Answer:
r=3
Step-by-step explanation:
24π=2π(r^2+r)
Divide each side by 2 pi
24π/2π =2π/2π(r^2+r)
12 = r^2 +r
Subtract 12 from each side
12-12 = r^2 +r -12
0 = r^2 +r -12
Factor
What number multiply to -12 and add to 1
4*-3 = -12
4-3 = 1
0= (r+4) (r-3)
Using the zero product property
r+4 =0 r-3 =0
r+4-4 =0-4 r-3+3=0+3
r = -4 r = -3
Assuming r is the radius, r must be positive
r =3
Help again Please ..thank you whoever helps I’ll mark u Brainliest :)
Answer:
2
Step-by-step explanation:
The median is the middle. The middle of 5 numbers is the third number. the list goes through 12235 so the median is 2
Use the quadratic formula to solve the equation. 2x^2-6x+1=0 Enter your answers, in simplified radical form, in the boxes.
x=__or x=
please send me image and explain work
Answer:
(3 (pm) sqrt(7))/2
Step-by-step explanation:
First step: Identify a,b, and c
a=2
b=-6
c=1
Second step: Find b^2-4ac (this is called the discriminant-I will call this D)
(-6)^2-4(2)(1)=36-8=28
Third step: Find the square root of the discriminant aka sqrt(D)
sqrt(28)
Let's see if we can simplify sqrt(28)
Here is there a factor of 28 that is a perfect square? How about 4? Yep!
sqrt(28)=sqrt(4)sqrt(7)=2sqrt(7).
Fourth Step: What is -b? If b=-6 then -b=6.
Fifth step: What is 2a? 2(2)=4
So the formula is
x=(-b (pm) sqrt(D))/(2a)
or
x=(step4 (pm) step 3)/(step 5)
x=(6 (pm) 2sqrt(7))/4
Simplify
x=(3 (pm) sqrt(7))/2
*pm means plus or minus
*sqrt( ) means square root of the number that follows in the ( )
Answer:
Just took it!
Step-by-step explanation:
the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?
Answer:
the domain is from -5 to infinity
Step-by-step explanation:
f(x+5)+3=√x+5 +3
x+5>0
x>-5
the domain is from -5 to infinity
Answer:
A. {x | x > –5}
the greater than sign should be greater than or equal to
What value of c makes the polynomial below a perfect square?
x^2+14x+c
c=
A) 196
B) 49
C) 7
D) 28
Answer:
The value for c is B. 49
James wants to build a wooden barrel to hold rain water to use for irrigation. He wants the height of the barrel in feet to be 4 less
than the area of the base in square feet. He also wants the area of the base in square feet to be equal to its perimeter in feet. He
also needs to place a pump inside the barrel to move the collected water. After the pump is put inside the barrel, he needs it to
still hold at least 90 cubic feet of water
The cost for the materials to build the barrel will be 58 per square foot. Since the barrel is meant to catch rain water, he will not
need a top. The cost of the pump is proportional to its volume. For each cubic foot of volume that the pump takes up the cost
will be 550 James can only afford to spend up to $1,100 on this project
If x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet, then which
of the following systems of inequalities can be used to determine the dimensions of the barrel and the volume of the pump?
Answer:
Step-by-step explanation:
To create a system of inequalities, write an inequality to model each condition that must be satisfied in the given situation.
It is given that x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet.
Write an inequality to represent the amount of water that the barrel needs to hold after the pump is inserted. To find the volume of the barrel, multiply the area of the base by the height of the barrel. Then subtract the volume that will be taken up by the pump from that amount.
x(x-4) - y ≤ 90
To find the cost of the supplies for the barrel, find the surface area by multiplying the perimeter of the base by the height of the barrel and then adding the area of the base. Since there is no top, the area of the base only needs to be added once. Then, multiply the cost per square foot by the surface area.
To find the cost of the pump, multiply the cost per square foot of the pump by its volume.
Write an inequality representing the total cost. The cost must be less than or equal to $1,100.
8(x(x-4)+x) + 50y ≤ 1,100
Combining both of the inequalities gives the following system of inequalities.
x(x-4) - y ≤ 90
8(x(x-4)+x) + 50y ≤ 1,100
Answer:
The answer is
x(x-4) - y GREATER THAN OR EQUAL TO 90
8(x(x-4) + x) +50y LESS THAN OR EQUAL TO 1,100
Step-by-step explanation:
You can hear the following number:
500 million, 900
How do you write it using digits?
Answer:
Using digits it would look like 5,000,900
2 Points
Each exterior angle of a regular polygon measures 24°. How many sides
does the polygon have?
O A. 15
O B. 24
O C. 16
O D. 18
SUBMIT
The number of the sides of the polygon will be 15. Then the correct option is A.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Each exterior angle of a regular polygon measures 24°.
Then the number of the sides of the polygon will be
Let n be the number of the sides. Then we have
360° / n = 24°
n = 360° / 24°
n = 15
Then the number of the sides of the polygon will be 15.
Then the correct option is A.
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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
–2.2, –11.8, –19.8
–3, –11.8, –25
–3, –9.6, –22.8
0, –6.6, –19.8
Answer:
–3, –9.6, –22.8
Step-by-step explanation:
Given rule is:
[tex]A(n) =-3+(n-1)(-2.2)[/tex]
So,
For first term:
[tex]A(1) =-3+(1-1)(-2.2)\\A(1) = -3 +0\\= 0[/tex]
For fourth term:
[tex]A(4) =-3+(4-1)(-2.2)\\=-3+(3)(-2.2)\\=-3+ (-6.6)\\=-3-6.6\\= -9.6[/tex]
For tenth term:
[tex]A(10) =-3+(10-1)(-2.2)\\=-3+(9)(-2.2)\\=-3+ (-19.8)\\=-3-19.8\\= -22.8[/tex]
The first, fourth and tenth terms are -3, -9.6 and -22.8 respectively.
So, third option is correct ..
Given a cone with a volume of 288, and height 7 in., find the base radius of the cone. Use 3.14 for pi. Round your answer to the
tenths place.
Answer:
The radius of the base is [tex]r=6.3\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=288\ in^{3}[/tex]
[tex]h=7\ in[/tex]
[tex]\pi=3.14[/tex]
substitute and solve for r
[tex]288=\frac{1}{3}(3.14)r^{2} (7)[/tex]
[tex]864=(3.14)r^{2} (7)[/tex]
[tex]r^{2}=864/[(3.14)(7)][/tex]
[tex]r=6.3\ in[/tex]
Which equation can be used to calculate the area of the shaded triangle in the figure below?
Answer:
A
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 14 and h = 4, hence
A = [tex]\frac{1}{2}[/tex] (14 × 4) = 28
What is half of a number z
Answer:
[tex]\frac{1}{2} z[/tex]
Step-by-step explanation:
Factorise:b+√b-12
An easy one.
Answer:
Step-by-step explanation:
If you let b = x^2 the problem becomes a whole lot easier. Note that x = √b
x^2 + x - 12
Now factor this trinomial.
(x + 4)(x - 3)
Now put b back into the equation
(√b + 4)(√b - 3)
Christopher has six times as much money as Michael. If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael. How much money do Christopher and Michael have before and after earning $60 and $80, respectively?
Answer:
360 and 60.
Step-by-step explanation:
Let Christopher earns x amount of money and y be money earned by Michael.
Firstly, Christopher has six times as much money as Michael so,
x=6y........ (i)
If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael so,
x+60=3(y+80)
From (i),
6y +60= 3(y+80)
3(2y+20)=3(y+80)
2y+20=y+80
2y-y=80-20
y=60
Substituting value of y in equation (i),
x=6×60=360.
Therefore, Christopher earned 360 and Michael earned 60.
Final answer:
Initially, Michael has $60, and Christopher has $360. After Michael earns $80 and Christopher earns $60, Michael will have $140, and Christopher will have $420.
Explanation:
Let's denote Christopher's initial amount of money as C and Michael's initial amount of money as M.
According to the given information, Christopher has six times as much money as Michael: C = 6M.
When Michael earns $80, and Christopher earns $60, Christopher will then have three times as much money as Michael: C + $60 = 3(M + $80).
Now we can solve these two equations together:
C = 6M
C + $60 = 3(M + $80)
Substitute the expression from the first equation into the second equation:
6M + $60 = 3(M + $80)
6M + $60 = 3M + $240
Combine like terms:
6M - 3M = $240 - $60
3M = $180
Divide both sides by 3:
M = $60
Use the value of M to find C:
C = 6M = 6 × $60
C = $360
Now, adding their respective earnings:
Michael's new total: $60 + $80 = $140
Christopher's new total: $360 + $60 = $420
The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x +1
f(x) = x2 -3x - 3
f(X) = x2 + 6x + 3
f(x) = x2 - 6x - 1
f(x) = x² - 6x - 1
To find the axis of symmetry, use the axis of symmetry formula: -b\2a, according to the Quadratic Equation y = Ax² + Bx + C. You understand?
Answer:
[tex]f(x) = x^2 - 6x -1[/tex]
Step-by-step explanation:
To find axis of symmetry we use formula
[tex]x=\frac{-b}{2a}[/tex]
[tex]f(x) = x^2 + 3x +1[/tex]
a=1, b=3
[tex]x=\frac{-3}{2}[/tex]
[tex]f(x) = x^2 -3x - 3[/tex]
a=1, b=-3
[tex]x=\frac{3}{2}[/tex]
[tex]f(x) = x^2 + 6x + 3[/tex]
a=1, b=6
[tex]x=\frac{-6}{2}=-3[/tex]
[tex]f(x) = x^2 - 6x -1[/tex]
a=1, b=-6
[tex]x=\frac{6}{2}=3[/tex]
21. Which property is represented by the
equation below?
2/3 x 3/2=1
A. Multiplicative Inverse Property
B. Multiplicative Identity Property
C. Distributive Property
D. Commutative Property of
Multiplication
Answer:
A. Multiplicative Inverse Property
X=1
Step-by-step explanation:
First, you do is multiply fractions from left to right.
[tex]\frac{2*3}{3*2}x=1[/tex]
Then, you can cancel the fraction out.
Common factor term of 2.
[tex]=\frac{3}{3}[/tex]
Divide the numbers.
[tex]\frac{3\div3=1}{3\div3=1}=1[/tex]
[tex]x*1=1[/tex]
X=1 is the correct answer.
Multiplicative Inverse Property is the correct answer.
What is the solution for this equation 3(80-9x)=x-96
Answer:
X=12
Step-by-step explanation:
3(80-9x)=X-96 Distribute 3 through the parenthesis
240-27x=x-96
Move the variable to the left side and change its sign
Move constant to the right side and change its sign
-27x-x+240=-96
collect the like terms
calculate the difference
-28x=-336
Divide both sides of the equation by -28
x=12
Working out diameter and radius from circumference. How.
Answer:
d = 28 cm
r = 14 cm
Step-by-step explanation:
Circumference = Pi × Diameter
( Divide both sides by Pi )
Circumference ÷ Pi = Diameter
28 ÷ π = Diameter
Diameter = 28
Radius = Half the diameter
28 ÷ 2 = 14
Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?
AB
CD
FG
HJ
Answer:
HJ
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
so
The slope of the line that is parallel to a line that has a slope of 3 is equal to 3
Verify the slope of the blue and red line , because their slopes are positive
Blue line
we have
C(-3,0),D(3,2)
The slope m is equal to
m=(2-0)/(3+3)
m=2/6
m=1/3
Red line
we have
H(-1,-4),J(1,2)
The slope m is equal to
m=(2+4)/(1+1)
m=6/2
m=3
therefore
The answer is the red line HJ
In the word "COURSE” what is the probability of choosing a vowel?
Answer:
3 vowel in the word and theres 6 letters so 50% 3/6
Step-by-step explanation:
Can someone please help me out
Answer:
3 + 3 + 12 + 8 + 8Step-by-step explanation:
We have:
two triangles with base b = 6 and height h = 1
two rectangles with length l = 4 and width w = 2
one reactangel with length l = 6 and width w = 2.
The formula of an area of a triangle:
[tex]A_T=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_T=\dfrac{(6)(1)}{2}=3[/tex]
The formula of an area of a rectangle:
[tex]A_R=lw[/tex]
Substitute:
[tex]A_{R_1}=(4)(2)=8\\\\A_{R_2}=(6)(2)=12[/tex]
The surface area of the prism:
[tex]S.A.=A_T+A_T+A_{R_1}+A_{R_1}+A_{R_2}[/tex]
[tex]S.A.=3+3+8+8+12[/tex]
What is 4 divided by 1/3 write in fractions
Answer:
the answer is 12.
Step-by-step explanation:
the explanation is in the image above
Hope this helps
Use a transformation to solve the equation. w/4 = 8 can you also leave a detailed explanation on how this equation = 32
Answer:
w=32
Step-by-step explanation:
w/4 = 8
4/1 * w/4 = 8*4
w=32
What is the simplified form of x+6/2x+5 + x+5/x+3
Answer:
Step-by-step explanation:
6/2 evaluates to 3
Multiply x and 3
Multiply x and 1
The x just gets copied along.
The answer is x
x
6/2*x evaluates to 3x
x+6/2*x evaluates to 4x
x+6/2*x+5 evaluates to 4x+5
4x + x = 5x
The answer is 5x+5
x+6/2*x+5+x evaluates to 5x+5
To divide 1 by x
The x just gets copied along in the denominator.
The answer is
5/x evaluates to
The answer is
x+6/2*x+5+x+5/x evaluates to
5 + 3 = 8
The answer is
B
x+6/2*x+5+x+5/x+3 evaluates to
The final answer is
B
What is the solution to log 25x = 3?
Answer: x=40
Step-by-step explanation:
The solution to log (25x) = 3 is 40. This is calculated by using log rules.
What are the rules of a logarithmic function?A function that has log terms is said to be a logarithmic function.
Some of the rules for solving log functions are as follows:
The basic form of a logarithmic function is [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex].Product rule: [tex]log_b(x)+log_b(y)=log_b(xy)[/tex]Quotient rule: [tex]log_b(x)-log_b(y)=log_b(\frac{x}{y})[/tex]Power rule: [tex]log_b(x)^n=nlog_b(x)[/tex]Identity rule: [tex]log_b(b)=1[/tex] where [tex](b^1=b)[/tex]Finding the solution for the given function:Given that,
log (25x) =3
Using basic form [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex]
Here base b=10, m=25x and n=3
Then,
log (25x) =3
⇒ [tex]25x = 10^3[/tex]
⇒ 25x = 1000
⇒ x = 1000/25
∴ x = 40.
Hence the solution of the given function is 40.
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-5=c/7 solve equation
Answer:
c=−35
Step-by-step explanation:
Let's solve your equation step-by-step.
−5=
c
7
Step 1: Simplify both sides of the equation.
−5=
1
7
c
Step 2: Flip the equation.
1
7
c=−5
Step 3: Multiply both sides by 7.
7*(
1
7
c)=(7)*(−5)
[tex]\frac{c}{7} = -5[/tex]
***I switched the order of c/7 and -5. It means the same thing, but I just find it easier this way
To solve for c you must isolate this by bringing 7 to the other side. To do this you must multiply 7 to both sides. This will cancel 7 from the left side (the right side in the way the equation is written in the question) and bring it over to the right side
[tex]7(\frac{c}{7} ) = -5 * 7[/tex]
c = -35
Hope this helped!
~Just a girl in love with Shawn Mendes
A class of 20 students is visiting the fair today. Each student is 16 years old or younger and will participate in
either the Hay Bale Toss or the Pie Eating Contest. If all 20 students joined the same event, how would the shape
of the histogram change compared to the original?
The histogram would change due to the different distribution of ages when all 20 students join the same event.
Explanation:A histogram is a graphical representation of the distribution of numerical data. It consists of bars, where the length or height of each bar corresponds to the frequency or relative frequency of data within a specific interval or range. Histograms provide insights into data patterns and distributions.
The histogram would change when all 20 students join the same event compared to the original because the distribution of ages would be different. The original histogram would show the number of students participating in each event, while the new histogram would show the number of students in each age group. The new histogram would have different bars representing each age group, and the heights of these bars would be determined by the number of students in each age group.
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KLMN and PQRS are similar trapezoids. which side of PQRS corresponds to LM
Answer:
QR
Step-by-step explanation:
KLMN is in the same spot as PQRS
Answer:
QR corresponds to LM
Step-by-step explanation:
Two figures are said to be similar if they have same shape but not necessarily same size.
Two polygons are said to be similar if their corresponding angles are equal and corresponding sides are proportional .
A trapezoid is a polygon in which a pair of sides is parallel .
Here, two trapezoids are given i.e KLMN, PQRS.
As KLMN and PQRS are similar, so their angles are equal i.e
[tex]\angle K=\angle P\,,\,\angle L=\angle Q\,,\,\angle M=\angle R\,,\,\angle N=\angle S[/tex]
Also, corresponding sides are proportional i.e
[tex]\frac{KL}{PQ}=\frac{LM}{QR}=\frac{MN}{RS}=\frac{KN}{PS}[/tex]
Therefore, side QR corresponds to LM.
solve for x.
3x-12y=27
Answer: x=4y+9
Step-by-step explanation:
All of the variables, 3x, 12y, and 27 can be divided y 3, so we will simplify by dividing the whole equation by 3.
3x/3-12y/3=27/3
Which is equal to....
x-4y=9
Now you can move -4y over to the right side by changing its sign...
x=4y+9
Let the equation be 3x - 12y = 27 then, the value of x = 9 + 4y.
How to find the value of x?Given: 3x - 12y = 27
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Solve the value of x, then
Add 12y to both sides
3x - 12y + 12y = 27 + 12 y
Simplifying the above equation, we get
3x = 27 + 12y
Divide both sides by 3, then we get
[tex]$\frac{3 x}{3}=\frac{27}{3}+\frac{12 y}{3}$$[/tex]
Therefore, the value of x = 9 + 4y.
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An exam was given to a group of freshman and sophomore students. The results are below:
Freshman: 106 got A’s, 130 got B’s, and 149 got C’s.
Sophomore: 192 got A’s, 118 got B’s, and 168 got C’s.
If one student is chosen at random from those who took the exam, find the probability that:
b)The student was a freshman or received a C .
c) The student was a sophomore, given they got a
C.
d) The student got an A, given they are a freshman.
*round to 4 decimal places as needed*
Jodi invested $497.50 in a regular savings account that paid simple interest at a rate of 3.5% per year. How much was her investment worth in one year?
Answer:
17.41
Step-by-step explanation:
497.50 x 0.035
Jodi's investment will earn $17.41 in interest in one year at an interest rate of 3.5%. Therefore, after one year, her investment will be worth $514.91.
Explanation:To find out how much Jodi's investment is worth in one year, we can use the formula for simple interest, which is Interest = Principal x Rate x Time. In this case, the principal is $497.50, the rate is 3.5% (or 0.035 in decimal form), and the time is 1 year.
So, the interest earned in one year would be $497.50 x 0.035 x 1 = $17.41.
To find the total worth of her investment after one year, we add the interest earned to the initial principal. So, $497.50 (the principal) + $17.41 (the interest) = $514.91. Therefore, her investment is worth $514.91 after one year.
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