Answer:
A. [tex]Claire = 20250[/tex]
B. [tex]Richard = 9350[/tex]
C. Height = 3.2 feet
D. Charges = $760
Step-by-step explanation:
Given
[tex]Claire = 50x^2 + 250[/tex]
[tex]Richard = 40x^2 + 350[/tex]
Solving (a): Claire's 20ft charges
In this case, x = 20
Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(20)^2 + 250[/tex]
[tex]Claire = 50(400) + 250[/tex]
[tex]Claire = 20000 + 250[/tex]
[tex]Claire = 20250[/tex]
Solving (b): Richard's 15ft charges
In this case, x = 15
Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(15)^2 + 350[/tex]
[tex]Richard = 40(225) + 350[/tex]
[tex]Richard = 9000 + 350[/tex]
[tex]Richard = 9350[/tex]
Solving (c): Height which they both charge the same;
This implies that
[tex]50x^2 + 250 = 40x^2 + 350[/tex]
Solving for x [Collect Like Terms\
[tex]50x^2 - 40x^2 = 350 - 250[/tex]
[tex]10x^2 = 100[/tex]
Divide both sides by 10
[tex]x^2 = 10[/tex]
Take square roots of both sides
[tex]x = \sqrt{10}[/tex]
[tex]x = 3.2ft[/tex] (Approximated)
Hence; Height = 3.2 feet
Solving (d): How much they charge when the charge the same amount.
Substitute 3.2 for x in any of the given equation
[tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(3.2)^2 + 250[/tex]
[tex]Claire = 50*10.24 + 250[/tex]
[tex]Claire = 512 + 250[/tex]
[tex]Claire = 762[/tex]
[tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(3.2)^2 + 350[/tex]
[tex]Richard = 40 * 10.24 + 350[/tex]
[tex]Richard = 409.6 + 350[/tex]
[tex]Richard = 759.6[/tex]
The reason for the difference is due to approximation
Hence, they both charge approximately 760
If AC = 40, find the length of JK.
Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
the triangles are all similar, because they have proportional sides and equal angles.
if you assume the smallest, equal part of side to be x
the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .
since they're similar, ratio of their corresponding sides is constant or equal.
[tex] {BK\over BC}={JK \over AC}[/tex]
BK/BC=3/5
and AC=40
so JK = 40*3/5=24
A pyramid has a square base with an area of 169 ft.² what is the perimeter of the base of the pyramid
Answer:
52
Step-by-step explanation:
Square root of 169 is 13.
SInce it is a square all sides are same length. So you could do 13x4 or 13+13+13+13. Both will equal to 52.
The perimeter of the base of the pyramid is 52 square feet.
Given that,
The pyramid contains a square base having an area of 169 square feet.
We know that,
Area of the square = side^2
169 = side^2
So, the side is 13 feet.
So, the perimeter should be
= 4 × sides
= 4 × 13
= 52 feet
Therefore, we can conclude that The perimeter of the base of the pyramid is 52 square feet.
Learn more about the square here: brainly.com/question/14198272
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
The tens digit of a two-digit number is three times greater than the ones digit. The difference between twice the original number and half the number obtained after reversing the digits is 108. What is the original number? Show your work.
Answer:
Now solve these two equations.ull get andwer
The original number will be "63".
Let,
The ten's digit be "x".One's digit be "y".The equation will be:
→ [tex]x=y+3[/tex]...(equation 1)
Original number will be:
→ [tex]10x+y[/tex]
then,
→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]
→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]
→ [tex]40x+4y-10y-x = 216[/tex]
→ [tex]39x-6y=216[/tex]...(equation 2)
By using (equation 1) and (equation 2), we get
→ [tex]39(y+3)-6y=216[/tex]
→ [tex]39y+117-6y=216[/tex]
→ [tex]33y=99[/tex]
→ [tex]y = \frac{99}{33}[/tex]
→ [tex]= 3[/tex]
Now,
[tex]x = y+3[/tex]
[tex]=3+3[/tex]
[tex]=6[/tex]
hence,
The original number will be:
= [tex]10x+y[/tex]
= [tex]10\times 6+3[/tex]
= [tex]60+3[/tex]
= [tex]63[/tex]
Thus the above approach is right.
Learn more:
https://brainly.com/question/285966
I got this wrong please help me get the right answer in the first little box marked in red. thx
Answer:
The inverse is 1/2x +2
Step-by-step explanation:
f(x) = 2x-4
y= 2x-4
To find the inverse
Exchange x and y
x = 2y-4
Solve for y
Add 4 to each side
x+4 = 2y
Divide by 2
x/2 + 4/2 = 2y/2
1/2x +2 = y
The inverse is 1/2x +2
Plz help with this question! What is 1/3 * 3/5 * 5/7 ... * 97/99
Answer:
Step-by-step explanation:
(1/3)*(3/5)*(5/7)*.......*(93/95) * (95/97) * (97/99)
The denominator of each fraction will cancel out the numerator of the next fraction.
Take a close look
Therefore the result is 1/99
HOPE IT HELPS!!
The product of the geometric series is 1/99.
The product is a geometric series with first term 1/3 and common ratio 2/3. The number of terms is 49. The sum of the series is 1/99.
Here's the explanation:
A geometric series is a series where each term is multiplied by a constant value to get the next term. The constant value is called the common ratio.
In this case, the first term is 1/3 and the common ratio is 2/3. This means that each term is multiplied by 2/3 to get the next term.
The number of terms in the series is 49. This means that there are 49 terms in the series, starting with 1/3 and ending with 97/99.
The sum of the series is 1/99. This can be found using the formula for the sum of a geometric series:
S = a × (1 - [tex]r^{n}[/tex]) / 1 - r
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/3, r = 2/3, and n = 49. Substituting these values into the formula, we get:
S = (1/3) × (1 - (2/3)49) / 1 - (2/3) = 1/99
Therefore, the product is 1/99.
Learn more about geometric series here: brainly.com/question/30264021
#SPJ2
What is the area of the trapezoid shown below?
Answer:
180 units
Step-by-step explanation:
In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.
a²+b²=c²
a= 7
b=x
c= 25
7²+x²=25²
49+x²=625
Subtract 49 from both sides
x²=576
x=24
The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.
A= 1/2 (24 x 7)
A=84
Now, we need to find the area of the rectangle.
Formula for area of rectangle: A= bh
A= bh
A= 4 x 24
A= 96
Next, we add the areas of both shapes to get the area of the entire figure.
96+84=180
Area of figure= 180
Answer:
area = 180
Step-by-step explanation:
will make it simple and short
area of a trapezoid = (a + b) h/2
h = sqrt(25² - 7²) = 24
Area = (4 + 11) * 24/2
area = 180
what is the answer to (x+1)(3x+2)
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°
What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.
Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer: D) right 9 units
Step-by-step explanation:
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
a is the vertical stretch or shrink(x, h) is the vertex→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
The graph of y = f(x) will shift right 9 units.
Step-by-step explanation:
If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.
1. An average orange has a mass of 270 grams. What is the mass of 8 oranges in kg?
.
.
2. 1 milliliter of ink can print 50 pages of text. If you had 100 gallons of ink then how many pages could you print? 1 gallon = 3.79L
.
.
3. If you are driving 55 miles per hour, how many feet per second are you traveling?
Convert hours to minutes:
Convert minutes to seconds: Convert miles to feet:
.
.
4. Ivan’s car has 40 L gas tank. If gas costs $3.67 per gallon how much does it cost to fill her tank?
1 L = .264 gallons
Convert liters to gallons: Calculate the cost of gasoline:
.
.
5. A child requires a 5 mL dose of medicine each day. How many days would a liter of this medicine last?
Answer:2.the answer is 189,250pages
Step-by-step explanation:
1L=1000ml
3.785=?3785
1ml=50pages
3785ml=?
The answer is 189,250
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
1 person = 40 min = 1 bag, 4 person = ? min = 1575 bags
Answer:
15 750 minStep-by-step explanation:
4 person = 1575 bags
1 person = 1575:4 = 393.75 bags
40 min = 1 bag
393,75 bags = 40 min•393,75 = 15 750 min
The population of fruit flies tripled every day and the population today is 200 fruit flies.
a) Write an equation modeling the growth in the population of fruit flies.
b) What was the population of fruit flies 3 days ago?
Answer:
Equation = 600nNumber of fruit flies after 3 days = 1800 fruit fliesStep-by-step explanation:
Given:
Number of fruit flies = 200
Rate of growth = 3 times per day
Find:
A . Equation
B . Number of fruit flies after 3 days
Computation:
A . Equation = 3n(200)
Equation = 600n
B. Number of fruit flies after 3 days
Number of fruit flies after 3 days = 600(3).
Number of fruit flies after 3 days = 1800 fruit flies
Evaluate the function below at x=7. Then enter your solution rounded up to 2 decimal places. 1500•1.09^x
Answer:
Value of the function will be 2742.06
Step-by-step explanation:
Given function is,
f(x) = 1500(1.09)ˣ
By substituting the value of x we can find the value of the given function.
For x = 7,
f(7) = 1500(1.09)⁷
= 1500(1.828)
= 2742.0587
≈ 2742.06
Value of the function will be 2742.06
Answer ASAP, will give brainliest!!
Answer:
Step-by-step explanation:
77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)
find the sum of partial fraction for x^4/(x-1)(x²-4)
Answer:
see attachment
Step-by-step explanation:
Write an expression to represent the product of 6 and the square of a number plus 15.
Answer:
6x^2 + 15
Step-by-step explanation:
We don't know what the square of a number is, so we represent it as x^2
The first part tells us to find the product of 6 and the square of a number, so
6x^2
The second part tells us to add 15 so,
6x^2 + 15
The expression that should be represented is [tex]6x^2 + 15[/tex]
Given that
The product of 6.The square of number + 15.Based on the above information,
Let us assume the number should be x
So, from the above information, the expression should be [tex]6x^2 + 15[/tex]
Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]
Learn more about the equation here:brainly.com/question/21105092?
What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
Four witches are making a brew.Patricia puts in x frogs legs.sheila puts in five more than patricia.Anne puts double the amount that Sheila adds,and Winifred adds three times the number Sheila adds.
write down an algebraic expression for:
Sheila. Anne. Winifred
Answer:
see explanation
Step-by-step explanation:
Given Patricia puts in x frogs legs, then
Sheila puts in x + 5 ( 5 more than Patricia )
Anne puts in 2(x + 5) ( double the amount of Anne )
Winifred puts in 3(x + 5) ( three times the number of Sheila )
Write 3.6 as a percent.
Answer:
360%
Step-by-step explanation:
You have to multiply 3.6 by one hundred to get the percentage. When you multiply decimals by numbers that are multiples of ten, you move the decimal place to the right of the number by the number of zeroes that is in your number. Sorry if its confusing.
Examples: 3.76 * 100 = 376. You move the decimal to the right two spaces
46.263 * 1000 = 46263. You move the decimal to the right three spaces. Hope you understand.
4x3+ 13x2 + 5x- 4 is divided by x+ 1?
Answer:
The quotient to this equation is 4x² + 13x + 1
Step-by-step explanation:
When we divide exponents, we subtract the exponential numbers.
4x³ + 13x² + 5x - 4 / x + 1
Now, we divide. For this problem, we are only dividing the like terms of x because anything divided by 1 will equal to itself.
4x² + 13x + 5 - 4
Now, we combine like terms.
4x² + 13x + 1
I need help on this can someone help
Answer:
1:3
Step-by-step explanation:
[tex]3:9\\= 1: 3[/tex]
Answer:
1 : 3
Step-by-step explanation:
pears : apples
3 9
Divide each side by 3
3/3 9/3
1 : 3
how many are 9 raised to 2 ???
Answer:
[tex]\boxed{81}[/tex]
Step-by-step explanation:
9 raised to 2 is
=> [tex]9^2[/tex]
=> 9 * 9
=> 81
A sprinter run 400 meter in 54 second.what about s the runner's average running rate in meter per second?round to the nearest tenth
Answer:
7.4
Step-by-step explanation:
400 ÷ 54 =7.407407...
7.407407... rounded to the nearest tenth is 7.4
I hope this helps... and plz mark me brainliest!!!
Type the correct answer in the box. Use numerals instead of words.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
5.75 cm
The area of the shape is
square centimeters.
Answer:
35 cm squared
Step-by-step explanation:
Triangle area = bxh 2 = 5.75 x 8 / 2 = 23
Trapezium Area = a+b /2 x h = 8 + 4 /2 x 2 = 12
23 + 12 = 35
Hope that helped!!! k
HE SODA MACHINE
The soda machine at your school offers several types of soda. There are two buttons for your favorite drink, Blast,
while the other drinks (Slurp, Lemon Twister, and Diet Slurp) each have one button.
Describe the input and output of this soda machine.
While buying a soda, Ms. Whitney pushed the button for Lemon Twister and got a can of Lemon Twister.
Later she went back to the same machine, again pushing the Lemon Twister button, but this time she got a can
of Blast. Is the machine functioning consistently? Why or why not?
BLAST
BLAST
BLUSO
ooo
Students, write your resnonsel
Answer:
yes and no
Step-by-step explanation:
if a machine is work a lot lot LOT, then it might be jamed
or the teacher might have accidentally pressed blast and you might have not seen the buttons correctly
( also i am not a student of yours )
This table represents a quadratic function.
What is the value of “a” in the function’s equation?
A. -1/2
B. 1/2
C. 2
D. 1
Answer:
I think 1/2 is the ans
Step-by-step explanation:
quadratic function equation
would help
Please help I did the first 2 already.
The answer to C is 1.5 or 3/2
Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2
