Answer:
h(f(x)) = 2x - 11Step-by-step explanation:
f(x) = x - 7
h(x) = 2x + 3
To find h(f(x)) substitute f(x) into h(x) that's replace every x in h(x) by f(x)
That's
h(f(x)) = 2(x - 7) + 3
h(f(x)) = 2x - 14 + 3
We have the final answer as
h(f(x)) = 2x - 11Hope this helps you
can u help me ASAP. i need to know how to do it step by step
Answer:
19
Step-by-step explanation:
[tex]f(x) =4x^3-8x^2+ax+b[/tex] has a factor [tex]2x-1[/tex] and
when divided by [tex]x+2[/tex], remainder is 20.
To find:Remainder when divided by (x-1) ?
Solution:
[tex]2x-1[/tex] is a factor
[tex]2x - 1 = 0 \Rightarrow x = \frac{1}{2}[/tex] when we put this value of x to the function, it will become 0.
i.e.
[tex]\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)[/tex]
Remainder is 20 when f(x) is divided by [tex]x+2[/tex]
i.e.
[tex]f(-2) =20[/tex]
[tex]\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)[/tex]
Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):
[tex]5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}[/tex]
By equation (1):
[tex]a+2(18) = 3\\\Rightarrow a = -33[/tex]
So, the equation becomes:
[tex]f(x) =4x^3-8x^2-33x+18[/tex]
[tex]\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}[/tex]
So, when divided by (x-1), remainder will be 19.
I need domain and range
Answer:
Domain: all real numbers/ (-inf,inf)/ -inf<x<inf
Range: all real numbers greater than -4/ [-4,inf)/ -4≤y<inf
Step-by-step explanation:
the graphs/equations of ALL quadratics (parabolas) have a domain of all real numbers
The vertex of the parabola is at y=-4 so the range cannot be any less than that, and then both ends point up, so they will continue on for infinity.
Hope i could help!
HELP ME!!!!And I mark as BRAINLIEST✨✨make sure show proper working
Answer:
54 km/h
Step-by-step explanation:
From H to G:
Let the distance be x km.
Average speed = distance/time
60 = x/ 3
60*3 = x
x = 180 km
From G to F:
Let the distance be y km.
Average speed = distance/time
45 = y/2
45*2 = y
y = 90 km
From H to F:
Total distance = x + y = 180 + 90 = 270 km
Total time = 3 + 2 = 5 hours
Average speed from H to F
= Total distance/ total time
= 270/ 5
= 54 km/h
Point T is on line segment SU. Given ST=13 and TU=5, determine the length SU.
Answer:
[tex]SU=18[/tex]
Step-by-step explanation:
The segments ST and TU make up the line segment SU. Add the values to find SU:
[tex]ST+TU=SU\\\\13+5=18[/tex]
The length of SU is 18.
The length of SU is 18 units.
We have a point T is between S and U.
We have to determine the length SU.
What is Line Segment?A line segment is a part of a line having two end - points.A line segment has a definite length.According to the question -
ST = 13 units
TU = 5 units
Now -
SU = ST + TU = 13 + 5 = 18 units
Hence, the length of SU is 18 units.
To solve more questions on Line Segments, visit the link below-
brainly.com/question/19569734
#SPJ2
in this figure ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90cm^2. Find PT:TR please help me
Answer: The required ratio is PT:TR = 1:2.
Step-by-step explanation:
Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².
To find : PT:TR
.i.e. Ratio of PT to TR.
Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]
[tex]=\dfrac{4\ cm}{8\ cm}[/tex]
Divide numerator and denominator by 4 , we get
[tex]\dfrac{1}{2}[/tex]
Therefore, the required ratio is PT:TR = 1:2.
A zoo train ride costs $4 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 27, and the total money collected was $60. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers? 1) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 2) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 3) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60 4) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60
Answer:
11 adults and 16 children
Step-by-step explanation:
a + c = 27 and 4a + c = 60
3a = 60 - 27 = 33
a= 11
so c = 16
I need some help plsssssssssssss
Answer:
See below.
Step-by-step explanation:
p: Atlanta is the capital of Georgia.
q: There are 4 feet in a yard.
p is true; q is false
11. p V q:
Atlanta is the capital of Georgia, or there are 4 feet in a yard.
Truth value: true since one of the statements is true.
12. p ▲ q:
Atlanta is the capital of Georgia, and there are 4 feet in a yard.
Truth value: false since not both statements are true.
13. p ▲ ~q:
Atlanta is the capital of Georgia, and there are not 4 feet in a yard.
Truth value: true since both of the statements are true.
11. ~p V q:
Atlanta is not the capital of Georgia, or there are 4 feet in a yard.
Truth value: false since both statements are false.
Answer:
Step-by-step explanation:
Help me on Domain and Range
Answer:
Domain: 0 ≤ x < 9
Range: 0 < y ≤ 3
Step-by-step explanation:
The domain is the set of all values used for x-coordinates of all points on the curve.
The range is the set of all values used for y-coordinates of all points on the curve.
Look at the graph. The leftmost point is (0, 3). That point is included in the graph since there is no open circle there.
So far we know this:
Domain goes from 0 to ...
Range goes from 3 to ...
Now we look at the rightmost point. It is (9, 0), but there is an open circle on it, so that point itself is not included in the domain or range.
Now we know this:
Domain goes from 0 to just less than 9.
Range goes from 3 to to just more than 0.
Domain: 0 ≤ x < 9
Range: 0 < y ≤ 3
Give the values of a, b, and c needed to write the equation's general form.
1/4x^2+5=0
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{4} x^2+5=0[/tex]
For this equation: [tex]a=0.25, b=0, c=5[/tex]
[tex]0.25x^2 + 0x + 5 = 0[/tex]
Step 1: Use quadratic formula with [tex]a=0.25, b=0, c=5.[/tex]
[tex]x = \frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex]
[tex]x = \frac{-(0) ± \sqrt{(0)^2 -4 (0.25) (5) } }{2(0.25)}[/tex]
[tex]x = \frac{0 ± \sqrt{-5} }{0.5}[/tex]
Answer : No Real Solutions.
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
A square has a perimeter of 48 in. Find the perimeter of a triangle with each side 4 inches longer than the side of the square.
Answer:
48 in.
Step-by-step explanation:
square
P = 4s
4s = 48 in.
s = 12 in.
triangle
s = 12 in. + 4 in.
s = 16 in.
P = 3s = 3(16 in.)
P = 48 in.
Questions attached below (❁´◡`❁)
Problem 2
Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]
Also, he forgot about the plus/minus.
This is what his steps should look like
[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]
There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation
Let's try out x = 7
x^2 - 6x - 7 = 0
7^2 - 6(7) - 7 = 0
49 - 42 - 7 = 0
0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1
====================================================
Problem 3
We will have
a = 1, b = -4, c = 3
plugged into the quadratic formula below to get...
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]
The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.
how many are 2 raised to 2 ???
Answer:
[tex]\huge \boxed{4}[/tex]
Step-by-step explanation:
2 raised to 2 is also the base 2 with an exponent of 2.
[tex]2^2[/tex]
2 is squared or multiplied by itself.
[tex]2^2 =2 \times 2 = 4[/tex]
90 to the nearest tenth
Answer:
90
Step-by-step explanation:
Hey there!
Well 90.000 to the nearest tenth is just 90 because there is no decimal places to round.
Hope this helps :)
Answer:
90
Step-by-step explanation:
90 has 0 ones so 90 is just 90, but rounded...
Whats the mean of the box plot 50 60 70 80 90 100
Answer:
75
Step-by-step explanation:
Mean = sum of all numbers / how many of numbers
=> 50 + 60 + 70 + 80 + 90 + 100 / 6
=> 450 / 6
=> 75
So, the mean of this data is 75.
the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear is
Answer:
2/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
Since we are to find the probability that 2 randomly selected points from Q,R,S,T and W are non-collinear
Non collinear points are points that doesn't lie on the same straight line. From the diagram given, the two point that are non colliear are (QR, QS, QT and QW making 4 2random non collinear points. Hence out expected number of outcome is 4.
For the total possible outcome, we are to find the number of ways we can randomly select two points from the 5 points given and this can be done using the combination rule.
This can therefore be done in 5C2 number of ways.
5C2 = 5!/(5-2)!2!
5C2 = 5!/3!2!
5C2 = 5*4*3*2*1/3*2*2
5C2 = 5*2
5C2 = 10 different ways
Hence the total possible outcome is 10
Therefore, the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear will be 4/10 = 2/5
Make the biggest possible number using the digits below only once 3 , 1 , 3 answer
Answer:
331
Step-by-step explanation:
A number with 3 digits: using only
3, 1, 3
then:
3>1
the biggest possible number is:
331
Answer:
331
Step-by-step explanation:
Possible Combinations:
133
313
331
Out of these combinations, using process of elimination, we can determine that 331 is the greatest value out of the three numbers provided.
he greatest common factor of each term in the expression 60 a b minus 72 b is 12b. Which choice shows the expression written as a product?
Answer:
Hey there!
60ab-72b
12b(5a-6)
The GCF is 12b.
Let me know if this helps :)
Answer:
b
Step-by-step explanation:
Nan left her house at 1 p.m. driving at a constant speed of 40 miles perhour. If she continues at that same speed for the entire trip, she will reach
her destination at 4:45 p.m. If Nan were to drive 10 miles per hour faster,
how much quicker would she arrive?
Answer:
45 minutes faster
Step-by-step explanation:
Distance:
40 x 3.75 = 150
If travel 50 miles/h:
150/50 = 3
3.75 - 3 = 0.75 of hour
45 minutes
Hope that helped!!! k
what is the perimeter of the rhombus ?
Answer:
20 units
Step-by-step explanation:
To find the hypotenuse length of one of the sides of this rhombus we have to use the pythagoram theorem.
if you make the point (1,0) the origin, we can see that it forms a triangle, with a base of 3, and a height of 4, next to the BE line.
a^2+b^2=c^2
9+16=c^2
25=c^2
c=5
if each diagnol length is 5 units long, the perimeter is
20 units.
Answer:
20 units.
Step-by-step explanation:
Formula for the perimeter of a rhombus = 4a.
Meaning all sides multiplied by 4
The point (1,0) is made A.
From D to F is 8 units, and from E to G is 6 units. Half of 6 is 3, and half of 8 is 4.
Imagine a right-angled triangle on one side of the rhombus(eg. ∆GAD), meaning that you'll have to find the hypotenuse.
*Use Pythagoras Theorem*
x² = 3² + 4²
x² = 9 + 16
x = √25
x = 5
The perimeter of the rhombus if one side is 5 units:
5 units × 4 sides = 20 units.
This rectangular patio is tiled using 50 cm by 50 cm square tiles. How many tiles are used?
Answer:
60 tiles are used
Step-by-step explanation:
1m equals 100 cm.
5m equals 500
3m equals 300
the whole thing is 500 by 300 which when you multiply gives you
150,000. When you multiple 50 by 50 it gives you 2,500. So when you divide 150,000 by 2,500 it gives you a total of 60 tiles. HOPE THIS HELPS
Answer:
60 tiles
Step-by-step explanation:
First, I would convert cm to m to make it easier
50 cm is .5 m
Now we can find how many tiles across it takes to make one row (5m)
.5 goes into 5, 10 times
That means we need 10 tiles across to fill one row
Now we need to find how many tiles it takes to fill up a column (3m)
.5 goes into 3, 6 times
It takes 6 tiles to fill up a column
Now we know it takes 10 tiles across and 6 vertically
10x6=60
60 tiles
URGENT PLS HELP ASAP! THANK YOU :)
Answer:
box 1 and box2 are correct.
what is the gcf of 3x^2 +9
Answer:v
Step-by-step explanation:
3(x^2+3)
the gcf is 3
Answer: 3 is the gcf
Step-by-step explanation:
3 is a factor of both 3 and 9. 1 is the other common factor. 3 is the greatest common factor. If you were looking at larger numbers with many common factors like 24 and 48, factors include 1,2,3,4,6,8,12,&24 You might find other smaller factors useful, but most of the time it's the gif that needs to be factored out: 3(x^2 + 3)
(If gets it right get's brainliest)If the hypotenuse of an isosceles right triangle is 14, what is the area of the triangle?
Answer:
49 unit²
Step-by-step explanation:
Right triangle with equal legs given, let the leg be x.
Hypotenuse of isosceles right triangle is
√x² + x² = x√2Area of triangle:
1/2ah= 1/2x²Since we have hypotenuse = 14 units:
x√2=14x= 14/√2Then area:
1/2x² = 1/2*(14/√2)² = 1/2*14²/2 = 7² = 49 unit²On a plane trip, baggage over 40 pounds is
charged at the rate per pound of 1% of the one-
way fare. The charge for a bag weighing 52
pounds on a trip where the one-way fare is $98
is:
HELP PLEASEE!! QUICK!!
Answer:
$11.76
Step-by-step explanation:
Given:
Baggage having its weight greater than 40 pounds is charged at rate of 1% of the one-way fare .
Here, as per statement One way fare of a trip = $98
Weight of bag on that trip = 52 pounds
To find:
Charge for bag for this trip = ?
Solution:
Weight greater than that of 40 pounds = Given total Weight of baggage - 40 pounds
As per the given statement:
Weight greater than that of 40 pounds = 52 - 40 pounds = 12 pounds
Charges on extra baggage = weight in pounds more than 40 multiplied by 1% of one-way fare.
Given that this trip has one way fare = $98.
The charge for a bag weighing 52 pounds = 1% of 98 \times 12
[tex]\Rightarrow \dfrac{1}{100}\times 98 \times 12\\\Rightarrow 98 \times 0.12\\\Rightarrow \bold{\$11.76}[/tex]
So, the answer is $11.76.
What is the responsible estimate of 6207 divided 214
Answer:
31
Step-by-step explanation:
We want to estimate 6207 / 214
Round 6207 to 6200
and 214 to 200
6200/200
62/2 = 31
We know that our estimate will be a little high since we are rounding the denominator down
The school's square parking lot has an
area of 3025 ft2. What is the length of each
side of the parking lot?
Answer:
The answer is 55ftStep-by-step explanation:
Since the school's parking lot is a square,
Area of a square = l²
where l is the length of one side
From the question
Area = 3025ft²
We have
3025 = l²
Find the square root of both sides
l = √3025
l = 55ft
The length of each side of the parking lot is 55ft
Hope this helps you
Choose all of the expressions that are equal to −9. |−9| −(−9) −|−9| −|9| the distance from zero to nine the opposite of nine
Answer:
|−9|, −|−9| and −|9|Step-by-step explanation:
Before we choose all the expression that is equal to -9, we must understand that the modulus of a value can return both its positive and negative value. For example, Modulus of b can either be +b or -b i.e |b| = +b or -b
Hence the following expression are all equal ro -9
a) |−9| is equivalent to -9 because the absolute value of -9 i.e |−9| can return both -9 and 9
b) −|−9| is also equivalent to -9. The modulus of -9 is also equal to 9, hence negating 9 will give us -9. This shows that −|−9| = −|9| = −9
c) −|9| is also equivalent to -9. This has been established in b above.
Answer: -|-9|, -|9|, and the opposite of nine
Step-by-step explanation: The absolute value symbol is | |. |-9| is 9 but add that - to it and it's -9. The absolute value of 9 is 9, add the - to it to get -9.
the opposite of 9 is -9.
Anyone the answers? Please help
Answer:
1.) 3 shovels/7 buckets
2.)7 buckets/3shovels
Find the formula for the inverse function.f(x)=2/3-4x
Answer:
f exponent − 1 ( x ) = -X/4 + 1/ 6
Plz mark brainlyest
Step-by-step explanation:
Please please please please help
Answer:
m = 9
Step-by-step explanation:
8/12 = 6/m
8m = 72
m = 9