The required vertex form of the given equation is y = x² - 4x + 7.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
y = (x - 2)² + 3
Simplifying the expression,
y = x² -4x + 4 + 3 {since (a - b)² = a² + b² -2ab}
y = x² - 4x + 7
Thus, the required vertex form of the given equation is y = x² - 4x + 7.
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a = 2bh+6
make b subject algebraic expression
Answer:
b = (a - 6)/2h
Step-by-step explanation:
a = 2bh + 6 (subtract 6 from both sides)
a - 6 = 2bh (divide both sides by 2)
(a - 6)/2 = bh (divide both sides by h)
(a - 6)/2h = b
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17. The Bricklayer needs 100 pieces of angle, each to be cut 54 3/16" long. 1 point
How many can be cut from a 20% length (do not include waste or thickness of
cut)? How many pieces of 20' angle are needed in order to have the 100
pieces?
The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
How to determine the number
From the information given;
The bricklayer needs = 100 pieces of angle
The number of cuts = 54
Length of cuts = 3/ 16'' Inches
a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts
= 20/ 100 × 3/ 16 × 54
= 0. 2 × 0. 1875 × 54
= 2. 0
The number of cuts would be 2
b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle
= 100/ 20
= 5 pieces
The number of pieces of 20' angle is 5
Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
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How many full cases and additional items are needed to fulfill the order? 50 8
The computation illustrate that there'll be 13 cases and 2 additional units.
How to illustrate the information?From the information given, it was stated that 80 units are needed, 6. units per case.
Therefore, the number of cases will be:
= 80/6
= 13 remainder 2.
Therefore, there'll be 13 cases and 2 additional units
Complete information
80 units are needed, 6. units per case. What is the number of cases and the number of additional units?
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help me pls: what is
four and two eighths minus two and five eighths equals
Answer:
13/8
Step-by-step explanation:
4 2/8 - 2 5/8
34/8 - 21/8 = 13/8
1 5/8 as a mixed fraction
Question 2: Xiulin and Meifang had an equal number of postcards. Meifang gave some of her postcards to Xiulin. After that, Meifang had 76 fewer postcards than Xiulin. Given that Meifang had 72 postcards left, find the number of postcards Xiulin had at first.
110 postcards Xiulin had at first.
What is algebric equation?Algebric equation is a mathematical statement in which two equation set equal to each other.
Let the number of postcards belonging to Xiulin and Meifang be x.
Let the number of postcard Meifang gave to Xuilin be 'a'
Number of postcard left with meifang
=> x-a = 72
=> x = 72+a
Meifang had 76 fewer postcards than Xiulin.
so, (x+a)-72=76
72+a+a-72=76
2a = 76
a = 38
meifang give 38 cards to xuilin
x = 72+38
= 110
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The profit function for a certain commodity is given by () = 110 − 2 − 1000. Find the level of production that yields maximum profit and hence find the maximum profit.
Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.
What is the maximum profits unit?With a profit function:
=-x² + 110x - 1,000
Using a parabola function, we know:
= -b / 2a
The maximum units is:
= -110 / (-2 x 1)
= 55 units
The maximum profit is:
= -(55)² + (110 x 55) - 1,000
= $2,025
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Hector wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 4 feet and bases of 6 feet and 10 feet is shown.
$136
$128
$112
$32
The total cost to laminate the table top is $128.
What is the total cost to laminate the table top?A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.
The first step is to determine the area of the table top.
Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
0.5 x (6 + 10) x 4 = 32 square foot
Now, multiply the area by the cost per square foot
32 x 4 = $128
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5660 and his stock in Company B was worth $2500. The stock in Company A has increased 5% since last year and the stock in Company B has increased 9%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary)
Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The values of the stocks of Company A and Company B, after the increase are given, respectively, by:
Company A: 5660 x 1.05 = $5,943.Company B: 2500 x 1.09 = $2,725.The total values are given as follows:
Before the increase: 5660 + 2500 = 8160.After the increase: 5943 + 2725 = 8668.The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:
P = (8668 - 8160)/8160 x 100% = 6.2%.
The total percentage increase in the investor's stock account was of 6.2%.
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A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?
Answer:
B: 8.3
Step-by-step explanation:
We will substitute 600 to the y, since our final answer will be a number that makes the value of the stock reach $600.
log (y) = 0.30x + 0.296
Replacing y with 600, the equation becomes:
log (600) = 0.30x + 0.296
2.78 = 0.30x + 0.296
To move all the x and real numbers to different sides, we take 0.296 away from both sides to form:
2.78 - 0.296 = 0.30x
2.484 = 0.30x
x = 8.28
The approximation of 8.28 will be rounded to 8.3.
Then our final answer will be B: 8.3
Please help me put them in correct place
The inequalities that match the given expressions are
x ≤ 95
x > 100
5x ≤ 100
20 ≤ x ≤100
respectively
Writing linear inequalitiesFrom the question, we are to match the statements with the corresponding inequalities
Nora's height(x) is at least 5 cm less than Stacy who is 100 cm tallx ≤ 100 -5
x ≤ 95
Temperature(x) is greater than the boiling point of water (100 °C)x > 100
John buys x chocolates worth $5 each but he has only $100 in his pocket5x ≤ 100
Ronny decided not to exceed 100L of water usage and ends up using at least 1/5th of this limit every dayx ≤ 100
and
x ≥ 1/5 × 100
x ≥ 20 ≡ 20 ≤ x
∴ 20 ≤ x ≤100
Hence, the inequalities that match the given expressions are
x ≤ 95
x > 100
5x ≤ 100
20 ≤ x ≤100
respectively
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-14x^2+1035x-10266
The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13
Quadratic equationy = -14x² + 1035x - 10266
solve the quadratic equation-14x² + 1035x - 10266 = 0
x = -b ± √b² - 4ac / 2a
= -1035 ± √1035² -4(-14)(-10266) / 2(-14)
= -1035 ± √1071225 - 574896 / -28
= -1035 ± √496329 / -28
x = 1035 / 28 ± √496329 / 28
x = 11.80 or 62.13
The maximum value of x is 62.13
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express using positive exponent
[tex] {3c}^{ - 2} [/tex]
Answer: [tex]\frac{3}{c^2}[/tex]
Step-by-step explanation:
This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].
A bag contains 2 yellow balls, 3 green balls, 5 red balls and 6 black balls.
What is the probability of either a yellow ball or a red ball being drawn if
only one ball is drawn?
Answer:
7/16
Step-by-step explanation:
(2+5)/(2+3+5+6) = 7/16
The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
According to the given question.
Numnber of yellow balls = 2
Number of green balls = 3
Number of red balls = 5
Number of black balls = 6
So,
The total number of balls in a bag = 2+ 3+ 5 + 6 = 16
And,
The sum of yellow and red ball = 2 + 5 = 7
Therefore,
The probability of either a yellow or a red ball being drawn if only one ball is drawn
= [tex]\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}[/tex]
[tex]= \frac{7}{16}[/tex]
Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
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Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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solve the following portion for x/11=8/3. round to nearest tenth
– 42 – 54 + 96 =
what is the answer
Answer:
Answer:the answer is zero
Answer:the answer is zero Step-by-step explanation:
Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero
[tex] - 42 - 54 + 96 = 0[/tex]
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
How to use weighted averages to find the correct juice concentration
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
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Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?
Abiding by the two rules, the number of variable names we can have in Python are; 63
How to name variables in Python Programming?The rules for python are given as;
1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).
1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.
2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.
Now, abiding by the two rules above, the number of variable names we can have in Python are;
26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names
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The area of a rectangle is 44 ft², and the
Length of the rectangle is 3 ft less than twice
The width. Find the dimensions of the rectangle.
Answer:
Width = 5.5ft, Length = 8ft.
Step-by-step explanation:
Area of Rectangle = Length x Width
Let w be the Width of the rectangle.
From the information given from the question,
Length = 2w - 3 (3ft less than twice the width)
Area of Rectangle = [tex](2w-3)w\\=2w^{2} -3w[/tex] = 44
Now we can solve for w to find the dimensions.
[tex]2w^{2} -3w-44=0[/tex] (Quadratic Equations)
We can use the Quadratic formula to find w.
[tex]w=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
Since a = 2, b = -3 and c = -44,
[tex]w=\frac{-(-3)+/-\sqrt{(-3)^{2}-4(2)(-44) } }{2(2)} \\= 5.5 or -4 (reject)[/tex]
We reject negative values here.
Therefore, the width of the Rectangle = 5.5ft
While the length of the rectangle = 2(5.5) - 3 = 11 - 3 = 8ft
Will give 80 points!
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 60 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students under age 15 travel to school by car? Round to the nearest whole percent.
11%
18%
41%
Answer:
There are about 80 students age 15 and above take a car to school.
Step-by-step explanation:
1. For all the columns the total has been given.
2. Bus is taken as 60 as walk/bike has been given 65 under age 15.
3. 195 row total Age 15 and above has been provided and updated.
4. Walk/Bike 152, 65 is already given Age 15 and above difference is 87.
5. Bus 60 under age 15 is already given total 110 difference is 50.
6. Age 15 and above 65,50,195 (Total) is already given row difference is 80.
7. Car is Age 15 and above is 80 and Total column is 98 difference is 18.
8. Age 15 and above take car is 80.
Answer:
its 41%
Step-by-step explanation:
i took the test
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the population standard deviation is 40 . Round your answer to next whole number.
Using the z-distribution, it is found that a sample of 171 should be selected.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, the parameters are:
[tex]z = 1.96, \sigma = 40, M = 6[/tex]
Hence we solve for n to find the needed sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{40}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 40 \times 1.96[/tex]
[tex]\sqrt{n} = \frac{40 \times 1.96}{6}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2[/tex]
n = 170.7.
Rounding up, a sample of 171 should be selected.
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I'm have some issues with the problem shown in the screenshot and would love some help.
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.Maximum volume of the box is approximately 1048.6 in.³How can the dimensions and volume of the box be calculated?The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let x represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, V, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]
Which gives;
[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]
6•x² - 106•x + 315 = 0
[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
Width ≈ 18 - 2×4.55 in. = 8.89 in. Length of the box ≈ 35 - 2×4.55 in. = 24.89 in. Height = x ≈ 4.55 in.The maximum volume of the box, V ≈ 1048.6 in.³Learn more about differentiation and integration here:
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Is x – 5 a factor of the function f(x) = x3 – 5x2 + 7x – 35? Use the Remainder Theorem to justify your answer.
Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,
Remainder theoremIn order to determine whether x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35, we will show that f(5) = 0
Substitute x = 5 into the function to have;
f(5) = 5^3 – 5(5)^2 + 7(5) – 35
f(5) = 125 - 125 + 35 - 35
f(5) = 0
Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,
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for this graph, mark the statements that are true.
Answer:
C,D
Step-by-step explanation:
C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0
D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.
Which is the graph of the inequality?
5y+x>−10
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
We can simplify the inequality to:
y > (-1/5)*x - 2
From that, we conclude that the correct option is the last one.
Which is the graph of the given inequality?
Here we have the inequality:
5y + x > -10
If we isolate y, we get:
y > (-10 - x)/5
y > (-1/5)*x - 2
Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.
From that we conclude that the correct option is the last one:
"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."
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The length of a rectangle is 1 yd more than double the width, and the area of the rectangle is 66 yd^2 . Find the dimensions of the rectangle.
The dimensions of the rectangle as described in the task is; 12.4 by 5.7 yd.
What is the dimension of the rectangle?Since the area, length and breadth of the rectangle are as described, it follows that;
66 = x(2x+1)
66 = 2x² + 1
x² = 32.5
x = 5.7
Therefore, the dimensions are 5.7 and 12.4.
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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
Answer:
She does not get bonus points and she ends up at level 5.
Equation: 4 - 6 + 8 -1 = 5
Equation using only addition: 4 + -6 + 8 + -1 = 5
I hope this helps!
Find the value of all trigonometric functions of 135°
Answer:
sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2
cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2
tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1
csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2
sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2
cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1
Step-by-step explanation:
hope this helps
The total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16
what is the price of each cap?
what is the price of what umbrella ?
If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.
Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.
We have to find the price of one umbrella and one cap.
We have to form equations first to find the price of umbrella and cap.
Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.
let the price of umbrella be x and price of cap is y.
We know that total cost is equal to price of one unit multiplied by the units.
According to question.
2x+y=20----------1
x+2y=16-----------2
Multiply equation 2 by 2 and then subtract resulted equation from equation 1.
2x+y-2x-4y=20-32
-3y=-12
y=-12/-3
y=4
put the value of y in equation 2 to get the value of x.
x+2y=16
x+2*4=16
x+8=16
x=16-8
x=8
Hence the price of one umbrella is $8 and the price of one cap is $4.
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One-fifth of a number x is less than 8. Find the greatest possible prime number x.