Answer:
Solution of the equation 4x + 5 = 3x + 4 is:
x= -1
Step-by-step explanation:
We are given a equation:
4x + 5 = 3x + 4
We have to solve the equation for x
4x+5=3x+4
subtracting both sides by 4
4x+5-4=3x+4-4
4x+1=3x
subtracting both sides by 4x
4x|+1-4x=3x-4x
1= -x
⇒ x= -1
Hence, solution of the equation 4x + 5 = 3x + 4 is:
x= -1
At a physics convention, 10 companies set up equal sized square booths in a row along one wall of the convention center. The booths are adjacent to each other and a 4-ft wide walkway surrounds the block of booths on three sides. The total area of the booths and walkway is 2300 ft2. What is the side length of each booth?
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Which statement is true about the equation 3/4 z = 1/4 z - 3 + 5?
It has no solution.
It has one solution
It has two solutions.
It has infinitely many solutions.
You are stacking books into a shipping box that is 15 inches high. Each book is 1.25 inches thick. How many books can you fit in a stack?
Which is not a true statement
0.3711 >0.3801
Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit?
Answer:
Stock A: 1
Stock B: 1 and 2
Stock C: 1,7,4
Grace was given the description “three less than the quotient of a number squared and nine, increased by eight” and was asked to evaluate it when n = 6. Her work is shown below.
Step 1: mc021-1.jpg
Step 2: mc021-2.jpg
Step 3: mc021-3.jpg
Step 4: mc021-4.jpg
Step 5: 7
In which step did she make an error?
step 1
step 2
step 4
step 5
Grace made an error in Step 5 of evaluating the expression 'three less than the quotient of a number squared and nine, increased by eight' when n = 6. The correct evaluation should result in 12, not 7 as she calculated. Hence, the error is in Step 5, where she incorrectly concluded that the expression equals 7.
Explanation:The question asks us to identify the step at which Grace made an error in evaluating the expression given the description “three less than the quotient of a number squared and nine, increased by eight” when n = 6. Without seeing the exact steps Grace took, we can still solve the expression ourselves.
Firstly, let's translate the description into an algebraic expression using n as our number:
“Three less than the quotient of a number squared and nine” can be expressed as ((n^2)/9) - 3.
Then, we “increase by eight” to get the final expression: ((n^2)/9) - 3 + 8.
If n = 6, we substitute in the value to get: ((6^2)/9) - 3 + 8, which simplifies to (36/9) - 3 + 8 = 4 + 8 = 12.
Thus, the correct answer when evaluating the expression for n = 6 is 12. Grace's error appears to have occurred in Step 5, where she incorrectly evaluated the final sum as 7.
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5.
(05.03 MC)
Freddy reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
Which equation best models the relationship between x and y? (1 point)
y = –5x + 40
y = –40x + 280
y = –40x + 200
y = –5x + 200
Which of this is tru
Tony misplaced 7 stamps from his collection. He knows that each stamp of his worth $0.15 and that the total value of them is now only $5.55. write an -EQUATION- to determine the number of stamps (s) that tony originally had.
P = KT/V solve for k
we have
[tex]P=\frac{KT}{V}[/tex]
Solve for K means clear the variable K
so
Multiply both sides by [tex]V[/tex]
[tex]PV=V\frac{KT}{V}[/tex]
[tex]PV=KT[/tex]
Divide both sides by [tex]T[/tex]
[tex]PV/T=KT/T[/tex]
[tex]K=PV/T[/tex]
therefore
the answer is
[tex]K=PV/T[/tex]
Ankur estimated the quotient of 15 1/3 divided by (-4 2/3) to be 3. Which best describes his error?
Answer:
the anwser is b hope it helped
-1 = n+5 what does n equal to
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Match the graph with the correct equation.
y – 5= –(x + 3)
y – 3 = –(x + 5)
y – 3 = (x + 5)
y + 3 = –(x + 5)
Answer: The correct option is (B) [tex]y-3=-(x+5).[/tex]
Step-by-step explanation: We are given to match the graph shown with the correct equation.
From the graph, we note that
(-5, 3) and (0, -2) are two points that lie on the line graph.
So, the slope of the given graph is
[tex]m=\dfrac{-2-3}{0-(-5)}\\\\\\\Rightarrow m=\dfrac{-5}{5}\\\\\Rightarrow m=-1.[/tex]
Since the point (-5, 3) lies on the line, so its equation in point-slope form will be
[tex]y-3=m(x-(-5))\\\\\Rightarrow y-3=-(x+5).[/tex]
Thus, option (B) is CORRECT.
Which of these shows 7 + 2y rewritten using the commutative property of addition?
7y + 2
2y + 7
7 − 2y
2y − 7
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What is the value of x in the equation −x = 6 − 4x + 18?
24
8
−8
−24
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
The correct answers about these solids are that:
The bases are congruent.The volume of the first solid is twice as much as the volume of the second solid. If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.What is a congruent baseThis is used to tell that the base of the triangles are the same and they have the same shape.
The volume of the first triangle is
[tex]2X^2h\\\\X^2h[/tex]is the volume of the second triangle.
The ratio is 2: 1
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Answer:
a, d, e
Step-by-step explanation:
3/8 of the people at a fun fair were children 3/4 of the remaining people were men there were 140 children than women how many people went to the funfair
A scale on a map says that 1 inch represents 60 miles. If the distance between two points on the map is 2 1/2 inches, how many miles are between the two points?
To find the number of miles between the two points, we need to calculate the distance represented by 2 1/2 inches on the map.
Given that the scale states 1 inch represents 60 miles, we can use this information to determine the distance in miles represented by each inch on the map. So, if 1 inch equals 60 miles, then we can write this as the ratio: 1 inch / 60 miles. To find the distance represented by 2 1/2 inches on the map, we can multiply the ratio by the number of inches: [tex](2 1/2 inches) × (1 inch / 60 miles)[/tex]. Simplifying this expression, we get: ([tex]5/2 inches) × (1 inch / 60 miles).[/tex]
Now, we can multiply the numerators and denominators together: [tex](5/2) × (1/60) = 5/120 = 1/24[/tex]. Therefore, [tex]2 1/2 i[/tex]nches on the map represents 1/24 of the actual distance between the two points. Now, to find the actual distance in miles, we can divide 60 miles (representing 1 inch on the map) by 24: 60 miles [tex]/ 24 = 2.5[/tex] miles. Thus, the two points on the map are approximately 2.5 miles apart from each other in actual distance.
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Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equiation to find the number of drinks she needs to sell to sell to earn $100
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Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
At the end of 3 month both have equal number of CDs i.e. 33
Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs.
Equation, is values of two expression that are equal.
Let x represent the number of months and y the number of CDs.
now
For Tom
Y = 30 + X
for Nita
Y = 18 + 5X
now solving both equation
30 + X = 18 + 5X
4X = 12
X = 3
for X = 3 y = 33
Thus At the end of 3 month both have equal number of CDs i.e. 33
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Two equations are shown: Equation A y = 4 over x + 3 Equation B y = −2x − 4 Which statement best compares the graphs of the two equations? Both are nonlinear. Both are linear. Equation A is nonlinear and Equation B is linear. Equation A is linear and Equation B is nonlinear.
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Answer:
The answer is C. Equation A is nonlinear and Equation B is linear.
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What is the degree measure of the supplement of the complement of a 42-degree angle?
Triangle xyz is reflected across the y axis and x = 4,-5 what are the coordinates of x
Answer:
[tex]\tilde{x}=(-4,-5)[/tex]
Step-by-step explanation:
When we reflect a point [tex]P=(p_x,p_y)[/tex] over the y-axis, it's reflected to the point [tex]\tilde{P}[/tex] with the same y-coordinate as P and whose x-coordinate is minus the x-coordinate of P, hence
[tex]\tilde{P}=(-p_x,p_y).[/tex]
Therefore, in our particular case the point x=(4,-5) is reflected to the point
[tex]\tilde{x}=(-4,-5).[/tex]
Two spheres of the same density have a ratio of 9 to 16 in surface area. If the small sphere weighs 15 kg, what does the large sphere weigh?
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The table shows the height of a plant as it grows.
a. Model the data with an equation.
b. Based on your model, predict the height of the plant at 12 months
1.If 70% is £14, what is the full cost
2.4 bags of cement do 18msquared, how many msquared can be done with 7 bags
3.5x+1=3
4.find the nthe term of this sequence 7,12,17,22,27
4.if t(n)=6n+2 what is the 3rd term
Is 5 3/7 real and irrational or real and rational?
A tree casts a shadow that is 18 feet in length. If the angle of elevation is 28 degrees, which of the following best represents the height of the tree?
to find the height
multiply the length of shadow by the tangent of the angle
18 * tan(28) =9.5708
the tree is around 9.6 feet tall
The angle of elevation is the angle at which the object is viewed from below. The height of the tree is 8,45feet
Angle of elevationThe angle of elevation is the angle at which the object is viewed from below.
If tree casts a shadow that is 18 feet in length at the angle of 28 degrees, the height is calculated as:
sin theta = opposite/hypotenuse
sin 28 = H/18
H = 18sin28
H = 8.45 feet
Hence the height of the tree is 8,45feet
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Translate the sentence into an inequality.
Six subtracted from b is at most 21.