First you must distribute the numbers outside the parentheses to the numbers inside the parentheses
Let's start with the first one:
9(x-2) + 3(5-2x) = 2
9(x - 2)
9*x + 9*-2
9x + (-18)
9x - 18
so...
9x - 18 + 3(5-2x) = 2
Now on to the second set of parentheses:
9x - 18 + 3(5-2x) = 2
3(5 - 2x)
3*5 + 3*-2x
15 + (-6x)
15 - 6x
so...
9x - 18 + 15 - 6x = 2
Now you must combine like terms. This means the numbers with the same variables must be combined...
First set of like terms:
9x - 18 + 15 - 6x = 2
9x + (-6x)
3x
so...
3x - 18 + 15 = 2
Second set of like terms:
3x - 18 + 15 = 2
-18 + 15
-3
so...
3x - 3 = 2
Now bring -3 to the right side by adding 3 to both sides (what you do on one side you must do to the other). Since -3 is being negative on the left side, addition (the opposite of negative/subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
3x + (- 3 + 3) = 2 + 3
3x + 0 =5
3x = 5
Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.
3x/3 = 5/3
x = [tex]\frac{5}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
EASY QUESTION PLEASE HELP
Answer:
Yea its table 1
Step-by-step explanation:
Answer:
The answer is the first table, or Table 1.
Step-by-step explanation:
Happy to help! c:
HELP! i'll give brianliest and lots of points, and if u will explain, explain it so a dumb person can understand, if u can't then just give me a straight answer
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answer:
Step-by-step explanation:
There is a standard cost just for renting the car.
Let the daily cost = x
Let the addon be = z The add on is the amount they charge just to give you the keys and do the paper work. It might include insurance.
y = z + 4x
y = 180
z = ??
x = 4
y = 325
z = ??
x = 9
Equation 1: 180 = z + 4x
Equation 2:325 = z + 9x
Subtract (1) from (2)
325 = z + 9x
180 = z + 4x Subract
145 = 5x Divide by 5
145/5 = 5x/5
x = 29
What you have found is the daily cost. Now you have to find the fixed cost.
y = 29x + z
180 = 29*4 + z
180 = 116 + z Subtract 116 from both sides
180 - 116 = z
z = 64
Answer: Part A
y = 29x + 64
Part B
f(x) = 29x + 64
Part C
So what are the intervals?
Vertically each square is worth:
Horizontally: each square is worth.
How is the y axis labeled?
How is the x axis labeled? [e
Graph the points by letting
x = 2 days
x = 4 days
x = 6 days
I'm including the graph. You should be able to answer it just by looking at the graph. No single answer will be wrong. There are all sorts of ways of setting up the axis.
Can someone help me with this
Hello There!
Your answer is the last option r*n^2
I plugged in the values for each of these dilations.
Solve the equation for x.
3(6x - 1) = 12 Please help I've tried doing the math and I can't find out what I'm doing wrong
Answer:
edg 2021 answer is A
Step-by-step explanation:
Multiply and simplify the product. –12i × 3i Select the product. 36 -36 36i -36i
Answer:
36
Step-by-step explanation:
–12i × 3i
Multiply the numbers
-12*3 = -36
Multiply the imaginary number
i*i= i^2
We know i^2 = -1
-36 * -1 = 36
Answer:
36Step-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=(\sqrt{-1})^2=-1\\\\-12i\times3i=(-12)(3)i^2=(-36)(-1)=36[/tex]
Let f(x) = - 4x - 1 and g(x) = x2 + 3.
Find (fog)(4)
Then (fog)(4) =
. (Simplify your answer)
Answer:
- 77
Step-by-step explanation:
To evaluate, substitute x = 4 into g(x) then substitute the value obtained into f(x).
g(4) = 4² + 3 = 16 + 3 = 19
f(19) = (- 4 × 19) - 1 = - 76 - 1 = - 77
if f(x)=3x^2 and g(x)=x+2, find (f*g)(x)
Answer:
(f+g)(x) = 3x^2 + x + 1
how would you solve x in this equation?
1.4(2x+3) = 0.9(3x-2)
Answer:
x = -60
Step-by-step explanation:
1.4(2x+3) = 0.9(3x-2)
(1.4)(2x) + (1.4)(3) = 0.9(3x) - 0.9(2)
2.8x + 4.2 = 2.7x - 1.8
2.8x - 2.7x = -1.8 -4.2
0.1x = -6
x = -60
Answer:
x = - 60
Step-by-step explanation:
1.4(2x+3) = 0.9(3x-2) Remove the brackets
2.8x + 4.2 = 2.7x - 1.8 Subtract 4.2 from both sides
2.8x +4.2-4.2 = 2.7x - 1.8- 4.2
2.8x = 2.7x - 6 Subtract 2.7x from both sides
2.8x-2.7x = - 6
0.1x = - 6 Divide by 0.1
0.1x/0.1 = - 6/0.1
x = - 60
The temperature in Tampa Fonda is 15 degrees warmer than twice the temperature in Chicago, Illinois. The temperature in Tampa is 75 degrees. Write an equation to determine
the temperature in Chicago
The temp of Chicago is 30 degrees.
15 degree MORE than TWICE the temp of Chicago. 75-15=60/2. Hope this helps.
Answer:
2x + 15 = 75
Step-by-step explanation:
2 represents the twice, the x represents the unknown answer (Chicago), the + 15 is when it says florida is 15 degrees warmer
Fill in the blank of the triangle below x=
ANSWER
[tex]37.53units[/tex]
EXPLANATION
From the given right angle triangle the known angle is 47°
The side length which is x units is opposite to the known angle.
We also know a side length 35 units which is adjacent to the given angle.
We use the tangent ratio to obtain,
[tex] \tan(47 \degree) = \frac{opposite}{adjacent} [/tex]
[tex]\tan(47 \degree) = \frac{x}{35} [/tex]
[tex]x = 35\tan(47 \degree) = 37.53 \: units[/tex]
Answer:
x = 37.53 units
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
From the figure we can see a right angled triangle with one angle is 47° and adjacent side length of that angle is 35
To find the value of x
From the figure we can write,
Tan 47 = Opposite side/Adjacent side
= x/35
x = 35 * Tan 47
= 37.53 units
A grocery store donated 60 dozen hot dog rolls to the local Youth Baseball League for their Opening Day ceremonies. A total of 679 hotdogs were served. (Hint: a dozen contains 12 items) a) How many dozen rolls were used? (Express your answer in mixed number form)
Answer:
7 7/12
Step-by-step explanation:
Find the amount of rolls in all that were donated:
60 x 12 = 720.
The total amount used is 679. Subtract 679 from 720:
720 - 629 = 91.
Find the amount per dozen. Divide 91 with 12:
91/12 = 7 7/12
7 7/12 is your answer.
~
The local Youth Baseball League used 56 dozen rolls with 7 extra rolls for a total of 679 hot dogs, which is expressed as 56 7/12 dozen.
Explanation:The local Youth Baseball League served a total of 679 hot dogs using rolls from the grocery store.
If a dozen represents 12 items, we need to calculate how many dozens of rolls were used in this circumstance.
Since 679 hot dogs were served and each dozen contains 12 rolls, we can divide 679 by 12 to find the number of dozens.
Dividing 679 by 12, we get:
679 ÷ 12 = 56 dozens with a remainder of 7.
Therefore, 56 dozen rolls were fully used, with an additional 7 rolls from another dozen.
To express this in mixed number form, it would be 56 7⁄12 dozen rolls.
What is 2^(4/3)
equal to?
Answer:
∛16
Step-by-step explanation:
First, remember that the denominator always goes outside the radical and the numerator inside. so with that, it looks like this.
∛2^4
simplify.
∛16
Which of the following choices gives you a slope of 3?
Answer: Could you list the choices?
20 POINTS!!! NEED HELP ASAP!!!
Which exponential function is represented by the table?
f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)
Answer:
c
Step-by-step explanation:
Simplify square root 18
Answer:
3√2
Step-by-step explanation:
√18 = √9 x √2 = 3√2
Start by making a factor tree for 18.
18 factors as 6 x 3 and 6 factors as 2 x 3.
Look for pairs of factors that are the same.
In this case, the 3's match up.
So a 3 will come out of the radical.
Whatever does not pair up stays inside.
In this case, the 2 goes inside.
So our answer is 3√2.
Give the solution of the equation x+7/ 5 =10
Answer:
see below
Step-by-step explanation:
x + 7/5 = 10
Subtract 7/5 from each side
x+7/5 -7/5 = 10 -7/5
x = 10-7/5
Get a common denominator
x = 50/5 - 7/5
x = 43/5
As a mixed number
x = 8 3/5
Or if the equation was
(x+7)/5 = 10
Multiply by 5
(x+7)/5 *5 = 10*5
x+7 = 50
Subtract 7 from each side
x+7-7 = 50-7
x = 43
Answer:
x = 43/5
Step-by-step explanation:
Subtract 7/5 from both sides.
x + 7/5 - 7/5 = 10 - 7/5
x= 43/5
Help me please with this
Answer:
(b) 240
Step-by-step explanation:
First, we use the Pythagorean formula using the given side lengths to find x. Then we use x to find the side lengths. Then we add the side lengths to find the perimeter.
Pythagorean theorem formula:
a^2 + b^2 = c^2
(x - 20)^2 + (x - 40)^2 = x^2
x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2
x^2 -120x + 2000 = 0
(x - 100)(x - 20) = 0
x - 100 = 0 or x - 20 = 0
x = 100 or x = 20
We see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. The only valid solution is x = 100.
perimeter = sum of the lengths of the sides
perimeter = x + x - 20 + x - 40
perimeter = 3x - 60
Replace x with 100.
perimeter = 3(100) - 60
perimeter = 300 - 60
perimeter = 240
Two cylinders. The smaller cylinder has height labeled as 1 cm. The larger cylinder has height labeled as 3 cm.
The cylinders are similar. The volume of the larger cylinder is 2106 cubic centimeters. What is the volume of the smaller cylinder?
93 cm3
81 cm3
78 cm3
65 cm3
Answer: third option.
Step-by-step explanation:
You know that the height of the smaller cylinder is 1 cm and the height of the larger cylinder is 3 cm, then you can find the volume ratio. This is:
[tex]Volume\ ratio=(\frac{1\ cm}{3\ cm})^3\\\\Volume\ ratio=\frac{1}{27}[/tex]
Knowing that the volume of the larger cylinder is 2,106 cubic centimeters, you need to multiply it by the volume ratio to find the volume of the smaller cylinder.
Therefore:
[tex]V_{smaller}=\frac{1}{27}(2,106\ cm^3)\\\\V_{smaller}=78\ cm^3[/tex]
ANSWER
The correct answer is C
EXPLANATION
We have that, the smaller cylinder has height 1 cm and the larger cylinder has height 3cm.
The scale factor of similarity is
[tex]k = \frac{1}{3} [/tex]
That's if the smaller cylinder is the image.
The volume of the larger cylinder is 2106 cm³.
To find the volume of the smaller cylinder, we multiply the volume of the larger cylinder by k³
[tex]( { \frac{1}{3} })^{3} \times 2106 {cm}^{3} [/tex]
[tex]{ \frac{1}{27} } \times 2106 = 78 {cm}^{3} [/tex]
How many solutions does the following equation have?
-2z+10+7z=16z+7
Start with
[tex]-2z+10+7z=16z+7[/tex]
Simplify the left hand side by summing like terms (the one involving z):
[tex]5z+10 = 16z+7[/tex]
Subtract 5z from both sides:
[tex]10 = 11z+7[/tex]
Subtract 7 from both sides
[tex]3 = 11z[/tex]
Divide both sides by 11:
[tex]z = \dfrac{3}{11}[/tex]
The equation has one solution and the solution is z = 3/11.
What is simplification of an equation?Simplification of an equation is the process of writing an equation in the most efficient and compact form without affecting the value of the original equation.
For the given situation,
The equation is -2z+10+7z=16z+7
The equation can be simplified as
⇒ [tex]-2z+10+7z=16z+7[/tex]
⇒ [tex]-2z+7z-16z=7-10[/tex]
⇒ [tex]-11z=-3[/tex]
⇒ [tex]z=\frac{-3}{-11}[/tex]
⇒ [tex]z=\frac{3}{11}[/tex]
Hence we can conclude that the equation has one solution and the solution is z = 3/11.
Learn more about simplification of an equation here
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In a candy bar, 165 calories are from sugar. There are 250 calories in the candy bar. What percent of the calories are from sugar?
82%
60%
58%
66%
Answer: You can simply find out the percentage of the calories from the sugar with this formula :
165/250 x 100%
You will find out that the percentage would be 66 %
hope this helps!
Step-by-step explanation:
•••••Answer this question thanks •••••
2b < 10
b < 5
How to draw it:
1. Draw a hollow point on number "5"
2. Draw a small vertical line on the top of the point.
3. Draw a long honrizontal line from that vertical line to the left to the end, and add an arrow.
First divide 2 to both sides to isolate b. Since 2 is being multiplied by b, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.
2b ÷ 2 < 10 ÷ 2
1b < 5
b < 5
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:
b < 5
aka b is less then five
This means that the graph will have an empty circle and the arrow will go to the left of 5.
The graph is in the image below:
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the slope of (0,32) and (100,212)
Answer:
( 212 - 0 )/ ( 100 - 32 ) = 212 / 68 = 3.11 ;
Step-by-step explanation:
Let m = slope
m = (delta y)/(delta x)
m = (212 - 32)/(0 - 100)
m = 180/(-100)
m = -180/100
You can reduce -180/100 to the lowest term. I'll let you do that.
What is the product of (2x-1)(x+4)
Answer:
[tex]\large\boxed{(2x-1)(x+4)=2x^2+7x-4}[/tex]
Step-by-step explanation:
[tex](2x-1)(x+4)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(2x)(x)+(2x)(4)+(-1)(x)+(-1)(4)\\\\=2x^2+8x-x-4\qquad\text{combine like terms}\\\\=2x^2+(8x-x)-4\\\\=2x^2+7x-4[/tex]
Please help me on this I’m so tired and I can’t sleep until my progress is at 80 and this is the end of my year it’s at 79%
Answer:
The answer is the bottom left
Evaluate 2(x + 1) - 3 when x = 6.
ОА. 5
ов. 8
Ос. 11
OD. 10
Answer:
C. 11
Step-by-step explanation:
Evaluate 2(x + 1) - 3 when x = 6.
2(x + 1) - 3 <== substitute 6 for x
2(6 + 1) - 3 <== distribute 2
2(6) + 2(1) - 3
12 + 2 - 3 <== add and subtract
14 - 3
11 <== answer
Hope this helps!
Hey there!
2(x + 1) - 3
= 2(6 + 1) - 3
= 2(7) - 3
= 14 - 3
= 11
OR
2(x + 1) - 3
= 2(6 + 1) - 3
= 2(6) + 2(1) - 3
= 12 + 2 - 3
= 14 - 3
= 11
Therefore, your answer is: 11
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which is the measure of the third angle in the similar triangles below?
Answer choices
25
65
85
115
Answer:
65
Sorry if im wrong
Julio bought 10 shares of Apex Co. for $50 each and later sold all of them at
$55 each. This transaction resulted in what type of event?
O
A. Capital profit
O
B. Capital gain
O
C. Capital win
O
D. Capital loss
Answer: B. Capital Gain
Step-by-step explanation:
Sanjay needs 90 meters of fence to go around a rectangular garden.
The length l of the garden is three times its width w.
Three of these equations give the correct value for w.
Which equation does NOT?
w+3w=90
w+3w+w+3w=90
2⋅w+2⋅3w=90
2⋅(3w+w)=90
To find the perimeter of a rectangle you can multiply the length by 2 and the width by 2, or you can add the four sides together.
The wrong equation is w + 3w = 90 because it only has one width and one length, which would be half the total perimeter.
Final answer:
The equation that does not correctly represent the width w of Sanjay's rectangular garden given the total fence length and length-width relationship is w + 3w = 90, as it simplifies to 4w = 90, which is not the correct equation for this context.
Explanation:
The question asks to identify which equation does not correctly represent the width w of Sanjay's rectangular garden, given that the total length of the fence is 90 meters and that the length l of the garden is three times its width w. We know the perimeter P of a rectangle is given by P = 2l + 2w, where l is the length and w is the width.
We can substitute l = 3w into the perimeter formula to get P = 2(3w) + 2w, which simplifies to P = 6w + 2w or P = 8w. Given that P = 90, the correct equation is 8w = 90. Now, let's examine the provided equations:
w + 3w = 90 simplifies to 4w = 90.
w + 3w + w + 3w = 90 simplifies to 8w = 90, which is the correct equation.
2 · w + 2 · 3w = 90 simplifies to 2w + 6w = 90 which simplifies to 8w = 90, which is also correct.
2 · (3w + w) = 90 simplifies to 2 · 4w = 90 which simplifies to 8w = 90, which is again correct.
Thus, the equation that does not give the correct value for w is w + 3w = 90.
Which of these ordered pairs is a solution to the inequality
y< x + 12
-2, 5
0, 1
15, 0
-5, 0
All of the above.
To check if an ordered pair is a solution to the inequality, plug in the ordered pair into the inequality and see if the inequality checks out.
[tex]y<x+12[/tex]
(-2,5)
[tex]5<-2+12[/tex]
[tex]5<10[/tex]
So this ordered pair works.
(0,1)
[tex]1<0+12[/tex]
[tex]1<12[/tex]
So this ordered pair works as well.
(15,0)
[tex]0<15+12[/tex]
[tex]0<27[/tex]
So this ordered pair works.
(-5,0)
[tex]0<-5+12[/tex]
[tex]0<7[/tex]
So this ordered pair works as well.
Lilly and Laura pooled their money to purchase
their brother, Liam, a video game for his birthday.
The video game cost a total of $45. If Laura was
only able to contribute of what Lilly did, how
much did Laura put toward the present?
Answer: $22.50
Step-by-step explanation: let x represent the amount Laura and Lilly contributed each. If Laura and Lilly contributed the same amount, x+x=2x=45. If 2x=45, divide both sides by 2 to find the value of x. 45/2= 22.5.
Laura contributed $15 toward the purchase of the video game.
Explanation:The question is asking to determine the amount contributed by Laura to buy a video game for their brother, Liam, if the entire cost of the game is $45 and Laura contributed half as much as Lilly. For simplicity, let's assume Lilly contributed x dollars. Then Laura, contributing half as much, would have contributed x/2 dollars. Given that their total contribution is $45, we set up the equation x + x/2 = 45. Solving for x, we find that Lilly contributed $30 and Laura, half of this, contributed $15.
Learn more about Proportions here:https://brainly.com/question/34018947
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