The functions f(x) and g(x) are defined below.
Which expression is equal to f(x) · g(x)?
Answers
none of the above
Step-by-step explanation:This question wants you to see that the radical can be simplified because it is ...
[tex]f(x)=\sqrt{(x+6)^2}[/tex]
The answer choices show you are expected to simplify this to ...
... f(x) = x +6
Then
... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C
_____
However,
... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x
so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.
The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).
Related Questions
Brainliest + Points!
Please show work!
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the red region?
A.
0.25
B.
0.33
C.
0.67
D.
0.75
Answers
work:
Answer:
C
Step-by-step explanation:
The target area is shown in the attached picture.
We want to figure out probability of hitting red region.
The area of the figure is the area of the red square, which is 196.
Area of red region is area of whole square (196) minus area of blue square (64). So we have:
Area of red region = 196 - 64 = 132
Probability of hitting red region is 132 divided by total, which is 196.
[tex]\frac{132}{196}=0.67[/tex]
Answer choice C is right.
after 8% discount from the list price, the sale price price of a poster was $17.48. what was the list price of poster.
Answers
Final answer:
To find the list price of the poster after an 8% discount, subtract 8% of the list price from the list price and set it equal to the sale price.
Explanation:
To find the list price of the poster, we need to first calculate the original price before the discount. Let's assume the list price is 'x' dollars. After an 8% discount, the sale price of the poster is $17.48.
We can set up an equation to solve for the list price: x - 8% of x = $17.48. To calculate 8% of x, we multiply x by 0.08.
So the equation becomes: x - 0.08x = $17.48. Combining like terms, we get 0.92x = $17.48. Dividing both sides by 0.92, we find that x = $19.
I need help with this question show steps! Quickly please!
Answers
Answer:
y+9 =-5(x-2) point slope form
y = -5x-1 slope intercept form
Step-by-step explanation:
If we have a slope and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y--9 = -5(x-2)
y+9 =-5(x-2)
If you want to write it in slope intercept form, distribute the -5
y+9 = -5x+10
Subtract 9 from each side
y+9-9 = -5x+10-9
y = -5x-1
if an equilateral triangle has an angle of 3 X what is the value of X
Answers
Answer:
x = 20
Step-by-step explanation:
In an equilateral triangle, everything is the same; line length and angles. Each angle in an equilateral triangle is:
180 ÷ 3 = 60
So 3x = 60
Divide both sides by 3 to get x:
x = 20
Hope this helps!
How long (to the nearest foot) is Kentucky Avenue between c street and d street?
Answers
Answer:
Kentucky Avenue is 575 ft between C street and D street
Step-by-step explanation:
x / (460 ft) = (1000 ft) / (800 ft)
Divide the right side:
x / (460 ft) = 1.25
To solve for "x", multiply both sides by 460 ft:
(460 ft) [x/(460)] = (460) (1.25)
x = 575 ft
Hope this helped :)
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part 1: If x represents the number of checks Cecily writes per month, what expression represents the monthly fee in dollars charged by checking account A?
Part 2: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same in fees?
Answers
Answer:
(1) 0.08x + 16
(2) 0.08x + 16=0.12x + 14
Step-by-step explanation:
Checking account A has a monthly fee of $16 and a per-check fee of $0.08
Per check fee is a constant rate that is 0.08
Let x represents the number of checks Cecily writes per month
1 check fee = 0.08
x checks fee = 0.08x
monthly fee is $16 , we add that as well
So total monthly fee charges for account A is
0.08x + 16
checking account B has monthly fee of $14 and a per-check fee of $0.12.
1 check fee = 0.12
x checks fee = 0.12x
monthly fee is $14 , we add that as well
So total monthly fee charges for account B is
0.12x + 14
(2) To find number of checks write per month for the accounts to charge the same in fees
WE set both expression , account A = account B
0.08x + 16=0.12x + 14
Subtract 0.12x on both sides
-0.04x + 16 = 14
Now subtract 16 on both sides
-0.04x = -2
Divide by -0.04 on both sides
So x= 50
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
Answers
The expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
1. Calculate the sale price after the markdown:
Original price: x dollars
Markdown rate: 20%
Sale price after markdown: x * (1 - 0.20) = 0.8x dollars
2. Calculate the amount of sales tax:
Sales tax rate: 6%
Sales tax amount: 0.06 * 0.8x = 0.048x dollars
3. Calculate the correct total sale price:
Sale price after markdown + Sales tax amount = 0.8x + 0.048x = 0.848x dollars
4. Analyze the given expressions:
x * (1 - 0.20) + 0.06x: This expression correctly calculates the discount and adds the sales tax to the original price, so it represents the total sale price.
x * (1 - 0.20) + 0.06 * 0.8x: This expression also correctly calculates the discount and adds the sales tax to the discounted price, so it represents the total sale price.
x * (1 - 0.20 + 0.06): This expression combines the discount and sales tax into a single percentage (14%), but it applies this percentage to the original price (x) instead of the discounted price (0.8x). This leads to an overestimation of the final sale price, so it does not represent the correct total price.
0.8x + 0.048x: This expression correctly calculates the sum of the discounted price and the sales tax amount, so it represents the total sale price.
Therefore, the expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
Complete question:
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
x * (1 - 0.20) + 0.06x
x * (1 - 0.20) + 0.06 * 0.8x
x * (1 - 0.20 + 0.06)
0.8x + 0.048x
HELPP!!!
Find m angle 1 and m angle 3 in the kite.
Answers
Answers:
Angle 1 is 40 degrees
Angle 2 is 90 degrees
Angle 3 is 50 degrees
===========================================
Explanations:
Triangle ABC is a reflection of triangle ADC over the line AC. Doing this reflection forms the kite ABCD. Or you can think of it as gluing two congruent triangles together (ABC and ADC). We can prove the two triangles ABC and ADC congruent by the SSS congruence property. Then we use CPCTC (corresponding parts of congruent triangles are congruent) to prove that angle 1 is 40.
Let E be the intersection of the two diagonals. Through similar reasoning as earlier, we can prove that triangle AEB is congruent to triangle AED, so that leads to angle 2 being 90 degrees because this angle adds to its counterpart to get 180. Both unknown angles are x each meaning x+x = 180 leads to x = 90. One property of kites is that the diagonals are perpendicular.
Triangle AED is a right triangle as discussed above. Therefore, the angle 3 and the 40 degree angle are complementary. If angle 3 is y, then y+40 = 90 giving y = 90-40 = 50, which is why angle 3 is 50 degrees.
Using angle theorems, the value of the angles m1 and m3 are 40° and 50° respectively.
Taking the midpoint of DB as O ;
Angle OAD and Angle OAB are equal
OAD = 40° ; OAB = 40°
A right angle is formed at O ;
Hence,
(O + D + A) = 180°
90° + D + 40° = 180° (Sum of interior angles of a triangle)
D = 180 - 130
D = 50°
Hence, m∠3 = 50°.
Therefore, the value of the angles m1 and m3 are 40° and 50° respectively.
Order the numbers 0.64,
2/3 , 65%, and
7/10 from least to greatest. (3 points)
Answers
Answer:
.64 < 65 % < 2/3 < 7/10
Step-by-step explanation:
To order all the numbers from least to greatest, but all the numbers in the same form (fraction, decimal, or percent). I will put them all in decimal form so that I can compare them.
0.64, .64
2/3 , =.666666repeating
65% = 65/100 = .65
7/10 = .7
.64< .65<.6666repeating<.7
but we need to put them in their original form
.64 < 65 % < 2/3 < 7/10
Given 4x =
a + b/8c
, rearrange the equation for a, in terms of b, c, and x
Answers
To rearrange the equation for a, subtract b/8c from both sides: a = 4x - b/8c.
Explanation:To rearrange the equation for a, we start with the given equation 4x = a + b/8c. First, we isolate a by subtracting b/8c from both sides, giving 4x - b/8c = a. Therefore, the equation for a in terms of b, c, and x is a = 4x - b/8c.
what is a equivalent expression for 2(c+c+c)
Answers
Answer: 2(C^3) or 2(C to the third power)
Step-by-step explanation: C^3 is the same thing a c+c+c
Hope this helps!
Triangle CDE and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of CE is equal to the slope of CG?
A) 2 − 3
2 − 0
= 3 − 1
4 −0
B) 3 − 2
2 − 0
= 3 − 1
4 − 0
C) 2 − 3
0 − 2
= 3 − 1
0 − 4
D) 3 − 2
0 − 2
= 3 − 1
0 − 4
Answers
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(2, 2), C(0, 3) and G(4, 1), C(0, 3).
Substitute:
[tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}\to\boxed{D}[/tex]
Answer: The correct option is (D) [tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Step-by-step explanation: Given that ΔCDE and ΔCFG are similar right triangles.
We are to select the correct proportion that can be used to show that the slope of CE is equal to the slope of CG.
We know that the slope of a line passing through two points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the given figure, we note that the co-ordinates of the points C, E and G are
C(0, 3), E(2, 2) and G(4, 1).
So, the slope of line CE is given by
[tex]m_1=\dfrac{2-3}{2-0},[/tex]
and the slope of line CG is given by
[tex]m_2=\dfrac{1-3}{4-0}.[/tex]
Since the lines CE and CG are same, they must be parallel and hence they have equal slopes.
Therefore,
[tex]m_1=m_2\\\\\\\Rightarrow\dfrac{2-3}{2-0}=\dfrac{1-3}{4-0}\\\\\\\Rightarrow \dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Thus, (D) is the correct option.
Which expression is equivalent to (5 × 6)×(3 × 2)?
A) (5 + 6) + (3 + 2)
B) (5 + 6)×(3 + 2)
C) (5 × 6) + (3 × 2)
D) (3 × 2)×(5 × 6)
Answers
Answer:
The original equation contains 3 multiplications.
When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.
This would make D, the same.
D) (3 × 2)×(5 × 6)
If the area of a rectangle is 8x^2+10x-3 and it’s width is 2x+3 what is the perimeter of this rectangle?
Answers
Answer:
192
Step-by-step explanation:
Debbie cut cord to sixths she is five of the pieces to make necklaces she used equal length of the remaining cord for each of four bracelets what fraction of the original cord did Debbie use for each bracelet
Answers
Answer:
¹/₂₄
Step-by-step explanation:
Debbie used ⅚ of the cord for necklaces.
That left ⅙ of the cord for four bracelets.
Each bracelet used:
Fraction of cord = ⅙ ×¼ = ¹/₂₄
Debbie used ¹/₂₄ of the cord for each bracelet.
Which tool(s) are needed to construct a perpendicular bisector of a line segment?
Answers
Answer: compass and straightedge or ruler
Perpendicular bisector of a line segment
Geometry construction using a compass and straightedge
compass and straightedge or ruler
Step-by-step explanation:
Answer:
You need a straight edge and a compass.
Step-by-step explanation:
The straight edge should not be marked in any way. You are not allowed to put a mark on the straight edge at all. The only property it has is that it has no curvature in any direction.
The compass must be flexible and at the same time it must be able to stay at one radius unless changed by the owner. It's only property is that it can draw a perfect circle once the radius of the circle has been chosen,
What is the solution to the following system? 3x+3y=10
-9x-9y=-30
Answers
Answer:
Infinite number of solutions.
Step-by-step explanation:
We have the equations,
1. 3x+3y=10
2. -9x-9y= -30
Now, if we multiply equation 1 with -3, we will obtain equation 2.
i.e. -3×(3x+3y)= -3×10
i.e. -9x-9= -30
So, we see that both the equations are same.
The equation 3x+3y=10 will have solution for many values of x and y.
Hence, the system will have infinite number of solutions.
Answer:
Infinite Solution
Step-by-step explanation:
Given :
[tex]3x+3y=10[/tex] -----(A)
[tex]-9x-9y = -30[/tex] ------(B)
To Find : Solution of the given system of equations
Solution :
We will solve it by using substitution method
Finding the value of x from equation (B)
⇒[tex]-9x-9y = -30[/tex]
⇒[tex]-9x= -30+9y[/tex]
⇒[tex]x= \frac{-30+9y}{-9}[/tex]
⇒[tex]x= \frac{-10+3y}{-3}[/tex]
Putting this value of x in equation (B)
⇒ [tex]3( \frac{-10+3y}{-3})+3y=10[/tex]
⇒[tex]10-3y+3y = 10[/tex]
⇒[tex]10= 10[/tex]
Since x and y both gets eliminated from the equation we got 10 = 10
Since the equations represent the same line.
If a consistent dependent system that has an infinite number of solutions
Hence there is infinite solution .
find the length of side x in simplest radical form with a rational denominator
Answers
Answer:
[tex]\dfrac{10\sqrt{3}}{3}[/tex]
Step-by-step explanation:
You want the length of the hypotenuse in a 30°-60°-90° right triangle with long leg 5.
RatioThe ratios of side lengths in a 30°-60°-90° triangle is ...
1 : √3 : 2
Multiplying these values by 5/√3 gives ...
5/√3 : 5 : 10/√3
That is, the length of the side marked X is 10/√3.
RationalizeThe denominator can be rationalized by multiplying the fraction by 1 in the form of (√3)/(√3):
[tex]X = \dfrac{10}{\sqrt{3}}=\dfrac{10}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\\\boxed{X=\dfrac{10\sqrt{3}}{3}}[/tex]
Find the slope of the line that passes through the pair of points.
(-40.86,5.6) and (0.86,4.2)
simplify
Answers
Answer:
-.033557047
Step-by-step explanation:
Slope = (y2-y1)/ (x2-x1)
= (4.2 - 5.6)/(.86- 40.86)
= -1.4/ (.86 + 40.86)
= -1.4/41.72
-.033557047
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:
[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]
Answer: The slope = - 5/149 A 63 kg object needs to be lifted 7 meters in a matter of 5 seconds. Approximately how much horsepower is required to achieve this task?
A. 1.16 hp
B. 864.36 hp
C. 441 hp
D. 0.59 hp
Answers
Answer:
1.16 horse power. Option A.
Step-by-step explanation:
Work done = m g h = 63 * 9.81 * 7 = 4326.21 joules
Power = 4326.21 / 5 = 865.24 Watts
1 Horse power = 746 watts so the answer is 865.24 / 746 = 1.16 HP to nearest hundredth.
Answer:
1.16 hp
Step-by-step explanation:
how would you graph the following systems of equations ?
y= -3x -7
x- 2y=-14
Answers
y=-3/1x+-7
x-2y=-14
-2y=-14-x
y=7+1/2x
Start with the b variable so for problem 1 put a dot on 0,-7 and for problem 2 put a dot on 0,7
Then from -7 for problem 1 depending on whether the slope is negative or positive go down 3 and over right 1 therefore another point for problem one is marked, at 1,-10; for problem 2 up 1 and to the right 2; 2,8
For problem one connect the dots of 0,-7 and 1,-10
For problem two connect the dots of 0,7 and 2,8
What is the equation in slope intercept form of the line that is perpendicular to the given line and passes through the point (-4,-3)
Answers
Answer:
b no is the right answer i think
twice the difference of a number and 6 equals 8
translate sentence into equation
Answers
Answer:
2*(n-6) = 8
Step-by-step explanation:
Twice the difference of a number and 6 equals 8
Equals means =
Difference means subtract
2*(n-6) = 8
Larue score 10 points less than three times the number of points that Ross scored Livia scored 11 points how many points did Ross score?
Answers
Let R = points for Ross
L = 3R - 10
L = 11
11 = 3R-10
3R = 21
R = 7 points scored by Ross
so 7 points
hope it helps
plz mark as brainliest
can some one explain how to do these problems
Answers
Answer:
the slope is 0.
Step-by-step explanation:
You can use the slope equation
[tex]\frac{y-y}{x-x}[/tex]
and plug in your points
[tex]\frac{10-10}{4-1}[/tex]
[tex]\frac{0}{3}[/tex]
slope = 0
What is the supplement of a 47 angle?
Answers
Answer:
133° angle
Step-by-step explanation:
Note that "supplement" means 180°.
To find the supplement of the angle given (47°), subtract the given measurement with the total supplementary measurement.
180 - 47 = 133
The supplement of a 47° angle is 133°.
~
Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant. The total cost C for picking strawberries is a function of x, the kilograms of strawberries picked. Write the functions formula. C=
Answers
Answer:
C = 6 + 7.5 x
Step-by-step explanation:
Given,
The amount is $24.75 for entrance and 2.5 kilograms of strawberries.
⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75
Since, Entrance fee = $ 6,
And, the price for each kilogram of strawberries is constant.
⇒ $ 6 + 2.5 × 1 kilograms of strawberries = $24.75
⇒ 2.5 × 1 kilograms of strawberries = 18.75
⇒ 1 kilograms of strawberries = $ 7.5.
Thus, the cost of x strawberries = 7.5 x
Also, the total charge for x strawberries = Entrance fee + the cost of x strawberries
= 6 + 7.5 x
⇒ C = 6 + 7.5 x
Which is the required function formula.
A plane has 360360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class.
How many seats are there in each class?
Answers
Answer:
There are 260 seats in the economy class and 100 seats in the business class. A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 55 seats in business class.
What is the probability the spinner will land on a dotted region?
A- 25%
B- 33%
C-37.5%
D- 50%
Dotted Regions Include- 25%, 12.5%, and 12.5%
Stripped Regions Include- 12.5%, and 25%
White Region Includes- 12.5%
Answers
The probability for the spinner landing on the dotted region is 1/2.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The probability for the given case is evaluated as,
P(Spinner lands on dotted region) = Total space for dotted region/100
= (25 + 12.5 + 12.5)/100
= 50/100
= 1/2
Hence, the probability that the spinner will land on a dotted region is 1/2.
To know more about probability click on,
https://brainly.com/question/11234923
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54d.
Change the following expression into a single fraction:
5b − 2/b