Answer:
(-1, -9/2) minimum true
1/2 (x+1)^2 -9/2 is the vertex form false
the axis of symmetry is at the x value of the vertex x=-1 false
The parabola opens up since the x^2 coefficient is positive false
x=-4 x=2 true
Step-by-step explanation:
f(x) = 1/2x^2 +x - 4
Factor out 1/2
f(x) = 1/2 (x^2 +2x - 8)
Factor
f(x) = 1/2 ( x+4)(x-2)
Finding the zeros
0= 1/2 ( x+4)(x-2)
Using the zero product property
x+4 = 0 x-2=0
x=-4 x=2
The vertex is 1/2 way between the zeros
(-4+2)/2 = -2/2 = -1
f(-1) = 1/2 (-1+4) (-1-2) = 1/2(3)(-3) =-9/2
The vertex is (-1, -9/2)
The parabola opens up since the x^2 coefficient is positive so this is the minimum
f(x) = 1/2 (x+1)^2 -9/2 is the vertex form
the axis of symmetry is at the x value of the vertex x=-1
how to bring the polynomial to the standard form p(x) x^2-2x+4) (x^2+2x+4)
[tex]\rightarrow\sf((p(x) {x}^{2} + 2x + 4)( {x}^{2} + 2x + 4)) \\ = \sf {ax}^{2} + bx + c \\ = \sf(p(x) {x}^{2} {x}^{2} + p(x) {x}^{2} (2x) + p(x) {x}^{2} \times 4 + 2x \times {x}^{2} + 2x(2x) + 2x \times 4 + {4x}^{2} + 4(2x) + 4 \times 4) \\ = \sf( {x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16) \\ \rightarrow \large\boxed{\sf\red{{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}[/tex]
Answer:[tex]\large\boxed{\sf{\red{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}[/tex]
[tex]\color{red}{==========================}[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
✍︎ꕥᴋɪᴍ ᴀʀᴀꕥ
find the measure of the largest exterior angle
Answer:
116 degrees
Step-by-step explanation:
To find the answer, we must know what the sum of exterior angles are on a given shape, which is 360 degrees.
So, let's put the equation up.
8x-21+4x-13+5x-11+6x+14=360
Let's add all the x variables together to simplify it. And also add the number together too.
8x+4x+6x+5x= 23x
(-21)+(-13)+(-11)+14 = -31
The equation we have is in its initial simplified version. Let's simplify it even more to solve.
23x-31=360
Add 31 to both sides.
23x=391
Divide 23 on both sides to find x.
391/23 = x
x= 17
Let's put the value x in each exterior angle.
A= 8(17)-21 = 115 degrees
B= 6(17)+14 = 116 degrees
C= 5(17)-11 = 74 degrees
D= 4(17)-13 = 55 degrees
From the work above, we know B is the largest exterior angle, which is 116 degrees.
Hope this helps!
A water company charges $20 for service and 2.75 for every 1000 gallons of water use in month construct a linear model to represent the water bill; how much would you be charged bill how much would you be charged if you use 5000 gallons of water this month
Answer:
5000
Step-by-step explanation:
⁉️⁉️
Ravi bought 50kg rice at the rate it tk40 per kg and sold it at the rate of tk44 per kg. What is the amount of profit or loss?
Here is your Answer
Step-by-step explanation:
Ravi bought rice = 50kg
Rate it =40kg
Sold it at the rate = = 44kg
Answer: -34Mark me as brainlist and give me 20 thx plshelp needed right away this is timed
HELP ASAP!!!!!!!PLEASE SHOW WORK!!!!!! !!!!!
Answer:
Area = 12.82 miles²
Step-by-step explanation:
Area of a triangle with two adjacent sides and the inscribed angle between these side is given by,
Area = [tex]\frac{1}{2}ab[\text{sin(C)}][/tex]
By substituting the values of sides a, b and the angle C,
Area = [tex]\frac{1}{2}(5.7\times 9.3)[\text{sin}(14^{\circ})][/tex]
= 12.82 square miles
The following data on price () and the overall score for stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is
(y-hat) = 27.922+0.302x
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Required:
Does the t test indicate a significant relationship between price and the overall score?
Answer:
Relationship exists between price and overall score
Step-by-step explanation:
Given the data:
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Using the correlation Coefficient calculator ; the correlation Coefficient, R = 0.875
H0 : no relationship exists
H1 : relationship exists
Using the R Coefficient ;
The test statistic :
T = r / √(1 - r²) / (n - 2)
n = 6
The test statistic :
T = 0.875 / √(1 - 0.875²) / (4)
T =0.875 / 0.05859375
T = 0.9333
The Pvalue from test statistic :
df = n - 2 ; 6 - 2 = 4
Pvalue(0.933, 4) = 0.02246
At α = 0.05
Pvalue < α ; We reject H0 ; and conclude that relationship exists between price and overall score
66. If the length of one side of a triangle 6 and the length of another side is 2, which of the following cannot be the length of the third side of the triangle?
A) 8
B) 7
C)
D) 5
Answer:
A)
Step-by-step explanation:
what is C ? 6 ?
if that is the case, then my answer is A) 8
why ? because then the other 2 sides together are just as long as this third side, and we would have just a flat line with the length of 8.
every side in a triangle must be shorter than the other two sides together.
but - fully formally such a flat line could be considered a special triangle with 2 angles of 0 degrees and one angle of 180 degrees.
that is why I am asking about the missing C answer. it could be a trick question. but if C is truly 6, then yes, A is the right answer. if C is larger than 8, then C is the right answer.
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies. how many different choices are available ?
a. 78
b. 34
c. 32
d.39
Answer
I guess
39 different choice are available
The perimeter of a rectangle is 90. One side of the rectangle is twice the length of the other.
What is the length of the longer side?
Answer:
30
Step-by-step explanation:
p=2l+2w
p=2(2w)+2w
p=4w+2w
p=6w
p=90
90=6w
15=w
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
It's a 30-60-90 triangle, so n = 2×4√6/√3 = 8√2
What is the solution set of 7 x2 + 3 x = 0? {0, 3/7} {0, -3/7} {0, -4/7}
Answer:
[tex]{ \tt{7 {x}^{2} + 3x = 0 }} \\ { \tt{x(7x + 3) = 0}}[/tex]
Either x = 0 or ( 7x + 3 ) = 0 :
[tex]{ \tt{7x + 3 = 0}} \\ { \tt{x = - \frac{3}{7} }}[/tex]
Answer:
[tex]{ \bf{(0, \: - \frac{3}{7}) }}[/tex]
Could someone help with question 7?
Answer:
x=35
Step-by-step explanation:
since the two triangles are similar, we can set up a proportion to find x:
4/14=10/x
4x=140
x=35
HELP What is true about the dilation?
On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), (3, 0).
It is a reduction with a scale factor between 0 and 1.
It is a reduction with a scale factor greater than 1.
It is an enlargement with a scale factor between 0 and 1.
It is an enlargement with a scale factor greater than 1.
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Answer:
(d) enlargement with scale factor greater than 1
Step-by-step explanation:
The image is obviously larger than the pre-image, so the dilation is an enlargement. The scale factor associated with an enlargement is always greater than 1.
__
Additional comment
In this drawing, the scale factor in the vertical direction is 8/2.5 = 3.2. The scale factor in the horizontal direction is 9/3 = 3.0. The scale factors are different in the different directions.
Answer:
D.
Step-by-step explanation:
Which phrase describes an unknown or changeable quantity
Answer:
a variable
Step-by-step explanation:
because it varies
Name different types of triangles and illustrate how you can introduce each triangle to the foundation phase learner during a lesson presentation. Mention the resources that you will use
The types of triangles are: equilateral, isosceles, scalene, right angled, acute angled and obtuse angled triangle.
Triangles are plane shapes with three straight sides. Triangles are classified with respect to either their length of sides, or the measure of each internal angles.
1. Classification of triangles with their length of sides:
i. Equilateral triangle: This implies a triangle with equal length of sides.
ii. Isosceles triangle: This triangle has two of its side with equal length.
iii. Scalene triangle: In this triangle, non of its sides has equal length.
2. Classification of triangles with their internal angles:
i. Acute angled triangle: This triangle has all its angles less than [tex]90^{o}[/tex].
ii. Right angled triangle: This has one of its angles to be a right angle.
iii. Obtuse angled triangle: This triangle has one of its internal angles to be greater than [tex]180^{o}[/tex].
Therefore, there are generally six types of triangles of two classes.
Resources: Set squares, triangular prism, marking board and a marker etc.
For more information: https://brainly.com/question/18075714
An astronaut on the moon throws a baseball upward. the astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 50 ft per sec. the height s of the ball in feet is given by the equation s=-2.7t^2+50t+6.5 , where t is the number of seconds after the ball was thrown. complete parts a and b.
Answer:
Step-by-step explanation:
This was answered in question #24217201. It's the exact same question, but you forgot to put what parts A and B are. The answers and the work are there.
Simplify the radical expression.
Step-by-step explanation:
the answer is in the image above
Answer:
[tex]-\sqrt{5q^{3} } \times3\sqrt{35}[/tex]
[tex]-\sqrt{5} \times\sqrt{q^{3} } \times3\sqrt{5} \times\sqrt{7}[/tex]
[tex]-15\sqrt{7q^{3} }[/tex]
------------------------
Hope it helps...
have a great day!!
Brad is 12 years older than Sam. If Brad were 8 years older than he is now, he would
be twice as old as Sam. How old is Sam now?.
Answer:
Sam is 20 years old.
50 POINTS PLEASE HELP ME
Answer:
4 -6x^2
Step-by-step explanation:
f°g = f(g(x))
We place g(x) in for x in the function f(x)
= 4-2(g(x)) = 4-2(3x^2) = 4 -6x^2
B.4-6x²
Answer:
Solution given:
f(x)=4-2x
and
g(x)=3x²
now
f o g(x)=f(g(x))=f(3x²)=4-2*3x²=4-6x²
Find the measure of missing angle
Answer:
58 degrees
Step-by-step explanation:
90 - 32 = 58
What is cube root 16y^4/x^6
in simplest form?
Cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
What is cube root?" Cube root is defined as the number when multiply three times and produce result as one original number one time."
According to the question,
Given expression,
[tex]\frac{16y^{4} }{x^{6} }[/tex]
Cube root of the given expression is,
[tex]\sqrt[3]{\frac{16y^{4} }{x^{6} }} \\\\\implies \sqrt[3]{\frac{(2)^{3}(2) y^{3} (y)}{(x^{2}) ^{3} }}\\\\\implies \frac{2y}{x^{2} } \sqrt[3]{2y}[/tex]
Hence, cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
Learn more about cube root here
https://brainly.com/question/12726345
#SPJ3
Answer:
B on edge
trust me bro
Needs 20 characters even though the picture says it all.
On a piece of paper, graph y = 4x - 2. Then determine which answer matches the graph you drew.
Answer:
it's A
Step-by-step explanation:
start at 2 on the y axis and go up 4 and right 1
WILL GIVE BRAINLIEST!!!!!!! A boy had 20 cents. He bought x pencils for 3 cents each. If y equals the number of pennies left, write an equation showing the dependence of y on x. What is the domain of the function?
Answer:
[tex]\displaystyle \text{Function: }{y=20-3x,\\\text{Domain: }(-\infty, \infty)\text{ or }\mathbb{R}[/tex]
Step-by-step explanation:
If the boy initially had 20 cents, then the total number of cents he will have left after purchasing [tex]x[/tex] pencils is equal to the total cost of the pencils subtracted from 20. The total cost of [tex]x[/tex] pencils, in cents, is equal to [tex]3x[/tex], since each pencil is 3 cents.
Therefore, the total amount, in cents, that the boy has left, [tex]y[/tex], is equal to [tex]20-3x[/tex]:
[tex]\displaystyle \text{Equation: }\boxed{y=20-3x}[/tex]
The domain of this function is [tex](-\infty, \infty)[/tex] or all real numbers [tex]\mathbb{R}[/tex].
Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What's the largest possible radius for her circle, in meters?
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Answer:
9 m
Step-by-step explanation:
The relationship between radius and circumference is ...
C = 2πr
Daphne wants r an integer such that ...
60 m ≥ 2πr
r ≤ (60 m)/(2π)
r ≤ (30/π) m ≈ 9.549 m
The largest integer radius Daphne can use is 9 meters.
What is the x- intercept y =2x^2-8x+6?
Answer:
see your answer in the image
with full detail
mark me brainlist
Step-by-step explanation:
Answer:
(3,0) , (1.0)
Step-by-step explanation:
What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2,4)
Answer:
[tex]y=-2.5x-9[/tex]
Step-by-step explanation:
One is given the following equation.
[tex]5x + 2y = 12[/tex]
The problem asks one to find a line that is parallel to this one, and passes through the point: [tex](-2, 4)[/tex]. The equation of the given line is in the standard format. The easiest approach to solve this problem is to change the equation of the given line into the slope-intercept format. The solve intercept format follows the following general equation:
[tex]y=mx+b[/tex]
Where (m) is the slope of the line and (b) is the y-intercept. Manipulate the given equation such that it follows this format:
[tex]5x+2y=12\\2y=12-5x\\y=6-2.5x\\\\y=-2.5x+6[/tex]
One property of parallel lines is that they have the same slope. Therefore, if one uses the slope-intercept format to represent the slope of the parallel line, then one can state the following:
[tex]y=-2.5x+b[/tex]
Substitute a given point on this line ([tex]-2,4[/tex]) , and solve for (b) to find (b):
[tex]y=-2.5x+b\\(4)=-2.5(-2)+b[/tex]
Simplify,
[tex]4=-2.5(-2)+b\\-4=5+b[/tex]
Inverse operations,
[tex]-4=5+b\\-9=b[/tex]
Substitute this back into the equation in slope-intercept form to find the equation of the parallel line:
[tex]y=-2.5x-9[/tex]
find the equation of a line perpendicular to 4x-y=4 that contains the points (0,3)
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Answer:
x + 4y = 12
Step-by-step explanation:
The perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. Then those new coefficients can be used with the coordinates of the given point to find the required constant.
line: 4x -y = 4
perpendicular line: x +4y = constant
Through (0, 3):
0 +4(3) = constant = 12
The perpendicular line has standard form equation x +4y = 12.
Answer:
Step-by-step explanation:
y=-1/4x+3
GEOMETRY HELPPP PLEASEEE
Answer:
Step-by-step explanation:
