50 POINTS!!!!!!!!!!!!!
Solve 4x+2 = 12 for x using the change of base formula log base b of y equals log y over log b.

Answer: x = -6, and y = -6  (-6, -6)

Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,

y = 2x + 6

Having taken note of this, we can now go on to the other equation and substitute for the value of y.

Hence, from equation 1,

4x - 4y = 0 (substitute for the value of y)

4x - 4(2x + 6) = 0

4x - 8x - 24 = 0

-4x -24 = 0

Add 24 to both sides of the equation

-4x = 24

Divide both sides of the equation by -4

x = -6

Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.

Therefore,

y = 2x + 6

y = 2(-6) + 6

y = -12 + 6

y = -6.

So, x = -6 and y = -6

6 3/11 that well be the answer

Answer:6 3/5

Step-by-step explanation: 10 2/5 - 3 4/5 = 33

5

= 63

5

= 6.6

Answer:

18.19

Step-by-step explanation:

$20-15%=$17

$17+7%=18.19

Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.

To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:

Let's apply these steps to the given information:

Step 1: Discount amount = $20 x 15% = $3

Step 2: Discounted price = $20 - $3 = $17

Step 3: Sales tax amount = $17 x 7% = $1.19

Step 4: Total amount paid = $17 + $1.19 = $18.19

Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.

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Answer:

59

Step-by-step explanation:

77+(-18)=59

Check:

59-77=(-18)

Hoped this helped !

Cheers, Z.

Answer:

59

Step-by-step explanation:

59-77=-18

77+-18=59

Answer:

Scalene triangle

Step-by-step explanation:

It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides

Answer:

4

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

-6m + 9

-3(2m - 3)

Answer:

I think it's c sorry if I am wrong.

Step-by-step explanation:

Answer: 19 and 31

Step-by-step explanation: Make the first number x, the second number y.

The sum of x and y is 50: x+y=50

x is 43 less than 2y: x=2y-43

replace x in equation x+y=50 with x=2y-43: 2y-43+y=50

combine like terms: 3y-43=50

add 43 to both sides: 3y=93

divide both sides by 3: y=31

replace y in equation x+y=50 with y=31: x+31=50

subtract 43 31 from both sides: x=19

the solution to the question is the first number is 19, the second number is 31

The two numbers that sum up to 50 with one being 43 less than twice the other, we set up a system of equations, solve for one variable, and then substitute it back into the other equation, resulting in the numbers 19 and 31.

The question asks us to find two numbers whose sum is 50 and where the first number is 43 less than twice the second number. To solve this, we can create a system of equations to represent the given conditions. Let the first number be x and the second number be y.

According to the question, the sum of the two numbers is 50, which gives us our first equation:

x + y = 50 (Equation 1)

The first number x is 43 less than twice the second number y. This provides the second equation:

x = 2y - 43 (Equation 2)

We now have a simple system of two linear equations:

x + y = 50

x = 2y - 43

We can substitute the second equation into the first to solve for y:

(2y - 43) + y = 50

3y - 43 = 50

Add 43 to both sides:

3y = 93

Divide both sides by 3:

y = 31

We can now substitute y = 31 back into Equation 2 to find x:

x = 2(31) - 43

x = 62 - 43

x = 19

Therefore, the two numbers are 19 and 31.

Answer:

2

Step-by-step explanation:

do like terms

1/4 x 8 = 2

divide un-like terms

4x ÷ 8 = 2

Answer:

YES

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

-4/-0.2

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

Answer:

One triangle

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify the length sides of triangle

Applying the triangle inequality theorem

1) 3+5 > 6 ---> is true

2) 3+6 > 5 ---> is true

3) 5+6> 3----> is true

therefore

One triangle can be drawn with the given lengths

With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.

The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.

Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.

Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.

[tex]y = 48.28(1.06)^t[/tex] is the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Solution:

Given that,

In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28

During the next 20 years, the price increased an average of 6% each year

The increasing function is given by:

[tex]y = a(1+r)^t[/tex]

Where,

y is the value after t years

t is the number of years

a is the initial value

r is rate of increase in decimal

From given,

a = 48.28

[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]

Substituting the values we get,

[tex]y = 48.28(1+0.06)^t\\\\y = 48.28(1.06)^t[/tex]

Thus the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Answer: For the figure on the left {c}, the Area is 30m (squared) and the Perimeter is 46m.

For the figure on the right {d}, the Area is 32cm (squared) and the Perimeter is 34cm

Step-by-step explanation: (Please refers to the attached diagram)

We shall start with the diagram on the left. The first thing is to break it down into regular shapes, such as rectangles, squares, etc. The dotted line that runs from point C to point G divides the figure into two rectangles which are ABCG {or X} and GDEF {or Y}. Line AG measures 10m since it’s the same length as line BC. Similarly line GF measures 2m since it’s the same length as line DE. So rectangle “X” has dimensions;

L = 10, W = 1

Area of a rectangle = L x W

Area = 10 x 1

Area = 10m

Similarly rectangle Y has dimensions L= 10m and W = 2m

Hence area of rectangle “Y” is computed as

Area = L x W

Area = 10 x 2

Area = 20m

Area of the entire figure is derived as

Area of rectangle X + Area of rectangle Y, which is

10m + 20m = 30m {squared)

The perimeter of rectangle X is given as Perimeter = 2(L + W)

Perimeter = 2(10 + 1)

Perimeter = 2(11)

Perimeter = 22m

Also, perimeter of rectangle Y is derived as

Perimeter = 2(L + W)

Perimeter = 2(10+ 2)

Perimeter = 2(12)

Perimeter = 24m

Therefore the perimeter of the entire figure is derived as

Perimeter of rectangle X + perimeter of rectangle Y, which is

22m + 24m and that equals 46m

For the second figure on the right side of the page, we shall also break it down with the dotted lines that runs from point E to point G. That leaves us with rectangle ABGF {or P} and rectangle EGCD {or Q}.

Rectangle “P” has dimensions L= 4 and W = 2

Area of rectangle P = 4 x 2

Area of rectangle P = 8cm

Similarly area of rectangle Q is given as Area of Q = 8 x 3

Area of Q = 24cm

Area of the entire figure is derived as

Area of P + Area of Q,

8cm + 24cm

= 32cm {squared}

To compute the perimeter of rectangle P

Perimeter of a rectangle = 2(L + W)

Perimeter of rectangle P = 2(4 + 2)

Perimeter of rectangle P = 2(6)

Perimeter of rectangle P= 12cm

Similarly Perimeter of rectangle Q = 2(L + W)

Perimeter of rectangle Q = 2(8 + 3)

Perimeter of rectangle Q = 2(11)

Perimeter of rectangle Q = 22cm

Hence, perimeter of the entire figure is derived as perimeter of rectangle P + perimeter of rectangle Q which equals

12cm + 22cm and that equals

34cm.

Without knowing the function itself, it's impossible to definitively say which of the values (-6,-2,4,7) is an output. Any of these numbers could potentially be an output depending on the function.

In the context of this question, an output of a function refers to the result you get after substituting an input (or value from the domain) into the function. For example, if we have a function f(x) = x+2, and we input the value 3 (from our domain), our output (or range) will be 5. Unless we know the actual function, it's difficult to determine which of the listed values (-6,-2,4,7) is an output because any of these could potentially be an output depending on the function. Thus, without additional context, the statement 'Which value is an output of the function?' cannot be definitively answered.

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The output of a function is -6.

The output of a function is the value that the function produces when a certain input is given. In the table above, the function is f(x). We are given that x can be any of the values -6, -2, 4, or 7. We want to know which of the values -6, -2, 4, 7, or 12 is an output of the function.

To find out, we can look at the table. We see that the only value in the table that is an output of the function is -6. This is because when we plug in x = -6 into the function, we get f(x) = -6.

Therefore, the answer is -6.

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x + (-4) = 10.

We can use the positive - negative rule.

x + (-4) = 10.

x - 4 = 10.

x = 10 + 4

x = 14.

Answer:

She spend $32,640 on cruises.

Step-by-step explanation:

Given:

Shane spends 48% of her income on cruises.

If she makes $68,000 per year.

Now, to find the money she spend on cruises.

Shane makes income per year = $68,000.

Percent Shane spends of her income on cruises = 48%.

Now, to get the income she spends on cruises:

48% of $68,000.

[tex]=\frac{48}{100} \times 68000[/tex]

[tex]=0.48\times 68000[/tex]

[tex]=\$32,640.[/tex]

Therefore, she spend $32,640 on cruises.

Answer:

x= - 3.5

y= - 6.5

Step-by-step explanation:

-3x+y = 4 equation 1

-9x + 5y = -1 equation 2

and

equation 1 can be written as

y = 4+ 3x

so put this in equation 2

-9x + 5 ( 4+ 3x) = -1

-9x +20 +15x = -1

6x = -21

X= -21 ÷ 6

X = - 3.5

so put this value of x in equation 1 to find value of y

-3 ( -3.5) + y = 4

10.5 + y = 4

y = 4 - 10.5

Y = - 6.5

Answer:

x= - 3.5

y= - 6.5-

Answer: 8%

Step-by-step explanation: 370 * 8% = 29.60

Answer: 8% sales tax rate

Step-by-step explanation:

First, you need to find what percentage 29.60 is from 370, so you divide 29.60 by 370 and you get 0.08 then you multiply that by 100 to get your answer in percent. 100 multiplied by 0.08 would be 8%.

Answer:

The variable that has the highest power is considered to be the degree of polynomials in an algebraic equation.

A column:

1) [tex]4x^3[/tex] .

The degree is 3.

2)[tex]x^2+4[/tex].

The degree is 2.

3) [tex]x-2[/tex]

The degree is 1.

B column:

1) [tex]2x^2+1[/tex]

The degree is 2.

2) [tex]x^2-x[/tex]

The degree is 2.

3) [tex]x^3-5x^2+1[/tex]

The degree is 3.

A×B columns:

While Multiplying two terms in a equation, if the variables are same then multiply the constant value and sum the exponent value.

1) [tex](4x^3)(2x^2+1)[/tex].

=[tex]8x^5+4x^3.[/tex]

The degree is 5.

2) [tex](x^2+4)(x^2-x)[/tex].

=[tex]x^4-x^3+4x^2-4x[/tex].

The degree is 4.

3) [tex](x-2)(x^3-5x^2+1)[/tex].

[tex]=x^4-5x^3+x-2x^3+15x^2-3.\\=x^4-7x^3+15x^2+x-3.[/tex]

The degree is 4.

Hey there!

First off, I’m going to assume that the 2 in the second term is an exponent. If it isn’t, let me know and I’ll fix the answer.

Anyways, let’s start by plugging the values for the variables into the equation.

36(3)-8(-6)^2

Square -6

108-8(36)

Multiply.

108-288

Subtract.

-180

Your answer is -180.

Hope this helps!

Answer:

2108

Step-by-step explanation:

Divide 67,456 by 32, using long division.

1) How many times 32 go into 67? (2 times, with a remainder of 3)

2) Bring down the 4.

3) How many times does 32 go into 34? (1 time, with a remainder of 2)

4) Bring down the 5

5) How many times does 32 go into 25? (0 times, so write 0)

6) Bring down the 6.

7) How many times does 32 go into 256? ( 8 times, no remainder)

8) Your answer is 2108

Answer:

A, D, E

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{50}{400} = \frac{5}{40} = \frac{1}{8} = 0.125[/tex]

Answer:

[tex]y=3x[/tex]

Step-by-step explanation:

Let

x ----> the number of kids in a group

y ----> the total number of caramel chews Erica gives to that group

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Find the value of the constant of proportionality k

take a ordered pair from the data in the table and determine the value of k

For x=2, y=6 ----> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3\ caramels/kid[/tex]

therefore

[tex]y=3x[/tex]

Answer:

120.6

Step-by-step explanation:

Since we know that 67 percent of coins are quarters.

Total coins = 180

67% of 180= 180 * 67/100

120.6.

So he has about 120.6 quarters.

Answer:

126 quarters

Step-by-step explanation:

67% ≈ 70%

70% = 70/100

70% = 7/10

180 * 7/10 = 126 quarters

Answer:

4/7

Step-by-step explanation:

1/6-8/6=-7/6

-[1/6-8/6]=7/6

---------------------

(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7

The terms in the expression 2 + 6 + 10b - 8a are 2, 6, 10b, and -8a, where 2 and 6 are constants, and 10b and -8a are variable terms.

The terms in the expression 2 + 6 + 10b – 8a are 2, 6, 10b, and –8a. A term is a single mathematical expression which can be a number, a variable, or numbers and variables multiplied together. Here, the numbers 2 and 6 are called constant terms because they don’t change, 10b is a variable term which means it has a number (coefficient) and a variable (b), and similarly, –8a is a variable term with a negative coefficient and the variable a.

Step-by-step explanation:

We find,

[tex](x+2y)^7[/tex]

To find, the binomial expansion of of [tex](x+2y)^7[/tex] = ?

We know that,

[tex](x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n[/tex]

∴ [tex](x+2y)^7[/tex]

Here, n = 7, x = x and y = 2y

[tex](x+2y)^7[/tex]= [tex]^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7[/tex][tex]=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

∴ The binomial expansion of of [tex](x+2y)^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

Thus, the required "option 4)"  is correct.

Answer:

D. x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7

Step-by-step explanation: