Answer: [tex]x=-5, -3[/tex]
Step-by-step explanation:
[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]
Explain the similarities and differences between the two relationships in this situation.
Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answer:
[tex]4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x[/tex]
Rewrite 9 as 3²:
[tex]\implies \displaystyle \int \dfrac{4}{x\sqrt{3^2+(\ln(x))^2}}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2+x^2} \textsf{ use the substitution }x=a \tan\theta}[/tex]
[tex]\textsf{Let } \ln x=3 \tan \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{3^2+(\ln x)^2} & =\sqrt{3^2+(3 \tan\theta)^2}\\ & = \sqrt{9+9\tan^2 \theta}\\ & = \sqrt{9(1+\tan^2 \theta)}\\ & = \sqrt{9\sec^2 \theta}\\ & = 3 \sec\theta\end{aligned}[/tex]
Find the derivative of ln x and rewrite it so that dx is on its own:
[tex]\implies \ln x=3 \tan \theta[/tex]
[tex]\implies \dfrac{1}{x}\dfrac{\text{d}x}{\text{d}\theta}=3 \sec^2\theta[/tex]
[tex]\implies \text{d}x=3x \sec^2\theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned} \implies \displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x & = \int \dfrac{4}{3x \sec \theta} \cdot 3x \sec^2\theta\:\:\text{d}\theta\\\\ & = \int 4 \sec \theta \:\: \text{d}\theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle 4 \int \sec \theta\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{7 cm}\underline{Integrating $\sec kx$}\\\\$\displaystyle \int \sec kx\:\text{d}x=\dfrac{1}{k} \ln \left| \sec kx + \tan kx \right|\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies 4\ln \left| \sec \theta + \tan \theta \right|+\text{C}[/tex]
[tex]\textsf{Substitute back in } \tan\theta=\dfrac{1}{3}\ln x :[/tex]
[tex]\implies 4\ln \left| \sec \theta + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]
[tex]\textsf{Substitute back in } \sec\theta=\dfrac{1}{3}\sqrt{9+(\ln x)^2}:[/tex]
[tex]\implies 4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]
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Kenneth wants to sew a tent, including the bottom so that it is entirely enclosed. He has a rectangular piece of canvas with dimensions of 12 feet by 20 feet. The front and back of the tent will be identical triangles, measuring 6 feet across at ground level, with two 5-foot sides meeting at the top. The depth of the tent will be equal to three times the height of the front of the tent. What is the depth of the tent?
Based on the calculations, the depth of tent is equal to 12 feet.
How to calculate the depth of the tent?Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):
Triangle ABC is an isosceles triangle (AB = AC).The front and back of the triangle are identical triangles.Side AD is perpendicular side BC.CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:
AC² = AD² + DC²
AD² = AC² - DC²
AD² = 5² - 3²
AD² = 25 - 9
AD² = 16
AD = √16
AD = 4 feet.
Also, we would determine the area of the triangle (ABC):
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Substituting the given parameters into the formula, we have;
Area = 1/2 × 6 × 4
Area = 12 feet².
Depth of tent = 3 × height of ADC
Depth of tent = 3 × 4
Depth of tent = 12 feet.
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A retailer allowed 4% discount on his goods to make 20% profit and sold a refrigerator for Rs 10,848 with 13% VAT. By how much is the discount to be increased so that he can gain only 15%?
The discount to be increased so that he can gain only 15% is 8%.
What is a discount? Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Since sales discounts lower the cost of a product, they are not considered costs. These monetary discounts provided to consumers do, however, have an impact on a company's financial statements. Thus they must be reported as a decrease in revenue under the accounts receivable line item.How much is the discount to be increased so that he can gain only 15%:
The cost price of the goods - y.
The selling price of the goods - x.
The selling price is
1.2y (100% + 20% = 120%).
The refrigerator was sold at 13% VAT at Rs. 10848:
=> 1.2y + 13%(1.2y) = 10848
=> 1.2y + 0.156y = 10848
=> 1.356y = 10848
=> y = 8000
Thus, the cp is Rs 8000.
The selling price is:
=> 0.96x = 1.2y
=> 0.96x = 1.2(8000)
=> x = 10000
The selling price is Rs. 10000
For a profit of 15%, that is 1.15(8000) = 9200, the discount is:
(1 - discount)10000 = 9200
1 - discount = 0.92
Discount = 1 - 0.92 = 0.08 or 8%
How much is the discount to be increased so that he can gain only 15%: Discount=8%
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An amusement park sells adults' and
children's passes. An adult's pass is $25,
and a child's pass is $15. A group spent
$440 on 20 passes. How many children's
passes did the group purchase?
A
Answer:
6 children passes
Step-by-step explanation:
a = adult and c = children
25a + 15c = 440 and a + c = 20
c = 20 - a
25a + 15(20-a) = 440
25a + 300 - 15a = 440
25a - 15a = 440 - 300
10a = 140
a = 140/10
a = 14 and this is 14 adult tickets
Now we plug the a value into the equation to find the c value
14 + c = 20
c = 20 - 14
c = 6
Verify answer:
25(14) = 15(6) = 440
350 + 90 = 440
440 = 440
Help please! What is the correct answer and how do I solve for R?
quien me hace una canción de ley de los cosenos de C por favor le doy 100 estrellas y corona
Answer:
..........................................
Give the missing angle as a bearing.
North
70⁰
Answer:
30°
Step-by-step explanation:
To make sure it's complete
ASAP NOW
below is the question
The mean of the data set A is 4.58 while the mean of data set B is 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The mean of a set of numbers is the average of that group of number. It is the ratio of the sum of the data to the total number of data.
Mean of data set A = [(3 * 1) + (4 * 3) + (5 * 2) + (6 * 2) + (7 * 3) + (8 * 1)] / (1 + 3 + 2 + 2 + 3 + 1) = 4.58
Mean of data set B = [(4 * 2) + (5 * 2) + (6 * 2)] / ( 2 + 2 + 2) = 5
The mean of the data set A is 4.58 while the mean of data set B is 5.
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
Three students want to estimate the mean word length of the same book. To do this, each student randomly chose 4 words from the book and recorded their lengths. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. (number of letters) Sample mean 3, 3, 4, 7 - 8, 2, 3, 6 - 8, 5, 2, 4 (b)Use the table to calculate the range of the sample means. Range of sample means: (c)The students are going to use the sample means to estimate the mean word length in the book. Select all the true statements below. The mean of the sample means will tend to be a worse estimate than a single sample mean. A single sample mean will tend to be a worse estimate than the mean of the sample means. The closer the range of the sample means is to 0, the more confident they can be in their estimate. The farther the range of the sample means is from 0, the more confident they can be in their estimate.
The solutions to the questions are given below
a)
sample(n) word length sample mean
1 5,4,4,2 3.75
2 3,2,3,6 3.5
3 5,6,3,3 4.25
b)R =0.75
c)
The mean of the sample means will tend to be a better estimate than a single sample mean.The closer the range of the sample means is to 0, the more confident they can be in their estimate.What is the students are going to use the sample means to estimate the mean word length in the book.?The table below shows sample means in the table.
sample(n) word length sample mean
1 5,4,4,2 3.75
2 3,2,3,6 3.5
3 5,6,3,3 4.25
b)
Generally, the equation for is mathematically given as
variation in the sample means
R =maximum -minimum
R=4.25-3.5
R =0.75
c)
In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.
They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.
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How does changing the function from f(x) = -5 cos 2x to g(x) = -5 cos 2x-3 affect the range of the function?
Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).
Answer:
See below.
In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a
Step-by-step explanation:
Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1
If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a
An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.
But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.
Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2
Mr. Salazar assigns the same number of homework questions each school day. The ratio table below shows the total number of homework questions assigned after a certain number of school days.
Homework
Number of days
Total number of questions
4
20
8
40
11
55
16
?
After 16 days, how many total homework questions have been assigned?
After 16 days, the total homework questions that have been assigned would be 80 questions.
How many homework questions would be assigned after 16 days?
Ratio expresses the equivalent relationship between two numbers. It shows the frequency of the number of times that one value is contained within other value(s).
A ratio table can be described as table that shows equivalent values between two numbers.
The first step is to determine the ratio between the number of days and the total number of questions.
Ratio = money saved / money earned
8/10 = total number of questions / number of days
55 / 11 = 5
Now, multiply the ratio gotten in the previous step by the number of days
Total number of homework questions = number of x ratio
5 x 16 = 80 questions
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area of an isosceles triangle is 60 square cm. If the measure of its equal sides is 13 square cm then find the base sides.
The base side of the isosceles triangle in discuss as described in the task content is; 10cm.
What is the length of the base side of the isosceles triangle?According to the task content, the area of the isosceles triangle is 60 square cm.
Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.
Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.
Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Using a quadratic regression equation, it is found that the prediction of volunteers in year 10 is of:
A. 47.
How to find the equation of quadratic regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:
(1, 20), (2,17), (3, 16), (4,16), (5,18), (6,21), (7,25), (8,31)
Inserting these points into the calculator, the prediction of y for a value of x is given as follows:
y = 0.702x^2 - 4.726x + 23.857
Hence, when x = 10, the prediction is:
y = 0.702 x 10² - 4.726 x 10 + 23.857
y = 47.
Hence option A is correct.
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17. In a spelling competition, school X had 12 more participants than school Y and 18 fewer participants than school Z. The ratio of the number of boys to the number of girls in school X, Y and Z were 1:2, 1:5 and 2: 1 respectively. There were 50 more girls than boys in total from the 3 schools. How many participants from the 3 school were there in all?
There were 204 participants from the three schools
How to determine the number of participants?The given parameters are:
X = 12 + Y
X = Z - 18
Girls = Boys + 50
The ratios of the number of boys to girls in the schools are:
1 : 2
1 : 5
2 : 1
This means that:
School X: Boys = 1/3 and Girls = 2/3School Y: Boys = 1/6 and Girls = 5/6School Z: Boys = 2/3 and Girls = 1/3So, we have:
Boys = 1/3X + 1/6Y + 2/3Z
Girls = 2/3X + 5/6Y + 1/3Z
Substitute the above equations in Girls = Boys + 50
2/3X + 5/6Y + 1/3Z = 1/3X + 1/6Y + 2/3Z + 50
Evaluate the like terms
1/3X + 2/3Y - 1/3Z = 50
Multiply through by 3
X + 2Y - Z = 150
So, we have:
X = 12 + Y
X = Z - 18
X + 2Y - Z = 150
Substitute X = 12 + Y in X = Z - 18 and X + 2Y - Z = 150
12 + Y = Z - 18 ⇒ Y - Z = 30
12 + Y + 2Y - Z = 150 ⇒ 3Y - Z = 138
Subtract Y - Z = 30 from the equation 3Y - Z = 138 to eliminate Z
2Y = 108
Divide by 2
Y = 54
Substitute Y = 54 in X = 12 + Y
X = 12 + 54
X = 66
Substitute X = 66 in X = Z - 18
66 = Z - 18
Solve for Z
Z = 66 + 18
Z = 84
So, the total number of participants from the 3 schools is
Total = X + Y + Z
This gives
Total = 66 + 54 + 84
Evaluate the sum
Total = 204
Hence, there were 204 participants from the three schools
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A polynomial function that describes an
enclosure is
V(x) = 1500x-x^2
, where
X
is the length of the fence in feet. What is the maximum area of the enclosure? <<<
The maximum area of the enclosure is 562500 square feet
How to determine the maximum area?The function is give as:
V(x) = 1500x - x^2
Differentiate
V'(x) = 1500 -2x
Set to 0
2x = 1500
Divide by 2
x = 750
Substitute x = 750 in V(x) = 1500x - x^2
V(x) = 1500*750 - 750^2
Evaluate
V(x) = 562500
Hence, the maximum area of the enclosure is 562500 square feet
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Area=
Help me please asap.
Thanks so much :)
The area of the given parallelogram is 8 square units
Area of a parallelogramA parallelogram is a 2 dimensional figure with 4 sides and angles. From the given diagram, the opposite sides are equal and the sum of the adjacent angles are supplementary
The formula for calculating the area of a parallelogram is expressed as:
A = base * height
From the given diagram
Base = (4, 0) = 4 units
Height. = (2, 0) = 2 units
Substitute the given values into the formula to have:
A = 4 units * 2 units
A = 8 square units
Hence the area of the given parallelogram is 8 square units
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According to USA Today, the average cost of a private university is $50,000 with a population standard deviation of $2,500. 100 universities are randomly selected and the average income of those 100 universities was $49,450. Using the 5 step hypothesis testing process, can you support the claim that the average cost of private universities are decreasing? Use a .01 significance level. (Use the z or t value of -2.2) What is your conclusion based on p-value?
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
What are the hypothesis tested?At the null hypothesis, it is tested if the average cost is still of $50,000, that is:
[tex]H_0: \mu = 50000[/tex]
At the alternative hypothesis, it is tested if the average cost is decreasing, that is:
[tex]H_1: \mu < 50000[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]
z = -2.2.
What is the p-value and the conclusion?Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.
Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
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Anais bought yards of ribbon. she had feet inches of ribbon left after trimming some curtains. how many inches of ribbon did anais use to trim the curtains?
Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.
What is Unit Conversion?
Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion. The units are expressed using scientific notation and converted into numerical values as per the quantities.Anais bought 2 1/2 yards of ribbon.
And she had 2 feet 8 inches left after trimming some curtains.
The first thing to do is to convert all units to inches;
From standard conversion rate.
1 yard = 36 inches
As such 2 1/2 yards of ribbon in inches will be:
= 2 1/2 × 36 inches
= 5/2 × 36 inches
= 5 × 18 inches
= 90 inches of ribbon bought.
Similarly, since 1 foot = 12 inches.
The amount of curtains left after trimming is:
= ( ( 2 × 12 ) + 8 )inches
= (24 + 8) inches
= 32 inches
If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.
It implies that the number of inches of ribbon that Anais used is:
= 90 inches - 32 inches
= 58 inches
Therefore, we can conclude that Anais used 58 inches of ribbon.
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The complete question is-
Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?
Anais used _____ inches of ribbon.
Select the correct answer.
What is the solution to the equation?
2(x + 7) = 8
OA. -15 and 1
OB. -15
OC. 1
OD.
no solution
Answer:
Option D is correct.
No solution
Step-by-step explanation:
2(x+7)=8
Apply 2 into bracket:
2x+14=8
2x=8-14
2x=-6
Divide both sides by 2:
x=-3
hence here is no option for x=-3, so answer is no solution.
April was asked to determine whether f(x)=x^3 -1 is even, odd, or neither. Here is her work:
April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took [tex]f(-x) = - f(x)[/tex], which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].
A function f(x) is said to be odd or even when it completes the condition:
f(-x) = -f(x), for f(x) to be an odd function, andf(-x) = f(x), for f(x) to be an even function.In the question, we are given that April was asked to determine whether [tex]f(x) = x^3 - 1[/tex], is even, odd, or neither, and are shown her work.
We are asked whether April's work is correct, and if not, what is the first step where April made a mistake.
To check for a function is even or odd, we first calculate f(-x).
April's first step was also finding f(-x), which she found accurately as [tex]f(-x) = -x^3 - 1[/tex].
Next, we need to check whether f(-x) is equal to f(x), -f(x), or neither, to check if the function is even, odd, or neither, respectively.
April, also choose the right step of checking, but did a mistake in checking, since f(-x) ≠ f(x), and also, f(-x) ≠ - f(x), since, [tex]- f(x) = -(x^3 - 1)[/tex] = [tex]-x^3 + 1[/tex], which is not equal to f(-x).
Thus, April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took f(-x) = - f(x), which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].
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A study of college freshmen found that students who watched tv for more than one hour each night gained 15 pounds in the first semester, compared to those who watched less than one hour. they concluded that there is an association between watching tv and weight gain in college freshmen. which study design did they most likely use?
Answer:
C. They most likely used an observational study asking students to keep track of their TV habits and weight.
A. This is an experiment because a treatment was applied to a group.
Step-by-step explanation:
According to our question:
1. The study concluded that there is a relation between watching TV and the weight gain in college freshmen.
Now, this is possible when a group of college students were asked to participate to watch TV for more than 1 hour for a specific amount of time and have a record of their weights.
So, the study is an observational study where the habits and weights of college students were observed.
Hence, option C is correct.
2. The students were divided onto two groups where one group used the computer program and the other did not to check the improvement in the reading levels.
This means that the students were given a procedure to follow during the study in order to see the results..
So, the study is an experiment where a treatment is applied to the group of students.
Hence, option A is correct.
Answer: C
For the people who want only one answer and not 2 for the question if you can only submit one answer :)
The area of a painting is 4081 c m squared.
If the width of the painting is 53 cm, what is its length, in centimeters?
Type your numerical answer below (without units). If necessary, round to the nearest integer.
The length of the rectangle is 77cm.
According to the statement
we have given that the area of a painting is 4081 c m squared. and width of the painting is 53 cm.
And we have to find the Length of the painting.
So, For this purpose
Area of rectangle is the region occupied by a rectangle within its sides. It depends on its sides.
So, the formula to find the area of rectangle is
Area = Length*Breadth
4081 = L*53
L = 4081/53
L = 77 cm.
So, The length of the rectangle is 77cm.
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Translate the triangle by
(-2 and -4)
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on
each queen bed. In one house, she decorated 1 twin bed and 1 queen beds and used a total of 15 pillows. At another house, she used
21 pillows to spruce up 2 twin beds and 1
queen beds. How many decorative pillows did the realtor arrange on each bed?
The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.
Simultaneous equationlet
Number of decorative pillows for twin bed = xNumber of decorative pillows for queen bed = yx + y = 15
2x + y = 21
From equation (1)
x = 15 - y
Substitute x = 15 - y into (2)2x + y = 21
2(15 - y) + y = 21
30 - 2y + y = 21
- 2y + y = 21 - 30
-y = -9
y = 9
Substitute y = 9 into
x + y = 15
x + 9 = 15
x = 15 - 9
x = 6
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Orlando is 12 years older than Omar. Carl is three times older than Orlando. The sum of their ages is 68.Find the ratio of Omar’s age to Carl’s age to Orlando’s age.
Step-by-step explanation:
let's name the variables for the age of the people as the people themselves :
orlando = omar + 12
carl = 3×orlando
carl + orlando + omar = 68
using the first equation in the second equation, and then that result and the first equation in the third equation :
carl = 3×(omar + 12)
3×(omar + 12) + (omar + 12) + omar = 68
3×omar + 36 + omar + 12 + omar = 68
5×omar + 48 = 68
5×omar = 20
omar = 4
orlando = omar + 12 = 4 + 12 = 16
carl = 3×orlando = 3×16 = 48
the ratio omar : carl : orlando
4 : 48 : 16 = 1 : 12 : 4
Find the surface area of the prism.
Answer:
204
Step-by-step explanation:
6*10=60
6*6=36
6*8=48
2((10*6)/2)=60
60+60+36+48=204
On Wednesday, 1/3 of the students in Mr. Short's homeroom had drama practice, and 1/4 of his other homeroom students had band practice. If 6 students had band practice, how many students are in Mr. Short's homeroom?
Answer:
36
Step-by-step explanation:
Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:
Let x = the number of students in the homeroom
1/3 x have drama
1/4 (x - 1/3x) have band, and we are told 6 students have band, so
1/4 (x - 1/3 x) = 6
1/4 (2/3 x) = 6
2/12 x = 6
1/6 x = 6
6 × 1/6 x = 6 × 6
1 x = 6 × 6
x = 36
Answer:
36
Step-by-step explanation:
Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that
6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$
so n = 6 x 6 = 36 students.
3x+5<6x+8
4x+3 is <7x+5
The solution to the inequalities 3x + 5 < 6x + 8 and 4x + 3 < 7x + 5 is x > -1 and x > -2/3 respectively
InequalityInequality signs are;
Greater than >Less than <Equal to =Less than equal to ≤Greater than equal to ≥3x + 5 < 6x + 8
collect like terms3x - 6x < 8 - 5
-3x < 3
divide both sides by -3x > 3/-3
The inequality sign is flipped from < to greater than because of the division with negative value.
x > -1
2. 4x + 3 < 7x + 5
collect like terms4x - 7x < 5 - 3
-3x < 2
divide both sides by -3The inequality sign is flipped from < to greater than because of the division with negative value.
x > -2/3
Learn more about inequality:
https://brainly.com/question/25275758
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