The required system of equations is x+y = 21 and 7x +14y = 252.
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.
Let the number of small boxes be x.
Let the number of large boxes be y.
The volume of each small box is 7 cubic feet.
The volume of each large box is 14 cubic feet.
The total number of boxes is 21.
Total volume of all boxes is 252 cubic feet.
So, x+y = 21.
This is the first equation.
Also, the total volume is equal to the sum of the volumes of all individual boxes.
So, 7x + 14y = 252
Thus, the required system of equations is x+y = 21 and 7x +14y = 252.
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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.
What are system of equations?A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.
Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.
Given total number of boxes shipped is 21. Therefore using the concept of equation,
x + y = 21 --- (1)
Total volume of small box is given by:
Total volume of small box = (Volume of a small box) * (Number of small box)
Total volume of small box = 7x
Similarly the total volume of large box is,
Total volume of small box = 14y
Given the total volume of carried box is 252 cubic feet. Using the concept of equations,
7x + 14y = 252 ---(2)
The equations (1) and (2) gives the required system of equations.
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4. The Johnsons' bill at a restaurant is $124.00. How much money should the Johnsons leave if they plan to tip their waiter 15%?
Answer:
142.6
Step-by-step explanation:
100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6
Hope that helped
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer: x=5
Step-by-step explanation:
Answer:
(x - 1)² = 16
Step-by-step explanation:
x² - 2x - 15 = 0
x² - 2x + 1 = 15 + 1
(x - 1)² = 16
A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?
Answer:
The Answer is 20 inches tall
Find the 56th term of the following arithmetic sequence 7,10,13,16
The 56th term of the following arithmetic sequence 7,10,13,16 is 172.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given
Arithmetic sequence 7,10,13,16.
We have to find the 56th term.
The common difference between terms: 10 - 7 = 3
Using the arithmetic progression formula:
nth term = first term + (n-1)* common difference
56th term = 7 +(56-1) 3
56th term = 7 + 55×3
56th term = 7 + 165
56th term = 172
Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.
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Prove that tan(A+B)
cot(A−B)
=
2−2
2−2�
Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
tan(A+B)/cot(A-B)
tan(A+B)/1/tan(A-B)
(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)
tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB
We know algebraic identity
(a+b)(a-b)=a²-b²
(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)
tan²A-tan²B/1-tan²Atan²B
Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
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Karima made 9 pairs of earrings in 9 hours. At this rate: How long will it take Karima to make 12 pairs of earrings?
Answer:
12 hours
Step-by-step explanation:
1 pair per hour ?
Punch recipe. Orange juice, 3, 1/3. Grape juice six and 1/2. Cherry juice. 4 and 1/8. Club soda, one and 1/4. About how much fruit juice,(orange, grape, and cherry) is used in the punch.
answers.
11 cups
12 cups
13 cups
14 cups
Answer:
14 cups
Step-by-step explanation:
3 + 6 = 9
9 + 4 = 13
13 + 1 = 14
14 plus fraction
149 cars are waiting to take a ferry across the channel. Each ferry can only hold 18 cars. How many trips will it take to get all the cars across?
5
8
6
9
Answer: the answer is 8
Step-by-step explanation:
The Answer is: 8
Simply divide 149 by the numbers you see,
Diego is also training for the tournament. The graph shows the relationship between the time in the distant he rows how many meters does Diego Roper minute
Diego rows 300 meters per minute
How to determine the the number of rows per minuteInformation given in the question include
The graph shows the relationship between the time in the distant, Diego rows
The data is plotted as a linear function
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
the slope, m calculating using the points on the graph (1, 300) and (2, 600)
m = (y₀ - y₁) / (x₀ - x₁)
m = (600 - 300) / (2 - 1)
m = 300 / (1)
m = 300
The number of meters Diego rows per minute is solved to be 300
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0=x2+18x+45
I need help with this place
The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)
How to factorise quadratic equation?A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.
Therefore, quadratic equation can be represented as follows:
ax² + bx + c
where
a, b and c are constantHence, let's factorise x² + 18x + 45 = 0
x² + 18x + 45 = 0
Let's find the two numbers to add to get 18 and multiply to get 45
Therefore, the numbers are 3 and 15
x² + 18x + 45 = 0
x² + 3x + 15x + 45 = 0
x(x + 3) + 15(x + 3) = 0
(x + 3)(x + 15) = 0
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A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
A. Find a mixture that will make the same shade of green but a smaller amount.
B. Find a mixture that will make the same shade of green but a bigger amount.
C. Find a mixture that will make the different shade of green that is bluer.
D. Find a mixture that will make the different shade of green more yellow.
(Please provide a detailed expiation/step-by-step).
To determine a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number.
How to find a mixture that will make the same shade of green but a smaller amount?To solve this problem, we can use the principle of proportionality, which states that if two ratios are equal, then the quantities they represent are proportional.
A. To find a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number. For example, if we divide both amounts by 2, we get 1 cup of yellow and 1.75 cups of blue. This will create a smaller amount of the same shade of green.
B. To find a mixture that will make the same shade of green but a bigger amount, we can multiply both the yellow and blue amounts by the same number. For example, if we multiply both amounts by 2, we get 4 cups of yellow and 7 cups of blue. This will create a larger amount of the same shade of green.
C. To find a mixture that will make a different shade of green that is bluer, we can increase the amount of blue relative to the amount of yellow. For example, we could use 2 cups of yellow and 4 cups of blue, which would create a green that is bluer than the original shade.
D. To find a mixture that will make a different shade of green that is more yellow, we can increase the amount of yellow relative to the amount of blue. For example, we could use 3 cups of yellow and 2 cups of blue, which would create a green that is more yellow than the original shade.
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Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday. He also has a part-time job that pays $8 per hour. How many hours will he need to work to have $250 in his bank account?
Choose the equation that correctly models the situation. The letter h represents the hours Ike will need to work.
(250−126)h=20+8
126+20+8+250=h
126+20+8h=250
250+126+20=8h
Answer:
126+20+8h=250
Step-by-step explanation:
What is the term to term rule for this sequence ? 625,125,25,5,1
The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
How to know whether a given sequence is geometric?In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.
The given sequence is as follows,
625, 125, 25, 5, 1
The first term is given as a₁ = 625
And, the ratio of the consecutive terms are,
125/625 = 1/5
25/125 = 1/5
Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.
The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.
Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
Hence, the term for the given sequence can be written in general form as aₙ = 625 × (1/5)ⁿ⁻¹.
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The choices below are data sets. In the choices, w is a constant. Each choice has the same mean.
Which choice has the greatest standard deviation?
A.)
w-2, w-1, w, w + 1, w+ 2
B.)
w-2, w-2, w, w + 2,w+2
C.)
w-3, w-1, w, w + 1, w+3
D.)
w-3, w, w, w, w +3
Answer:
C)w-3, w-1, w, w + 1, w+3
Step-by-step explanation:
I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.
C) is the correct answer, the data points do not repeat and are spread out more than A.
You can check this by calculated each standard deviation (but only if you are crazy ;] )
Hope this helps,
:]
i need help fast pleaseeeeeeeeeee :) (:()
Answer:
translation down 2 and reflection across x axis
The formula K=1/2mv² is used to find the kinetic energy of an object in
motion using its mass, m, and its velocity (speed), v. Solve the equation
for the mass, m.
What is the Equation?
Is it: m = K/2v²
Answer:
m = 2k/v²
Step-by-step explanation:
K = ½mv²
multiply both sides by 2
2 × k = ² × ½mv²
2k = mv²
divide both sides by (v²)
m = 2k/v²
i hope this helped
Annabelle kicks a football. Its height in feet is given by h = -16t² + 96t
where t represents the time in seconds after kick. What is the football's greatest height?
The kicked football is an example of a projectile. The football's greatest height is 144 m.
What is the projectile?A projectile is any object that is launched into space and moves under the influence of gravity and air resistance. A kicked football is a good example of a projectile. Given the height of the kicked football to be:h = -16t² + 96tThus, the height of the kicked football is a function of time taken. So that differentiating the equation of the height with respect to time, we have;0 = -32t + 9632t = 96t = [tex]\frac{96}{32}[/tex] = 3
Thus the greatest height of the kicked football is attained when the time is 3 seconds.
Thus,h = -16t² + 96t = -16 (3)² + 96 (3) = -144 + 288h = 144
Therefore the football's greatest height is 144 m.
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PLEASE HELP!!!!!! It’s algebra
When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
What is a annual inflation rate?
A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.
Here, we have
Given
The cost of the gallon of milk earlier was $2.81
The cost of a gallon of milk now is $3.48.
The total time period is 10 years.
r = (F/P)ⁿ⁻¹ - 1
r = {(3.48/2.81)^(1/10) - 1}×100
r = {(1.238)^(1/10) - 1}×100
r = 0.0215 ×100
r = 2.15
Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
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would somebody be nice enough to help me with this? i’m confused
The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
What is the Angle-Angle similarity theorem of triangles?
The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In the given figure,
In ΔPQR and ΔPXY
∠P ≅ ∠P ----- Common Angle
∠PQR ≅ ∠PXY ----Corresponding angles.
So, ΔPQR ~ ΔPXY -----(AA test)
Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
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Which of the following is a point on the line defined by the parametric equations below?
[x(t)=t+7
y(t) = 5-2t
○ (3,10)
○ (7,0)
O (8,3)
O (2,1)
The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.
What is an example of a parametric equation?Well, a parametric equation is an equation where the variables (usually x and y) are expressed in terms of a third parameter, usually expressed as t. For example: Consider the equation of a circle with radius r and center at (0,0) : x2+y2=r2 x 2 + y 2 = r 2 .parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. More than one parameter can be employed when necessary.If there are m free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors: x = s1v1 + s2v2 + ··· + smvm. This is called a parametric equation or a parametric vector form of the solution.Types of Parametric test–
Two-sample t-test.Paired t-test.Analysis of variance (ANOVA)Pearson coefficient of correlation.To learn more about parametric refer to:
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1) Is the pattern linear? If yes, state the initial value and constant rate
2) Is the pattern discrete or continuous? How can you tell
1. It can be piecewise linear; from x = 1 to x = 4, the y-value increases by the same amount each time. From x = 0 to x = 1, the y-value stays the same.
However, if it is supposed to be a single function, it would be non-linear because it changes slope.
2. It is discrete because there is no data between the points.
explain the process of the square root of 80n3
The square root of 80 is 4√5 ≅ 8.92.
What is a square root of a number?
In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.
Using Prime Factorization:
The first step in this method is to find the prime factors of 80.
80 = 2 × 2 × 2 × 2 × 5
To find the root from here, we can simplify this to
√80 = √(2 × 2 × 2 × 2 × 5)
√80 = 4√5
We can either leave it at this or find the root of 5 which is 2.23 and simplify further.
Hence, Square Root of 80 = 4√5 ≅ 8.92.
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Andrew invet $200 into an account with a 2. 9% interet rate that i compounded emiannually. How much money will he have in thi account if he keep it for 5 year? Round your anwer to the nearet dollar
Andrew will have $251.91 in his account after 5 years, assuming he does not add or withdraw any money from the account and that interest is compounded semiannually at a rate of 2.9%.
What Does an Interest Rate Mean?The fee that a lender assesses on a borrower is known as the interest rate, which is expressed as a percentage of the principal, or the loaned amount. Usually, the annual percentage rate (APR), which is how loans' interest rates are expressed, is indicated (APR).
What is the process of an interest rate?Once your loan is fully repaid, interest will have an impact on the overall cost you pay. For instance, if the interest rate on a $100 loan is 5%, you will have to pay the lender $105 in order to repay the money. $5 will be profit for the lender.
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Rick bought 5 yogurt bars at a snack shop. Each yogurt bar cost $1.80. Complete the table to show the price of 2, 3, 4, and 5 yogurt bars.
By using multiplication, it can be calculated that
The complete table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
This is a word problem on multiplication
Cost of 2 yogurt bars = $1.80 [tex]\times[/tex] 2 = $3.60
Cost of 3 yogurt bars = $1.80 [tex]\times[/tex] 3 = $5.40
Cost of 4 yogurt bars = $1.80 [tex]\times[/tex] 4 = $7.20
Cost of 5 yogurt bars = $1.80 [tex]\times[/tex] 4 = $9.00
So the table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
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Herb and Marci Jordan obtained an installment loan that has a 10% APR to purchase a dishwasher that sells for $699. 95. They agree to make a down payment of 20% and to make 12 monthly payments. What is the finance charge?
$699.95×20%=$139.99, is the finance charge.
What is finance charge?A finance charge is any fee that reflects the cost of credit or borrowing under American law.
Some forms of credit have fees and interest that accrue over time. [1] In addition to interest, it also includes additional costs, like those for financial transactions.
The Truth-in-Lending Act and Regulation Z, which were issued by the Statutory Reserve Board, contain information about the federal definition of a finance charge.
A financing charge in personal finance is just the cash amount paid to borrow money, whereas interest is the amount paid as a percentage, such as the annual percentage rate (APR).
Compared to standard dictionary definitions or accounting definitions, these definitions are more specific.
Lenders and creditors both calculate finance charges in different ways. a majority.
Hence, $699.95×20%=$139.99, is the finance charge.
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The typing rate per minute of a person who can type 225 words in 7.5 minutes.
Answer: 30 wpm.
Step-by-step explanation:
Do 225 divided by 7.5 and you get 30.
30 words in one minute.
1) Triangle ABC has vertices A(6,2), B(3,4), and C (2,8). If the triangle is rotated
counterclockwise, what are the coordinates of the image A'B'C'?
90°
2) Which transformation(s) preserve congruence?
3) Which transformation(s) produce similar figures that are not congruent?
1) image of the coodinate A(6,2) be A'(-2,6)
image of the coodinate B(3,4) be B'(-4,3)
image of the coodinate C(2,8) be C'(-8,2)
2) A transformation that preserves congruence is called an isometry
3) A dilation would produce a similar figure.
What do you mean by transformation?
Transformation is a collective term for four specific ways of manipulating the shape and position of points, lines, or geometric figures. The original shape of the object is called the master, and the final shape and position of the object is the image under transformation. There are four types of transformations in mathematics
1) When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).
Therefore, image of the coodinate A(6,2) be A'(-2,6)
image of the coodinate B(3,4) be B'(-4,3)
image of the coodinate C(2,8) be C'(-8,2)
2) A transformation that preserves congruence is called an isometry. In other words, a transformation in which the Image and Pre-Image have the same side lengths and angle measurements. Translations, reflections, and rotations are isometries.
3) A dilation would produce a similar figure.
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A company manufactures water bottles. The list below describes the number of water bottles manufactured in three months.
• February: 4, 100 water bottles
• March: 7% more water bottles in February
• April: 500 more water bottles in March
What is the percent change, to the nearest percent, in the number water bottles the company manufactured from February to April. show your work
Answer:
19%
Step-by-step explanation:
You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.
ChangeThe change from February to March is given as 7%.
The change from March to April is 500 bottles. In terms of the February quantity, this is ...
500/4100 × 100% ≈ 12.2%
Then the total of changes from February to April is ...
change = 7% +12.2% = 19.2% ≈ 19%.
The number of bottles manufactured increased by about 19% from February to April.
__
Additional comment
When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.
Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.
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Which table of values represents the equation y = 7x - 3?
The table of values which represent the equation y = 7x - 3 is: table D.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;
For ordered pair (-2, -1), we have:
y = 7x - 3
-1 = 7(-2) - 3
-1 = -14 - 3
-1 = -17 (False).
For ordered pair (-2, -19), we have:
y = 7x - 3
-19 = 7(-2) - 3
-19 = -14 - 3
-19 = -17 (False).
For ordered pair (-2, -15), we have:
y = 7x - 3
-15 = 7(-2) - 3
-15 = -14 - 3
-15 = -17 (False).
For ordered pair (-2, -17), we have:
y = 7x - 3
-17 = 7(-2) - 3
-17 = -14 - 3
-17 = -17 (True).
In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.
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Find the product of 7/30? multiplied by 5/14 simplify your answer
Answer:
Should be 1/12
Step-by-step explanation:
7/30x5/14
Simply multiply the numerators and denominators separately:
5/14× 7/30 = 5 × 7/14 × 30 = 35/420
After reducing the fraction, the answer is
1/12