The rule of reflection for the points (x, y) for the graph is (y, - x).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The preimage of the given line has points(x, y), B(2, 3) and C(1, 6).
Now, The graph has been translated down 2 units and reflected 180° along the x-axis so the image of the graph has points(y, - x) B'(3, - 2) and C'(6, - 1).
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find the area of quadrilateral
Answer:
here is answer try this type
please help!! will do anything
Answer:
y = 41.51 mu = 27.89 mStep-by-step explanation:
Assumed it is similar triangles
Then the ratio of corresponding sides will be equal:
48/74 = y/64 = u/43Find missing sides by using the ratio:
y = 64*48/74 = 41.51 mu = 43*48/74 = 27.89 mSolve the inequality 4/3|1/4x+3|<4
Ox>-13 and x < -11
Ox<-13 and x > -11
Ox>-24 and x < 0
Ox>-24 and x > 0
The inequality 4/3|1/4x+3|<4 are Ox>-13 and x < -11 or Ox<-24 and x > 0
How do we determine the absolute values?We can begin by isolating the absolute value on one side of the inequality:
4/3|1/4x+3|<4
|1/4x+3|<3/2
We can then split this inequality into two cases, one for when 1/4x+3 is positive and one for when it is negative:
1/4x+3>0: 1/4x+3>3/2, so multiplying both sides by 4, we get x>-13 and x<-11
1/4x+3<0: 1/4x+3<-3/2, so multiplying both sides by -4, we get x<-24 and x>0
So, the solution is: Ox>-13 and x < -11 or Ox<-24 and x > 0
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The double number line shows that 42 people watched Deon's new video today.
People
Percentage
0
0
42
100
People
0%
Complete the table to show different percentages of the number of people who watched the
video.
42
100%
Percentage
100% of 42 people
50% of 42 people
150% of 42 people
The different percentages are, 42%, 21% and 63%.
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolize it.
There is no dimension to percentages. As a result, it is known as a dimensionless number. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Now, according to the given information, the double number line shows that 42 people watched Deon's new video today.
Now, we are to find,
100% of 42 people.
This is, (100/100)*42 = 42%.
Again, 50% of 42 people is,
(50/100)*42 = 21%.
Again, 150% of 42 people is,
(150/100)*42 = 63%.
Hence, the percentages are, 42%, 21% and 63%.
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Answer:
Answers are in the explaination.
Step-by-step explanation:
100% of 42 people answer is 42
50% of 42 people answer is 21
150% of 42 people answer is 63
Which of the following shapes is the cross-section for a cone?
O A. Pentagon
O B. Square
O C. Triangle
O D. Circle
Answer:
The choose (D)
D. Circle
I hope I helped you^_^
The required cross-section for a cone is a circle. Option D is correct.
What is a conic section?A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.
Here,
The cross-section of a cone is a circle.
A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.
Therefore, the correct answer is option D.
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Write and solve an equation to find the value of x.
THEN Using your answer, find the perimeter of the triangle.
Answer:
Perimeter of the triangle is 58
Step-by-step explanation:
create an equation
(x+3)2+(2x-1)2=(x-7)+(4x-8)+(3x+1)
2x+6+4x-2=x-7+4x-8+3x+1
combine like terms
6x+4=8x-14
18=2x
x=9
now we substitute in the expression to find the perimeter
9-7=2
36-8=28
27+1=28
2+28+28=30+28=58
What is the area of a circle to the nearest foot of the circumference of the circle is 8 ft ?
Answer:
16π ft²
Step-by-step explanation:
To calculate the area we require the radius.
Given circumference (C) = 8π , then
2πr = 8π ( divide both sides by 2π )
r = 4
Then area (A) is
A = πr² = π × 4² = 16π ft²
Write the quadratic function f(x) = x2 + 8x + 3 in vertex form.
find two possible functions f, given the second-order derivative. (enter your answers as a comma-separated list.) f ''(x)
The two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x.
The derivative of the first derivative of the given function is known as the second order derivative. We can learn about the slope of the tangent at a particular position or the instantaneous rate of change of a function at that point from the first-order derivative at that point.
F”(x)= x^2+6
F’(x)= \int f"(x) dx
= \int( x^2+6) dx
= \frac{x^3}{3}+6x+c_1 c_1 is the integral constant.
F(x)= \int f\prime(x) dx
= \int f (\frac{x^3}{3}+6x+c_1) dx
= \frac{x^4}{12}+3x^2+c_1x+c_2
(i) if c_1=0 , and c_2=0
F(x)= \frac{x^4}{12}+3x^2
(ii) if c_1=1, and c_2=0
F(x)= \frac{x^4}{12}+3x^2+x
Therefore the two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x
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The solutions of a quadratic equation are x=−7 and 5 . Which could represent the quadratic equation, and why? Responses
The quadratic equation x^2 + 2x - 35 = 0 represents the solutions x = -7 and 5.
To find the quadratic equation with the given solutions of x = -7 and 5, we can start by using the fact that the solutions of a quadratic equation can be written in the form:
(x - x1)(x - x2) = 0,
where x1 and x2 are the solutions. Substituting the given solutions, we have:
(x - (-7))(x - 5) = 0,
which simplifies to:
(x + 7)(x - 5) = 0.
Expanding this expression gives us the quadratic equation:
x^2 + 7x - 5x - 35 = 0,
x^2 + 2x - 35 = 0.
Therefore, the quadratic equation that represents the given solutions of x = -7 and 5 is x^2 + 2x - 35 = 0.
To confirm that this equation indeed has the given solutions, we can solve it. Using the quadratic formula, which states that for a quadratic equation ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation x^2 + 2x - 35 = 0, a = 1, b = 2, and c = -35. Plugging these values into the formula, we get:
x = (-2 ± √(2^2 - 4(1)(-35))) / (2(1)),
x = (-2 ± √(4 + 140)) / 2,
x = (-2 ± √144) / 2,
x = (-2 ± 12) / 2.
This simplifies to x = 5 or x = -7, which are the given solutions.
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1. Dei has $10 to spend on nail polish. With
tax each bottle costs $2.49. Can Dei buy 3
bottles of nail polish?
Answer:
Yes she can
Step-by-step explanation:
Answer:
yes it would be 7 dollars
If the matrix of coefficients of a system of n linear equations in n unknowns is singular, then the system has infinitely many solutions. (a) Always true (b) Sometimes true (c) Never true, (d) None of the above
A system of n number of linear equations in n unknowns has an many number of solutions if the coefficients of matrix is unique. The assertion is always accurate. The given statement is always true.
From the question, the given statement is:
A system of n linear equations in n unknowns has an endless number of solutions if the matrix of coefficients is unique. The assertion is always accurate.
The given statement is always true.
Consider the system of equations Ax = b. If A is single, there is no A-inverse. As a result, there is no one approach to solve the system. Then, there are still two options:
There are countless options.No answers.We can't tell which condition is right only examining the matrix [A b]. There exists an endless number of solutions if [A b] is equal to A's rank.
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Consider the graphs of the following lines.
3x - 5y = 2
3x + 5y = -2
Find the slope m of each line.
3x - 5y = 2
m₁ =
3x + 5y = -2
m2 =
8.6A.
4
Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.
What is slope of the line?The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as
Line slope is a measure of the steepness or direction of a line in the coordinate plane.
m = Δy/Δx
where,m is the slope
Given,
equations of the line
3x - 5y = 2
Moving 3x to RHS
-5y = -3x + 2
y = (3/5)x - 2/5
comparing with slope intercept equation of the line y = mx + c
slope m₁ = 3/5
Now, equation
3x + 5y = -2
moving 3x to RHS
5y = -3x - 2
y = (-3/5)x - 2
comparing with slope intercept equation of the line y = mx + c
slope m₂ = -3/5
Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.
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See attached picture, is there a way to enter equations or algebraic symbols?
SOLUTIONS
Solve a given equations or algebraic symbols?
\(\begin{gathered} f(x)=x^2+2x \\ g(x)=1-x^2 \end{gathered}\)(A)
\(\begin{gathered} (f+g)(x)=(x^2+2x)+(1-x^2) \\ collect\text{ like terms} \\ x^2-x^2+2x+1 \\ (f+g)(x^)=2x+1 \end{gathered}\)(B)
\(\begin{gathered} (f-g)(x)=(x^2+2x)-(1-x^2) \\ =x^2+2x-1+x^2 \\ =x^2+x^2+2x-1 \\ (f-g)(x)=2x^2+2x-1 \end{gathered}\)(C)
\(\begin{gathered} fg(x)=(x^2+2x)(1-x^2) \\ =x^2-x^4+2x-2x^3 \\ fg(x)=-x^4-2x^3+x^2+2x \end{gathered}\)(D)
\(\begin{gathered} \frac{f}{g}(x)=(x^2+2x)\div(1-x^2) \\ =\frac{x^2+2x}{1-x^2} \end{gathered}\)determine the mode(s) of the following data set, which represents the number of new seeds planted in the garden for 15 varieties of sunflower.
Based on the given data set, we can only determine a single mode, which is 4.
To determine the mode(s) of the given data set representing the number of new seeds planted in the garden for 15 varieties of sunflower, we need to find the value(s) that appear most frequently.
Here are the steps to find the mode(s):
1. Organize the data set in ascending or descending order to make it easier to identify repeated values. For example, let's say the data set is: 4, 5, 6, 2, 7, 4, 3, 5, 2, 4, 6, 4, 7, 3, 4.
2. Count the frequency of each value in the data set. In our example, we have:
- Value 2 appears 2 times.
- Value 3 appears 2 times.
- Value 4 appears 5 times.
- Value 5 appears 2 times.
- Value 6 appears 2 times.
- Value 7 appears 2 times.
3. Identify the value(s) with the highest frequency. In our example, the value 4 appears most frequently with a count of 5 times.
Therefore, the mode of the data set is 4, indicating that the number 4 is the most common value among the number of new seeds planted in the garden for the 15 varieties of sunflower.
It's important to note that in some cases, there may be multiple modes if two or more values have the same highest frequency.
However, based on the given data set, we can only determine a single mode, which is 4.
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Jack sketches ΔABC. The measure of angle B is 6 degrees less than twice the measure of angle A. The measure of angle C is 111°.
Which equation can be used to find the measure of Angle A? What is the measure of Angle A?
The equation that can be used to find the measure of Angle A is (b) a + 2a - 6 + 111 = 180, a = 25
Which equation can be used to find the measure of Angle A?From the question, we have the following parameters that can be used in our computation:
Angle B = 6 degrees less than twice the measure of angle A
Angle C = 111 degrees
These mean that
b = 2a - 6
c = 111
The sum of angles in a triangle is 180
So, we have
a + 2a - 6 + 111 = 180
What is the measure of Angle A?In (a), we have
a + 2a - 6 + 111 = 180
Evalate the like terms
3a = 75
So, we have
a = 25
Hence, the equation is a + 2a - 6 + 111 = 180
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Triangle ABC is a right triangle.What is the relationship between angles A and B?
Answer:
Step-by-step explanation:
They're congruent.
Determine all the values 1∧( sqrt. of 2). A. sin( sqrt. of 2kpi)+1cos (sqrt. of 2kpi) C. cos(2sqr. of 2kpi)+icos (sqrt. of 2kpi) B. cos( sqrt. of 2kpi)+isin (sqrt. of 2kpi ) D. cos (2sqrt. of 2kpi ) +isin(sqrt. of 2kpi ) 8. Evaluate cosh (i 4
π
). A. 1.414214∠270 ∘
B. 0.707107∠0 ∘
C. 1.414214∠180 ∘
D. 0.707107∠90 ∘
9. Determine the complex number equivalent to tanh( 4
π
) where pi=3.1416. A. 0.8660∠−90 ∘
B. 1.2246∠90 ∘
C. 1.142∠180 ∘
D. 0.70717∠0 ∘
10. Evaluate sinh(5+5j). A. 23.15−j78.28 B. 21.05−j71.16 C. 25.47−j64.69 D. 19.14−j86.11
The value of cosh (i4π ) A. 1.414214 or ∠270°.
The complex number equivalent to tan h ( 4π ) is D. 0.70717∠0°.
The value of sin h (5+5j) D. 19.14 −j86.11.
2. The hyperbolic cosine function, cosh(z), is defined
as\((e^z + e^{(-z))\)/2.
Substituting z = i x 4π:
So, cosh(i 4π) = \((e^{(i 4\pi)} + e^{(-i 4\pi)})\)/2.
Using Euler's formula, \(e^{(ix)\) = cos(x) + i sin(x):
cosh(4πi) = (cos(4π) + i sin(4π) + cos(-4π) + i sin(-4π))/2.
cosh(4πi) = (1 + i x 0 + 1 + ix 0)/2 = 2/2 = 1.
Therefore, the answer is A. 1.414214 or ∠270°.
9.The hyperbolic tangent function, tanh(z), is defined as
\((e^z + e^{(-z))\)/(\((e^z + e^{(-z))\).
Substituting z = 4π:
tanh(4π) = \((e^{(4\pi)} - e^{(-4\pi))}/(e^{(4\pi)} + e^{(-4\pi)).\)
Since \(e^{(ix)\)= cos(x) + i sin(x):
So, tanh(4π) = (cos(4π) + i sin(4π) - cos(-4π) - i sin(-4π))/(cos(4π) + i sin(4π) + cos(-4π) + i sin(-4π)).
Simplifying cos(4π) = 1 and sin(4π) = 0:
tanh(4π) = (1 + i x 0 - 1 - i x 0)/(1 + i x 0 + 1 + i x 0) = 0/2 = 0.
Therefore, the answer is D. 0.70717∠0°.
3. The hyperbolic sine function, sinh(z), is defined as \((e^z - e^{(-z))\)/2.
Substituting z = 5 + 5j:
sinh(5+5j) = (\(e^{(5+5j)} - e^{(-(5+5j))\))/2.
sinh(5+5j) =\((e^5 e^{(5j)} - e^5 e^{(-5j)\))/2.
Using Euler's formula, \(e^{(ix)\) = cos(x) + i sin(x):
sinh(5+5j) = (\(e^5\) (cos(5) + i sin(5)) - \(e^5\) (cos(-5) + i sin(-5)))/2.
Simplifying cos(5) and sin(5) gives real and imaginary parts:
sinh(5+5j) = (\(e^5\) cos(5) - \(e^5\) cos(5) + i(\(e^5\) sin(5) - \(e^5\) sin(-5)))/2.
sinh(5+5j) = i\(e^5\) sin(5).
Therefore, the answer is D. 19.14 −j86.11.
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Find the median.......
Answer:
(i) mean: 5.4 median: 5.5 mode: 8
(ii) mean: 4.6 median: 5 mode: 5
(iii) mean: 17.5 median: 4 mode: 4
Step-by-step explanation:
Hope this helps :) please mark me Brainliest
Can someone solve then explain the process of solving this?
CORRECT ANSWER 42 degrees = Angle A
explanation-
When solving for a triangle, regardless of shape, the angles will always have to add up to 180 degrees. We are given that the angle at the top (let's call it C) is 79 degrees. 180 minus 79 is 101. This means of the two angles left, we have 101 degrees that need to be filled between angle A and the unnamed angle. We are given the variable X in order to add among our angles to try and solve them. X+48 will give us angle A and X+65 will give us the unnamed angle. However, 65 and 48 added to 79 will give us more than 180, which means our X is less than 1.
The easiest way to solve for X is to start to subtract numbers by our given.
-2 + 48 is 46 and -2 + 65 is 63. 63 plus 48 is still more than 101. So this is incorrect.
Correct answer - X = -6. -6 + 48 is 42, and -6 + 65 is 59. 59+42 is 101. So our angle A is 42 degrees.
I hope this helps & good luck !
Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes asâ 2, 3,â 4, 5,â 6, 7,â 8, 9,â 10, 11, 12. Because there are 11â outcomes, heâ reasoned, the probability of rolling must be . What is wrong withâ Bob's reasoning
In the question given that :he reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11
From the question, we have the information available is:
Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
and, there are 11 outcomes, he reasoned, the probability of rolling a nine must be one eleventh.
To write the what is wrong with Bob's reasoning.
Now, According to the question:
In the probability:
He rolled 11 times:
So, we can represent the \(w_2\) is the outcome with the sum of pints in two die are 2.
Then the probability is:
\(P(w_2 = 2) = (\frac{1}{6} ).(\frac{1}{6} )=\frac{1}{36}\neq \frac{1}{11}\)
So, in the question given that :he reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11.
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2x+3y=1470 changed to slope intercept form, write a description which is clear precise and correct of how to graph the line using the slope intercept method,changes equation to to function notation and explains clearly what the graph of the equation represents. graph the equation and labels the intercept correctly. Write at least 3 sentences explaining how the graphs of the two equations are the same and how they are different.
Answer:
y= 490 - 2x
Step-by-step explanation:
Answer: Do I get brainliest if I try? 7 = 490 - 2x
Step-by-step explanation:
what us the value of y?
Answer:
the value of y is 50 degree
we say a definite integral is improper if one is infinite, or if the is infinite.
One _____is infinite, or if
The_______is infinite
From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.
One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.
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What is the aim of hypothesis testing? What does hypothesis
testing achieve that could not be otherwise achieved?
2) give an example showing all the steps of the hypothesis
testing:
State a claim that
The aim of hypothesis testing is to make inferences or conclusions about a population based on sample data. It allows us to objectively analyze the evidence provided by the data and make decisions based on that evidence. By comparing the observed data to what would be expected under a specific hypothesis, hypothesis testing helps us evaluate whether the data supports or contradicts the claim being tested.
Hypothesis testing provides a structured and systematic approach to assess the validity of a claim or hypothesis. Hypothesis testing achieves several objectives that cannot be otherwise achieved:
Objectivity: Hypothesis testing provides a framework that helps remove personal biases and subjectivity from the decision-making process. It requires formulating clear hypotheses, defining appropriate statistical tests, and following predetermined rules to reach conclusions. This objectivity ensures that decisions are based on evidence rather than personal opinions or preferences.
Quantification of uncertainty: Hypothesis testing allows us to quantify the level of uncertainty associated with the conclusions drawn from the sample data. It provides measures such as p-values and confidence intervals that indicate the likelihood of obtaining the observed results under the null hypothesis. These measures help in assessing the strength of evidence and determining the level of confidence in the conclusions made.
Generalization to the population: Hypothesis testing enables us to make inferences about the population based on the sample data. By testing a hypothesis on a representative sample, we can draw conclusions that extend beyond the observed data. This generalization provides insights and knowledge about the larger population, allowing us to make informed decisions and predictions.
Example of hypothesis testing:
Claim: A new fertilizer leads to an increase in crop yield by at least 10%.
Step 1: Formulate the null and alternative hypotheses:
Null hypothesis (H0): The new fertilizer has no effect on crop yield or increases it by less than 10%.
Alternative hypothesis (Ha): The new fertilizer increases crop yield by at least 10%.
Step 2: Set the significance level (alpha):
Determine the desired level of significance to make a decision. Let's assume alpha = 0.05.
Step 3: Collect and analyze the data:
Implement the new fertilizer on a sample of crops.
Measure the crop yield for each sample plot and calculate the sample mean.
Step 4: Conduct the hypothesis test:
Use an appropriate statistical test, such as a one-sample t-test, to compare the sample mean to the hypothesized value of 10% increase.
Calculate the test statistic and the corresponding p-value.
Step 5: Make a decision and interpret the results:
If the p-value is less than the significance level (alpha), reject the null hypothesis.
Conclude that there is evidence to support the claim that the new fertilizer increases crop yield by at least 10%.
If the p-value is greater than the significance level (alpha), fail to reject the null hypothesis. Conclude that there is insufficient evidence to support the claim.
Step 6: Draw conclusions and report the findings:
Summarize the results, including the test statistic, p-value, and the decision made.
Provide interpretations and recommendations based on the findings, considering the limitations and context of the study.
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Which of the following is equivalent to 3x - 4y = 6?
Answer:
A
Step-by-step explanation:
-4y = -3x + 6
4y = 3x - 6
y = 3/4 x - 6/4
y = 3/4 x - 3/2
Please help! My assignment is due today! Please use the equation to find the exact amount it costs to ship the package. P.S. don't put it in a file, as I cannot reach it.
Kayla developed a study to determine the populations of fish in
a lake. She took two random samples in the winter and again in
the summer. She organized her data in the following table. What valid inference can Kayla make about the entire fish population in the pond. Select all that apply.(There are two correct answers)
Answer:
7.81 units
Step-by-step explanation:
To find the distance between two points, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates given in the problem, we can plug in the values into the formula:
d = √((4 - (-2))^2 + (1 - (-4))^2)
Simplifying this expression, we get:
d = √((6)^2 + (5)^2)
d = √(36 + 25)
d = √61
Therefore, the distance between the two points (-2,-4) and (4,1) is √61 (square root of 61), which is approximately 7.81 units.
91. in a certain state, the sales tax rate
increased from 7.0% to 7.5%. what
was the increase in the sales tax on a
$200 item?
a. $1
b. $10
c. $14
d. $15
It is important to know about the percentage first, the percent number is per 100. It can be determined by this formula
A% = A/100
where A is the value or the price
From the text we know that :
initial tax rate = 7.0%
final tax rate = 7.5%
item price = $200
By using percentages, we can know the tax price
Initial tax price
initial tax price = initial tax rate x item price
initial tax price = 7.0% x 200
initial tax price = 7/100 x 200
initial tax price = $14
Final tax price
final tax price = final tax rate x item price
final tax price = 7.5% x 200
final tax price = 7.5/100 x 200
final tax price = $15
The increase in sales tax = Final tax price - Initial tax price
The increase in sales tax = $15 - $14
The increase in sales tax = $1
Hence, the increase in the sales tax is $1.
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Isabella invested $1300 in an account that pays 4.5% compounded annually. Assuming no deposits or withdrawals are made , find how much money Isabella would have in the account 14 years after her initial investment . Round to the nearest tenth.