Hello!
[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]
- Separate the function into parts to determine the domain of each part.
[tex]\bf ( x + 3 )^{2} \\ x + 3 \\ 5 [/tex]
- The domain of a polynomial function is the set of all real numbers.
[tex]\bf x ∈ ℝ [/tex]
Domain: ( -∞; ∞ )
[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]
- Write the second degree function in standard form.
[tex]\bf y = x^{2} + 6x + 4 [/tex]
- Identifies the coefficients a and b of the second degree function.
[tex]\bf a = 1, b = 6 [/tex]
- Find the x coordinate of the vertex by substituting a = 1 and b = 6 in x = -b / 2a.
[tex]\bf x = -\frac{6}{2×1} [/tex]
[tex]\bf x = -\frac{6}{2} [/tex]
[tex]\bf x = -3 [/tex]
- Calculates the value of the function for x = -3.
[tex]\bf y = ( x + 3 )^{2} - 5 [/tex]
[tex]\bf y = -5 [/tex]
Range: ( -3; -5 )
Answer: No answer
Good luck! :)
Guided Practice
Use the vertical motion formula h = –16t2 + vt + c.
A child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft. Substitute the values into the vertical motion formula and let h = 0. Use the quadratic formula to solve for t. How long is the ball in the air?
A.
0.8 s
B.
0.8 s or –0.2 s
C.
0.2 s
Answer:
t = -0.22secs and 0.85secs
Step-by-step explanation:
Given the expression
h = –16t² + vt + c.
If a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft, then;
v = 10, c = 3
Since we are to let h = 0, then the equation becomes:
0 = –16t² + 10t + 3
Multiply through by a minus sign
16t² - 10t - 3 = 0
Factorize the reulting expression:
t = -(-10)±√(-10)²-4(16)(-3)/2(16)
t = 10±√100+192/32
t = 10±√292/32
t = 10±17.09/32
t = 10-17.09/32 and 10+17.09/32
t = -7.09/32 and 27.09/32
t = -0.22secs and 0.85secs
Answer:
0.8 s
Step-by-step explanation:
I got it right in grandpoint.
what is the answer to this?
Answer:
x is any number
y depends on x value
The length of a rectangular playing field is 5m longer than its width. If the perimeter of the field is 150m,find it's width
Answer:
35
Step-by-step explanation:
Make equations, l = w+5 and 2l + 2w = 150
Substitute w+5 into 2l + 2w = 150
Simplify to get 4w + 10 = 150
Subtract 10 from both sides to get 4w = 140
Divide both sides by 4 and you get 35 as width
Answer:
The width of the field is 35 meters.
Step-by-step explanation:
Recall that the perimeter of a rectangle is given by:
[tex]\displaystyle P = 2(w+\ell)[/tex]
Where w is the width and l is the length of the rectangle.
We know that the perimeter is 150 meters. Thus:
[tex]150=2(w+\ell)[/tex]
Divide both sides by two:
[tex]75=w+\ell[/tex]
We are given that the length is five meters longer than the width. So:
[tex]\ell = w+5[/tex]
Substitute:
[tex]75=w+(w+5)[/tex]
Combine like terms:
[tex]75=2w+5[/tex]
Subtract five from both sides:
[tex]70=2w[/tex]
And divide both sides by two. Hence:
[tex]w=35[/tex]
Thus, the width of the rectangular field is 35 meters.
can you write to me explaining this please
Answer:
In addition, from the response shown, using a graphical calculator brings the following benefits:
1) You can write the system of linear equations as big as you want. This is: systems 3 * 3, 4 * 4, 5 * 5.
2) The response to systems of equations greater than 2 * 2 can be complicated when you graph the solution, therefore, the graphing calculator can be much more efficient in these cases.
3) You can write the linear equations in any way. Resolving by hand you should probably rewrite the system of equations to find the solution.
Step-by-step explanation:
Answer:
Step-by-step explanation:
It is much simpler to graph and find the intersection points between the equations, which would be the solutions to the system, than graphing it by hand which would lead to some errors.
Express 3.023 in P form where p and q are integers and q= 0 D
Given:
The number is 3.023.
To find:
The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].
Solution:
The given number is 3.023. It can be written as:
[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]
[tex]3.023=\dfrac{3023}{1000}[/tex]
It cannot be simplified further because 3023 and 1000 have no common factors.
Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].
Enter the coordinates of the point
on the unit circle at the given angle. 0°
The points are ( 1,0) (0,1) .
The coordinates of the point on the unit circle -The coordinates for the points lying on the unit circle and also on the axes are (1,0), (–1,0), (0,1), and (0,–1). These four points (called intercepts) are shown here. When you square each coordinate and add those values together, you get 1. They're the sine and cosine values of the most common acute-angle measures.a.) We seek the coordinates on the unit circle that represent an angle of 0 degrees.
The points on the unit circle are often provided by,
( cosθ, sinθ )
In order to do so,
θ= 0
to acquire,
(cos(0),sin(0))
(1,0)
b. With regard to the location on the unit circle where the angle is 90 degrees,
We swap out
θ = 90
to acquire,
(cos(90),sin(90))
This is condensed to, (0,1)
Learn more about the coordinates of the point on the unit circle brainly.com/question/10169163
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Answer: 1,0
is the actual answer
Căn 84 bình phương trừ 37 bình phương chia 47
Answer:
[tex]\sqrt{84^{2} } -37^{2} /47[/tex]=257 9/47
Step-by-step explanation:
the function f(x) = -5x^2 +3 is defined over the domain -4< x < -1. find the range of this function.
a. 8 < f(x) < 83
b. 8 ≤ f(x) ≤ 83
c. -77 < f(x) < -2
d. 8 < f(x) < 23
Answer:
[tex]choice \: c. \: - 77 < f(x) < - 2[/tex]
Step-by-step explanation:
Find the y-values of the functions endpoints.[tex]f( - 4) = - 5 ({ - 4}^{2}) + 3 = - 77[/tex]
[tex]f( - 1) = - 5( { - 1}^{2}) + 3 = - 2[/tex]
Thus finding the range of F(x).
The range of the given function is - 77 < f(x) < - 2.
What is the range of a function?"The range of a function is a set of all the images of elements in the domain."
The given function is:
f(x) = - 5x² + 3
It is defined over the domain - 4 < x < - 1.
For x = - 4, f(x) = - 5(- 4)² + 3 = - 80 + 3 = - 77
For x = - 1, f(x) = - 5(- 1)² + 3 = - 5 + 3 = - 2
Therefore, the range of the given function f(x) is:
- 77 < f(x) < - 2.
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Help,anyone can help me do quetion,I will mark brainlest.
5.
1m = 0.001 km
So, 1m² = 10^-6
Area = 5027 m² = 5027 × 10 ^-6 km²
6.
1mm = 0.1 cm
1mm² = 10^-2
Area = 210× 297 mm² =62370 mm² = 62370 ×10^-2 cm²
SOMEONE HELP ME PLEASE
9514 1404 393
Answer:
1/12
Step-by-step explanation:
The probability of any given outcome is the ratio of the number of ways that outcome can happen to the total number of outcomes.
P(4) = 1/6 . . . . . roll = 4 is one of 6 possible outcomes
P(odd) = 3/6 = 1/2 . . . . . of the 6 possible outcomes, 3 are odd
__
The two rolls of the die are presumed to be independent, so the probability of the two outcomes is the product of their individual probabilities.
P(4 & odd) = (1/6)(1/2) = 1/12
In a car dealership, all of the vehicles are either
a sedan or a SUV. If 36 sedans are sold and 36
SUVs are added, there will be an equal number
of sedans and SUVs. If 8 SUVs are sold and 8
sedans are added, there will be twice as many
sedans as SUVs. How many sedans were at the
dealership before any vehicle was sold?
Answer:
The number of sedans before any vehicle was sold is 168
Step-by-step explanation:
Let's define the variables:
x = number of sedans
y = number of SUVs
We know that:
"If 36 sedans are sold and 36 SUVs are added, there will be an equal number of sedans and SUVs"
If 36 sedans are sold, the new number of sedans is:
x - 36
if 36 SUVs are added, the new number of SUVs is
y + 36
And these numbers are equal, then:
x - 36 = y + 36
We also know that:
" If 8 SUVs are sold and 8 sedans are added, there will be twice as many
sedans as SUVs. "
If 8 SUVs are sold, the new number of SUVs will be:
y - 8
If 8 sedans are added, the new number of sedans wil be:
x + 8
From this we can write the equation:
(x + 8) = 2*(y - 8)
x + 8 = 2*y - 16
Then we have two equations:
x - 36 = y + 36
x + 8 = 2*y - 16
We want to find the number of sedans, x, then we need to isolate the other variable in one of the equations, let's isolate y in the first one:
Let's isolate x in the first one:
x - 36 - 36 = y
x - 72 = y
Now we can replace it in the other equation:
x + 8 = 2*y - 16
x + 8 = 2*(x - 72) - 16
Now we can solve this for x.
x + 8 = 2*x - 144 - 16
8 + 144 + 16 = 2x - x
168 = x
The number of sedans before any vehicle was sold is 168
20 POINTS AND BRAIN LIESTJ ulia s urveyed the pl ayers on her so ccer team to see how many hou rs each mem ber prac ticed during the week. Her data is shown in the histo gram.
A histogram titled Prac tice Time has number of hours on the x -axis and number of players on the y-axis. 0.1 to 0.5 hours is 5 players, 0.6 to 1: 6, 1.1 to 1.5: 5, 1.6 to 2: 2, 2.1 to 2.5: 1, 2.6 to 3: 2, 3.1 to 3.5: 2, 3.6 to 4: 1, 4.1 to 4.5: 1.
Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.
Answer:
the left side of the histogram is the mirror image of the right side.
Use the distributive property to write equivalent expressions.
Someone please help, ty!
Answer:
For the question below, you will need to find the GCF of 45 and 60. In this instance it is 5, so it will be outside the box. The GCF answers will be inside the parenthesis, which is 7 and 12.
45x + 60 = 5(7x + 12)
In this question you have to multiply 2 with every number inside the parenthesis. So 2 × 10x and 2 × 4.
2(10x+4) = 20x + 8
Hope this helped.
PLEASE HELPPPPPP WILL GIVE BRANLIST
Answer:
x = 1
Step-by-step explanation:
2(76x - 1) = 150
76x - 1 = 75
76x = 76
x = 1
1/x^-2 x=7 yeet yeet
Answer:
49
Step-by-step explanation:
x = 7
1 / x^-2
= x^2
= 7^2
= 49
Answer: 49
Step-by-step explanation: yeet
how coming -17/18 please explain
find the value of x.
2+3
12
5
1.2
6.6
07
12
Answer:
x = 7
Step-by-step explanation:
The triangles are similar
12/8 = (x+3+5)/(x+3) cross multiply expressions
12x + 36 = 8x + 64
12x - 8x = 64 - 36
4x = 28 divide both sides by 4
x = 7
Answer??? if you want u can answer as u like....
60, because 6 times 10 is just that
Answer:
60
Step-by-step explanation:
6x10 is 60
What is the distance between (4, -10) and (4,-4)?
Answer:
For x there is no distance since they are both for. For y, they are -6 apart.
Step-by-step explanation:
Answer:
Fox x Diya is no distance since they are both for they are six apart
Step-by-step explanation:
(4-10)
and= just opposite size (10- 4) .
10 -4 = 6 answer 6
and (4-4)
answer is
0
the answer is six apart
understand
It is given 5 and h + 1 are the roots of the quadratic equation x² + (k - 1)x - 5 = 0,where h and k are constant.Find the value of h and k.
pls help me,i'll mark u as the brainliest!
Answer:
Hello,
k=-3 and h=-2
Step-by-step explanation:
[tex]5\ is\ a \ root \of \ x^2+(k-1)*x-5=0\\\\5^2+(k-1)*5-5=0\\\\5*(k-1)+20=0\\\\k-1=\dfrac{-20}{5} \\\\k=-4+1\\\\\boxed{k=-3}\\[/tex]
h+1 is thus a root of x²+(-3-1)*x-5=0
x²-4x-5=0
x²+x-5x-5=0
x(x+1)-5(x+1)=0
(x+1)(x-5)=0
h+1=-1
h=-2
WORTH 90 POINTS WILL MARK BRAINLY PLEASE HELP ME ASAP
Answer:
they are congruent.
Step-by-step explanation:
just move A down to -1 and and you can see they are the same.
Answer:
they are congruent.
Step-by-step explanation:
just move the A shape down to -1 and and you can see that they are the same.
Can you answer this math homework? Please!
Answer:
10 T Shirts to have 105 dollars
Step-by-step explanation:
[tex]10.5x = 7.5x + 30[/tex]
[tex]3x = 30[/tex]
[tex]x = 10[/tex]
Which of the following is an arithmetic sequence? 1, -3, 9, -27,... -2, 4, -6, 8, ... -8, -6, -4, -2, ... 2, 4, 8, 16, ...
Answer:
Given the proposed interrogate, the answer(s) to the following are identified as “-8, -6, -4, -2…” and “2, 4, 8, 16”.
Step-by-step explanation:
Accountable Conditions: Although the question implies there is only one individual mathematical statement which fits the conditions stated in the interrogate, both sequences listed above fit such, thus are both correct.
To evaluate for such, a comprehension of an “Arithmetic Sequence” is obligated:
In arithmetic sequences, the presence of a consecutive deviation or fixed pattern must be consistent and present throughout each and individual number or value contained within the particular set.
For Example: 3, 5, 7, 9, 11, 13, …
The deviation, or the number required to produce the subsequent value is identified as +2.
Now, apply such definitions to the peculiar problem:
A. 1, -3, 9, -27,… has -4, +12, -36, hence is not consistent. Thus, A cannot be correct.
B. -2, 4, -6, 8,… has +6, -10, +14, hence does not obtain a persistent consecutive pattern.
C. -8, -6, -4, -2… has +2, +2, +2, hence is consistent. Thus, C is correct.
D. 2, 4, 8, 16,… has +2, +2, +2, hence is consistent. Thus, D is correct.
THE SPEED OF A CAR IS 144 KM/HR WHAT US ITS SPEED IN M/S
Answer:
40 m/s
Step-by-step explanation:
144 X (5/18) = 8X5 = 40
What is one way a person can increase the wages he or she expects to earn?
A. By deciding not to get a high level of education
B. By choosing a job with a high market value
C. By reducing overall productivity in a year D. By advocating against minimum wage regulations
The correct way for a person can increase the wages he or she expects to earn is,
⇒ By choosing a job with a high market value.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
To find one way for a person can increase the wages he or she expects to earn.
Since, We know that;
A job with a high market value give more income than another things.
Thus, The correct way for a person can increase the wages he or she expects to earn is,
⇒ By choosing a job with a high market value.
Learn more about the mathematical expression visit:
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Pls help meeee thank you
Answer:
7/12
Step-by-step explanation:
add up all of the buttons
30+40+50=120
add up all of the blue and red buttons
30+40=70
then divide the added values
70/120
simplify
7/12
Answer:
7/12
Step-by-step explanation:
It will be seven 7 by 12
if 3x-4=2(y-2)
find x_y
Answer:
x = 2y/3
y = 3x/2
Answer:
Step-by-step explanation:
Find sin R.
a. sin R= 29/21
b. sin R= 21/20
c. sin R= 20/29
d. sin R= 21/29
Answer:
sin R = 20 / 29
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin R = opp / hyp
sin R = 20 / 29
The histogram below represents a data distribution with uniform class
widths. Which of the following is the median of the data distribution?
6
5
4
3
2
1
9 10
A. 4
B. 6
C. 5
c
D. 7
Answer:
C. 5
Step-by-step explanation:
The given data can be presented as follows;
[tex]\begin{array}{ccc}x&&y\\2&\leftrightarrow &1\\3&\leftrightarrow &4\\4&\leftrightarrow &6\\5&\leftrightarrow &7\\6&\leftrightarrow &6\\7&\leftrightarrow &3\\8&\leftrightarrow &2\\9&\leftrightarrow &1\\10&\leftrightarrow &1\end{array}[/tex]
We find the sum of the data points as follows;
n = 1 + 4 + 6 + 7 + 6 + 3 + 2 + 1 + 1 = 31
The median will be located in the (n + 1)/2 th data point
Therefore the median is the (31 + 1)/2 = 16th data point
The sum of the first three bars on the histogram = 11
The sum of the first four bars on the histogram = 18
Therefore, the 16th data point is located in the fourth bar which has x value of 5
The median is therefore, C. 5
math simplify (7a+5b-2c) + (5a+7b) + (2a-7c) + (2a-5b+3c) algebra
Answer:
[tex]-10a^2+25ab-15ac+12a+12b-2c[/tex]
Step-by-step explanation:
[tex](7a+5b-2c)+(5a+7b)+(2a-7c)+(2a-5b+3c)[/tex]
Distribute:
[tex]=7a+5b-2c+5a+7b+(2a)(2a)+(2a)(-5)+(2a)(3c)+(-7a)(2a)+(-7a)(-5b)+(-7a)(3c)[/tex]
[tex]=7a+5b-2c+5a+7b+4a^2-10ab+6ac-10a^2+35ab-21ac[/tex]
Combine all like terms:
[tex]=(4a^2-14a^2)+(-10ab+35ab)+(6ac-21ac)+(7a+5a)+(5b+7b)+(-2c)[/tex]
[tex]=-10a^2+25ab-15ac+12a+12b-2c[/tex]
