The length and width of the rectangle are: 10 inches and 5 inches.
What is a rectangle?Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Given:
Area of the rectangle = 104 sq. inchesLength of the rectangle is 5 inches more than the width.To find: the length and width of the rectangle.
Finding:
Let the width of the rectangle be 'x'
Then the length of the rectangle = x + 5
Now, area of the rectangle = width (length)
=> 104 = x ( x + 5)
=> x² + 5x - 104 = 0
=> x² + 13x - 5x - 104 = 0
=> (x + 13) (x - 5) = 0
Since the lengths can't be negative, x = 5, i.e., the width of the rectangle = 5 inches
=> Length = 5 + 5 = 10 inches
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A cold drink initially at 35 f warms up to 42 f in min while sitting in a room of temperature 72f. how warm will the drink be if left out for 30 min?
[tex]$$\begin{aligned}&T^{\prime}=-k(T-72) \quad T(0)=35 \text { (given) } \\&\frac{d T}{T-72}=-k d t-\left\{q^n(1)\right. \\&\text { Solphy } k g^n(1) \\&\ln (T-72)=0-k t+1 \\&T-72=e^{-k t+t} \\&T-72=e^{-k t} e^l \\&\text { let } e^r=C \\&T-72=C e^{-k t} \\&T=72+C e^{-k t} \\&T(t)=72+c e^{-k t}(2)\end{aligned}$$[/tex][tex]$T(t)=72+c e$ Now at $t=Q \mathrm{~mm} \quad T=42$ given Now at $t=Q \min T=$$$\begin{aligned}&\text { yed: } 72+4 e^{-k t} \\&35=72+c e^{-k 0} \\&C=-37 \\&\text { at }+=2 \text { min } T=42 \\&\text { a gaim puting in \&qn } \\&42=72-3+e^{-2 k}\end{aligned}$$[/tex][tex]$$\begin{array}{rl}-\frac{30}{37} & =e^{-2 k} \\e^{-2 k} & =\frac{30}{37} \\-2 k & =\ln \left(\frac{30}{37}\right) \\k & =0.1048 \\p 1 h y & m n \\T(t) & =72-37 e^{-0.1048+} \\T(15) & =72-37 e^{-0.1048 \times 15} \\T(15) & =72-37 \times 1 \\T(15) & =64.31 \\& =\end{array}$$[/tex]
What is Fahrenheit?The unit is the degree Fahrenheit, represented by the sign °F. There are various accounts of how he initially defined his scale, but the initial paper suggests that the lower defining point, 0 °F, was established as the freezing temperature of a brine solution made from a combination of water, ice, and ammonium chloride (a salt). The other limit established was his best estimate of the average human body temperature, originally set at 90 °F, then 96 °F (about 2.6 °F less than the modern value due to He did, however, mention a midpoint at 32 °F, which would be the temperature of ice water.
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hte number of left handed people in the world is one-tenth the number of right handed people. the percent of right-handed people
The percentage of right-handed people is 1%.
What do you mean by the term percent?Percent signifies out of one hundred. It is frequently represented by the symbol "%," even when there aren't 100 entries. After that, the figure is scaled so that it can be put in comparison with 100. Additionally, changes in numerical quantities are denoted by percentages.
We have a bowl of fruit, for instance, with three apples and one orange. Three out of four, or 3/4, or 75 out of 100, or 75 percent, are apples.
A ratio can also be expressed as a fraction or decimal in addition to being written as a percentage. There are methods for converting decimals or fractions to percentages.
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Tom wants to buy 3 3/4 cups of almonds. There are 5/8 of a cup of almonds in each package. How many packages of almonds should Tom buy?
Hi i need help with my work
The equation to express the relationship will be y = 5.05 + 2.45x.
How to illustrate the information?Worth of the card = $5.06
It should be noted that the card increases by $2.45.
Therefore, the equation to express the relationship will be:
y = 5.06 + (2.45 × x)
where x = number of years.
y = value of the card.
y = 5.05 + 2.45x
In conclusion, the equation to express the relationship will be y = 5.05 + 2.45x.
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What is the absolute value of
x = 8 and x = 18
Answer:
8, 18
Step-by-step explanation:
The absolute value is the distance of the point from 0. In this question, it would be the number itself.
Answer:
The answer would be 8 and 18
Step-by-step explanation:
To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations. Solve | x | + 2 = 5. Isolate the absolute value.
ASAP GIVING BRAINLYIEST
Which of the following is true?
|−4| < 3
|−4| < |3|
|−3| < −4
|−3| < |−4|
Step-by-step explanation:
- 4.3 its the same as (-4.3)
how can you describe the graph of equation ax + by = c
The standard form of a line is simply a special way of writing the equation of a line. You are probably already familiar with the slope-intercept form of a line, y = mx + b. The standard form is just another way to write this equation and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements). As you will see in the lesson below, every line can be expressed in this form.
Note that the requirements on A, B, and C vary a bit from textbook to textbook. While they technically can be any real numbers, it is most common to write them as integers and to keep A positive. It is also common to require that A, B, and C share no common factors.
Ax+By=C
THE STANDARD FORM OF A LINE: Ax+By=C
The result is referred to as the standard form of the line: Ax+By=C. We should always be able to convert from one form of an equation to another. For example, if we are given a line in the slope-intercept form, we should be able to express it in the standard form, and vice versa
he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations
Now ,
A=0
B=0
A and B are not both zero, the graph of Ax + By = C is always a line.
when ,
The graph of Ax + By = C, where A and B are not both zero
A[tex]\neq[/tex]0
B[tex]\neq[/tex]0, is a line.
Divide both sides by B. Because the form Ax + By = C can describe any line,
it is called the standard form of an equation for a line.
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what Is the expanded notation for 8013
Answer:
8.013 x 10^3
Step-by-step explanation:
I need help with this question
The graphed function is decreasing on this following interval:
(-5, 5).
When a function is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
From this problem, there is only one interval, from x = -5 to x = 5, hence the interval is (-5, 5).
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12-(8+1)^2
explain please
Answer:
steps
12-(8+1)^2
=12-9^2
12-81
=-69
Step-by-step explanation:
Find the value of h.
75 ft
h 75 ft
42 ft
The value of h in the given diagram is 72 ft. The correct option is the third option 72
Calculating the height of a triangleFrom the question, we are to calculate h. h is the height of the triangle
First, we will the determine half the length of the base of the triangle.
Half the length of the base of the triangle = 42 ft/2
Half the length of the base of the triangle = 21 ft
Thus,
By the Pythagorean theorem, we can write that
75² = 21² + h²
5625 = 441 + h²
h² = 5625 - 441
h² = 5184
h = √5184
h = 72 ft
Hence, the value of h in the given diagram is 72 ft. The correct option is the third option 72
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Mandy has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years?
To the nearest cent, the amount she would have in 2 years is $44.10
What is future value of the deposit in savings account?
The future value of the savings account deposit is accumulated balance in the account after 2 years which includes the initial deposit plus interest earned over 2 years
FV=PV*(1+r)^N
FV=accumulated balance after 2 years=unknown
PV=initial deposit=$40
r=interest rate per year=5%
N=number of years that the deposit would last=2
FV=$40*(1+5%)^2
FV=$44.10
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for 1983 through 1989, the per capita consumption of chicken in the u.s. increased at a rate that was approximately linear. in 1983, the per capita consumption was 33.3 pounds, and in 1989 it was 48 pounds. write a linear model for per capita consumption of chicken in the u.s. let t
In 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.
What is per capita consumption?Per capita consumption is the yearly use of services and goods by each individual, calculated by dividing the total population's use of goods and services. This variable measures personal economic well-being directly.So,
According to the data, per capita consumption was 39.7 pounds in 1983 and 47 pounds in 1989.Per capita consumption is the yearly use of services and goods by each individual, calculated by dividing the total population's use of goods and services. This variable measures personal economic well-being directly.Assume t=0 corresponds to the year 1980.As a result, we can express the given data as ordered pairs (3,39.7) and (9,47).We can compute a linear function that passes through these points.Let us first calculate the slope of the linear function:
[tex]m=\frac{y_2-y_1}{t_2-t_1}=\frac{47-39.7}{9-3}=\frac{7.3}{6}=\frac{73}{60}[/tex]The required linear function can be written as:
[tex]y-39.7=\frac{73}{60}(t-3)[/tex]When we simplify this, we get:
[tex]y=\frac{73}{60} t+\frac{721}{20}[/tex]To calculate per capita consumption in 1995, enter t=15 into this function.
[tex]y=\frac{73}{60}(15)+\frac{721}{20}=54.3[/tex]Therefore, in 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.
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The correct question is given below:
For 1983 through 1989, the per capita consumption of chicken in the u.S. Increased at a rate that was approximately linear. In 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds. Write a linear model for per capita consumption of chicken in the u.S. Let t represent time in years, where t = 3 represents 1983. Let y represent chicken consumption in pounds. What would you expect the per capita consumption of chicken to be in 1995? What would you expect the per capita consumption of chicken to be in 1995?
4(18g-12)=12(6g-4)+4
Help me solve this please
Answer:
No solution.
Step-by-step explanation:
4(18g - 12) = 12(6g -4) + 4
4(18g) - 4(-12) = 12(6g) - 12(-4) + 4
72g + 48 = 72g + 48 + 4
72g + 48 = 72g + 52
72g -72g + 48 = 72g -72g + 52
48 = 52 This is a false solution so there is no solution. No value for x will make this equation true.
An item is regularly priced at 20$ . Hong bought it at a discount of 65% off the regular price . how much did Hong pay ?
If m/CDE is a straight angle, DE bisects m/GDH, mZGDE = (8x-1), m/EDH = (6x +
m/CDF = 43°, find each measure.
x =
m/GDH=
mZFDH=
m/FDE =
Answer:
From the way the problem is worded:
CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.
EDH is outside CDE and is of measure 6x + 15.
Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.
Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.
A circle centered at the origin contains the point (4, -3).
Select all points that also lie on the circle.
A. (-3,-4)
B. (0,4)
C. (3,-2)
D. (5,0)
The two points that also lie on the circle are:
A (-3,-4) and D (5,0)
Which points also ie on the circle?We know that a all the points on a circle are equidistant to the center of the circle, and in this case, the center is the origin (0, 0).
We know that the point (4, -3) lies on the circle, so the radius of the circle is:
R = √( (4 - 0)^2 + (-3 - 0)^2) = √25 = 5
So, any point that is at 5 units of the origin will also lie on the circle.
These points are:
A: (-3, -4)
R = √( (-3 - 0)^2 + (-4 - 0)^2) = √25 = 5
And the point D: (5, 0)
R = √( (5 - 0)^2 + (0 - 0)^2) = √25 = 5
So the correct options are A and D.
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Tom needs to drive a total of 13 miles. So far, he has driven 7.3 miles. How many more miles must Tom drive?
Answer:5.7 more miles that Tom has to drive
Step-by-step explanation: you add a extra zero to the 13 which would look like 13.0 and then put the 7.3 under 13.0 and it would look like this
13.0
7.3 and you subtract like normal
What is the value of f(-7)
Answer:
What's f(x)?
Step-by-step explanation:
How to work out (-4,-7),(7,5)
Answer: y = 12/11 x + -12/11
Step-by-step explanation:
m = y2 -y1/x2 -x1
x1 = -4
x2 = 7
into m = y2 - y1/x2 -y1
y1 = -7
y2 = 5
m = 12/11
x = -4 into y = mx + b
y = -7
b = - 12/11
y = 12/11x + -12/11 into
y = mx + b :
y + 12/11x + -29/11
Find the value of x so that the line through the pair of points has the given slope.
Points: (x,4) and (5,10)
Slope: 3
What does x =?
Write and solve a word problem that can be modeled by the quotient-84 divided by 3
Answer:
-28
Step-by-step explanation:
-84/3=-28
-28 is the answer to the problem
x/5 - 4 = 1 solve. show work using inverse operations
Answer:
25
Step-by-step explanation:
x/5-4=1
x/5=1+4
x/5=5
x=5×5
x=25
Find the distance between (0, -8) and (3, -2). Express your answer as a simplified radical, if possible.
O 5√3
O22.5
O √45
O 3√5
Answer:
3√5
Step-by-step explanation:
You use the Distance Formula to solve this.
d=√(x2-x1)^2 + (y2-y1)^2
Plug in your points.
d=√(3-0)^2 + (-2- -8)^2
Subtract and square.
d=√9 + 36
Add
d=√45
The square root of 45 is 6.70, so you would look for radicals.
3√5 is 45. <3
Pls help it’s due soon
Answer: the answer is c!
Step-by-step explanation:
What is the most specific name for the figure? I NEED THE ANSWER
The most specific name for the figure in the image is a Rectangle. Option B
This is further explained below.
What is the most specific name for the figure?Generally, According to the principles of Euclidean geometry, a Rectangle is considered to be a regular quadrilateral since it has four sides of equal length amongst opp two sides
Another way to describe it is as a rectangle with two neighboring sides that have the same length.
The term coordinate is pronounced exactly the same as o-ordinate. When used as an adjective, these phrases might signify to have the same status or rank, to have something to do with coordination, or to have something to do with an intersection of indices.
In conclusion, A Rectangle is the most accurate description of the shape that can be seen in the picture. Alternative B
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A school field trip cost $1,144 for a class of 22 students. What is the cost for each student?
Which table represents a linear function?
Answer:
Option C.
Step-by-step explanation:
For a table to be linear, the table must have a constant and even rate of change, meaning as X, the input, increases by 1, Y, the output, increases evenly by a random number we're gonna name "a". Now, a, in this case, is -8. The numbers increase evenly by -8(a), which would classify that function as linear. Thus, option C. is the correct answer.
5. Molly, Milo and Morgan shared a pan of brownies
1
baked by Mom. Molly ate of the pan of
4
2
brownies, Milo ate
of the pan of brownies and
6
1
-
-
Morgan ate of the brownies. What fraction of
3
the brownies was left over?
Please write your answer in simplest form.
6.
The fraction of the brownies left is 1/12.
We need to find out what fraction of the brownies is left.
Let " r " denote the fraction that is left.
Then we have r + 1/4 + 2/6 + 1/3 = 1
⇒ r + 1/4 + 1/3 + 1/3 = 1 (Writing the fraction 2/6 in the simplest form)
⇒ r + 1/4 + 2/3 = 1
⇒ r + (3 + 8)/12 = 1 (taking LCM of 4, 3 and adding the fractions 1/4 and 2/3)
⇒ r + 11/12 = 1
⇒ r = 1 - 11/12
⇒ r = (12 - 11)/12
⇒ r = 1/12.
Therefore, the fraction of the brownies left is 1/12.
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Disclaimer:
The fractions provided in the question are not clear.
Assuming the following to answer the given question.
Molly ate 1/4 of the brownies,
Milo ate 2/6 of the brownies, and
Morgan ate 1/3 of the brownies.
The data set shows the number of actors used in several school plays across Des Moines.
1. Which is greater the mean or median?
2. Would the mean or median be impacted more if we added the number 60 to the data set? Explain your reasoning
The box plot below show the distribution of the average amount of hours athletes were in the weight room per month.
1. Although the schools both have the same IQR, which school will have a greater variability? Explain your reasoning
2.Is the maximum value for school 1 an outlier? Explain your reasoning using the formula
3. A new athlete started attending school 2 and spends so many hours in the weight room that they are considered a outlier how many hours did the student need to spend in the weight room for school 2 to be considered an upper end outlier? Explain your reasoning using the formula.
The comparison of the mean and median of the data set of the dot plot in the first part and the variability and outlier of the dataset in the box and whiskers plot in the second part are;
First part;
1. The median is greater than the mean.
2. Both the mean and median will increase
Second part;
1. School 1 has greater variability
2. The maximum value of school 1 is not an outlier
3. The new athlete needs to spend 21 hours or more
How can the dot and box and whiskers plots be analyzed?First part;
1. The value in the dot plot are;
10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19
The number of data points = 36
The mean = The sum of the above data divided by 36
Using an online calculator of data sets, we have;
The mean = 15.194The median = 15.5Therefore;
The median is greater than the mean.2. The addition of 60 to the dataset will increase the number of data points from 36 to 37, thereby changing the median, which is the middle value to the 19th number, which is 16, while the mean value will also increase to 16.405, therefore;
The mean and median will both increaseSecond part;
1. A measure of variability of a box plot is the range, which is the difference between the largest and smallest values.
The range of school 1 is; 16 - 1 = 15
The range of school 2 is; 14 - 1 = 13
Therefore;
School 1 has greater variability.2. The maximum value of school 1 is 16
The inter quartile range of school 1 is; IQR = 10 - 4 = 6
An outlier = Q3 + 1.5 × IQR
The third quartile, Q3, for school 1 = 10Which gives;
An outlier ≥ 10 + 1.5 × 6 = 19
The maximum value for school 1 = 16 < 19, is not an outlier.3. Q3 for school 2 = 12
IQR for school 2 = 12 - 6 = 6
Which gives;
Outlier for school 2 ≥ 12 + 1.5 × 6 = 21
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