hello
the answer to the question is (10, - 2)
Answer:
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]
Midpoint = [tex](\frac{8+12 }{2} , \frac{3+(-7)}{2} )[/tex]
Midpoint = [tex](\frac{20 }{2} , \frac{-4)}{2} )[/tex]
Midpoint = (10, -2)
NEED HELP ASAP!! What is the probability that either event will occur?
The value of probability P (A or B) is,
⇒ P (A or B) = 48
We have to given that,
The Venn diagram of the probability is shown in image.
Now, By given diagram,
⇒ P (A) = 24 + 14
⇒ P (A) = 38
⇒ P (B) = 24 + 10
⇒ P (B) = 34
⇒ P (A and B) = 24
We have to given that,
The expression is,
P (A or B) = P (A) + P (B) - P (A and B)
Substitute all the values, we get;
P (A or B) = 38 + 34 - 24
P (A or B) = 48
Thus, The value of probability P (A or B) is,
⇒ P (A or B) = 48
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Evaluate 3x2 + 3x - 9, when x = 2
Answer:
9
Step-by-step explanation:
3x^2 + 3x - 9
Substitute x = 2 into the equation.
3(2)^2 + 3(2) - 9
3(4) + 6 - 9
12 + 6 - 9
18 - 9 =
9
If fifteen cubed shape gift boxes can be covered by roll of wrapping paper, show by means of calculation that the area is 3.6m if the length is 20 cm
The total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.
To calculate the total surface area of 15 cubed-shaped gift boxes, we need to find the surface area of one gift box and then multiply it by the total number of boxes.
The surface area of a cube can be calculated using the formula:
Surface Area = 6 * [tex](side length)^2[/tex]
Given that the length of each side of the cube-shaped gift box is 20 cm, we can substitute this value into the formula:
Surface Area of one gift box = 6 * (20 cm)^2
= 6 * [tex](400 cm^2)[/tex]
= 2400 [tex]cm^2[/tex]
Since we have 15 gift boxes, we multiply the surface area of one gift box by 15:
Total Surface Area = Surface Area of one gift box * Number of gift boxes
= 2400 [tex]cm^2 * 15[/tex]
= 36000 [tex]cm^2[/tex]
Now, we need to convert the area from square centimeters [tex](cm^2[/tex]) to square meters [tex](m^2).[/tex] There are 10000 square centimeters in a square meter:
Total Surface Area in square meters = Total Surface Area in square centimeters / 10000
= 36000 [tex]cm^2[/tex] / 10000
= 3.6[tex]m^2[/tex]
Therefore, the total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.
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HELP PLEASE
If two identical mass planets were suddenly moved from 1 million miles apart to 2 million miles apart, the gravitational force between them would be 1/4 as much as its original value.
True OR
False
The gravitational force between two planets of equal mass that were abruptly moved from a distance of 1 million miles to a distance of 2 million miles would be only one-fourth as strong as it had been before.
True. The gravitational force between two masses is inversely proportional to the square of their separation, as stated by Newton's law of universal gravitation.
The gravitational attraction between two planets of the same mass would drop by a factor of 1/22 or 1/4 if the distance between them increased from 1 million miles to 2 million miles.
As a result, the gravitational force would be reduced to 1/4 of what it was before.
Therefore, the gravitational attraction between two planets of the same mass would drop by a factor of 1/4 (or 1/22) if their separation doubled (from 1 million miles to 2 million miles).
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A dog is tied to a wooden stake in a backyard. His leash is 2 meters long and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in?
which of the following is not a characteristic of both surveys and observational studies?
a. the researcher direct control over at least one variable
b. data are collected about population
c. the researcher does not control or change the population
d. results are not used to prove cause and effect
The characteristic of the researcher having direct control over at least one variable to both surveys and Observational .
The option that is not a characteristic of both surveys and observational studies is:
a. The researcher has direct control over at least one variable.
Surveys and observational studies have several characteristics in common, such as collecting data about a population and not proving cause and effect. However, the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies.
In a survey, the researcher collects data by asking questions to individuals or groups. They do not have direct control over the variables being studied but rather collect information based on participants' responses. The researcher's role is primarily in designing the survey, selecting the sample, and analyzing the data.
In an observational study, the researcher observes and records data without intervening or manipulating any variables. The researcher does not have control over the variables being observed; instead, they observe and document the existing conditions or behaviors.
the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies. Both methods involve data collection about a population and do not establish cause and effect relationships, but control over variables is not a shared characteristic.
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What is the volume of a hemisphere with a diameter of 60.9 in rounded to the nearest tenth of a cubic inch
The volume of the hemisphere with a diameter of 60.9 inches rounded to the nearest tenth is 59131.7 inches³.
Given that,
Diameter of a hemisphere = 60.9 inches
We have to find the volume of the hemisphere.
We know that, radius is half the measure of the diameter.
Radius of the hemisphere = 60.9 / 2 = 30.45 inches
Volume of a hemisphere is,
Volume = 2/3 π r³
Here r is the radius
Substituting,
Volume = 2/3 π (30.45)³
= 59131.7 inches³
Hence the volume is 59131.7 inches³.
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Which regression model best represents the total number of bacterial clusters in terms of number of elapsed days?
The choice of the best Regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.
The regression model best represents the relationship between the total number of bacterial clusters and the number of elapsed days, we need to examine the data and consider different regression models.
There are several types of regression models commonly used, including linear regression, polynomial regression, exponential regression, and logarithmic regression. Each model represents a different functional form and can capture different types of relationships between variables.
Without specific data or context provided, it is challenging to determine the exact regression model that best represents the relationship. However, I can briefly explain the characteristics and typical use cases for each regression model:
1. Linear Regression: This model assumes a linear relationship between the variables, where the dependent variable changes linearly with respect to the independent variable. It is suitable when the relationship appears to be a straight line on a scatter plot.
2. Polynomial Regression: This model captures non-linear relationships by including higher-order terms of the independent variable, such as quadratic (x^2), cubic (x^3), or higher-degree terms. It is suitable when the relationship seems to follow a curve rather than a straight line.
3. Exponential Regression: This model assumes an exponential relationship between the variables, where the dependent variable changes exponentially with respect to the independent variable. It is suitable when the data exhibits rapid growth or decay.
4. Logarithmic Regression: This model assumes a logarithmic relationship between the variables, where the dependent variable changes logarithmically with respect to the independent variable. It is suitable when the relationship shows diminishing returns or saturation.
the best regression model, it is important to visually analyze the data through a scatter plot and assess the linearity or curvature of the relationship. Additionally, statistical measures such as the coefficient of determination (R-squared) and residual analysis can help evaluate the goodness of fit for different models.
the choice of the best regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.
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6
K
22
8
Find volume
Based on the image you provided, it appears to be a rectangular prism (a box) with given dimensions. To find the volume of the rectangular prism, we can use the formula:
Volume = Length × Width × Height
From the image, we can see the following dimensions:
Length = 6 cm
Width = K cm
Height = 22 cm
To find the volume, we need to know the value of K. Unfortunately, the value of K is not provided in the image or the previous conversation.
If you provide the value of K, I can calculate the volume of the rectangular prism for you.
NEED HELP ASAP!!!!!!!
ESTIMATE 11 4/5 DEVIDE BY 3 1/5
Answer: 59/16 or 3 11/16
Step-by-step explanation:
11 4/5 ÷ 3 1/5
= 59/5 ÷ 16/5
= 59/5 x 5/16
= 59 x 5/ 5 x 16
= 295/80
= 295 ÷ 5/ 80 ÷ 5
= 59/16
= 3 11/16
Use the number line to find an equivalent fraction
The equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.
To find an equivalent fraction using a number line, we need to determine a fraction that represents the same value as the given fraction.
Let's assume the given fraction is 1. On a number line, the fraction 1 can be represented as the distance between 0 and 1. Now, we want to find an equivalent fraction, so let's choose a different representation on the number line.
To find an equivalent fraction that represents the same value, we can divide the number line segment between 0 and 1 into equal parts. Let's say we divide it into 4 equal parts.
Now, we need to determine which of the four equal parts represents the fraction 1. Since we divided the segment into four equal parts, each part represents 1/4 (one-fourth) of the whole segment.
Therefore, the equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.
So, the equivalent fraction for 1 is 1/4.
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Im trying to brush up on my math skills before i start college since ive been out of hs for 2 years now and i cannot for the life of me remember how to simplify a one part factorial.. im dealing with
5!
7!
9!
in my head i thought i should just multiply it out like
5! = 5 * 4 * 3 * 2 * 1 = 120 etc.. but is that simplifying it?
Hey there!
5!
= 5(4)(3)(2)(1)
= 20(3)(2)(1)
= 60(2)(1)
= 120(1)
= 120
Therefore, your answer should be: 120
7!
= 7(6)(5)(4)(3)(2)(1)
= 42(5)(4)(3)(2)(1)
= 210(4)(3)(2)(1)
= 840(3)(2)(1)
= 2,520(2)(1)
= 5,040(1)
= 5,040
Therefore, your answer should be: 5,040
9!
= 9(8)(7)(6)(5)(4)(3)(2)(1)
= 72(7)(6)(5)(4)(3)(2)(1)
= 504(6)(5)(4)(3)(2)(1)
= 3,024(5)(4)(3)(2)(1)
= 15,120(4)(3)(2)(1)
= 60,480(3)(2)(1)
= 181,440(2)(1)
= 362,880(1)
= 362,880
Therefore, your answer should be: 362,880
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A clothing store sells T-shirts, t, for $8 a shirt, and shorts, s, for $12 each. The
store earned $180 revenue last month. The store sold three times as many T-
shirts as shorts. Using the method of substitution, how many T-shirts and
shorts did the store sell?
A. t= 8; s = 12
B. t= 15; s=5
OC. t= 5; s = 15
OD. t = 12; s = 8
Answer: B. t= 15; s=5
Step-by-step explanation:
We will create a system of equations.
8t + 12s = 180
t = 3s
Next, we will substitute this value of t into the first equation and solve for s.
8t + 12s = 180
8(3s) + 12s = 180
24s + 12s = 180
36s = 180
s = 5 shirts
Lastly, we will substitute this value of s back into t = 3s and solve for t.
t = 3s
t = 3(5)
t = 15 shirts
7-8.- Encuentra los números que hacen falta en las siguientes sucesiones:
0.5, 1.25, 2.0, 2.75,
4.25,
512, 256, 128, 64, 32, 16, 8, 4,
5.75, 6.50, 7.25, 8.0
1,
..25, 125
The missing numbers in the sequences are:
Sequence 1: 3.50
Sequence 2: 3.50
Sequence 3: 2
Sequence 4: 8.00
Sequence 5: 25
Let's analyze the given sequences to find the missing numbers:
Sequence 1:
0.5, 1.25, 2.0, 2.75, ?
Observing the pattern, it appears that each term is obtained by adding 0.75 to the previous term.
Applying this pattern, the missing number would be 2.75 + 0.75 = 3.50.
Sequence 2:
4.25, ?
Looking at the sequence, it seems to be decreasing by 0.75 between each term.
Applying this pattern, the missing number would be 4.25 - 0.75 = 3.50.
Sequence 3:
512, 256, 128, 64, 32, 16, 8, 4, ?
Here, each term is obtained by dividing the previous term by 2.
Applying this pattern, the missing number would be 4 / 2 = 2.
Sequence 4:
5.75, 6.50, 7.25, ?
In this sequence, each term is obtained by adding 0.75 to the previous term.
Applying this pattern, the missing number would be 7.25 + 0.75 = 8.00.
Sequence 5:
1, ?, 25, 125
Observing the pattern, it seems that each term is obtained by multiplying the previous term by 25.
Applying this pattern, the missing number would be 1 x 25 = 25.
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A young artist went to an art shop to buy a canvas. There were many sizes from which to choose. Some were standard sizes and some were custom-made. She wanted her next piece to incorporate the Golden Ratio, so she decided to buy the canvas whose dimensions most closely matched the Golden Rectangle. Here are the sizes that were available:
24" x 36"
24" x 40"
10" x 16"
26" x 16"
20" x 12"
Which canvas should the artist buy? Show your work.
The artist should buy the canvas with dimensions [tex]$10" \times 16"$[/tex]. This canvas has an aspect ratio of [tex]1.6[/tex], which is the closest among the available options to the Golden Ratio of [tex]1.618[/tex].
To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratio for each canvas and compare it to the Golden Ratio.
The Golden Ratio, also known as Phi [tex]($\varphi$)[/tex], is approximately [tex]1.618[/tex].
Let's calculate the aspect ratios for each canvas:
Canvas 1: [tex]$24" \times 36"$[/tex]
Aspect ratio = [tex]$\frac{36}{24} = 1.5$[/tex]
Canvas 2: [tex]$24" \times 40"$[/tex]
Aspect ratio = [tex]$\frac{40}{24} \approx 1.667$[/tex]
Canvas 3: [tex]$10" \times 16"$[/tex]
Aspect ratio = [tex]$\frac{16}{10} = 1.6$[/tex]
Canvas 4: [tex]$26" \times 16"$[/tex]
Aspect ratio = [tex]$\frac{16}{26} \approx 0.615$[/tex]
Canvas 5: [tex]$20" \times 12"$[/tex]
Aspect ratio = [tex]$\frac{12}{20} = 0.6$[/tex]
To find the canvas that most closely matches the Golden Ratio, we need to choose the canvas with an aspect ratio closest to [tex]1.618[/tex].
Calculating the differences between the aspect ratios and the Golden Ratio:
Canvas 1: [tex]$|1.5 - 1.618| \approx 0.118$[/tex]
Canvas 2: [tex]$|1.667 - 1.618| \approx 0.049$[/tex]
Canvas 3: [tex]$|1.6 - 1.618| \approx 0.018$[/tex]
Canvas 4: [tex]$|0.615 - 1.618| \approx 1.003$[/tex]
Canvas 5: [tex]$|0.6 - 1.618| \approx 1.018$[/tex]
The canvas with the aspect ratio closest to the Golden Ratio is Canvas 3: [tex]$10" \times 16"$[/tex], as it has the smallest difference of approximately [tex]0.018[/tex].
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Image shows an isosceles triangle.
The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides?
Explain how you know. Provide at least one reason for your answer
The hypotenuse of a 45°-45°-90° triangle measures 7 StartRoot 2 EndRoot units.
The side length of the leg of the special right triangle is equal to 7√2 / 2 units.
How to find the leg length of a special right triangle
In this problem we find the case of special right triangle known as 45° - 90° - 45° triangle, where internal angles are 45°, 90° and 45° and whose side relationship is shown below:
r = √2 · x = √2 · y
Where:
x, y - Legsr - Hypotenuse.If we know that r = 7, then the side length of the leg is:
x = y = √2 · r / 2
x = y = √2 · 7 / 2
x = y = 7√2 / 2
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If the blank is 23, what is X?
Step-by-step explanation:
For angles outside circle angle = 1/2 ( large arc - small arc)
46 = 1/2 [ 21x-5 - (x + blank) ]
92 = 21x -5 - x -blank
97 = 20x - blank
97 = 20x - 23
120 = 20 x
x = 6
Information included on the W-4, except?
The solution is: we can say that we would need to include all of this information on a W-4 form except for information that is not related to your tax situation or employment, such as your favorite color or hobbies.
Here, we have,
W-4 form is a tax form that employees in the United States use to provide their employers with information about their tax situation.
The form includes information such as the employee's name, address, social security number, number of dependents, and filing status.
Therefore, we can say that we would need to include all of this information on a W-4 form except for information that is not related to your tax situation or employment, such as your favorite color or hobbies.
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Thirty-five coloured balls were shared among four teams such that one team takes all the red balls. If the remainder is shared to the other teams in the ratio 4:3:2 and the smallest share was 6 balls, how many red balls were there?
The Shares for the other teams are indeed 12, 9, and 6, respectively, confirms that the solution is correct,there were 8 red balls.
The problem step by step. We are given the following information:
1. The total number of balls is 35.
2. One team takes all the red balls.
3. The remainder (non-red balls) is shared among the other teams in the ratio 4:3:2.
4. The smallest share is 6 balls.
Let's assume the number of red balls is "r". Therefore, the number of non-red balls is 35 - r.
According to the ratio, the shares for the other teams are:
Team 1: (4/9) * (35 - r)
Team 2: (3/9) * (35 - r)
Team 3: (2/9) * (35 - r)
Given that the smallest share is 6 balls, we can set up the equation:
(2/9) * (35 - r) = 6
To solve this equation, we can simplify and solve for "r":
(35 - r) = (9/2) * 6
35 - r = 27
r = 35 - 27
r = 8
Therefore, there were 8 red balls.
To verify the solution, we can calculate the shares for the other teams:
Team 1: (4/9) * (35 - 8) = 4 * 27/9 = 12
Team 2: (3/9) * (35 - 8) = 3 * 27/9 = 9
Team 3: (2/9) * (35 - 8) = 2 * 27/9 = 6
The shares for the other teams are indeed 12, 9, and 6, respectively, which confirms that the solution is correct.
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Find the missing coordinate in the ordered pair ( 1, b )
if it is a solution to the equation x + y = 10
a - 7
b 4
c 9
d -5
The missing coordinate to complete the ordered pair is (9). The ordered pair is (1, 9).
How to Find the Missing Coordinate of an Ordered Pair?An ordered pair is a mathematical concept that consists of two elements, typically represented as (x, y), where x is the first element, also known as the x-coordinate, and y is the second element, also known as the y-coordinate.
It is also known as coordinates, the point (x, y) on a graph where x and y are real numbers.
If x + y = 10, then we can find the missing coordinate by substituting the given x-coordinate (1) into the equation, x + y = 10:
[tex]\sf x + y = 10[/tex]
[tex]\sf y = 10 - 1[/tex]
[tex]\sf y = 9[/tex]
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A set of 10 cards were labeled as a EXPRESSION what is the sample space for choosing one car
The Sample space, a clear set of possible outcomes for choosing one card from the set.
The sample space for choosing one card from a set of 10 labeled cards, where each card is labeled with an expression, would consist of all the possible outcomes of this selection process.
Since there are 10 cards in the set, the sample space would consist of the individual expressions labeled on each card. Let's assume the expressions on the cards are labeled as follows:
Card 1: Expression 1
Card 2: Expression 2
Card 3: Expression 3
...
Card 10: Expression 10
{Expression 1, Expression 2, Expression 3, ..., Expression 10}
This sample space represents all the possible outcomes when selecting one card from the set. Each outcome corresponds to one specific expression labeled on a card.
the sample space only includes the individual expressions and not any particular order or arrangement of the cards. The order of the expressions does not matter in this case, as the focus is solely on the expressions themselves.
the sample space, we establish a clear set of possible outcomes for choosing one card from the set.
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The Parks and Recreation Department is planning to host sports camps for students during the summer. Option 1 is to have 8 Soccer and 1 Baseball camp sessions that would last 94 days altogether. Option 2 has 3 Soccer and 5 Baseball camp sessions that would last 100 days. How many days are needed to run each of the camps sessions for each sport?
Learning goal: I can use the substitution method to solve linear systems of equations Using x,y
The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .
Here, we have,
given that,
The Parks and Recreation Department is planning to host sports camps for students during the summer.
Option 1 is to have 8 Soccer and 1 Baseball camp sessions that would last 94 days altogether.
Option 2 has 3 Soccer and 5 Baseball camp sessions that would last 100 days.
now, let,
x days for Soccer and, y days for Baseball camp, are needed to run each of the camps sessions .
then, we have,
8x + y = 94 .....1
3x+ 5y = 100 .....2
solving we get,
equation 1 => 40x + 5y = 470
now, subtracting, we get,
37x = 370
so, x = 10
now, solving we get,
y = 14
Hence, The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .
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Choose the equation that satisfies the data in the table.
The equation that satisfies the data in the table is: A. y = 2/15(x) + 2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (2 - 0)/(0 + 15)
Slope (m) = 2/15
At data point (0, 2) and a slope of 2/15, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 2/15(x - 0)
y = 2/15(x) + 2.
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write and solve an euation to find the measure of angle x
Step-by-step explanation:
angle x = 180 - 90 - 60 degrees ( because the anglse of atriangle add to 180 degrees)
x = 30 degrees
Look at the chart showing a clothing store's daily stock data for the past month. Which statement is a fair conclusion based on the cha
71.21 +0.27 (+0.38%)
Previous Close
Open
Day's Range
52 Week Range
Volume
C.
70.94 1D 5D 1M 6M YTD1Y 5Y Max
71.18
OD.
70.93-71.96
48.56-78.70
5,983,993
Apr 30
May 8
A.
The stock price is down for the day by 0.27%.
в.
The open price is down from the previous close price.
C.
The current stock price is up for the day by 0.38%.
D.
The price over the period of one month has increased.
Based on the given information, the fair conclusion would be:
C. The current stock price is up for the day by 0.38%.
The statement mentions that the stock price is up for the day, which is indicated by the positive change of 0.27 (+0.38%).
Samuel was given the diagram below and asked to prove that AC ED. What
would be the reasoning for the third step of the proof?
Given: Quadrilateral ABCD is a rectangle.
Prove: AC & BD
Statements
1. Quadrilateral ABCD is a rectangle
2. AB & CD
3. ZBAD ZCDA
4. AD AD
5. ABAD ACDA
6. AC BD
B
A
Reasons
Given
Opposite sides of a rectangle are equal
Reflexive Property of Equality
SAS Triangle Congruence Theorem
Corresponding parts of congruent
triangles are congruent
C
O
The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:
1. Given: Quadrilateral ABCD is a rectangle.
2. Given: AB & CD (Opposite sides of a rectangle are equal).
3. To prove: AC & BD.
To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.
Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.
4. Given: AD = AD (Reflexive Property of Equality).
5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).
6. By step 3, ZBAD = ZCDA.
7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.
Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.
Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."
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Ivanna received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.03 per pound. After buying the coffee, she had $47.88 left on her card. How many pounds of coffee did she buy?
Answer:
4 pounds
Step-by-step explanation:
First, we can calculate how much money Ivanna spent by subtracting her remaining balance after buying the coffee from the original amount on the gift card.
amount spent = $80 - $47.88 = $32.12
Now, we can calculate how many pounds of coffee she bought by dividing the amount she spent by the price rate of coffee by pound.
[tex]\$32.12 \div \dfrac{\$8.03}{1 \text{ lb}}[/tex]
[tex]= \$32.12 \times \dfrac{1 \text{ lb}}{\$8.03}[/tex]
[tex]= \dfrac{32.12}{8.03} \text{ lb}[/tex]
[tex]= \boxed{4 \text{ lb}}[/tex]
So, Ivanna bought 4 pounds of coffee.
Answer: Ivanna bought 4 pounds of coffee for an amount of$32.12.
Step-by-step explanation:
According to the question,
Money with Ivanna initially: $80
Money with Ivanna later: $47.88
step 1: here we need to find the difference between the amount initially and later,
Difference between the amount initially and later: $80 - $47.88 = $32.12
Given,
Price of coffee per pound: $8.03
Step 2: now we divide the amount spent by the price per unit of coffee,
that is: $32.12/$8.03 = 4
so the answer is Ivanna bought 4 pounds of coffee for an amount of$32.12
Read more about the basics of maths,
https://brainly.in/question/234448
From the point A (1,-2), a perpendicular is drawn to the line 2x + 3y = 9 to meet it at M. Find the
coordinates of M and the length of AM.
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Explanation:
The standard form for linear equations is Ax+By = C. Anything perpendicular to this would be of the form Bx-Ay = D.
The equation 2x+3y = 9 gives
A = 2B = 3C = 9The perpendicular template goes from Bx-Ay = D to 3x-2y = D.
Plug in the coordinates of (1,-2) to compute D.
3x-2y = D
D = 3x-2y
D = 3*1 - 2*(-2)
D = 7
Therefore, the perpendicular equation is 3x-2y = 7
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We need to solve this system
[tex]\begin{cases}2x+3y = 9\\3x - 2y = 7\end{cases}[/tex]
to locate point M.
There are a few methods. I'll use substitution.
Solve the 1st equation for x.
2x+3y = 9
2x = -3y+9
x = (-3y+9)/2
x = -1.5y + 4.5
Then substitute this into the other equation to solve for y.
3x - 2y = 7
3( x ) - 2y = 7
3( -1.5y+4.5 ) - 2y = 7
-4.5y + 13.5 - 2y = 7
-6.5y + 13.5 = 7
-6.5y = 7-13.5
-6.5y = -6.5
y = -6.5/(-6.5)
y = 1
Use that to determine x.
x = -1.5y + 4.5
x = -1.5*1 + 4.5
x = 3
Point M is located at (x,y) = (3, 1)
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Use the distance formula to find the distance from A(1,-2) to M(3,1)
[tex]A = (x_1,y_1) = (1,-2) \text{ and } M = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-3)^2 + (-2-1)^2}\\\\d = \sqrt{(-2)^2 + (-3)^2}\\\\d = \sqrt{4 + 9}\\\\d = \sqrt{13}\\\\d \approx 3.605551\\\\[/tex]
Segment AM is exactly [tex]\sqrt{13}[/tex] units long.
That is approximately 3.605551 units.
You can use a tool like GeoGebra to confirm the answers are correct.
4. Glenda drove at a steady rate on a road trip.
Write an equation to represent the relationship
between time x and distance y. Which of the
points (52), (1.5, 78), and (-2.5, -130) are on
the graph of the relationship? Explain.
Answer: mi = 52 x h or y = 52 times x
distance (mi) = y
time (h) = x
It goes 52 miles per hour! Hope this helps.