Find the x-intercept(s) and the coordinates of the vertex for the parabola y= x^2 -8x + 12. if there is more than one x-intercept, separate them with commas.
Answer:
(i) x-intercepts: (2, 0), (6, 0)
(ii) vertex : (4, -4)
Explanation:
y = x² - 8x + 12
To find x intercepts, [set y = 0]
x² - 8x + 12 = 0x² - 2x - 6x + 12 = 0x(x - 2) - 6(x - 2) = 0(x - 6)(x - 2) = 0x = 6, x = 2x-intercepts: (2, 0), (6, 0)
To find vertex:
x = -b/2a
= -(-8)/2(1)
= 4
y = x² - 8x + 12
= 4² - 8(4) + 12
= -4
Vertex : (4, -4)
Solve the equation for y=0
x²-8x+12=0x²-6x-2x+12=0x(x-6)-2(x-6)=0(x-2)(x-6)=0x=2,6X inetercepts (2,0) and (6,0)
Vertex :-
x coordinate
-b/2a8/24Y coordinate
4²-8(4)+12-4Verted at (4,-4)
complete the square to solve the equation below. check all that apply.
x^2 + 8x - 1 = 19
Answer:
B and D
Step-by-step explanation:
First take the equation and subtract 19 on both sides. You get x^2+8x-20=0
using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)
simplify it and you get x= (-8 +or- 12) / 2
Separate the equation into two and you get (-8 + 12) / 2 and (-8 - 12) / 2
first one gives: 4/2=2
second gives -20/2=-10
answer x=-10,2
On a number line, 1.84 would be located ______. Choose all answers that make a true statement.
1.84
《--|----|----|----|----|----|----|----|----|----|--》
A. between 1.74 and 1.94
B. to the left of 1.85
C. to the right of 1.83
D. between 1 and 2
Answer:
All answers are correct.
Step-by-step explanation:
A. 1.84 is between 1.74 and 1.84.
B. 1.84 < 1.85. Lower values go to the left.
C. 1.84 > 1.83. Higher values go to the right.
D. 1.84 is between 1.0 and 2.0.
4.
The graph below shows the distance traveled by a person biking at a rate of 6
miles per hour.
The equation is d = 6t, where t is the number of hours and d is the distance traveled
Write an equation that represents the distance traveled by a person who can bike
at a rate of 8 miles per hour.
Answer:
d=8t
Step-by-step explanation:
Can someone help me with this, it’s geometry and it’s so confusing
Answer:
Draw a line from one point A to B into the XY line in a angle
Draw a line parallel to the lines
Point a dot in the middle and name it O
Step-by-step explanation:
Hope it helps
solve the inequality 5x+3> 48
Answer:
x > 9
Step-by-step explanation:
for this inequality, we want to isolate x, so that we know the inequality of x
5x + 3 > 48
- 3 -3 {subtract 3 from both sides to get x alone}
5x > 45
/5 /5 {divide both sides by 5 to find 1x}
x > 9
So , x > 9 is the inequality in terms of x {is the solution}
hope this helps! :)
Answer:
[tex]\huge\boxed{\sf x > 9}[/tex]
Step-by-step explanation:
Given inequality:5x + 3 > 48
Subtract 3 to both sides
5x > 48 - 3
5x > 45
Divide 5 to both sides
x > 9
[tex]\rule[225]{225}{2}[/tex]
Which polynomial is in standard form?
1+2x-8x^2+6x^3
2x^2+6x^3-9x+12
6x^3+5x-3x^2+2
2x^3+4x^2-7x+5
The only equation that is written in descending order is
2x³+4x²-7x+5 , Option D is the correct answer.
What is a Polynomial ?A polynomial is a mathematical expression consisting of variables , constants and mathematical operators.
The standard form of a polynomial is
[tex]\rm a_1x^n +a_2x^{n-1}+............+a_0[/tex]
The only equation that is in its standard form or in other words
The only equation that is written in descending order is
2x³+4x²-7x+5 , Option D is the correct answer.
To know more about Polynomial
https://brainly.com/question/11536910
#SPJ1
12% profit on a computer is Rs.540.
(i) Find the cost price of the computer.
(ii) Find the sale price of the computer.
Answer:
the cost price is Rs. 4500 and the sale price is Rs. 5040.
Step-by-step explanation:
Let the cost price of the compute be Rs. x.
The profit earned is, Rs. 540.
The profit percentage is, 12%.
The formula to compute profit is:
Profit = SP - CP
\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500
Compute the selling price as follows:
SP = CP + profit
= 4500 + 540
= 5040
Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.
The figure shows part of the concrete slab which is used to make drains and its cross-section. it is made up of a cuboid of dimensions 120 cm by 60 cm by 40 cm, with a half-cylinder horizontally carved out of it.
(i) find the area of the cross-section ABCDEFG.
(ii) find the volume of the concrete slab.
(iii) find the total surface area of the concrete slab.
(iv) find the mass of the concrete slab if the density of concrete is 2300 kg/cubic m, giving your answer in kg.
(i) The area of the cross section ABCDEFG is 1771.6cm³
(ii) The volume of the concrete lab is 212592 cm³
(iii) the total surface area of the concrete slab is 30284 cm²
(iv) The mass of the concrete slab is 40746.8 kg/m³.
Given, dimensions are 120 cm by 60 cm by
40 cm.
(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2
= 1771.6 cm³
(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10 ₋10)/2)² . 120
= 212592 cm³
(iii) The total surface area is:
=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120
= 30284 cm²
(iv) Mass of the concrete slab given density is 2300 kg/m³
Mass = Volume × density
Mass = 17.716 m³ × 2300
= 40746.8 kg/m³
Hence we get the mass as 40746.8 kg/m³.
Learn more about "Mensuration" here-
brainly.com/question/26398444
#SPJ10
pls hurry i really i need to finish
What steps are used to solve this equation?
x
2
= 7
Answer:
x=3.5
Step-by-step explanation:
x × 2 = 7
÷2 ÷2
x=3.5
a town B is 12km from another town A on a bearing of 47degree and another C is 8km from town B on a bearing of 124degree.how far is town A from town C?what is the bearing of A from C
Answer:
Distance between A and C = 16km
Bearing of A from C = 257°
Step-by-step explanation:
please see photo for detailed analysis
Which point is a solution to the system?
O (-1, 6)
O (0, 22)
O (2,9)
O (8, 2)
Answer: (2,9)
Step-by-step explanation:
It lies in the region that is shaded both red and blue (representing the fact that it satisfies both inequalities).
Solve using a formula. Please don't guess, I would like professionals to take a look
Let's take this problem step by step:
What we know:
[tex]x+y=4\\xy=-2[/tex]
Before we solve, let's do one thing that will help us out greatly later down the road:
[tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation
Let's rearrange the problem a little bit:
[tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]
Combine fractions of common denominators:
[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]
Now's let factor everything apart:
[tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]
Let's use what we know and our useful equation:
[tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]
The value is 440
Answer: 440
Hope that helps!
#LearnwithBrainly
HELP! WILL GIVE BRAINLEST
Examine the following diagram: in the photo I attached of the question
What is the measure of DBC?
2°
6°
41°
49°
Answer:
Option C: 41
Step-by-step explanation:
<ABD+<CBD=90
<ABD=8x+1
<CBD=6x+5
(8x+1)+(6x+5)=90
Combine like terms
(8x+6x)+(1+5)=90
14x+6=90
14x=90-6
14x=84
divide both sides by 14
x=6
Now we plug that value into <DBC = 6x+5
6(6)+5=
36+5
41
Let's take this problem step by step:
∠ABC is 90 degrees
⇒ made up of two angles ⇒ ∠ABD and ∠DBC
⇒ in mathematical equation form:
[tex]ABD + DBC= ABC[/tex]
Since ∠ABD = 8x + 1 and ∠DBC = 6x+5
[tex]8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6[/tex]
Let's plug it into ∠DBC = 6x+5
∠DBC = 6x+5 = 6(6)+5=41
Answer: ∠DBC = 41
Hope that helps!
#LearnwithBrainly
what is the gradient if y=-x+3
Answer:
Slope = - 1
Step-by-step explanation:
The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex] is the intercept on [tex]y[/tex] axis.
Hence, in [tex]y=-x+3[/tex] , slope is -1 and intercept on [tex]y[/tex] axis is 3.
The graph of y = f(x) is shown below. Find the value of ƒ (-2).
Answer: f(-2) = 8
Step-by-step explanation: On the graph there’s a point (-2,8), so f(-2), which just means -2’s y value on the graph, is 8.
This probability distribution shows
the
typical grade distribution for a Geometry
course with 35 students.
Grade
B
F
Frequency
5
10
15
3
2
Find the probability that a student earns
a
grade of B or C.
p=[?]
Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
if the ratio of the sides of a triangle are 13:14:15 and its perimeter is 84 cm, find the area of the triangle.
Answer:
The ratio of sides of triangle = 13:14:15
perimeter = 84 CM
perimeter of a triangle = Sum of all sides
let the sides of a triangle be 13x, 14x and 15x
84 = 13x + 14x + 15x
84 = 42x
x = 2
13x = 13* 2 = 26 CM
14x = 14*2 = 28 CM
15x = 15*2 = 30 CM
i need help finding this for clever
Answer:
The dog is 16 years old.
Step-by-step explanation:
X/4 + 6 = X/8 + 8
X/4-X/8 = 8-6
0.125X = 2
X = 2/0.125
X = 16
Answer:
16 years old
Step-by-step explanation
Dividing the dog’s age by 4 and adding 6
D÷4 + 6
dividing the dog’s age by 8 and adding 8
D÷8 + 8
equating both
D÷4 + 6 = D÷8 + 8
=> D÷4 - D÷8 = 2
multiplying by 8 both sides
=> 2D - D = 16
=> D = 16
hence, the dog is 16 years old
Again, simple questions! asap help please!
15 points!
Answer:
3) r = 1.5
7) y = 18
11) x = -10
Step-by-step explanation:
3) Isolate the variable by dividing each side by factors that don't contain the variable.
7) Solve for y by simplifying both sides of the equation, then isolating the variable.
11) Move all terms that don't contain x to the right side and solve.
number machine n -5 x 4
What is the independent variable in the equation y=-5x+2?
Answer: x
Step-by-step explanation:
For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.
Kojo is twice as old as Esi who in turn is 5 years older than kwaku .if their total age is 47 . How old is each of them?
The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
What is an Equation ?An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.
Let the age of Kwaku is x
Let the age of Esi is y
From the given data
The age of Kojo is 2y
y = x +5
Sum of their age = 47
2y = 2x +10
therefore the equation formed is
x + y +2y = 47
x + x+5 + 2x +10 = 47
4x +15 = 47
4x = 32
x = 8
y = 13
2y = 26
Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
To know more about Equation
https://brainly.com/question/10413253
#SPJ1
Part 1: complete the operations geometrically. vector operations to draw the resultant vector draw 2u + 4v.
Vectors are elements of the vector space, and they can be illustrated by diagrams.
How to draw the vector 2u + 4v?The vector expression is given as:
2u + 4v
Split the vector expressions, as follows:
y1 = 2u
y2 = 4v
Next, we have:
y = y1 + y2
See the attachment for the graph of 2u + 4v.
Read more about vectors at:
brainly.com/question/14480278
#SPJ1
√m is an integer.
Given that the value of "m" lies between between 2929 and 3939
Write down the value of "m"
Answer:
There are 8 possible answers for the value of m
Step-by-step explanation:
3025 (55^2), 3136 (56^2), 3249 (57^2)...., 3844(62^2)
The square of the numbers 55-62 could be a solution set for m.
HELP ASAP/NOW...NO LINKS OR JOKING PLS
Answer:
D. 0 < x < 20
Explanation:
Domain is in the x axis, Range lies in the y axis.
Here it is seen that function's domain lies between 0 to 20.
Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'Here, as the circle's are open. Domain: 0 < x < 20
Additionally,
Range: -10 < f(x) < 0solve for z z - 6 < 3
Step-by-step explanation:
[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]
Hope it helps
Z – 6 < 3
Z < 3 + 6
Z < 9
✯Hope this helps✯✿..๑... Ziddi girl ♡..✧can someone please help meee
Answer:
-10
Step-by-step explanation:
y2- y1 -7 -3
---------- ----------
x2 - x1 -6 6
What is the simplified form of this expression? (3 − 13x − 7x2) − (5x2 12x − 10)
Answer:
-12x²-25x+13
Step-by-step explanation:
First open parenthesis.
(3 − 13x − 7x²) − (5x² + 12x − 10)
3 − 13x − 7x² − 5x² - 12x + 10
Now combine like terms.
3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²
Now put into standard form, exponents greatest to least.
-12x²-25x+13
Hope this helps!
If not, I am sorry.
Answer:-12x²-25x+13
Step-by-step explanation: