Given:
The function is:
[tex]f(x)=-(x+5)(x+1)[/tex]
To find:
The range of the function.
Solution:
We have,
[tex]f(x)=-(x+5)(x+1)[/tex]
It can be written as:
[tex]f(x)=-(x^2+x+5x+5)[/tex]
[tex]f(x)=-(x^2+6x+5)[/tex]
Add and subtract square of half of coefficient of x, i.e., [tex]\left(\dfrac{6}{2}\right)^2=9[/tex].
[tex]f(x)=-(x^2+6x+9-9+5)[/tex]
[tex]f(x)=-(x^2+2(x)(3)+3^2-4)[/tex]
[tex]f(x)=-(x^2+2(x)(3)+3^2)+4[/tex]
[tex]f(x)=-(x+3)^2+4[/tex]
On comparing this equation with [tex]f(x)=a(x-h)^2+k[/tex], we get
[tex]a=-1[/tex], it means the graph of the function is a downward parabola and the vertex is the point of maxima.
[tex]h=-3[/tex]
[tex]k=4[/tex]
The vertex of the function is (-3,4). So, the value of the function cannot be greater than 4.
Therefore, the range of the function is all real numbers less than or equal to 4.
Note: All options are incorrect.
Lucy's dog sleeps 14 hours a day. What percent of the day does her dog spend sleeping?
Answer:
58.3333
Step-by-step explanation:
make 14/24 into a fraction with a denominator of 100, and you get 58.333333 over 100
Lucy's dog sleeps for 58.3% of the whole day.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Lucy's dog sleeps 14 hours a day, we need to find that how much percent of the total day, her dog sleeps.
We know, there are 24 hours in a day,
Percentage = 14% of 24
= 24x14/100
= 58.3333333333 ≈ 58.3%
Hence, Lucy's dog sleeps for 58.3% of the whole day.
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SUBJECT: Graphs and Function
Identify the range of the function shown in the graph.
Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?
40
80
100
120
Answer:
The answer to this question is 80 times.
Answer:
80
Step-by-step explanation:
Instructions: Find the missing length
What is the approximate length of the line segment?
(1, -1)
(6,-8)
Answer:
8.6023
Step-by-step explanation:
length = √[(x2-x1)^2+(y2-y1)^2]
=√[(1-6)^2+(-1--8)^2] =√74 =8.6023
You are making pudding for five friends. The recipe calls for 1/4 cup of sugar per serving. How much sugar do you need?
Answer:
1 1/4 cups I think..
Step-by-step explanation:
1/4 times 4 is 1, plus another 1/4 for the 5th friend is 1 1/4 cups.
Answer:
[tex]\frac{5}{4}[/tex] or [tex]1\frac{1}{4}[/tex] cups
Step-by-step explanation:
This question asks how much total sugar will be needed for 5 servings of 1/4 cup. In other words, this is asking for 1/4 cup to be added together 5 times. However, repeated addition is just multiplication, so this can become a multiplication problem. To do this make both terms a fraction by putting 5 over 1. This looks like: [tex]\frac{5}{1} *\frac{1}{4}[/tex]. Then, simply multiply the numerators together and the denominators together. This equals [tex]\frac{5}{4}[/tex]. If needed this can be put into the mixed fraction of [tex]1\frac{1}{4}[/tex] cups.
I NEEDDDDD HELPPPP ITS URGENTTTT!!!!!!!
Answer:
r=7, Center:(4,8)
Step-by-step explanation:
( x - h )^2 + ( y - k )^2 = r^2 is the general formula for circle where radius is square root of r^2 and the center is (h,k).
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
A. {(6, 5)}
B. {(5, 6)}
C. {(13/5, 6/5)}
D. {(6/5, 13/5)}
Step-by-step explanation:
+ Both equations
You will get : 5x=13 ; x=13/5
and put x to the first equation
2*13/5-y=4
y=6/5
(13/5;6/5)
Answer is C
Someone can help me with this ? I don’t understand
Answer:
-3
Step-by-step explanation:
The derivative of f(x) = x3 – 12x + 5 is 3x2 – 12 . Find the coordinates of the turning points of f(x)
Answer:
(-2, 21) and (2, -11) let me know if anything didn't make sense
Step-by-step explanation:
Try and put the symbols in, so for x to the third power write x^3 just makes it all much easier.
The turning point is when a graph changes from increasing to decreasing, or the other way around. What this means is that its slope is changing from positive to negative, or the other way around.
The derivative allows you to find the slope at any point of a graph. If you are unfamiliar witht his concept let me know and I can go more into it.
Since the derrivative tells you the slope, if you find a spot where it equals 0 then you know before that point it was positive or negative, and then after that point it was the opposite. In other words it changes, so it's exactly what we are looking for. Also if a derrivative is ever non existant, like in the square root function the numbers under the square root cannot be negative, so any x value that makes them negative doesn't exist, this means you would want to check these point too because they can be turning points as well.
There are certain special cases where a derivative does not coss 0, and if that happens then the original function does not have a turning point. So keep that in mind.
The derivative is 3x^2 - 12. So we want to find when this equals 0. We also know it always exists so only need to worry about the 0s. Hopefully you are familiar with quadratics having two zeroes, if not let me know.
3x^2 - 12 = 0
3x^2 = 12
x^2 = 4
x = 2 and-2
So these are the turning points. You should double check though and choose an x value below -2, then between -2 and 2, then larger than 2 and make sure the signs swap.
These are the x values of the turning points. Solve f(x) at these points to find the y values. so f(-2) = (-2)^3 - 12(-2) + 5 = 21 and f(2) = -11 so now we know the turning points are (-2, 21) and (2, -11)
The coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
What is differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations. The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
The turning point is when a graph changes from increasing to decreasing, or the other way around that means, its slope is changing from positive to negative.
Given that the derivative of f(x) = x³ – 12x + 5 is 3x² - 12.
Since the derrivative tells the slope, if you find a spot where it equals 0 then before that point it was positive or negative, and then after that point it was the opposite.
The derivative is 3x² - 12.
3x² - 12 = 0
3x² = 12
x² = 4
Thus, x = 2 and-2
So, these are the turning points.
Now Solve f(x) at these points to find the y values.
so f(x) = x³ – 12x + 5
f(-2) = (-2)³ - 12(-2) + 5 = 21
f(2) = -11
Hence, the coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
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Theodore recently hired a contractor to do some necessary work. On the final bill, Theodore was charged a total of $715. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $50, how many hours of labor was needed to complete the job?
Answer:
Hours of labor needed = 8 hour
Step-by-step explanation:
Given:
Amount total charged = $715
Listed amount = $315
Hourly rate for labor = $50
Find:
Hours of labor needed
Computation:
Total amount of labour = Amount total charged - Listed amount
Total amount of labour = 715 - 315
Total amount of labour = $400
Hours of labor needed = Total amount of labour / Hourly rate for labor
Hours of labor needed = 400 / 50
Hours of labor needed = 8 hour
x= 3/4 , y= - 2/5 then x+ y =
Step-by-step explanation:
Given
x = 3/4
y = -2/5
Now
X + y = 3/4 - 2/5
[tex] \frac{3 \times 5 - 2 \times 4}{20} [/tex]
[tex] = \frac{15 - 8}{20} [/tex]
[tex] = \frac{7}{20} [/tex]
Answer:
7/20
Step-by-step explanation:
x=3/4
y= -2/5
x+y=?
to get the sum, plug in x=3/4 into the x and y= -2/5 into the y
1. x + y = ?
2. 3/4 + (- 2/5) = ?
3. 3/4 - 2/5 =?
4. find the lcm of 4 and 5 to get the common denominator (in this case, the lcm of 4 and 5 is 20)
5. multiply 3/4 by 5 (numerator and denominator) and 2/5 by 4 (numerator and denominator)
6. 15/20 - 8/20 = 7/20
the answer is 7/20
help please dilations geometry
Answer:
A' (8,16)
B' (8,-4)
C' (-16,4)
Answered by GAUTHMATH
use the ratio of a 45-45-90 triangle to solve for the variables
Answer:
1:1:√ 2
Step-by-step explanation:
Answer:
u = 14
v = 14
Step-by-step explanation:
since both angles around the 90 degree angle are the same, also the sides need to be of equal length. v = u
so, we can use Pythagoras
(14×sqrt(2))² = u² + u² = 2u²
196×2 = 2u²
196 = u²
u = 14 = v
29 cm
21 cm
What is the length of the missing leg?
a
centimeters
Step-by-step explanation:
Use phytogoras theorem
[tex] \sqrt{ {29}^{2} } - \sqrt{ {21}^{2} } \\ \\ \\ square \: root \: the \: whole \: eq \\ \\ \\ = 20cm[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
please help again with translations
Answer:
A -1,7
B 1,5
C -2,4
Step-by-step explanation:
What's the answer to this?
Answer:
2, 0, 1
Step-by-step explanation:
In quadratic equations if b^2-4ac is greater than 0, 2 solutions. if equal, 1, if less, 0.
Write the quadratic equation whose roots are −2 and −5, and whose leading coefficient is 4.
URGENT PLS
Answer:
Step-by-step explanation:
quadratic equation is 4(x+2)(x+5)=0
4(x²+5x+2x+10)=0
4x²+28x+40=0
Answer:
f(x) = 4(x+2)(x+5)
Step-by-step explanation:
The quadratic function is
f(x) = a(x-b1)(x-b2) where a is a coefficient and b1 and b2 are the zeros
f(x) = a(x --2)(x--5)
f(x) = a(x+2)(x+5)
The leading coefficient is a and we know a =4
f(x) = 4(x+2)(x+5)
Given that sin 0 = 21/29, what is the value of cose, for 0° <0<90°? please help
Answer:
3rd option
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ( subtract sin²x from both sides )
cos²x = 1 - sin²x ( take the square root of both sides )
cosx = ± [tex]\sqrt{1-sin^2x}[/tex]
Given
sinθ = [tex]\frac{21}{29}[/tex] and 0 < θ < 90 , then
cosθ
= [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex]
= [tex]\sqrt{1-\frac{441}{841} }[/tex]
= [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{\sqrt{400} }{841}[/tex] = [tex]\frac{20}{29}[/tex]
In the following diagram, BAC = 46 degrees, and AD is the bisector of BAC. Find BDA
Answer:
67 degrees
Step-by-step explanation:
We have a right triangle with the following known values:
B = 90
A = 23 (46/2=23 since AD is the angle bisector)
D = ?
180 = 90 + 23 + D and we solve
67 = D
find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Apply the leg rule to find the value of x.
Leg rule is given as:
Hypotenuse/leg 1 = leg 1/part 1
Hypotenuse = 400
Leg 1 = x
Part 1 = 144
Plug in the known values into the formula
400/x = x/144
Cross multiply
x*x = 144*400
x² = 57,600
Take the square root of both sides
√x² = √57,600
x = 240
What is the negative square root of 0.25?
Answer:
-0.5
Step-by-step explanation:
How do I solve this: h + 6/5 = 2
what represents the distance traveled and time spent traveling
Answer:
b) y
Step-by-step explanation:
joannes speed = 250/2.5 =100km/h
francois speed = 100-10 = 90km/h
after 5h, francois would have travelled 450
O 131 If cos 23°=P, express without the use of a calculator the following in terms of p.
Cos203°
Answer:
cos203° = - p
Step-by-step explanation:
Using the addition formula for cosine
cos(a + b) = cosacosb - sinasinb
cos203°
= cos(180 + 23)
= cos180°cos23° - sin180°sin23°
= cos180°. p - 0
= - 1 . p
= - p
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
The complete table of the function is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
The equation missing from the question is:
[tex]y = 72 - 12x[/tex]
To complete the table, we simply calculate the y value for each x value;
When [tex]x = 0[/tex], [tex]y = 72 - 12 * 0 = 72[/tex]
When [tex]x = 1[/tex], [tex]y = 72 - 12 * 1 = 60[/tex]
When [tex]x = 2[/tex], [tex]y = 72 - 12 * 2 = 48[/tex]
When [tex]x = 3[/tex], [tex]y = 72 - 12 * 3 = 36[/tex]
When [tex]x = 4[/tex], [tex]y = 72 - 12 * 4 = 24[/tex]
When [tex]x = 5[/tex], [tex]y = 72 - 12 * 5 = 12[/tex]
When [tex]x = 6[/tex], [tex]y = 72 - 12 * 6 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
To create a graph of f(x), we simply type [tex]y = 72 - 12x[/tex] on a drawing tool and the graph will be generated.
See attachment for graph
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Answer:
Step-by-step explanation:
A. Explain why the point (100,2) is on the graph.
B. What is the x-intercept of the graph? Explain how you know.
49
C. When will the graph meet the line y = 5? Explain how you know.
Answer:
the log function is the "inverse" function of an exponential function
by definition [tex]log_{a} b = c[/tex] then [tex]a^{c} = b[/tex]
in this problem you have [tex]log_{10} 100[/tex]
thus what x solves this ? [tex]10^{x} = 100[/tex] the answer is [tex]10^{2}[/tex]
thus (100,2)
B) the x intercept is when y = 0
[tex]10^{0} = 1[/tex]
x intercept at (1,0)
C) at 100, the curve will hit y = 5000
Step-by-step explanation:
The diagonals of a rhombus are perpendicular
Answer:
true
Step-by-step explanation:
PLZ PLZ PLZ PLZ hurry
Answer:
4/3
Step-by-step explanation:
To find the slope, we can use the slope formula
m= (y2-y1)/(x2-x1)
= ( -1 - -13)/( 3 - -6)
= (-1+13)/( 3+6)
= 12/9
= 4/3
Answer:
G. [tex]\displaystyle \frac{4}{3}[/tex]
Step-by-step explanation:
Hi there!
[tex]slope=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-6,-13) and (3,-1)
[tex]slope=\displaystyle \frac{-1-(-13)}{3-(-6)}\\\\slope=\displaystyle \frac{-1+13}{3+6}\\\\slope=\displaystyle \frac{12}{9}\\\\slope=\displaystyle \frac{4}{3}[/tex]
Therefore, the slope of the line is [tex]\displaystyle \frac{4}{3}[/tex].
I hope this helps!
It takes 25 minutes to fry a burger at Jill street, how long will it take to fry 13 burgers
Answer:
325 minutes
Step-by-step explanation:
We can use a ratio to solve
25 minutes x minutes
------------------ = ---------------
1 burger 13 burgers
Using cross products
25*13 = 1x
325 = x
325 minutes
Answer:
325 minutes or 5 hours and 25 minutes
Step-by-step explanation:
If it takes 25 minutes to fry a single burger, assuming only one burger can be made at a time, you must multiply the time per burger by how many burgers are made. So. 25(13) = 325 minutes or 5 hours and 25 minutes.
