Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.

[tex]m-16[/tex] when m is 30

Substitute for m with given value:

[tex](30)-16[/tex]

[tex]=\fbox{14}[/tex]

Answer:

Step-by-step explanation:

a.we can get the equation is m-16 = 30-16=10+20-10-6=10-6+20-10=4+10=14

answer is 14

Answer:

95.25 or 95

Step-by-step explanation:

[tex]C=2\pi r[/tex]

C = 2 x [tex]\pi[/tex] x 15 = 94.24778in = 94.25 or 95

Hope I helped you my dear friend.

37.5% of the cars have a fuel efficiency of at least 35 miles per gallon.

To find the percentage of cars that have a fuel efficiency of at least 35 miles per gallon,

We first need to determine how many of the eight cars meet that threshold.

To do this, we can compare each car's fuel efficiency to 35 miles per gallon, and count the number that is greater than or equal to 35.

Identify the cars that have a fuel efficiency of at least 35 mpg: 42, 42, 54,

count the number of cars which is 3

divide it by 8 which is the total number of cars

Multiply the result by 100 to get the percentage, so:

3/8 * 100 = 37.5%

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The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

The  polynomial has the zeros 1,-2i and 3 is =  x³ - 5x² + 11x -15.

A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).

A polynomial function is a function that only uses non-negative numeric powers or only positive integer exponents of something like a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1.

given zeros are 1-2i and 3 .

The polynomial function  p(x) is

[x - (1+2i)] × [x - (1 - 2i)] × (x - 3)

[(x - 1) - 2i] × [(x - 1) + 2i] × (x - 3)

[(x - 1)² - (2i)² × (x - 3)]

∴ (x² - 2x + 1 + 4)(x - 3)

∴  (x² - 2x + 5)(x - 3)

The  polynomial has the zeros 1,-2i and 3 is =  x³ - 5x² + 11x -15.

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On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]

630000/25000

25.2

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As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.

Here,

In New York City, a one-bedroom apartment will cost $1600 in 2020.

Y = mx + c is frequently used as the formula for a straight line graph, where;

gradient = m

The vertical intercept is given by c.

With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.

This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.

y = 40(20) + 800 = $1600

As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

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Proportion of cars which are yellow -

= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)

= 1 - 0.96

= 0.04

Answer:

A) 0.04

Step-by-step explanation:

edge 2023

Answer:

Step-by-step explanation:

20)63(3

    -60

   -------

        3

so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.

so 3 children get 1 toy more.

Hence 3 children get 3+1=4 toys (each)

Step-by-step explanation:

x + 6y = 8 ........... ( ×2 ) ....... ( 1 )

2x + 4y = -8 ......... ( × 1 ) ....... ( 2 )

2x + 12y = 16

- - -

2x + 4y = -8

+12y - ( +4y ) = 16 - 8

12y - 4y = 8

8y = 8

divide both sides by the coefficient of y ( 8 )

8y / 8 = 8 / 8

y = 1

substitute for x in equation ( 1 )

x + 6y = 8

x + 6 ( 1 ) = 8

x + 6 = 8

x = 8 - 6

x = 2

x = 2 , y = 1

17. The triangles can be proven congruent by the SSS theorem.

18. The triangles cannot be proven congruent by the HL theorem, as it is not known if the triangles are right triangles.

The side-side-side congruence theorem, abbreviated as SSS, means that if two triangles have three equal side lengths, then the triangles are congruent.

In item 17, we have that:

As the three triangles are equal, then the SSS theorem can be used to prove the congruence of the two triangles.

The HL theorem represents the hypotenuse and leg theorem, which means that if two right triangles share a hypotenuse measure along with a leg measure, then they are congruent.

Hence item 18 cannot be proven congruent by the HL theorem, as there is no information regarding whether the triangles are right triangles.

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The cost of a one mile ride is given as follows:

$6.

The cost per mile is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function that gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is of:

y = 4(1) + 2 = $6.

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Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

Note that equation 1 matches the Line Graph in option (B), equation 2 matches option (C), and equation 3 matches option (A).

It is a graph that depicts a line connecting many points or a line indicating the relationship between the points. The graph depicts quantitative data between two changing variables by connecting a sequence of succeeding data points with a line or curve.

With regard to the above-given graphs,

The inequalities are given as

1. 4x + 3 > 15 or —6x ≥ 12

2. —8x > —24 and —10 ≤ 2x -6

3. -29 ≤ 9x -2 < 16

Note that the way to identify the plots on the line graphs is by solving the above equations.

1) 4x + 3 > 15 or —6x ≥ 12

2) —8x > —24 and —10 ≤ 2x -6

To solve for x in  —8x > —24, divide both sides by -8

x > 3;

So solve for —10 ≤ 2x -6; add 6 from both sides and divide by 2

-4/2 ≤ x

-2 ≤ x  or x ≥ -2

3) -29 ≤ 9x -2 < 16

To solve this inequality, you can start by isolating the variable on one side of the inequality. To do this, you can add 2 to both sides to get:

-29 + 2 ≤ 9x < 16 + 2

-27 ≤ 9x < 18
Now divide both sides by 9 to get:

-3 ≤ x < 2

This means that x can be any number that is greater than or equal to -3 and less than 2.

Given the above results, it is correct to state that equation 1 matches option (B), equation 2 matches option (C), and equation 3 matches option (A).

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Full Question:

See the attached.

The solution for the given system of equations:

x = 6 and y = 6.

Kana is incorrect about the solutions of the given equations.

Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.

Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c

Identity: a + 0 = a , a ⋅ 1 = a

Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1

Distributive: a ( b + c ) = a b + a c

Given equations,

4x-2y=12        -----(a)

2x+2y=24            -----(b)

Multiplying -2 to the equation (b) like kana solution

-2 (2x+2y=24 )

By Distributive property

-2(2x+2y) = -2(24)

- 4x - 4y = - 48     ---------(c)

Now adding equation (a) and equation(c)

    4x - 2y = 12

  - 4x - 4y = - 48

__+___+____+__

         - 6y  =  -36

⇒ y = 36/6 = 6.

Putting value of y in equation (b).

2(x) + 2(6) = 24

2x + 12 = 24

2x = 24 - 12

2x = 12

x =12/2 = 6

By the above calculation,

Value of x = 6 and

value of y = 6.

Hence, for the system of equations given

the solutions are:

x = 6 and y = 6

which proves that Kana is incorrect that there are no solutions.

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From the graph, it can be seen that it took 4 days to mow 30 lawns. 12 lawns can be mowed in 1 days.

Analyzing numerical data can be done using graphical representation. It uses a diagram to show the relationship between the data, ideas, information, and concepts. One of the most crucial learning strategies, it is also simple to understand. The kind of information in a particular domain is always a factor.

Examples include pictures, sketches, line art, graphs from mathematics, charts, diagrams, typography, numbers, symbols, geometric patterns, engineering drawings, or other images. Often, text, illustration, and color are combined in graphics.

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The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

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Complete question is: What is the difference between Minimum or maximum value?

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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Answer:

The correct equation is: 6 + p = 15; p = 9.

Step-by-step explanation:

In this equation, p represents the cost of the popcorn, and the equation states that the total cost of my friend's purchase (the cost of the drink plus the cost of the popcorn) is $15. Therefore, the cost of the popcorn must be $9.

Answer:

Option D)

Step-by-step explanation:

Overall cost of both the items = $15

Cost of the drink = $6

Cost of popcorn = p

To Find : The equation that represents the Overall cost and the cost of the Popcorn

p + 6 = 15

p = 15 - 6

p = 9

Hence , the correct answer is p = 15 - 6; p = 9

Therefore , the solution of the given problem of function comes out to be 2.

A function connects various inputs together or produces a single output from each input. Simply explained, a function is a collection of equations that are linked to a single, identifiable output. A statement, rule, or law which explains the connection between two variables is known as a function in mathematics (the dependent variable). When a rule of this type is applied, there is just one output. by photographer Alex Federspiel. 

Here,

=> (1−α)(1−β)(1+α)(1+β)

​=>(1−α−β+αβ)​ /(1+α+β=αβ)

=> (1−(α+β)+αβ ) / ( 1+(α+β)+αβ)

=>(1 + 2/3 + 1/3 )/ (1 -2/3 + 1/3)

​=> 2 x 3 /2  =3

=> (1−α)(1+β)+(1−β)(1+α) / (1+α+β+αβ)

=> 3(2−2αβ)/2

​

=>3(1−αβ)

=>3(1− 1/3 )

=>2

Therefore , the solution of the given problem of function comes out to be 2.

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Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

a. The table for the relation is given by the image shown at the end of the answer.

b. The domain and range of the relation are given as follows:

c. The relation is a function, as it value of the input is mapped to a single value of the output.

The ratio between the total cost and the number of vehicles is obtained as follows:

k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.

Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:

y = 0.75x.

For which:

The domain and range are given as follows:

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Answer:

R=17

Step-by-step explanation:

R=17

It says the whale has swam upwards and jumps to a heigh less then 17 and it says model the possible change in the number of feet, (R)

Thus R=17 Will Be correct

Therefore, the result of the above linear equation problem's solution is hence The lines do not intersect, hence there are no solutions and an inconsistent system.

In algebra, a linear equation is one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear.

Here,

The lines in this system have the same slope even though the values of b vary.

This indicates the parallel lines.

The lines do not intersect, hence there are no solutions and an inconsistent system.

Since the lines are different, the equations are independent.

The result of the above graph problem's solution is hence The lines do not intersect, hence there are no solutions and an inconsistent system.

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The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.

An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.

y=mx+c

Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.

[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]

[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]

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5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.

5b) Through the lease, the customer saves $14,760.

5c) The lease options for the lessee after returning the car include:

6a) The after-tax cost of the Honda Civic is $32,199.35.

6b) The value of the vehicle that needs to be financed is $26,199.35.

6c) The monthly payment will be $567.26 for 4 years.

6d) After four years, the total amount paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)

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