Two more times company B charge per snack than company A
What is meant by ratio?A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, and that of lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values.
From the two tables,
0.5/0.25=2
1/0.5=2
1.5/0.75=2
2/1=2
Therefore, 2 more times company B charge per snack than company A
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20
Write "less" or "greater" in the blank.
972 is
than 792
Answer:greater
Step-by-step explanation:
Answer:
972 is greater than 792.
1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2003 through 2014 can be approximated by 7.4x-y=-254 The number of network and data analyst jobs for the same years can be approximated by 12.4x-y=-231. For both equations, x is the number of years since 2003 and y is the number of jobs in thousands.
a. Use addition method to solve the following system of equations
{7.4x-y=-254
{12.4x-y=-231
The solution, rounded to the nearest whole number is: ?
Pls help!!!
Number of years since 2003 x=5 years and number of jobs in thousand y=288.
What is addition method of algebra?In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.
Why is addition method called elimination method?while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.
Given equation, 7.4x-y= -254
12.4x-y = -231
using addition method
-5x= -23
after solving x=4.6
x= 5 (nearest whole number)
y = 288.04
y =288
hence, number of years 5
number of jobs in thousand =288
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Which of the following equations has a solution different from the rest? (1 point)
¾ x+5=− ¼
½ x−3= ½
−1/7 x−34=¼
−0.35x−0.52=1.93
Answer: (-1/7)x - 34 = 1/4
Step-by-step explanation: The solution for all other equations is 7 and for the 3rd equation, the solution is 239.75 or 959/4
1) 3/4 X +5=-1/4
x=-7
2) 1/2X - 3 = 1/2
x=7
3) x = -137×7 /4
4) x= -7
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What is transpose of matrix
Step-by-step explanation:
it is the process of changing rows to columb
Find the value of x using the picture
The value of x is 91/9.
What is the value of X triangle?
The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
(9x+1)+ 88
Remove parentheses: (a)=a
9 x+1+88=180
Add the numbers: 1+88=89
9 x+89=180
Move 89 to the right side
9 x=91
Divide both sides by 9
[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]
Simplify
[tex]x=\frac{91}{9}$$[/tex]
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Answer:
x = 5
Step-by-step explanation:
You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.
Base angleEach base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...
9x +1 = 90 -(88/2)
9x = 45 . . . . . . . . . . subtract 1
x = 5 . . . . . . . . . divide by 5
The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off
$25,000 in student loan debt. What is the college graduate's new net worth?
O$16,081
O $21,167
O$13,833
O $33,097
The college graduate's new net worth is given as follows:
$13,833.
How to calculate the net worth?The net worth of a company or of a person is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts of the person.
The assets if the student are given as follows:
Signing bonus: $10,000.Furniture: $14,278.Savings Account Balance: $4,337.Car Value: $14,950.Computer and Software: $11,774.The liabilities of the student are given as follows:
Car Loan: $3,250.Credit Card Balances: $5,129.Student Loans: $58,097 - $25,000 = $33,097.Thus the student's net worth is calculated as follows:
(10000 + 14278 + 4337 + 14950 + 11774) - (3250 + 5129 + 33097) = $13,863.
Which is closest to the third option among those given.
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Answer:
the correct answer is 12057
Step-by-step explanation:
in order to calculate net worth, add up the assets, and then subtract the debt. be sure to pay attention to details
heres an UNRELATED TO THE QUESTION example:
i have...
$500 in my savings
$20 in my wallet
but im $200 deep in credit card debt..
(add 500 + 20, then subtract 200)
net worth: 320
What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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The wholesale price for a chair is $169. A certain furniture store marks up the wholesale price by 16%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.
Need Help!
The price of the chair in the furniture store is $94.
How to calculate the price of the chair in the furniture store?Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.
The price of the chair in the furniture store will be:
= $169 + (16% × $169)
= $169 + $27.04
= $196
The price is $194.
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two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price
Store B offers better $0.85 per-roll price than store A.
What is division?One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.
Given, two stores sell identical sandwich rolls in different size packages.
Store A sells a six-pack for $5.28.
To find the unit price,
we take division of 5.28 with number 6.
The unit price of sandwich roll for store A,
= 5.28 / 6
= $0.88
To find the unit price of sandwich roll for store B,
we take division of 3.40 with number 4.
= 3.40 / 4
= $0.85
And $0.85 < $0.88.
Therefore, Store B offers better per-roll price.
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An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
By solving a linear equation, it can be calculated that-
The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet
What is a linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, the linear equation is
Let the time taken by the airplane to meet the same altitude be t minutes
An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.
So altitude of the first airplane after t minutes = 55800 - 3500t
At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.
Altitude of second airplane = 2700t
By the problem,
The linear equation is
55800 - 3500t = 2700t
2700t + 3500t = 55800
6200t = 55800
t = 9 minutes
Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet
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Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to
clean 2 hamster cages.
Complete the table.
Minutes
15
Cages cleaned 2 4
Graph the data from the table.
Cages cleaned
20
18
16
14
12
10
8
30 55
•
90
8 10
The complete table will be;
Minutes 15 30
Cages cleaned 2 4
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Now,
Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Hence, By definition of proportion we get;
Let the time to clean 4 hamster cages = x
So, We get;
⇒ 15 / 2 = x / 4
⇒ 15×4 / 2 = x
⇒ 30 = x
⇒ x = 30
Thus, It take 30 minutes to clean the 4 hamster cages.
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Davina charges $15 an hour to weed gardens. What does she charge to weed a garden for 1, 2, 3, and 4 hours?
Answer:
1 - $15
2- $30
3 - $45
4 - $60
Step-by-step explanation:
$15/hour
1 - $15 =1*15
2- $30 =2*15
3 - $45 =3*15
4 - $60=4*15
What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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Q9.
Rachel, Samina and Tom share £600 between them.
2
Rachel gets 2/5 of the £600
ima
Samina gets 1/4 of the money that is left over.
Tom gets the rest of the money.
Tom says,
"I would have got more money if we had shared the £600 equally between us."
Is Tom correct?
You must show how you get your answer.
No. Tom is not correct.
If the money were split equally everyone would've gotten £200.
But, if everyone went by the mentioned distribution, then,
Rachel would get = 2/5 x 600 = £280
Remainder money = 600 - 280 = £320
Samina would get = 1/4 x 320 = £80
Tom would get the remaining money = 600 - (280 + 80)
= 600 - 360
= £240
Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.
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A random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the test statistic is?
Answer:
Step-by-step explanation:
Sorry if this is different, but based on what I read, here is the answer.
100 x 0.85 = 85
therefor it is 85%, which is significantly more than 80%
what is the total surface area of the triangular prism in square centimeters?
A 240 cm^2
B 368 cm^2
C 320 cm^2
D 344 cm^2
Answer:
D
Step-by-step explanation:
base area = (6 · 4)/2 = 24/2 = 12 cm²
half base length = 6 : 2 = 3 cm
leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm
perimeter = (5·2) + 6 = 10 + 6 = 16 cm
lateral area = 16 · 20 = 320 cm²
surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²
how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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maria has type b blood. she can safely receive blood transfusions from people with blood types o and b. what is the probability that a randomly chosen person from the united states can donate blood to maria?
The probability that a randomly chosen person from the united states can donate blood to maria is 0.50
considering blood to be of types A,B,AB and O
further all blood groups are equi probable
Probability of blood type A = probability of blood type B = probability of blood type AB = probability of blood type O = x
Probability of blood type A + probability of blood type B + probability of blood type AB + probability of blood type O = 1
⇒ 4x = 1
⇒ x = 1/4
Probability that a random person will have blood of type B or O = x+x
= 1/4 + 1/4
= 1/2
= 0.50
Hence we get the required answer.
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3, 1.6, 2.8, 2.5, 1.7, 2.8
What is the mean absolute deviation of these numbers?
The mean absolute deviation of the given numbers is 0.5.
What is a mean?The mean is the sum of all values divided by the total number of values.
The mean of the given number is obtained by dividing the sum of the values by its total number of value.
i.e. (1.6+1.7+2.5+2.8+2.8+3)/6 = 2.4
Then taking the difference of each number from the mean.
i.e. (1.6-2.4), (1.7-2.4),(2.5-2.4),(2.8-2.4),(2.8-2.4),(3-2.4)
i.e. -0.8,-0.7,0.1,0.4,0.4,0.6
Take the sum of the absolute value of the above numbers
i.e. |-0.8+-0.7+0.1+0.4+0.4+0.6| = 3
Divide 3 by 6 to obtain mean absolute deviation.
i.e 3/6 = 1/2 =0.5
Hence, 0.5 is the mean absolute deviation of the given numbers.
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Let f(x) be a 4th-degree polynomial function with zeroes 1,-1, and 3-i. If f(0)=20, write the equation in:
a) Factored form
b) Standard form
The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10
How to determine the polynomial expression?Factored form
The given parameters are
Degree = 4Zero = 1,-1, and 3-iThere are complex numbers in the above zeros
This means that, the other zero is
Zeros = 3 + i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))
This gives
P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)
Evaluate the products
P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]
So, we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
P(x) = (x - 1)(x + 1)[(x - 3)² + 1]
The standard form
In (a), we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
Expand
P(x) = (x² - 1) * (x² - 6x + 9 + 1)
So, we have
P(x) = (x² - 1) * (x² - 6x + 10)
Remove the brackets
P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10
Evaluate the like terms
P(x) = x⁴ - 6x³ + 9x² + 6x - 10
Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10
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the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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write a system of three linear equations with three variables each that has the unique solution . write your equations in standard form. use the variables , , and with non-zero coefficients.
the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
2x + 3y + 4z = 30
3x + 4y + 5z = 45
5x + 6y + 7z = 75
The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.
The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.
The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.
Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
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50 points please help asap
The domain is set of all real numbers and the range is y ≥ -4
How to determine the domain and the range of the function?From the question, we have the following parameters that can be used in our computation:
The equation is given as
g(x) = |x + 4|
The domain
The above equation is an absolute value equation
An absolute value equation can take any value as its input
This means that the domain is the set of all real numbers
When represented as an interval, we have
The domain is (-∝, ∝)
Also, we have
-∝ < x < ∝
Hence, the domain is the set of all real numbers
The range
Here, we have
g(x) = |x + 4|
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-4, 0)
Remove the x value
y = -4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
[-4, ∝)
Another representation is
y ≥ -4
So, the range is y ≥ -4
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Jin went to the grocery store and bought bottles of soda and bottles of juice. Each
bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar.
Jin purchased a total of 16 bottles of juice and soda which collectively contain 300
grams of sugar. Graphically solve a system of equations in order to determine the
number of bottles of soda purchased, x, and the number of bottles of juice
purchased, y.
Answer: x = 6, y = 10; as a point, that would be (6, 10).
Step-by-step explanation:
To do it graphically, you would just graph the equations 25x + 15y = 300 and x + y = 16. Then, you would find the intersecting point.
To do this, you should convert to point-slope format.
15y = -25x + 300 and x + y = 16
1) y = -5/3x + 20 and 2) y = -x + 16
Now, for equation 1, you start at the y-intercept (0, 20) and for every increase of 1 on the x-axis, you decrease -5/3 on the y-axis. To graph this in the software, you click on the point (0, 20) and on another point on the line y = -5/3x + 20. (Any will do, but it should be an integer. (3, 15) works.)
Do the same for equation 2. Start at the y-intercept (0, 16) and decrease 1 for every increase of 1 on the x-axis.
Look for the point(s) where the lines intercept. It is (6, 10). If you have the time, you can verify this algebraically.
