The number of soda bottles = 4
The number of sugar bottles = 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
Let the number of soda bottle = x
And, The number of sugar bottle = y
Since, Total number of bottles = 11
So, We can formulate;
⇒ x + y = 11 .... (i)
And, Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
So, We can formulate;
⇒ 45x + 15y = 285 ... (ii)
Multiply by 15 in equation (i) and subtract from (ii), we get;
⇒ 45x + 15y - 15x - 15y = 285 - 165
⇒ 30x = 120
Divide by 30;
⇒ x = 4
Hence, x + y = 11
4 + y = 11
y = 11 - 4
y = 7
So, The number of soda bottles = 4
The number of sugar bottles = 7.
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Which of the following properly describe
"slope"? Select all that apply.
0
A)
ratio of the change in y-values
(rise) for a segment of the graph to
the corresponding change in x-
values (run)
OB) x₂-x₂
y₂-M1
C) ₂-₁
x₂-x₂
D) run/rise
☐ E) rise/run
Please Help i will give brainliest Its a emergency please help with this equation i am not sure what to do its a math problem
Answer:
the last choice is the 6th term of expression
Step-by-step explanation:
all the work and steps is in the pic go check it out sorry if wrong and have a wonderful day:)
-
у
0
1
1
3
2
9
3
27
A pottery studio has 11 pounds of clay. It takes 7/8 of clay to make a coffee mug find 11 divided by 7/8.Then interpret the question.
The number of coffee mugs that can be made is 12.
How to calculate the fraction?From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.
The number of coffee mugs that can be made will be:
= Number of pounds of clay / Fraction used for each mug
= 11 / 7/8
= 11 × 8/7
= 88 / 7
= 12
There'll be 12 coffee mugs.
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what is the answer to (-6, 9), (7, -9)?
Answer:
100000000000000000000000000000
Step-by-step explanation:
Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
The person that has the higher average speed is Teresa.
How to find average speed?Average speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
Therefore, Karl drove 40 miles in 50 minutes and Teresa drove 35 miles in 42 minutes.
The person that has the higher average speed can be calculated as follows;
average speed of Karl = distance / time
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minutes
average speed of Teresa = distance / time
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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To mail a letter to Vienna, Austria the post office charges a flat rate of $5.50 and an additional $0.25 for every ounce the letter weighs. The cost of mailing a letter is
determined by the equation y = 0.25x + 5.50, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 1 of 2: Graph the equation by finding two points that satisfy the equation and plotting them on the graph. To plot a point, click on the appropriate position on
the graph. You may move a point by clicking and dragging.
Answer:
Step-by-step explanation:
See attached graph
Two pints selected are:
2 packages = $6
5 packages = $6.80
Can someone please help me?
There is a profit made by the Mia in that particular month of the amount $350.
What is meant by the term revenue?The total amount of money produced by sale of products or services connected to the company's main operations is referred to as revenue.The total earnings as well as profit of a company is referred to as income or net income.Net revenue along with net income are both useful in determining a company's financial strength, although they are not exchangeable.For the given question,
The table is given for the revenue and expenses made by Mia.
The total revenue made by Mia in that particular month is $9,550.
The total fixed expenses are $9,000.
The variable expense is $200.
Thus, the difference in the expense is-
Difference = Revenue - fixed expense - variable expense
Difference = $9,550 - $9,000 - $200.
Difference = $350
As, the difference is positive there is profit made by Mia.
Thus, there is a profit made by the Mia in that particular month of the amount $350.
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help me if you love Markiplyer and want to see his OF
It is to be noted that, given the dilation factor stated above, the coordinates of S' is (4, 3).
What is a dilation in math?The mathematical Definition of Dilation is given as a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
The computation for the above result is given as follows:
Given that RST has vertices R(0,0), S(6, 3), and T(3, -3); and
The image R'S'T' is the image of RST after a dilation with center (0,0) with scale factor 2/3,
We must determine the coordinates of point S'.
The coordinates of S' can be determined by multiplying both the x and y - coordinates of the point S with the scale factor 2/3.
Let us look at x- coordinate with point S and multiply it with the scale factor of 2/3.
we have: 6 x 2/3 = 4
Hence, x- coordinate for S' = 4
Redo for Y
3 x 2/3 = 3
Hence, y- coordinate for S' = 3
Hence the coordinates of S' is (4, 3).
Hence having applied the principle of dilation, the coordinates of S' are (4,3)
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6. If f(x) = x2 - 1, which of the following is equal to g(x) = f(x - 3)?
A.g(x) = x/ +8
B.g(x) = x2 + 6x+8
C.g(x)= x2 - 6x + 8
D.g(x) = x2 + 6x- 10
( x - 2) ( x - 4 ) is function which is equal to g(x) .
In the simplest terms, what is a function?
As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.f(x) = x² - 1
f( x - 3 ) = ( x - 3 )² - 1
= x² + 9 - 6x -1
= x² -6x + 8
= x² -4x -2x + 8
= x( x - 4 ) -2( x - 4)
= ( x - 2) ( x - 4 )
g(x) = f(x - 3)
= ( x - 2) ( x - 4 )
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What is the rate of change (slope) and the initial value (y-axis) for this table?
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24
Find the Value of X in each case. RSM geo Lesson 9, 24d
The value of x in the triangle is 17 degrees.
How to find angle in a triangle?A triangle is a polygon with three sides and angles.
The sum of angles in a triangle is 180 degrees.
Therefore, ABC is a triangle and CDE is a also a triangle.
Let's find the angle x in the triangle CDE.
Hence,
∠ACB = 180 - 4x - 49 (sum of angles in a triangle is 180 degrees)
∠ACB = 180 - 49 - 4x
∠ACB = 131 - 4x
Therefore,
180 = ∠DCE + ∠DEC + ∠CDE
∠CDE = 100°
∠DEC = x
∠DCE = ∠ACB = 131 - 4x
Hence,
180 = 131 - 4x + x + 100
180 = 231 - 4x + x
180 - 231 = -3x
-51 = -3x
divide both sides by -3
x = -51 / -3
x = 17
Therefore,
x = 17
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If a = -3x and b = -2i, then find the value of the ab² in fully simplified form.
The value of the expression ab² is 12x where a = -3x and b = -2i
How to evaluate the expression?From the question, the values of the variables are given as
a = -3x and b = -2i
The expression to calculate is then calculated as
ab²
Substitute the known values in the above equation
So, we have the following equation
ab² = (-3x) * (-2i)²
Evaluate the exponent
So, we have the following equation
ab² = (-3x) * -4
Evaluate the product
So, we have the following equation
ab² = 12x
Hence, the solution to the expression is 12x
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Each serving ofsalad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar. A tablespoon of olive oil costs $0.13 and a tablespoon of vinegar costs $0.04. What is the cost of x servings of dressing in dollars?
The cost of x servings of dressing in dollars will be $0.43x.
According to the question,
We have the following information:
Each serving of salad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar.
Cost of 1 tablespoon of olive oil = $0.13
Cost of 1 tablespoon of vinegar = $0.04
So,
The cost of each serving of salad = Cost of 3 tablespoons of olive oil + cost of 1 tablespoon of vinegar
The cost of each serving of salad = 3*0.13 + 0.04
The cost of each serving of salad = $(0.39+0.04)
The cost of each serving of salad = $0.43
Now,
The cost of x servings of salad = $0.43x
(Note that if we have to find the cost of more than 1 product than the number has to be multiplied with the cost of one product.)
Hence, the cost of x servings of salad dressing is $0.43x.
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{(2, 1), (-7, -1), (-5, -5), (9, -4), (-3, -3) }
Domain:
Range:
Here are the scores that Jenna has received on her seven quizzes: 16, 11, 20, 16, 12, 17, 18 What is the lower quartile?
Based on the scores that Jenna received on her quizzes, the lower quartile can be found to be 12
How to find the lower quartile?To find the lower quartile, use the formula:
= (Number of scores + 1) x 1/4
But before that, you need to arrange the scores that Jenna received, from ascending order:
11, 12, 16, 16, 17, 18, 20
Then use the formula to find the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
It is in the second position. The lower quartile score is therefore 12.
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Based on the scores that Jenna received on her quizzes, the lower quartile would be; 12
What is quartile?Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
To determine the lower quartile, use the formula as;
= (Number of scores + 1) x 1/4
But before that, we need to arrange the scores that Jenna received, from ascending order which is;
11, 12, 16, 16, 17, 18, 20
Thus, use the formula for the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
Hence, It's in the second position. The lower quartile score is; 12.
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suppose the length of a rectangular room is (x + 4) meters and the width is (x - 4) meters, what expression that can be used to represent the area of the room?
Answer:
Step-by-step explanation:
area=l*w
(x+4)(x-4)
x^2-16 (use foiling)
for rayleigh winds with an average wind speed of 8 m/s: a. how many hours per year do the winds blow at less than 13 m/s? (5') b. how many hours per year are wind speeds above 25 m/s? (5')
A. 7658.8 hr/year
B. 4.082 hr/year
C. 99206 kwh
Moreover, The annual average wind speed was calculated directly at 4.56 m/s. Using the Weibull distribution, the annual wind speed is 4.55 m/s, while using the Rayleigh distribution it is 4.523 m/s. The annual wind power density was directly calculated to be 114.54 W/m2.
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Arianys is driving to a concert and needs to pay for parking. There is
an automatic fee of $11 just to enter the parking lot, and when she
leaves the lot, she will have to pay an additional $3 for every hour she
had her car in the lot. How much total money would Arianys have to
pay for parking if she left her car in the lot for 4 hours? How much
would Arianys have to pay if she left her car in the lot for t hours?
Cost of parking for 4 hours:
Cost of parking for t hours:
Pls help me
Answer:
c = 3t + 11
t = time in the lot
c = total cost
4 hours the cost will be $23
Step-by-step explanation:
Cost for 4 hours.
c = 3t + 11
c = 3(4) + 11
c = 12 + 11
c= $23
The following shape consists of a rectangle and a triangle. Determine its area.
Answer:
72 cm²
Step-by-step explanation:
You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.
AreaThe area of the rectangle is ...
A = bh
A = (8 cm)(7 cm) = 56 cm²
The area of the triangle is ...
A = 1/2bh
A = 1/2(8 cm)(4 cm) = 16 cm²
Total areaThe total area is the sum of the areas of the parts:
total area = rectangle area + triangle area
= (56 cm²) +(16 cm²) = 72 cm²
The area of the shape is 72 cm².
__
Additional comment
You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm wide rectangle with the same base.
The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.
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Factor Completely.. Please help with this I am really behind..
The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)
What is factorization?In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.
The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).
This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)
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what does x = to in the equation 4x +4<9x +8?
The given inequality is expressed as
[tex]4x\text{ + 4 }\leq\text{ 9x + 8}[/tex]The first step is to collect like terms. Thus, we have
[tex]\begin{gathered} 4x\text{ - 9x }\leq\text{ 8 - 4} \\ -\text{ 5x }\leq\text{ 4} \\ \end{gathered}[/tex]We would find x by dividing both sides of the inequality by - 5. Since - 5 is negative, the inequality symbol would be reversed. Thus, we have
[tex]\begin{gathered} \frac{-\text{ 5x}}{-\text{ 5}}\ge\frac{4}{-\text{ 5}} \\ x\text{ }\ge\text{ }\frac{-\text{ 4}}{5} \end{gathered}[/tex]P.L.Z HELP. 50pts
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Slope-intercept form: y=-2/3=x+490 The slop is -2/3 and the y-intercept is unknown.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answer:
[tex]y=-\dfrac{2}{3}x+490[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]2x + 3y = 1470[/tex]
To change the equation to slope-intercept form, isolate y:
[tex]\implies 2x + 3y -2x=1470 -2x[/tex]
[tex]\implies 3y=-2x+1470[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{-2x+1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+\dfrac{1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+490[/tex]
Therefore:
[tex]\textsf{Slope} =-\dfrac{2}{3}[/tex][tex]\textsf{$y$-intercept}=490[/tex]To graph this line with the slope-intercept method:
Plot the y-intercept at (0, 490).The slope gives us the change in y-values over the change in x-values (rise over run). Therefore, use the slope to plot the next few points by mapping 3 units to the right and 2 units down each time:To write the equation in function notation, replace the y-variable for f(x).
[tex]\implies f(x)=-\dfrac{2}{3}x+490[/tex]
The graph of the function represents:
The number of wrap lunch specials sold given the number of sandwich lunch specials sold.The y-intercept of the graph is (0, 490).
To find the x-intercept, set the function to zero and solve for x:
[tex]\implies -\dfrac{2}{3}x+490=0[/tex]
[tex]\implies -\dfrac{2}{3}x=-490[/tex]
[tex]\implies -2x=-1470[/tex]
[tex]\implies x=735[/tex]
Therefore, the x-intercept is (735, 0).
The graph of the function is attached.
If Sal's total profit on lunch specials for the next month is $1,593 (where the profit amounts are the same) the equation would be 2x + 3y = 1593 and the function would be:
[tex]g(x)= -\dfrac{2}{3}x+531[/tex]
As the coefficient of the x-variable has not changed, the slopes of the two functions are the same.
As the total profit has changed, the intercepts are different.
The y-intercept of the first function is (0, 490) and its x-intercept is (735, 0). Whereas the y-intercept of the second function is (0, 531) and its x-intercept is (796.5, 0).
There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person uses at least 2 facilities?
4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is
4/36=1/9
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
If four people use all three facilities,
then 16 - 4 = 12 of them use the gym and the track but not the pool, and 9 - 4 = 5 of them use the pool and the track but not the gym.
The pool and gym are used by 19 - 4 = 15 individuals, however the track is not used.
4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is
4/36=1/9
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What is r + s + t when r = 25, s = –11, and t = –7?
Answer:
7
Step-by-step explanation:
Whats the answer to x + 23 12
A.8
B.-11
C.-6
D.6
Answer:
-11
Step by step explanation:
-11+23=12
Every computer that a business owner purchases will lose most of its value after 5 years of use. The owner plans to purchase a computer for $2,100 and replace it after 4 years.Part BMethod 2 of determining the computer's value is to reduce its value by 30% after each year of use.Which function, g(n), represents the value of the computer after years of use for Method 2?g(n) = 0.3n(2,100)g(n) = 0.7 (2.100)g(n) = 2.100(0.3)^ng(n) = 2.100(0.7)^n
Answer:
D. g(n)=2100(0.7)^nD. g(n)=2100(0.7)^
Explanation:
• The purchase price, i.e. the initial value of the computer = $2100.
,• The rate at which its value reduces = 30%.
To determine the computer's value after n years of use, we use the depreciation formula below:
[tex]A(n)=P(1-r)^n[/tex]In this case:
• The Principal, P = $2100
,• The rate, r = 30%
Substitute these values into the formula.
[tex]\begin{gathered} g(n)=2100(1-30\%)^n \\ =2100(1-\frac{30}{100})^n \\ =2100(1-0.3)^n \\ \implies g(n)=2100(0.7)^n_{} \end{gathered}[/tex]The function g(n) that represents the value of the computer after n years of use is Option D.
draw a model to represent 2 1/4 and write it as an improrer frrcation
The improper fraction equivalent of the fraction 2 1/4 is 9/4.
Improper fraction:
Basically, the improper fraction is also the fraction where the numerator is greater than or equal to the denominator.
Given,
Here we have the mixed fraction 2 1/4.
And we have to convert this mixed fraction into improper fraction.
The conversion from mixed fraction to an improper fraction will follow the following formula,
numerator = (denominator × whole number) + numerator of mixed fraction
Based on the this rule, the numerator of the improper fraction is,
=> numerator = (4 x 2) + 1
=> numerator = 8 + 1
=> numerator = 9
The denominator will remain same.
Therefore, the resulting improper fraction is 9/4.
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Two observers are standing on shore 20 mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. one observer is 10 miles from the sailboat and the other observer is 25 miles from the sailboat. round to the nearest degree
Using the law of sines, supposing C = 30º, the angle of each observer with the sailboat is:
Observer A: 136º.Observer B: 14º.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A has length a.The length of the side opposite to angle B has length b.The length of the side opposite to angle C has length c.The lengths and the sine of the angles are related according to the following rule:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The measure of angle B is found as follows:
sin(B)/10 = sin(C)/20
sin(B)/10 = 0.5/20 (sin(C) = 0.5)
sin(B) = 5/20
sin(B) = 0.25
B = arcsin(0.25)
B = 14º.
The measure of angle A is found as follows:
sin(A)/25 = sin(C)/20
sin(A)/25 = 0.5/20 (sin(C) = 0.5)
sin(A) = 12.5/20
sin(A) = 0.625
A = arcsin(0.625)
A = 136º.
Missing informationThe problem is incomplete, hence we suppose that the angle C is of 30º and problem asks for the angle measure of each angle.
(drawing is not to scale).
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Modeling with Mathematics:
A square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.
a) The area of the new parking lot is represpresented by (100+ x)(100 – x).
Find this product.
b) Does this area of the parking lot increase, decrease, or stay the same? Explain your thinking. (You can use example values for x to help explain.)
Answer:
a) Difference of squares:
[tex]10000 - {x}^{2} [/tex]
b) The area of the parking lot decreases because x^2 is subtracted from 10,000.
[tex]10000 - {1}^{2} = 10000 - 1 = 9999[/tex]
[tex]10000 - {2}^{2} = 10000 - 4 = 9996[/tex]