Answer:
To make it clearer, I just put every thing under the formal form
f(x) = [tex]\left \{ {{2x^2-1~~~~if~~~~ x\leq -1} \atop {3x+2~~~~~if~~~~~x>-1}} \right.[/tex]
Step-by-step explanation:
Now, you have 2 equations with 2 conditions. One is > -1, and one is < -1.
The question is about f (5). So, which equation you use to replace x = 5? The first one or the second one? and why?
Answering those questions help you understand how it works.
A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 890 cubic centimeters. Which equation can be used to find the area of the circular base?
Answer: its A
sorry if im wrong
The equation 890 = 1/3 B(46) can be used to find the area of the circular base .
What is Area ?Area is the space enclosed within the perimeter of the given shape.
It is given in the question that Area of the base of a volcano has to be determined.
The structure of a volcano is that of a Cone
Area of a conical structure is given by
V = (1/3) * height * (radius)²
890 = 1/3 (radius)²(46)
V = 890 h = 46
area of a circle = π (radius)²,
890 = 1/3 B(46)
If B = (radius)²
Therefore Option D is the correct answer
890 = 1/3 B(46) equation can be used to find the area of the circular base .
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Factor the gcf 15m^3+24m^2+25m+40
Answer:
Step-by-step explanation:
3m^2(5m+8) + 5(5m +8)
(3m^2+5)(5m+8)
Brainliest question please help me now plz
Answer:
B
Step-by-step explanation:
trust me bro i gotchu
The volume of prism A is 60 cubic units, and the volume of prism B is half the volume of prism A. What is the value of a?
Answer:
5
Step-by-step explanation:
V= Bh
volume of figure A is 60, and the volume of figure B is half.
figure B:
B= 3*4
B= 12
60=12*h
5=h
the value of a is 5.
The value of a in the prism is 3 units.
What is prism?In three-dimensional space,
a prism is a polyhedron where two ends are similar.
Given:
The volume of prism A is 60 cubic units,
and the volume of prism B is half the volume of prism A.
The base area of the prism B is 20 square units.
The volume of the prism,
V = Ba, where B is the base area and a is the height.
So,
60 = 20a
a = 3 units
Therefore, the value of a is 3 units.
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The complete question:
The volume of prism A is 60 cubic units, and the volume of prism B is half the volume of prism A. The base area of the prism B is 20 square units.
What is the value of a?
The length of a rectangle is two more than three times its width. If the perimeter of the rectangle is 60 m, find its length and width.
Answer:
The length and width of the rectangle are 23 m and 7 m respectively.
Step-by-step explanation:
P = 2L + 2W
P (perimeter of the rectangle) = 60 m
L (length of the rectangle) = 2 + 3W. W is the width of the rectangle
Therefore, L = 2 + 3W
P = 2L + 2W
60 = 2(2 + 3W) + 2W
60 = 4 + 6W + 2W
60 - 4 = 8W
56 = 8W
W = 56/8 = 7 m
L = 2 + 3W = 2 + 3(7) = 2 + 21 = 23 m
L = 23 m
W = 7 m
A ball is kicked from an initial height of 2.5 feet with an initial velocity of 45 feet per second. The function ƒ(x) = −16x^2 + 45x + 2.5 models its
path, where x is the time (in seconds) the ball travels and ƒ(x) is the height (in feet) the ball is kicked. What is the height of the ball 2 seconds after it is kicked?
Answer:
28.5 ft
Step-by-step explanation:
The height of a ball is given by the equation ƒ(x) = −16x² + 45x + 2.5 where x is the tome the ball travels. To find the height of the ball after a seconds, we substitute a in place of x, the equation becomes:
ƒ(a) = −16a² + 45a + 2.5.
Therefore if the height of the ball is needed to be found after 2 seconds, we find f(2).
ƒ(2) = −16(2)² + 45(2) + 2.5 = -64 + 90 + 2.5 = 28.5 ft
f(2) = 28.5 ft
Solve the following:
A) 2(x+3)=x-4
b) 4(5x-2)=2(9x+3)
Answer:
[tex] A) \: x = - 10 \\ B) \: x = 7 [/tex]
Step-by-step explanation:
[tex]A) \\ = > 2(x + 3) = x - 4 \\ \\ = > (2 \times x) + (2 \times 3) = x - 4 \\ \\ = > 2x + 6 = x - 4 \\ \\ = > 2x - x + 6 = - 4 \\ \\ = > x + 6 = - 4 \\ \\ = > x = - 4 - 6 \\ \\ = > x = - 10 \\ \\ \\ B) \\ = >4(5x-2)=2(9x+3) \\ \\ = > (4 \times 5x) - (4 \times 2) = (2 \times 9x) + (2 \times 3) \\ \\ = > 20x - 8 = 18x + 6 \\ \\ = > 20x - 18x - 8 = 6 \\ \\ = > 2x - 8 = 6 \\ \\ = > 2x = 6 + 8 \\ \\ = > 2x = 14 \\ \\ = > x = \frac{14}{2} \\ \\ = > x = 7[/tex]
What is the equation for the blue line?
Answer:
y = - 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-2}{0+1}[/tex] = - 3
The line crosses the y- axis at (0, - 1) ⇒ c = - 1
y = - 3x - 1 ← equation of line
What is the HIGHEST common factor
of the set of numbers (54, 72, 90}?
Answer:
18
Step-by-step explanation:
54/18=3
72/18=4
90/18=5
Answer:
18
Step-by-step explanation:
GCF of 54, 72, 90 is:
54÷3= 18
72÷4= 18
90÷5= 18
The GCF of 54, 72, and 90 is 18.
x : 28 = 7 : x calculate the positive value of x .
answer is 2.
x is divided by 28 and 7 is divided by x
after that cut 28 by 7
and the anwer will be x square = 4
and the square will go to 4
and four will be root 4
and the answer will be x = 2
the probability of rolling factors of 6 on both dice
Answer:1/6
Step-by-step explanation:
Need help with this!!
Answer:
last one
Step-by-step explanation:
the domain includes all real numbers and the range is y>0
Solve the system of equations:
y = x + 2
y= x2 + 5x + 6
A. (0,2)
B. (-2,0)
C. (0, 2) and (2, 4)
O D. (-2,0) and (-3,0)
SUBMIT
The solution for equation is at (-2, 0).
What is linear equation?
When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
Both linear equations with one variable and those with two variables exist.
Given equations,
y = x + 2
y = x² + 5x + 6
substitute value of y in second equation
x + 2 = x² + 5x + 6
x² + 4x + 4 = 0
x² + 2x + 2x +4 = 0
x(x +2) + 2(x + 2) = 0
(x + 2)(x + 2) = 0
x = -2
and y = x + 2
y = -2 + 2 = 0
Hence, the solution of equation is at x = -2 and y = 0.
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Choose one question from the chart and complete it showing all steps. :)
Answer:
Question 1
Volume of a cylinder = πr²h
r= radius h= height
diameter = 2*radius
diameter = 2* 4cm= 8cm
Volume = π × 4² × 11
= 553.14cm³
Find the 22nd term in the arithmetic sequence -5, -9, -13, -17, -21
Answer:
-93
Step-by-step explanation:
it decreases by four every time, so take -4 times 22 and then subtract 5.
HELP ME Please i struggle with this
Answer:if you are looking for the hypotenuse use Pythagoras theorem 17.2047
Step-by-step explanation:square both the base and height .Add their total then find the square root
A fish jumps out of water. The function y = −16t 2 + 11t models the height, in feet, of the fish above water after t seconds. A) How long is the fish out of water? B) What is the maximum height of the fish above the water?
Answer:
A) The fish was out of water for 0.6875 seconds.
B) Maximum height = 5.672
Step-by-step explanation:
Height is modeled by;
y = -16t² + 11t
A) To find total time of the fish out of water, we need to find the x - intercept. That is the points where y = 0
So, 0 = -16t² + 11t
So the roots of this equation are;
t = 0 or 0.6875
Thus,the fish was out of water for 0.6875 seconds.
B) y = -16t² + 11t
The x coordinate of the vertex is at - b/2a
For y = -16t² + 11t
a = -16, b = 11, c = 0
So, -b/2a = -11/(2*-16) = 11/32
The maximum height will be at the y-coordinate of the vertex.
Thus, we need to find f(11/32)
f(11/32) = -16(11/32)² + 11(11/32) = 1.890625 + 3.78125 = 5.671875 ≈ 5.672
Jacob wants to know the favorite sport among sixth grade students. Which types of survey below with give Jacob valid results?
A) randomly survey students in the middle school
B) randomly survey six grade students inside the football store
C) randomly survey six grade students inside the school cafeteria
D) randomly survey six grade students inside the tennis shop
Answer I think
:randomly survey six grade students in the school cafeteria
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Randomly surveying 6th graders in the school cafeteria would give jacob valid results because A wouldn't be reliable, because he just wants 6th graders, and B and D would be selective as it would be inside a football store, implying that most 6th graders in there would be tending towards football, and D would be inside a tennis shop, which would imply that most 6th graders there would prefer football. Therefore, the cafeteria would yield the most reliable results.
The pictures above please help
How do I do congruent figures
Answer:
make them the same
Step-by-step explanation:
hope this helps
100 POINTS 4(5n-7)+10n+2 9(x+3)=4x-3 2(12-8x)=x-11x pls help
Answer:
see below
Step-by-step explanation:
4(5n-7)+10n+2
Distribute
20n -28 +10n+2
Combine like terms
30n-26
Assuming you meant =
4(5n-7)=10n+2
Distribute
20n -28 =10n+2
Subtract 10n from each side
20n-10n-28 = 10n-10n+2
10n-28 =2
Add 28 to each side
10n-28+28=28+2
10n=30
Divide by 10
10n/10 =30/10
n=3
9(x+3)=4x-3
Distribute
9x+27 = 4x-3
Subtract 4x from each side
9x-4x+27 = 4x-4x-3
5x +27 =-3
Subtract 27 from each side
5x+27-27 = -3-27
5x = -30
Divide by 5
5x/5 = -30/5
x=-6
2(12-8x)=x-11x
Combine like terms
2(12-8x) = -10x
Divide by 2
12-8x = -5x
Add 8x to each side
12-8x+8x = -5x+8x
12 = 3x
Divide by 3
12/3 =3x/3
4=x
Answer:
See explaination
Step-by-step explanation:
Assuming that these are three different problems:
1) 4(5n-7) = 10n+2
Distribute:
4(5n-7) = 10n+2
20n - 28 = 10n + 2
Combine like terms, isolate, and solve:
10n = 30
n = 3
2) 9(x+3) = 4x-3
Distribute:
9(x+3) = 4x-3
9x+27 = 4x - 3
Combine like terms, isolate, and solve:
5x = -30
x = -6
3) 2(12-8x) = x-11(i assumed the extra x was a typo)
distribute:
24-16x = x-11
Combine like terms, isolate, and solve:
35 = 17x
x = 35/17
simplify 6*3+4+2*3(15)+*2
Answer:
114.
Step-by-step explanation:
remove parenthesis multiply the numbers 6 x 3 + 1818 + 4 + 2 x 3 x 15 + 2
multiply the numbers 2 x 3 x 15 + 90
18 + 4 + 2 + 90 + 2
add the numbers : 18 + 4 + 2 + 90 + 2
= 114!
PLEASE HELP ASAP 100 PTS WILL MARK BRAINLYIEST If f(x) = (x + 7)^2, which of the following is g(x), based on the translation? g(x) = (x + 9)^2 g(x) = (x + 5)^2 g(x) = (x + 7)^2 + 2 g(x) = (x + 7)^2 − 2
Answer: g(x)=(x+7)²-2
Step-by-step explanation:
For this problem, you will need to know what each part fo the function does. You can see that g(x) is the bottom function and f(x) is the to function. F(x) has traveled down to -2. You know that the y-intercept is -2. The only answer choice with -2 as y-intercept is g(x)=(x+7)²-2.
Answer:
g(x) = (x + 7)^2 -2
Step-by-step explanation:
f(x) = (x + 7)^2
We are shifting the function down 2 units
f(x) -b where b is 2
g(x) = f(x) -2
g(x) = (x + 7)^2 -2
What is the smallest prime that is a factor of the sum 51 + 1?
Answer:
2
Step-by-step explanation:
51+1 = 52
Since 52 is even, obviously the answer is 2.
Hope this helps.
Good Luck
A triangular prism has a height of 9 m. The area of a triangular base measures 16 m². What is the volume of a triangular prism?
Possible answers are 15,60,72,144 cubic meters. What one is correct?
Answer:
144m^3
Step-by-step explanation:
Find the missing number___:7 = 12:21
A. 3
B. 4
C 14
D 12
Answer:
B. 4 would be your answer.
Step-by-step explanation:
7 x 3 = 21
4 x 3 = 12
:)
Answer:
B. 4.
Step-by-step explanation:
Let the number be x then
x/7 = 12/21
Crossmultiply:
x = 7*12 / 21
x = 12 / 3 = 4.
If y is directly proportional to x and y = 5 when x = 2, find the value of y when
x = 7
Answer:
I think that y=17.5 when x=7
Which object shown below could we slice perpendicular to its base/face to create a trapezoid cross-section
Answer:
B
Step-by-step explanation:
The algebraic rule for a reflection over the x-axis is one for the following:
Answer: C
Step-by-step explanation:
Reflection in the x -axis:
A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is (x,y)→(x,−y) .
On a farm, 34 of each acre is planted with blue spruce trees. If there are 16 12 acres of trees on the farm, how many acres are planted with blue spruce trees?
Answer:
1209 acres
Step-by-step explanation:
On the farm, 3/4 of the acre is planted with blue spruce trees.
There are 1612 acres on the farm. Therefore, the number of acres planted with blue spruce trees is:
3/4 * 1612 = 1209 acres
