If f(x) = 2x² +3 and g(x)=x2-7, find (f- g)(x)
A. 3x²2²-10
B. x² + 10
C. x²-4
D. 3x²2²-4
APEX FUNCTIONS PLEASE HELP
Answer: D
Step-by-step explanation:
Two security cameras are positioned on the ceiling of a gym 10 m apart. When camera has an angle of depression of 50° to a point on the floor and the other camera has an angle of depression of 60° to the same point calculate the height of the gym.
When camera has an angle of depression of 50° to a point on the floor and the other camera has an angle of depression of 60° to the same point calculate the height of the gym, the height of gym is 7.05 m
What is angle of depression?When the observer is above the object they are looking at, an angle of depression is created. An angle below the horizontal line drawn with the level of the observer's eye and the line connecting the object with the observer's eye is created when an observer looks at an object that is placed at a distance lower than the observer.
Lets name the points on the triangles as A, B ,C
m∠ABC = 180° - 60° + 50°
= 70°
Now, the sine theorem defines
[tex]\frac{AB}{sin50\textdegree}[/tex] = [tex]\frac{AC}{sin70\textdegree}[/tex] = [tex]\frac{10}{sin70\textdegree}[/tex]
AB = 8.15 meters
Now using the area of triangle formula
area∠ABC = 1/2 × AB × AC × sin∠BAC = 1/2 × h × AC
⇒ 1/2 × 8.15 × 10 × √3/2 = 1/2 × h × 10
⇒ 8.15 × √3/2 = h
⇒ h = 7.05
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Can someone please help ASAP assignment due tomorrow!
No 4.
The area of the large square = 9/4 square inches
There is a total of 25 small equally sized squares inside the large square.
The shaded portion given contains 4 such small equally-sized squares. This shaded portion has an area of 9/25 square inches.
We will first find the area of one small sized square and then will use it to find the area of the large square as the large square is made of 25 such small squares.
That is, area of 4 small squares = 9/25
So area of one small square = Area of 4 small squares/ 4
= (9/25)/4
= 9/(25 x 4)
= 9/100 square inches
Now to find the area of the large square, multiply the area of one small square with the total number of small squares contained in the large square.
That is, Area of the large square = (9/100) x 25
= 9/4 square inches
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Is 1270.8 cm significantly high?
A. No, because it is below the lower limit separating value.
B. Yes, because it is between the limits separating values.
C. No, because it is above the upper limit separating value.
D. No, because it is between the limits separating values.
E. Yes, because it is above the upper limit separating value.
F. Yes, because it is below the lower limit separating value.
To determine the boundaries separating numbers that are significantly low or significantly high, apply the range rule of thumb.
How do you identify the limits separating values that are significantly low or significantly high?To determine the boundaries separating numbers that are significantly low or significantly high, apply the range rule of thumb. Males had pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute, according to Data Set 1 "Body Data" in Appendix B.
A limit exists a specific value to which a function approaches. Estimating a limit usually means finding what value y exists as x approaches a certain number.
Therefore, the correct answer is option A. No, because it is below the lower limit separating value.
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Simplify (-4b)(-19b).
76b
-76b
766²
-76b²
2 In (x - 5) = In (x + 10) + In 4
answer:
the solution is: x = 15
.Higher Order Thinking Ari walked 22 miles
at a constant speed of 2 miles per hour. Beth
walked 1 miles at a constant speed of
1 miles per hour. Cindy walked for 1 hour
and 21 minutes at a constant speed of
1 miles per hour. List the three people in order
of the times they spent walking from least time
to greatest time.
The three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .
In the question ,
it is given that
Ari walked a distance of 22 miles with speed of 2 miles per hour .
Beth walked a distance of 1 mile with the speed of 1 mile per hour.
Cindy walked for the time 1 hour and 21 minutes .
converting 21 minutes to hours , we get
= 1 hr 21 min
= 1+21/60
= 27/20
= 1.35 hours ....(i)
time required for Ari to walk 22 miles with speed of 2 miles per hour is
time = distance/speed
time = 22/2 = 11 hours ...(ii)
time required for Beth to walk 1 miles with speed of 1 miles per hour is
time = 1/1 = 1 hours ....(iii)
From equation (i) , (ii) and (iii) ,
the order of the time they spent walking from least to greatest time is
1 hours < 1.35 hours < 11 hours
Therefore , the three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .
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In a small town, the population increased from 25,000 people in 2010 to
32,000 people in 2020. What is the percent increase in population? What is the answer
Answer:32000 - 25000 =7000 increase percentage = increase amount
Step-by-step explanation:
Find the circumference of a circle with
diameter, d = 7.65m.
Give your answer rounded to 2 DP.
Answer:
24.03
Step-by-step explanation:
We know that the formula is pie squared times radius but the radius is half of the diameter but you can also do pie times diameter and get the same answer.
1/9 times blank equals 4/27
The correct value in the blank of the statement "1/9 times blank equals 4/27" is; 4/3
How to divide fractions?We are given the expression that 1/9 times blank equals 4/27.
Let the missing term be identified as y. Thus, we have;
1/9 * y = 4/27
In Mathematics, the reciprocal of any quantity is, one divided by that quantity. For any number 'b', the reciprocal will be 1/b. If the given number is multiplied by its reciprocal, we get the value 1.
To get the missing value y, we will use multiplication property of equality to multiply both sides by 9 to get;
1/9 * y * 9 = 4/27 * 9
y = 4/27 * 9
y = 4/3
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Just in need of help please
The complete details on the table are
Shape: Length Height Area of 1 Number Total area
Square 12 12 144 1 144
Triangle 12 15 90 4 360
The surface area is 504 square inches
How to determine the surface area?The square prism represents the given parameter
On the figure, we have the following highlights:
Shape: Square
Number of shapes = 1Base length = 12 inchesHeight = 12 inchesAlso, we have
Shape: Triangle
Number of shapes = 4Base length = 12 inchesHeight = 15 inchesThis means that
Area of 1 square = Base length * Height
Area of 1 square = 12 inches * 12 inches
Area of 1 square = 144 square inches
So, the area of all squares in the figure is
Area of all squares = 1 * 144 square inches
Area of all squares = 144 square inches
Also, we have
Area of 1 triangle = 0.5 * Base length * Height
Area of 1 triangle = 0.5 * 12 inches * 15 inches
Area of 1 triangle = 90 square inches
So, the area of all triangles in the figure is
Area of all triangles = 4 * 90 square inches
Area of all triangles = 360 square inches
The surface area of the figure is
Surface area = Area of all triangles + Area of all squares
This gives
Surface area = 360 square inches + 144 square inches
Evaluate
Surface area = 504 square inches
Hence, the surface area of the prism is 504 square inches
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solve g(x) = "-x^2" "-7" when x=-3
Solution of the given function g(x) = "-x^2" "-7" when x=-3 = 2.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function called g is defined by the notation y=g(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The output value, also known as the dependent variable, is denoted by the letter y, or g(x).
Given function
g(x) = -x² -7When x = -3
Whenever you're given a function, you simply plug in the x value you're given and then calculate the result.
g(-3) =(-3²) - 7
g(-3) =(9) - 7
g(-3) =9 - 7
g(-3) =2
Hence, When x=-3 = 2, the given function g(x) has a solution of "-x2" "-7."
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5:2:11=___:6____
Can you please help me I am stuck
between 1/4 aand 9/2 which fraction is greater
Answer: the answer is 9/2
Identify the vertex, min/max values, and x-
intercepts. Then graph.
y=x²-1
x-intercepts; plug in 0 for y and then solve
0 = x^2 - 1
1 = x^2; x = -1 & x = 1
vertex; (0,-1); the only translation was the point was moved down one unit
min/max; the graph does not have a max because it is a positive graph w/ positive infinity. The minimum would be (0,-1), the lowest point.
! For graphing I recommend using desmos.
ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
The most appropriate choice for profit and loss will be given by
Uncle Ben will feed his cows 2 pounds of grain supplement.
What is profit and loss?
If the selling price is more than the cost price, then the difference between the selling price and the cost price will give the profit.
If the selling price is less than the cost price, then the difference between the selling price and the cost price will give the loss.
Here,
For 1 pound
Cost price of grain supplement = [tex]0.70 \times 1[/tex]
= $[tex]$0.70[/tex]
Selling price of milk = [tex]0.20 \times 5[/tex]
= $[tex]1[/tex]
Profit = $([tex]1 - 0.70[/tex])
= $0.30
For 2 pounds
Cost price of grain supplement = [tex]0.70 \times 2[/tex]
= $[tex]$1.40[/tex]
Selling price of milk = [tex]0.20 \times 9[/tex]
= $[tex]1.80[/tex]
Profit = $([tex]1.80 - 1.40[/tex])
= $0.40
For 3 pounds
Cost price of grain supplement = [tex]0.70 \times 3[/tex]
= $[tex]$2.10[/tex]
Selling price of milk = [tex]0.20 \times 12.3[/tex]
= $2.46
Profit = $([tex]2.46 - 2.10[/tex])
= $0.36
For 4 pounds
Cost price of grain supplement = [tex]0.70 \times 4[/tex]
= $[tex]$2.80[/tex]
Selling price of milk = [tex]0.20 \times 15.5[/tex]
= $3.1
Profit = $([tex]3.1 - 2.80[/tex])
= $0.30
For 5 pounds
Cost price of grain supplement = [tex]0.70 \times 5[/tex]
= $[tex]$3.50[/tex]
Selling price of milk = [tex]0.20 \times 18[/tex]
= $3.60
Profit = $([tex]3.60 - 3.50[/tex])
= $0.10
For 6 pounds
Cost price of grain supplement = [tex]0.70 \times 6[/tex]
= $[tex]$4.20[/tex]
Selling price of milk = [tex]0.20 \times 20[/tex]
= $4
Loss = $([tex]4.20 - 4[/tex])
= $0.20
For 7 pounds
Cost price of grain supplement = [tex]0.70 \times 7[/tex]
= $[tex]4.90[/tex]
Selling price of milk = [tex]0.20 \times 21.5[/tex]
= $[tex]4.30[/tex]
Loss = $([tex]4.90 - 4.30[/tex])
= $0.60
For 8 pound
Cost price of grain supplement = [tex]0.70 \times 8[/tex]
= $[tex]$5.60[/tex]
Selling price of milk = [tex]0.20 \times 22.5[/tex]
= $[tex]4.50[/tex]
Loss = $([tex]5.60 - 4.50[/tex])
= $1.10
For 9 pounds
Cost price of grain supplement = [tex]0.70 * 9[/tex]
= $[tex]6.30[/tex]
Selling price of milk = [tex]0.20 * 23[/tex]
= $[tex]4.60[/tex]
Loss = $([tex]6.30 - 4.60[/tex])
= $1.70
Since profit from 2 pounds of grain supplement is the most, Uncle Ben will feed his cows 2 pounds of grain supplement.
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Complete Question
Farmer Ben knows that feeding a grain supplement to his cows will produce more milkaccording to the following schedule:
ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
The table has been attached here
maths question photo attached
The exact area of the shaded region is: (2 - √6)/8 cm².
What is the Area of a Triangle?The area of a triangle = 1/2(base)(height).
The area of the shaded region = area of triangle ABD - area of triangle ACD.
Area of triangle ABD:
Base of triangle ABD = AD = √2/2
Height of triangle ABD = BD = √2/2
Area of triangle ABD = 1/2(√2/2)(√2/2)
Area of triangle ABD = 2/8 = 1/4 cm²
Area of triangle ACD:
Base of triangle ACD = AD = √2/2
Height of triangle ACD = CD = √3/2
Area of triangle ACD = 1/2(√2/2)(√3/2)
Area of triangle ACD = √6/8 cm²
Area of the shaded region = 1/4 - √6/8
Area of the shaded region = (2 - √6)/8 cm²
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Is the following relation a function?
A) Yes
B) No
Answer:
I say b
Step-by-step explanation:
Write an equation of a line parallel to y = 2x - 1 that passes through the point (-3, 1)
The equation of the parallel line to y = 2x - 1, that passes through (-3, 1) is: y = 2x + 7.
How to Write the Equation of Parallel Lines?Two lines that are parallel to each other would always have the same slope (m). In the slope-intercept form of the equation that represents a line, y = mx + b, the slope of the line is represented as "m", while the y-intercept is represented as b.
Given:
A point (-3, 1)
Equation, y = 2x - 1. The slope (m) = 2. Since parallel lines have the same slope (m), therefore, the line that passes through (-3, 1) also have a slope (m) = 2.
Substitute (x, y) = (-3, 1) and m = 2 into y = mx + b:
1 = 2(-3) + b
1 = -6 + b
1 + 6 = b
b = 7
To write the equation of the parallel line to y = 2x - 1, substitute m = 2 and b = 7 into y = mx + b:
y = 2x + 7.
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200-80/1 or (as shown on the sheet)
200-80
------------
1
Answer:
120
Step-by-step explanation:
200 - 80 = 120
so 120 / 1 = 120
Answer:
200-80/1 which means (200-80) divided by 1
200 and 80 is in bracket so we solve it first:
200-80=120
now 120/1= 120
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The diagonal of a triangle measures 18.2 inches. The width is 6.7 inches. What is the perimeter of the rectangle? (This has to do with Pythagorean Theorem)
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{18.2}\\ a=\stackrel{adjacent}{6.7}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{18.2^2 - 6.7^2}=b\implies \sqrt{286.35}=b\implies 16.92\approx b[/tex]
m is directly proportional to r squared. when r=2 m=14. work out the value of m when r=12
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"m" proportional to }r^2}{ {\Large \begin{array}{llll} m=kr^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} r=2\\ m=14 \end{cases}\implies 14=k(2)^2 \\\\\\ \cfrac{14}{2^2}=k\implies \cfrac{7}{2}=k\hspace{15em}\boxed{m=\cfrac{7}{2}r^2} \\\\\\ \textit{when r=12, what is "m"?}\qquad m=\cfrac{7}{2}(12)^2\implies m=504[/tex]
Four friends go to a theater and sit in a row. What is the probability that two of them, Nathan and Violetta, are NOT neighbors?
Answer: 3/4 im pretty sure
Step-by-step explanation:
Answer: 1/2
Step-by-step explanation:
When Violetta goes first, their are 4/24 possibilities. Same for Nathan.
The rest are just both 2/24 possibilities. Therefore, the answer is 1/2.
Find the area of the following polygon if AB= 12 cm, AC = 2.4 cm, CE = 6 cm, AD 4.8 cm, CF = GE = 3.6 cm, DH = 2.4 cm. =
Answer:
50.40 cm2
Step-by-step explanation:
Area of the polygon AFGBH = Area of ∆ACF + Area of rectangle FCEG + Area of ∆GEB + Area of ∆ABH
= 3.6 cm2 + 4.32 cm2 + 21.6 cm2 + 6.48 cm2 + 14.4 cm2
= 50.40 cm2
Hence, the required area = 50.40 cm2.
Write in exponential notation.
(-6)(-6)(-6)(-6) =
Answer:
[tex] ( - 6) {}^{4} [/tex]
Step-by-step explanation:
-6 is being multiplied repeatedly 4 times so
[tex]( - 6) {}^{4} [/tex]
One of the humpback whales in a pod has a maximum speed of 690 meters per minute. If
the whale is swimming south at one-third of its top speed, how far will the whale travel in
4 minutes?
Write your answer as a whole number.
690 ÷ 3 = 230
230 × 4 = 960
a whale will go 960 meters
solve for p
4 (p - 9) < -12
Divide both sides by 4. Since 4 is >0, the direction of inequality remains the same.
[tex]\boldsymbol{\sf{p-9 < \dfrac{-12}{4} }}[/tex]
Divide −12 by 4 to get −3.
p - 9 < -3Add 9 to both sides.
p < -3 + 9Add −3 and 9 to get 6.
p < 6Are 36²y²-25y and 11x²y² equivalent?
Answer: No both equations dont have x
Step-by-step explanation:
1. Complete the following transactions and explain how they would appear in your register.
• You open your bank account on April 16 with a tax refund check of $145.00.
• You pay SellUPhone $65.34 on April 18. (Check 794)
• You deposit your paycheck on April 23. ($9.76/hour for 35 hours)
• You buy $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24
using your debit card.
The following banking transaction completed will appear in the register as follows:
DATE COMPUTATION BALANCE ($)
April 16 145.00 145.00
April 18 145.00-65.34=79.66 79.66
April 23 79.66+(9.76)(35)=421.26 421.26
April 24 421.26-(61.32)(1.04)=357.49 357.49
What is a banking transaction?Any money that transfers into or out of your bank account is considered a bank transaction. Cash withdrawals and deposits, cheques, internet payments, debit card charges, wire transfers, and loan payments are all examples of bank transactions.
In most contexts, the term "register" refers to the process of documenting an event, transaction, name, or other information, or an accumulation of recorded data, often comprising historical events, transactions, names, or other information. Alternatively, the phrase can refer to a record of all debit account charges.
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Please help now
Joy buys a shirt using a coupon for 75% off one item. She pays only $15.00 for a shirt. How much
did the shirt cost originally?
Answer:
$60.00
Step-by-step explanation:
15 is 25% of a number. 25 times 4 equals 100. so 15 times four is 60, making 60 the 100%
Work Shown:
x = original price
75% of x = 0.75x = amount saved
x - 0.75x = 0.25x = final price after discount = 15
0.25x = 15
x = 15/0.25
x = 60