Answer:
B
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) and
f(x) - g(x) = 4x² + 1 - (x² - 5) = 4x² + 1 - x² + 5 = 3x² + 6 → B
To find (f-g)(x), we simply subtract g(x) from f(x) and combine like terms. The resulting function is (f-g)(x) = 3x^2 + 6, therefore the correct answer is B. 3x^2 + 6.
To find (f-g)(x), we subtract the function g(x) from f(x). Given f(x) = 4x^2 + 1 and g(x) = x^2 - 5, we perform the subtraction:
f(x) - g(x) = (4x^2 + 1) - (x^2 - 5)
First, distribute the negative sign through the g(x) function:
f(x) - g(x) = 4x^2 + 1 - x^2 + 5
Now, combine like terms:
f(x) - g(x) = 4x^2 - x^2 + 1 + 5
f(x) - g(x) = 3x^2 + 6
So the correct answer is B. 3x^2 + 6.
Min's hose can pump 21 gallons of water every hour. How many gallons of water will he fill up if he runs the hose for 2/3 of an hour?
Answer:
14
Step-by-step explanation:
21 divided by 3 =7 7 per 1/3
7x2=14
Final answer:
Min will fill up 14 gallons of water if he runs his hose, which pumps 21 gallons per hour, for 2/3 of an hour.
Explanation:
If Min's hose can pump 21 gallons of water every hour, and he runs the hose for 2/3 of an hour, you would calculate the total gallons of water filled by multiplying the rate (21 gallons/hour) by the time (2/3 hour).
To find out how much water Min fills up:
Multiply the amount of water his hose pumps per hour by the fraction of the hour he runs it.21 gallons/hour × 2/3 hour = 14 gallons.Therefore, Min will fill up 14 gallons of water if he runs the hose for 2/3 of an hour.
If f(12) = 100(0 .50)12, which expression gives f(x)? Explain.
A . f(x) = 12^x
B . f(x) = 100^x
C . f(x) = 100(x)^12
D . f(x) = 100(12)^x
Answer:
[tex]f(x)=100(0.50)^{x}[/tex] or [tex]f(x)=100(1/2)^{x}[/tex]
Step-by-step explanation:
we have
[tex]f(12)=100(0.50)^{12}[/tex]
we know that
f(12) is the value of the function for x=12
therefore
The function f(x) should be
[tex]f(x)=100(0.50)^{x}[/tex] or [tex]f(x)=100(1/2)^{x}[/tex]
Answer:
D . f(x) = 100(1/2)^x
Step-by-step explanation:
If f(12) = 100(0 .50)¹²
∴ f(x) = 100(1/2)ˣ
Emma has 5 3/8 punds of potato salad and 2 7/8 pounds of egg salad for a picnic. How many more pounds of potato salad than egg salad does Emma have? A - 3 pounds B- 2 3/4 pounds C - 2 1/2 pounds D - 2 1/4 pounds
Answer:
The correct answer option is C. [tex]2\frac{1}{2}[/tex] pounds
Step-by-step explanation:
We are given that Emma has [tex]5\frac{3}{8}[/tex] pounds of potato salad and [tex]5\frac{3}{8}[/tex] pounds of egg salad for a picnic.
We are to find out how much more pounds Emma has of potato salad than the egg salad.
To find this, we simple need to subtract the pounds of egg salad from the pounds of potato salad.
[tex]5\frac{3}{8} - 5\frac{3}{8}[/tex] [tex]=\frac{43}{8} -\frac{23}{8} =\frac{43-23}{8} = 2\frac{1}{2}[/tex] pounds
an online retailer sells cans of tennis balls look at the first rule to find the unit rate then use the unit rate to complete the table to show the cost of ordering 100 and 250 cans.
please help as soon as possible.
To find the unit rate, divide total cost by number of cans bought.
$30 / 12 cans = $2.50 per can.
Now multiply the unit cost by the number of cans you want to buy:
2.50 x 100 = $250.00
2.50 x 250 = $625
What is the value of x?
Answer options: 15, 35, 25, 30
➷ Angles subtended by the same arc are equal
Therefore, x = 30 degrees.
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The answer is 30 Degrees
..............................................
Which of the following could be the equation for a parabola that opens to the left with vertex (-17,2)?
Answer:
C
Step-by-step explanation:
Just plugging in the given x or y values, you can rule out both A and B, only C and D work out logically.
-17=-3(2-2)²-17
-17=0-17
-17=-17✓
2=3(x+17)1+2
2=0+2
2=2✓
With parabolas, if you're talking in terms of y=x², it will be vertical. If talking in terms of x=y², it will be horizontal. As we're looking for something horizontal (open to the left), we need a x=y² formula. Of C and D, only C is an x=y² formula, and thus the answer.
HELP PLX 46 POINTS!
The diameter of the semicircle with center O, shown below, is 4 units. What is the area of the shaded region?
Answer:
Area = 2
Step-by-step explanation:
Givens
The leg and the height of the right angle triangle are both radii of the semi circle.
The diameter of the semicircle is 4
Solution
radius = diameter /2
radius = 4/2
radius = 2
Area = 1/2 * b * h
b = 2
h = 2
Area = 1/2 * 2 * 2
Area = 2
Answer:
2 units²
Step-by-step explanation:
The diameter is 4 units.
The radius is 4/2 = 2 units.
The two legs of the triangle are a measure of 2 units or just the radius length.
Area of triangle = bh × 1/2
2 × 2 × 1/2
4/2 = 2
How did the absent minded professor burn his ear?
He was ironing when the phone rang.
The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. The mirror focused the sunlight onto his ear, causing it to burn.
Explanation:The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. When the professor held the mirror close to his ear and exposed it to sunlight, the mirror focused the sunlight onto his ear, causing it to burn.
The concave mirror has a curve that causes the light rays to converge at a specific point called the focal point. This concentrated light energy resulted in the burning sensation on the professor's ear.
This phenomenon is similar to using a magnifying glass to focus sunlight onto an object and create heat. The concave mirror acted as a magnifying glass, amplifying the intensity of the sunlight and leading to the ear burn.
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There are 5 marbles. There are RED, GREEN, and BLUE. The BLUE marble is 2 more than RED and GREEN combined. The RED marble is 1 less than GREEN. How many does each colored marble have?
Answer:
1/4 of a red marble
5/4 green marbles
14/4 blue marbles.
Step-by-step explanation:
Make a system of equations.
There are 5 marbles, so r + g + b = 5.
There is 2 more of blue marbles than red + green so b - 2 = r + g
There is 1 less red marble than green marbles so g = r + 1.
Then substitute.
b - 2 = r + r + 1
b = 2r + 3
r + r + 1 + 2r + 3 = 5
4r + 4 = 5
4r = 1
r = 1/4
g = 1/4 + 1
g = 5/4
1/4 + 5/4 + b = 5
6/4 + b = 20/4
b = 14/4
Plug them back into the equation and it checks out.
*Note : I don't know how this would work in real life but it's the answer.
Could someone please explain how to do this?
The answer is D because 127° is = p
180-127=p. P=53
180-116=r. R=64
53+64+q=180
117+q=180
Subtract 117 from both sides
Q= 63
Please help me with this
Answer:
44
Step-by-step explanation:
A=a+b
2h=6+5
2·8=44
How do you express the ratio 3.5 : 2.5 in its simplest form?
Answer:
2.5×2=5
3.5×2=7
RATIO OF 2.5 AND 3.5 IS EQUAL TO 5:7
PLZZ MARK MY ANSWER BRAINIEST
Step-by-step explanation:
sharon is 3 years old less than twice her younger brother's age. Let (s) repressent sharons age and (b) repressent her brother's age. which equation could be used to show sharons age?
A: s = 3-2b
B: b = 2x-3
C: s = 2b-3
D: b = 3 -2x
E: s = 3b-2
If Sharon is 3 years younger, then it's s = 3-b. However, it's twice her brothers age, which makes the formula our final answer, A, or [tex]s = 3 - 2b[/tex]
The correct option is A
The graph of an equation representing a direct variation passes through the point (6, 10). Give another point with integral coordinates that is also on the graph of this equation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{6},\stackrel{y}{10})\qquad \textit{we know that } \begin{cases} x=6\\ y=10 \end{cases}\implies 10=k6\implies \cfrac{10}{6}=k\implies \cfrac{5}{3}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{3}x}[/tex]
to get another point, we simply can pick a random independent variable, namely "x", say hmmmm x = 9, thus
[tex]\bf y=\cfrac{5}{3}(\stackrel{\stackrel{x}{\downarrow }}{9})\implies y=5\cdot \cfrac{9}{3}\implies y=10~\hspace{7em}\boxed{(9, 10)}[/tex]
To find another point with integral coordinates on the graph of the equation representing a direct variation, we can use the given point (6, 10) and the fact that the equation represents a direct variation. By finding the value of the constant of variation, we can substitute an integral x-value to find the corresponding y-value for another point on the graph.
Explanation:To find another point with integral coordinates on the graph of the equation representing a direct variation, we need to use the given point (6, 10) and the fact that the equation represents a direct variation. A direct variation equation has the form y = kx, where k is the constant of variation. In this case, we can use the given point to find the value of k. When x = 6 and y = 10 in the equation y = kx, we can substitute these values to solve for k: 10 = k * 6. Solving for k, we get k = 10/6 = 5/3.
Now that we know the value of k, we can find another point with integral coordinates. Let's try x = 3. Using the equation y = kx, we can substitute x = 3 and k = 5/3 to find y: y = (5/3) * 3 = 5.
So, another point with integral coordinates on the graph of the equation representing a direct variation is (3, 5).
Is 23/40 a rational or irrational number? I'm not sure how to solve this one.
Answer:
23/40 is a rational number
Step-by-step explanation:
an irrational number cannot be written as a fraction - with a finite end. An irrational number would be a repeating decimal
In the given question, 23/40 is a rational number.
Explanation:A rational number is any number that can be expressed as the quotient or fraction of two integers (whole numbers), where the denominator is not zero. Rational numbers include fractions and terminating or repeating decimals, but not irrational numbers like the square root of 2.
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. To determine if 23/40 is a rational or irrational number, we need to check if it can be expressed as a ratio of two integers. The numbers 23 and 40 are both integers, and the denominator is not zero, so 23/40 is a rational number.
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Which of the following is the graph of f(x) = x2 − 4x − 5?
A. graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B. graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C. graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D. graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)
Answer:
Minimum at (2,-9) and intercepts are (-1,5)
Step-by-step explanation:
f(x) = [tex]x^2 -4x-5[/tex]
completing square method adding and subtracting the square of half of coefficient of 4 ,we get
f(x) = [tex]x^2 -4x+4 -4 -5[/tex]
f(x) =[tex](x-2)^2 -9[/tex]
on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]
where k is suppose to be the minimum value
on comparing it we get k = -9
which is minimum value of f(x)
at x =2
and if we find the zeros of
[tex]x^2 -4x-5[/tex] ,we get
[tex]x^2 -5x+x -5[/tex]
[tex]x^2 -4x-5[/tex]
x(x-5)+1(x-5)
(x+1)(x-5)
on setting it equals zero ,we get
x+1 =0 and x=5
x =-1 and x=5
therefore option A is answer
Minimum at (2,-9) and intercepts are (-1,5)
Is 976-522 more or less than 400? Explain how you can tell without finding the exact difference
[tex]\bold{Hey\ there!} \\ \bold{976-522=454}\\ \boxed{\boxed{\bold{Thus, 400\ is\ \underline{LESS\ THAN}\ 976-522}}} \\ \bold{Just\ solve\ your\ particular\ equation} \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Write an expression that, when simplified is equivalent to 15x +7
Answer:
2(7.5x+3.5)
Step-by-step explanation:
I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.
Katrina owns a 9-acre farm. Last month, she bought her neighbor’s adjoining 8-acre farm. How large is Katrina’s farm now?
Answer:
17 acres
Step-by-step explanation:
9 acres + 8 acres = 17 acres, if that wasn't what the question meant please let me know and I'll change the answer or try to help clear confusion.
Solve the following equation. Then place the correct number in the box provided. 3x + 1 + 5x = 7 +15 + 7x find X
What is the value of x?
A.31
B.41
C.29
D.60
180-59=121
121+30=151
180-151=29.
C is the answer.
What is the product? (7x2y3)(3x5y8)
i don't know if this is the correct answer 3360y^2
Answer:
Product [tex](21) ( x^{7})(y^{11})[/tex].
Step-by-step explanation:
Given : [tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
To find : product .
Solution : We have given that
[tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
Combine like terms
[tex](7 * 3) ( x^{2}*x^{5})(y^{3}*y^{8})[/tex].
By the exponential rule : if the base of two exponent is same then power must be added . [tex]x^{a} *x^{b} = x^{a+b}[/tex].
Then
[tex](21) ( x^{2+5})(y^{3+8})[/tex].
[tex](21) ( x^{7})(y^{11})[/tex].
Therefore, Product [tex](21) ( x^{7})(y^{11})[/tex].
Could someone help me plz???
The correct answer is B. approximately 250g
Which of the following equations will make a V-shaped graph?
y = |x|
y = 2x
x 2 + 5 = y
y = 1/3x
Y=|x|. An absolute value has a V shape.
Final answer:
The equation that will make a V-shaped graph is y = |x|, as it plots the absolute value of x, creating a V shape by reflecting points on the positive side of the y-axis for both positive and negative values of x.
Explanation:
The student asked which of the following equations will make a V-shaped graph. The answer is y = |x|. This is because the absolute value function produces a graph that is V-shaped, reflecting the positive distance from zero for both positive and negative values of x. The other options presented, such as y = 2x, would produce a straight line; x² + 5 = y (correctly read as y = x² + 5) would produce a parabola; and y = 1/3x would also result in a straight line, just with a different slope. Only the graph of y = |x| has the distinct V shape as it plots the absolute value of x, meaning it reflects the points on the positive side of the y-axis for both positive and negative values of x.
in a bag if marbles there are 7 blue, 6 red, pick one marble out. without replacing the first marble pick another marble out. how many ways can u pick two red marbles?
Answer:
1
Step-by-step explanation:
If you only take out 2 marbles, you have to take out red marbles both times to have 2 red marbles. There is no other option.
i need help with algebra asap some help me please 8s^2 - 10st + 3t^2
[tex]8 {s}^{2} - 10st + 3 {t}^{2} \\ = 8 {s}^{2} - 4st - 6st + 3 {t}^{2} \\ = 4s(2s - t) - 3t(2s - t) \\ = (2s - t)(4s - 3t)[/tex]
What is 10 minutes before 9
➷ To figure this out, you need to understand that there are 60 minutes in an hour
Subtract 10 from this value:
60 - 50
As it isn't 60 minutes, it wouldn't be 9 anymore
9-1 = 8
The correct answer would be: 8:50
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help and show work for #7
Answer:
If you give the diameter and the radius, as well as the circumference, I will be of more help :)
Step-by-step explanation:
I hope this helps, if it doesn't then just message me and ill be more than happy to help :)
Examine the two-step equation. − 7 4 + x 4 = 2 Which property of operations allows you to add the same constant term to both sides?
Answer:
The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation
Step-by-step explanation:
if a−b=c,then a−b+b=c+b,or a=c+b
Answer:
addition property of equality
Step-by-step explanation:
Which statement BEST describes how the graph of g(x)=-3x^2 compares to the graph of f(x)=x^2?
Reminder:(Number 12 for the picture has the answers for the question)
Answers are attached in the 2 pics below. Please check!