Natalia Leon bought a new bicycle for $248. The sales tax rate is 6 percent. What is the total purchase price
a. $368.22
C. $262.88
b. $234.66
d. $12.40

Solved given expression for x using the change of base formula log base b of y equals log y over log b is 4.459

Answer: Option D

Step-by-step explanation:

Given Expression:

             [tex]2^{x-1}=11[/tex]

To solve this, first convert the exponential form into log form

If  [tex]a^{x}=b[/tex] then [tex]\log _{a}(b)=x[/tex]

So, when comparing the given expression with above,  a = 2, x = x – 1 and b = 11 .

            [tex]2^{x-1}=11[/tex] become [tex]\log _{2}(11)=x-1[/tex]

Now, apply change of base formula to remove base 3

             [tex]\log _{a}(y)=\frac{\log y}{\log a}[/tex]

Hence,

            [tex]\log _{2}(11)=\frac{\log 11}{\log 2}[/tex]

Substitute [tex]\log _{2}(11)=x-1[/tex] in above expression, we get

           [tex]\frac{\log 11}{\log 2}=x-1[/tex]

           [tex]\frac{1.0414}{0.301}=x-1[/tex]

           x – 1 = 3.459

          x = 3.459 + 1 = 4.459

Final answer:

To solve the equation 2^(x - 1) = 11 for x, one can use the change of base formula by taking the logarithm of both sides, rewriting the equation using logarithm properties, isolating x, and then simply calculating using a calculator, which results in x ≈ 1.289.

Explanation:

To solve 2(x − 1) = 11 for x using the change of base formula, take the logarithm of both sides of the equation and use the formula logb(y) = log(y) / log(b), where y is the number we want to take the logarithm of and b is the base of the logarithm.

Let's start the process:

Now, calculate the right side of the equation using a calculator:

Hence, the correct answer is B) 1.289.

Answer:

Few of the following CASES can be the solutions:

1. (7 cm , 3 cm,  10 cm)     2.(14 cm , 3 cm,  5 cm)

3.(35 cm , 3 cm,  2 cm)    4.(7 cm , 6 cm, 5 cm)

5.(7 cm , 15 cm, 2 cm)

Step-by-step explanation:

Here, the volume of the box of granola bars  = 210 cubic cm.

Let us assume the length of the box = l

The width of the box = w

and The height of the box = h

Also, the box is in shape of a cuboid.

VOLUME OF A CUBOID = Length x Width x Height

⇒l x b x  h = 210   .... (1)

Now, we need to find such combinations of (l,b,h) such that their product is  210 cubic centimeters.

There are many number of possible such combinations.

Few of the following CASES can be the solutions:

1. (7 cm , 3 cm,  10 cm)

2.(14 cm , 3 cm,  5 cm)

3.(35 cm , 3 cm,  2 cm)

4.(7 cm , 6 cm, 5 cm)

5.(7 cm , 15 cm, 2 cm)

There can be any other possible such solution as well.

Answer:

Step-by-step explanation:

   1                7              7       <== numerator

--------     X   ------   =   --------

  6                 8             48    <== denominator

" the product " is the result of multiplying

so the product of the numerators is 7

The product of the numerators is 7.

All fragments correspond of a numerator and a denominator and they're separated by a vertical bar known as the fractional bar.

Given:

We have have to multiply the fraction 1/6 to 7/8.

First, the product of Numerator

1 x 7 = 7

and, product of Denominator

6 x 8 = 48

Thus, the product of the numerators is 7.

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ2

Answer:

The amount of sales in order to meet her goal must be greater than or equal to $20,000

Step-by-step explanation:

Let

x----> represent the amount of sales Liz will need

we know that

The amount of sales for the month multiplied by the commission rate as a decimal plus the fixed amount must be greater than or equal to $2,800 each month

so

The inequality that represent this situation is

[tex]0.03x+2,200\geq 2,800[/tex]

solve for x

subtract 2,200 both sides

[tex]0.03x \geq 2,800-2,200[/tex]

[tex]0.03x \geq 600[/tex]

divide by 0.03 both sides

[tex]x \geq \$20,000[/tex]

The amount of sales in order to meet her goal must be greater than or equal to $20,000

Answer:

Step-by-step explanation:

8(4x + 8) = 160.....distribute the 8 thru the parenthesis

8(4x) + 8(8) = 160

32x + 64 = 160....subtract 64 from both sides

32x + 64- 64 = 160 - 64

32x = 96

x = 96/32

x = 3 <===

All real solutions is the answer

Answer:  distance = 406 miles

speed = 58 miles/hr

Step-by-step explanation:

4 hours - 232 miles

1 hr - 232/4

7 hours - 232/ 4 x 7 = 406 miles

Therefore , her distance is 406 miles for 7 hours.

Speed = distance / time

speed = 406/7 = 58 miles/hr

4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.

Solution:

Let us assume that x is the required pounds sugar to make 5% syrup

[tex]\Rightarrow\frac{x}{\text{total quantity}}=5\%[/tex]

which is [tex]\frac{x}{5}=5\%[/tex]

On solving we get,

[tex]\Rightarrow\frac{x}{5} =0.05 [5\%=\frac{5}{100}][/tex]

[tex]\Rightarrow x = 5\times0.05\rightarrow x=0.25[/tex]

If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,

[tex]5 \text{ lbs }-0.25 \text{ lbs }=4.75 \text{ lbs }[/tex]

So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.

Answer:

4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.

Solution:

Let us assume that x is the required pounds sugar to make 5% syrup

which is  

On solving we get,

If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,

So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

These are two lines with different slopes and y intercepts so they will intersect once

Final answer:

Explaining how to find the number of solutions in a system of linear equations.

Explanation:

The given equations are:

y = x - 3

4x - 10y = 6

To find the number of solutions, we can solve these equations simultaneously.

Substitute y = x - 3 into the second equation and solve for x to find the value of y. If the solution leads to a valid pair of x and y that satisfies both equations, then there is one unique solution, otherwise there are no solutions.

Answer: 25422

Step-by-step explanation:

6(4000+237)

6(4000) + 6(237)

24000 + 1422

24000+1422=25422

Answer:

  6·4237 = 25422

Step-by-step explanation:

This is the way multiplication by hand is usually done.

  6(4237) = 6(4000 +200 +30 +7) = 6·4000 +6·200 +6·30 +6·7

  = 24000 +1200 +180 +42

  = 25200 +222 . . . . . add first two terms and last two terms

  = 25422

Answer:

A. is Obtuse scalene triangle.

Step-by-step explanation:

Hope this help

Answer:

c i think

Step-by-step explanation:

The question involves solving simultaneous linear equations, a high school level topic in mathematics. Methods like substitution or elimination can be used to find the values of the variables.

The student's question involves solving simultaneous linear equations, which is a topic in mathematics. To solve the given system of equations, one can use methods such as substitution, elimination, or matrix operations like determinants. The elimination method can be particularly efficient. For example, you can multiply the first equation by a number that will allow the x or y terms to cancel out when added or subtracted from the second equation. After simplifying, you're left with one equation in one unknown, which can be easily solved. Then, back-substitute the known value into one of the original equations to solve for the other variable.

Given the equations 3x + 7y = -5 and 8x + 9y = 6, we may choose to multiply the first equation by 3 and the second by 7 (to eliminate the x terms) or to multiply the first equation by 8 and the second by 3 (to eliminate the y terms). Once one variable is eliminated, we solve for the other and use it to find the value of the remaining variable.

Answer:

[tex] x\geqslant 300[/tex]

x is greater then or equal to 300

=============================================

Work Shown:

f(x) = 6x + b

f(5) = 6(5) + b .... replace every x with 5

f(5) = 30 + b

1 = 30 + b ..... replace f(5) with 1, since f(5) = 1 was given.

1-30 = 30 + b - 30 .... subtract 30 from both sides

-29 = b

b = -29

-----------

The function f(x) = 6x+b turns into f(x) = 6x+(-29) which is equivalent to f(x) = 6x-29

Plugging in x = 5 leads to

f(x) = 6x-29

f(5) = 6(5) - 29

f(5) = 30 - 29

f(5) = 1

So we have confirmed the answer.

Answer:

Step-by-step explanation:

f(5) = 1

6*5 + b = 1

30 + b = 1

b = 1 - 30 = -29

b = -29

Answer:25.12

Step-by-step explanation:

Option C: Three-fourths greater-than two-thirds

Solution:

Option A: A number line going from negative 1 to 1.

Explanation: A number line is used to define a point in a given interval. And hence, a number line does not goes from negative 1 to 1.

Thus, this statement is false.

Option B: One-half less-than one-third

Explanation: The statement can be written as

[tex]\begin{array}{c}{\frac{1}{5}<\frac{1}{3}} \\{0.5<0.33}\end{array}[/tex]

which is not possible.

Hence, this inequality is false.

Option C: Three-fourths greater-than two-thirds

Explanation: The statement can be written as

[tex]\begin{array}{c}{\frac{3}{4}>\frac{2}{3}} \\{0.75>0.667}\end{array}[/tex]

which is true.

Hence, this inequality is true.

Option D: Negative one-fourth less-than negative two-thirds

Explanation: The statement can be written as

[tex]\begin{aligned}-\frac{1}{4} &<-\frac{2}{3} \\-0.25 &<-0.667\end{aligned}[/tex]

This is not possible.

Hence, this inequality is false.

Option E: Negative 1 greater-than three-fourths

Explanation: The statement can be written as

[tex]\begin{array}{l}{-1>\frac{3}{4}} \\{-1>0.75}\end{array}[/tex]

This is not possible.

Hence, this inequality is false.

Answer:

the person who answered this question is actually correct she just put option c when its actually option d people make mistakes its okay thats how u learn

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation of a line in a standard form.

Convert to the slope-intercept form:

[tex]2x-y=-1[/tex]         add y to both sides

[tex]2x-y+y=-1+y[/tex]

[tex]2x=-1+y[/tex]            add 1 to both sides

[tex]2x+1=-1+1+y[/tex]

[tex]2x+1=y\to y=2x+1[/tex]

The slope intercept form of the given equation is y = 2x+1

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

(ii) 3x + 5 = 15

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, an equation of a line, 2x-y = -1, we need to convert this into slope intercept form,

The standard form of the equation of a line in slope intercept form, is given by :

y = mx+c

Where, m = slope of the line, c is the y-intercept,

So, the given equation is 2x-y = -1,

Add y both the side,

2x-y+y = -1+y

2x = -1+y

Add 1 in both sides,

2x+1 = y+1-1

y = 2x+1

Hence, the slope intercept form of the given equation is y = 2x+1

Learn more about equations, click;

https://brainly.com/question/29657992

#SPJ2

Area of the doghouse =- 32.5 sq. ft

Solution:

Given height = 5 ft, base1, [tex]b_1[/tex] = 5ft

Base2, [tex]b_2[/tex] = [tex]b_1+3=5+3=8[/tex] ft

Area of the trapezoid = [tex]\frac{1}{2}\times height\times (base1 +base2)[/tex]

                                   [tex]=\frac{1}{2}\times 5\times (5+8)[/tex]

                                   [tex]=\frac{1}{2}\times 5\times 13[/tex]

                                   [tex]=\frac{1}{2}\times 65[/tex]

                                   [tex]=32.5[/tex] sq. ft

Area of the trapezoid = 32.5 sq.ft

Hence the area of the doghouse is 32.5 sq. ft.

Answer:

The answer is 13 if you count 0.

Step-by-step explanation:

The sequence is as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

Also, have a great day and Happy Valentines! <3

We want to analyze the terms of the given expression.

15) second term, z/3

16) third term, 2*w

The given expression is:

1 + z/3 + 2*w

15) We want to find which part of the expression is a quotient.

A general quotient is something of the form a/b, so compared with the expression, the term that is a quotient is the second term; z/3.

Where the first number, z, is called the numerator and the second is called the denominator.

Notice that the variable z is on the numerator, so this would be a linear dependence with z.

16) We want to find which part of the expression is a product of two factors.

It is the third term, 2*w

Where the two factors are 2 and w.

Again, the variable si w, and we are multiplying it by a constant number, 2.

So we also have a linear dependence with w.

If you want to learn more, you can read:

https://brainly.com/question/7510157

In the expression 1 + z/3 + 2w, the quotient is z/3, where z is the numerator and 3 is the denominator. The product of two factors is 2w, with 2 and w being the factors.

The student asked about parts of the expression 1 + z/3 + 2w.

15) Quotient in the Expression

The quotient refers to the result of division. In the expression given, the quotient is z/3. Its parts are the numerator z, which is the value being divided, and the denominator 3, which is the value by which z is divided.

16) Product of Two Factors in the Expression

The product refers to the result of multiplication. In the expression, the product is 2w. Its parts are the two factors being multiplied: the constant 2 and the variable w.

Answer:

[tex]c\leq -32[/tex]

Step-by-step explanation:

Let

c ---> the number

we know that

The number c plus 6 must be less than or equal to -26

so

The inequality that represent this situation is

[tex]c+6\leq -26[/tex]

Solve for c

Subtract 6 both sides

[tex]c\leq -26-6[/tex]

[tex]c\leq -32[/tex]

The solution for c is the interval (-∞,-32]

All real numbers less than or equal to -32

In a number line, the solution is the shaded area at left of c=-32 (closed circle)

see the attached figure to better understand the problem

Answer:

The correct answer is indeed 3.5 :)

Step-by-step explanation:

just took the test <3 hopes this help

The value of x is 3.5.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Right triangle with vertices labeled as A, B, and C.

Side C B is the base and the top vertex is A.

Side A B contains a midpoint D.

A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D.

Side A C= 5.

Base C B = 6.

Line Segment A D = x.

Segment B D=4.2.

4.2/6=x/5

Apply cross multiplication

4.2×5=6x

21=6x

Divide both sides by 6

x=3.5

Hence, the value of x is 3.5.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ6

Answer:

-99 is less than -98

-99 is less than -97

-99 is less than -96

.

.

.

-99 is less than -1

-99 is less than 0

-99 is less than (any posifive number)

Answer:

Y=x+1...written on the line between c and b

Step-by-step explanation:

CB is perpendicular to EF.

The slope is 1, the y intercept is 1

Therefore. Y =mx+B is y=1x+1

Answer:

Option C. 832 miles

Step-by-step explanation:

Ashley travels between 204 and 272 miles in every 4 hours.

That means she travels between 51 [tex](\frac{204}{4}miles)[/tex] and 68 ([tex]\frac{272}{4}miles)[/tex] per hour.

Therefore, in 12 hours she will travel between 612 (51×12 miles) miles and 816 (68×12 miles).

Since she has already traveled 118 miles before 12 hours then the distance traveled by her till now will be between 730 (612+118 miles) and 934 (816+118 miles).

From the given options, Option C. 832 miles is the reasonable measure of Ashley's distance from the starting point.

Step-by-step explanation:

Answer:

Step-by-step explanation: You would do 5x+20+x+40=180

Then you would add 5x and x together and you would also add 20 and 40 together and then you get: 6x+60=180

You would then subtract 180-60 and then you should get 6x=120 and the you would divide from both sides and you should get x=20 you would then plug it into both angles So 5(20)+20 and you should get 120 for the left angle and then you would do the next angle which would be 20+40=60 for the right angle

Short version:

5x+20+x+40=180

6x+60=180

6x=120

X=20

Answer:

the question lacks the full information and is incomplete.

Step-by-step explanation:

Answer:

Cost of one glove pair is $ 8.50 and the cost of one hat is $6.50

Step-by-step explanation:

Let g represents the cost of one gloves pair

h represents the cost of one hat

Then

Cody brought two pairs of gloves and four hats for $43.00

This can be written as

2g + 4h = 43-------------------(1)

Tori bought two pairs of gloves and two hats for 30.00

This can be written as

2g + 2h = 30------------------(2)

Subtracting (2) from (1)

2g + 4h = 43

2g + 2h = 30

(-)

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

0g + 2h = 13

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

2h =13

h = 13 / 2

h = 6.5---------------------(3)

Substituting (3) in (2)

2g + 2(6.5) = 30

2g + 13 = 30

2g = 17

g = 17 / 2

g = 8.5

So one hat is $6.50 and one pair of gloves is $8.50.