There is no such vector-valued function r(t) that satisfies the given condition.
I. There is no such vector ū that satisfies u + ū = (1, 2) because if we add any vector to u, we change its direction and magnitude, but the vector ū should have the same magnitude and opposite direction to u.
II. Let v = (1, 3, -1). Then u + v = (2+1, 1+3, 3-1) = (3, 4, 2) and u x v = (-5, 7, -1). So u x v = u + v. Therefore, v satisfies the given condition.
III. There is no such vector-valued function r(t) because if r(t) = (x(t), y(t)) satisfies the condition that r'(t) = 2r(t), then we have:
x'(t) = 2x(t) and y'(t) = 2y(t)
These are two separate first-order differential equations, which have general solutions of the form:
x(t) = c1e^(2t) and y(t) = c2e^(2t)
where c1 and c2 are constants determined by the initial conditions. However, the vector-valued function r(t) = (x(t), y(t)) cannot have a constant magnitude because its components are functions of t that grow exponentially with time. Therefore, there is no such vector-valued function r(t) that satisfies the given condition.
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HELP ASAP 20 POINTS 7th grade math
a) The probability of picking a blue tile = 1/5
b) The probability of picking a yellow tile = 1/2
c) The probability of picking a red tile = 3/10
Given data ,
Let the total number of tiles in the bag = 10 tiles
The number of blue tiles = 2
The number of red tiles = 3
The number of yellow tiles = 5
So , probability of picking a blue tile = 2/10 = 1/5
Now , probability of picking a yellow tile = 5 / 10 = 1/2
And , probability of picking a red tile = 3/10
Hence , the probability is solved
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Seven cousins will devide the contents of a box of popcorn among them. If the box contains 43.75 ounces of popcorn how many ounces of popcorn will each cousins get
Answer: 6.25
Step-by-step explanation:
You have to divided 43.75 ounces by 7 which equals 6.25
Nathaniel kicks a football. The graph below shows the height of the football h
in meters after t seconds. After how many seconds does the football hit the
ground?
The number of seconds where the football hit the ground is 2 seconds
After how many seconds does the football hit the groundFrom the question, we have the following parameters that can be used in our computation:
The graph
The number of seconds where the football hit the ground is when the graph intersects with the x-axis at the second time
In this case, the point is (2, 0)
Also, the seconds is represented by x
So, we have
x = 2
Hence, the seconds the football hits the ground is 2
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After selling some old books and toys, Gwen and her brother Max had 5 one-dollar bills, 6 quarters, and 8 dimes.
Part A:
What is the total amount of money earned?
Part B:
Max and Gwen decide to divide the money equally. Max said that he and Gwen cannot get even amounts of money because 5 one-dollar bills cannot be divided evenly. Do you agree with Max? Explain.
a) The total amount of money earned is 7.30 dollars.
b) Max is wrong, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.
a) To find the total amount of money earned, we need to convert the number of quarters and dimes to dollars.
6 quarters = 6 * 0.25 = 1.50 dollars
8 dimes = 8 * 0.10 = 0.80 dollars
The total amount of money earned is:
5 dollars + 1.50 dollars + 0.80 dollars = 7.30 dollars
b) Max is incorrect. The total amount of money earned is an odd number ($7.30), which means it is impossible to divide it equally between two people in whole dollar amounts. However, it is possible to divide the total amount equally if we allow for fractions of a dollar.
For example, if we split the money equally, Gwen and Max would each get $3.65. This means that Gwen would get 3 dollars and 65 cents, while Max would also get 3 dollars and 65 cents.
Therefore, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.
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[tex]\frac{1}{4} x \frac{25}{25} =[/tex]
The value of the product is 1/4
How to determine the productTo determine the value of the product, we need to take note that fractions are described as the part of a whole number, element, or variable.
In mathematics, there are different types of fractions, namely;
Simple fractionsComplex fractionsImproper fractionsProper fractionsMixed fractionsFrom the information given, we have that;
1/4 × 25/25
Now, multiply the numerators
25/4(25)
Multiply the denominators
25/100
Divide the values
1/4
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Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.Dkf(x, y, z) = fz(x, y, z)
Therefore, the statement is false in general, and the equality Dkf(x, y, z) = fz(x, y, z) holds only when k = z.
The symbol Dk denotes the k-th partial derivative with respect to the variable k, so Dkf(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable k.
On the other hand, fz(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable z.
These two partial derivatives are generally not equal. For example, consider the function f(x, y, z) = x² + y² + z². Then:
Dxf(x, y, z) = 2x
Dyf(x, y, z) = 2y
Dzf(x, y, z) = 2z
In this case, we have Dzf(x, y, z) = fz(x, y, z) = 2z, so the statement is true when k = z.
However, if we consider k = x or k = y, then the statement is false in general. For example, when k = x, we have:
Dkf(x, y, z) = Dxf(x, y, z) = 2x
fz(x, y, z) = partial derivative of f with respect to z = 2z
Since 2x is generally not equal to 2z, the statement is false when k = x.
Similarly, the statement is false when k = y, because Dyf(x, y, z) is generally not equal to fz(x, y, z).
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²
The standard form for finding the equation of a circle is expressed as;
(x-a)² + (y-b)²=r²
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following diameter = 12 units
radius = 12/2 = 6 units
If the centre lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)² + (y-3)² = 6² equivalent to x²+ (y-3)² = 36
Hence, the equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²
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Graph the function below and identify the key characteristics. f(x)= 2√x+7 -1 y Domain: Range: End Behavior: As x→∞, f(x) →_ As x-00, f(x) →. Endpoint: Inc. Interval: Dec. Interval:
[tex]2 \sqrt{x + 7} - 1[/tex]
The key features of f(x) = 2√[x + 7] - 1 are
Domain: x ≥ -7Range: f(x) ≥ -1End behavior: As x ⇒ +∝, f(x) ⇒ +∝Identifying the key characteristicsFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2√[x + 7] - 1
The graph of the function is attached, where we have the following features
Domain: x ≥ -7Range: f(x) ≥ -1End behavior: As x ⇒ +∝, f(x) ⇒ +∝Read more about functions at
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If Z is a standard normal random variable, then P(-1.75 ZS -1.25) is: O a. 0.106 O b. 0.040 OC. 0.854 O d. 0.066
The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.
Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.
Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25
Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211
Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709
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pls help How is the equation of a hyperbola different from the equation of an ellipse?
Answer:
1) The sum of the distances between the points on the ellipse and the foci is constant, whereas the difference between the distances between the points on the hyperbola and the foci is constant.
2) The equation of an ellipse is in the form (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axes, respectively. In contrast, the equation of a hyperbola is in the form (x^2/a^2) - (y^2/b^2) = 1, where a and b are also the lengths of the semi-major and semi-minor axes, respectively, but the difference between a and b determines the shape of the hyperbola.
Step-by-step explanation:
Can someone help me asap? It’s due today!!
Answer:
D. There are no outliers
Step-by-step explanation:
So if you open your eyes and count the numbers you'll realize that 2 is in fact an outlier
if a = -2 and b = 3 what will be the value of b^a
Answer:
If a = -2 and b = 3, then b^a can be calculated as follows:
b^a = 3^(-2)
To find the value of 3^(-2), we can use the rule that says:
a^(-b) = 1 / a^(b)
Thus,
3^(-2) = 1 / 3^2 = 1 / 9
Therefore, the value of b^a, or 3^(-2) is 1/9.
Step-by-step explanation:
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums. Find the number of djembe drums you sold.
The number of djembe drum sold is 8
What is profit?Profit is the money you have left after paying for business expenses. This means after deducting the money of expenses from the selling price , the remainder is profit.
Therefore , profit = selling price - cost price
set of claves = $5
set of maracas = $14
a drum = $16
Selling price of drum = 16 × x =16x
selling price of claves = 6×5 = 30
selling price of maracas = 14 × 12 = 168
total selling price =$( 16x+30+168)
cost price = 326-( 16x+30+168)
Therefore,
326 = 16x+30+168-(326-16x-30-168)
326 = 16x +30+168-326+16x+30+168
326 = 32x+60+336-326
326+326-336-60 = 32x
32x = 256
divide both sides by 32
x = 256/32
x = 8
Therefore the number of drums sold is 8
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Which point justifies the shaded area by satisfying StartFraction (y + 1) squared Over 6 EndFraction minus StartFraction (x + 2) squared Over 24 EndFraction greater-than-or-equal-to 1?
(12, 6)
(–2, 6)
(8, –6)
(–1, –2)
Please help asap test is timed!
(–2, 6) are the points that justify the shaded area
We can substitute the values of x and y from each point into the inequality and check if the inequality is satisfied or not.
Let's check each point:
For points (12, 6):
[tex](y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (12+2)^2/24 \\= 49/6 - 196/3 \\= -57.33[/tex]
Here, the value of the expression is less than 1, so this point does not justify the shaded area.
For points (–2, 6):
[tex](y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (-2+2)^2/24 \\= 49/6[/tex]
Here, the value of the expression is greater than or equal to 1, so this point does justify the shaded area.
For points (8, –6):
[tex](y+1)^2/6 -(x+2)^2/24 \\= (-6+1)^2/6 - (8+2)^2/24 \\= 25/6-100/24[/tex]
Here, the value of the expression is greater than or equal to 1, so this point does not justify the shaded area.
For point (–1, –2):
[tex](y+1)^2/6 -(x+2)^2/24 \\= (-2+1)^2/6 - (-1+2)^2/24 \\= 1/6 - 1/24 \\= 1/8[/tex]
Here, the value of the expression is less than 1, so this point does not justify the shaded area.
Therefore, the points that justify the shaded area are (–2, 6).
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Identify the prime numbers in the following lists. a. 5, 7, 12, 11b. 14, 6, 3c. 31, 17, 9, 15d. 782, 61, 2
a. The prime numbers in this list are 5 and 7. b. There are no prime numbers in this list. c. The prime numbers in this list are 31 and 17. d. The prime numbers in this list are 61 and 2.
a. In the list 5, 7, 12, 11, the prime numbers are 5, 7, and 11. Prime numbers are numbers greater than 1 that have only two factors, 1 and themselves.
b. In the list 14, 6, 3, the prime number is 3. The other numbers have more than two factors, making them not prime.
c. In the list 31, 17, 9, 15, the prime numbers are 31 and 17. The numbers 9 and 15 have more than two factors, so they are not prime.
d. In the list 782, 61, 2, the prime numbers are 61 and 2. Number 2 is the smallest prime number, and 61 has only two factors, 1 and 61. The number 782 has more than two factors, so it is not prime.
To summarize, the prime numbers in each list are: a. 5, 7, 11; b. 3; c. 31, 17; d. 61, 2.
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the sanders garden shop mixes two types of grass seed into a blend. each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. type a seed costs $1 and type b seed costs $2. if the blend needs to score at least 300 points for shade tolerance, 400 points for traffic, and 750 points for drought resistance, how many pounds of each seed should be in the blend?
1. Shade Tolerance: The blend needs to score at least 300 points for shade tolerance.
Total: x * Shade Tolerance points + y * Shade Tolerance points ≥ 300
2. Traffic: The blend needs to score at least 400 points for traffic.
Total: x * Traffic points + y * Traffic points ≥ 400
3. Drought Resistance: The blend needs to score at least 750 points for drought resistance.
Total: x * Drought Resistance points + y * Drought Resistance points ≥ 750
To determine the number of pounds of each seed that should be in the blend, we need to use a system of equations. Let x be the number of pounds of type A seed and y be the number of pounds of type B seed in the blend.
The shade tolerance score for the blend can be expressed as:
x(80) + y(200) ≥ 300
The traffic score for the blend can be expressed as:
x(120) + y(100) ≥ 400
The drought resistance score for the blend can be expressed as:
x(200) + y(150) ≥ 750
We also know that the total amount of seed in the blend is x + y.
We want to minimize the costs of the blend, so we can set up the following equation for the total cost:
1x + 2y = Total cost
Now we can solve this system of equations using any method we prefer. One common method is to use substitution.
First, we can use the shade tolerance equation to solve for y in terms of x:
y ≥ (300 - 80x)/200
Next, we can substitute this expression for y in the traffic equation:
x(120) + ((300 - 80x)/200)(100) ≥ 400
Simplifying and solving for x, we get:
x ≥ 1.5
So the minimum amount of type A seed needed in the blend is 1.5 pounds. We can use this value to solve for y:
y ≥ (300 - 80(1.5))/200 = 1.05
So the minimum amount of type B seed needed in the blend is 1.05 pounds.
Since we want to minimize costs, we want to use the minimum amount of each seed necessary to meet the requirements. Therefore, we should use 1.5 pounds of type A seed and 1.05 pounds of type B seed in the blend.
We need the values for Shade Tolerance, Traffic, and Drought Resistance points for both Type A and Type B seeds to set up the inequalities. Please provide the points for each seed type, and I can help you determine the number of pounds needed for each seed in the blend.
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How many seconds are equal to 1 minutes
Answer: 60 seconds
Step-by-step explanation:
Answer:
Step-by-step explanation:
60 seconds
lori took a trip during her recent trip to NYC. They charged a flat rate of $2.50, plus an additional $3.00 per mile. Lori only has $20
A right rectangular prism is sliced in a way such that the plane passes through three intersecting edges, cutting off a corner of the prism, what is the resulting cross section?
When a right rectangular prism is sliced in a way that the plane passes through three intersecting edges, cutting off a corner of the prism, the resulting cross section is a triangle.
Imagine a rectangular prism with the vertices A, B, C, D and H in order to understand this. Assume that the edges AE, and AG are crossed by the plane as it cuts off the corner indicated by vertex A. The triangle formed by the intersection of the plane and the prism will therefore have vertices at positions EFG.
The resulting cross section is a triangle EFG, which is a part of the original rectangular prism. The shape and size of the triangle will depend on the dimensions and orientation of the prism, as well as the specific location where the plane intersects the edges.
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not rushing anyone but if someone wants to help rq thatd be great
a. The solution to the equation f - 13 = 51 is f = 64.
b. The solution to the equation x/10 = 4 is x = 40.
a. f - 13 = 51
Step 1: Add 13 to both sides to isolate f.
f - 13 + 13 = 51 + 13
Step 2: Simplify.
f = 64
Step 3: Check the answer by substituting f = 64 back into the original equation.
64 - 13 = 51
51 = 51
The answer checks out.
b. (x/10) = 4
Step 1: Multiply both sides by 10 to isolate x.
10(x/10) = 4(10)
Step 2: Simplify.
x = 40
Step 3: Check the answer by substituting x = 40 back into the original equation.
40/10 = 4
4 = 4
The answer checks out.
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Are the data shown in this line plot skewed left, skewed right, or not skewed?
Responses
skewed left
not skewed
skewed right
The data plot in the line plot are skewed right
Given data ,
Let the data be shown in the graph be a line plot
Now , A line plot, also known as a dot plot, is a graphical representation of data where data points are shown as dots along a number line.
A right-skewed line plot would have more dots towards the lower end of the number line, with fewer dots towards the higher end.
From the line plot , we can see that most data points are placed on the lower end of the line plot
Hence , the data is skewed right
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what is the nature of the roots? Discriminant:81
The nature of the roots of a quadratic equation in which case, the discriminant is; 81 is; The roots are 2 distinct real roots.
What is the nature of the roots given a discriminant of 81?It follows from the task content that the nature of the roots of a quadratic equation in which case, the discriminant is 81 is to be determined.
Recall; when the discriminant of a quadratic equation is greater than 0; the equation is said to have two real distinct roots.
Ultimately, for the given equation in discuss whose discriminant is 81 is such that; it has two real distinct roots.
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A planet travels 5.782× 10⁸ km in its orbit each day .How far will it travel in 800 years ? Use 1 year ≈ 365.25 days.
Step-by-step explanation:
this is just plain multiplication.
we know how far it travels on one day.
that multiplied by 365.25 is his fast it travels in one year.
that multiplied by 800 gives us how fast it travels in 800 years.
5.782 × 10⁸ × 365.25 × 800 = 5.782×365.25×800 × 10⁸ =
= 1,689,500.4 × 10⁸ = 1.6895004 × 10¹⁴ km
what do we mean when we use the term "variable" in statistics
In statistical analysis, variables are often used to describe and explain relationships between different variables or to predict outcomes based on certain variables.
In statistics, a variable is a characteristic or attribute that can take on different values or levels for different individuals or objects being studied. Variables can be classified as either quantitative or qualitative.
Quantitative variables are numerical in nature and can be further classified as discrete or continuous. Discrete variables can only take on specific values (such as the number of children in a family), while continuous variables can take on any value within a certain range (such as a person's height or weight).
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In a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within her jurisdiction. The assessor suspects that important variables affecting selling price (Y, measured in thousands of dollars) are the size of a house (X1, measured in hundreds of square feet), the total number of rooms (X2), age (X3), and whether or not the house has an attached garage (X4, No = 0, Yes 1). = Y = a + B1X1 + B2X2 + B3X3 + B4X4 + € = = = = -8.962, Now suppose that the estimate of the model produces following results: a = 182.550, bi = 4.067, b2 3.422, b3 0.019, b4 : 0.571, Sb2 = 3.225, Sb3 = 0.432, S14 = 7.302, R2 = 0.946, F-statistic = 43.61, and se = 7.923. Note that the sample consists of 15 randomly Sbl = = selected observations. According to the estimated model, holding all else constant, an additional year in age means the market value by approximately Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining the market value of residential property? Check all that apply. Size of the house (X1) Total number of rooms (X2) O Age (X3) Having an attached garage (X4) What proportion of the total variation in sales is explained by the regression equation? O 0.432 O 0.436 O 0.946 reject the null hypothesis that neither of the independent variables explains a significant (at The given F-value shows that the assessor the 0.05 level) proportion of the variation in income. Which of the following is an approximate 95 percent prediction interval for the selling price of a 15-year-old house having 16.00 hundred sq. ft., 3 rooms, and an attached garage? O (212.833, 244.525) O (233.365, 265.057) O (220.756, 236.602)
Previous question
According to the estimated model, holding all else constant, an additional year in age means the market value decreases by approximately $190 (0.019 x 1000).
The size of the house (X1) and the total number of rooms (X2) appear to be statistically significant (at the 0.05 level) in explaining the market value of residential property.
The proportion of the total variation in sales explained by the regression equation is 0.946.
The given F-value shows that the assessor can reject the null hypothesis that neither of the independent variables explains a significant (at the 0.05 level) proportion of the variation in income.
An approximate 95 percent prediction interval for the selling price of a 15-year-old house having 16.00 hundred sq. ft., 3 rooms, and an attached garage is (212.833, 244.525).
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please and thank you
1.) The probability that the spinner will land on C would be = 1/8
2.) The probability of not spinning on C would be = 7/8
How to calculate the probability of the given event?To calculate the probability the formula that should be used would be as follows;
Probability = possible outcome/sample space.
For question 1.)
sample space = 8
possible outcome = 1
probability = 1/8
For question 2.)
sample space = 8
possible outcome = 7
probability = 7/8
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You will construct the incenter. You will need to construct the angle bisectors of
To construct the incenter of a triangle, construct the angle bisectors of each angle of the triangle. Here are the steps to construct the incenter of a triangle:
Draw the three sides of the triangle using a straightedge.
Choose one of the angles of the triangle and draw its bisector. To do this, place the point of your compass on the vertex of the angle, and draw an arc that intersects both sides of the angle. Without changing the width of your compass, place it on each of the two points where the arc intersects the sides of the angle, and draw two more arcs that intersect. The point where these two arcs intersect is the point where the angle bisector meets the opposite side of the triangle.
Repeat step 2 for the other two angles of the triangle. You should now have three lines that intersect at a single point.
The point where all three angle bisectors intersect is the incenter of the triangle.
Note that the incenter of a triangle is the center of the circle that can be inscribed inside the triangle.
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The derivation of the Quadratic Formula is shown by completing the square and applying square roots. What is the missing step?
A. x^2+b/a · x+c=0
B. ax^2+b/a · x+c/a=0
C. ax^2+b/a · x+c=0
D. x^2+b/a · x+c/a=0
Answer: x^2 + bx/a + c/a = 0
Step-by-step explanation:
the step simplifies the division of a:
0 divided by anything is still zero, so you can remove the a denominator
a/a = 1, and is therefore irrelevant, so ax^2 / a = x^2
the rest can stay
PLEASE HELP!!! (LOOK AT THE PICTURE)
Answer:
1.4
Step-by-step explanation:
Question 2 (Essay Worth 10 points)
(01.02, 01.03 MC)
Part A: Maci made $300 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $60 in tips. Write an equation
to represent this situation and solve the equation to determine how many appointments Maci had. (5 points)
Part B: Logan made a profit of $350 as a mobile groomer. He charged $55 per appointment and received $35 in tips, but also had to pay a rental fee for the truck of
$10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had. (5 points)
Answer:
Part A: 4
Part B: 7
Step-by-step explanation:
Part A:
60x + 60 = 300
60x = 240
x = 4
Part B:
55x - 10x = 350
45x = 350
x = 7