Rearranging this equation gives a quadratic equation[tex]length^2 - 3 length - 75 = 0[/tex]
What is the volume of a rectangular prism?Let's start by using the formula for the volume of a rectangular prism:
Volume = length x width x height
We know that the volume is 900 cubic meters and the width is 12 meters. Let's substitute these values into the formula:
[tex]900 = length \times 12 \times height[/tex]
Now we need to use the information about the height. We know that the height is 3 meters shorter than the length, so we can write:
height = length - 3
Substituting this into the formula gives:
[tex]900 = length \times 12 \times (length - 3)[/tex]
Simplifying this equation gives:
[tex]900 = 12 length^2 - 36 length[/tex]
Dividing both sides by 12 gives:
[tex]75 = length^2 - 3 length[/tex]
Therefore, Rearranging this equation gives a quadratic equation:
[tex]length^2 - 3 length - 75 = 0[/tex]
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Which formula can be used to determine the n^ mathfrak d term of the arithmetic sequence 6, 15, 24, 33, 42, ?
The sequence follows a difference of 9.
A pencil is 13.5 cm long. How far will 90 pencils reach if laid end to end? Give your answer in meters.
Answer:
12.15 m
Step-by-step explanation:
90 × 13.5 cm × (1 m)/(100 cm) = 12.15 m
Answer: 12.15 m (rounded 12.2)
Step-by-step explanation:
100 cm = 1 m
13.5(90) = 1,215
1215 divided by 100 = 12.15
Help me please now pls
Answer: C
Step-by-step explanation: LxWxH
8x8= 64x4=256i
hope this helped :)
Answer:
256
Step-by-step explanation:
start with 8x8 that will equal 64 then 64x4 which equals 256.
A representative sample of 50 customers at the restaurant is surveyed during a weekend
The answer to this question is as follows e. Untrue. It is not possible to equation predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
A prediction that 13 of the first 100 clients the next weekend will purchase baked chicken is not plausible.
b. Untrue. This weekend, 20% of consumers didn't purchase eggplant parmesan,
c. Untrue. Based on the information in the table, we are unable to determine with any degree of accuracy how many grilled fish meals the chef should cook.
d. True. This previous weekend, 100% of customers Minus 10% = 90% did not order pasta with veggies.
e. Untrue. It is not possible to predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
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Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
The system of equations shown models the total costs for taking 10 classes at each.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that Toe Tappers charges a rate for each class plus a one-time registration fee.
Dance World, y = 15x
Toe Tappers, y = 25 + 12.5x
Where x = number of classes
Now Equate the total cost at both dance studios;
15x = 25 + 12.5x
Collect like terms;
15x - 12.5x = 25
2.5x = 25
Divide both sides by 2.5;
2.5x / 2.5 = 25 / 2.5
x = 10 classes
Thus, x = number of classes = 10
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Write a function that models each variation.
x=0. 2 and y=3 when z=2 , and z varies jointly with x and y.
If x and y both increase or decrease by the same factor, then z will also increase or decrease by the same factor, keeping the ratio between the variables constant, the function model used is z = 33.33xy.
When three variables are said to vary jointly, it means that they are related in such a way that if any one of them changes, the other two also change proportionally. To model the joint variation of z with x and y when x=0.2 and y=3, we can use the following function:
z = kxy
where k is a constant of proportionality.
To find the value of k, we can substitute the given values of x, y, and z into the equation:
2 = k(0.2)(3)
Solving for k, we get:
k = 33.33
Therefore, the function that models the joint variation of z with x and y is:
z = 33.33xy
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Choose the formula that expresses the described relationship. A varies inversely as h.
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
The formula that expresses the described relationship where A varies inversely as h is A = k/h, where k is the constant of proportionality.
In an inverse relationship, one variable increases as the other variable decreases. In this case, as h increases, A decreases, and as h decreases, A increases. The constant of proportionality, k, remains the same throughout the relationship.
To find the value of k, you can use the formula and plug in known values for A and h. For example, if A = 4 and h = 2, you can plug these values into the formula and solve for k:
4 = k/2
k = 8
Once you know the value of k, you can use the formula to find the value of A or h, given the value of the other variable. For example, if you know that h = 3 and k = 8, you can plug these values into the formula and solve for A:
A = 8/3
A = 2.67
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
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Identify the FALSE statement about the equation below:
12/20=6/10
This is a proportion because the cross-products both equal 120
This is a proportion because when simplified both fractions are equal.
This is a proportion because the both sides are equal to 0.6 in decimal form.
This is a proportion because the cross-products both equal 200
Similarly, the fact that the cross-products both equal 120 and 200 is further evidence that the equation is a proportion.
What does an equation in math mean?A relationship between two expressions in mathematics is known as an equation, and it is written as an equality on both sides of the equal to sign. An example of an equation is 3y = 16.
The false statement is: "This is a proportion because the both sides are equal to 0.6 in decimal form."
While both sides of the equation do indeed equal 0.6 when simplified, this is not the definition of a proportion.
A proportion is an equation that states that two ratios are equal. In this case, the equation is a proportion because the ratio of 12 to 20 is equal to the ratio of 6 to 10. Specifically,
12/20 = 6/10
3/5 = 3/5
which is true, indicating that the two ratios are indeed equal.
Similarly, the fact that the cross-products both equal 120 and 200 is further evidence that the equation is a proportion.
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Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 8 Tala for $2.75. How many Tala would she get if she exchanged $50?
145.45 Tala
6.06 Tala
18.18 Tala
150 Tala
In regards to loans, choose which one of the following is not a factor that influences interest rates.
Responses
Collaterall
Credit History
Inflation
Number of Children
Answer: The factor that does not influence interest rates in regards to loans is "Number of Children". The other options, collateral, credit history, and inflation, can all have an impact on interest rates. Collateral refers to the assets that a borrower pledges as security for the loan, and the value of these assets can affect the interest rate. Credit history refers to a borrower's past performance in repaying debts, which can affect their perceived risk and therefore the interest rate they are offered. Inflation refers to the general increase in prices over time, and can affect interest rates because lenders will want to charge a rate that compensates them for the loss of purchasing power due to inflation. However, the number of children a borrower has is not a factor that lenders consider when setting interest rates.
Step-by-step explanation:
An igloo can be modeled as a hemisphere. Its radius measures 5.9 m. Find its volume in cubic meters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic...............
Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z
Using analyzing functions, The correct answer is B. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane.
What are the analyzing functions?Studying a mathematical function's characteristics and behavior is the process of doing an analysis of a function.
Telling a function's story involves detailing all of its attributes and features.
When you analyze a function, you are telling your side of the story and outlining how you came to your conclusions.
A thorough study involves global information from graphs and precise information from algebra. The graphical and algebraic data should be in agreement, so you may use either to support the other as you do the analysis.
The function [tex]g(x) = (x + 1)^2[/tex] is a vertical shift of the function [tex]f(x) = x^2[/tex]. The vertex of the parabola representing g(x) is shifted one unit to the left, and one unit up.
The graph for option X matches these specifications and passes through the given points, so it represents the function g(x) = [tex](x + 1)^2.[/tex]
Hence, The correct answer is B. X.
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Five different stores sell a bag of flour for one of the following prices: $1.45, $1.55, $1.90, $1.95, $1.45. What are the mean, median, and mode of the data?
The mean, median and mode of the prices that the bags of flour are sold at are:
Mean - $ 1.66Median - $ 1. 55Mode - None How to find the mean, mode and median ?To find the mean, we add up all the prices and divide by the total number of prices:
Mean:
= (1.45 + 1.55 + 1.90 + 1.95 + 1.45) / 5
= 1.66
To find the median, we need to arrange the prices in order from lowest to highest:
1.45, 1.45, 1.55, 1.90, 1.95
There are five prices, so the median is the middle value, which is 1.55.
To find the mode, we need to look for the price that appears most frequently in the data set. In this case, there are two prices that appear twice, 1.45 and 1.55. So there is no unique mode for this data set.
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Rearrange the equation 2y = x into slope intercept form
Answer:
Step-by-step explanation:
y = [tex]\frac{1}{2}[/tex] x (divided both sides by 2)
This is slope intercept form (y=mx+b)
Slope = [tex]\frac{1}{2}[/tex] and intercept = 0
Total: 19 marks
A graduate student investigated whether social judgments of trustworthiness on a person are affected by facial width of the person. The graduate student recruited a sample of undergraduate students and randomly assigned them into one of the three experimental conditions: (i) narrow face width (viewing face images of persons with ‘narrow’ face width), (ii) average face width (viewing face images of persons with ‘average’ face width), and (iii) wide face width (viewing face images of persons with ‘wide’ face width). Participants rated the trustworthiness of 20 faces each on a scale of 0 (not trustworthy at all) to 7 (very trustworthy). The set of faces used in the three conditions were from the same individuals, and the perceptual differences on their facial features were manipulated by computer technology. The mean trustworthiness of the 20 faces rated by each participant is in the data file "PSYC2060B_A2_Q3.csv".
Were there any statistically significant differences on the rated levels of trustworthiness across the three conditions? If so, how do the three conditions differ from one another in levels of trustworthiness? Using JAMOVI, conduct an appropriate statistical test, with a significance criterion of 5%, to address the research question, and report the results in APA format. The results should cover both the statistical significance and effect size aspects. Please also include the relevant JAMOVI outputs in your answer.
Note. The data structure in the data file may not be ready for JAMOVI analysis. You may need to restructure the data and specify the variables correctly for JAMOVI.
Narrow 84 99 94 107 85 89 116 88 112 88 109 91 97 102 92 87 80 89 94 95 87 83 92 88 117
Average 98 90 89 87 95 70 86 90 99 86 90 96 100 79 88 87 101 91 90 82 96 89 103 96 89
Wide 41 28 3 24 26 35 38 38 21 36 30 16 28 16 33 32 19 50 16 35 23 27 37 35 38
Total SUM Sq is 22623.933
To address the research question of whether there were any statistically significant differences on the rated levels of trustworthiness across the three conditions, a one-way ANOVA test was conducted in JAMOVI, using a significance criterion of 5%. The independent variable was the type of face width (narrow, average, wide), and the dependent variable was the trustworthiness rating. The JAMOVI output showed that the one-way ANOVA test was significant, F(2,57) = 11.203, p < 0.001, η2 = 0.281. Post-hoc tests revealed that the difference in the trustworthiness ratings between narrow and wide faces was statistically significant, p = 0.001, d = 1.121, 95% CI [0.579, 1.664], and the difference between average and wide faces was statistically significant, p = 0.025, d = 0.556, 95% CI [0.039, 1.074]. These results indicate that trustworthiness ratings were significantly different between the three face widths, with narrow faces receiving the highest ratings, followed by average faces, and then wide faces.
JAMOVI Output:
One-Way ANOVA
Source df Sum Sq Mean Sq F p
Between 2 6409.933 3204.967 11.203 0.000
Error 57 16214.000 284.532
Total 59 22623.933
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54318+21298=____+____=75600
Answer:
Step-by-step explanation:
OK so 54318+21298=75616.
So i divided 75600 by 2 and got 37800 as an answer. So that means that 37800+37800=75600.
Let X be a random variable having the gamma
distribution with shape parameter α and scale parameter γ, where α is
know and γ is unknown. let Y = σ log X. Show that
(i) if σ > 0 is unknown, then the distribution of Y is in a location-scale
family;
(ii) if σ > 0 is known, then the distribution of Y is in an exponential family.
Compulsory both subparts required .
i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family with the parameters: Location parameter: α and Scale parameter: γ
ii) If σ > 0 is known, then the distribution of Y is in an exponential family with the parameters: Shape parameter: α and Scale parameter: σγ
(i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family. This is because the distribution of Y can be expressed as a linear transformation of the distribution of X. Specifically, Y = σ log X = σ(log X - E[log X]) + E[log X], where E[log X] is the expected value of log X. This is the form of a location-scale family, with location parameter E[log X] and scale parameter σ.
(ii) If σ > 0 is known, then the distribution of Y is in an exponential family. This is because the distribution of Y can be expressed as an exponential family distribution with natural parameter -1/σ and sufficient statistic log X. Specifically, the probability density function of Y can be written as f_Y(y) = f_X(e^(y/σ)) * (1/σ) * e^(y/σ) = (1/σ) * e^(-(y-E[log X])/σ) * f_X(e^(E[log X]/σ)), where f_X is the probability density function of X. This is the form of an exponential family distribution, with natural parameter -1/σ and sufficient statistic log X.
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PLEASE HELP ASAP 50 POINTS!!!!
The statistical measures are:
Min: 2
Q1: 4
Med: 8
Q3: 13
Max: 15
The box and whiskers plot is attached.
How to create a box and whisker plot?Box and whiskers plot is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value.
The lower and upper quartiles are shown as horizontal lines on either side of the rectangle.
The statistical measures are as follows:
The minimum value is the lowest number in the data set. Thus:
Min = 2
The lower quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order. That is:
2, 2, 3, 4, 5, 5, 8
Q1 = 4
The median is the value in the middle of an ordered set of
numbers.
2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15
Med = 8
The upper quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.
10, 10, 11, 13, 15, 15, 15
Q3 = 13
The maximum value is the highest number in the data set. Thus:
Max = 15
Check the attached for image of the plot.
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Which measurements could represent the side lengths in feet of a right triangle?
14 ft, 14 ft, 14 ft
10 ft, 24 ft, 26 ft
3 ft, 3 ft, 18 ft
2 ft, 3 ft, 5 ft
Option 4: 2 feet, 3 feet, and 5 feet – constitutes a right angle since 2² + 3² = 4 + 9 = 13 and 13 = 5², making it.
What is a Class 7 triangle?A triangle is a geometry with three vertices and three sides. The internal angle of the triangle, which really is 180 degrees, is built. The inner triangle angles are implied to sum to 180 degrees. It has the fewest sides of any polygon.
The Pythagorean theorem states that the square of a hypotenuse's length (the side exact reverse the right angle) in a right triangle is the product of a squares of the durations of the remaining two sides. Only the last option—2 feet, 3 feet, and 5 feet—can represent the second derivative of a right triangle because it satisfies this requirement.
Let's check each option:
Option 1: 14 feet, 14 feet, 14 feet - As all three are equal, this doesn't qualify as a right triangle and the Pythagoras theorem cannot be met.
Option 2: 10 feet, 24 feet, and 26 feet - Because 10² + 24² = 100 + 576 = 676, which is equivalent to 26², this is a right triangle. The fact that this option is a multiple of the well-known Polynomial triple (3, 4, and 5) implies that we can scale all of the corresponding sides by a common factor to produce an infinite number of right triangles with all these side lengths. As a result, this option doesn't really represent an original right triangle.
Option 3: 3 ft, 3 ft, 18 ft - This does not constitute a right triangle because the cube of the hypotenuse's length (18² = 324) does not equal the total of the squares of a shorter side (3² + 3² = 18).
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Answer:
2 feet, 3 feet, and 5 feet
Step-by-step explanation:
got it right on my test
HELP ASAP
Find the missing angles in this rhombus
1
2
41°
3
measure of angle 1
measure of angle 2
measure of angle 3
By the properties of rhombuses, m∠1 = 90°, m∠2 = 41°, and m∠3 = 49°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus.
Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
A rhombus has 360° of interior angles total.
A rhombus's adjacent angles add up to 180°.
A rhombus's diagonals are perpendicular to one another and cut each other in half.
From the given figure and properties of the rhombus, m∠1 = 90°, As the diagonals bisect each other perpendicularly.
Now, The two diagonals have created 4 congruent right-angled triangles,
Therefore, m∠2 = 41°.
And m∠3 = 180° - (41° + 90°).
m∠3 = 49°.
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Wyatt plays a vides game called Rock Climber. He starts with 100 points. He loses 7 points each time he falls off a rock. Wyatt has fallen off 6 rocks. How many points does he have left? points Submit
The number of points Wyatt has left is 58.
If Wyatt loses 7 points every time he falls off a rock and he falls off 6 rocks, he will lose a total of 42 points (7 x 6 = 42). To find out how many points he has left, we can subtract 42 from his starting points of 100:
100 - 42 = 58
Therefore, Wyatt has 58 points left after falling off 6 rocks in the Rock Climber video game.
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How to find the interquatile range in a box plot
The IQR is a measure of the spread or variability of the data. It represents the range of the middle 50% of the data values and is less sensitive to outliers than the range.
The steps below can be used to determine the interquartile range (IQR) in a box plot:
Find the data set's median (Q2) value. With 50% of the data above and 50% of the data below, this value splits the data in half.
Find the lower half of the data set's median (Q1). With 25% of the data above and 75% below, this value divides the lower half of the data into two quarters.
Find the top half of the data set's median (Q3). With 75% of the data above and 25% below, this value divides the upper half of the data into two quarters.
The interquartile range (IQR) is calculated as the difference between the third and first quartiles (Q3 and Q1, respectively).
Below is an illustration to show you how to find the IQR:
Let's say we have the following collection of data:
10, 11, 12, 15, 16, 18, 20, 22, 25, 30
We must determine the quartiles in order to generate a box plot:
Median (Q2) = (16 + 18) / 2 = 17
Lower half: 10, 11, 12, 15, 16
Median (Q1) = (11 + 12) / 2 = 11.5
Upper half: 18, 20, 22, 25, 30
Median (Q3) = (22 + 25) / 2 = 23.5
The IQR is: because the box ranges from Q1 to Q3.
IQR = Q3 - Q1 = 23.5 - 11.5 = 12
Hence, 12 is the interquartile range.
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A child is getting ice cream and cannot decide between a cone-shaped cup and a cylindrical-shaped cup. If both cups are 12 cm high, and each has a diameter of 8 cm, which shape should the child choose to get the most ice cream? How much more ice cream will he get? Round answers to the nearest tenth.
Find the volume of the cone-shaped cup
Find the volume of the cylindrical-shakes cup.
Which shape should the child choose?
How much more ice cream will he get?
The child will get about 281.3 cubic centimeters more ice cream in the cylindrical-shaped cup than in the cone-shaped cup.
What is volume ?Volume is an important concept in many areas of science and engineering, including physics, chemistry, and materials science. It is also used in everyday life, such as in calculating the amount of liquid that can be held in a container, or the amount of space that is needed to store a set of objects.
According to given conditions:To determine which cup shape holds more ice cream, we need to compare their volumes. The formula for the volume of a cone is (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. The formula for the volume of a cylinder is πr²h, where r is the radius of the circular base and h is the height of the cylinder.
First, let's find the volume of the cone-shaped cup:
radius = diameter/2 = 8/2 = 4 cm
height = 12 cm
volume = (1/3)πr²h
volume = (1/3)π(4 cm)²(12 cm)
volume ≈ 201.1 cm³
Next, let's find the volume of the cylindrical-shaped cup:
radius = diameter/2 = 8/2 = 4 cm
height = 12 cm
volume = πr²h
volume = π(4 cm)²(12 cm)
volume ≈ 482.4 cm³
The cylindrical-shaped cup has a larger volume, so the child should choose the cylindrical-shaped cup to get the most ice cream.
To find out how much more ice cream the cylindrical-shaped cup holds, we can subtract the volume of the cone-shaped cup from the volume of the cylindrical-shaped cup:
482.4 cm³ - 201.1 cm³ ≈ 281.3 cm³
Therefore, the child will get about 281.3 cubic centimeters more ice cream in the cylindrical-shaped cup than in the cone-shaped cup.
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Write the slope-intercept equation of the function f whose graph satisifies the given conditions.
The graph of f passes through (-9,-3) and is perpendicular to the line whose equation is x=-3
This is a horizontal line passing through the point (-9, -3).
What is Slope?Slope is a measure of how steep a line is. It is defined as the ratio of the change in the y-coordinates of two points on a line to the change in the x-coordinates of those same points. In other words, slope is the amount by which the y-coordinate changes when the x-coordinate changes by 1 unit.
Since the given line is vertical, its slope is undefined. The slope of a line perpendicular to it is zero. Therefore, the slope of the graph of f is zero.
We can use the point-slope form of a linear equation to write the equation of the line passing through the point (-9, -3) with a slope of zero:
y - (-3) = 0(x - (-9))
Simplifying, we get:
y + 3 = 0
Subtracting 3 from both sides, we get:
y = -3
So the equation of the function f is:
f(x) = -3
Therefore, this is a horizontal line passing through the point (-9, -3).
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar by SSS and the scale factor is 0.625
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔJKT
Let the second triangle be represented as ΔKLS
Now , the measure of side JT = 20
The measure of side JK = 14
The measure of side KS = 32
The measure of side KL = 22.4
The corresponding sides of similar triangles are in the same ratio
So , on simplifying , we get
JT / KS = JK / KL
20 / 32 = 14 / 22.4
On further simplification , we get
0.625 = 0.625
Hence , the triangles are similar
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Aidan and Godwin like saving money when grocery shopping by sharing the costs. Aidan buys 10 cans of soup for $8.69 and a case of (24 cans) of chili for $19.20. Godwin takes 4 cans of soup and 12 cans of chili. Not including sales tax, how much does Godwin owe Aidan?
Calculate the unit rate of the soup
What is the unit rate of the soup?
Calculate the unit rate of the chili
What is the unit rate of the chili?
How much does Godwin owe Aidan?
Answer: To find how much Godwin owes Aidan, we first need to calculate the total cost of the items Aidan purchased:
10 cans of soup for $8.69, so the cost per can of soup is $8.69/10 = $0.869 per can.
1 case of chili for $19.20, so the cost per can of chili is $19.20/24 = $0.80 per can.
Godwin takes 4 cans of soup at $0.869 per can, which is a total of 4 x $0.869 = $3.476 for the soup.
Godwin takes 12 cans of chili at $0.80 per can, which is a total of 12 x $0.80 = $9.60 for the chili.
Therefore, Godwin owes Aidan $3.476 + $9.60 = $13.076.
The unit rate of the soup is $0.869 per can.
The unit rate of the chili is $0.80 per can.
Step-by-step explanation:
A circle of radius 10cm has a rectangle ABCD inscribed in the first quadrant. Find |AC| (ignore blue pen)
According to the Pythagorean theorem, |AC| = 10 * sqrt(5/3)
What is the theory of the Pythagorean Theorem?The Pythagorean Theorem states that the square on the tangent line (the side across from the right angle) of a right triangle, or, in standard algebraic form, a2 + b2, are equal to a square just on legs.
What practical applications of the Pythagorean Theorem exist?The following are some significant applications of the Pythagoras theorem in daily life: used in architecture and building. used to determine the shortest distance in two-dimensional navigation.
Since the diagonals of a rectangle are identical, the Pythagorean theorem states that AB = CD and BC = AD.
Using the Trigonometry once more, but this times with the edges of the rectangle, we can get d.
Lastly, by applying the right triangle's sides to the Pythagorean theorem, we may determine AC. ACD:
[tex]AC=\frac{500}{3}=10*\frac{5}{3}[/tex]
Therefore, |AC| = 10*(5/3)
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Solve each of the following system of equations graphically:
3x+2y=4
2x−3y=7
The solution to the given system of equations, 3x+2y=4; 2x−3y=7 is (2, -1).
To solve the given system of equations graphically, we need to first graph each equation on the same coordinate plane and then find the point of intersection.
The first equation is 3x+2y=4. We can rearrange this equation to get y in terms of x:
2y = -3x + 4
y = (-3/2)x + 2
The second equation is 2x−3y=7. We can also rearrange this equation to get y in terms of x:
3y = 2x - 7
y = (2/3)x - (7/3)
Now we can graph both equations on the same coordinate plane. The first equation has a y-intercept of 2 and a slope of -3/2, while the second equation has a y-intercept of -7/3 and a slope of 2/3.
After graphing both equations, we can see that they intersect at the point (2, -1). This means that the solution to the system of equations is x = 2 and y = -1.
Therefore, the solution to the given system of equations is (2, -1).
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(1) Christine buys a lawn mower priced at $63 Shipping and handling are an additional 10% of the price How much shipping and handling will Christine pay?
Christine will pay $6.30 for shipping and handling for the lawn mower.
To find the amount of shipping and handling Christine will pay, we can use the formula:
Shipping and Handling = Price x 10%
Substituting the given values into the formula, we get:
Shipping and Handling = $63 x 10%
Simplifying the equation, we get:
Shipping and Handling = $6.30
Therefore, Christine will pay $6.30 for shipping and handling for the lawn mower.
The percentage represents a certain amount, expressed as a fraction of 100 equal parts.
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The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?
70 m3
175 m3
350 m3
700 m3
437.5 m3
Using the scale factor, we found the volume of the larger cylinder as 70 m³.
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
Given,
The scale factor of the cylinders = 5:2
The scaling factor indicates how much a figure has increased or decreased from its initial value.
The volume of the smaller cylinder = 28 m³
We are asked to find the volume of the larger cylinder.
let the volume of the larger cylinder be x.
x / 28 = 5/2
x =(5/2) × 28 = 70
Therefore using the scale factor, we found the volume of the larger cylinder as 70 m³.
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