a=0; b=6; c=8
Equation of parabola: y=6x+8.
What is the parabola?In mathematics, a parabola is a planar curve that is mirror-symmetrical and generally U-shaped. It matches a variety of seemingly dissimilar mathematical formulations, all of which identify the same curves.
A point and a line are two ways to describe a parabola a plane curve produced by a point moving so that its distance from a fixed point equals its distance from a fixed line:
Apollonius, who discovered numerous features of conic sections, is credited with the name "parabola." It signifies "application," referring to the "application of regions" notion, which, as Apollonius demonstrated, has a connection with this curve.
A banana's curving shape is quite similar to a parabola. As a result, it is one of the best instances of parabolic objects in common use.
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4x – 1 = 7x – 16
Solve the problem
(Show your work)
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define equation
4x - 1 = 7x - 16
Step 2: Solve for x
Subtract 4x on both sides: -1 = 3x - 16Add 16 to both sides: 15 = 3xDivide 3 on both sides: 5 = xRewrite: x = 5Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 4(5) - 1 = 7(5) - 16Multiply: 20 - 1 = 35 - 16Subtract: 19 = 19Here we see that 19 does indeed equal 19.
∴ x = 5 is a solution to the equation.
Answer:
4x−1=7x−16
Step 1: Subtract 7x from both sides.
4x−1−7x=7x−16−7x
−3x−1=−16
Step 2: Add 1 to both sides.
−3x−1+1=−16+1
−3x=−15
Step 3: Divide both sides by -3.
−3x
−3
=
−15
−3
x=5
Step-by-step explanation:
Please help will mark brainy
what is the area and the perimeter
Answer:
C, Perimeter is 40
Step-by-step explanation:
To find perimeter add up all the sides, to find area, multiply the sides.
What is the price per pound of watermelon?
A. $0.25
B. $0.75
C. $1.40
D. $7.50
Answer:
B. 0.75
Step-by-step explanation:
this is what I think cuz the graph at 1 is 0.75
half of a number, decreased by 10 is -13. in equation form pls
i will give first and best brainliest
Answer:
[tex]\dfrac{1}{2}x-10=-13[/tex]
Step-by-step explanation:
Let x be the unknown number.
Given:
Half of a number → ¹/₂xDecreased by 10 → -10Is -13 → = -13Therefore, the equation is:
[tex]\boxed{\dfrac{1}{2}x-10=-13}[/tex]
Solving for x
To solve, add 10 to both sides:
[tex]\implies \dfrac{1}{2}x-10+10=-13+10[/tex]
[tex]\implies \dfrac{1}{2}x=-3[/tex]
Multiply both sides by 2:
[tex]\implies 2 \cdot \dfrac{1}{2}x=2 \cdot -3[/tex]
[tex]\implies x=-6[/tex]
Equation :-
→ (1/2)x - 10 = -13
Solution :-
→ x = -6
Step-by-step explanation:
The equation will be,
→ (1/2)x - 10 = -13
Now the required value of x will be,
→ (1/2)x - 10 = -13
→ (1/2)x = -13 + 10
→ x = -3 × 2
→ [ x = -6 ]
Hence, the value of x is -6.
Kerry has a collection of 1,100 baseball cards. Of these baseball cards, 40% are dated before 1970, 25% are dated from 1970 to 2000, and the rest are dated after 2000. How many baseball cards in Kerry’s collection are dated after 2000?
Answer:
385 cards
Step-by-step explanation:
First, find 40% and 25% of 1100.
2/5 * 1100
2200/5 = 440 cards dated before 1970
1/4 * 1100
1100/4 = 275 cards dated between 1970 and 2000
Then add the two amounts together.
440 + 275 = 715 cards between pre-1970 and 2000
After that, subtract your new sum from 1100.
1100 - 715 = 385 cards after 2000
(Or to make it easier, just find 35% of 1100.)
Denise is going to the county fair this weekend. The admission to the fair is $5 and the cost per ride is $0.50. If her parents gave her $20, write and solve a linear equation to find how many rides she can go on.
Answer:
she can go on 30 rides I think
Answer:
30 rides
Step-by-step explanation:
Ok first you have to subtract 5 because you payed 5$ to get in and then you divide 15$ by 0.50 and that will give you 30. So she can ride 30 rides total!
Izinho do Shanghai Financial Center, o Jin Mao Tower é um imponente arranha-céu inaugurado em 1999. Com 88 andares (referência ao número oito, símbolo de sorte e prosperidade na cultura chinesa) e uma altura de 420 m, a torre tem um shopping, discotecas, bares, cafés, restaurantes, escritórios e o hotel Grand Hyatt. Suponha que uma réplica do Jin Mao Tower seja construída na razão de 1:80 e colocada em exposição no chão de um salão de 9 m de altura. A distância entre o topo dessa réplica e o teto desse salão será de
Answer:
[tex]3.75\ \text{m}[/tex]
Step-by-step explanation:
A escala da réplica é [tex]1:80[/tex]. Isso significa que 1 metro da réplica da escala representa 80 metros do edifício real.
Portanto, 1 metro do edifício real representa [tex]\dfrac{1}{80}[/tex] metros da réplica.
Precisamos encontrar a altura da réplica
[tex]420\ \text{m}=420\times\dfrac{1}{80}=5.25\ \text{m}[/tex]
Assim, a réplica da escala terá uma altura 5.25 m.
Está colocado numa sala com 9 m de altura.
A distância entre o topo da réplica e o teto do corredor é [tex]9-5.25=3.75\ \text{m}[/tex].
What is the volume of this sphere?
Use a 3.14 and round your answer to the nearest hundredth.
5 cm
cubic centimeters
Answer:
523.33 cm³
Step-by-step explanation:
The volume of a sphere is [tex]\frac{4}{3}[/tex]πr³
[tex]\frac{4}{3}[/tex]π * (5)³
[tex]\frac{4}{3}[/tex]π * 125
523.333 mm³
Are these two problems proportional or non-proportional? Why or why not? Explain your reasoning below.
y=3/4x
y=1/2x-6
Given:
[tex]y=\dfrac{3}{4}x[/tex]
[tex]y=\dfrac{1}{2}x-6[/tex]
To find:
Whether the above functions are proportional or non-proportional?
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
The proportional relationships are in the form of [tex]y=kx[/tex] and they passes through (0,0).
Putting x=0 and y=0 in the given equations.
[tex]y=\dfrac{3}{4}x[/tex]
[tex]0=\dfrac{3}{4}(0)[/tex]
[tex]0=0[/tex]
It is a true statement.
[tex]y=\dfrac{1}{2}x-6[/tex]
[tex]0=\dfrac{1}{2}(0)-6[/tex]
[tex]0=0-6[/tex]
[tex]0=-6[/tex]
It is a false statement.
Therefore, [tex]y=\dfrac{3}{4}x[/tex] is proportional and [tex]y=\dfrac{1}{2}x-6[/tex] is non-proportional.
Last week, it rained x inches. This week, the amount of rain decreased by 5%. Which expressions represent the amount of rain that fell this week? Match all that apply to "does represent" match the rest to "does not represent".
A. g−0.05
B. g−0.05g
C. 0.95g
D. 0.05g
E. (1−0.05)g
I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05
Can you have a triangle with sides 6, 7, and 2?
PLZ ANSWER. UR THE BEST IF U DO. I’LL GIVE BRAINLIEST
You basically can solve for hypothetical sides of this triangle using sohcahtoa backwards. In the first column, it says that adjacent/hypotenuse = .97. We can come up with two values that satisfy this equation. For example, the adjacent side can be .97 and the hypotenuse can be 1. These values don't matter as long as adjacent/hypotenuse is .97.
The second column tells us that opposite/hypotenuse = .26. At this point, we already have a hypothetical hypotenuse with a length of 1, so we can plug that in and find that the opposite side of C is .26.
Now that we have a hypothetical triangle with sides .97, .26, and 1, you can use these values as well as sohcahtoa to solve for the rest with respect to angle A. Keep in mind that the line AB is .26 and that the line BC is .97.
Help me please,I really need help lol
The interval notation for the solution to the given inequality is:
(6,∞).
What is the solution to the inequality?The inequality is solved similarly to an equality, applying the operations to isolate the variable.
For this problem, the inequality is given by:
3(3a - 6) > 12.
Dividing both sides by 3:
3a - 6 > 12.
Then:
3a > 18
a > 18/3
a > 6.
In interval notation, the solution is:
(6,∞).
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Consider the line y=-2/7x-7
and the point is (-7,-4) what would the perpendicular line be and the parallel be
Answer:
a) The equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]
b) The equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]
Step-by-step explanation:
We are given the line: [tex]y=-\frac{2}{7}x-7[/tex]
The slope of the above equation is: [tex]m=-\frac{2}{7}[/tex] (By comparing with general form [tex]y=mx+b[/tex] where m is slope)
a) Find equation of line perpendicular to above line and passes through point (-7,-4)
If two lines are perpendicular there slopes are opposite reciprocal i.e [tex]m_1=-\frac{1}{m_2}[/tex]
The slope of new line will be: [tex]m = \frac{7}{2}[/tex]
Now finding y-intercept using slope and point (-7,-4)
[tex]y=mx+b\\-4=\frac{7}{2}(-7)+b \\-4=\frac{-49}{2}+b \\b=-4+\frac{49}{2}\\b=\frac{-8+49}{2}\\b=\frac{41}{2}[/tex]
So, the equation of line perpendicular to above line and passes through point (-7,-4) will be:
[tex]y=mx+b\\y=\frac{7}{2}x+\frac{41}{2}[/tex]
So, the equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]
b) Find equation of line parallel to above line and passes through point (-7,-4)
If two lines are parallel there slopes are same i.e [tex]m_1=m_2[/tex]
The slope of new line will be: [tex]m = -\frac{2}{7}[/tex]
Now finding y-intercept using slope and point (-7,-4)
[tex]y=mx+b\\-4=-\frac{2}{7}(-7)+b \\-4=-2(-1)+b\\-4=+2+b \\b=-4-2\\b=-6[/tex]
So, the equation of line parallel to above line and passes through point (-7,-4) will be:
[tex]y=mx+b\\y=-\frac{2}{7}x-6[/tex]
So, the equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]
A seagull is 12 feet above the surface of the ocean. A fish is 3 feet below the surface of the water. How far apart are the seagull and the fish?
Answer:
15
Step-by-step explanation:
12+3=15
Mulitiply. What is the product (3*10^(9))*(2*10^(17)) in scientific notation
Answer:
6*(10^26)
Step-by-step explanation:
Please mark as brainliest
grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. which equation can he use to find n, the number of gallons of water he should remove? 3.52 (22 minus n)
The correct option is C. 3.52/(22 - n) = 24/100.
The equation which can be used to find n, the number of gallons of water he should remove is 3.52/(22 - n) = 24/100.
What is mathematical expression?Mathematical symbols can represent numbers (constants), variables, functions, operations, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.
Monomial expressions are the most common type of algebraic expression. Expression of a binomial. Expression of a polynomial are two other types of expressions.Now, as per the given question.
22 gallons of water is evaporated from the grant plans which is 16% ammonia solution to make a 24% ammonia solution.
First, we determine how much ammonia is in 22 gallons of 16% ammonia solution.
16% x 22 gal = 3.52 gal
That after water evaporates, the quantity of ammonia remains constant, however the total quantity of solution is diminished by the quantity of water that evaporates.
Amount of ammonia: 3.52 gal
Amount of water that sustained: 22 - n
Requires concentration of ammonia is 24% = 24/100
The measurement will be formatted as follows:
(3.52)/(22 - n) = 24/100
Therefore, the equation which is used for the formation of the number of gallons of water he should remove ammonia is (3.52)/(22 - n) = 24/100.
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The complete question is -
Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. which equation can he use to find n, the number of gallons of water he should remove?
The options are-
A. 3.52(22 - n) = 0.24
B. (22 - n)/3.52 = 24/100
C. 3.52/(22 - n) = 24/100
D. 3.52 + (22 - n) = 0.24
HELP PLS!!!!!
Jason, Mario, April, and Tiffany each set a goal to run 20 miles a week. This table shows how much of each runner's goal has been met.
Which list shows the numbers in the table in order from least to greatest?
35, 0.35, 58, 58%
0.35, 35, 58, 58%
0.35, 58%, 35, 58
35, 0.35, 58%, 58
Answer:
0.35, 58%, 35, 58
Step-by-step explanation:
58% = .58
Please help fast! Comment only if you know it’s multiple-choice QUESTION 13 ILL GIVE EXTRA POINTS
Answer:
B m pretty sure...
Step-by-step explanation:
At 7:00 pm, the temperature was -7 °F. The next morning the temperature had raised
to 42 °F. How many degrees F. did the temperature change?
Answer:
49 degrees
Step-by-step explanation
Answer:
I think 49 °F
Step-by-step explanation:
42 - (-7) = 49 °F
So the temperature raised 49 degrees since 7pm last night.
I think thats right. :)
HELPPPPPPPP IM IN CLASS!!:
-2 1/3 + -1 3/4
Then explain and show your work!!
Answer:
-4.08333
Step-by-step explanation:
2 1/3 + 1 3/4 = 4912 = 4 112 ≅ 4.0833333. Spelled result in words is forty-nine twelfths (or four and one twelfth)
An inground rectangular pool has a concrete pathway surrounding the pool. If the pool is 16 feet by 32 feet and the entire area of the pool including the walkway is 924 ft2, find the width of the walkway.
Answer:
Width of walkway = 3.71625 feet
Step-by-step explanation:
Let the width of the walkway be w. Then the length of entire area of the pool including the walkway is 32 + 2w and the breadth of the entire walkway is 16 + 2w since there is a width of w on both sides of length and breadth
Total Area of pool with pathway
(16+ 2w)(32+2w) = 924
Using the FOIL method we can expand the term on the left as follows:
= [tex]\sf 16\cdot \:32+16\cdot \:2w+2w\cdot \:32+2w\cdot \:2w[/tex]
= [tex]\sf 512+96w+4w^2[/tex]
Rearrange terms to get
[tex]\sf 4w^2 + 96w + 512[/tex]
So we get
[tex]\sf 4w^2 + 96w + 512 = 924[/tex]
Subtract 924 from both sides
[tex]\sf 4w^2 + 96w + 512 - 924 = 0[/tex]
==> [tex]\sf 4w^2 + 96w -412 = 0[/tex]
This is a quadratic equation of the form [tex]\sf ax^2 + bx + c[/tex] whose roots(solutions) are
[tex]\displaystyle \sf x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a = 4, b = 96 and c = -412
Plugging in these values we get
[tex]\sf w_{1,\:2}=\dfrac{-96\pm \sqrt{96^2-4\cdot \:4\left(-412\right)}}{2\cdot \:4}[/tex]
[tex]\sf \sqrt{96^2-4\cdot \:4\left(-412\right)}\\\\ = \sqrt{96^2+4\cdot \:4\cdot \:412} \\\\= \sqrt{96^2+6592} \\\\= \sqrt{9216+6592} \\\\= \sqrt{15808} = 125.73\\\\[/tex]
So
[tex]w_{1,\:2}=\dfrac{-96\pm \:125.73}{2\cdot \:4}[/tex]
[tex]w_1=\dfrac{-96+125.73}{2\cdot \:4},\:w_2=\dfrac{-96-125.73}{2\cdot \:4}[/tex]
We can ignore w₂ since it is a negative value
So
[tex]\sf w = \dfrac{-96 + 125.73}{8} = 3.71625\; feet[/tex]
[tex]\boxed{ \mathsf{Width\; of\; walkway = 3.71625\;feet}}[/tex]
- 51/5
is this rational or irrational?
Answer:
irrational
Step-by-step explanation:
Answer:
I think irrational but I can be wrong
What is 0. 36 written as a rational number?
helppppppp
I promise I will mark you brainlist as soon as I see your answers if you help me with this!
Answer:
E. 10 feet
F. RS
Step-by-step explanation:
E. Height of actual tree = [tex]\frac{2.5}{1.5}[/tex] × 6 inches
= 10 feet
F. CD is like ST but bigger.
DA is like TQ but bigger.
AB is like QR but bigger.
BC is like RS but bigger.
Their proportion stays the same.
Answer:
BC=SR
Step-by-step explanation:
BC and SR both have the same length in their sides. Therefore SR is the "?".
I didn't fully understand the question, but its alright.
Need help ASAP pls!!
Answer:
Rotate Each dot in the proper way each right angle is 90 Degrees
Step-by-step explanation:
Rotate the Coordinates
pretty simple
Find the value of X
Answer:
i got 0 for the value of x
Step-by-step explanation:
A map has a scale of 2.4 centimeters equals to 500 miles if two cities are 10 centimeters apart from the map how many miles apart are they in real life
Answer:
hi
Step-by-step explanation:
hi
Jonah earns $12.50 per hour as a marketing intern.
If he works for 4.5 hours, how many dollars does he
earn?
8
8.2
9
56.25
Answer:
its D/ 56.25
Step-by-step explanation:
because the other numbers are too small
if 1/6 of a number,plus one third returns two-thirds of that number what is the number
please help!!!!
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
let n be the number , then
[tex]\frac{1}{6}[/tex] n + [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex] n
multiply through by 6 ( the LCM of 6 and 3 ) to clear the fractions
n + 2 = 4n ( subtract n from both sides )
2 = 3n ( divide both sides by 3 )
[tex]\frac{2}{3}[/tex] = n
Answer:
[tex]{\mathsf {n=\frac{2}{3}}}[/tex]
Step-by-step explanation:
In word problems like this, you have to break down the problem description into math form
This is an equation description so we need a variable to work with. Let's call this variable n
1/6th of this number can be translated to:
[tex]\displaystyle \mathsf {\frac{1}{6}n}[/tex]
1/6th of this number plus one-third translates to:
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3}[/tex]
1/6th of this number, plus one-third returns two-thirds of that number
returns is just a fancy way of saying equal to.
So returns two-thirds of that number translates to
= two-thirds of that number
Two-thirds of the number is
[tex]\displaystyle \mathsf {\frac{2}{3}n}[/tex]
So putting all this together we get the equation
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3} = \frac{2}{3}\mathsf n[/tex]
We have to now solve for the equation.
Bring all the n terms to the left side and the constant(1/3) to the right to solve for n
[tex]\displaystyle \mathsf{ Subtract\:}\frac{1}{3}\mathsf {\:from\:both\:sides}[/tex]
[tex]\mathsf {\frac{1}{6}n+\frac{1}{3}-\frac{1}{3}=\frac{2}{3}n-\frac{1}{3}}[/tex]
Simplify to get
[tex]\mathsf {\frac{1}{6}n=\frac{2}{3}n-\frac{1}{3}}[/tex]
Subtract [tex]\mathsf {\frac{2}{3}}[/tex] from both sides
[tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n=\frac{2}{3}n-\frac{1}{3}-\frac{2}{3}n}[/tex]
Simplify to get
[tex]\mathsf{\frac{1}{6}n-\frac{2}{3}n= -\frac{1}{3}}[/tex]
The left side term is [tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n}[/tex]
Factor out the common term [tex]n[/tex]:
[tex]\mathsf {n\left(\frac{1}{6}-\frac{2}{3}\right)}[/tex]
[tex]\mathsf {\frac{1}{6}-\frac{2}{3}=-\frac{1}{2} }[/tex]
So we get our equation as
[tex]\mathsf {-\frac{1}{2}n=-\frac{1}{3}}[/tex]
Multiply both sides by -2 to get
[tex]\boxed {\mathsf {n=\frac{2}{3}}}[/tex]