Question:
Given f(x) = 3x-1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
Answer:
The value of x is 4 for g(x) = f(2)
Solution:
Given that,
[tex]f(x) = 3x-1\\\\g(x) = 2x - 3[/tex]
We have to find the value of "x" such that g(x) = f(2)
Let us first find f(2)
Substitute x = 2 in f(x) function
[tex]f(x) = 3x-1\\\\f(2) = 3(2) - 1\\\\f(2) = 6 - 1 = 5[/tex]
Thus f(2) is 5
Now find: g(x) = f(2)
Equate given function of g(x) and f(2) which is found to be 5
[tex]g(x) = f(2)\\\\2x - 3 = 5\\\\\text{Move the constants to other side }\\\\2x = 5 + 3\\\\2x = 8\\\\\text{Divide both sides of equation by 4 }\\\\x = 4[/tex]
Thus for x = 4 , we get g(x) = f(2)
Roman purchased 2 1/2 pounds of
chocolate covered peanuts for $9.75.
What was the price per
pound?
Answer:
$3.90 is the answer.
Step-by-step explanation:
9.75 ÷ 2.5 = 39/10 (3.9).
To check do 3.9 × 2.5 = 9.75.
Final answer:
To determine the price per pound of chocolate covered peanuts, divide the total cost ($9.75) by the total weight (2.5 pounds), resulting in $3.90 per pound.
Explanation:
The question asks to calculate the price per pound of chocolate covered peanuts Roman purchased.
Here is a step-by-step explanation:
First, it is important to take note of the total weight of the chocolate covered peanuts, which is 2 1/2 pounds or 2.5 pounds.
Next, we look at the total price paid for the 2.5 pounds, which is $9.75.
To find the price per pound, divide the total price by the total weight: $9.75 ÷ 2.5 pounds.
The price per pound turns out to be $3.90.
Therefore, the price per pound of the chocolate covered peanuts is $3.90.
how to solve 5×743=(_×700)+(_×40)+(_×3)
Answer:
Step-by-step explanation:
5*743=(5*700)+(5*40)+(5*3)
Four tomatoes cost $3.40. What is the unit rate?
Answer:
$0.85 per tomato
Step-by-step explanation:
A unit rate is the cost for one item. Like $0.99 for this one bag of skittles.
So $3.40 divided by four is $0.85.
The unit rate would be 0.85. If you divide 3.40 by 4 you 0.85
Which function represents g(x), a reflection of f(x)=4(1/2)^x
across the x-axis?
Answer:
[tex]g(x)=-4(\frac{1}{2})^x[/tex]
Step-by-step explanation:
Given:
The parent function is given as:
[tex]f(x)=4(\frac{1}{2})^x[/tex]
The function [tex]g(x)[/tex] is a reflection of the parent function about the x-axis.
Now, in order to find the function g(x), we need to use the rules of function transformations.
As per transformation rules, when a function is reflected about the x-axis, the function rule is given as:
[tex]f(x)\to-f(x)[/tex]
So, the new function or the reflected function is the negative of the original function.
Therefore, the reflected function [tex]g(x)[/tex] is given as:
[tex]g(x)=-f(x)\\\\g(x)=-4(\frac{1}{2})^x[/tex]
Hence, the function that represents the reflection of the given function across the x-axis is [tex]g(x)=-4(\frac{1}{2})^x[/tex]
What is the value of log5^{125}?
The value of [tex]\log_5{125}[/tex] is 3.
Solution:
Step 1: Given expression is [tex]log_5{125}[/tex].
125 can be expressed as [tex]5^3.[/tex]
[tex]\log_5{125}=\log_5{5}^3[/tex]
Step 2: Using log rule: [tex]\log_a{x^b}=b\log_a{x}[/tex]
[tex]\log_5{5}^3=3\log_5{5}[/tex]
Step 3: Using log rule: [tex]\log_a{a}=1[/tex]
[tex]\log_5{5}= 1[/tex]
⇒ [tex]3\log_5{5}= 3(1)[/tex]
⇒ [tex]3\log_5{5}= 3[/tex]
∴ [tex]\log_5{125}=3[/tex]
Hence the value of [tex]\log_5{125}[/tex] is 3.
What is the distributive property to create an equivalent expression to 9x+21
Answer:
3(3x+7)
Step-by-step explanation:
9x+21=3(3x+7)
3 more than twice as many oranges equals 18
Answer:
15/2
Step-by-step explanation:
2x+3=18
2x=18-3
2x=15
x=15/2
wide all along its perimeter. What is an expression for
A portrait without its frame has a height 1.5 times its width w, in inches. Its frame is 2 in wide all along its perimeter what is an expression for
the area of the framed portrait in terms of w?
O A 1.5w2 + 5w + 4
B. 1.5w? + 8w + 8
C
1.5w2 + 8,5W + 16
O
D. 1.5w2 + 10w + 16
Answer:
1.5w² + 10w + 16 sq, inches.
Step-by-step explanation:
The height of the portrait without the frame is 1.5 times its width.
Let the height is 1.5w inches and width is w inches.
Now, the frame around the portrait is 2 inches wide.
So, the dimensions of the portrait with frame are (1.5w + 4) inches by (w + 4) inches.
Therefore, the area of the framed portrait will be
(1.5w + 4)(w + 4)
= 1.5w² + 10w + 16 sq, inches. (Answer)
at a currency exchange,8 u.s dollars can be exchanged for 6 euros. how many euros will you receive for 1 u.s dollar
You will receive 0.75 euros for 1 U.S dollar.
Explanation:In this currency exchange, you receive 6 euros for every 8 U.S dollars. To find out how many euros you will receive for 1 U.S dollar, you can set up a proportion.
Let x represent the number of euros you will receive for 1 U.S dollar. The proportion can be set up as follows: 8 U.S dollars / 6 euros = 1 U.S dollar / x euros.
Now, cross-multiply and solve for x: 8x = 6 * 1. Divide both sides by 8 to isolate x, and you will find that x = 0.75 euros.
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A jar contains 6 blue marbles, 4 yellow marbles, and 10 green marbles. What is the probability of randomly choosing a blue marble, replacing it, and then choosing a yellow marble?
Answer:4 out of 19
Step-by-step explanation:
you add them all and then say 4 because that is yellows amount of marbles
HELP!!! A cell phone is 132 mm long and 57 mm wide. What is ratio of the width and length in simplest form.
The ratio of width to length in simplest form is 19 : 44
Solution:
Given that, A cell phone is 132 mm long and 57 mm wide
Length of cell phone = 132 mm
Width of cell phone = 57 mm
We have to find the ratio of width and length in simplest form
[tex]\frac{Width}{Length} = \frac{57}{132}\\\\\text{Reduce to lowest terms }\\\\\frac{width}{length} = \frac{57 \div 3}{132 \div 3}\\\\\frac{Width}{Length} = \frac{19}{44}[/tex]
In ratio form, we know that,
[tex]\frac{a}{b} = a : b[/tex]
Writing in ratio form, we get
Width : length = 19 : 44
Thus the ratio of width to length in simplest form is 19 : 44
Help i don’t understand
Answer:
VERTICAL LINES
Step-by-step explanation:
Round 75,218 to the nearest thousand
75,000
Explanation:
The 200 would round down.The 18 would round down aswell.This results in getting the answer 75,000.
Answer:
The answer is 75,000
Step-by-step explanation:
To work this out you need to put a line after the thousand like this 75|218 Then if the numer after is 5 or above you round the number up eg 75|818 Would round to 76000
Which of the following is the best description for this pair of angles?
Answer:
Supplementary
Step-by-step explanation:
Supplementary angles add to 180 degrees.
Answer:
Supplementary
Step-by-step explanation:
VSW and TSW combine and make 180. Complementary is when they make up to 90
An exotic dancer pole is 16 feet tall. How tall would the pole be if 2 more poles were added on top?
Answer:48 feet
Step-by-step explanation:
16x3=48
Answer:38 feet tall
Step-by-step explanation:
3 1/3 of it is 10
Find the number
Answer:
3
Step-by-step explanation:
3 times 3 is 9
1/3 of 3 is 1
add them to get 10
Answer:
3
Step-by-step explanation:
[tex]3x \times \frac{1}{3} x = 10 \\ \frac{10}{3} x = 10 \\ 10x = 30 \\ x = 3[/tex]
x-wanted number
What is a point slope equation of the line with slope - 13 that goes through
the point (5,7)?
O A. y+7=-13(x+5)
O BY+5=-13(x+ 7)
OG 1-7=-13(x - 5)
O D. y-5=-13(x-7)
Answer:
C. y - 7 = -13(x - 5)
Step-by-step explanation:
The point-slope equation for a straight line is
y - y₁ = m(x - x₁)
where m is the slope and(x₁, y₁) is a point on the line.
If m = -13 and (5, 7) is the point, the equation is
y - 7 = -13(x - 5)
some of Helen's plants need water every day, some need water every other day,and others need water every third day. if she waters them all today, how many days will it be before she waters them all again
Answer:
6 days
Step-by-step explanation:
Answer:
Step-by-step explanation:
You have to find the Least common Multiple of 1,2,3
LCM (1,2,3) = 6
8 2/5 - 5 3/5 need help solving step by step
Answer: 2 and 4/5
Explanation: To subtract mixed numbers, first subtract the fractions. Notice here however that we have 2/5 - 3/5 which will give us a negative fraction. Since this will cause us a lot of trouble, instead, let's rewrite the first mixed number.
We can do this by thinking of 8 and 2/5 as 7 + 1 and 2/5 or 7 + 7/5 by changing 1 and 2/5 to the improper fraction 7/5. So 8 and 2/5 can be written as 7 and 7/5.
So we have 7 and 7/5 - 5 and 3/5.
Now, subtract the fractions. So we have 7/5 - 3/5 which is 4/5. Then subtract the whole numbers so we have 8 - 5 which is 2.
2 and 4/5 is in lowest terms so 8 and 2/5 - 5 and 3/5 is 2 and 4/5.
if angles of a triangle are 2 is to 3 is to 4 is to .find the value of each angle
Answer:
Angles of triangle are 40°,60° and 80°.
Step-by-step explanation:
Given:
if angles of a triangle are 2 is to 3 is to 4.
Let the common factor between the angles be 'x'.
So we can say that;
Angle 1 = [tex]2x[/tex]
Angle 2 = [tex]3x[/tex]
Angle 3 = [tex]4x[/tex]
We need to find the value of each angle.
Solution:
Now we know that;
"Sum of all angles of triangle is 180°."
framing in equation form we get;
[tex]Angle \ 1+Angle\ 2+Angle \ 3 =180[/tex]
Substituting the values we get;
[tex]2x+3x+4x=180\\\\9x=180[/tex]
Dividing both side by 9 we get;
[tex]\frac{9x}{9}=\frac{180}{9}\\\\x=20[/tex]
Angle 1 = [tex]2x=2\times20=40\°[/tex].
Angle 2 = [tex]3x=3\times20=60\°[/tex]
Angle 3 = [tex]4x=4\times20=80\°[/tex]
Hence Angles of triangle are 40°,60° and 80°.
The radius of a circle is 2 meters. What is the circle's circumference?
(Another part with the picture(Will give brainiest))
Answer:
C≈12.57
Step-by-step explanation:
The formula for circumference if 2(3.14) * r
The r represents the radius do you would just take 2 * 3.14 which is 6.28.
Next, you would take 6.28 * r (which is 2 meters) and you get 12.566, but if you're rounding it would be 12.57.
Make sure to label your answers
I hope this helped!
SOLVE THE EQUATION
10=8h
h=?
Answer: h = 1.25
Step-by-step explanation:
divide 10 by 8 to get 1.25 or 5/4
In this question, you're solving for h.
Solve for h:
10=8h
"h" can't have a number next to it, it has to be by itself, so divide both sides by 8
1.25 = h
Answer:
1.25 = h
Dedra is making headband to sell to her friends.Each headbands requires 1 7/8 feets fabric.If dedra plans to make 14 headbands than how much fabric will she need .
Answer:
26.25 feets
Step-by-step explanation:
Given:
Each headbands requires 1 7/8 feets fabric
Dedra has to make 14 headbands .
Question asked:
how much fabric will she need to make 14 headbands = ?
Solution:
By applying unitary method :
Length of fabric require to make a headband = [tex]1\frac{7}{8}[/tex]
= [tex]\frac{15}{8}[/tex]
Length of fabric require to make 14 headbands = [tex]14\times\frac{15}{8}[/tex]
= [tex]\frac{210}{8}[/tex]
= [tex]26.25 feets[/tex]
Therefore, Dedra needs 26.25 feets fabric to make 14 headbands.
Is a rectangle always a parallelogram?
Yes or No
Yes, a rectangle is always a parallelogram.
The answer is yes.
Rectangles are quadrilaterals with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal.
AB= 7x-6 BC= 12-2x B is the midpoint of AC. Find AB
Answer:
8
Step-by-step explanation:
set 7x-6 = 12-2x because midpoint segments are equal to each other than solve
9x-6=12
9x=18
x=2
then substitute in values.
B is the midpoint of AC. Using this information, we can set up an equation to solve for AB. After solving for x, we substitute the value back into the equation to find AB. The length of AB is 8 units.
Explanation:We are given that B is the midpoint of AC. This means that the lengths AB and BC are equal. We can set up an equation to solve for AB.
AB = BC
7x-6 = 12-2x
Now we can solve for x and then find AB.
Bring like terms together:
7x + 2x = 12 + 6
9x = 18
Divide both sides by 9:
x = 2
Now substitute the value of x back into the equation for AB:
AB = 7(2) - 6
AB = 14 - 6
AB = 8
Therefore, AB is equal to 8 units.
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8 less than 5 times a number
Answer:109
Step-by-step explanation:
The inequality obtained from the given statement; 8 less than 5 times a number is 8< 5x.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.
Such values are called solution to that equation or inequality.
A Set of such values is called solution set to the considered equation or inequality.
Given statement; 8 less than 5 times a number
We know that the 8 is less than 5 times a number So, we first put 8 <.
From the given, we have the value 5 being multiplied by a number, that number can be any variable unless that specifically state which variable to use.
Thus, the inequality;
8< 5x
Hence, The inequality obtained from the given statement; 8 less than 5 times a number is 8< 5x.
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Mr Miller drove 568 miles last week. This week he drove 308 miles on Tuesday and 97 miles on Wednesday. What was the number of miles he drove in these two weeks?
The number of miles Mr Miller drive was 973 miles.
Step-by-step explanation:
Given,
Miles driven on first week = 568 miles
Miles driven on Tuesday this week = 308 miles
Miles driven on Wednesday this week = 97 miles
Total miles driven = Miles in first week + Miles on Tuesday + Miles on Wednesday
Total miles driven = 568 + 308 + 97 = 973 miles
The number of miles Mr Miller drive was 973 miles.
Keywords: addition
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right triangle ABC has to legs of lengths 9 cm (AB) and 12 cm (AC). what is the length of the third side (BC)?
a. 6 cm
b. 8 cm
c. 14 cm
d. 15 cm
Answer:
D. 15 cm
Step-by-step explanation:
9² + 12² = x²
81 + 144 = x²
225 = x²
√225 = x
15 = x
2. What are the means of the following proportion?
3/15 = 12/60
A. 15 and 12
B. 3 and 15
C. 3 and 60
D. 12 and 60
Answer:
Step-by-step explanation:
A) 15 and 12
The following graph shows the solution to which system of inequalities?
Answer:
y ≤ 3x-4
-1 ≤ y ≤ 2
step by step explanation:
the highlighted area is situated under the line of equation y=3x-4 and respectivelybetween the two lines of equations y=-1 and y=2
Then the system of inequalities is :
y ≤ 3x-4
-1 ≤ y ≤ 2
Answer:
y ≤ 3x-4
-1 ≤ y ≤ 2