The quadratic function only has a maximum at y = 2, and:
Domain: All real numbers.Range: y ≤ 2Increases in: (-∞, 2)Decreases in: (2, ∞)How to find the minimum or maximum of the given function?Here we have a quadratic function:
y = -x^2 - 4x - 2
Because the leading coefficient is negative, we know that the parabola opens downwards, then we only have one maximum which is at the vertex.
The x-value of the vertex is at:
x = -(-4)/(2*-1) = 4/-2 = -2
Evaluating in that x-value we will get the maximum:
y = -(-2)^2 - 4*-2 - 2 = -4 + 8 - 2 = 2
The maximum is y = 2.
Then:
The domain is the set of all real numbers like in all quadratics.
The range is the set y ≤ 2
And the function increases in (-∞, 2)
And decreases on (2, ∞).
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Johannes Kepler thought that the Platonic solids were related to the orbits of the planets. He made models of each of the Platonic solids. He made a frame of each of the Platonic solids by fashioning together wooden edges. How many edges did Kepler have to make for the cube?
In order to construct frames for each of the platonic solids, Kepler has to construct nine wooden edges for the cube. These edges will then be pieced together to make the frames.
The Edges of Kepler:He created models of each of the platonic solids since it is shown in the data that they are connected to the planets' orbits. Kepler fashioned wooden edges to form each of the platonic solids into a frame.
Two of the six planets identified at the time were regarded to be platonic solid cubes. The three-dimensional shape of a cube has 12 edges and 8 corners.
Thus, there are 4 x 2 + 1 edges.
= 9
Kepler must create nine wooden edges for the cube in order to piece together wooden edges to form frames for each of the platonic solids.
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1
Write an equation for the line parallel to the given line that contains C.
C(2,7); y=-3x+5
The equation of the parallel line is
(Use integers or fractions for any numbers in the equation. Simplify your answer.)
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so gradient of line is -3.
Equation of line is y = -3x + c.
Substitute C(2,7) into the equation to find c.
7 = -3(2) + c
c = 13
Hence, equation of line is y = -3x + 13.
Use AC method to solve this (please help!)
20x^2-13x-15
Please explain step by step!
( 5x + 3 )( 4x - 5 ) is the factorized form of the polynomial 20x² - 13x - 15 using the AC method.
How to factor a polynomial?AC Method is simply a method of factoring trinomials in the form ax² + bx + c.
Given the polynomial in the question;
20x² - 13x - 15
Compare to the form ax² + bx + c
a = 20b = -13c = -15To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;
a × c = 20 × -15 = -300
and whose sum is;
b = -13
Now, factor -13 and of -13x
20x² - 13(x) - 15
We know that -13 is the same as 12 - 25
20x² + (12 - 25)(x) - 15
20x² + (12 - 25)x - 15
Apply distributive property
20x² + 12x - 25x - 15
Group the terms
(20x² + 12x) - 25x - 15
Now, factor out the greatest common factor from each group
4x( 5x + 3 ) - 5( 5x + 3 )
( 5x + 3 )( 4x - 5 )
Therefore, the factorized form of the polynomial is ( 5x + 3 )( 4x - 5 ).
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Find the equation of the line passing
through the points (4, 2) and (6, 10).
y=[?]x+[ ]
Answer:
y = 4x - 14
Step-by-step explanation:
The equation of a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
We can calculate the slope with the two given points. Slope is the Rise/Run between these 2 points:
(4,2) and (6,10)
Rise: 10 - 2 = 8
Run: 6 - 4 = 2
Slope = Rise/Run = 8/2 = 4
m is 4, so we can write: y = 4x + b
We can find b by entering either of the given points and solving for b. I'll use (4,2):
y = 4x + b
2 = 4*(4) + b
2 = 16 + b
b = -14
The equation becomes y = 4x - 14
See the attached graph.
Please help I am so lost
Part A-Well, Miranda is going 4mph, so the answer would be t=m/4, because it's how many miles she's traveled divided by 4 to get how long she's been skiing. With the info we have, we could also write 0.5=2/4
Part B-So, we have that m=5.2, so we do t=5.2/4 5.2/4=1.3, so we have 1.3=5.3/4. So, she's been skiing for 1.3 hours.
To convert miles per hour to feet per second, which conversion factor would not be used?
To convert miles per hour to feet per second the conversion factor that wouldn't be used is option d: 1 mi/5280 ft and 5 miles per hour will be equal to 7.34 feet per seconds.
As per the question statement, we are asked that which of the given conversion factors, will not be used for converting miles per hour to feet per second.
We should be knowing the following values for conversion:
we know, 1 mile = 1.6 km = 5280 feet
and 1 hour = 60 minutes = 3600 seconds.
Now, mi/hr * 1hr/60min * 1min/60sec * 5280ft/mi
Note that units all cancel out leaving only ft/sec
Hence option d : 1 mi/5280 ft is not appropriate for converting mi/hr to ft/sec.
For e.g., 5 miles per hour = 5*5280/3600
5 mil/hr = 7.34 ft/sec
Hence, to convert miles per hour to feet per second the conversion factor that wouldn't be used is option d: 1 mi/5280 ft and 5 miles per hour will be equal to 7.34 feet per seconds.
Conversion factor: A conversion factor is a number that is used to multiply or divide one set of units into another.To learn more about conversion factor, click on the link given below:
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through: (1,-4), slope =-6
Answer:
y = -6x + 2
Step-by-step explanation:
(1, -4) m = -6
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-4)= -6 (x - 1)
y + 4 = -6x + 6
-4 -4
------------------------
y = -6x + 2
I hope this helps!
Karl wants to lose some weight by burning extra calories each week (2 kg =
approx. 3000 calories). He plans to achieve this by riding a bicycle, which
burns 350 calories an hour, and by walking, which burns 200 calories an
hour. If Karl has 10 hours per week to devote to exercise, determine the
combination of walking and cycling that will allow him to achieve his goal
of burning exactly 3000 calories.
Karl must cycle for seven hours and stroll for three hours each week in order to burn precisely 3000 calories.
How is the combination of walking and strolling calculated for burning exactly 3000 calories?Given:
No. of calories to burn by Karl = 3000
No. of calories burnt per hour by walking = 200
No. of calories burnt per hour by cycling = 350
No. of hours per week for Karl = 10
To find: No. of hours required to exercise through walking and cycling for burning 3000 calories.
Let W be the no. of hours required to burn calories in one hour by walking.
Let C be the no. of hours required to burn calories in one hour by cycling.
Formulating the given information
W+C = 10 ⇒ (1)
200W + 350C = 3000
Multiplying equation (1) by 200
200W + 200C = 2000
Subtracting equation (3) from equation (2)
150C = 1000
C ≈ 7
Substituting in equation (1)
W + C = 10
W + 7 = 10
W = 3
Therefore W = 3 and C = 7
Karl must cycle for seven hours and stroll for three hours each week in order to burn precisely three thousand calories.
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A trout was swimming 9 feet below the surface of a lake. It dove down 8 more feet to search for food. What is the position of the trout now relative to the surface?
To solve the problem, Denise subtracted
–
9–8 and came up with an answer of
–
17 feet. Is Denise correct? Why or why not?
The position of the trout now relative to the surface is -17 feet. Therefore, Denis is wrong.
What is an expression?It should be noted that a expression shows the relationship between the variables.
From the information, a trout was swimming 9 feet below the surface of a lake and it drove down 8 more feet to search for food.
The position will be the addition of the feets. This will be:
= -9 + (-8)
= -9 - 8
= -17 feet
The position is -17 feet.
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2(x-0.1x-2.70)=56.70 step by step pls
For the given equation 2(x-0.1x-2.70)=56.70, the value of x is 7.76
How are equations used?The equals sign is used in mathematical formulas to show that two expressions are equal. The first stage in resolving a variable equation is determining the values of the variables that lead to equality. The variables for which the equation must be solved are known as the unknown variables, while the values of the unknown variables that satisfy the equality are referred to as the equation's solutions. Identity equations and conditional equations are the two types of equations.
Given equation, 2(x-0.1x-2.70) = 56.70
or, 2(0.9x-2.70) = 56.70
or, 1.8x - 5.40 = 56.70
or, 1.8x = 56.70+5.40
or, x = 62.10/1.8 = 7.76
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Trevor makes some flapjacks using this recipe and uses 200g of syrup. What quantity of butter should he use
Answer:
The quantity of butter that was used will be 100g.The total quantity of flapjacks that was made will be 450g.Step-by-step explanation:
How to illustrate the information?It should be noted that the ratio of syrup, sugar, butter and oats was illustrated as:
1:2:3
Therefore, when 50g of syrup was used, the quantity of butter that was used will be:
= 50 × 2 = 100g
The rural quantity of flapjacks that was made will be:
= 50 + 100 + 100 + 200.
= 450g
Therefore, the total quantity of flapjacks that was made will be 450g.
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Write an equation for a parabola with x-intercepts (-1,0) and (3,0) which passes through the point (2,-6).
Answer:
f(x) = a·(x + 1)·(x - 3)
f(2) = a·(2 + 1)·(2 - 3) = a·3·(-1) = -3·a = -6 --> a = 2
f(x) = 2·(x + 1)·(x - 3)
f(x) = 2·(x^2 - 3·x + x - 3)
f(x) = 2·(x^2 - 2·x - 3)
f(x) = 2·x^2 - 4·x - 6
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many students are boys?
Answer:
There are 15 boys.
Step-by-step explanation:
Let x represent the answer!
it would be 4x+3x=35
add 4x+3x
7x=35
divide 35 by 7
x=5
multiply 5 x 4 then you get 20 girls
then multiply 5 x 3 to get 15 boys.
your welcome <3
I need help finding how many notes there are? the ratio of coins to notes in a bag is 3 to 8. if there are a total of 24 coins how many notes are there?
The ratio of coins to notes in a bag is 3 to 8.
The total number of coins is 24.
Let there be y number of notes in the bag. Then we can write,
[tex]\frac{3}{8}=\frac{24}{y}[/tex]On solving we get,
[tex]\begin{gathered} 3y=24\times8 \\ y=\frac{24\times8}{3}=64 \end{gathered}[/tex]Thus there are 64 notes in the bag.
Find the surface area of this cylinder.
Round to the nearest tenth.
12cm
SA = [?] cm²
3cm
Enter
Answer:
approximately 282.74
Step-by-step explanation:
plss hurry i need to do this today
Answer:
I do not think that you can write √2 as a fraction. (4/3)² is 16/9.
Step-by-step explanation:
For √2 it cannot be written as a fraction because it has an infinite amount of decimals. For (4/3)² that equals 16/9 so you would place it on the second number line two ninths before 2.
Hope this helps!
In the figure below, m < 1 = (x + 14) and m < 2 = 3x
Find the angle measures.
The angle measures are;
m < 1 = 33°
m < 2 = 57°
How to determine the anglesIt is important to note that complementary angles are defined as pairs of angles that sum up to 90 degrees.
From the information given, we have the angle measures as;
m < 1 = (x + 14) m < 2 = 3xThis can be represented as;
m < 1 + m < 2 = 90
Now, let's substitute the values into the equation, we have;
(x + 14) + 3x = 90
expand the bracket, we have;
x + 14 + 3x = 90
collect like terms
4x = 90 - 14
subtract the values
4x = 76
Make 'x' the subject of formula, we get;
x = 76/4
x = 19
Then,
m < 1 = (x + 14) = 19 + 14 = 33°
m < 2 = 3x = 3(19) = 57°
Hence, the values are 33° and 57° respectively.
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The complete question is;
In the figure below, m < 1 = (x + 14) and m < 2 = 3x, are both complementary to each other
Find the angle measures.
The image of the point (-1, -3) under a translation is (-4,-2). Find the
coordinates of the image of the point (3, 1) under the same translation.
Answer:
[tex]image = (0 \: \: 2)[/tex]
John cashed a check for $630. The teller gave him three 50-dollar bills, eighteen 20-dollar bills, and t 10-dollar bills. Determine the value of t.
$630
The value of t is $12.
Solution:
3 x 50 = 150
18 x 20 = 360
The sum is 360 + 150 = 510. Then subtract the value 510 from 630.
$630 - 510
$120
120 / 10 = 12
Subtract the null hypothesis mean from the sample mean. Divide the difference by the sample standard deviation. Multiply the result by the square root of the sample size. The t value measures the magnitude of the difference relative to the variability of the sample data. In other words, T is simply the calculated difference expressed in units of standard error.
The larger the size of T the more evidence against the null hypothesis. The important t-value is the limit of the t-distribution. The t distribution is a probability distribution used to compute population parameters when the sample size is small and the population variance is unknown. The T-score is used to analyze whether to support or reject the null hypothesis.
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7. Two students solved the problems below. One of the students made an error. Explain the
student's error and how you would help the student get the correct answer.
MARIELBI
18.66 +3
6.33
NICO
62.4 13
+
4.8
Answer: If two students solved the problems below one of the students made an error. Mary is wrong while Nico is correct.
Error in calculation
Mary =66÷3 = 6. 33 (Wrong)
Nico= 62.4÷13=4.8 (Correct)
Hence.
Mary:
Using calculator 66/3 will gives us 22 and not 6.33.
66÷3=22
Nico
Using calculator 62.4/12 will give us 4.8 which means that Nico was correct.
Therefore If two students solved the problems below one of the students made an error. Mary is wrong while Nico is correct.
Please help, thank you
Answer:
Step-by-step explanation:
Because 2x+19 and x + 23 are alternative exterior angles, they have an equal value. Thus:
2x+19 = x + 23
Solve for x:
x + 19 = 23
x = 4
Find the amount of money
accumulated after investing a
principle P for years t at interest
rate r, compounded continuously.
P = $15,500 r=9.5% t=12
Round your answer to the nearest cent (hundredth).
Answer:
$48,464.91
Step-by-step explanation:
expand and simplify (x+3)(x+5)
Answer:
x^{2} +8x+15
Step-by-step explanation:
Use Distributive Property:
(x+3)(x+5)
[tex]x^{2}+5x+3x+15[/tex]
[tex]x^{2} +8x+15[/tex] Answer
Answer: x ^ 2 + 8x + 15
Step-by-step explanation: You can use the FOIL method to multiply. F - first two variables, so the two x.
x • x = x^2
O - outside, the outermost variables in the parenthesis, which would be x and 5.
x • 5 = 5x
I - inside, the innermost variables in the parenthesis, which would be x and 3.
x • 3 = 3x
L - last two variables, so 3 and 5.
3 • 5 = 15
Altogether:
x^2 + 5x + 3x + 15, which simplifies to x^2 + 8x + 15.
Image & example for clarity! Hope this helped!
Bronze is an alloy made of copper and tin. The ratio of copper to tin is 23 to 2 if a bronze statue has a mass of 50kg, what is the mass of copper in the statue
The mass of copper in the statue is 46kg.
Ratio of cooper to tin is 23 to 2 and similarly it would be 46 to 4, which adds up to 50. So the mass of cooper in the statue is 46kg.
What is mass?It is one of the fundamental quantities of physics and a fundamental property of matter. We can define mass as a measure of the amount of matter in a body. The SI unit of mass is the kilogram (kg).
The bit mass does not change at any time. Only in certain extreme cases, when enormous amounts of energy are given or taken from the body. For example: in a nuclear reaction, a small amount of matter is converted into a huge amount of energy, which reduces the mass of the matter.
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Just this quick problem, thanks!
8.81(v − 89) − 10 = 16.43
Answer: v = 92
Step-by-step explanation:
8.81. (v – 89) – 10 = 16.43
8.810 +8.81. -89 – 10 = 16.43
8.81v – 784.09 – 10 = 16.43
8.81v – 794.09 = 16.43
8.81v – 794.09 = 16.43
(8.810 – 794.09) + 794.09 = 16.43 + 794.09
8.81v = 16.43 + 794.09
8.81v = 810.52
8.81v = 810.52
810.52
(8.81) 8.81
8.81
810.52 / 8.81
v = 92
What is the value of this expression? 5/6 - (1/8 divided by 3/4)
As given by the question
There are given that a expression
Now,
Simplify the above expression
[tex]\begin{gathered} \frac{5}{6}-(\frac{1}{8}\times\frac{4}{3})=\frac{5}{6}-\frac{1}{6} \\ =\frac{5-1}{6} \\ =\frac{4}{6} \\ =\frac{2}{3} \end{gathered}[/tex]Hence, the value of the given expression is shown below:
[tex]\frac{2}{3}[/tex]Please help Solve the following equations.
Answer: 0 & -7
Step-by-step explanation:
Answer:
12. 0
13. -7
Hope this helps :)
If you need an explanation just comment!
"If marco uses the scale 3 cm to 100 mi.., are the distances longer or shorter, or the same sized. explain"
edit: I kinda need this quick before 3!
If the scale used is 3cm to 100mi, the distances will be larger, because 100 miles is a lot more than 3 centimeters.
Are the distances shorter or larger?A change of scale is what we use to represent large objects (or smaller objects) in diagrams.
They allow us for example to have a big drawing of a cell, or put an area of the size of a country in a A4 piece of paper.
In this case, the change of scale is:
3cm to 100mi
This means that each 3 centimeters in the real object will measure 100 miles in the scale diagram, so the distances in the diagram will be larger, as 100 miles is a lot more than 3 centimeters.
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((3,5), (3,2), (0, 6), (2, 7)}
What is the input of the relation?
x = { 0, 3, 2}
The input of relation ((3,5), (3,2), (0, 6), (2, 7)} is x= { 0, 3, 2}.
What is a relation?A relation between two sets is a collection of ordered pairs that each contain one object from the other set. If the ordered pair (x,y) is in the relation and the object x is from the first set and the object y is from the second set, the objects are said to be related. A relation is a type of function.A relation from A to B is a collection of ordered pairs (a, b) in which an A and b B. A relation from A to B, in other words, is a subset of A B.
Here given a relation ,
((3,5), (3,2), (0, 6), (2, 7)}
We know that input x and output y together form a relation ,
Here x is the input.
so in this relation , Input = x = { 0, 3, 2}
Output y = { 2, 5,6,7}
∴ Input of the given relation ((3,5), (3,2), (0, 6), (2, 7)} is x = {0, 3, 2}.
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write a percent that is between 3/4 and 7/9
Answer:
76%
Explanation:
We want to write a percentage that is between 3/4 and 7/9.
First, begin by converting each of the fractions to its decimal equivalent.
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{7}{9}\approx0.78 \end{gathered}[/tex]Thus, we can say that:
[tex]\begin{gathered} 0.75<0.76<0.78 \\ 0.76=0.76\times100=76\% \end{gathered}[/tex]A percentage that is in between 3/4 and 7/9 is 76%.
