To find f(a) for the given function, substitute a for x in the function and simplify the expression.
Explanation:Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.
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Divide 30 by 1/2 and add 10 what is the answer?
Given the function f(x)=-5x^2-x+20 find f(3)
f(3) = -5*3^2 - 3 + 20 = -5*9 - 3 + 20 = -45 - 3 + 20 = -28;
Answer: - 28
Step-by-step explanation:
f(x) = -5x^2 - x + 20
To find f(3), we simply put x = 3 and then simplify
f(3) = - 5(3)^2 - 3 + 20
= -5(9) - 3 + 20
= -45 - 3 + 20
= -48 +20
= -28
f(3) = -28
Which equation represents the value of x?
remember Pythagorean theorem
if we have a right triangle with legs a and b and hytponuse c then
[tex]a^2+b^2=c^2[/tex]
we are given a right triangle with legs x and y and hypotohuse 10
so therfor
[tex]x^2+y^2=10^2[/tex]
[tex]x^2+y^2=100
solve for x
minus y² from both sides
[tex]x^2=100-y^2[/tex]
sqare root both sides
[tex]x=\sqrt{100-y^2}[/tex]
the answer is the 4th option
An equation represents the value of x is x=√100-y².Therefore, option D is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given triangle ABC, AB=x units, BC=y units and AC=10 units
By using Pythagoras's theorem, we get
10²=x²+y²
x²=100-y²
x=√100-y²
Therefore, option D is the correct answer.
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What happens when you multiply a positive number by a positive number less than 1?
A high-speed bullet train travel 900 feet in 5 seconds at this rate how far would it travel in 1 minute
Suppose we did an experiment to gather data on the number of un-popped kernels of microwave popcorn. Half of the students in your class took home a bag, put it in the freezer overnight, and popped it the next day. The other half took the bag, left it on their kitchen counter overnight, and popped it the next day. Each group counted the number of un-popped kernels. Are these data paired or independent
The data collected on the number of un-popped kernels of popcorn, where one group's bags were frozen and the other's were left at room temperature, are considered independent. This is because each bag was only subjected to one condition and was not measured in both conditions, which would be necessary for paired data.
In the question provided, students collected data on the number of un-popped kernels of microwave popcorn where one group froze the popcorn while the other left it at room temperature. To determine whether the data are paired or independent, we need to understand the nature of the experiment setup.
Since every student’s popcorn was subject to a unique condition (frozen or room temperature) and they're not measured in both conditions, we can deduce that the data here are independent. This means that the outcome of one does not influence the outcome of the other.
In comparison to a scenario where the same item or subject is tested under two different conditions the popcorn experiment does not meet this criterion; that would be an example of paired data. An unpaired test such as the unpaired t-test may be appropriate here if we want to assess the effects of freezing on the number of un-popped kernels compared to leaving them at room temperature. Each bag of popcorn represents an independent sample from the population of all popcorn bags.
98,464 rounded to the nearest ten thousand is
Please help not really sure what to do here.
Which of the following shows the proper steps to construct a perpendicular bisector of a segment through any point?
Identify the variables, the constant, the coefficients, and the exponents in the algebraic expression: 5x + 3y^{2} + 4. (The 2 is supposed to be little on top of the "y")
The algebraic expression 5x + 3y² + 4 has variables x and y, the constants 5, 3, and 4, the coefficients are 5 and 3 and the exponents are 1 and 2.
What is an algebraic expression?An algebraic equation consists of terms separated by the operation of addition and subtraction.
We know in an algebraic expression a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+aⁿ,
x's are variables a's are constants and n's are exponents.
∴ In the algebraic expression 5x + 3y² + 4,
Constants are the numerical values which are 5, 3, and 4.
The variables are x and y and the exponents are the powers of the variables 2 for y and 1 for x and the coefficients are 5 and 3.
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The sum of two positive numbers is 42. What is the smalles possible value of the sum of their squares?
A student solved the problem below by first dividing 20 by 10. What mistake did the student make?
A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answer:
Sample Response: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.
Define the function g(x) in terms of f(x)
What is the value of the expression “two less than six times the difference of a number and five” when n = 9?
Answer:
22
Step-by-step explanation:
The value of expression is 22.
Step-by-step explanation:
Given the statement “two less than six times the difference of a number and five” when n = 9. we have to find the value of expression formed by the above statement.
Difference of a number n and 5 gives (n-5)
Now, we have to write two less than 6 times the difference, we get the expression 6(n-5)-2
Here, the number n is 9
∴Value of expression is 6(9-5)-2=6(4)-2=24-2=22
Hence, the value of expression is 22.
Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.
The radius of the incircle centered at point P is ? units.
Answer:
The answer is 7 units
Step-by-step explanation:
I don't know but I got it right
I think you dont need to calculate anything they gave us the answer when they said PZ=7
The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.
Answer:
Step-by-step explanation:
We assume the box is open-top.
If the width of the box is represented by w, then its length is 2w. The area of the base is then w·2w = 2w².
The combined area of the sides is the product of the perimeter of the base, 2(w+2w) = 6w and the height, 0.5, so is 3w.
Since the base area is 1.08 m² less than the lateral area, we have
... 2w² = 3w -1.08
... 2w² -3w +1.08 = 0 . . . . rearrange to standard form
... w² -1.5w +0.54 = 0 . . . make the leading coefficient 1 (divide by 2)
... (w -0.9)(w -0.6) = 0 . . . factor
The width of the box may be either 0.6 meters or 0.9 meters.
The volume is the product of width, length, and height
V = w·2w·0.5 = w²
V = 0.36 m³ . . . or . . . 0.81 m³. . . . . . (there are two possible answers)
The coordinates of the vertices of quadrilateral RSTU are R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4) . Which statement correctly describes whether quadrilateral RSTU is a rectangle?
Answer:
For k12- the answer is Quadrilateral RSTU is not a rectangle because it has no right angles.
Step-by-step explanation:
Solution: A quadrilateral RSTU whose vertices are R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4).
RS = [tex]\sqrt{(4+4)^{2}+(-1-1)^{2}} =\sqrt{64+4}= \sqrt{68}[/tex]
ST= [tex]\sqrt{(4-3)^{2}+(-1+6)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]
TU=[tex]\sqrt{(3+5)^{2}+(-6+4)^{2}}= \sqrt{64+4}= \sqrt{68}[/tex]
UR =[tex]\sqrt{(-5+4)^{2}+(-4-1)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]
→RS=TU, and ST=UR⇒ Opposite sides are equal.
Slope of RS = [tex]\frac{-1-1}{4+4} = \frac{-2}{8}= \frac{-1}{4}[/tex]
Slope of TS= [tex]\frac{-6+1}{3-4} =\frac{-5}{-1}=5[/tex]
Slope of RS × Slope of TS = -1/4 × 5 = -5/4 ≠ -1, So lines are not perpendicular.
∴ quadrilateral RSTU is not a rectangle.
What is the perimeter of a polygon with vertices at (-6,-1) (-3,-4) (6,5) and (3,8) ?
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN△LMN?
Answer:
Step-by-step explanation:
The area of the triangle inside the rectangle is calculated by using the formula for the area of a triangle, 1/2 * base* height. Given the base is the length of the rectangle and the height is the breadth of the rectangle, we substitute these measurements into the formula to determine the area. Area of triangle LMN is 15.6 square cm.
Explanation:To determine the area of the triangle inside the rectangle, we first need to understand the relationship between these two shapes. Given the base of the triangle, LN, is the same as the length of the rectangle, 6.5 cm, and the triangle is between the parallel lines of the rectangle, we can infer that the height of the triangle is the same as the breadth of the rectangle, which is 4.8 cm.
Now, the area of a triangle is given by the formula 1/2 * base * height.
Substituting the given measurements into this formula, we get
= 1/2 * 6.5 cm (base) * 4.8 cm (height)
= 0.5 * 6.5 cm (base) * 4.8 cm (height)
= 15.6 square cm
This will give us the area of the triangle LMN.
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The complete question is given below:
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN?
The length of rectangle and triangle are same, 6.5 cm. The breadth of rectangle is 4.8 cm. The triangle lies between the parallel lines of rectangle with base LN.
Mark borrowed $5,500 at 11.5 percent for five years. What is his monthly payment?
A. $131.50
B. $173.50
C. $120.95
D. $150.22
Answer:
C option is correct
Step-by-step explanation:
Given: payment borrowed (P)= $5,500
rate (r)=11.5 or 0.115
Time(t)= 5 years
Compound monthly(k)=12
To find : Monthly payment (M)
Formula used : [tex]M= P/(\frac{1-(1+\frac{r}{k})^{-kn}}{\frac{r}{k}})[/tex]
Solution : [tex]M= 5500/(\frac{1-(1+\frac{0.115}{12})^{-60}}{\frac{0.115}{12}})[/tex]
by solving we get, M =$120.95
therefore, option C is correct
Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices
R'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:
It should be C aka 270°
Step-by-step explanation:
Answer:
3 option is correct.
Step-by-step explanation:
Given Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices R'(0, –2), S'(0, –4), and T'(–3, –1).
We have to tell the rule describes the transformation.
A rotation is transformation that turns a figure about a fixed point. An object and its rotation are the same shape, but the figures may turned or rotate in different directions.
Here, the coordinates shift after rotation according to the rule
(2,0) → (0,-2) i.e (x, y) → (y, -x)
As, Rotation of 270º on coordinate axes.
(x, y) → (y, -x)
which match to the given rule.
hence, 3 option is correct.
what are the roots of x in -10x^2 + 12x - 9=0
Answer:
k=-11
Step-by-step explanation:
Correct for plato
A computer company can sell 130 boxes of printer paper each week at a price of $9 per box. For each $1 increase in the price, it will sell 10 fewer boxes per week. What price per box will provide the maximum revenue for the computer company?
$9
$10
$11
$12
The maximum revenue for the computer company is achieved at the price of $11 per box which is calculated based on the decrease in quantity sold with every $1 increase in price.
Explanation:To find the price per box that will provide the maximum revenue for the computer company, we need to analyze how changes in price affect the number of boxes sold and the revenue generated. The company sells 130 boxes of printer paper each week at $9 per box. For each $1 increase in price, it will sell 10 fewer boxes.
Let's define the revenue function as R(p) where p is the price per box. The initial revenue is 130 boxes × $9. For each $1 increase, the revenue function becomes (130 - 10(p - 9)) × p. We need to find the value of p that maximizes this revenue function.
Let's calculate:
At $9: R($9) = 130 × $9 = $1170At $10: R($10) = (130 - 10(1)) × $10 = 120 × $10 = $1200At $11: R($11) = (130 - 10(2)) × $11 = 110 × $11 = $1210At $12: R($12) = (130 - 10(3)) × $12 = 100 × $12 = $1200We can see that the revenue is maximum at $11 per box. So, the price per box that will provide the maximum revenue for the computer company is $11.
HELP ME!!!!!!!!!!!!!!!1 translate each sentence into an equation
1- 7 berries are 5 less than twice the number of berries Mickey had for lunch.
2- Negative 4 times the difference of a number 7 is 12
Jordan bought 9 pounds of fruit. He paid $2.39 a pound for 5 pounds. He paid $1.99 a pound for the rest. How much did Jordan spend on fruit? (please let me know how you did it)
Martha is cycling at a speed of 20 kilometers per hour. how long will it take her to cover a distance of 60 kilometers?
A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.
|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.
The sum of two numbers is seventy-two. Twice one of them equals ten times the other. What are the numbers?
Bill takes the commuter train to work every day. during the morning commute, a train arrives every 25 min. if bill arrives at the station at a random time for the morning commute, what is the probability that he will have to wait at least 5 min for a train?
Find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384. A. 5.1318 B. 38.5947 C. 4.9185 D. 43.5132
To find the difference, first find the product of 21.33 and 2.04, then find the sum of 1.115, 3.18, 22.0613, and 12.2384, and finally subtract the sum from the product. The correct answer is 4.9185.
To find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384, follow these steps:
Calculate the product of 21.33 and 2.04:The difference is 4.9185, which corresponds to option C in the given choices.