Given f(x) = x squared - 1 and g(x) = x+ 2, what is the value of h(-2) where h(x) = f(g(x))?
Answer: [tex]h(-2)=-1[/tex]
Step-by-step explanation:
We need to find [tex]f(g(x))[/tex]. Substitute the function [tex]g(x)[/tex] into the function [tex]f(x)[/tex]:
[tex]f(g(x)) = (x+ 2)^2- 1[/tex]
Now, we know that the function [tex]h(x)[/tex] is [tex]h(x)=f(g(x))[/tex], then:
[tex]h(x)=(x+ 2)^2- 1[/tex]
In order to find the value of [tex]h(-2)[/tex], we must substitute [tex]x=-2[/tex] into the function [tex]h(x)=(x+ 2)^2- 1[/tex].
Therefore, the value of [tex]h(-2)[/tex] is:
[tex]h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1[/tex]
The diagram above shows the plan of a drive way to a house.
The driveway is made from concrete. The perimeter of the driveway is 64 m. The concrete is 15 m thick. Now calculate the volume of concrete used for the driveway. Give your answer in cubic meters..
A challenging question.. Someone please help me..
First you want to find the area of the driveway. The easiest way to do this is to separate the rectangles. The area of the small rectangle will be 6 because 2x3=6, the area of the large rectangle will be 216 because 18x12=216. Then you will add the two areas back together, 216+6=222. Using the formula volume=baseXheight you will do 222x15 to get 3,330 cubic meters (because height and depth work the same)
The volume of the driveway is calculated by multiplying the area of the driveway by the thickness. The volume will be in cubic meters if all measurements are in meters. For accurate calculation, more specific dimensions are needed beyond just perimeter and thickness.
Explanation:
To help calculate the volume of the concrete used in the driveway, you'll need the perimeter and the thickness of the driveway. The perimeter being stated as 64m doesn't give us enough detail because to calculate the volume of a prism (which the driveway essentially is), we need the area of the base (in this case the area of the driveway's surface), not just the perimeter.
However, if we assume that the driveway is of a standard shape like a rectangle and you also have the structural width, you could calculate the area and then the volume. Here's a generic explanation:
1. If you have a rectangular drive, area would be calculated as length * width.
2. You then calculate volume by multiplying the area by the thickness of the driveway. That is, Volume = area * thickness.
Note: This will give you the volume in cubic meters provided all measurements were in meters.
For us to compute this for your driveway, we'd need more dimensions in addition to the 15m thickness and 64m perimeter.
Learn more about Volume Calculation here:https://brainly.com/question/34259963
#SPJ11
You put the names of all the students in your class in a paper bag. There are 19 boys and 12 girls. If you draw a name at random, what is P(boys name)?
Your question is asking what the probability of picking up a boys name out of the paper bag.
Answer: [tex]\frac{19}{31}[/tex]In order to solve this problem, we're going to have to find the total amount of names in the paper bag and the amount of boy names there are.
When you read the question, you would find some key information in it.
Key Information:
19 boys
12 girls
With the information above, we can find the probability of picking out a boy name out of the paper bag.
To find the porbability, we're going to need to get the total amount of names in the paper bag. We would just add 19 + 12.
[tex]19+12=31[/tex]
Now, we know that there are 31 total names in the bag.
But, we are trying to find the chances of pulling out a boys name. There are 19 boy names in the bag.
We would use the number 19 as our numerator and 31 as our denominator.
Your fraction should look like this:
[tex]\frac{19}{31}[/tex]
The fraction above would represent the probability to pick out a boy name.
Since 19 is a prime number, we wouldn't simplify the fraction.
Therefore, the chances of picking out a boy name from the paper bag is [tex]\frac{19}{31}[/tex]
[tex]\frac{19}{31}[/tex] should be your FINAL answer.
I hope this helps!Best regards, MasterInvestorI need some help in this question
bought a new tent to take on the next Cub Scouts camping trip. The center pole of the to tent is 16 ft. tall and the sides of the tent are 20 ft. on the slant. How wide is the base of the tent?
Answer:
24 ft
Step-by-step explanation:
The is a center pole and two side poles and the bottom. This triangle can be broken into 2 smaller triangles. When finding the base this requires the quadratic formula. a^2+b^2= C^2
We are given a and c. A is 16 and c is 20. The equation can be changed to c^2-a^2=b^2.
20^2-16^2=b^2
400-256=b^2
144=b^2
12=b
But remember there are two triangles so the base is 2b which is 24
Which of the following is not equal to sin(-230°)?
sin(130°)
-sin(-50°)
sin(50°)
sin(-50°)
Answer:
sin(-50°) is not equal to sin(-230°)
Step-by-step explanation:
You will be required to use a scientific calculator for this.
Step 1 : Find out the value of sin(-230°)
sin(-230°) = 0.766
Step 2 : Find out all the other values and see if they are 0.766 or not.
sin(130°) = 0.766 (It is equal to sin(-230°))
-sin(-50°) = 0.766 (It is equal to sin(-230°))
sin(50°) = 0.766 (It is equal to sin(-230°))
sin(-50°) = -0.766 (It is not equal to sin(-230°))
!!
Answer:
sin(-230°) =sin(50°)
Step-by-step explanation:
1) sin(-a) = -sina
note : 2) sina = sinb : a=b or a+b =180°
in this exercice :
sin(-230°) = - sin(230°) = - sin(-50°)=- (-sin(50°)) =sin(50°) because :
sin(230°) = sin(-50°) because ; 230°+(-50°) =180°
sin(230°) = -sin(50°)
I need help with B, C, and D
B)
as you recall yesterday, the "far arc near arc" formula, well, notice, the angle at XDY intercepts the circle at XY, with a "near arc" of 100°, and a "far arc" of 360° - 100° = 260°.
so using the far arc near arc formula
[tex]\bf \measuredangle D=\cfrac{260-100}{2}\implies \measuredangle D=\cfrac{160}{2}\implies \measuredangle D = 80[/tex]
the twin angles at A and C will take the slack from all interior angles of 180° - 80° = 100°, so then ∡A = ∡C = 50°.
In order for the data in the table to represent a linear function
with a rate of change of -8, what must be the value of m?
Om = 2
Om = 3
Om = 19
m = 35
Answer:
m = 19
Step-by-step explanation:
With a rate of change of -8
27 - 8 = 19
16 - 8 = 11
so m = 19
Answer:
Third option: [tex]m=19[/tex]
Step-by-step explanation:
The rate of change is the slope of the line.
The formula for calculate the slope is:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
You know that:
[tex]slope=-8\\y_2=m\\y_1=27\\x_2=11\\x_1=10[/tex]
Then, you can substitute them into the formula:
[tex]-8=\frac{m-27}{11-10}[/tex]
Finally, you must solve for "m":
[tex]-8=\frac{m-27}{11-10}\\\\-8(1)=m-27\\\\-8+27\\\\m=19[/tex]
Use the graph of the function y=4^x to answer the following questions
The domain of a function is all the x-values which it passes through. The function is a continuous exponential function, and therefore, it will contain every x value. The answer is:
The domain of the function is negative infinity to positive infinity.
Hope this helps!!
The domain of a function is the set of input values, the function can take.
The domain of the function is negative infinity to positive infinity,
The function is given as:
[tex]\mathbf{y = 4^x}[/tex]
The function is an exponential function, and there are no restriction as to the input values of an exponential function.
i.e: [tex]\mathbf{(-\infty, \infty)}[/tex]
Hence, the domain of the function is negative infinity to positive infinity,
Read more about domain at:
https://brainly.com/question/17440903
6+18p-5=8p+13-2 slove for p
Answer:
p = 1
Step-by-step explanation:
6+18p-5=8p+13-2 Collect the like terms on the left and right side
6 - 5 + 18p = 8p + 13 - 2
1 + 18p = 8p + 11 Subtract 1 from both sides.
18p = 8p + 11 - 1 Combine
18p = 8p + 10 Subtract 8p from both sides
18p - 8p = 10 Combine the left
10p = 10 Divide by 10
10p/10 = 10/10
p = 1
Patterns and lines for (0,0) (4,-12)
what is the meaning of the slope of mr taylor's line? pls help! a lot of points
Answer:
The slope is the percentage of test score per number of days absent
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
y -----> is the percentage of test score
x ----> is the number of days absent
so
That means -----> The slope is the percentage of test score per number of days absent
In this problem the slope is negative
so
If the percentage test score increases----> the number of days decreases
If the percentage test score decreases----> the number of days increases
The following system has a solution of x=-5, y=9, z=11.
4x+y+z=12
-4x-y-z=-10
5y-z=9
Please select the best answer from the choices provided
T
F
Answer:
Step-by-step explanation:
false
The sum of one-third of a number and three-fourths of the number exceeds that number by one.
Which equation could be used to find the number?
1/3n = 3/4n + 1
1/3n + n 3/4= n - 1
1/3n + n 3/4= n + 1
The answer would be...
1/3n + 3/4n = n + 1
^^^That would be the last option
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
The correct answer is last option
1/3n + n 3/4= n + 1
Step-by-step explanation:
It is given that,the sum of one-third of a number and three-fourths of the number exceeds that number by one
To find the correct option
Let 'n' be the number, one- third of the number = 1/3(n)
three - fourths of the number = 3/(4n)
Therefore the equation becomes,
1/(n) + 3/4(n) = n + 1
Therefore the correct answer is last option
F= 8/5 (c) + 40 when c=5
Answer:
F = 48
Step-by-step explanation:
F= 8/5 (c) + 40
Let c=5
F = 8/5 * 5 +40
= 8 + 40
= 48
The angles below are supplementary. What is the value of x?
6x + 48)
Answer:
8 is your answer.
Step-by-step explanation:
If i think that i'm doing this right.
6x + 48
6 6 divide by 6 on both sides.
x = 8
Hope my answer has helped you!
Name
12. Rhea used a Venn diagram to sort shapes. What label
could she use for circle A?
Polygons with all
Sides of Equal Length
Answer:
poloygons with right angles
Step-by-step explanation:
The Venn diagram A have polygons having right angle.
What is Venn Diagram?
A Venn diagram is a diagram that employs circles to depict the relationships between items or finite groupings of things. Circles that overlap share characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for visualising the similarities and differences between two concepts.
We have Venn diagram having geometrical shapes
In Venn diagram A the geometrical shapes are
Right angled TriangleRectanglePentagonThus, the Venn diagram A have polygons having right angle.
Learn more about Venn diagram here:
https://brainly.com/question/29301560
#SPJ3
A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?
Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds
Answer:
Option 2 - Approximately 24–36 pounds
Step-by-step explanation:
Given : A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed.
To find : What range of weights would 99.7% of the dogs have?
Solution :
The range of 99.7% will lie between the mean ± 3 standard deviations.
We have given,
Mean weight of Eskimo dogs is [tex]\mu=30[/tex]
Standard deviation of Eskimo dogs is [tex]\sigma=2[/tex]
The range of weights would 99.7% of the dogs have,
[tex]R=\mu\pm3\sigma[/tex]
[tex]R=30\pm3(2)[/tex]
[tex]R=30\pm6[/tex]
[tex]R=30+6,30-6[/tex]
[tex]R=36,24[/tex]
Therefore, The range is approximately, 24 - 36 pounds.
So, Option 2 is correct.
Answer:
B: Approximately 24–36 pounds
Step-by-step explanation:
Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1. Btw the variable I used was "f".
Answer:
$[tex]4f[/tex]
Step-by-step explanation:
Let's assume [tex]f[/tex] represents the number of pounds of fruit.
We need to multiply the number of pounds of fruit by the cost per pound.
This is $[tex]f * 4[/tex], or in a simpler form, $[tex]4f[/tex].
In this context, the variable 'f' represents the number of pounds of fruit. In the expression '4f', it means that for every pound of fruit, which costs $4, you multiply the number of pounds by that price to get the total cost.
Explanation:The problem is asking us to provide an equation for the total cost of fruit based on the cost per pound, which is $4. As you identified the variable 'f' in the previous question, let's use that to stand for the number of pounds of fruit.
The written expression for the total cost would then be 4f. This expression says that the total cost is four times the number of fruit pounds ('f') purchased
Learn more about Algebraic Expressions here:https://brainly.com/question/953809
#SPJ3
Answer this question thanks :)
First multiply 2 to both sides to isolate h. Since 2 is being divided by h, multiplication (the opposite of division) will cancel 2 out (in this case it will make 2 one) from the right side and bring it over to the left side.
4 < [tex]\frac{h}{2}[/tex]
4 * 2 < [tex]\frac{h}{2}[/tex] * 2
8 < h
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
8 < h OR h > 8
aka 8 is less then h OR h is greater then 8
This means that the graph will have an empty circle and the arrow will go to the right of 8. Look at image below
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
h>8
Step-by-step explanation:
4<h/2
multiply both sides by 2
8<h
Four different sets of objects contain 4, 5, 6, and 8 objects, respectively. How
many unique combinations can be formed by picking one object from each
set?
Answer:
960
Step-by-step explanation:
We can find the number of unique combinations by
Multiplying 4*5*6*8
960
There are 960 possible choices by picking 1 from each group
How many cubes with side lengths of 1/4 does it take to fill the prism?
Answer:
[tex]\large\boxed{224\ cubes}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}\\\\\text{Calculate the volume of a prism:}\\\\V_{p}=(2)\left(\dfrac{7}{4}\right)(1)=3.5\ cm^3\\\\\text{Calculate the volume of a cube:}\\\\V_c=\left(\dfrac{1}{4}\right)^3=\dfrac{1}{64}\ cm^3\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{3.5}{\frac{1}{64}}=3.5\cdot64=224[/tex]
[tex]\bold{METHOD\ 2}\\\\2cm:\dfrac{1}{4}cm=2\cdot4=8\\\\\dfrac{7}{4}cm:\dfrac{1}{4}cm=\dfrac{7}{4}\cdot\dfrac{4}{1}=7\\\\1cm:\dfrac{1}{4}cm=1\cdot4=4\\\\8\cdot7\cdot4=224\ (cubes)[/tex]
What is the domain of the function y=^3squareroot of x
PLEASE HELP
Answer:
[0,∞)
Step-by-step explanation:
We can easily solve this question by plotting the equation with the use of a plotting tool or any graphing calculator.
The equation is
y=3^(√x)
Please see attached image
Since the x is inside a square root, we know that x must be greater or equal to zero.
By looking at the graph, we can check that the domain of the function is
[0,∞)
Does the image represent A function or a relation?
6
4
2
what about this picture/function/expression?
well, we have 3 points over the y-coordinate, but but but, every point has the same x-coordinate, whatever that might be, and so they form a vertical line.
does this straight vertical line pass the vertical line test? nope.
other way to see it is, a function has no x-repeats, the x-coordinate for every point must not be repeated, in this case it is the same for all, so it repeats thrice, so is not a function, just a relation.
What is the degree of x^5 - 4x + 2?
A. 3
B. 4
C. 6
D. 5
Answer:
D. 5
Step-by-step explanation:
x^5 - 4x + 2
The degree of the polynomial is the degree of the highest term
x^5: 5th
4x: 1st
2: 0
So the degree of the polynomial is degree 5
if f(x)=3x+10x and g(x)=4x-2, find (f-g)(x)
Answer:
(f-g)(x) = 9x + 2
Step-by-step explanation:
(f-g)(x) = (3x+10x) - (4x-2)
= 3x + 10x - 4x + 2
= 9x + 2
Step-by-step explanation: would be the other answer for APEX as of 9/13/19
The perimeter of rectangular photo is 72cm. The length is twice the width what are and width of the photo?
(Hint: The formula for perimeter is 2w+ 21= P where w is the width I is the length and P is the perimeter.)
Answer:
w =12 cm
l = 24 cm
Step-by-step explanation:
P = 2w + 2l
We know the perimeter is 72 and the length is twice the width (l = 2w)
Substituting P = 72 and l = 2w
72 = 2w + 2(2w)
72 = 2w+ 4w
Combine like terms
72 = 6w
Divide each side by 6
72/6 =6w/6
12 = w
Now we need to find l
l = 2w
l =2*12
l = 24
Each day for several days, the change in the price of a share of stock was -$3. The total change in price during those days was -$36. Over how many days is the price decline?
12
Step-by-step explanation:
-36/3 is -12 which means 12 days of decline thank u come again
Final answer:
To determine the number of days over which the price of a stock declined by $36 at a rate of $3 per day, divide the total change by the daily change, resulting in 12 days.
Explanation:
The problem described is a typical arithmetic problem where we want to find out over how many days a stock has declined in price if it dropped by a certain amount each day. To solve this, let's use linear equation reasoning. The total change in the price of the stock is -$36, and the daily change is -$3. We can express the total change (T) as the product of the daily change (d = -$3) and the number of days (n), so we have T = dn.
To find the number of days, we rewrite this equation as n = T/d, and substitute the given values to get n = -$36/-$3. Thus, n = 12. Therefore, the price of the stock declined over 12 days.
True or False ? The distance formula is equivalent to the Pythagorean theorem if you are
trying to find the distance between a point in the plane and the origin.
I believe that it is true due to it, the distance formula uses x and y coordinates. So, they're the same thing in two different types, or so..
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Which graph shows the solution to the inequality -3x-7 <20?
Answer:
Graphs..?
Step-by-step explanation:
For this case we must indicate the graph of the following inequality:
[tex]-3x-7 <20[/tex]
We add 7 to both sides of the inequality:
[tex]-3x <20 + 7\\-3x <27[/tex]
We divide between -3 to both of the inequality taking into account that the meaning changes:
[tex]x> \frac {27} {- 3}\\x> -9[/tex]
Answer:
[tex]x> -9[/tex]
See attached image