Tthe the number of smallmouth bass Chelsie caught = 37
and the number of salmon she caught = 15
Here, x represents the number of smallmouth bass Chelsie caught. and y represents the number of salmon she caught.
Chelsie caught 52 fish today.
So we get an equation,
x + y = 52
Also, for smallmouth bass, she caught seven more than 2 times the amount of salmon she caught.
So we get an equation,
x = 7 + 2y
So, we get a system of equations:
x + y = 52 ..........(1)
x = 7 + 2y .......(2)
Substitute above value of x in equation (1)
(7 + 2y) + y = 52
7 + 3y = 52
3y = 45
y = 15
Substitute above value of y in equation (2),
x = 7 + 2(15)
x = 37
Therefore, she caught 37 smallmouth bass and 15 salmon.
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Is the function linear or nonlinear?
y = 3 x 2 + 7
Answer:
y= 13
Step-by-step explanation:
y+3x2+7
y=6+7
y=13
x y
0 13
1 13
linear
Prepare to analyze the data (step 1): identify and classify the variable(s) you will use. Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Gender Alcohol Height Cheat
Indicating whether the variable is relevant to the questions, and Identifying the variable as either categorical or quantitative.
Gender - Categorical and Nominal Alcohol - QuantitativeHeight - QuantitativeCheat - CategoricalRather than straightforward explanations. Anything may be measured using it. It can also do mathematical calculations, which is essential for data analysis.
To completely understand all of the facets of quantitative data, statistical analysis—the discipline of obtaining, analysing, and presenting enormous volumes of data to uncover patterns and trends—is used. This calls for quantitative analysis employing a wide variety of data.
Categorical data is data that may be arranged into groups or categories using names or labels.
The approach is based on algorithms that assess each component of a data collection individually, compare them to other individual data sets, and look for particular similarities.
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Complete question:
identify and classify the variable(s) you will use.Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Group of answer choices
Gender [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Alcohol [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Height [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitative Cheat [ Choose ] Relevant - categorical Not relevant - categorical Relevant - quantitative Not relevant - quantitativeWhich expression is equivalent to
(3x^2 + 2x - 4) + (5x^2 - 4x + 5) ?
8x^2 + 6x + 9
8x^2 + 2x + 1
8x^2 - 2x + 1
8x^2 + 6x + 9
Answer:
8x^2-2x+1
explaniationfirst remove the bracket 3x^2+2x-4+5x^2-4x+5then collect like term3x^2+5x^2+2x-4x-4+5 then the answer will be 8x^2-2x+1 thank you!!!!!anet wants to solve the equation y + StartFraction y squared minus 5 Over y squared minus 1 EndFraction = StartFraction y squared + y + 2 Over y + 1 EndFraction. What should she multiply both sides of the equation by?
y
y2 – 1
y + 1
y2 + y + 2
y² - 1 should be multiplied on both sides to solve the equation.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
(y² - 5) / (y² - 1) = (y² + y + 2) / (y + 1)
This can be written as,
y² - 1 = (y + 1) (y - 1)
So,
Multiplying y² - 1 on both sides.
(y² - 1) x (y² - 5) / (y² - 1) = (y² - 1) x (y² + y + 2) / (y + 1)
(y² - 5) = (y² + y + 2) (y - 1)
y² - 5 = y³ + y² + 2y - y² - y - 2
y² - 5 = y³ + y - 2
y³ - y² + y - 2 + 5
y³ - y² + y + 3
Thus,
Multiplying y² - 1 on both sides will solve the equation.
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Choose the best method for solving and solve. Show your work.
y=-2x+17
y=8-x
Answer:
x = [tex]-3[/tex]; y = 11
Step-by-step explanation:
These two equations are linear simultaneous equations. They can be solved either by substitution, elimination or graphical method:
Substitution:
[tex]y = 8 - x[/tex] ------- (equation i)
[tex]y = 2x + 17[/tex] ---- (equation ii)
Substitute (equation i) into (equation ii):
[tex]8 - x = 2x + 17[/tex]
Bring all the like terms together. In addition x has to be isolated and made the subject of the equation:
[tex]8 - 17 = 2x + x[/tex]
[tex]-9 = 3x[/tex]
x = [tex]-\frac{9}{3}[/tex]
∴ x = [tex]-3[/tex]
Substitute this value of x in any of the equations to solve for y:
[tex]y = 8 - (-3)[/tex]
[tex]y = 8 + 3[/tex]
∴ y = 11
This ordered pair of [tex](-3, 11)[/tex] is a solution for both linear simultaneous equations. In addition, this particular pair is known as the 'point of intersection'.
WILL MARK BRAINLIEST !!! please help and show work !!
Find the equation of the line passing through (1,5) and parallel to y = 3x - 1.
Answer:
Step-by-step explanation:
Finding an equation of a line can be condensed into 2 easy steps. Step one is to establish the basic form of the equation, including it's slope.
1) Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero). We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3. Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:
y = 3x + b.
2) The second step is finding the value of b. We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5). Easy: just enter this point in the equation we have so far: y = 3x + b:
y = 3x + b
5 = 3*(1) + b for point (1,5)
b = 2
The equation becomes y = 3x + 2
See the attached graph. [Extra credit]
The lines are parallel, and the y-intercept for the second line (b) is (0,2).
i need help
solve for a
x = 4
-- All angles of a triangle add up to 180° --
-- the inverse of a trianglenis equal to its opposite angle of intersection--
1) build equation
180° = 20° + (4 + 6x) + (32x + 4)
2) solve
180-20 = 4 + 6x + 32x + 4
160 = 8 + 38x
152 = 38x
152/38 = x
x = 4
verify
180 = 20 + (4 + 6x) + (32x + 4)
180 = 20 + (28) + (132)
180 = 180 so x = 4
How are the properties of exponents used when dividing a polynomial by a monomial?
Answer:
a couple different obes
Step-by-step explanation:
there are five
Six percent commission on first $10,000. Eight percent commission over $10,000. Find the total graduated commission on $13,200.
An amount of $ 13,200 has a total comission of 856.
How to determine the total comission for an amount of money
Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:
C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)
C = 856
The graduate must pay a total comission of $ 856 for an amount of $ 13,200.
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Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. But the early-bird special on Saturday morning offers 8 games for $30. How much more does glow-bowling cost per game? $ per game
The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. Then the rate is given as,
⇒ $22.50 / 5
⇒ $4.5 per game
But the early-bird special on Saturday morning offers 8 games for $30. Then the rate is given as,
⇒ $30 / 8
⇒ $3.75 per game
The difference is given as,
D = $4.5 - $3.75
D = $0.75 per game
The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.
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7-2 Enrichment
Multiplying Polynomials
An architect is preparing to design an office building. She creates a sketch of the basic shape of the structure and
the relative dimensions of each piece shown. The angles in the sketch are all right angles. Find the volume of the structure using each approach. Draw lines on the sketches and record your expressions.
1. Divide the structure into two different rectangular
prisms. Add the volumes of the two prisms to create
an expression for the total
Volume
2. Divide the structure into three different rectangular
prisms. Add the volumes of the three prisms to create
an expression for the total volume.
3. View the structure as one prism with 2 equal sized prisms. Find the volume of the large prism and subtract the volumes of the smaller pieces to find the expression for the total volume!!
Thanks for helping!! (We are learning polynomials right now, like (2+x)^2 for clarification for the problems!!!) :)
The volumes of the structure are:
1. (8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)
2. (8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)
3. (8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]
What is polynomial expressions?A polynomial expression is an algebraic expression consisting of variables and coefficients, and involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Examples include 2x^3 - 5x^2 + 3x + 1 and 4y^2 + 7y - 2.
1.We can divide the structure into two rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of the second prism are 12(8 + x)(3 + x). To find the total volume, we can add the volumes of the two prisms:
(8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)
2.We can also divide the structure into three rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(3 + x), the dimensions of the second prism are 12(8 + x)(3 + x), and the dimensions of the third prism are 12(6 + 3x)(3 + x). To find the total volume, we can add the volumes of the three prisms:
(8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)
3.We can view the structure as one large rectangular prism with two smaller rectangular prisms removed, as shown in the sketch. The dimensions of the large prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of each small prism are 12(8 + x)(3 + x). To find the total volume, we can subtract the volumes of the two small prisms from the volume of the large prism:
(8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]
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Tuga has 2⅔ pounds of sweet potatoes. She needs 40 ounces of sweet potatoes to make chili. Which statement explains if Tuga has enough sweet potatoes to
make chili? (1 pound = 16 ounces)
Answer:
Step-by-step explanation:
Convert pounds to ounces:
2[tex]\frac{2}{3}[/tex] = 2.667
2.667 lb x 16 oz/lb = 42.7 oz
42.7 > 40, therefore Tuga has enough sweet potatoes to make chili
If the point (1,a) lies on the line y = 3x - 5, what is the value of a?
Answer:
a = - 2
Step-by-step explanation:
Since the point (x, y) = (1, a) lies on the line, substituting this value of x = 1 should give the corresponding value of y which is a
y = 3x - 5
At (1, a)
a = 3(1) - 5
a = 3 - 5
a = - 2
Answer
what is the volume ?
so let's take a peek at the triangular pyramid, hmm it has a base of well, the base is a triangle, so we can say the triangle has a base of 10 and a height of 8, thus and area of (1/2)*10*8, and the pyramid has a height of 9.
[tex]\textit{Volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(10)(8)\\[1em] h=9 \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(10)(8) \right](9) \\\\\\ V=\cfrac{1}{3}(40)(9)\implies V=\cfrac{360}{3}\implies V=120~m^3[/tex]
there are 'b' daffodil bulbs in a bag. i buy 4 bags, but 5 of the bulbs have gone bad and will not grow. if i still have 55 bulbs that will grow, calculate the number of bulbs in each bag.
Solve this problem:
㏒₅₄168=?
If:
a = ㏒₇12
b = ㏒₁₂24
Answer:
㏒₅₄168 = (1+ab)/(8a-5ab)
Step-by-step explanation:
You want ㏒₅₄168 written in terms of a and b, where ...
a = ㏒₇12b = ㏒₁₂24Log expressionsThe rules of logarithms are relevant here:
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]
In order to simplify the writing in what follows, we want to define ...
p = log(2)q = log(3)r = log(7)Now, we can write the equations ...
a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]
b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]
Using these, we can solve for p and q:
2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]
(3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]
Using your favorite solution method for linear equations, you find ...
p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)
q = (-ar(3 -2b)/(-1) = ar(3 -2b)
Desired logarithmSubstituting these expressions into ...
[tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]
__
Additional comment
The calculator confirms the result.
HELP PLEASE LOOK AT IMAGEE BELOW
Answer:
y = 7x -9
Step-by-step explanation:
This is a linear equation.
The change in y over the change in x is 9. The y-intercept will be (0, -9).
If you follow the pattern as x is -1 and you go up 1 to zero, the the y goes up 7 from -16 to get -9
Answer:
y = 7x - 9
Step-by-step explanation:
y = 7x - 9
Let checks
-16 = 7(-1) - 9
-16 = -16
-23 = 7(-2) - 9
-23 = -23
So, y = 7x - 9 is the correct answer.
35. Solve the equation and check your solution: -2(x + 2) = 5 - 2x
Answer:this equation is not right.so,it does not have any solutions
Step-by-step explanation:
because if we try to solve it we get,
-2x-4=5-2x
-4-5=-2x+2x
-9=0
so,this equation is not right.
Answer:
equation has no solution
Step-by-step explanation:
- 2(x + 2) = 5 - 2x ← distribute parenthesis on left side
- 2x - 4 = 5 - 2x ( add 4 to both sides )
- 2x = 9 - 2x ( add 2x to both sides )
0 = 9 ← false statement
this false statement indicates the equation has no solution
Who knows the answer to this ?
Answer:
angle 1 is 28 degrees angle 2 is 62 degrees
DONT FORGET TO PUT THE DEGREES SIGN
Step-by-step explanation:
since it is a right angle, angle 1+ angle 2 is 90 degrees.
So,
2x+(x+48)=90
3x=90-48
3x=42
x=14
angle 1=28 angle 2=62
please check if my answers are correct in these algebra questions
The value of the expressions will be:
x + y + x + y + 2x + 2z.= 4x + 2y + 2z
6a² - 5a²b - 4a² - 3a²b = 2a² - 8a²b
2(x + 3y) - 2x = 6y
3x(2 + x) - x² = 2x² + 6x
How to calculate the expressionAn expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The value of the expressions will be:
x + y + x + y + 2x + 2z
= 4x + 2y + 2z
6a² - 5a²b - 4a² - 3a²b
= 2a² - 8a²b
2(x + 3y) - 2x
= 2x + 6y - 2x
= 6y
3x(2 + x) - x²
6x + 3x² - x²
= 2x² + 6x
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(35) MOVIE RENTALS The number of copies of a movie rented at a video kiosk decreased at a constant rate of 5 copies per week. The 6th week after the movie was released 4 copies were rented. How many copies were rented during the second week?
Answer:
25 copies rented
Step-by-step explanation:
r = r1 - 5t, t is time in weeks, r is the number of copies rented, r1 how many people were renting at the start
we know on the 6 weeks passed and 4 copies were rented
4 = r1 - 5(6)
4 = r1 - 30; add 30 on both sides
34 = r1
r = 34 - 5t now plug t = 2 in for this function
r = 34 - 5(2)
r = 35 - 10
r = 25 copies rented
ben and chris start at the same time from places 96miles apart to cycle toward each other, ben at 16mph and chris at 12mph. if ben rests for 1/2 hour on the way, after how many hours will they meet?
Ben and Chris will meet after 3.5 hours.
What is the LCM?The least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Given:
Ben and Chris start at the same time from places 96 miles apart to cycle toward each other,
Ben at 16mph and Chris at 12mph.
The LCM of 12 and 16 is,
= 48.
So, they will meet after 3.5 hours.
Therefore, they will meet after 3.5 hours.
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A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet.
Which expression best represents the value of pi
In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is 43.96 feet/ 14 feet.
How can the value of pibe calculated?The concept that will be use here is Circumference. we were given Circumference of the circle as 43.96 feet
where the Diameter of the circle is 14 feet, then we can find the Circumference of the circle as( πd)
Then ( πd) = 43.96 feet
π= 43.96 feet/ 14 feet
Therefore, option C is correct.
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The Brunsons had a new concrete patio installed in the shape of a semicircle as shown.
Mr. Brunson wants to cover the patio with concrete sealer. What is the area he will need to cover with concrete sealer? Use 314 for R. Round to the nearest hundredth
if necessary.
Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.
What is area of a circle ?
Area of circle can be defined as product of pi and square of radius .
To find the area of the semicircle, we need to use the formula for the area of a circle, but divide it by 2 since we only have half of a circle. The formula for the area of a circle is:
A = πr²
where A is the area of the circle, and r is the radius.
In this case, we have a semicircle, so we need to use half of the formula:
A = (πr²)/2
We are given that R = 314, so we can substitute that into the formula:
A = (π(314)²)/2
Using a calculator and rounding to the nearest hundredth, we get:
A ≈ 49106.15
Therefore, Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.
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What is 6d greater than or equal to -84
Answer:
d ≥ - 14
Step-by-step explanation:
6d ≥ - 84
Divide by 6 both sides
6d/6 ≥ - 84/6
d ≥ - 14
400 students are asked how they travel to school.
45% of the students take the bus to school.
The remaining students travel by car or walk to school.
20 more students walk than travel by car.
How many students walk to school?
Answer:
120 student
Step-by-step explanation:
We know
45% of the students take the bus to school
100% - 45% = 55%
So, 55% travel by car or walk to school
400 x 0.55 = 220 students
So, 220 student travel by car or walk to school
We know
20 more students walk than travel by car
220 - 20 = 200 students
200/2 = 100 students
100 + 20 = 120 students
So, 120 students walk to school
i need to find 2 standard form equations that represent the table.
We can find the two linear equations by using the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
For the first equation:
Using the first point (-2, 8), we have m = (y2 - y1) / (x2 - x1) = (-3 - 8) / (-2 - (-2)) = -11/0, which is undefined. This means the first line is a vertical line.
The equation can then be written as x = -2, since the x-coordinate is constant.
For the second equation:
Using the second point (-1, 4), we have m = (y2 - y1) / (x2 - x1) = (-2 - 4) / (-1 - (-2)) = -2.
The equation can then be written as y - 4 = -2(x + 1), or y = -2x - 2.
Thus, the system of linear equations is:
x = -2
y = -2x - 2
Written in standard form:
x + 0y = -2
-2x + y = -2
Justice rents a car for a deposit of $50 and $20 a day. When he turns it in he owes $490. How many days did he have the car?
Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.
What do we mean by rent?Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc.
According to the information in the question:
Deposit = $50
Rent cost per day for the car = $20
Total amount that Justice has to pay = $490
∴ Total number of days that Justice kept the car = (490 - 50)/20
= 440/20
= 22 days
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The number of days did he have the car are 22.5 days.
Explain about rent.a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.
According to question:Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.
To find out how many days he had the car, we can set up an equation:
$50 + (number of days x $20) = $490.
Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.
So Justice had the car for approximately 22.5 days.
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Question 6 (1 point)
A food company is designing boxes for several products. Each box is a rectangular prism.
The company also wants to offer a family size box of cereal. The family size box will be a dilation of the single serving 1. 2-ounce box. It
must contain 18. 75 ounces of cereal. What scale factor does the company need to use for the family size box? Explain or show your
reasoning
The company need to use for the family size box use a scale factor of 15.625 times greater.
Box Volume Scale Factor CalculationTo find the scale factor, we first need to determine the ratio of the volume of the family size box to the volume of the single serving box. The volume of a rectangular prism is given by the product of its length, width, and height. Let's assume the single serving box has dimensions l, w, and h. The volume of the single serving box is then lwh.
The volume of the family size box is 18.75 ounces, and since the single serving box is 1.2 ounces, the scale factor is the ratio of the volume of the family size box to the volume of the single serving box:
(18.75)/(1.2) = 15.625
Therefore, the company needs to use a scale factor of 15.625 to create the family size box from the single serving box. This means that the length, width, and height of the family size box will each be 15.625 times greater than the corresponding dimension of the single serving box.
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Enter the common ratio for the geometric sequence below. 4 , 8 , 16 , . . .
Answer:
its ×2
Step-by-step explanation:
4×2 = 8
8×2=16
..............