In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.
You have:
available money = 40$
package cost = 8$
Then, you calculate the quotient between available money and package cost:
[tex]\frac{40}{8}=5[/tex]Hence, you can buy 5 packages of diapers with 40$
Two quarters of the basketball game are complete. Now it is half time. Explain how this could be
Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.
The entirety of a basketball game is composed by:
4 quarters.
Hence the mid-point of the game is calculated as follows:
0.5 x 4 quarters = 2 quarters.
This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.
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A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The c
at least 380 tons of regular-grade and 610 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 17 tons o
hour. The second mine produces 20 tons of regular-grade and 10 tons of low-grade ore per hour. The operating cost of the first mine is $
operating cost of the second mine is $28,000 per hour. The first mine can be operated no more than 40 hours a week, and the second ml
more than 27 hours a week. How many hours per week should each mine be operated to minimize the cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
Answer :
first mine : 40 hour(s)
Second mine : 7 hour(s)
The start of an arithmetic sequence is
17, 21, 25, 29,
21,
The rule for the sequence can be written in the form
In
= en + d, where c and d are numbers.
a) By first calculating the values of c and d, work out the rule
for the sequence.
b) What is the value of 211?
The equation of the sequence is xₙ = 4n + 17 and the 11th term is 61
The equation of the sequenceFrom the question, we have the sequence to be
17, 21, 25, 29, 21
The form of the sequence is given as
xₙ = cn + d
From the question, we have the first term to be 17
This means that
d = 17
So, we have
xₙ = cn + 17
When n = 1, we have x = 21
So, we have
21 = c + 17
Evaluate
c = 4
Substitute c = 4 in xₙ = cn + 17
xₙ = 4n + 17
The value of x₁₁This means that
n = 11
So, we have
x₁₁ = 4 * 11 + 17
Evaluate
x₁₁ = 61
Hence, the value is 61
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Which of these shapes are a trapezoid?
Answer: The Pink one
Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.
Use the graph of f(x) = √x to graph each function.
7. g(x)=√x- 4
8. g(x)=√x +3
9. g(x)=√x + 6 − 4
10. g(x)=√x - 7+3
Use the graph of f(x) = 1/x to graph each function.
11. g(x) = 1/x +4
12. g(x) = 1/x - 6
13. g(x) = 1/x-6 + 8
14. g(x) = 1/x+7 -4
the graphs are attached herewith , where the label of the graph are :
along X-axis: 1 square division = 10 units
along y-axis: 1 square division: 10 units
The problem we dealing with is related to manipulating graphs.For the question 7 to 10, the commonly given function is f(x)= √x, if the g(x) is nothing but the f(x-c) or f(x+c), so for the g(X) to be f(x-c), then a graph of that particular function turns to stretch downward whereas, for the f(x+c), it stretches upward.
So, for 7 g(x)=√x- 4 where -4 is c so the g(x) = f(x-c) so the point for the graphs will stretch downward compare to the pint of the functions f(x)= √x.
8. g(x)=√x +3
here g(x)= f(x+3), so the pints stretched upward
9. g(x)=√x + 6 − 4=√x + 2
here additional number for the points ar 2, as it positive one, so the point of the function g(x), stretches upward
10. g(x)=√x - 7+3=√x -4
here the c is -4, so the point of the g(x), stretches downward.
Same for the questions 11 to 14, the common function is f(x) = 1/x ,for which which g(x) = f(x-c) or f(x+c), for positive c , the graph stretches upward otherwise it moves downward
11. g(x) = 1/x +4
here the c is positive, the graph stretches upward for the g(x)
12. g(x) = 1/x - 6
here the c is negative, the graph stretches downward for the g(x)
13. g(x) = 1/x-6 + 8= 1/x+2
here the c is positive, the graph stretches upward for the g(x)
14. g(x) = 1/x+7 -4= 1/x+3
here the c is positive, the graph stretches upward for the g(x)
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Standard form 10x-7y=-3
Answer:
x= −3/10
y= 3/7
Step-by-step explanation:
In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
By using the linear equation y=3x we draw the graph for proportional relationship.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same
the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0).
By the definition of proportional relationship of graph, we can reduce relationship between the values on the x-coordinate and y-coordinate of the given graph
As they are proportional and represented by euation
y = 3x
Where, x represent the time and y represent the number of sit-ups.
Hence by using the linear equation y=3x we draw the graph for proportional relationship.
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Find the vertex of the function given below.
y = 2x² + 4x+1
A. (3,-4)
B. (-1,-1)
C. (1,7)
D. (-4,9)
The function has the vertex value of (-1, -1)
How to calculate the vertex of the function?From the question, the definition of the functuion is given as
y = 2x² + 4x + 1
Start by differentiating the function
This is done as follows
y' = 4x + 4
Next, we set the differentiated equation to 0
So, we have the following equation
4x + 4 = 0
This gives
4x = -4
Divide by 4
x = -1
Next, we substitute x = -1 in the given equation y = 2x² + 4x + 1
So, we have the following equation
y = 2(-1)² + 4(-1) + 1
Evaluate
y = -1
Recall that
x = -1 and y = -1
So, we have
(-1, -1)
Hence, the vertex of the function is (-1, -1)
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The vertex of the given function y = 2x² + 4x+1 is (-1, -1) which is the correct answer would be an option (B).
The function is below given by,
y = 2x² + 4x + 1
Differentiate with respect to x to get the derivative of the above function,
y' = dy/dx = d/dx (2x² + 4x + 1)
y' = 4x + 4
Equating the derivative of the function to zero
y' = 0
4x + 4 = 0
4x = -4
Divide by 4 into both sides of the equation,
x = -1
Substitute x = -1 in the given function y = 2x² + 4x + 1
y = 2(-1)² + 4(-1) + 1
y = 2(1) - 4 + 1
y = -1
Therefore, the vertex of the given function is (-1, -1).
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Cylon Raiders attack the Battlestar
Galactica at regular time intervals called
centons, that form three consecutive odd
Integers whose sum is 75. Find the number of
centons between each Cylon attack.
The number of centons between each Cylon attack are 21, 23 and 25.
What are the number of centons?An odd number is a number that is not perfectly divisible by 2. For example, 3 is an odd number because it is not perfectly divisible by 2.
A consecutive number is a number that follows each other on the number line. Consecutive odd numbers are odd numbers that follow each other on the number lines.
Let x represent the first odd number.
The next odd number : x + 2
The third odd number : x + 4
x + (x + 2) + (x + 4) = 75
Add similar numbers: 3x + 6 = 75
3x = 75 - 6
3x = 66
x = 21
The second numbers : 21+ 2 = 23
The third number = 21 + 4 = 25
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What is the value of p will the function be continuous?
The value of p that will guarantee the continuity of the function is given as follows:
p = 6.5.
What is the continuity concept?A function defined by f(x) is continuous at a point x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In the context of this problem, the continuity of the function will be guaranteed if the lateral limits at x = -1 are equal.
To the left of x = -1, the function is less than -1, hence the lateral limit is:
lim x -> -1^- f(x) = lim x -> -1 (-2x² - 8x + 3) = -2(-1)² - 8(-1) + 3 = 9.
To the right of -1, the function is greater than -1, hence the lateram limit is:
lim x -> -1^+ f(x) = lim x -> -1 (4x + 2p) = 4(-1) + 2p = -4 + 2p.
The lateral limits have to be equal for the function to be continuous, hence:
-4 + 2p = 9
2p = 13
p = 13/2
p = 6.5.
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What is the explination to the answer if I factor out the coefficient of 3/8d+3/4?
The fraction of coefficient factor out is 3/8.
What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals. The numerator and denominator of positive common fractions are natural numbers.
The given expression is , 3/8d+3/4
From this, we have to eliminate the fraction for that we have to make common denominators like that,3/8 d + (3 * 2) / (4 * 2)=> 3/8 d + 6/8
Next, take out the common value i.e, 3/8=> 3/8 ( d + 2)
Therefore, the coefficient factor out is 3/8.
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Answer the 3 question in the photo for EASY points ( 20 points )
HELP ME PLEASE! THIS IS URGENT!!
For what value of x will the line passing through the following pairs of points be veritcal? F(3-2x, 12) and G(x+9, 7)
By solving a linear equation, we will see that the points are vertical only if the value of x is -2.
For which value of x are the points vertical?
We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:
x₁ = x₂
y₁ ≠ y₂
In this case, the two points are:
F(3-2x, 12) and G(x+9, 7)
The y-component is different, so we only need to have:
3 - 2x = x + 9
This is a linear equation, below I will solve it:
3 - 2x = x + 9
3 - 9 = x + 2x
-6 = 3x
-6/3 = x
-2 =x
The points are vertical if x = -2.
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What is the lowest common multiple of six and nine
Answer: 18
Step-by-step explanation: it is the smallest one in both tables.
1x6=6 2x6=12 3x6=18
1x9=9 2x9=18
hope this helped
What is the
domain?
Help me plssss
Sandra is using the point-slope form y - y₁ = m(x-x₁) to graph the equation y+2=(x-3). She completed the following steps.
Step 1: Plot a point at (3, 2).
Step 2: Plot a point 5 units up and 4 units left from (3, 2), at (-1, 3).
Step 3: Connect the points with a line.
In which step did Sandra make her first mistake?
What mistake did Sandra make?
She make mistake in her first step. She plot a point at (3,2) instead of (3,−2).
Sandra is using the point-slope form [tex]y - y_{1} = m(x-x_{1})[/tex] to graph the equation [tex]y+2=(x-3)[/tex].
She completed the following steps.
1) Firstly she plot a point at (3,2)
2) Then she plot a point 5 units up and 4 units left from (3,2), at (−1,3).
3) Then she connect the points with a line.
She using the point slope for to graph the equation.
The point slope form is [tex]y - y_{1} = m(x-x_{1})[/tex].
The equation is [tex]y+2=(x-3)[/tex].
Now we compare the given equation to the point slope form.
After comparing we get
[tex]y_{1}[/tex] = -2 and [tex]x_{1}[/tex] = 3
So we have to plot a point at (3,-2) but she plot point at (3,2).
She make mistake in her first step.
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Ten years ago, Ade's age was half the age of his brother Femi. Today, Ade is 12 years old. How old is Femi now?
Answer: Femi is 14 years old
Step-by-step explanation: ten years ago ade was 2 and ade is half the age of Femi so that means Femi was 4 at that time since 2 is half of 4 and since he is 12 ten years later Femi is 14 ten years later.
What percentage of this shape is shaded?
36% of the shape is shaded in the given figure.
What is termed as the percentage?The term percent is derived from the Latin texts per centum, which means "by the hundred," so a percent indicates however many parts you possess out of a total of 100. Percentages can be expressed as fractions as well as decimals. Simply divide a percentage by 100 to get a fraction. Percentages are simple to calculate if you have exactly 100 items, but it is uncommon for the quantity of an item to be exactly 100.For the given question.
The shape of the boxes with some shaded part is given.
The total number of small parts in the figure is 25.
The total of shaded parts is 9.
Let 'x' be the percentage of shaded region.
Then,
x% of 25 = 9
25x/100 = 9
x = 900/25
x = 36%
Thus, the shaded percentage is found as 36%.
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Ryan has a deck that measures 3 feet by 8 feet. He wants to increase each dimension
by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
The dimensions of the deck would be increased by 1 feet.
How much should he increase each dimension?Area of a rectangle = length x width
Initial area of the deck = 3 x 8 = 24 feet²
Area of the deck when it is increased = (1 + 0.50) x 24 = 36 feet²
Length of the deck after it is increased = 3 + x
Width of the deck after it is increased = 8+ x
Area of the new deck : (3 + x) + (8 + x) = 36
24 + 3x + 8x + x² = 36
x² + 8x + 3x + 24 - 36 = 0
x² + 11x - 12 = 0
The solutions of the quadratic equation are -1 and 12
-1 + x = 0
x = 1
or
12 + x = 0
x = -12
Thus, the dimension of the deck would be increase by 1 feet.
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please help me on thisss
Answer: The first one
Step-by-step explanation:
(Inv. 1)*30. Multiple Choice Tika's math class began 18 minutes ago. Theclass will end in 37 minutes. Which equation can be used to find thelength in minutes of Tika's math class?A 18 + m = 37Bm – 37 = 18C 37 - m = 18D 18 – m = 37
Step 1
Let the length in minutes of Tika's class be m
His class had lasted already for 18 minutes
His class had 37 more minutes to end.
Step 2
Get the equation
[tex]\begin{gathered} 18\text{ + 37 = m} \\ To\text{ suit the options} \\ 18\text{ = m-37} \\ \text{Therefore,} \\ m-37\text{ = 18} \end{gathered}[/tex]Hence the answer is option B ------ ( m - 37 = 18)
A string measures 30 cm about how many lnches long is the string
A bear cub weighs 8,800 grams in
March. After three months, it weighs
68.2 kg. How much weight did the cub
gain during the three months?
Answer:33 oz in march
Step-by-step explanation:
without graphing f(x) = 3x - 1.3, determine if the graph goes through each point (1/3, -0.3). Answer quick i will give brainliest
Answer:
Yes, it does.
Step-by-step explanation:
The most appropriate choice for function and graph of a function will be given by-
The graph passes through [tex](\frac{1}{3}, -0.3)[/tex]
What is function and graph of a function?
A function from A to B is a rule that maps to each elements of A, a unique element of B.
A is the domain of the function and B is the co-domain of the function.
A collection of all points of the form [tex](x, f(x))[/tex] is called graph of the function.
Here,
[tex]f(x) = 3x - 1.3[/tex]
Putting [tex]x = \frac{1}{3}[/tex]
[tex]f(\frac{1}{3}) = 3 \times \frac{1}{3} -1.3\\[/tex]
[tex]= 1-1.3\\[/tex]
[tex]= -0.3[/tex]
So, the graph passes through [tex](\frac{1}{3}, -0.3)[/tex]
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60 cents as percent of $3
60 cents is 20% of $3.
What is the percentage?In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."
Given Data
60 cents as a percent of $3
1 dollar = 100 cents
$3 dollar = 300 cents
Percentage:
[tex]\frac{Value}{Total value}[/tex] × 100
[tex]\frac{60}{300}[/tex] ×100
20%
60 cents in 20% of $3.
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The complete question is:
"60 cents is what percent of $3."
Write the slope-intercept form of the equation of the line through the given point with the given
slope.
through: (4, -1), slope = -1/2
Answer: y=-1/2x+1
Step-by-step explanation: plug in numbers to find y intercept (b).
-1=-1/2(4)+b
-1=-2+b
b=1
y=-1/2x+1
help me with this please!!
y -intercept #4 the starting value
(1 , 7.5) #3 the value after 1 year
because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.
Solve the equation for the given variable. (type "no solution" if the equation has no solution and type "all
real numbers" if the equation is valid for all possible x-values)
4(4x + 2) + 2(9x + 4) + 3 = 34x + 19
Answer:
all real numbers
Step-by-step explanation:
4(4x+2)+2(9x+4)+3=34x+19
16x+8+18x+8+3=34x+19
34x+19=34x+19
all real numbers
:]
A soap company wants to use a cylindrical container to hold their new liquid soap
A. solve the formula for h
B. what is the height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches? Round to the nearest tenth
A. The formula for h is h = V / πr².
B. The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches is 8 inches.
How to calculate the value?The volume of a cylinder is calculated thus:
= πr²h.
where π = 3.142
r = radius
h = height
Therefore, the height will be:
V = πr²h
We have to make h the subject of the formula. This will be:
h = V / πr²
The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches will be:
h = V / πr²
h = 56.52 / (3.142 × 1.5²)
h = 56.52 / 7.0695
h = 8
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-5w/9 = 30 solve for w and simplify your answer as much as possible
After simplification of the given expression -5w /9 =30 , value of w is equal to -54.
As given in the question,
Given expression is equal to :
-5w / 9 = 30
Simplification of the given expression to get the value of w is :
-5w / 9 = 30
Multiply both the side of the given expression by 9 we get ,
-5w = 30 × 9
Divide both the side of the given expression by -5 we get,
-5w /-5 = ( 30 × 9 ) / -5
⇒ w = -(6 × 9 )
⇒ w = -54
Therefore, after simplification of the given expression -5w /9 =30 , value of w is equal to -54.
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