Answer:
A parabola is a curve with a focus and a directrix. The focus is any point is at an equal distance while the directrix is a fixed line. The vertex of the parabola is (2,1), the two points to the right are (3,4) & (4,13) while the two points to the left are (1,4) & (0,13).
Given that:
y = 3(x - 2)² +1
A parabola is represented as:
y = a (x − h)² + k
Where:
Vertex = (h, k)
So, by comparison; the vertex of the function is:
Vertex = (2, 1)
To plot two points to the right, we select x values greater than 2.
Let: x = 3
So, we have:
y = 3(x - 2)² + 1
y = 3(3 − 2)² + 1
y = 4
Let x = 4
y = 3(x - 2)² + 1
2:37
4G 15%
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Mathematics
5 points
Let x = 4
y = 3(x - 2)² +1
y = 3(4-2)² + 1
y = 13
To plot two points to the left, we select x values less than 2.
Let: x = 1
So, we have:
y = 3(x - 2)² +1
y = 3(1 − 2)² + 1
y = 4
Let x = 0
= 3(x - 2)² + 1 y =
y = 3(02)² +1
= 13
In conclusion:
• The vertex of the parabola is (2,1)
• The two points on the right are (3,4) and (4,13)
• The two points on the left are (1,4) and (0,13)
Solve for x.
−5x−8>22
Enter your answer in the boxes to correctly state the solution.
[tex]\\ \tt\longmapsto -5x-8>22[/tex]
[tex]\\ \tt\longmapsto -5x>30[/tex]
[tex]\\ \tt\longmapsto -x>30/5[/tex]
[tex]\\ \tt\longmapsto -x>6[/tex]
[tex]\\ \tt\longmapsto x>-6[/tex]
Answer:
[tex] - 5x - 8 > 22[/tex]
[tex] - 5x > 22 + 8[/tex]
[tex] - 5x > 30[/tex]
[tex]x > \frac{30}{ - 5} [/tex]
[tex]x > - 6[/tex]
what are the factors of -30 and the sum of 4?
Answer:
Answer: 30 = 1 x 30, 2 x 15, 3 x 10, or 5 x 6. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Prime factorization: 30 = 2 x 3 x 5.
Step-by-step explanation:
Still stuck? Get 1-on-1 help from an expert tutor now.
Answer: 30 = 1 x 30, 2 x 15, 3 x 10, or 5 x 6. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Prime facto...... 30 = 2 x 3 x 5.
sorry if im wrong and have a wonderful day!!!!!
Suppose y varies directly with x. If y = 3 when x = 2, find y when x = 3.
A *9/2
B *2/3
C *3/2
D *2/9
Answer:
9/2
Step-by-step explanation:
Direct variation is
y = kx where k is the constant of variation
Substitute into the equation to find k
y=3 and x=2
3 = k*2
Solve for k
3/2 = k
y = 3/2 x
We know x =3
y = 3/2 * 3
y = 9/2
Answer:
A
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 3 when x = 2 , then
3 = 2x ( divide both sides by 2 )
[tex]\frac{3}{2}[/tex] = k
y = [tex]\frac{3}{2}[/tex] x ← equation of variation
When x = 3 , then
y = [tex]\frac{3}{2}[/tex] × 3 = [tex]\frac{9}{2}[/tex] → A
How many 1/4
gram dosages of medication can be obtained from a container
holding 3/8
gram of the medication?
The quantity of dosages of medication that can be obtained from the container is 1.5 dosages.
Given the following data:
Mass of medication = [tex]\frac{1}{4}[/tex] grams.Mass of container = [tex]\frac{3}{8}[/tex] grams.To calculate the quantity of these dosages of medication that can be obtained from the container:
How to calculate the dosages.In this exercise, you're required to determine the amount of dosages of medication can be obtained from the container. Thus, we would divide the given mass of container by the mass of medication as follows:
[tex]Quantity = \frac{\frac{3}{8}}{\frac{1}{4}}[/tex]
Simplifying further, we have:
[tex]Quantity = \frac{3}{8} \times 4\\\\Quantity = \frac{12}{8} \\\\Quantity = \frac{3}{2}[/tex]
Quantity = 1.5 dosages.
Read more on word problems here: brainly.com/question/13170908
can I have help pls
Answer: C
Step-by-step:
Its x = 6
What is the next number in the sequence?
6,12,24,48
A 72
B 96
C 108
D112
E 124
If you roll a 6-sided die, what is
the probability that you will get a
number greater than 5?
3-5/7 helpme helpme helpme helpme helpme
Answer:
the answer in fraction form is 16/7
Step-by-step explanation:
but if you want it in decimal form its 2.2857142857
you can also round it off to 2.3
Somebody please help!
How do I factor the expression 2x^2-20x^5?
Answer:
[tex]2x^2(1-10x^3)[/tex]
Step-by-step explanation:
Factor [tex]2x^2-20x^5[/tex]
Apply the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]\implies 2x^2-20x^2x^3[/tex]
Rewrite 2 as 2 · 1 and 20 as 2 · 10:
[tex]\implies 2 \cdot 1x^2-2 \cdot 10x^2x^3[/tex]
Factor out common term [tex]2x^2[/tex]:
[tex]\implies 2x^2(1-10x^3)[/tex]
For each expression, write an equivalent expression that uses only addition.
20−9+8−7
4x−7y−5z+6
-3x−8y−4−87z
Answer:
1) 28 - 16 = 12
2) 4x + 6 -7y -5z
3) -3x -8y - 4 - 87z
These were all mostly simplified already.
Hope this helps!
8 1/2=7 ?/2
NEED HELP ASAP:)
Answer:
3
Step-by-step explanation:
8 1/2 = 17/2 - 14/2 = 3/2
The diagonal of a rectangle is 2under root 13cm.If its length and breadth are in the ratio 3:2, then find its area.
Answer:
Given :
The diagonal of a rectangle is 2 ✓13 cm.
The length and breadth are in the ratio
3:2.
To find :
The Area of the rectangle.
Solution :
Given that
The ratio of the length and breadth of a rectangle = 3:2
Let they be 3X cm and 2X cm
We know that
The diagonal of a rectangle = √(1²+b³)
units
The diagonal of the rectangle
= √[(3X)³+(2X)³] cm
= √(9x³+4x²) cm
=> √(13X²) cm
=> √13 X cm
According to the given problem
The diagonal of the rectangle = 2√13 cm
=> ✓13 X = 2 √13
=> X = 2√13/√13
=> X = 2 cm
If X = 2 cm then 3X=3(2) = 6 cm
If X = 2 cm then 2X = 2(2)=4 cm
Length = 6 cm
Breadth = 4 cm
We know that
Area of a rectangle = length breadth sq.units
Area of the given rectangle = 6 cm x 4 cm
= 24 cm²
Help me solve this pls
Check the picture below.
Make sure your calculator is in Degree mode.
Luke can paint 91 portraits in 7 weeks.
How many portraits can Luke paint in 4 weeks?
MA
portraits
As
he can paint ( 4 / 7 ) * 91 paintings in 4 weeks
4 / 7 = 0.57142857142
0.57142857142 * 91 = 52 paintings in 4 weeks
If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
Answer:
Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer is option (c) -0.4
The value of x to the nearest tenth is -0.4
Logarithmic expressionGiven the following expressions
(0.2)x = 2 and log 2 = 0.3010
Taking log of both sides of (0.2)x = 2
log (0.2)x = log 2.
x log (0.2) = 0.3010,
x [log 2 - log 10] = 0.3010.
Note that log2 2 = 1
x [log 2 - 1] = 0.3010
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306
Hence the value of x to the nearest tenth is -0.4
Learn more on logarithm here: https://brainly.com/question/25710806
Answer is option (c) -0.4
write 34.24 as a mixed numbers
Answer:
34 6/25
Step-by-step explanation:
A mixed number is a whole number in front of a fraction. Keep 34 as the whole number. .24 is really 24/100, but you can simplify it to 6/25.
During, an Experiment, The temperature of a solution changes from 9 4/5 F to 17 1/4 F.
What is the percent of increase in the temperature of the solution?
Enter your answer in the box as a percent rounded to the nearest hundredth
Using improper fractions, it is found that the percent of increase in the temperature of the solution was of 76.08%.
How to convert improper fractions to standard fractions?The conversion is made according to the following formula:
[tex]a\frac{b}{c} = a + \frac{b}{c} = \frac{ac + b}{c}[/tex]
In this problem, the initial temperature was given by:
[tex]9\frac{4}{5} = 9 + \frac{4}{5} = 9.8[/tex]
The final temperature was given by:
[tex]17\frac{1}{4} = 17 + \frac{1}{4} = 17.25[/tex]
What is the percent change?The percent change is given by the change divided by the initial temperature, and multiplied by 100%. Hence:
[tex]C = \frac{17.25 - 9.8}{9.8} \times 100\% = 76.02\%[/tex]
To learn more about improper fractions, you can take a look at https://brainly.com/question/24606703
10=8x^2+2x in standard form with the steps
Answer:
8x=10
Step-by-step explanation:
hope helps
calculate without using calculate
3(-2+4)
Answer: 6
Step-by-step explanation:
Parentheses- (-2+4)= (2)
Multiply 3(2)= 6
Jamie’s father has asked him to paint the fence around their home. If the fence is 119.5 years long, and Jamie can paint an average of 4.78 yards of the fence per hour, how many hours will it take for Jamie to finish painting the fence?
Answer:
25 hours
Step-by-step explanation:
119.5 yards divided by 4.78 yards per hour = 25 hours
Is log(0.3) greater than or less than 0? Justify your answer.
Which equation represents the number of crops in row n?
Answer:
9n=3(4)n
Step-by-step explanation:
The farmer has a very insufficient way of farming he is a fake farmer if he only plants 3 crops a row and than 12 in the next he most likely has no pattern but if we do trigonometrically mitochondria math we can figure out that his patter does exist but only to him. since the farmer goes but he goes up by four cuz 3 x 4 is a number 12 and than 12 x 4 is 48 which the farmers produce will all die on his crusty land.
For the past two weeks, Benita has been recording the number of people
at Eastside Park at lunchtime. During that time, there were 50 or more
people at the park 9 out of 14 days.
What is the experimental probability that there will be 50 or more people at the park during lunchtime on the fifteenth day?
Answer:
a)9/14
b)5/14
Step-by-step explanation:
For the past two weeks, Benita has been recording the number of people at Eastside Park at lunchtime
Layla made chili for a football party. She started making the chili at 3:45 P.M. It took 40 minutes to prepare and assemble the ingredients. Then, the chili had to simmer for 45 minutes. What time was the chili ready?
Answer:
5:10 P.M
Step-by-step explanation:
3:45 P.M + 0hrs 40 min = 4:25 P.M
4:25 P.M + 0hrs 45 min = 5:10 P.M
The chili was ready at 5:10 P.M.
Keyla has one pizza. She wants to share her pizza
with her 5 tiends (and herself) How much pizza will
each person receive!
Answer:
1/6 or 16.7%
Step-by-step explanation:
1 (herself)
5 (her friends)
1 + 5 = 6
1/6 ≃ 0.167 ≃16.7%
Hope this helps!
Use the given point on the circle to find the value of cosine. Recall r=sqrt x^2+y^2 and cos 0=x/y
Answer:
cosine=-1/2
Step-by-step explanation:
Solve the following equation:
3x = -12
a.
b.
X = 2
x = -2
No real solutions
X= 2
C.
d.
Answer:
x = -4
Step-by-step explanation:
3x=-12
Using the division property of equality, we can divide both sides by 3 to isolate x...
x=-12/3
x = -4
Need help with this, its important.
Proper latex may not appear in website then see attached picture!
[tex] \tt \looparrowright \: 2 {b}^{3} + 5 = 2 {(3)}^{3} + 5[/tex]
[tex] \\ \\ [/tex]
[tex] \tt \looparrowright \: 2 {b}^{3} \cancel{ + 5} = 2 {(3)}^{3} \cancel{ + 5}[/tex]
[tex] \\ \\ [/tex]
[tex] \tt \looparrowright \: 2 {b}^{3} = 2 {(3)}^{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \looparrowright \cancel 2 {b}^{3} = \cancel 2 {(3)}^{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \looparrowright {b}^{3} = {(3)}^{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \looparrowright {b} = 3[/tex]
anyone knows the answer?
What percent of 200 is 150