Answers
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+3}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{3}{2(-1)}~~,~~8-\cfrac{3^2}{4(-1)} \right)\implies \left( \cfrac{3}{2}~~,~~ 8+\cfrac{9}{4}\right)\implies \left( \cfrac{3}{2}~~,~~ \cfrac{41}{4}\right)[/tex]
now, for the solutions, or namely the x-intercepts, we simply set y = 0 and solve for "x", now this one doesn't factor into integers nicely, so we'll need to use the quadratic formula to get them.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+3}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{ - 3 \pm \sqrt { 3^2 -4(-1)(8)}}{2(-1)}\implies x = \cfrac{-3\pm\sqrt{9+32}}{-2}\implies x = \cfrac{3\mp\sqrt{41}}{2}[/tex]
[tex]x = \begin{cases} \cfrac{3-\sqrt{41}}{2}\\[2em] \cfrac{3+\sqrt{41}}{2} \end{cases}\qquad \leftarrow \qquad na mely\textit{ solutions or zeros or x-intercepts}[/tex]
Related Questions
A 13 foot ladder is placed
5 feet away from a wall
How many feet up the wall
will the ladder reach?
Answers
Answer: 12 feet up
Step-by-step explanation:
This problem models a right triangle, in which the ladder is the hypotenuse and the distance away from the wall is one of the legs. Thus, you may use the Pythagorean Theorem (a^2 + b^2 = c^2)
[tex]a^2+b^2=c^2\\5^2+b^2=13^2\\25+b^2=169\\b^2=144\\b=12[/tex]
N.B. There are some very useful sets of numbers that can help you with this unit.
They are called Pythagorean triplets, and they are the sets of whole numbers that make right triangles. The important ones are 3, 4, 5, and 5, 12, 13 (And their multiples, like 6, 8, 10(3,4,5 *2))
Hope it helps :) and let me know if you want me to elaborate further.
Three-fourths of the difference of a number and 7 is negative fifteen. What is the number? (Please solve very clear and step by step and I'll give u brainlest)
Answers
Answer:
- 13Step-by-step explanation:
Three-fourths of the difference of a number and 7 is negative fifteen:
3/4*(x - 7) = - 15x - 7 = - 15*4/3x - 7 = - 20x = 7 - 20x = - 13Let F(x) =( 3x/2) - (14/3) for x = 4. What is the value for F(x)
Answers
Answer:
f(4) = 1.4
Step-by-step explanation:
f(x) = (3x/2) - (14/3)
We are given that x = 4
f(4) = (3(4)/2) - (14/3)
f(4) = (12/2) - (14/3)
f(4) = 6 - (14/3)
14/3 as a decimal is 4.6
f(4) = 6 - 4.6
f(4) = 1.4 (approximately)
describe how you know this is a proportional relanshoships
Answers
Answer:
don't see the relationship, but if it's a proportional relationship it should have the same result every time you divide the x by the y or vice versa.
167.67 divided by 8.1
Answers
Answer:
167.67 divided by 8.1 = 20.7
express 7 minutes, 30 seconds as a percentage of 1 hour
Answers
Answer:
did u mean 7 minutes & 30 seconds or
do you need seperate percentage for each ???
Answer:
420 i think
Step-by-step explanation:
7 mins
7×60
=420
plus the 30sec
450 sec
450/3600×100
45000/3600
450/36
12.5
Pls help meeee the question is in the photo pls no links or fake answers pls answer both questions
Answers
Answer:
Step-by-step explanation:
First one is TRUE...you'd multiply by negative one third
Second is FALSE...no multiplication needed to get x as a positive.
Are the ratios 2:1 and 11:9 equivalent?
Answers
Answer: No
Step-by-step explanation:
2 is double 1.
Because 11 is not double 9, the ratios are not equivalent.
Hope it helps :)
whats the answer can someone answer please
Answers
Answer:
both are c
Step-by-step explanation:
1
2
3
4
5
6
7
8
9
10
Which graph shows a set of ordered pairs that represent a function?
oly
4
4
3
3
3
.
.2
.
2
.
2
1+
1
-5 -4 -3 -2 -11
1 2 3 4 5
-5-4-3-2-1
213
45
x
-5-4-3-2-11
1
2 3
5
-2
42
3
o
3
4
.
14
.
45
O
5
4
3
2
1
-54-3-2-11
2
4
5
X
Answers
3rd graph, far right on top
Step-by-step explanation:
Use the vertical line test to determine (one input for x cannot have two outputs of y)
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally
installed. Estimate the cost of having a 24 by 27 ft brick patio installed.
Answers
Answer: 4914
Step-by-step explanation:
multiply 15 and 20 to make 300
multiply 24 and 27 to make 648
set up proportion
[tex]\frac{300}{648}[/tex] × [tex]\frac{2275}{x}[/tex]
cross multiply
300x = 648(2275)
300x = 1474200
x = 4914
Four times the product of a number x and a number y is equal to 20.
Answers
Step-by-step explanation:
4x×y=20
.....
..................................
The expression for four times the product of a number x and a number y is equal to 20 is 4xy = 20.
Given,
Four times the product of a number x and a number y is equal to 20.
We need to write the expression.
What is the meaning of the mathematical terms?- 2 times M = 2 x M
- Product of M and N = M x N
- 3 more than M = M + 3
- 3 less than M = M - 3
Find the expression.
We have,
Four times the product of a number x and a number y is equal to 20.
Here,
The product of a number x and a number y can be written as:
= (x) x y
Four times the product of a number x and a number y can be written as:
= 4 x [ (x) x y ]
- is equal to 20 can be written as:
= 20
Now,
We get,
4xy = 20
Thus the expression for Four times the product of a number x and a number y is equal to 20 is 4xy = 20.
Learn more about how to write an expression here:
https://brainly.com/question/15284271
#SPJ2
Help help help please good luck be honest
Answers
Answer:
A'(-6,4) B'(2,2) C'(-2,-2)
Step-by-step explanation:
The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).
If p=7, then what is the value of 8×p−68×p-6?
A
6
B
9
C
50
D
56
Answers
Answer:
d
Step-by-step explanation:
you need to type it in the calculator and solve it
Complete the table of values for this equation: y = 3x +10 Enter your answer by filling in the boxes. x y 4 5 6
Answers
x=4,5,6
x=4
[tex]\\ \sf\longmapsto y=3(4)+10[/tex]
[tex]\\ \sf\longmapsto y=12+10=22[/tex]
x=5
[tex]\\ \sf\longmapsto y=3(5)+10=15+10=25[/tex]
x=6
[tex]\\ \sf\longmapsto y=3(6)+10=18+10=28[/tex]
Step-by-step explanation:
y = 3x + 10
x = 4, 5, 6Soo :
y = 3(4) + 10 = 12 + 10 = 22
y = 3(5) + 10 = 15 + 10 = 25
y = 3(6) + 10 = 18 + 10 = 28
find the perimeter of the triangular shaped sandwich
Answers
Answer:
P = 12 + 5x
Step-by-step explanation:
P = a + b + c
P = 7 + (x + 4) + (4x + 1)
= 7 + x + 4 + 4x + 1
= 12 + 5x
Multiply (3x+2)(x-6)
What is the middle term of the simplified answer?
Answers
Answer:
16x
Step-by-step explanation:
(3x + 2) (x - 6)
Multiply 3x by x and -6
3x^2 - 18x
Multiply 2 by x and -6
2x - 12
Combine like terms
3x^2 - 16x - 12
The middle term is 16x
.
Explain why the two figures below are not similar. Use complete sentences and
provide evidence to support your explanation. (10 points)
Answers
Answer:
These figures are not the same because the Slope of DE is not the same as the slope of JK.
Step-by-step explanation:
Slope of DE = -2/1
Slope of JK = -1
If they were similar, the slope would be the same, but the size would not.
-Chetan K
13. For a weekly car rental, a car-rental company charges customers a flat fee of $100 plus
10 cents for every mile traveled.
15 Write an equation for the amount, A dollars, of a weekly rental for a car that travels
m miles.
16
Create a table of m and A values using the equation from part a for 150, 200, and
250 miles.
Answers
Answer:
a) y = 0.10(16) + 100
y = $ 101.60
b) y = 0.10(150) + 100
y = $115
c) y = 0.10(200) + 100
y = $120
d) y = 0.10(250) + 100
y = $125
Step-by-step explanation:
Lindsey drew a scale of a city. the scale of the drawing is 1 inch = 3 yards. If the actual length of a neighborhood park is 114 yards, how long is the park in the drawing?
Answers
Answer:
38 in
Step-by-step explanation:
114 yds divided by 3 = 38 in
The price of gas goes up to $3.24 per gallon after a 9.4% increase. What was the price before the increase?
Answers
Answer:
i think this correct
Step-by-step explanation:
3.24=(1+9.4/100) x
then x= 2.961 $
d) A patient is given 11÷2ml of medicine three times a day. How long does a bottle of 132 ml of medicine last?
Answers
Answer: 8 days.
Explanation;
11/2 = 5.5
5.5 x 3 = 16.5
132/16.5 = 8
Answer:
8 days
Step-by-step explanation:
So, 11/2 * 3 = (33/2) = 16.5 ml
Let the number of days medicine last be 'x'.
⇒ 16.5 * x = 132
⇒ x = 132/16.5
⇒ x = 8.
Therefore, Medicines last for 8 days.
Hope it helps!
Both questions 7 and 8
Answers
9514 1404 393
Answer:
7. $10,459.28
8. $30,060.93
Step-by-step explanation:
Your table 12-2 will tell you the present-value multiplier of the annual payment for a 10-year annuity due will be ...
7%: 7.515232
11%: 6.537048
__
7. The 11% table value will be used with a payment of $1600 to find the present value:
6.537048 × $1600 = $10,459.28 . . . present value of the annuity due
__
8. The 7% table value will be used with a payment of $4000 to find the present value:
7.515232 × $4000 = $30,060.93 . . . present value of the annuity due
Find a 33 matrix Sij so that the product SijA is the same as the matrix A after applying the row operation Ri $ Rj .
Answers
Answer:
We want the ith row of the new matrix SijA to be the old jth row of A, so we need the ith row of Sij to extract the jth entry of column of A.
This mean the ith row of Sij must have a 1 in the jth entry and 0's everywhere else.
Similarly, the jth row of Sij must have a 1 in the ith entry and 0's everywhere else.
in the piecewise notation this is
(Sij)kl ={1 if k=i and l=j, 1 if k=k and l=i; 1 if k=l but k#i,j, 0 otherwise
Step-by-step explanation:
Bella conducted a scientific experiment. For a certain time, the temperature of a compound rose
3
1
3
3
3
1
degrees in
15
15 minutes. What was the rate, in degrees per hour, that the temperature of the compound rose?
Answers
Answer: 13 1/3 degrees per hour
Explanation: 10/3 x 4 = 40/3
40/3 = 13 1/3
There are a total of 66 people attending a carnival. The ratio of adults to children is 4 to 7. How many adults are attending the carnival? Enter your answer in the box. adults
Answers
Answer:
24 adults
Step-by-step explanation:
The equation to represent the scenario is
4x + 7x = 66
Combine like terms
11x = 66
Isolate x
x = 6
To find the amount of adults attending the carnival, substitute 6 with x.
6*4 = 24 adults
7*4 = 42 children
24 + 42 = 66 people in total
plz help with my math plz!!!!
Answers
Step-by-step explanation:
This is an isosceles triangle because in an isosceles triangle angles opposite to each of the equal sides must also be equal. Since the diagram shows 2 equal angles we can say its isosceles.
So 3(x+2) = 24
8= x+2
x = 6
Answer:
x = 6
Step-by-step explanation:
The triangle given is an isosceles triangle.
Which means, the two sides and the two angles will be the same.
One of the sides is 24.
The other is 3 ( x + 2 )
Hence, we will get this equation.
24 = 3 ( x + 2 )
24 = 3x + 6
24 - 6 = 3x
18 = 3x
6 = x
Thus, x = 6.
I hope it helps.
Which of the following is a solution to the given equation?
y=-3x - 7
A)
(-2,-1)
B)
(-1,-10)
C
(4,-5)
D
(3,-2)
Answers
Answer: A
Step-by-step explanation:
By replacing in the given equation:
y=-3x-7
y=-3(-2)-7
y=6-7
y=-1
But for choices B, C and D the given x values don't fit with the images.
g^x+1 =27 solve for x
Answers
Answer:x=-3.5
Step-by-step explanation:
The books have been sorted into fiction and nonfiction. The number of fiction books is 5 less than 4 times the number of nonfiction books. The books are 70% fiction. Choose the equation that best represents this scenario.
x over quantity 4 times x minus 5 end quantity equals 30 over 100
x over quantity 4 times x minus 5 end quantity equals 30 over 70
Answers
The number of fiction books are 7 and number of non fiction books are 3 respectively
let
number of fiction books = x
number of non fiction books = y
x = 4y - 5
Total books = z
x = 70% of z
y = 30% of z
x + y = z
4y - 5 + 30%(z) = z
4y - 5 + 0.3z = z
4y - 5 = z - 0.3z
4y - 5 = 0.7x
4y - 5 = 0.7z
4(0.3z) - 5 = 0.7z
1.2z - 5 = 0.7z
-5 = 0.7z - 1.2z
-5 = - 0.5z
z = -5/-0.5
z = 10
Therefore,
the number of non fiction = 30% of z
= 0.3 × 10
= 3
number of fiction = 70% of z
= 0.7 × 10
= 7
Learn more about equation:
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