Answer:
x = -7/2 and 3
Step-by-step explanation:
Use foil. Solve for x.
Answer:
The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3
Step-by-step explanation:
* Lets explain how to factor a trinomial in the form ax² ± bx ± c:
- Look at the c term first.
# If the c term is a positive number, then its factors r , s will both
be positive or both be negative.
# a has two factors h and k
# The sum of c and a is b.
# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs
# If the c term is a negative number, then either r or s will be negative,
but not both.
# a has two factors h and k
# The difference of c and a is b.
# The brackets are (hx + r)(kx - s) where a = hk , c = rs and b = rk - hs
* Lets solve the problem
∵ The equation is 2x² + x - 21 = 0
∵ The general form of the equation is ax² + bx + c = 0
∴ a = 2 , b = 1 , c = -21
∵ c is negative
∴ its factors r and s have different sign
∵ a = 2
∵ The factors of a are h , k
∵ 2 = 2 × 1
∴ h = 2 and k = 1
∵ -21 = 7 × -3
∴ r = 7 and s = -3
∵ The brackets are (hx + r)(kx - s)
∴ 2x² + x - 21 = (2x + 7)(x - 3)
∵ 2x² + x - 21 = 0
∴ (2x + 7)(x - 3) = 0
- Equate each bracket by 0
∴ 2x + 7 = 0 ⇒ subtract 7 from both sides
∴ 2x = -7 ⇒ divide both sides by 2
∴ x = -7/2 = -3.5
- OR
∴ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∴ The solutions are -3.5 and 3
* The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3
I ONLY HAVE TILL TONIGHT PLZ SAVE ME I WILL MARK YOU THE BRAINLEST IF YOU ANSWER MY FULL QUESTION
Answer:
This graph is a not a Function because it doesn't pass the vertical line test. The opened and closed circles are not in relation to the y-value and the x-value. This function also doesn't corresponds to one another, which messes up the domain and range.
Step-by-step explanation:
2x + y = 8 x + y = 4 The lines whose equations are given intersect at (4, 0) (0, 4) all points on the line
Answer:
(4,0)
Step-by-step explanation:
Plug them into see:
Check (4,0)
In order for the lines to intersect at (4,0) it must be on both lines.
2(4)+0=8 is true because it is saying 8=8
4+0=4 is true because 4=4
So (4,0) is a intersection point.
Check (0,4)
2(0)+4=8 is not true because it is saying 4=8
0+4=4 is true so it's on this line while not on the other line.
So (0,4) is not an interestion point for the mentioned lines.
Well all points can't be on the line since (0,4) is not on both lines but just one of them.
We could have solve this out instead plugging in but the problem gave us the option here with the choices.
The system of linear equations given intersects at the point (4, 0), and since these equations represent distinct lines, they only intersect at this single point.
The question involves solving a system of linear equations to find the point of intersection. The system given is:
2x + y = 8x + y = 4Let's solve the equations step by step:
Subtract the second equation from the first to eliminate y, getting 2x - x + y - y = 8 - 4, which simplifies to x = 4.Substitute x = 4 into the second equation: 4 + y = 4, solving for y, which gives y = 0.Therefore, the lines intersect at the point (4, 0).
To determine whether the lines intersect at all points on a line, note that these equations represent distinct lines with different slopes, meaning they only intersect at one point, facing the choice given, (4, 0) is correct.
Find the area of the parallelogram whose three of the vertices are (1, -2), (2, 3) and (-3, 2) in order. Also find its fourth vertex .
do it
like this
i have done by coordinates of geometry
Answer:
Area = 24 square unit,
Fourth vertex = (-4, -3)
Step-by-step explanation:
Suppose we have a parallelogram ABCD,
Having vertex A(1, -2), B(2, 3), and C(-3, 2),
Let D(x,y) be the fourth vertex of the parallelogram,
∵ The diagonals of a parallelogram bisect each other,
Thus, the midpoint of AC = midpoint of BD
[tex](\frac{1-3}{2}, \frac{-2+2}{2})=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]
[tex](\frac{-2}{2}, 0)=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]
By comparing,
[tex]-2=2+x\implies x=-4[/tex]
[tex]3+y=0\implies y = -3[/tex]
Thus, the fourth vertex is (-4, -3),
Now, the area of the parallelogram ABCD = 2 × area of triangle ABC (Because both diagonals divide the parallelogram in two equal triangles)
Area of a triangle having vertex [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,
[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
So, the area of triangle ABC
[tex]A=\frac{1}{2}|(1(3-2)+2(2+2)-3(-2-3)}|[/tex]
[tex]=\frac{1}{2}(1+8+15)[/tex]
[tex]=\frac{1}{2}\times 24[/tex]
[tex]=12\text{ square unit}[/tex]
Hence, the area of the parallelogram ABCD = 2 × 12 = 24 square unit.
Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay 4.5% interest, and stocks pay 10.4% interest. Country days invests $70000 more in bonds than CDs. If the annual income from the investments is $8555, how much was invested in stocks, bonds, and CDs?
Answer:
CDs — $10,000bonds — $80,000stocks — $45,000Step-by-step explanation:
Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:
c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested
0.0275c +.045b +0.104s = 8555 . . . . . total income earned
-c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs
Using the third equation to write an expression for b, we can substitute into the other two equations.
b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b
c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation
2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify
.0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn
.0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify
Using [eq4], we can write an expression for s that can be substituted into [eq5].
s = 65000 -2c . . . . . . . expression we can substitute for s
0.0725c +0.104(65000 -2c) = 5405
-0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify
c = 1355/.1355 = 10,000
s = 65000 -2×10000 = 45,000
b = 70000 +10000 = 80,000
The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.
_____
Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...
[tex]\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right][/tex]
Which expression has the same value as -18-(-9)?
0 -18+2
9 -12-(-3)
-10-5
Answer:
None of the given option is correct.
Step-by-step explanation:
The expression given is:
-18-(-9)
= -18+9
= -9
Now checking the options, which will have -9 as answer
1) 0 -18+2
= -18+2
= -16
As answer is not -9, so this is not a correct option
2) 9 -12-(-3)
= 9 - 12 + 3
= 0
As answer is not -9, so this is not a correct option
3) -10-5
= -10-5
= -15
As answer is not -9, so this is not a correct option
So, None of the given option is correct.
18. One biker rode at an average speed of 10.1 kilometers per hour. How far did
bikes
he ride in 5 hours?
Answer:
50.5 km
Step-by-step explanation:
If speed=distance/time, then distance=time*speed.
So we have the time and the speed to find the distance.
We just need to multiply 5 hours and 10.1 km/hour.
distance=(5 hours)(10.1 km/hour)
The time unit cancels and you are just left with the distance unit.
distance=50.5 km
Answer:50.5 km
Step-by-step explanation:
Which two operations are needed to write the expression that represents "eight more than the product of a number and
two"?
Answer:
Addition and Multiplication
Step-by-step explanation:
The keywords more than in this case means "addition", and the keyphrase product of a number and two means "multiplication". Here is what your expression should look like:
2n + 8
I am joyous to assist you anytime.
The average NBA ticket price for the 2018-2019 season is up 14.01% from the average ticket price of $78 during the 2015-2016 season. what is the average ticket price in 2018-2019? Round to the nearest penny.
The average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93
Given that the average NBA ticket price for the 2018-2019 season is up 14.01% from the average ticket price of $78 during the 2015-2016 season.
To find the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny.
Step 1: Find the increase ticket price by multiplying the increase % with the previous ticket price:
Increase ticket price = increase % x previous ticket price
Plugging the given data:
Increase ticket price = 14.01 % x 78
Convert percent into decimal:
Increase ticket price = 0.1401 x 78
On multiplying gives:
Increase ticket price = $10.9278
Step 2: Find the average ticket price in 2018-2019 by add it to previous year ticket price :
average ticket price= previous ticket price +Increase ticket price
Plugging the given data:
average ticket price=78 + 10.9278
On adding gives:
average ticket price=88.9278
Round to the nearest penny
average ticket price = $88.93
Therefore, the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93
Learn more about average here:
https://brainly.com/question/34397603
#SPJ4
Final answer:
The average NBA ticket price for the 2018-2019 season, based on a 14.01% increase from the 2015-2016 average of $78, is approximately $88.93 after rounding to the nearest penny.
Explanation:
To calculate the average NBA ticket price in the 2018-2019 season, we can use the percentage increase from the 2015-2016 season ticket price. We start with the average ticket price of $78 during the 2015-2016 season. According to the question, the ticket prices have increased by 14.01%. This percentage needs to be converted into a decimal (by dividing by 100) and then multiplied by the original average price to find the increase amount.
The calculation for the increase amount will be:
Convert the percentage increase into a decimal: 14.01% ÷ 100 = 0.1401.
Multiply this decimal by the original average price: 0.1401 × $78 = $10.9278.
Add this increase to the original average price to get the new average price: $78 + $10.9278 = $88.9278.
When we round this to the nearest penny, the new average ticket price for the 2018-2019 season is approximately $88.93.
Two angles of a triangle have the same measure and the third one is 15 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
The LARGEST angle has a measure of _____ degrees.
Answer:
70°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
let the equal angles be x then the third angle = x + 15
Sum the 3 angle and equate to 180
x + x + x + 15 = 180
3x + 15 = 180 ( subtract 15 from both sides )
3x = 165 ( divide both sides by 3 )
x = 55
Hence
The largest angle = x + 15 = 55 + 15 = 70°
A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water. 7 liters of yellow tint is added to the original mixture. What percent of yellow tint is in the new mixture? Answer must be correct to 1 decimal place.
Final answer:
To find the percent of yellow tint in the new mixture, we need to consider the original mixture and the additional 7 liters of yellow tint that was added. The new mixture has a percent of yellow tint of 38.6%.
Explanation:
To find the percent of yellow tint in the new mixture, we need to consider the original mixture and the additional 7 liters of yellow tint that was added.
The original mixture contains 30% yellow tint, which is equivalent to 30% of 50 liters, or 0.3 * 50 = 15 liters of yellow tint.
When the 7 liters of yellow tint is added, the total amount of yellow tint in the new mixture is 15 liters + 7 liters = 22 liters.
The new mixture has a total volume of 50 liters + 7 liters = 57 liters.
To find the percent of yellow tint in the new mixture, we divide the amount of yellow tint (22 liters) by the total volume (57 liters) and multiply by 100:
Percent of yellow tint = (22 liters / 57 liters) * 100 = 38.60% (rounded to 1 decimal place).
Final answer:
After adding 7 liters of yellow tint to the mixture, the new total volume of yellow tint is 22 liters, and the total volume of the mixture is 57 liters. Calculating the percentage, the mixture now consists of 38.6% yellow tint.
Explanation:
To calculate the new percentage of yellow tint in the mixture after adding 7 liters, we first need to determine how much of each component there was in the original mix.
Original amount of red tint: 25% of 50 liters = 12.5 litersOriginal amount of yellow tint: 30% of 50 liters = 15 litersOriginal amount of water: 45% of 50 liters = 22.5 litersAfter adding 7 liters of yellow tint, the new total amount of yellow tint becomes 15 liters + 7 liters = 22 liters. The total volume of the mixture is now 50 liters + 7 liters = 57 liters.
The new percentage of yellow tint is calculated as follows:
(Amount of yellow tint / Total volume) × 100 = (22 liters / 57 liters) × 100
This calculation gives us the new yellow tint percentage in the mixture:
(22 / 57) × 100 ≈ 38.6%
Therefore, the mixture now contains 38.6% yellow tint.
Q: Which best describes the demand for consumer goods in the 1920's.
Select one:
a. people were less likely to buy new goods.
b. the demand for consumer goods declined during the 1920's.
0 C. all of these are correct
d. people began buying more than they had the cash to pay for becaus
could access loans and buy things on credit.
NE
Answer:
d. people began buying more than they had the cash to pay for because they
could access loans and buy things on credit.
Step-by-step explanation:
In the 1920's, it was a period of prosperity and people in the middle class began to have more income available to purchase products. Also, there were more products available because of the assembly line production and the credits expanded which resulted in people being able to buy things that they couldn't purchase paying the full price. According to this, the answer is that the statement that best decribes the demand for consumer goods in the 1920's is that people began buying more than they had the cash to pay for because they could access loans and buy things on credit.
what is 2% out of 3000
Answer:
It would be 60.
Answer:
Step-by-step explanation:
(3000×2)/100 = 6000/100 = 60
If h(x) = (fog) (x) and h(x) = 4 square root x+7, find g(x) if f(x) = 4 square root x+ 1
Answer:
[tex]g(x)=x+6[/tex] is the answer
given
[tex]h(x)=4\sqrt{x+7}[/tex] and [tex]f(x)=4\sqrt{x+1}[/tex].
Step-by-step explanation:
[tex]h(x)=(f \circ g)(x)[/tex]
[tex]h(x)=f(g(x))[/tex]
Inputting the given function for h(x) into the above:
[tex]4\sqrt{x+7}=f(g(x))[/tex]
Now we are plugging in g(x) for x in the expression for f which is [tex]4\sqrt{x+1}[/tex] which gives us [tex]4\sqrt{g(x)+1}[/tex]:
[tex]4\sqrt{x+7}=4\sqrt{g(x)+1}[/tex]
We want to solve this for g(x).
If you don't like the looks of g(x) (if you think it is too daunting to look at), replace it with u and solve for u.
[tex]4\sqrt{x+7}=4\sqrt{u+1}[/tex]
Divide both sides by 4:
[tex]\sqrt{x+7}=\sqrt{u+1}[/tex]
Square both sides:
[tex]x+7=u+1[/tex]
Subtract 1 on both sides:
[tex]x+7-1=u[/tex]
Simplify left hand side:
[tex]x+6=u[/tex]
[tex]u=x+6[/tex]
Remember u was g(x) so you just found g(x) so congratulations.
[tex]g(x)=x+6[/tex].
Let's check it:
[tex](f \circ g)(x)[/tex]
[tex]f(g(x))[/tex]
[tex]f(x+6)[/tex] I replace g(x) with x+6 since g(x)=x+6.
[tex]4\sqrt{(x+6)+1}[/tex] I replace x in f with (x+6).
[tex]4\sqrt{x+6+1}[/tex]
[tex]4\sqrt{x+7}[/tex]
[tex]h(x)[/tex]
The check is done. We have that [tex](f \circ g)(x)=h(x)[/tex].
PLEASE HELP ME 20 POINTS !! tyvm
ASAP
Answer:
[tex]\large\boxed{m\angle S=78^o}[/tex]
Step-by-step explanation:
[tex]\text{If}\ \triangle MNP\cong\triangle QST,\ \text{then corresponding angles}\\\text{and corresponging sides are congruent.}\\\\\angle M\cong\angle Q\\\angle N\cong\angle S\\\angle P\cong\angle\\\\m\angle N=78^o,\ \text{therefore}\ m\angle S=78^o[/tex]
Consider the equation (x^m)=(x^13)^5 x(x^-8)^-5
The value of m is
A. 15
B. 28
C. 35
D. 70
Answer:
m = 106Step-by-step explanation:
[tex]x^m=(x^{13})^5x(x^{-8})^{-5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\x^m=(x^{(13)(5)})x(x^{(-8)(-5)})\\\\x^m=(x^{65})x^1(x^{40})\qquad\text{use} \ a^na^m=a^{n+m}\\\\x^m=x^{65+1+40}\\\\x^m=x^{106}\Rightarrow m=106[/tex]
Which of the fractions listed below are equal to 2⁄3?
Check all that are true.
6⁄9
1⁄3
3⁄2
4⁄6
1⁄6
which statements must be true about ru reflection of xyz across mn? select 3 options
Answer:BZ congruent to BZ'
XY congruent to X'Y'
X'Z'Y' 90 degrees
Step-by-step explanation:
Answer:
(1). m∠X'Z'Y'=90°
(2). m∠MCY=90°,
(3). Line segment BZ'≅ line segment BZ
Step-by-step explanation:
Line MN is reflecting line for ΔXYZ. Triangle X'Y'Z' is formed after reflection of ΔXYZ about a line MN. Therefore the line MN works like a symmetric axis of the given figure.
Hence
(1). m∠X'Z'Y'=90°, because ∠XYZ=90° and figure are symmetric about line MN.
(2). m∠MCY=90°, because figure is symmetric ,so line segment YY'⊥ line MN.
(3). Line BZ' ≅line BZ, because figure is symmetric about about symmetric axis line MN and Line BZ'= line BZ.
Please help me solve this problem !
[tex]f(3)=2^3=8[/tex]
Answer:
D. 8
Step-by-step explanation:
The value of f(3) in f(x)=2x is 8.
f(3)=2^3=8
What is 72/5 in decimal form
Answer:
14.4
Step-by-step explanation:
72/5 in decimal form equals 14.4
[tex]\frac{72}{5}[/tex] in decimal form is 14.4
[tex]\frac{72}{5}[/tex] is the same as 72 ÷ 5
72 ÷ 5 = 14.4
All we have to do to turn this fraction into a decimal is divide the fractions numerator by its denominator and we will get our decimal.
What theorem or postulate can be used to justify that AHIG EAFIE?
A. SAS
B. ASA
C. AAS
D. SSS
Answer:
ASA
Step-by-step explanation:
There is an included side in between both angles in each triangle.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
solve the following system of equations
2x – 3y = 6
4x+2y=4
Answer:
[tex]\boxed{(\frac{3}{2} ,-1)}[/tex]
Step-by-step explanation:
[tex]\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.[/tex]
It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).
Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).
[tex]2x-3y=6 \rightarrow -4x+6y=-12[/tex]
Now line up the equations (they are already lined up - convenient) and add them from top to bottom.
[tex]\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.[/tex]
The -4x and 4x are opposites, so they cancel out.
Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.
[tex]8y=-8[/tex]
Divide both sides by 8.
[tex]y=-1[/tex]
Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.
[tex]4x +2(-1)=4[/tex]
Simplify.
[tex]4x -2=4[/tex]
Add 2 to both sides.
[tex]4x=6[/tex]
Divide both sides by 4.
[tex]x=\frac{6}{4} \rightarrow\frac{3}{2}[/tex]
The final answer is [tex]x=\frac{3}{2} ,~y=-1[/tex].
[tex](\frac{3}{2} ,-1)[/tex]
factor the expression 6g^3 + 8g^2 - 15g - 20
Answer:
(3g+4) (2g^2-5)
Step-by-step explanation:
6g^3 + 8g^2 - 15g - 20
Lets factor by grouping
Taking a 2 g^2 out of the first two terms and -5 out of the last two terms
2g^2 (3g+4) -5(3g+4)
Factoring out (3g+4)
(3g+4) (2g^2-5)
Answer:
The factors are (3g+4)(2g^2-5)....
Step-by-step explanation:
The expression is:
6g^3 + 8g^2 - 15g - 20
Make a group of the first two terms and last two terms:
(6g^3 + 8g^2) - (15g + 20)
Now factor out the common from each group:
2g^2(3g+4)-5(3g+4)
(3g+4)(2g^2-5)
Therefore the factors are (3g+4)(2g^2-5)....
Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.
J = 90° J' = 90°
K = 65° K' = 65°
L = 25° L' = 25°
Which statement is true about this transformation?
Answer:
It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.
Step-by-step explanation:
Answer:C
Step-by-step explanation:
I know
What is the product?
(x^2-16)/(2x+8) x (x^3-2x^2+x)/(x^2+3x-4)
a. x(x-4)(x-1)/2(x+4)
b. x(x-1)/2
c. (x+4)(x-4)/2x(x-1)
d. (x-4)(x-1)/2x(x+4)
Answer:
Option A is correct.
Step-by-step explanation:
We need to find the product of
[tex]\frac{(x^2-16)}{(2x+8)} * \frac{(x^3-2x^2+x)}{(x^2+3x-4)}[/tex]
We know (a^2-b^2) = (a+b)(a-b)
so, (x^2-16) = (x)^2-(4)^2 = (x-4)(x+4)
2x+8 Taking 2 common from this term:
2x+8 = 2(x+4)
(x^3-2x^2+x) Taking x common from this term
x(x^2-2x+1) = x(x-1)^2 = x(x-1)(x-1)
(x^2+3x-4) factorizing this term
x^2+4x-x-4 = x(x+4)-1(x+4)
= (x-1)(x+4)
Now, Putting these simplified terms in the given equation:
[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)(x-1)}{(x-1)(x+4)}[/tex]
Now cancelling the same terms that are in numerator and denominator
[tex]=\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}\\=\frac{(x-4)(x)(x-1)}{2(x+4)}\\=\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
So, Option A is correct.
Answer:
=x(x-4)(x-1)/2(x+4)
Step-by-step explanation:
=x^2-4^2/2(x+4) * x^3-2x^2+x/x^2+3x-4
=(x+4)(x-4)/2(x+4) * x(x^2-2x+1)/x^2+3x-4
Factor x^2-2x+1 using the perfect square root
=(x+4)(x-4)/2(x+4) * x(x-1)^2/x^2+3x-4
Factor x^2+3x-4 using AC method.
=(x+4)(x-4)/2(x+4) * x(x-1)^2/(x-1)(x+4)
Cancel the common factor of x+4 and x-1
=(x-4)/2(x+4) * x(x-1)/1
=(x-4)x(x-1)/2(x+4)
Reorder the terms
=x(x-4)(x-1)/2(x+4)
PLEASE HELP, I NEED TO BE HELPED WITH THESE QUESTIONS
Answer:
[tex](f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}[/tex]
[tex]f(g(x))=x+1[/tex]
[tex]f(x)=x+9 \text{ and } g(x)=\frac{4}{x^2}[/tex]
[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]
Let me know if you have any questions about any of my work.
Step-by-step explanation:
You are given the following:
[tex]f(x)=\sqrt{3x+7} \text{ and } g(x)=\sqrt{3x-7}[/tex]
and asked to find [tex](f+g)(x) \text{ which means } f(x)+g(x)[/tex].
If you add those because we are asked to find f(x)+g(x) you get:
[tex]\sqrt{3x+7}+\sqrt{3x-7}[/tex]
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You are given the following:
[tex]f(x)=x^2+3 \text{ and } g(x)=\sqrt{x-2}[/tex]
and asked to find [tex]f(g(x))[/tex].
[tex]f(g(x))[/tex]
[tex]f(\sqrt{x-2})[/tex] I replaced g(x) with sqrt(x-2) because that is what it equals.
Now this last thing means to replace old input in x^2+3 with new input sqrt(x-2) giving us:
[tex](\sqrt{x-2})^2+3[/tex]
[tex]x-2+3[/tex]
[tex]x+1[/tex]
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We are given [tex]y=\frac{4}{x^2}+9[/tex] and asked to find g(x) and f(x) such that y=f(g(x)).
We have choices so let's use the choices:
Choice A:
[tex]f(g(x))[/tex]
[tex]f(\frac{4}{x^2}){/tex] I replace g(x) with 4/x^2:
[tex]\frac{4}{x^2}+9[/tex] I replaced the old input x with new input 4/x^2.
This was actually the desired result.
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To find the inverse of f(x)=3x-2 or y=3x-2, your objective is to swap x and y and then remake y the subject.
y=3x-2
Swap x and y:
x=3y-2
Now solve for y.
Add 2 on both sides:
x+2=3y
Divide both sides by 3:
(x+2)/3=y
y=(x+2)/3
[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]
Two classes are planning to go on a field trip together. One clas with 18 students is being joined by 6 boys and 11 girls from another class, giving an overall ratio of boys to girls on the field trip of 2 to 3. Boys made up what proportion of the original class?
To find the proportion of boys in the original class, divide the number of boys by the total number of students in the class.
Explanation:To find the proportion of boys in the original class, we need to compare the number of boys in the original class to the total number of students in the original class.
The original class had 18 students, and it was joined by 6 boys from another class. This means there are now 18 + 6 = 24 boys on the field trip.
The overall ratio of boys to girls on the field trip is 2:3, which means for every 2 boys, there are 3 girls. If we have 24 boys, we can find the number of girls by dividing 24 by 2 and then multiplying by 3. This gives us (24/2) * 3 = 36 girls.
So, the original class had 24 boys and 36 girls. To find the proportion of boys in the original class, we divide the number of boys (24) by the total number of students (24 + 36 = 60). This gives us 24/60 = 0.4, or 40%.
Two points are drawn on each side of a square with an area of 81 square units dividing the side into 3 congruent parts. Quarter-circle arcs connect the points on adjacent sides to create the figure shown. What is the length of the boundary of the bolded figure? Express your answer as a decimal to the nearest tenth.
Answer:
The length of the bold figure ABCDEFGH is 30.8 units
Step-by-step explanation:
* To solve the problem look to the attached figure
- There is a square of area 81 units²
∵ The area of the square = L² , where L is the length of the side of
the square
∵ The area of the square = 81 units²
∴ L² = 81 ⇒ take √ for both sides
∴ L = 9 units
- Two points are drawn on each side of a square dividing it into 3
congruent parts
∵ 9 ÷ 3 = 3
∴ The length of each part is 3 units
- Quarter-circle arcs connect the points on adjacent sides to create
the attached figure
∵ The radius of each quarter circle is 3 units
∵ The length of each side joining the two quarter circle is 3 units
∵ The figure ABCDEFGH consists of 4 quarters circle and 4 lines
- The length of the 4 quarters circle = the length of one circle
∵ The length of the circle is 2πr
∴ The length of the 4 quarters circle = 2 π (3) = 6π units
∵ The length of each line = 3 units
∴ The length of the figure = 6π + 4 × 3 = 30.8 units
* The length of the bold figure ABCDEFGH is 30.8 units
Answer:
30.8
Step-by-step explanation:
I really need help with 9 and 10 please.
Answer:
9) The equation that represents our monthly bill is y=20+0.05m.
10) The equation that gives us the cost for the month is y=5+0.1m.
Step-by-step explanation:
9) So if we are trying to find how much our monthly bill is where the monthly fee is 20 and we are charged $.05 per minute, then:
For 0 minutes, we spend 20 dollars in the month.
For 1 minute, we spend 20+.05=20.05 dollars in the month.
For 2 minutes, we spend 20+.05+0.05 or 20+2(.05)=20+.1=20.10 dollars in the month.
For m minutes, we spend 20+.05m.
The equation that represents our monthly bill is y=20+0.05m.
They gave us the y-intercept (the initial amount=20) and the rate (the slope=.05).
Remember: slope-intercept form is y=mx+b.
10) I'm going to shorten number 10.
They give us the rate=$.1/min and the initial cost=5 dollars.
The equation that gives us the cost for the month is y=5+0.1m.
solve the equation
log(5x)-log(x-3)=1
Answer:
x = 6
Step-by-step explanation:
Using the rules of logarithms
• log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
log(5x) - log(x - 3) = 1
log ( [tex]\frac{5x}{x-3}[/tex] ) = 1, then
[tex]\frac{5x}{x-3}[/tex] = [tex]10^{1}[/tex] = 10 ( cross- multiply )
10(x - 3) = 5x
10x - 30 = 5x ( subtract 5x from both sides )
5x - 30 = 0 ( add 30 to both sides )
5x = 30 ( divide both sides by 5 )
x = 6
Answer:
x =6
Step-by-step explanation:
log(5x) - log(x - 3) = 1
Recall that the logarithm of a fraction is the difference of the logarithms,
so, the difference between two logarithms is logarithm of the fraction. Then,
[tex]\begin{array}{rcll}\\\\\log \dfrac{5x}{x-3} & = & 1 &\\\\\dfrac{5x}{x - 3} & = & 10 & \text{Took the antilogarithm of each side}\\\\5x & = & 10(x - 3) & \text{Multiplied each side by x - 3}\\5x & = & 10x - 30 & \text{Distributed the 10}\\-5x & = & -30 & \text{Subtracted 10 x from each side}\\x & = & \mathbf{6} & \text{Divided each side by -5}\\\end{array}[/tex]
Check:
[tex]\begin{array}{rcl}\log(5\times6) - \log (6 - 3) & = & 1\\\log 30 - \log 3 & = &1\\\\\log \dfrac{30}{3} & = & 1\\\\\log 10 & = & 1\\1 & = & 1\\\end{array}[/tex]
OK.
Evaluate the expression
a-b/c*d
when a=48, b=18, c=3, and d=2
[tex]\huge{\boxed{36}}[/tex]
Substitute the values. [tex]48 - 18 \div 3 * 2[/tex]
Follow PEMDAS and multiply and divide first. [tex]48 - 6 * 2[/tex]
[tex]48 - 12[/tex]
Continue following PEMDAS and subtract. [tex]\boxed{36}[/tex]