To translate the function f(x) = x² to the left 8 units and up 2 units, the function rule for g(x) is g(x) = (x - 8)² + 2.
Explanation:To translate the function f(x) = x² to the left 8 units and up 2 units, we can use the transformation rules. The leftward translation can be achieved by subtracting 8 from the variable x in the function, resulting in g(x) = (x - 8)². The upward translation can be achieved by adding 2 to the function, resulting in g(x) = (x - 8)² + 2.
Therefore, the function rule for g(x) given f(x) = x² is g(x) = (x - 8)² + 2.
Final answer:
To find the function rule for g(x) when the graph of f(x)=x² is translated left by 8 units and up by 2 units, the new function is g(x) = (x + 8)² + 2.
Explanation:
The question pertains to transforming a function graphically. Given the original function f(x) = x² (a parabola opening upwards with its vertex at the origin), we are to translate this function to the left by 8 units and up by 2 units to get the new function g(x). To translate a function to the left by a units, you replace x with x + a. Similarly, to translate a function up by b units, you add b to the function.
Therefore, to translate the original function f(x) = x² to the left by 8 units and up by 2 units, the new function g(x) would be:
g(x) = (x + 8)² + 2
76 is what percent of 95
The scientific notation 2 ��� 10^2 has what value? 100
If a = b, then ac = bc. This is called the ________ ________ of equality. (2 words)
Mike has an adjusted gross income of $85,643. He claims two exemptions and can deduct $896 for state income tax, $2,145 for charitable donations, and $3,473 for medical expenses. If the standard deduction is $5,700 and exemptions are each worth $3,650, what is Mike’s total taxable income? a. $72,643 b. $75,479 c. $71,829 d. $66,129
The real answer is C. $71,829. Just took the engenuity test.
Mike's total taxable income is $71,829.
Explanation:To calculate Mike's total taxable income, we need to subtract his deductions and exemptions from his adjusted gross income. According to the given information, his adjusted gross income is $85,643. He claims two exemptions, which are each worth $3,650, so the total exemption amount is $7,300. He can deduct $896 for state income tax, $2,145 for charitable donations, and $3,473 for medical expenses. Thus, the total deduction amount is $6,514. Therefore, Mike's total taxable income is:
Total taxable income = adjusted gross income - (deductions + exemptions)
Total taxable income = $85,643 - ($6,514 + $7,300)
Total taxable income = $85,643 - $13,814
Total taxable income = $71,829
So, the correct answer is c. $71,829
The least common multiple of 20, 24, and 45 is _____.
a) 30
b) 180
c) 360
d) 21,600
Answer:
c)360
Step-by-step explanation:
The least common multiples is the smallest common multiple.
To find the common multiple you have to divide the option given by the numbers: 20, 24, and 45 and result of each operation should be an integer number.
Let's review why answers a) and b) are not common multiple.
Answer a) 30
45 ÷ 30= 1,5 .
1.5 is not integer number ,So, 30 is not multiple of 45.
Answer b)180
180 ÷ 24= 7.5
7.5 is not integer number, So, 180 is not multiple of 24.
c) If you divide 20, 24 and 45 divided 360, the result is an integer.
360÷20=18
360÷24=15
360÷45=8
360 is common multiple of the three numbers. And it is the LCM.
Jalil mixed 3/8 cup of sugar with 11/6 cups of water. How many more cups of water than sugar did he use in his mixture
Answer:
[tex]1\frac{11}{24}[/tex] cup more water than sugar
Step-by-step explanation:
Jalil mixed the number of cups of sugar = [tex]\frac{3}{8}[/tex]
with the number of cups of water = [tex]\frac{11}{6}[/tex]
We have to find the additional amount of water that is used in his mixture.
So we will subtract the amount of sugar from the amount of water.
[tex]\frac{11}{6}[/tex] - [tex]\frac{3}{8}[/tex]
= [tex]\frac{44-9}{24}[/tex]
= [tex]\frac{35}{24}[/tex]
= [tex]1\frac{11}{24}[/tex] cup
[tex]1\frac{11}{24}[/tex] cup more water is used in this mixture.
Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve
y=8-x^2 Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve
y=8-x^2
The given curve is a quadratic function and to find the area of a rectangle under it with maximum area, we consider the rectangle's base as an interval on x-axis and find the maximum value using calculus. The maximum area is achieved when x is sqrt(8/3).
Explanation:To find the largest possible area for a rectangle with its base on the x-axis and upper vertices on the curve y=8-x^2, we would use calculus, specifically optimization.
Consider the base of the rectangle as the interval [-x, x] along the x-axis. Hence, the width of the rectangle would be 2x and the height would be the value of the curve at any x, which is 8-x^2.
Therefore, the area A of the rectangle can be expressed as A = (2x)*(8-x^2) = 16x - 2x^3.
To maximize the area, we take the derivative of A with respect to x, set it equal to zero and solve for x. The derivative is A' = 16 - 6x^2. Setting this to 0, we get 6x^2 = 16 or x = √(8/3).
Substituting x = √(8/3) back into the original equation y = 8 - x^2 will give the maximum height of the rectangle, and hence its maximum area.
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If a and b are parallel lines and m <3 = 128º, what is the measure of <8?
A) 134º
B) 54º
C) 52º
D) 49º
Image Bellow :-)! thanks in advance! =]
Given the information that angle 3 is 128 degrees and lines a and b are parallel, angle 8 would also be 128 degrees. But none of the provided options matches 128 degrees, implying missing or incorrect information in the question.
Explanation:In geometry, if lines are parallel, the corresponding angles are equal. Given that a and b are parallel lines and angle 3 is 128°, if angle 8 corresponds to angle 3, angle 8 would also be 128°. However, the possible values provided don't include 128°. Therefore, there seems to be insufficient information or a mistake in the question to give a definite answer. All possible answers: A) 134º, B) 54º, C) 52º, D) 49º - don't match with 128º. Perhaps there's an intermediary step or piece of information missing.
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If b = 3, then 3x + y = 1 and bx - y = 3 are parallel.
True or
False ...?
Answer:I am absolutely sure that the task b = 3, then 3x + y = 1 and bx - y = 3 is NOT parallel, which means that the statement represented above is FALSE.
To make sure you can check it using : Hope now it's obvious. Regards!
Step-by-step explanation:
A local department store had a Saturday special. It offered an additional 25% discount on shirts that were already marked down 50%. How much did Megan pay for a shirt that originally sold for $40?
A. $10
B. $15
C. $20
D. $30
Multiply and reduce to lowest terms? 1. 2 1/7 * 4 3/8 = user: 10 1/4 - 9 5/6 =
What percent of 72 is 45
Find the measure of each exterior angle for a regular pentagon. Round to the nearest tenth if necessary.
A. 540 C. 360
B. 108 D. 72
The requried exterior angle of a regular pentagon measures 72 degrees. Option D is correct.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length and an equal measure of angle at the vertex.
Examples of polygons, equilateral triangles, squares, pentagons, etc
Here,
The measure of each exterior angle for a regular pentagon can be found by using the formula: exterior angle = 360 / number of sides.
For a regular pentagon, the number of sides is 5, so the formula becomes, exterior angle = 360 / 5 = 72 degrees.
Therefore, each exterior angle of a regular pentagon measures 72 degrees.
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Given this triangle find angle B to the nearest tenth of a degree if b=8 and c=12.
in 2015, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. At this rate, what would be the population in 2040? Round the the nearest whole number. Enter your answer in the box.
the answer is 12495, its correct jus took the test. (now u can give the brainliset to the other person) have a nice day :)
find the numbers preceding and succeeding the following number.... B0B base 12 ?
Write the scientific notation in numerals.
5.82 x 102
A biologist took a count of the number of fish in a particular lake, and recounted the lake’s population of fish on each of the next six weeks.
Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of fish at the lake on week 8.
P(x) = 13x^2 – 10x + 350; 917 fish
P(x) = 13x^2 – 10x + 350; 1,102 fish
P(x) = 18x^2 + 10x + 300; 1,252 fish
P(x) = 18x^2 + 10x + 300; 1,532 fish
Answer:
P(x) = 13x2 – 10x + 350; 1,102 fish
Step-by-step explanation:
Plug in week 8 for x.
[tex]P(x) = 13 * (8)^{2} - 10(8) - 350 =[/tex]
[tex]P(x) = 13 * 64 - 80 + 350 =\\\\ P(x) = 832 - 80 + 350 = 1102[/tex]
What linear function can be represented by the set of ordered pairs?
{(−4, 15), (0, 5), (4, −5), (8, −15)}
I've completed the test:
Final answer:
The linear function represented by the set of ordered pairs is y = -5x + 15.
Explanation:
A linear function can be represented by the set of ordered pairs {(−4, 15), (0, 5), (4, −5), (8, −15)}. To determine the linear function, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we can choose any two ordered pairs to find the slope, which is the change in y divided by the change in x. Let's choose (-4, 15) and (4, -5). The slope (m) can be calculated as (y2 - y1)/(x2 - x1).Substitute the slope (m) and one of the ordered pairs into the equation y = mx + b to find the y-intercept (b). We'll use (4, -5) as our point.Finally, substitute the calculated slope (m) and y-intercept (b) values into the equation y = mx + b to obtain the linear function.Therefore, the linear function represented by the given set of ordered pairs is y = -5x + 15.
Which of the following represents the set of possible rational roots for the polynomial shown below?
2x³+5x²-8x-10=0
a. {±2/5, ±1/2, ±1, ±2, ±2/5, ±1/5, ±1/10}
b. {±1/2, ±1, ±2, ±5/2, ±5, ±10}
c. {±1, ±2, ±4, ±5, ±10, ±20}
d. {1/2, 1, 2, 5/2, 4, 5, 10, 20} ...?
Answer:
Option b is correct
Step-by-step explanation:
Given the polynomial
[tex]2x^3+5x^2-8x-10=0[/tex]
we have to find the set of possible rational roots for the polynomial.
Rational root theorem states that if P(x) has any rational roots then they must be of form
[tex]\pm{\frac{\text{Factor of }a_0}{\text{factors of }a_n}[/tex]
Here [tex]P(x)=2x^3+5x^2-8x-10[/tex]
Factors of 10=1, 2, 5, 10
Factors of 2=1, 2
Possible rational roots are
[tex]\{\pm1, \pm\frac{1}{2}, \pm2, \pm\frac{5}{1}, \pm\frac{5}{2}, \pm 10\}[/tex]
Option b is correct
Change 5000 meters to kilometers.
In a translation, why is it important for every point to move the same direction and same distance?
what is the name of a number that can be written in the form a/b where a and b are integers and b cannot equal zero
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.
17=3(g+3)-g.
I also need the math
if g(x)= 5-x^2 what's g(g(x))
Which expression is equivalent to 4√32·√2 ?
16
42√42
162√162
32
Answer:
Yep, it's 32
Step-by-step explanation:
There were 7 field goals made in 14 attempts. how many goals should be made in 8 attempts
Which type of triangle will always have exactly 1-fold reflectional symmetry?
The absolute value of a number is always greater than its opposite. Is this true?
A) No; the absolute value of a negative number is equal to its opposite.
B) No; all negative numbers are greater than their opposites.
The absolute value of a positive number and its opposite is always equal. So the given statement is not true.
Absolute value represents the distance of a point from the origin. The distance of a positive number and its opposite will always be the same from the origin. Consider the following example:
The number is 5. The absolute value of 5 is | 5 | = 5
The opposite of 5 is -5. The absolute value of -5 is |-5| = 5
This shows the absolute value of a number and its opposite will always be equal. For any positive number x, we can write:
| x | = | -x | = x
So, the correct answer is:
A) No; the absolute value of a negative number is equal to its opposite.