The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply.-The vertex is the maximum value.
-The axis of symmetry is x = -1/2
-The domain is all real numbers.
-The range is all real numbers.
-The x-intercepts are at (−2, 0) and (1,0).
-The function is decreasing from (−∞, 6.75)
Answers
f(-1) = -3(-1)^2 - 3(-1) + 6 = -3(1) - (-3) + 6 = -3 + 3 + 6 = 6
f(-0.5) = -3(-0.5)^2 - 3(-0.5) + 6 = -3(0.25) - (-1.5) + 6 = -0.75 + 1.5 + 6 = 6.75
f(0) = -3(0)^2 - 3(0) + 6 = 0 + 0 + 6 = 6
From the above, the graph stopped increasing at x = -0.5 and started decreasing. Hence, the axis of symmetry is x = -1/2
The domain of all quadatic expression is all real numbers because there is no value of x for which f(x) does not exist.
The range is NOT all real numbers because for instance, there is no value of x for which f(x) = 7.
f(-2) = -3(-2)^2 - 3(-2) + 6 = -3(4) - (-6) + 6 = -12 + 6 + 6 = 0
f(1) = -3(1)^2 - 3(1) + 6 = -3(1) - 3 + 6 = -3 + 3 = 0
Hence, the x-intecepts are at (-2, 0) and (1, 0)
The function is INCREASING from (−∞, 6.75)
Answer:
I took the test on edge
Step-by-step explanation:
The vertex is the maximum value.
The axis of symmetry is x = negative one-half.
The domain is all real numbers.
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What percent of 128 is 32
A strong man takes 2 minutes to make one cut through a log. How long will he need to cut a ten-foot log into into 4 equal pieces?
Jonathan ran five days a week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance jonathan could have run any day this week
k = 10t-19k=10t−19
Answers
The value of k is -89
Explanation:
The given expression is
We need to determine the output k, when the input t is -7
Output k:
The value of the output k can be determined by substituting the input in the expression
Thus, we have,
Multiplying the terms 10 and -7, we have,
Simplifying, we get,
Thus, the value of k is -89
Answer:
-89
Step-by-step explanation:
khan
Answers
12 apples require 1 bag.
75 apples would require: 75 / 12
= 6.25 bags.
There can't be 6.25 bags. So he would need to buy 7 bags in all.
(x, y) Right-arrow (x + 3, y – 4)
(x, y) Right-arrow (x – 4, y + 3)
(x, y) Right-arrow (x + 4, y – 3)
https://gyazo.com/7f600cf22684259e421627eca2c910d4
Answers
According to translation rule When the coordinates are added to or subtracted from, the values of x and y change.
What are coordinates?
A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given four transformations of coordinates (x, y)
If the transformation occurs in the x-axis, then the coordinators move left or right.
If transformation occurs in the y-axis, then the coordinators move upwards or downwards
thus for (x, y ) => (x - 3), (y + 4)
From the given rule:
x is decreased by 3 and y is increased by 4 or in other words, we can say the graph moves downward by 3 units and to the right by 4 unit
for (x, y ) => (x + 3), (y - 4)
From the given rule:
x is increased by 3 and y is decreased by 4 or in other words, we can say the graph moves upward by 3 units and to the left by 4 units.
for (x, y ) => (x + 4), (y - 3)
From the given rule:
x is increased by 4 and y is decreased by 3 or in other words, we can say the graph moves upward by 4 units and to the left by 3 units.
Hence, using the rule of the translation The value of x and y will increase or decrease by adding or subtracting from the coordinates.
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Answer:
Step-by-step explanation:
(x, y) Right-arrow (x – 3, y + 4)
a
b
2
second one
after one
before 3
dos
Answers
Andrew needs at least a 74% on the final exam.
client's need? Round to the nearest tenth of a centimeter.
2.7 cm
4.9 cm
O 7.3 cm
24.0 cm
Answers
Answer:
Step-by-step explanation:
V=πr²h
=3.14*6*6*10
=1130.4 cm³
New cylinder:
h = 15cm
V= 1130.4 cm³
πr²h = 1130.4
3.14*r²*15=1130.4
r²=1130.4/15*3.14
r²=24
r=√24
r=4.898 = 4.9 cm
The radius be to meet the client's need is 4.9 cm.
What is Volume?
Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.
Volume is sometimes referred to as capacity.
We have,
Radius of cylinder (r)= 6 cm
Height of cylinder (h) = 10 cm
and, Height of new cylinder (H) = 15 cm
Radius of new cylinder = R cm
Now, Volume of cylinder can be compared as
πr²h = πR²H
6 x 6 x 10 = R² x 15
360 / 15 = R²
R² = 24
R= 4.9 cm
Thys, the radius is 4.9 cm.
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