ppm.
Analysis of the Chlorine Level Measurement:
As the lifeguard measures the chlorine level in the pool at 1.0 ppm, it falls below the acceptable range established by the inequality. Consequently, the lifeguard should add more chlorine to bring the concentration up to within the safe range, specifically, at least to the minimum safe level of 1.50 ppm.
How many edges does this figure have?
Answer:
please show the figure
Step-by-step explanation:
Which figure lol looool
(2,7); m = -4
What is the equation in point-slope form
Answer:
where m is the slope and b is your y intercept
your equation is y = 2/7(x) - 12
Step-by-step explanation:
What is 40percent of 50
Answer:
20
Step-by-step explanation:
25=50% so minus 5
Answer:
20
Step-by-step explanation:
Multiply 50 by 0.4
What is 36 divided by 25 in a simplified fraction
Answer:
It's already in it's most simplified form.
Step-by-step explanation:
Answer:
1 [tex]\frac{11}{25}[/tex]
Step-by-step explanation:
You want to write out the fraction from the division problem.
To do this you want to know that the number that is being DIVIDED BY (or 36 in this problem) is the numerator (the number on top in the fraction) and the number DIVIDING the number that is being divided by is the denominator (or 25 in this problem).
You can then write this as the fraction [tex]\frac{36}{25}[/tex] . Next you want to change this into a mixed number to simplify the fraction. To simplify you want to do 36-25 because 36 exceeds 25. 36-25=11. Because you have 11 remaining you would keep it with the 25th fraction. The completed fraction should look like this 1 [tex]\frac{11}{25}[/tex] .
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y
=
−
2
x
2
+
113
x
−
497
y=−2x
2
+113x−497
The company should sell each widget for $28.25, to the nearest cent.
To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.
For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.
How to solve c/-9+6=14
Answer:
c/9+6=14
9c=14-6
9c=8
c=8:9
c=1.125
Step-by-step explanation:
After solving this c/(-9+6) = 14 equation we get c = -42. To solve the equation c/(-9+6) = 14, we first simplify the expression inside the parentheses. (-9 + 6) equals -3.
Therefore, the equation becomes c/(-3) = 14. To isolate the variable c, we multiply both sides of the equation by -3. This gives us c = 14 * (-3), which simplifies to c = -42.
Hence, the solution to the equation is c = -42. Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions and be cautious when dealing with negative signs in equations.
To know more about equation :
https://brainly.com/question/29657983
#SPJ6.
which quadratic equation equivalent to (x+2)^2+5(x+2)-6=0
Answer:
[tex]\large\boxed{u^2+5u-6=0,\ where\ u=(x+2)}[/tex]
Step-by-step explanation:
[tex](x+2)^2+5(x+2)-6=0\\\\\text{Substitute}\ (x+2)=u:\\\\\underbrace{(x+2)}_{u}^{}^2+5\underbrace{(x+2)}_{u}-6=0\\\\u^2+5u-6=0[/tex]
Answer:
The answer is C
Step-by-step explanation:
What is the sale price if there is a 60% discount and the original price is $750?
Answer:
17
Step-by-step explanation:
50
Find y if y = -7x -6 and x=5
Answer: -41
Step-by-step explanation:
-7 × 5 = -35
-35 - 6 = -41
Answer:
-41
Step-by-step explanation:
Compute the perimeter of the figure given below. All angles are right angles.
Answer:
44
Step-by-step explanation:
10 + 12 + 4 + 4 + 6 + 8 = 44
The perimeter of the figure is 26 inches.
The perimeter of the figure is the total length of all the sides. To calculate the perimeter, we simply add up the lengths of all the sides:
Perimeter = 6in + 4in + 4in + 12in
Perimeter = 26in
Therefore, the perimeter of the figure is 26 inches.
For such more question on perimeter
https://brainly.com/question/397857
#SPJ3
Given: WZ is perpendicular to VY, WZ bisects VY, VZ = 2x+2, and ZY = 3x-4
What is VY?
18
28
14
6
Answer:
28
Step-by-step explanation:
VZ = ZY
2x +2 = 3x -4
6 = x . . . . . . . . add 4-2x to both sides
VZ = 2x +2 = 2(6) +2 = 14
Now we can find VY.
VY = VZ + ZY = 14 + 14 . . . . . . VY is the total of the two halves
VY = 28
How do you answer 64 divided by 2.56
Answer:
25
Step-by-step explanation: by dividing
The ratio of the number of flowers in basket A to the number of fliers in basket B is 5:2. If there are 40 flowers in basket B
Answer:
there would be 100 flowers in basket a
Step-by-step explanation:
for the second part of the ratio to be 40 you have to multiply the 2 by 20. to find out how many would be in basket a you do the same thing to the other side of the ratio and multiply 5 by 20 which gives you 100
A pickup truck carrying 1000 identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick?
Answer:
0.515
Step-by-step explanation:
10 to the 3rd power is 10^3 = 1000 bricks.
The weight of the full truck minus the weight of the empty truck is the weight of the bricks:
6755-6240 = 515 pounds of bricks
Pounds per brick:
515 / 1000 = .515 pounds per brick.
Evaluate: x/y for x= 3/10 and y= 4/5
A. 7/50
B. 7/15
C. 3/8
D. 12/50
C. 3/8 i think.......
Answer: 7/15
Step-by-step explanation:
Solve for x in the equation x squared + 14 x + 17 = negative 96. x = negative 7 plus-or-minus 4 StartRoot 6 EndRoot i x = –7 ± 8i x = 7 plus-or-minus 4 StartRoot 6 EndRoot i x = 7 ± 8i
Answer:
[tex]x=-7\pm8i[/tex]
Step-by-step explanation:
we have
[tex]x^{2} +14x+17=-96[/tex]
Equate to zero
[tex]x^{2} +14x+17+96=0[/tex]
[tex]x^{2} +14x+113=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +14x+113=0[/tex]
so
[tex]a=1\\b=14\\c=113[/tex]
substitute in the formula
[tex]x=\frac{-14\pm\sqrt{14^{2}-4(1)(113)}} {2(1)}[/tex]
[tex]x=\frac{-14\pm\sqrt{-256}} {2}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-14\pm16i} {2}[/tex]
[tex]x=-7\pm8i[/tex]
Answer:
its b on edge
Step-by-step explanation:
The jones family is taking a trip from seattle to san diego CA over the course of 3 days. They plan on traveling 200 miles more on the second day than they will on the first day. They will travel 75 miles less on the third day than they will on the first day. The total distance of the trip is 1058 miles. How many miles will they travel each day?
Jones family will travel for 311 miles on day 1 , 511 miles on day 2 and 236 miles on day 3.
It is given that on day 2 , Jones family travel for 200 miles more than day 1 and on day 3 for 75 miles less than day 1.
We have to find out distance travelled on each day of trip if total distance of trip is 1058 miles.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
As per the questions ;
Jones family has a trip of 3 days.
Let's assume they travel distance of x miles on first day.
Distance they will travel on second day = x + 200 miles
Distance they will travel on third day = x - 75 miles
Total distance of trip = 1058 miles
i.e.,
x + (x + 200) + (x - 75) = 1058 miles
3x + 125 = 1058
3x = 1058 - 125
3x = 933
x = 311 miles
So , they travel for a distance of 311 miles on day 1.
&
On day 2 ;
= 311 + 200
= 511 miles
&
on day 3 ;
= 311 - 75
= 236 miles
Thus , Jones family will travel for 311 miles on day 1 , 511 miles on day 2 and 236 miles on day 3.
To learn more about algebra click here ;
https://brainly.com/question/26479183
#SPJ2
Solve the proportion below.
54\x=9\7
x=
a. 36
b. 52
c. 63
d. 42
Answer:
Hi it’s c63
Step-by-step explanation:
Beacause 60+3=63
Answer:
x=42
Step-by-step explanation:
while swimming in the pool, you attempt to swim the whole length of the pool without getting a breath. you are able to do it 3 out 5 times you attempt. if you attempted to do it 10 times, how many did you make it?
Answer:
30 out of 50 times.
Step-by-step explanation:
1 attempt represents 3 out of 5 times.
10 attempts equals 1 attempt x 10.
Multiply numbers 3 and 5 by 10.
3 x 10 = 30
5 x 10 = 50.
Therefore, your solution is 30 / 50 times.
Using the probability of the initial success rate (60%), if you attempt to swim across the pool without taking a breath 10 times, you are expected to succeed 6 out of 10 times.
The question you're asking involves a simple concept in mathematics known as probability. The event of you being able to swim across the pool without taking a breath has so far occurred with a probability of 3 successes out of 5 attempts, or a 60% success rate. This is essentially an application of a ratio - you have succeeded 3 times for every 5 attempts you made. We can apply this ratio to predict outcomes over a larger number of trials.
If you were to attempt to swim across the pool without taking a breath 10 times and maintain the same success rate of 60%, you would be expected to make it 6 times out of 10 (since 60% of 10 is 6). Here's the breakdown:
Calculate the success rate from the initial trials: 3/5 = 60%
Apply that success rate to a larger number of trials: 60% of 10 = 6
Note that real-life scenarios might deviate slightly due to variability, but based on the given probability, we predict 6 successful swims across the pool in 10 attempts.1
A rectangle is 2 times as long as it is wide. If the area is 50 square feet, find its perimeter
Answer:
P=30
Step-by-step explanation:
width = x
length = 2x
2x^2=50
/2 /2
x^2=50
[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{25}[/tex]
x=5
width=5
length=10
2width + 2length = Perimeter
10+20=P
30=P
Final answer:
The width of the rectangle is determined to be 5 feet using the area formula, leading to a length of 10 feet. The perimeter is then calculated using the sum of twice the length and twice the width, resulting in a perimeter of 30 feet.
Explanation:
To solve for the perimeter of a rectangle where the area is 50 square feet and the length is twice the width, we first use the given information to set up an equation. Let the width be w feet. Therefore, the length will be 2w feet. The area A of a rectangle is given by the formula A = length times width, so in this case, A = 2w times w = 50.
Solving for w, we have w² = 25, which gives us w = 5 feet. The length, therefore, is 2 times 5 = 10 feet. The perimeter P of a rectangle is given by P = 2 times (length + width), so the perimeter of this rectangle is P = 2 times (10 + 5) = 30 feet.
Select 3 expressions that have a sum or difference of 3 /4 .
A . 1/2 + 2/4
B . 11/12 − 1/6
C. 3/5 + 3/20
D . 7/8 − 1/2
E . 2/3 + 1/12
Answer:
The Three expressions that have a sum or difference of 3 /4 .
B . 11/12 − 1/6
C. 3/5 + 3/20
E . 2/3 + 1/12
Step-by-step explanation:
The Three expressions that have a sum or difference of 3 /4 .
are
B . 11/12 − 1/6
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{1\times 2}{6\times 2}\\\\\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{3}{4}[/tex]
C. 3/5 + 3/20
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3\times 4}{5\times 4}+\dfrac{3}{20}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{12}{20}+\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3}{4}[/tex]
E . 2/3 + 1/12
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{2\times 4}{3\times 4}+\dfrac{1}{12}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{8+1}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{3}{4}[/tex]
Expressions B (11/12 − 1/6), C (3/5 + 3/20), and E (2/3 + 1/12) each simplify to a sum or difference of 3/4 after finding a common denominator and simplifying the fractions.
Explanation:To find 3 expressions that have a sum or difference of 3/4, let's evaluate each option given:
A. 1/2 + 2/4 simplifies to 1/2 + 1/2, which equals 2/2 or 1. This does not equal 3/4.B. 11/12 − 1/6 can be calculated by finding a common denominator, which would be 12. So, 1/6 is equivalent to 2/12. Thus, 11/12 − 2/12 equals 9/12, which simplifies to 3/4.C. 3/5 + 3/20 requires us to find a common denominator, which would be 20. So, 3/5 is equivalent to 12/20. Thus, 12/20 + 3/20 equals 15/20, which simplifies to 3/4.D. 7/8 − 1/2 requires a common denominator, which would be 8. So, 1/2 is equivalent to 4/8. Thus, 7/8 − 4/8 equals 3/8. This does not equal 3/4.E. 2/3 + 1/12 requires a common denominator, which would be 12. So, 2/3 is equivalent to 8/12. Thus, 8/12 + 1/12 equals 9/12, which simplifies to 3/4.Therefore, the three expressions that have a sum or difference of 3/4 are B, C, and E.
What is the scale factor?
Answer:
the scale factor is by what multiplier has a shape been increased by in size
I need help with this question
how do you represent x<-9/4 on a number line
Explanation:
Find -9/4 = -2 1/4 on the number line. Put an open circle at that point.
Shade the number line to the left of there, representing all values less than -9/4. The dot at -9/4 is open because it is not included in the graph.
A text message plan coasts $7 per month pluse $0.46 per text. Find the monthly cost for x text messages.
p = 7 + 0.46x is the monthly cost for x text messages
Solution:
Given that, A text message plan costs $7 per month plus $0.46 per text
To find: Monthly cost for "x" text messages'
Let "x" be the number of text messages in a month
From given information,
text message plan cost per month = $ 7
Cost for 1 text = $ 0.46
Let "p" be the Monthly cost for "x" text messages
Then, we get,
p = text message plan cost per month + (Cost for 1 text)(number of text messages in a month)
[tex]p = 7 + 0.46x[/tex]
Thus the monthly cost for x text messages is found