Answer:
[tex]a+b+c=10[/tex]
Step-by-step explanation:
We are given that the graph of the equation:
[tex]y=ax^2+bx+c[/tex]
Passes through the three points (0, 5), (1, 10), and (2, 19).
And we want to find the value of (a + b + c).
First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:
[tex]y=ax^2+bx+5[/tex]
Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:
[tex](10)=a(1)^2+b(1)+5[/tex]
Simplify:
[tex]5=a+b[/tex]
The point (2, 19) tells us that when x = 2, y = 19. Substitute:
[tex](19)=a(2)^2+b(2)+5[/tex]
Simplify:
[tex]14=4a+2b[/tex]
This yields a system of equations:
[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]
Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:
[tex]-10=-2a-2b[/tex]
Add the two equations together:
[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]
Combine like terms:
[tex]4 = 2a[/tex]
Hence:
[tex]a=2[/tex]
Using the first equation:
[tex]5=(2)+b\Rightarrow b=3[/tex]
Therefore, our equation is:
[tex]y=2x^2+3x+5[/tex]
Thus, the value of (a + b + c) will be:
[tex]a+b+c = (2) + (3) + (5) = 10[/tex]
A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. By how much % more is the marked price above the cost price?
Give full explanation
Answer:
Let the MP of 1 article = Rs 1
MP of 15 article = Rs 15
SP of (15+1) articles = 15 x 96/100
= Rs 14.40
CP of 16 article = 14.40/135 x 100
= Rs 32/3
CP of 1 article = 32/3x16
= Rs 2/3
Required % = 1/3 x 3/2 x 100
= 50
Given m
II
n, find the value of x.
m
n
20
119°
Please help
x=119
hope it doesn't help you!!
Diego's family truck holds 21 gallons of fuel. Each day the car uses 1.5 gallons of fuel. A warning light comes on when the remaining fuel is 2.5 gallons or less. Starting from a full tank, can Diego's family drive the car for 10 days without the warning light coming on? Explain or show your reasoning. Starting from a full tank, can Diego's family drive the car for 15 days without the warning light coming on? Explain or show your reasoning. Diego says the expression 21 - 1.5t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for? Write and solve an equation to determine the number of days Diego's father can drive the car without the warning light coming on. Write and solve an inequality that represents the number of days driven without the warning light coming on. Explain clearly what the solution to the inequality means in the context of this situation
Answer:
The inequality is 0.6x < 12.5
The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days
Step-by-step explanation:
14 gallons-1.5 gallons=12.5 gallons
we know that
If the remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on
so
Let
x ----> the number of days
0.6x < 12.5 inequality that represent the situation
Solve for x
x < 12.5/0.6
x < 20.8 days
The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days
What is value of x if 20x-10*110=50
Answer:
57.5
Step-by-step explanation:
20x - (10 x 110) = 50
=> 20x - 1100 = 50
=> 20x = 1150
=> x = 1150/20
=> x = 115/2
=> x = 57.5
A house has increased in value by 28% since it was purchased. If the current value is $288,000, what was the value when it
was purchased?
Answer:
$368,640
Step-by-step explanation:
288,000 * .28 = 80640
288,000 + 80640 = 368640
4. (03.05)
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period? (1 point)
The domain is all real numbers o through 9.
The domain is all integers o through 9.
The domain is positive real numbers.
The domain is all positive integers.
Answer:
B. domain is all integers 0 through 9
Step-by-step explanation:
Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.
The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.
1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."
Sameera purchased 3 (1/2) kg of apples and 4 (3/4) kg of oranges. What is the total weight of fruits purchased by her ?
Answer:
8 1/4 kg
Step-by-step explanation:
Add the weight of the fruits together
3 1/2 + 4 3/4
Get a common denominator of 4
3 2/4 + 4 3/4
7 5/4
7 4/4 + 1/4
8 1/4 kg
PLEASE HELP URGENTLY!!
Answer:
x = 69
Step-by-step explanation:
since AB is parallel to CD we can find the value of y with the following equation :
2y - 40 = 66 add 40 to both sides
2y = 110 divide both sides by 2
y = 55
from supplementary angles, we know that the exterior angle's measure is 124
since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle
y + x = 124 we found value of y earlier
55 + x = 124 subtract 55 from both sides
x = 69
Can Anyone please tell me How to Multiply 18√2×18√2...
Please show steps aslo..
Answer:
648
Step-by-step explanation:
18√2×18√2= (18√2)²
= (18)²×(√2)²
= 324×2
= 648
Work out the circumference of this circle 7.5
Answer:
47.12
Step-by-step explanation:
C=2πr=2·π·7.5≈47.12389
Solve 7x + 1 < 4(x - 2).
A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}
Given:- 7x + 1 < 4(x - 2)
Solving It:-7x + 1 < 4(x - 2)
7x + 1 < 4x - 8
7x - 4x < -8 -1
3x < -9
x < -9/3
x < -3
So Correct Solution Set Will BeC. {x | x < -3}Hope This Helps YouPlease help, explain too and I will give brainliest :)
Answer:
c
Step-by-step explanation:
Answer:
C. 37 degrees
Step-by-step explanation:
27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.
I'm sure you can do it with an actual formula, but i can't recall. Cheers
what would be the u to usub and what would be the steps to solving this integral?
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
pls help me solve this multiplication fractions. (show work)
Answer:
32:3/4
33:4/3
34:40
35:48
Does this graph show a function? Explain how you know.
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
The slope of a line is 5/9 and the slope of another line is -975. The two lines
are
Answer:
the third option - they are perpendicular to each other.
Step-by-step explanation:
for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.
and that is exactly what happened here.
Which equation represents a line that passes through ( -2 , 4 ) and has the slope of 2/5
Answer:
y = 2/5x +24/5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
y = 2/5x +24/5
Which table shows a proportional relationship between a and b?
Answer:
It is c
Step-by-step explanation:
Given sin
=
=
V23 and tan o
find cos 0.
23
11 )
12
?
COS 0 =
TO
Answer: [tex]\frac{11}{12}[/tex]
Step-by-step explanation:
Use trigonometry (shown in image below) to find the 3 side-lengths:
The side opposite of θ = [tex]\sqrt{23}[/tex]The base side adjacent to θ = 11The hypotenuse = 12According to right triangle trigonometry:
cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Substitute in the values:
cos θ = [tex]\frac{11}{12}[/tex]
No idea how to do
[tex]\frac{4r + 20}{r + 5}[/tex]
when r ≠ 5 ?
Factorize the numerator:
4r + 20 = 4r + 4×5 = 4 (r + 5)
I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:
(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4
Whats his mistake and the correct awnser
Answer:
θ ≈ 35.7°
Step-by-step explanation:
His mistake was in using the wrong trig. ratio
Instead of using cosine he should have used the sine ratio
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then
θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )
Part B
Question
Type the correct answer in the box.
The y-intercept of the parent function, f(x), is
I
The y-intercept of the child function, g(x), is
Answer:
The y-intercept of the parent function, f(x), is 0
The y-intercept of the child function, g(x), is 7
Step-by-step explanation:
Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.
The solution is :
Vertex is (-2, 0)
y-intercept is 4.
What is vertex?In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.
here, we have,
to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':
f(x) = (x+2)^2 = x2 + 4x + 4
Then, to find the vertex, we can use the formula:
x_v = -b / 2a
x_v = -4 / 2 = -2
Now, finding the y_vertex, we have:
f(x_v) = (-2)^2 + 4*(-2) + 4 = 0
So the vertex is (-2, 0)
To find the y-intercept, we make x = 0 and then find f(x):
f(0) = 0 + 0 + 4 = 4
So the y-intercept is 4.
To learn more on vertex click:
brainly.com/question/12563262
#SPJ2
complete question:
Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².
vertex: ( ? , ? )
y-intercept: ?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=
Answer:
k=10
Step-by-step explanation:
Brainliest please~
Answer:
K=10
Step-by-step explanation:
Correct on Plato
what is the solution to this equation?
5x-4+3x=36
A. x=16
B. x=5
C. x=20
D. x=4
B. x = 5
tip : if in a rush just plug in the number and see if its true
8x - 4 = 36
x = 5
i will brainliest
avoid spam
Express each of the following percentages as a fraction and simplify it.
(i) 25% (ii) 40% (iii) 16% (iv) 150%
(v) 120% (vi) 58% (vii) 32% (viii) 175%
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{25\%=\dfrac{25}{100}=\dfrac{1}{4} }[/tex] [tex]\sf{ 40\%=\dfrac{40}{100}=\dfrac{2}{5} }[/tex] [tex]\sf{16\%=\dfrac{16}{100}=\dfrac{4}{25} }[/tex][tex]\sf{150\%=\dfrac{150}{100}=\dfrac{3}{2} }[/tex][tex]\sf{120\%=\dfrac{120}{100}=\dfrac{6}{5} }[/tex][tex]\sf{58\%=\dfrac{58}{100}=\dfrac{29}{50} }[/tex][tex]\sf{32\%=\dfrac{32}{100}=\dfrac{8}{25} }[/tex][tex]\sf{175\%=\dfrac{175}{100}=\dfrac{7}{4} }[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\hookrightarrow\sf{ 25\% =\dfrac{25}{100}=\boxed{\bf \dfrac{1}{4} }} \\\hookrightarrow\sf{ 40\% =\dfrac{40}{100}=\boxed{\bf \dfrac{2}{5} }} \\\hookrightarrow \sf{16\%=\dfrac{16}{100}=\boxed{\bf\dfrac{4}{25}} } \\ \hookrightarrow\sf{150\%=\dfrac{150}{100}=\boxed{\bf\dfrac{3}{2} }} \\ \hookrightarrow\sf{120\%=\dfrac{120}{100}=\boxed{\bf\dfrac{6}{5} }} \\\hookrightarrow \sf{58\%=\dfrac{58}{100}=\boxed{\bf\dfrac{29}{50}} } \\\hookrightarrow \sf{32\%=\dfrac{32}{100}=\boxed{\bf\dfrac{8}{25} }} \\ \hookrightarrow\sf{175\%=\dfrac{175}{100}=\boxed{\bf\dfrac{7}{4}} } \\ [/tex]
Can someone please help, I'll give out 20 points !
Question - Where is the blue point on the number line?
Answer:
-6
Step-by-step explanation:
The number line is created by skip counting of 2.
So, -2 , then -4 and then -6.
So, blue dotted point is (-6)
Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?
1/9
9
-9
-1/9
Pls answer
Answer:
[tex]\boxed{\sf a = 9 }[/tex]
Step-by-step explanation:
Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,
[tex]\sf\longrightarrow 3x - 2y +7=0 [/tex]
[tex]\sf\longrightarrow 6x +ay -18 = 0 [/tex]
Step 1 : Convert the equations in slope intercept form of the line .
[tex]\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}[/tex]
and ,
[tex]\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a} [/tex]
Step 2: Find the slope of the lines :-
Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,
[tex]\sf\longrightarrow Slope_1 = \dfrac{3}{2} [/tex]
And the slope of the second line is ,
[tex]\sf\longrightarrow Slope_2 =\dfrac{-6}{a} [/tex]
Step 3: Multiply the slopes :-
[tex]\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1 [/tex]
Multiply ,
[tex]\sf\longrightarrow \dfrac{-9}{a}= -1[/tex]
Multiply both sides by a ,
[tex]\sf\longrightarrow (-1)a = -9 [/tex]
Divide both sides by -1 ,
[tex]\sf\longrightarrow \boxed{\blue{\sf a = 9 }} [/tex]
Hence the value of a is 9 .
63.89 X n = .6389 Solve for n *
A. 10
B. 100
C. .01
D. .1
Answer:
c. .01
Step-by-step explanation:
.6389 divided by 63.89
Which of the following represents x = 1/3y written in general form?
3x - y = 0
X-1/3y=0
1/3x-y=0
Answer:
x-⅓y=0
Step-by-step explanation:
thats the answer
brainly please
Answer: 3x-y=0
Step-by-step explanation:
X = 1/3y
X × 3 = 1/3 y × 3
3x = y
3x - y = y- y
3x- y = 0
Graph the following equations by plotting 3 points and then connecting the points to form a line. Show your work to find the 3 points and then list the ordered pairs you used as part of your answer.
Answer:
The way I would tackle these types of problems would be to make a table, then graph the points using the results I get.
Step-by-step explanation:
So explaining the table is kinda hard since I suck at explaining, so I've attached a file showing the table I've made for number 1.
First Step:
Make the table. Make it a 3x4 table. For the top row, put y, the equation (I put 'y=2x' as shown in number 1), then x. Then for the left column, go down by one box, then put: -1, 0, 1. Really, you can put any numbers, but to make it easy for yourself, just write the numbers I've listed. These will be your y-values you'll be substituting.
Second Step:
a.) Plugging in the numbers. For the middle column, I've put down y=2x in each box, as shown in my table. Then for each of those boxes, plug in the numbers to the left of them and substitute them for the y-value. For example, look at the second row. The left box has '-1', so I replaced the 'y' in the equation and got '(-1)=2x'.
b.) After substituting the y-values, solve for x. For this case, you'll need to divide both sides by 2. If it doesn't make much sense, think about a seesaw. If you have 5 pounds on both sides, the seesaw will stay balanced. Add an additional 5 pounds to one side, then the seesaw will start tipping towards the heavier sides. So in order to keep an equation balanced, you must do any action to both sides of the equation. After diving both sides by 2, you'll get the value for x.
Final Step:
After finding the x-values for each of the y-values, it's time to graph the equations. Remember, x is left to right and y is down to up. To graph them, let's use the second row for example. y=-1 and x=-0.5. So all you need to do is to start from the origin (0,0), then go half a unit to the left, as x is negative, then go a unit down, as y is negative, then make a point. The rest should be pretty straight forward.
After making all three points, just get a ruler or any straight edge, then align it along those three points, then just make a line, and boom! You've solved number 1! For the purpose of saving my time, I'm pretty sure you can solve the rest using what I've just told you. Good luck!
