y = 0.125x² - 3 is equation of parabola in vertex form
The standard form of the parabola is [tex]y = ax^{2} + bx + c[/tex]
The vertex form of parabola is [tex]y = a(x-h)^{2} + k[/tex]
where h and k are vertex of parabola. The vertex formula is used to find vertex coordinate of parabola .
Vertex point of parabola are usually represented by (h, k).
Given that the vertex of parabola is 0, -3
(h, k) = (0, -3)
h = 0 and k = -3
substituting the values of h and k in vertex form of parabola,
[tex]y = a(x-0)^{2} -3\\y = ax^{2} - 3[/tex]
Parabola is also passing through (12,15) means it should satisfy vertex equation of parabola
[tex]15= a(-12)^{2} -3\\15+3 = 144a\\18 = 144a\\a = \frac{18}{144}\\\\a = 0.125[/tex]
Substituting value of a
Vertex form of parabola is [tex]y = 0.125x^{2} - 3[/tex]
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Write the equation of the line that passes through the points `(1,\ -2)` and `(4,\ 4)`.
Andre has been offered an entry-level job. The company offered him $46,000 per year plus 3% of his total sales. Andre knows that the average pay for this job is $64,000, What would Andre's total sales need to be for his pay to be at least as high as the average pay for this job? (Your answer should be accurate to 2 decimal places.)
We know that:
- The company offered him $46,000 per year plus 3% of his total sales.
- the average pay for this job is $64,000
And we must find what would be the sales of Andre for his pay to be at least as high as the average pay for this job
To find it we can use a equation that represents the situation
We can use the next formula
[tex]\text{ average pay}=\text{ base salary}+\text{ 3\% of his total sales}[/tex]Analyzing the given information we know that
- avergare pay = 64000
- base salary = 46000
- 3% of total sales = 3% * x = 0.03 * x (x represents the total sales)
Now, replacing the values in the formula
[tex]64000=46000+0.03x[/tex]Since x represents the total sales we need to solve the equation for x
[tex]\begin{gathered} 64000=46000+0.03x \\ 64000-46000=0.03x \\ 18000=0.03x \\ \frac{18000}{0.03}=x \\ 600000=x \\ \Rightarrow x=600000 \end{gathered}[/tex]ANSWER:
Andre should have $600,000 in his total sales for his pay to be at least as high as the average pay for this job
A telephone plan consists of a monthly fee of $15 plus 20 cents per minute for long distance calls are made. Write an equation for the total monthly cost C, when n minutes are used for long distance calls.
a)Using the given information we can set the following equation:
[tex]C=0.20n+15[/tex]b) The graph of the linear equation above for up to and including 200 minutes is as follows:
Which corresponds to option B.
c) If n=40 then:
[tex]C=0.20\cdot40+15=8+15=23[/tex]Then the total monthly cost is $23.
d) If C=30, solving the first equation on the board for n we get:
[tex]\begin{gathered} 30=0.20n+15 \\ 0.20n=15 \\ n=75 \end{gathered}[/tex]Then the number of minutes is 75.
(d) In 7 years Bernard will be twice as old as he was 8 years ago. How old is Bernard now?
The present age of the Bernard is, 23.
What is age?
Given a date of birth, this free age calculator calculates age in terms of years, months, weeks, days, hours, minutes, and seconds.
Calculated using the population's arithmetic mean, average age. The median age is a factor that determines the population's average age.
As given, in 7 years Bernard will be twice as old as he was 8 years ago.
Let the present age of Bernard = x
Bernard age after 7 years = x + 7.
Bernard age before 8 years = x - 8.
From the given information,
2(x - 8) = x + 7
2x - 16 = x + 7
2x - x = 16 + 7
x = 23
Therefore, the present age of Bernard is 23.
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I don’t know how to solve this I would love some help and explanations oh now to solve it please
Given the point-slope equation
[tex]y+1=\frac{2}{3}(x-8)[/tex]Simplify as shown below
[tex]\begin{gathered} y+1=\frac{2}{3}x-8\cdot\frac{2}{3}=\frac{2}{3}x-\frac{16}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{16}{3}-1=-\frac{19}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{19}{3} \end{gathered}[/tex]The answer is -2x/3+y=-19/3. Write -2/3 in the first gap, 1 in the second gap, and -19/3 in the third one.
How to multiply fractions
[tex]\begin{gathered} \frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d} \\ \Rightarrow8\cdot\frac{2}{3}=\frac{8}{1}\cdot\frac{2}{3}=\frac{8\cdot2}{1\cdot3}=\frac{16}{3} \end{gathered}[/tex]How to add fractions,
[tex]\begin{gathered} \frac{a}{b}+\frac{c}{d}=\frac{\text{ad+cd}}{bd} \\ \Rightarrow-\frac{16}{3}-1=-\frac{16}{3}-\frac{3}{3}=\frac{-16\cdot3-3\cdot3}{3\cdot3}=\frac{-48-9}{9}=-\frac{57}{9}=-\frac{19}{3} \end{gathered}[/tex]Answer:
2x + -3y = 19
Step-by-step explanation:
In this question, they already gave you the equation of the line. But it is in point-slope form. We just need to rearrange the equation to look like:
Ax + By = C
A and B and C should be positive or negative whole numbers. So let's get rid of the fraction first.
y + 1 = 2/3 (x - 8)
You could use distributive property on the right side, but that is just going to make two terms have fractions. Instead, let's multiply both sides by 3 and get rid of the fraction.
3(y + 1) = 3• 2/3(x-8)
3(y + 1) = 2(x - 8)
Now use distributive property.
3y + 3 = 2x - 16
We need x and y on the left and plain numbers on the right.
3y + 3 = 2x - 16
Subtract 3
3y = 2x - 19
Subtract 2x
3y - 2x = -19
Rearrange the x and y terms, put x in the lead.
-2x + 3y = -19
This is almost standard form. The A is supposed to be positive. So change the sign of ALL the numbers. A is 2, the B is -3 and the C is 19. Those are the numbers that go in the blanks on your question.
The diameter of a circle is 16 kilometers. What is the angle measure of an arc bounding a sector with area 8pi square kilometers?
The angle that defines the arc is x = pi/4.
How to get the angle?For a circle with a radius R, the area of an arc defined by an angle x is:
A = (x/2)*R^2
In this case, the diameter is 16km, then the radius is given by:
R =16km/2 = 8km
Then the area is:
A = (x/2)*(8 km)^2
And this must be equal to 8*pi km^2
Then we can solve the equation:
(x/2)*(8 km)^2 = 8*pi km^2
(x/2)*64 = 8*pi
x = 2*8*pi/64 = pi/4
That is the measure of the angle.
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At a certain school 6/7 are girls 3/5 brought their lunch what fraction of students are girls who brought their lunch today write your answer in its simplest form
18/35 fraction of students are girls who brought their lunch today.
What is fraction ?A fraction is a mathematical concept that denotes a component of a whole or, more generally, any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.
CalculationLet's say,
Total number of students over school = x
Number of girls = (6/7)x
Number of girls who brought their lunch = 3/5 of (6/7)x
⇒ 3/5(6/7)x
⇒ (18/35)x
Hence "18/35 fraction of students are girls who brought their lunch today".
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Irma was in charge of keeping attendance for a local summer camp each year.
Summer camp attendance
Year Kids
2018 93
2019 92
2020 78
2021 75
2022 78
According to the table, what was the rate of change between 2018 and 2021?
According to the table, the rate of change between 2018 and 2021 was 22.22%
What is rate of change?A variable's rate of change over a predetermined amount of time. It is frequently used while discussing momentum and is typically represented as a ratio of one variable's change to another's corresponding change.
Given that,
Year Kids
2018 93
2019 92
2020 78
2021 75
2022 78
So, we have to calculate the rate of change between 2018 and 2021:
As we know, rate of change = (change in year / change in kids) × 100
rate of change = (4/ 18) × 100
rate of change = 22.22%
So, according to the table, the rate of change between 2018 and 2021 was 22.22%
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Find the measures of the numbered angles in the isosceles trapezoid shown below.
First, notice that since we have an isosceles trapezoid, the base angles will be equal, then:
[tex]\measuredangle3=60\degree[/tex]next, we have that the angles adjacent to opposite bases are supplementary, then we can write the following equation:
[tex]\measuredangle2+\measuredangle3=180[/tex]using the fact that the measure of angle 3 is 60 degrees, we can find the measure of angle 2:
[tex]\begin{gathered} \measuredangle2+60=180 \\ \Rightarrow\measuredangle2=180-60=120 \\ \measuredangle2=120 \end{gathered}[/tex]then, since angles 1 and 2 are also base angles, they are equal. Therefore, the measure of the anlges is:
[tex]\begin{gathered} \measuredangle1=120 \\ \measuredangle2=120 \\ \measuredangle3=60 \end{gathered}[/tex]Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y = 10x - 8
Step-by-step explanation:
The slope is "m", or how much the y-value changes on a line when the x-value changes by one.
The y-intercept is the y value of the line when it is intersecting the y-axis, or when the x-value is 0.
To find the slope, take 2 points from the graph and plug into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x\\_1}[/tex]
I'll use (0, -8) and (1,2).
Plug into the formula.
[tex]\frac{2--8}{1-0}[/tex]
[tex]\frac{10}{1}[/tex]
10
Slope = 10
To find the y-intercept, look at the table. What is the y-value when the x-value is equal to 0?
-8
y-intercept: -8
Slope-Intercept form:
y = mx + b
m: slope
b: y-intercept
y, x: leave as variables
y = 10x - 8
translate the sentence into an equation five time the sum of a number and 8 is equal to 4 use the variable b for the unknown number
Let us take the unknown number as b.
Sum of the number and 8 can be represented as,
8 + b
Therefore, five time the sum is,
5(8+b)
This is equal to 4, so,
5 (8 +b) = 4
This is the required equation.
The number is,
[tex]\begin{gathered} 5(8+b)=4 \\ 40+5b=4 \\ 5b=4-40 \\ 5b=-36 \\ b=-7.2 \end{gathered}[/tex]The number is, -7.2.
could you please help me out with a question
Circumference
Formula
C = 2*pi*r
Substitution
C = 2*(3.14)* (5)
Simplification
C = 31.4 m This is the Circumference
Area
Formula
A =pi*r^2
Substitution
A = 3.14*5^2
Simplification
A = 3.14*25
Result
Area = 785 m^2 This is the area
Find the correct graph that represents the inequality for the sentence.Kevin always has $5 or more in his pocket.
ANSWER:
STEP-BY-STEP EXPLANATION:
By the statement Kevin always has $5 or more, which means that x can be 5 or all values greater than this. So the correct graph would be the first option:
50 POINTS SHOW WORK PLEASE!!!! LORAN is a long-range hyperbolic navigation system. Suppose two LORAN transmitters are located at the
coordinates (-100,0) and (100,0), where unit distance on the coordinate plane is measured in miles A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 180 miles.
What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
Answer:
x²/10000 + y²/1900 = 1
Step-by-step explanation:
coordinates (-100,0) and (100,0) missing in Question
The center of the hyperbola is (0,0) = (h, k)
c = the distance form the center to either focal point = 100
c² = 100² = 10000
The differences from the receiver to the transmitters = 2a
2a = 180
=> a = 90
=> a² = 8100
b² = c² - a²
b² = 10000 - 8100
b² =1900
(x - h)²/a² + (y - k)²/b² = 1
=> x²/10000 + y²/1900 = 1
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penelope had 1/2 of her birthday cake leftover so she decided to take it to work. she shared her birthday cake equally among herself and four of her co workers. what fraction of the cake did each person get?
help please which one is it
The function B has a greater rate of change.
What is rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Therefore, rather than the size of each change individually, it is the rate—or the acceleration or deceleration of changes. In finance, rate of change is employed to comprehend price returns and spot trend momentum.
First to find the rate of change for function A.
Rate of change = [tex]\frac{0-5}{2.5-1.5} = \frac{-5}{1}=-5[/tex]
Function A has rate of change is -5.
Now consider, the second equation
y = -4.5x + 15
Since, the slope is rate of change for the equation.
So, function B has rate of change of -4.5
Now compare the rate of change for both the functions A and B
-5 < -4.5
Therefore, function B have greater rate of change.
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This was the answer I got but I am not sure it it is correct.
To find JL
We will first find the value of x
JK = KL
2(x+6) = 3x + 8
2x + 12 = 3x+ 8
subtract 2x from both-side of the equation
12 = 3x-2x + 8
12 = x+ 8
subtract 8 from both-side of the equation
12 - 8 = x+ 8 - 8
4 = x
x=4
JK = 2(x+ 6)
substitute x = 4 into the above
JK = 2(4+6)
JK=2(10)
JK=20
KL =3x+8
substitute x=4 into the above
KL = 3(4) + 8
KL = 12 + 8
KL=20
JL = JK + KL
= 20 + 20
= 40
JL = 40 units
1. Write 250 metres as a fraction of a kilometre.
Answer:1/4 or 0.25/1
Step-by-step explanation:
In 1 kilometer there are a thousand meters. So 250 is a quarter of 1000 which makes the fraction 1/4 or 0.25/1 whichever you need.
Perform the following food service calculation.
Meat to be served: fish fillet
Number of guests: 84
How much fish is needed?
____lbs.
The amount of fish needed to be served is 294 lbs
How to determine the amount of fish needed?From the question, we have the following parameters that can be used in our computation:
Meat to be served: 3.5 pounds fish fillet
Number of guests: 84
The amount of fish needed is calculated using the following equation
Amount of fish = Number of guests x Meat to be served
Substitute the known values in the above equation, so, we have the following representation
Amount of fish = 84 * 3.5
Evaluate the products
Amount of fish = 294
Hence, the amount needed is 294 pounds
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Possible question
Perform the following food service calculation.
Meat to be served: 3.5 pounds fish fillet
Number of guests: 84
How much fish is needed?
____lbs.
I really need help on this!!!
Answer:
a.
linear? yes
why? because it is straight line
domain? 8
range? 8
b.
linear ? no
why? because it's curved
domain? -4
range?4
2. The scale from the real Eiffel Tower to the scale model is 15 ft to 3 in. What is the unit rate?
Ok, so
If the scale from the real Eiffel Tower to the scale model is 15 ft to 3 in, the unit rate will be:
[tex]\frac{15ft}{3in}=5\frac{ft}{in}[/tex]This means that, in the scale:
5 ft = 1 in.
Then, the unit rate is 5.
Find the value of each variable. I need help solving this
Answer:
y = 75; z = 75
Step-by-step explanation:
105 and z are a linear pair and that means they add up to 180
they are on a straight line which is why they are a linear pair
105 + z = 180
subtract 105 to both sides
z = 75
now add all of the remaining sides and subtract that from 360 because a quadrilaterals angles add to 360
75 + 89 + 95 = 259
360 - 259 = y
360 - 259 = 101
y = 101
these are your answer
Answer:
y=95
z=105
Step-by-step explanation:
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3(8 – 4x) < 6(х – 5)
the inequality equation is
3(8 - 4x) < 6(x -5)
open the parentheses
3*8 - 3*4x < 6*x - 6*5
24 - 12x < 6x - 30
collect the like terms
24 + 30 < 6x + 12x
54 < 18x
divide both sides by 18
54/18 < 18x/18
3 < x
x > 3
The answer is x > 3
please help me its due soon and I don’t get it!!
Answer:
Step-by-step explanation:
These are tough, so picture a line ( graph) going up the picture.
I'm attaching my graph
M = 10*R
each raffle ticket cost 10 bucks
Given the regular decagon (10-sided polygon) pictured below, which statements are true? CHOSE 3 ANSWERS. EXPLAIN HOW YOU GOT THEM PLEASE!!
A:The polygon has 90° rotational symmetry.
B:The polygon has 144° rotational symmetry.
C:The polygon has point symmetry.
D:The polygon has 36° rotational symmetry.
The statements the polygon has 144° rotational symmetry, The polygon has point symmetry and The polygon has 36° rotational symmetry are true.
We have to find the symmetry.
A decagon is given as
Number of sides = 10
So rotational symmetry = [tex]\frac{360^{0} }{n}[/tex]
= [tex]\frac{360 }{10}[/tex]
= 36°
So rotational symmetry angles are multiple of 36°
So 36° x 4 = 144° is a rotational symmetry.
The all sides are congruent, so decagon as point symmetry.
Hence the answer is The statements the polygon has 144° rotational symmetry, The polygon has point symmetry and The polygon has 36° rotational symmetry are true.
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Which is the graph of the linear inequality y >-x-3
Answer:
The correct graph is shown below.
Hope this helps!
How would I approach this problem? I’m not sure how to solve measurements
To identify the mass of the solute, subtract the total mass by the mass of the graduated cylinder.
Thus, we have the following:
[tex]20.6g-2.55g=18.05g[/tex]To obtain the concentration of the solution, divide the obtained mass by the total volume and then simplify.
Thus, we have the following:
[tex]\frac{18.05g}{74.79mL}=\frac{1805g}{7479mL}\approx0.241g\cdot mL^{-1}[/tex]Are 3/11 and 17/6 proportional
Answer:
Step-by-step explanation:
NO! Hope I helped.
4.
Jada drinks a cup of tea every morning at 8:00 am. for 14 days. There is 40 mg of
caffeine in each cup of tea she drinks. 24 hours after she drinks the tea, only 6% of
the caffeine is still in her body.
How much caffeine is in her body right after drinking the tea on the first, second, and third day?
1st day:
2nd day:
3rd day:
mg.
mg.
mg.
The amount of caffeine in her body on the 1st day is, 2.4 mg
The amount of caffeine in her body on the 2nd day is, 4.8 mg
The amount of caffeine in her body on the 3rd day is, 7.2 mg
Given, Jada drinks a cup of tea every morning at 8:00 am. for 14 days. There is 40 mg of caffeine in each cup of tea she drinks. 24 hours after she drinks the tea, only 6% of the caffeine is still in her body.
So, the amount of caffeine in her body on the 1st day is,
40×6/100
24/10
= 2.4 mg caffeine
The amount of caffeine in her body on the 2nd day is,
= 2× 2.4
= 4.8 mg caffeine
The amount of caffeine in her body on the 3rd day is,
= 3× 2.4
= 7.2 mg caffeine
Hence, The amount of caffeine in her body on the 1st day is, 2.4 mg
The amount of caffeine in her body on the 2nd day is, 4.8 mg
The amount of caffeine in her body on the 3rd day is, 7.2 mg
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consider the following system of equations with the solution (1, 8). which system of equations would have the same solution?
Replacing x=1 in the equations to verify if the value of y is equal to 8, we have:
A.
y= 5*(1) + 3 = 8 (Multiplying and adding) (It is correct as the result for y is equal to 8)
y= 9*(1) - 1 = 8 (Multiplying and subtracting)(It is correct as the result for y is equal to 8)
B
y= 4*(1) + 2 = 6 ≠ 8 (Multiplying and adding) (It is not correct as the result for y is not equal to 8)
C
y= -2*(1) + 10 = 8 (Mulitplying and subtracting) (It is correct as the result for y is equal to 8)
y= 8*(1) + 1 = 9 ≠ 8 (Multiplying and adding) (It is not correct as the result for y is not equal to 8)
D.
y= 7*(1) -5 = 9 ≠ 8 (Multiplying and subtracting) (It is not correct as the result for y is not equal to 8)
The answer is the option A.