Answer:
Width: 4
Length: 6
Step-by-step explanation:
We can create a systems of equations for this problem, assuming W is width and L is length.
W = 3L-14
WL = 24
We can substitute W into the equation.
(3L-14)L = 24
3L²-14L = 24
3L² - 14L - 24 = 0
(3L+4)(L-6)=0
L = 6
Now we can find W by substituting L into the equation.
[tex]6\cdotw=24\\w = 4[/tex]
Hope this helped!
write the fraction for each of the following do number 3 and 4 thanks
Answer:
7
Step-by-step explanation:
Interpret the average rate of change of –14/3 that you found previously. What does this mean in terms of the waterslide, from x = 0 to x = 15?
Answer:
Solution: The average rate of change of represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
Explanation:
The rate of change shows the change in first variable with respect to change in second variable.
If the rate of chang is given by it means second variable is decrease by 14 if the first variable increase by 3.
In the context of water slide it shows that the vertical height of slide is decreased by 14 units as we cover the distance of 3 units.
If we cover the distance from x = 0 to x = 15, it means we cover the distance of 15 units.
Let the vertical height of the slide covered from x = 0 to x =15 be y.
It means when distance increased by 15 units the height of slide decreased by y units.
So rate of change = .
It is given that the rate of change is .
Equate both equations.
Therefore, the average rate of change of represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
Please Help ;-;" :Mr. Gordon’s science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type. ( Type 0=9/20) (Type A=41/100) (Type B=1/10) (Type AB=1/25) What is the probability that three students selected randomly from the class will have A, B, and AB blood, respectively? Explain how you would solve this problem.
Answer:
A = 6.9%
B = 0.1%
AB = 1.6%
Step-by-step explanation:
A=0.41=41/100
B=0.1=1/10
AB=0.25=1/25
41/100³ = 0.41³ = 0.069 = 6.9%
1/10³ = 0.1³ = 0.001 = 0.1%
1/25³= 0.25³ =0.016 = 1.6%
I did to the power of 3 because the equation just looks like this
41/100 x 41/100 x 4/100
this is because you are multiplying each number by the amount of students selected.
Find the lateral area of this pyramid
whose base is an equilateral triangle. Its
slant height is 12 in. and the length of each
side of the triangular base is 5
Answer:
90 in²
Step-by-step explanation:
The lateral area can be found using the formula ...
LA = (1/2)Ph
where P is the perimeter of the base and h is the slant height. For your dimensions, the lateral area is ...
LA = (1/2)(3×5 in)(12 in) = 90 in²
The lateral area is 90 square inches.
EBES
Given: f(x) = x2-3 and g(x) = x+1
The composite function of is
DONE
Answer:
A composite function means that you are evaluating one function into another function.
So, fog(x) can be written as:
f(g(x))
and gof(x) = g(f(x))
this means that instead of the variable "x", we are evaluating the functions with other function.
Let's solve this:
f(x) = x^2 - 3
g(x) = x + 1
then:
> gof(x) =g(f(x)) = f(x) + 1 = (x^2 - 3) + 1 = x^2 - 2
> fog(x) =f(g(x)) = g(x)^2 - 3 = (x + 1)^2 - 3 = x^2 + 2x + 1 - 3 = x^2 + 2x - 2
Determine whether the lines given by the vector equations r1=2i + 2j + 3k + s(i + 3j + k) and r2=2i + 3j + 4k + t(i + 4j + 2k) intersect. If they intersect, give the coordinates of their point of intersection.
Answer:
i -j +2k . . . at s=t=-1
Step-by-step explanation:
For the lines to intersect, there must be values of s and t that make the coordinates of r1 equal to those of r2.
Equating i coefficients, we have ...
2 +s = 2 +t
Equating j coefficients, we have ...
2 +3s = 3 +4t
Equating k coefficients, we have ...
3 +s = 4 +2t
The first equation tells us s = t. Using t = s in each of the other two equations, they become ...
2 +3s = 3 +4s ⇒ s = -1
3 +s = 4 +2s ⇒ s = -1
Then the point of intersection is where s = t = -1. That point is ...
(2 +s)i +(2 +3s)j +(3 +s)k = (2 -1)i +(2 -3)j +(3 -1)k
= i -j +2k . . . . the point of intersection
How many pumpkins are in Leonard's patch?
Answer:
You can do 4+5+8+6+2.
and It is 25.
so, 25 pumpkins!
Step-by-step explanation:
plz give me brainliest.
thank you and have a nice day!
Answer:
[tex]\huge\boxed{ 25\ pumpkins}[/tex]
Step-by-step explanation:
By looking at the given histogram and determining the no. of pumpkins, we get:
Number of Pumpkins = 4 + 5 + 8 + 6 + 2
=> 25 pumpkins
Kim is building a triangular dog pen. She will use an existing 10 m wall as one side. She will then build a fence going out at a 45°
angle on one side of the wall and a 65° angle on the other side. How much chain-link fence is needed to complete the fence?
es )
Answer:
17.2 ft
Step-by-step explanation:
The angle that the fence makes opposite the wall is ...
180° -45° -65° = 70°
The law of cosines can be used to find the lengths of fence needed.
The fence opposite the 45° angle will have a length of ...
short side = (10 ft)·sin(45°)/sin(70°) = 7.525 . . . feet
The fence opposite the 65° angle will have a length of ...
long side = (10 ft)·sin(65°)/sin(70°) = 9.645 . . . feet
Then the total length of fence required is ...
7.525 ft +9.645 ft = 17.170 ft
About 17.2 feet of chain-link fence is required to complete the enclosure.
_____
We have assumed there is no chain-link fence along the 10 ft wall.
_____
The Law of Sines tells you that for sides a, b, c and opposite angles A, B, C, you have ...
a/sin(A) = b/sin(B) = c/sin(C)
For some given side 'a' and opposite angle A, the other two sides can be found from their opposite angles as ...
b = sin(B)·a/sin(A)
c = sin(C)·a/sin(A)
6(y + 5) = 15y + 12
What value of y makes the equation true
Answer:
[tex]\boxed{y=2}[/tex]
Step-by-step explanation:
[tex]6(y + 5) = 15y + 12[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]6y+30=15y+12[/tex]
[tex]\sf Subtract \ 12 \ and \ 6y \ from \ both \ sides.[/tex]
[tex]6y+30-12-6y=15y+12-12-6y[/tex]
[tex]30-12=15y-6y[/tex]
[tex]18=9y[/tex]
[tex]\sf Divide \ both \ sides \ by \ 9.[/tex]
[tex]\displaystyle \frac{18}{9} =\frac{9y}{9}[/tex]
[tex]2=y[/tex]
Which point below is not on the graph of h(x) ^3√x+64 = ? (65, 5) (-37, 3) (-72, -2) (-64, 0)
Answer:
(-37, 3)
Step-by-step explanation:
Find the average rate of change of g(x)= – x2 over the interval [ – 8, – 2]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.
Answer:
[tex]Average\ Rate = 10[/tex]
Step-by-step explanation:
Given
[tex]g(x) = -x^2[/tex]
[tex](-8,-2)[/tex]
Required
Determine the average rate of change;
Average rate of change is calculated as thus;
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]
Where
[tex](a,b) = (-8,-2)[/tex]
i.e. a = -8 and b = -2
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
Calculating g(-2)
Substitute -2 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-2) = -(-2)^2[/tex]
[tex]g(-2) = -4[/tex]
Calculating g(-8)
Substitute -8 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-8) = -(-8)^2[/tex]
[tex]g(-8) = -64[/tex]
Substitute values for g(-2) and g(-8)
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]
[tex]Average\ Rate = \frac{60}{6}[/tex]
[tex]Average\ Rate = 10[/tex]
Hence, the average rate of change is 10
PLSSS HELP PLSSSSSSSS MARKING BRAINLIST QUESTION BELOW
Answer:
Hey there!
CarMart's rate of sales is 11 cars per day.
Winston's rate of sales is 10 cars per day.
Compared with CarMart, Winston is selling fewer cars per day.
Compared with CarMart, Winston started with 2 fewer cars.
Let me know if this helps :)
Answer:
CarMart's rate of sales is 11 cars in a day.
Winston's rate of sales is 10 cars in a day.
Compared with CarMart, Winston is selling less cars in a day.
Compared with CarMart, Winston started with two fewer cars.
Step-by-step explanation:
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!
Find the output, h, when the input, x, is -18.
h = 17 + x/6
Answer:
14
Step-by-step explanation:
The expression is h = 17 + x/6
Replace x by -18
● h = 17 + x/6
● h = 17 + (-18/6)
● h = 17 +(-3)
● h = 17 -3
● h = 14
So the output when x = -18 is 14
h=14
h=17+18/6
h=17+-3
h=17-3
h=14
Plzzz help I’ll give brainlest
Answer:
cos y = r/q
Step-by-step explanation:
If we know sin y = 7/q, then we know that the base is 7 and the hypotenuse is q due to sine = opposite/hypotenuse.
If we know tan y = 7/r, then we know that the base is 7 and the right side is r due to tan = opposite/adjacent.
Cos = adjacent / hypotenuse
So cos y = r/q, because the right side is r and the hypotenuse is q.
Answer:
ignore sorry
Step-by-step explanation:
Find the term that must be added to the equation x2+4x=1 to make it into a perfect square
The x term has a coefficient of 4. Take half of this to get 2, then square it to get 4. This is the value we add to both sides to get x^2+4x+4 = 5. Note how x^2+4x+4 factors into (x+2)^2
---------
Another example: Let's say we started with x^2+6x = 1. To complete the square, we need to add 9 to both sides. I start with 6 (the x coefficient) and cut that in half to get 3, then I squared that to get 9. So we add 9 to both sides getting x^2+6x+9 = 10 which becomes (x+3)^2 = 10
The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.
What is Quadratic equation?In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax^2 term.
For example
Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.
Given :
x²+4x=1
as, the x has coefficient 4.
so half the coefficient of x and add and subtract the square of the remaining.
x²+4x + 2 ² - 2² =1
Now, make the whole square term
x²+4x + 2 ² - 4 - 1=0
( x + 2)² -5= 0
Learn more about quadratic equation here:
https://brainly.com/question/2263981
#SPJ2
Which mean the same as 60%? Check all that apply
a.3/5
b. 0.06
c. 0.60
d. 6/10
e. 6/100
Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4 How much more is the rate of change of function A than the slope of function B? 3 6 2 9
Answer:
6
Step-by-step explanation:
Function A
y = 9x + 4
Function B
y = max+b
m = 3 and b = 4
y = 3x+4
The difference in the slopes is 9-3 = 6
Answer:
6
Step-by-step explanation:
The two functions are A and B.
A's equation is khown
● y =9x + 4
B is also khown. We should only gather tge information.
● the rate of change is 3
●the y-intercept is 4
So B's equation is:
● y = 3x + 4
3 is the rate of change wich is khown as the slope.
Divide A's slope by B's slope to khow how much A's slope is bigger than B's.
● 9/3 = 3
Substract 3 from 9 and you get the difference 9-3= 6
Solve for x. Just give the equations.
15.
[tex]FH=2\cdot UH\\\\5x-7=2\cdot19\\\\5x=38+7\\\\5x=45\quad|:5\\\\\boxed{x=9}[/tex]
16.
[tex]KU=UM\\\\3x+3=4x-4\\\\4x-3x=3+4\\\\\boxed{x=7}[/tex]
Answer:
15) x=9 16) x=7
Step-by-step explanation:
19(2)=5x-7
38=5x-7
5x=38+7
5x=45
x=45/5
x=9
-----------------
3x+3=4x-4
3=4x-3x-4
3=x-4
x=3+4
x=7
What is the determinant of k= 6 8 0 3
Answer:
18
Step-by-step explanation:
What is the number of real solutions? 2q^2−8q+4=0
Answer:
there's two
Step-by-step explanation:
q=(4-√24)/2=2-√6=-0.449
and
q=(4+√24)/2=2+√6=4.449
Find the greatest possible value for a+b+c+d if b is a positive integer and a,b,c,d satisfy the system of equations
a+b=c
b+c=d
c+d=a
Answer:
[tex]a+b+c+d = -5\cdot b[/tex]
Step-by-step explanation:
The given system of equations is now reduced:
1) [tex]a+b = c[/tex], [tex]b+c = d[/tex], [tex]c+d=a[/tex], [tex]b > 0[/tex] Given
2) [tex]a = c+d[/tex] By 1)
3) [tex](c+d)+b=c[/tex] 2) in 1)
4) [tex]d = b + c[/tex] By 1)
5) [tex][c+(b+c)]+b = c[/tex] 4) in 3)
6) [tex]2\cdot b + 2\cdot c = c[/tex] Algebra
7) [tex]c = -2\cdot b[/tex] Algebra
8) [tex]d = -b[/tex] 7) in 4)/Algebra
9) [tex]a = -3\cdot b[/tex] 7) and 8) in 2)/Algebra
10) [tex]a+b+c+d = -5\cdot b[/tex] 9), 1), 7) and 8)/Algebra/Result
Which of the following statements is true for a function with equation f(x) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.
Answer:
The graph has y-intercept (0,5) and increases with a constant ratio of 3
Step-by-step explanation:
The value of the function when x=0 is 5·3^0 = 5, so the y-intercept is (0, 5).
Each increase of 1 in x causes the function value to increase by a factor of 3, so the 'constant ratio' is 3. (That is the base of the exponential term.)
-15 POINTS- A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 4cm wide, and 12cm tall. If the company used 3840 cm³ of wax, how many candles did they make?
Answer:
16 candles
Step-by-step explanation:
first you must know what the volume of the rec prism is so multiply the b*h*w and you will have 240. divide 3840 by 240 and you will have 16
Answer:
16
Step-by-step explanation:
We need to find out the area of each candle. We can do this by multiplying all the lengths out and getting 240 [tex]cm^3[/tex] per candle. Now we divide 3840, the total amount of wax used, by 240 the amound needed for one candle, and we get 16. This means 16 candles were made.
Evaluate the following expression: 2 + 1 x 2 *Please help i don't have that much time*
Answer:
The answer to your question is 4.
Step-by-step explanation:
Evaluating and simplifying the expression comes to a result of four using the order of operations. Hope this helps you!
(k) 1 + tan 4A . tan 2A = sec 4A.
Please help me.... question from multiple angle of trigonometry!!!!!
it was a long proof...
follow the caption and steps and you'll understand it
proved...
Step-by-step explanation:
this is too easy method to solve this problem
Drag each value to the correct location on the equation. Each value can be used more than once.
Answer:
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
Step-by-step explanation:
If a quadratic equation is in the form of ax²+ bx + c = 0
Then the roots of this quadratic equation can be obtained by,
1). Factoring the expression.
2). By quadratic formula.
If we use the method to get the value of x or roots of the equation,
x = [tex]\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
where a, b and c are the coefficients used in the quadratic equation.
14. You bought shoes for $60. They were on sale for 40% off their original price.
a. Write a proportion to solve for the original price of the shoes.
b. Solve the proportion in part (a).
Two joggers start from different locations and simultaneously begin heading toward each other. One of the joggers jogs 19mph, while the other jogs 17mph. If the two joggers are 324 miles apart how many hours will it take before they meet?
Answer:
It would take 9 hours for them to meet.
Step-by-step explanation:
Total distance covered by both per hour: 19+17=36
The total time to go 324 miles for them: 324/36=9
A park is mapped on a coordinate plane, where C1, C2, C3, and C4 represent chairs and SW1, SW2, and SW3 represent swings. How far is C2 from SW1? A. 89−−√ units B. 145−−−√ units C. 97−−√ units D. 41−−√ units
Answer:
Option (B)
Step-by-step explanation:
To calculate the distance between C2 and SW1 we will use the formula of distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
d = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }[/tex]
Coordinates representing positions of C2 and SW1 are (2, 2) and (-6, -7) respectively.
By substituting these coordinates in the formula,
Distance between these points = [tex]\sqrt{(-6-2)^2+(-7-2)^2}[/tex]
= [tex]\sqrt{(64)+(81)}[/tex]
= [tex]\sqrt{145}[/tex] units
Therefore, Option (B) will be the correct option.
Find the length of MK¯¯¯¯¯¯ A. 7 B. 47 C. 19 D. 34
Answer:
19
Step-by-step explanation:
JH = 47 (70 - 23)
HM = 23
MK = 19 (42 - 23)
KU = 34 (81 - 47)
UC = 7 (47 - 40)
CN = 40
Answer:
19
Step-by-step explanation:
HM + MK = HK
23 + MK = 42
Subtract 23
MK = 42-23
MK =19
