The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)
What does the term Algebraic Expression means?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
Given the expression, we need to solve it by using the properties of basic multiplication.
= (8 - 2x)*(-0.25x)
= (8*(-0.25x)) + (-2x * (-0.25x))
= -2x + 0.5\(x^{2}\)
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SOMEONE PLEASE HELP ME
Answer:
27
Step-by-step explanation:
math
A rectangular frame has a diagonal with a length of 20 inches and a longer side with a length of 15 inches
Which of the following is closest to the length of its shorter side?
(1) 9.7 inches
(3) 13.2 inches
(2) 11.9 inches
(4) 14.8 inches
Answer:
(3)13.2
Step-by-step explanation:
c²=a²+b²
20²=15²+b²
20²-15²=b²
400-225=b²
175=b²
b=√175
b=13.2inches
The one-to-one function f is defined below.
f(x)= x/8x-3
Find f^-1(x),where f^-1 is the inverse of f. Also state the domain and range of f^-1 in interval notation.
The inverse of f, f^-1 = 8x / (x + 3)
To find the inverse function, let's consider the following steps:
Step 1: Replace f(x) with y. y = x/8x - 3
Step 2: Swap the x and y variables. x = y/8y - 3
Step 3: Solve for y. x(8y - 3) = y x 8y - 3x = y y = f⁻¹(x) = 8x / x + 3
Therefore, f⁻¹(x) = 8x / (x + 3)
The domain of f⁻¹ is all real numbers except -3, as it is not defined for x = -3.
Hence the domain is (-∞, -3) U (-3, ∞).
The range of f⁻¹ is also all real numbers except 0, as it is not defined for x = 0. Hence the range is (-∞, 0) U (0, ∞).
Thus, the domain and range of f⁻¹ are (-∞, -3) U (-3, ∞) and (-∞, 0) U (0, ∞) respectively, in interval notation.
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1. What is the definition of function?
Answer:
a technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. we can write the statement that f is a function from x to y using the function notation F:X~F
Write the expression as a number in scientific notation.
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
4.2 x 1010
3.4 x 1010
4.2 x 105
3.4 x 105
The expression as a number in scientific notation is 4.2 * 10^5
How to write the expression as a number in scientific notation?The expression is given as:
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
Rewrite properly as:
[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]
Evaluate the product of 7 and 5.4
So, we have:
[37.8* 10^3 * 10^4]/[9 * 10^2]
Evaluate the product of 10^3 and 10^4
So, we have:
[37.8* 10^7]/[9 * 10^2]
Evaluate the quotient of 37.8 and 9
So, we have:
[4.2 * 10^7]/[10^2]
Evaluate the quotient of 10^7 and 10^2
So, we have:
4.2 * 10^5
Hence, the expression as a number in scientific notation is 4.2 * 10^5
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simplify the sum w^2+2w-24/w^2+w-30 + 8/w-5
according to question the simplified expression is (w + 4) / (w - 5).
To simplify the expression (w^2 + 2w - 24) / (w^2 + w - 30) + 8 / (w - 5), we need to first factor the two quadratic expressions in the numerator and denominator of the first term:
w^2 + w - 30 = (w - 5)(w + 6)
w^2 + 2w - 24 = (w + 6)(w - 4)
So, the first term simplifies to:
(w + 6)(w - 4) / (w - 5)(w + 6) = (w - 4) / (w - 5)
Now, we can rewrite the entire expression as:
(w - 4) / (w - 5) + 8 / (w - 5)
To combine the two fractions, we need to find a common denominator, which is (w - 5). Then, we can add the numerators:
[(w - 4) + 8] / (w - 5) = (w + 4) / (w - 5)
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Which expression shows another way to write 36+16?
4(9)+4
4(9+4)
6(6+8)
Answer: 4(9+4)
Step-by-step explanation:
(4)(9) = 36
(4)(4) = 16
4(9+4) = 36+16
Find the surface area of the composite solid. Write your answer as a decimal.
Answer:
283.5 cm squared
Step-by-step explanation:
The surface area of a solid is basically just the sum of the areas of all the exterior sides. In this figure, we have 3 congruent triangles at the top, 3 congruent rectangles on the sides, and 1 triangle at the base. We need to find all these areas.
3 congruent triangles:
The area of a triangle is denoted by: A = (1/2) * b * h, where b is the base and h is the height.
Here, the base of one triangle is 10 and the height is 4. So:
A = (1/2) * b * h
A = (1/2) * 10 * 4 = 20
Since there are 3 such triangles, multiply 20 by 3:
20 * 3 = 60 cm squared
3 congruent rectangles:
The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.
Here, the length is 6 and the width is 10, so:
A = lw
A = 6 * 10 = 60
There are 3 such rectangles, so multiply 60 by 3:
60 * 3 = 180 cm squared
1 base triangle:
Again we use the formula A = (1/2) * b * h for this area.
Here, the base is 10 and the height is 8.7, so:
A = (1/2) * b * h
A = (1/2) * 10 * 8.7 = 43.5 cm squared
Add all these together:
60 + 180 + 43.5 = 283.5 cm squared
The answer is thus 283.5 cm squared.
Answer:
283.5 cm²
Step-by-step explanation:
3 rectangles + 3 triangles on top + triangular base
3(10×6) + 3(½×10×4) + (½×10×8.7)
180 + 60 × 43.5
283.5 cm²
How are the discounted fees related to the rental fee? a bike shop charge iready
Discounted fees serve to attract more customers, increase rental volume, and foster customer loyalty.
Discounted fees and rental fees in a bike shop are related in the sense that discounted fees usually represent a reduced or discounted rate applied to the standard rental fee. The discounted fees aim to incentivize customers and attract more business by offering lower prices for renting bikes.
Typically, bike shops have standard rental fees for different types of bikes and durations. These fees are set based on factors such as the type of bike, its condition, the rental duration (hourly, daily, weekly), and the market demand. However, bike shops may choose to offer discounts to certain customers or during specific periods to encourage more rentals.
Discounted fees can be applied in various ways:
1. Percentage discounts: The rental fee may be reduced by a certain percentage, such as 10% off the standard rental fee. For example, if the standard rental fee for a bike is $20 per day, a 10% discount would reduce the fee to $18.
2. Fixed amount discounts: A fixed dollar amount may be deducted from the standard rental fee. For instance, a bike shop may offer a $5 discount on all rentals, regardless of the rental duration or bike type.
3. Promotional discounts: Bike shops may introduce promotional offers or special deals that provide discounted fees for a limited time or specific circumstances. For example, they might offer discounted fees during off-peak seasons or for group rentals.
Discounted fees serve to attract more customers, increase rental volume, and foster customer loyalty. By offering lower prices, bike shops can incentivize potential customers to choose their services over competitors or encourage repeat business from existing customers.
discounted fees may reduce the rental revenue per transaction, the goal is to generate higher overall revenue by attracting a larger customer base and increasing rental frequency. The specific relationship between discounted fees and rental fees can vary based on the pricing strategy adopted by the bike shop and the market dynamics in which it operates.
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In the graph, what does A represent?
major axis
vertices
minor axis
foci
An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. In the graph, the A represents the minor axis of the ellipse.
What is the equation of ellipse if its major and minor axis and center are given?Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, and let the ellipse is centered on (h,k) with major ellipse parallel to x-axis, then the equation of that ellipse would be:
\(\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1\)
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
\(\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1\)
An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. Since an ellipse has two diameter, the major and the minor diameter. Therefore, in the graph, the A represents the minor axis of the ellipse.
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Find the equation of the line whose graph passes through (−2,−3) and has slope 5 .
Answer:
y +3 = 5(x +2)
Step-by-step explanation:
You want the equation of a line with slope 5 through the point (-2, -3).
Point-slope formThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
Applicationy +3 = 5(x +2) . . . . . . line with slope 5 through point (-2, -3)
__
Additional comment
This can also be written as ...
y = 5x +7 . . . . . . . . . subtract 3 and simplify
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* You have a dog that can run 5 km/hr. How fast can she run in mi/hr? (i.e. convert the rate to miles per hour) (1.6 km=1mi) DO NOT JUST TYPE THIS INTO A CONVERTER ONLINE. YOU WILL NOT GET THE ANSWER RIGHT. Express your answer as decimal, rounded to the nearest thousandth (three decimal places) in mi/hr - no spaces EXAMPLE: 78.345mi/hr
The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.
To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.
However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.
Therefore, the dog can run at approximately 3.125 mi/hr.
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Let x and y be real numbers such that x < 2y. Prove that if
7xy ⤠3x2 + 2y2, then 3x ⤠y.
To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.
Start by assuming the opposite, that is, 3x > y.
From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)
We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)
Simplifying, we get:
\(y(14x - 12y) \leq 0\)
Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.
If y ≤ 0, then 3x ≤ y is trivially true.
If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)
But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.
Therefore, we can conclude that 3x ≤ y.
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evaluate (3.02)(0.5)=
Answer:
1.51
Step-by-step explanation:
multiply the numbers together
Which of these tables is a non linear function
Answer:
C
Step-by-step explanation:
Because on all the graphs all the numbers on the Y side are essentially adding one. With the 3rd graph, it goes from 17 to 19, skipping 18. Therefore it is not linear.
J is the midpoint of
HI
and
GI
≅
GH
. Complete the proof that △GHJ≅△GIJ.
G
H
I
J
4) reflexive property
5) SSS
A chord that passes through the center of a circle is a
Answer:
A cord passing through the centre of the circle is called as its diameter
Step-by-step explanation:
brainliest plz
Answer:
Diameter
Step-by-step explanation:
Evaluate the following expression. 6^-1
Suppose you have a job that pays $13.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable I, that gives the amount of money, y, you will earn for working 2 hours in one week. y = _____ , Preview with ____ <= x <= ____ b. Use the function rule you have written in part a. to find the y values for the given z values: x = 10, y = ___ x = 20, y= ___
x = 30, y = ____. x = 40, y = ____ c. Construct a line graph from the information found in b. 520+ -480+ 440+ 400- 360 320- 280- 240 200 160+ 120+ 80- 40+ 10 20 30 40 Clear All Draw: Line Dot Open Dot d. State the domain and range of this function. Domain: ____ <= x <= ______
Range: <= y <= _____
e. What is the minimum amount you can earn in a week with this job? You'll earn at least $ ______.
What is the maximum amount? You can earn up to $ ____.
The maximum amount you can earn is $540
a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.
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what is the value of x?
Which of the following equations represent linear functions?
The picture will be shown
Help fast!! What is the exact volume of the cylinder?
36
324
54
18 in
Answer:
V = 54 pi in ^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi (3)^2 * 6
V = pi (9) *6
V = 54 pi in ^3
find the coordinates of the image given the coordinates of the preimage and the translation
The transformation is a translation of 7 units in the x-axis and (-1) in the y-axis.
We can write this transformation for a point P=(x,y) as:
\(P=(x,y)\longrightarrow P^{\prime}=(x+7,y-1)\)Then, if we apply the transformation to J, F and N we will get:
\(J=(-3,1)\longrightarrow J^{\prime}=(-3+7,1-1)=(4,0)\)\(F(-2,3)\longrightarrow F^{\prime}=(-2+7,3-1)=(5,2)\)\(N=(-2,0)\longrightarrow N^{\prime}=(-2+7,0-1)=(5,-1)\)The transformed points are J'=(4,0), F'=(5,2) and N'=(5,-1).
The number of years y is a function of the number of months m what is the equation
Answer:
y · m
Step-by-step explanation:
this is correct because you multiply y and m
A company has just paid a dividend of 4.91$. Its discount rate is 8.6%, and the expected perpetual growth rate is 3.6%. What would you expect to be the stock's price TODAY?
Based on the given dividend of $4.91, a discount rate of 8.6%, and an expected perpetual growth rate of 3.6%, we would expect the stock's price to be $98.20 today.
To determine the stock's price today, we can use the dividend discount model (DDM), also known as the Gordon growth model. The DDM calculates the present value of all future dividends, taking into account the required rate of return and the expected growth rate.
Let's plug in the values given in your question:
Dividend (D) = $4.91
Discount Rate (r) = 8.6% or 0.086
Perpetual Growth Rate (g) = 3.6% or 0.036
Now we can substitute these values into the formula to calculate the stock's price today:
Stock Price =4.91 - 0.086 = 0.036
Stock Price= 0.086−0.036 = 4.91
Simplifying the denominator:
Stock Price = 4.91/0.05
Stock Price=98.20
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Josiah has a loyalty card good for a discount at his local grocery store. The item he wants to buy is priced at $21, before discount and tax. After the discount, and before tax, the price is $18.27. Find the percent discount.
Answer:
13%
Step-by-step explanation:
21-18.27=2.73
2.73/21= 0.13
0.13 x 100=13%
Maya is working two summer jobs, making $21 per hour tutoring and making $8 per
hour clearing tables. In a given week, she can work a maximum of 13 total hours and
must earn at least $160. Also, she must work at most 7 hours tutoring and a
minimum of 3 hours clearing tables. If x represents the number of hours tutoring
and y represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
Answer:
yes it can be done.
14. Describe the typical quiz scores of the students. Explain your choice of measure.
To describe the typical quiz scores of the students, a common measure used is the mean, or average, score. The mean is calculated by summing up all the scores and dividing by the total number of scores.
Given its simplicity and simplicity in interpretation, the mean was chosen as a proxy for normal quiz scores. It offers a solitary figure that encapsulates the scores' median. We can figure out the pupils' overall performance on the quiz scores by computing the mean.
It's crucial to keep in mind, though, that outliers or extremely high scores dividing might have an impact on the mean. The mean may not be an accurate representation of the normal results of the majority of students if there are a few students who severely underperform or do very well on the quizzes.
To get a more thorough picture of the distribution of quiz results in such circumstances, it might be beneficial to take into account additional metrics like the median or mode.
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a student cost for last semester at her community college was $2200. She spent $308 of that on books. whats % of last semesters college costs was spent on books
Answer:14%
Step-by-step explanation:
Dived $308 by the total $2200 and you get a .14 multiply that by the 100 to get percentage and you get 14%
Write the inequality that represents the sentence, "Four less than a number is greater than 58."
Answer:
n-4>58
Step-by-step explanation:
Answer:
n-4>58
Step-by-step explanation: