Answers
Answer:
Disciminant of f = 0
x-intecept = [tex](\frac{3}{2}, 0)[/tex]
Step-by-step explanation:
Given the quadratic function, -4x² + 12x - 9
where a = -4, b = 12, and c = -9
The discriminant, b²- 4ac, is the expression inside the radical (numerator) of the quadratic formula:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}[/tex]
The first part of your given problem asks for the discriminant. Substitute the values for a, b, and c:
b²- 4ac = 12² - 4(-4)(-9) = 144 - 144 = 0 → This implies that the quadratic function has one real root.
Therefore, the disciminant of f is 0.
Next, the given problem asks for the x-intercepts. The x-intercept is the point on the graph where it crosses the x-axis. As I mentioned earlier, the function has one real root. Therefore, it means that there is only 1 x-intercept. To find out what the x-intercept is, use the quadratic formula:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]x = \frac{-12 +/- \sqrt{12^{2}-4(-4)(-9)} }{2(-4)}[/tex]
[tex]x = \frac{-12 +/- \sqrt{144 - 144} }{-8}[/tex]
[tex]x = \frac{-12}{-8} = \frac{3}{2}[/tex]
Therefore, the x-intercept is [tex](\frac{3}{2}, 0)[/tex].
Related Questions
Miguel Ponce has P1,500.00 cash. If he bought a pair of shoes for P1,325.00, what is the percent of the remaining cash he has left?
Answers
Answer:
Step-by-step explanation:
Cash remaining=P1, 500.00-P1,325.00
=P175
Percent of the remaining cash= Cash Remaining × 100
Cash he originally had
= P175 × 100
P1 500
=11[tex]\frac{2}{3}[/tex] %or 11.6666666% or 11.67% when rounded to two decimal places.
A percentage is a way to describe a part of a whole. The percent of the remaining cash he has left is 11.667%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Value of the Remaing Cash = P1,500.00 - P1,325.00
= P175.00
Now, the percent of the remaining cash he has left can be written as,
Percentage of remaining cash = (Remaining cash/ Total cash) × 100%
= (P175.00 / P1,500.00) × 100%
= 0.011667 × 100%
= 11.667%
Hence, the percent of the remaining cash he has left is 11.667%.
Learn more about Percentages here:
https://brainly.com/question/6972121
#SPJ2
ts 2
What is the slope of the line shown below?
y
40
30
20
10-
-40
30...20...10
11
20
30
40 X
10
-20
30
40
Answers
Hello there!
When we are given the graph of a line and two points on the graph, we can calculate the slope of the line using Rise/Run.
Rise=How many units we move up (here, the rise is 3)
Run=How many units we move left or right (Here, the run is 5)
So the slope of this line is [tex]\frac{3}{5}[/tex]
Hope this helps you!
~Just a joyful teen
[tex]SilentNature(GraceRosalia)[/tex]
2/9 divided by 5/12 in a simples form
answer is a fracton
Answers
Answer:
8 / 15
Step-by-step explanation:
2/9 ÷ 5/12
= 2/9 × 12/5 Reciprocal of 5/12
= 2×12 / 9×5 Multiply num. by num. and denom. by denom.
= 24 / 45 Find LCD
= 24 ÷ 3 / 45 ÷ 3 Divide num. and denom. by LCD to simplify.
= 8 / 15
Graph: y
2 + 5
y
X
y
8
6
4
2.
x
-4
-2.
2
4.
6
8
-2
-4
Draw
Click or tap the graph to plot a point.
Answers
The graph of [tex]y = \frac 34x +5[/tex] has a slope of 3/4 and a y-intercept of 5
The linear equation is given as:
[tex]y = \frac 34x +5[/tex]
Set x = 0
[tex]y = \frac 34 * 0 +5 = 5[/tex]
Set x = 1
[tex]y = \frac 34 * 1 +5 = 5\frac 34[/tex]
Set x = 2
[tex]y = \frac 34 * 2 +5 = 6\frac 12[/tex]
The above means that, the graph of [tex]y = \frac 34x +5[/tex] passes the following points
[tex](x,y) = \{(0,5), (1, 5\frac 34), (2,6\frac 12)\}[/tex]
See attachment for the graph of the linear function [tex]y = \frac 34x +5[/tex]
Read more about linear equations at:
https://brainly.com/question/14323743
solve for y 1/3x+2y=8
Answers
1. Simplify [tex]\frac{1}{3} x[/tex] to [tex]\frac{x}{3}[/tex]
[tex]\frac{x}{3} +2y=8[/tex]
2. Subtract [tex]\frac{x}{3}[/tex] from both sides
[tex]2y=8-\frac{x}{3}[/tex]
3. Divide both sides by 2
[tex]y=\frac{8-\frac{x}{3} }{2}[/tex]
4. Simplify [tex]\frac{8-\frac{x}{3} }{2}[/tex] to [tex]\frac{8}{2}[/tex] - x/3/2
y=8/2-x/3/2
5. Simplify 8/2 to 4
y=4-x/3/2
6. Simplify x/3/2 to x/3x2
y=4-x/3x2
7. Simplify 3x2 to 6
-y=4-x/6
What is the result when the number 24 is increased by 6%?
Answers
Answer:
24 increased by 6% = 25.44
Step-by-step explanation:
Introduction. Percent, p%
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
6% = 6/100 = 6 ÷ 100 = 0.06.
100% = 100/100 = 100 ÷ 100 = 1.
ncrease the number by 6% of its value.
Percentage increase = 6% × 24
New value = 24 + Percentage increase
Calculate the New Value
New value =
24 + Percentage increase =
24 + (6% × 24) =
24 + 6% × 24 =
(1 + 6%) × 24 =
(100% + 6%) × 24 =
106% × 24 =
106 ÷ 100 × 24 =
106 × 24 ÷ 100 =
2,544 ÷ 100 =
25.44
Calculate absolute change (actual difference)
Absolute change (actual difference) =
New value - 24 =
25.44 - 24 =
1.44
Proof.
Calculate percentage increase...
... And see if we get as a result
the absolute change (actual difference).
Percentage increase =
6% × 24 =
6 ÷ 100 × 24 =
6 × 24 ÷ 100 =
144 ÷ 100 =
1.44
So we have proven that the calculations are correct.
For positive numbers
Absolute change (actual difference) =
Percentage increase
Answer:
24 increased by 6% = 25.44
Absolute change (actual difference):
25.44 - 24 = 1.44
Answer:
24,06
Step-by-step explanation:
[tex] \sf 24 + 6 \%[/tex]
[tex] \sf = 24 + \frac{6}{100} [/tex]
[tex] = \sf \frac{2400}{100} + \frac{6}{100} [/tex]
[tex] \sf = \frac{2406}{100} [/tex]
[tex] \sf 24, 06[/tex]
how do u know its a square root ? do u divide?
Answers
5. A w-foot wide path is to be built around a rectangular space that is 80
feet by 50 feet. Write and simplify an expression for the total area.
Answers
To find the area of the path, we'll need to find the area of the space with the path and subtract the area of the inner space.
Total area: (80 + w)(50 + w)
Inner area: 80 x 50
Area of the path: (80 + w)(50 + w) - (80 x 50)
(4000 + 80w + 50w + w^2) - (4000)
4000 + 130w + w^2 - 4000
w^2 + 130w
w(w + 130)
Expression for the total area: (80 + w)(50 + w)
Expression for the area of the path: w(w + 130)
Hope this helps!! :)
Using the exchange rate £1 = $1.34, calculate how many £ are in $7.25. Give your answer rounded to 2 dp.
Answers
Answer:
£5.41
Step-by-step explanation:
7.25/1.34 = 5.41044...
Round = 5.41
I got Points to burn, here you go
6÷2(1+3)
Answers
Answer:
12
Step-by-step explanation:
huhiihiuhihihihihihi
Answer:
1+3=4 and 2 times 4 is eight. 8 divided by 6 is 1.33333333333333333333
5{[(4+6-8)-4]-(1+2⁴-3+6)}
Answers
Answer:
30
Step-by-sçtep explanation:
is 28.42 > 28. 404 true
Answers
Answer:
28.42 > 28.404
it is true
A fair coin is flipped ten times. What is the
probability of the coin landing heads up
exactly six times?
Answers
Answer:
It’s 105/512, or about 20.51%
Step-by-step explanation:
I don't know, I asked peeps
Given the vertex ( 4, 6 )and the point(1, -3), write the vertex form equation of the quadratic
function.
Answers
Answer:
[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]
Step-by-step explanation:
A given quadratic has its vertex at (4, 6) and the point (1, -3). We want to write the equation in vertex form of the quadratic.
Recall that vertex form is given by:
[tex]\displaystyle f(x) = a(x-h) ^2 + k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
Since our vertex is at (4, 6), h = 4 and k = 6:
[tex]\displaystyle f(x) = a(x - 4)^2 + 6[/tex]
To determine the leading coefficient, since we are given that (1, -3) is a point on the parabola, when x = 1, y = -3. Substitute and solve for a:
[tex]\displaystyle \begin{aligned} (-3) & = a((1)-4)^2 + 6 \\ \\ -3 & = a(-3)^2 + 6 \\ \\ 9a & = -9 \\ \\ a & = -1 \end{aligned}[/tex]
Hence, the leading coefficient a is -1.
Then our equation in vertex form is:
[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]
Please include working out. =D You will get 30 points for it.
Answers
Answer:
It should be c
Step-by-step explanation:
Your formula is
Number of color ball/total ball
so 8/20 x 7/19 x 3/18 then convert to fraction
The probability the first ball is red is 0.4 or 8/20 or 2/5
The probability the next is blue is 7/19
The probability of the next being white is 6/18 or 1/3.
Multiply them together because these are independent events that must all occur and we get 2*7*1= 14 as the numerator
5*19*3=285 for a total probability of 14/285.
CDoes anyone know the answer to 8% of 65?
Answers
Answer:
5.2
Step-by-step explanation:
I just used a calculator
Answer:
5.2
Step-by-step explanation:
You change 8% into a fraction so it will be 8/100. So the question will now be
8/100 X. 65/1
So when you multiply them you will get 5.2
MARK AS BRAINLIEST.
Is the following graph proportional or non-proportional?
Proportional
Non-Proportional
Not enough information
Answers
Answer:
non-proportional
Step-by-step explanation:
The line doesn't go through the origin and it's not a straight line therefore the graph is not proportional. Hope this helps :)
Answer:
Not proportional
Step-by-step explanation:
The graph is not proportional because the line doesn't go through the origin. If the line start from the origin and went up it would be a proportional graph.
Given f(x)=3x^2-5x+k and the remainder when f(x) is divided by x-4 is 38, then what is the value of k? brainliest for correct answer
Answers
Answer:
30
Step-by-step explanation:
please give me a brainlist
HIGHWAYS Interstate 90 is the longest interstate highway in the United States, connecting the cities of Seattle, Washington, and Boston,
Massachusetts. The interstate is 4,987,000 meters in length. If 1 mile = 1.609 kilometers, how many miles long is Interstate 90?
Oa 3.099,441 mi
Ob. 3099 mi
Oc. 8,024,083 mi
O d. 8024 mi
Answers
=============================================================
Explanation:
4,987,000 meters = 4,987 kilometers
Divide by 1000 to go from meters to kilometers. This is because 1 km = 1000 m. Or in short, we just chop off those last three zeros at the end.
Also, because 1 mile = 1.609 km (approximate), this means we divide by 1.609 when converting from km to miles
So,
4,987 km = 4987/(1.609) = 3,099.4406 miles approximately
This rounds to 3099 miles
----------------
You can optionally show your work like this:
[tex]4,987,000 \text{ m} * \frac{1 \text{ km}}{1000 \text{ m}}*\frac{1 \text{ mi}}{1.609 \text{ km}}\\\\ = \frac{4,987,000*1*1}{1000*1.609} \text{ mi} \\\\\approx 3099.4406 \text{ mi}\\\\ \approx \textbf{3099 mi}[/tex]
Notice that the "km" and "m" units cancel out when going from the first step to the second step. All that's left is the "mile" unit.
Please help me with question 8
Answers
Answer:
1.6
Step-by-step explanation:
sorry this is probably really weird to cut peanuts like this
Answer:
5/8 pounds
Step-by-step explanation:
5/2/4 Convert, then multiply by one fourth
Use point-slope form to write the equation of the line in slope-intercept form.
slope = -1 and passes through the point (-4, 10)
fill in the point-slope equation.
y - __= (x - __ )
Now write the equation in slope-intercept form. (y = mx + b)
Sope intercept Equation:
Answers
Answer:
y - 10 = -1 (x+4)
y = - x + 6
Step-by-step explanation:
y - 10 = - 1 (x - - 4)
y - 10 = -x - 4
y = -x - 4 + 10
Evaluate using suitable identity:
d). 9.9²
Answers
Step-by-step explanation:
9.9²
(10-0.1)²
= 10² -2 (10) (0.1) + 0.1²
= 100 -2 + 0.01
= 98.01
Hope it helps you
Answer:
★ Solution :-[tex]\sf \longmapsto 9.9^2[/tex]
[tex]\sf \longmapsto (a - b)^2 = a^2 - 2ab + b^2[/tex]
Here,
a = 10b = 0.1[tex]\sf \longmapsto (10 - 0.1)^2 = 10^2 - 2(10)(0.1) + 0.1^2[/tex]
[tex]\sf \longmapsto 10^2 - 2(10)(0.1) + 0.1^2[/tex]
[tex]\sf \longmapsto 100 - 2 + 0.01[/tex]
[tex]\sf \longmapsto 98.01[/tex]
In a department store, a $40 dress is marked, "Save 25%. What is the sale
price of the dress?
Answers
Answer:$30
Step-by-step explanation:
$40*25%=$10 discount
$40-$10= $30.00
Answer:
The dress' price is $30.
Step-by-step explanation:
The discount on the dress is for 25% off.
25% of $40, is $10.
$40 - $10 is $30, resulting in a sale price of $30.
Hope this helps!
please help :D i give brainliest
In an isosceles triangle, the length of the base is half of the length of a leg. The perimeter of this triangle is 50 cm. Find the lengths of all sides.
Answers
Answer:
10 cm, 20 cm, 20 cmStep-by-step explanation:
Let the base is x, then the legs are 2x each.
The perimeter is:
x + 2x*2 = 505x = 50x = 10The base is 10 cm and legs are 20 cm each.
4.The average temperature in the desert ecosystem can be 38°C in one 24-hour
period. Solve for F. Then, find the equivalent temperature in degrees Fahrenheit, F.
Answers
Answer:
someone please ananswer i need help
Step-by-step explanation:
HELP PLSSS THIS IS HARD SOMEONEEE
Answers
simplify this equation
-8 (7x - 4)
Answers
-56x+32
Hope this helps
Answer:
-8(7x-4)
-56x+32
Step-by-step explanation:
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d
d
d
d
d
If two books costs $90 how much for 5 book
Answers
Answer:
$450
Maybe this will help
QUICKLY! ILL GIVE BRAINLEST AND THANKS!!
The number of kilometer, k, an airplane flew is shown in the table, where the time, t, is hours after take off. Choose the most appropriate scale for graphing this data set.
Answers
Answer:
t one because changing for t is approximately 1
and for kilometers is better you choose 1000
If AABC = APQR, then
B = 4[?]
Answers
Answer:
Q that is your answer
Step-by-step explanation: