- 2/3 + (3/4 + 5/3)

Let's solve the left side first since there's no parentheses or multiplication.

30 + 86 = 116

Now we have 116 = 2 + 5(56 - 8)

Using PEMDAS, Parentheses first.

(56 - 8) = 48

Now we have 2 + 5(48)

Using PEMDAS, Multiplication next.

5 * 48 = 240

Using PEMDAS, Addition is next.

2 + 240 = 242

The equation 116 = 242 is false, as the values do NOT equal each-other.

116 ≠ 242

f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = - [tex]\frac{6}{7}[/tex]

partial equation is y = - [tex]\frac{6}{7}[/tex] x + c

to find c substitute (3, 5 ) into the partial equation

5 = - [tex]\frac{18}{7}[/tex] + c ⇒ c = [tex]\frac{53}{7}[/tex]

f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = [tex]\frac{2}{5}[/tex] x - 6 is in this form with slope m = [tex]\frac{2}{5}[/tex]

Parallel lines have equal slopes, thus

y = [tex]\frac{2}{5}[/tex] x + c is the partial equation of parallel line

to find c , substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{2}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex] ← equation of parallel line

The percent change is given by ...

... (percent change) = (new amount - old amount)/(old amount) × 100%

This can be rearranged to give a formula for the new amount. First, we'll rewrite it to a slightly different form.

... (percent change) = ((new amount)/(old amount) -1) × 100%

... (percent change)/100% = (new amount)/(old amount) -1 . . . . divide by 100%

... (percent change)/100% + 1 = (new amount)/(old amount) . . . add 1

... (old amount) × ((percent change)/100%) +1) = new amount . . . . multiply by old amount

We can now use this formula to find the new amount in each case.

13. 25 × (300%/100% +1) = 25 × 4 = 100 . . . . dollars

14. 160 × (-20%/100% +1) = 160 × 0.8 = 128 . . . . bananas

15. 56 × (-75%/100% +1) = 56 × .25 = 14 . . . . books

16. 52 × (25%/100% +1) = 52 × 1.25 = 65 . . . . companies

17. 12000 × (5%/100% +1) = 12000 × 1.05 = 12,600 . . . . miles

18. 710 × (-10%/100% +1) = 710 × 0.90 = 639 . . . . points

_____

Considering the above formula for percent change (or its "slightly different form"), you may want to reconsider your answers for problems 7–12.

1. The vertical asymptote requires the denominator have a zero at that location. The x-intercept requires the numerator have a zero at that location. The horizontal asymptote amounts to a multiplier of the function:

... y = 2(x +5)/(x -3)

2. The vertical asymptote requires the denominator have a zero at that location. The oblique asymptote is an add-on

... y = 1/(x +1) +(x +2)

... y = (x² +3x +3)/(x +1)

We can use rational functions to define functions with specific characteristics. A function with a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and x-intercept at x = -5 could be written as f(x) = 2(x + 5) / (x - 3). A function with a vertical asymptote at x = -1 and an oblique asymptote at y = x + 2 can be written as f(x) = (x^2 + x - 2) / (x + 1).

The subject here pertains to certain characteristics of functions, specifically regarding asymptotes and intercepts. In order to create a function with the required characteristics, you would typically use rational functions.

Vertical asymptotes occur when the denominator of a function is zero, horizontal asymptotes are connected to the degree of the polynomials in the function, and x-intercepts occur when the function itself equals zero.

Here's how we can write the function for each case:

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Answer:

You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.

Step-by-step explanation:

got it right

Answer: D

Step-by-step explanation:

The following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].

Given

Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu.

The previous menu had D dishes.

If it has 20% more, it must mean that it is 1.2 of the previous menu (Because it is 100 percent, plus an extra 20).

Therefore,

The following expressions could represent how many dishes crispy clovers new menu has;

[tex]\rm= D (100 \ of \ the \ previous \ menu) }+ \dfrac{1}{5} \rm \times { 20 \ percent \ D \ of \ the \previous \ menu}\\\\=D+\dfrac{1}{5}D[/tex]

Hence, the following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].

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Y = 1/2 + 5 , the slope of this equation is 1/2

The equations of the parallel lines must also have a slope of 1/2.

This is because parallel lines have the same value of slope.

Answer:

f(x)=x-1

Step-by-step explanation:

replace y by f(x) to obtain functional notation

f(x) = x - 1

see explanation below

(1) [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{10}[/tex] = 0.2

(2) [tex]\frac{6}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{24}{100}[/tex] = 0.24

(3) 2 [tex]\frac{3}{4}[/tex] = 2 +[tex]\frac{75}{100}[/tex] = 2.75

(4) 3 [tex]\frac{9}{10}[/tex] = 3 + 0.9 = 3.9

(5) 1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

(6) 3.29 = 3 [tex]\frac{29}{100}[/tex] = [tex]\frac{329}{100}[/tex]

(7) 0.65 = [tex]\frac{65}{100}[/tex] = [tex]\frac{13}{20}[/tex] in simplest form

(8) 5.6 = 5 [tex]\frac{6}{10}[/tex] = 5 [tex]\frac{3}{5}[/tex] = [tex]\frac{28}{5}[/tex]

(9) he is incorrect

[tex]\frac{3}{5}[/tex] × [tex]\frac{20}{20}[/tex] = [tex]\frac{60}{100}[/tex] = 0.6 ≠ 3.5

A.) If Grace and Claire’s parents each invested $7,600 into a college savings account when the girls were born, how much money will each girl have for college when she turns 18? Explain.

Answer/Explanation:

For Grace, I plugged in 18 for x.

Work:

y= 1000(18) + 7600

y= 18000 = 7600

y= 25600

For Claire, I had to first find the slop by using rise over run.

11600-10000/3= 800

So the formula for Claire is y= 800x + 7600 and then you just plug in 18 for x.

Work:

y= 800(18) + 7600

y= 14,400 + 7600

y= 22,000

Therefore, Grace would have $25,600 at the end of 18 years old and Claire would have $22,000 when she turns 18 years old.

                 I hope that helped you or anyone else!! :)

The amount of money that Grace and Claire will have for college when they turn 18 will be $25600 and $22000 respectively.

Based on the information given, the amount that Grace will make will be:

= 1000x + 7600

= 1000(18) + 7600

= 18000 + 7600

= 25600.

The amount that Claire will make will be:

= 800x + 7600.

= 14400 + 7600

= 22000

The functions show a positive correlation between time and the amount of money saved.

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A spreadsheet program, such as Google Sheets, will happily make a pie chart for you, even displaying the percentages. (See the attachment.)

To calculate the percentages, divide each of the numbers in your list by the total of those numbers, then multiply that ratio by 100%

For example, the total is 2175, so the percentage belonging to Winter is

... 234/2175 × 100% ≈ 10.75862% ≈ 10.8%

If you're constructing the pie chart by hand, the next thing you need to know is the central angle of the section of pie representing Winter. To find that, mutiply the percentage (or its corresponding fraction) by 360°.

... 10.8% × 360° ≈ 38.7°

You can plot this on your chart using a protractor.

To create a pie chart with percentages, determine the values, calculate the percentages, draw the sections, and label them accordingly.

To create a pie chart with percentages, follow these steps:

For example, if you have a pie chart representing the sales distribution of three products: A, B, and C, and their respective values are 100, 200, and 300, you would calculate the percentages as follows: A: (100 / 600) * 100 = 16.67%, B: (200 / 600) * 100 = 33.33%, C: (300 / 600) * 100 = 50%. Then, you would draw the pie chart with three sections, labeling each section with the product and its percentage.

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Try this solution (all the details are in the attached picture, answers are underlined with colour).

The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]

Further explanation:

Given:

The measure of angle A is [tex]\angle A = {60^ \circ }.[/tex]

The measure of angle C is [tex]\angle C = {45^ \circ }.[/tex]

The length of side AB is [tex]AB = 8[/tex]

Calculation:

The sum of all angles of a triangle is [tex]{180^ \circ }.[/tex]

[tex]\begin{aligned}\angle A + \angle B + \angle C &= {180^ \circ }\\{60^ \circ } + \angle B + {45^ \circ } &= {180^ \circ }\\{105^ \circ } + \angle B &= {180^ \circ }\\\angle B&= {180^ \circ } - {105^ \circ }\\\angle B&= {75^ \circ }\\\end{aligned}[/tex]

The sine rule in triangle ABC can be expressed as,

[tex]\begin{aligned}\frac{{BC}}{{\sin {{60}^ \circ }}}&=\frac{8}{{\sin {{45}^ \circ }}}\\BC&=\frac{8}{{\frac{1}{{\sqrt2 }}}}\times\frac{{\sqrt 3 }}{2}\\BC&= 9.80\\\end{aligned}[/tex]

The length of AC can be calculated as follows,

[tex]\begin{aligned}\frac{{AB}}{{\sin {{45}^ \circ }}} &= \frac{{AC}}{{\sin {{75}^ \circ }}}\\\frac{8}{{\sin {{45}^ \circ }}} \times \sin {75^ \circ }&= AC\\10.93 &= AC\\\end{aligned}[/tex]

The perimeter of triangle ABC can be obtained as follows,

[tex]\begin{aligned}{\text{Perimeter}}&= AB + BC + AC\\&= 8 + 9.80 + 10.93\\&= 28.73\\\end{aligned}[/tex]

The area of triangle ABC can be obtained as follows,

[tex]\begin{aligned}{\text{Area}}&=\frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2} \times 8 \times 10.93 \times \sin {60^ \circ }\\&= 4 \times 10.93 \times \frac{{\sqrt3 }}{2}\\&= 37.86\\\end{aligned}[/tex]

The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: angles, ABC, angle A=60 degree, perimeter, area of triangle, triangle ABC.

Solution: The Steps are defined below,

Explanation:

To divide a line segment in 2:3 using compass alexis has to follow many steps:

1) Draw a line segment ab of length x.

2) Draw a line ac which makes an acute angle with the line ab.

3) Since alexis has to divide the line is 2:3, so make 2+3=5 arc of equal length of ac with the help of compass.

4) Name the fifth arc as d, so join the fifth arc with point b.

5) The draw a parallel to the line bd, and passing through the 2nd acr of ad. mark the second are as m.

6) Let the parallel line intersect at point n. Where the parallel line intersect the line ab, that point divides the line segment ab is 2:3.

By using above steps we get the figure same as the figure given below.

The line [tex]\bf ab[/tex] can be divided into the ratio [tex]2:3[/tex] with the help of a compass.

Further explanation:

Given that Alexis is trying to partition a line segment [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex] with the help of compass.

There are different methods to divide a line segment in the given ratio, but we will use a simple method to divide the line [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex].

Given a line segment [tex]\bf ab[/tex], which is to be divided in the ratio of [tex]2:3[/tex].

First draw any ray [tex]\bf ax[/tex] which makes an acute angle with [tex]\bf ab[/tex].

Locate [tex]5[/tex] points [tex]\bf a_{1},a_{2},a_{3},a_{4}\text{ and }a_{5}[/tex] on the ray [tex]\bf ax[/tex] such that [tex]\bf aa_{1},a_{1}a_{2},a_{2}a_{3},a_{3}a_{4}[/tex] and [tex]\bf a_{4}a_{5}[/tex] are equal, with the help of a compass.

Since, Alexis is trying to divide the line [tex]\bf ab[/tex] into the ratio of [tex]2:3[/tex], therefore, the ray [tex]\bf ax[/tex] is divided into [tex]5(2+3)[/tex] points.

Now, join the point [tex]\bf b[/tex] with the point [tex]\bf a_{5}[/tex].

From the point [tex]\bf a_{2}[/tex], draw a line parallel to [tex]\bf ba_{5}[/tex] and this can be drawn by making an angle equal to [tex]\angle\text{aa}_{5}\text{b}[/tex].

Now, consider that the line that is drawn parallel to [tex]\bf ba_{5}[/tex] intersect the given line [tex]\bf ab[/tex] at the point [tex]\bf c[/tex].

The point of intersection on the line [tex]\bf ab[/tex] is the point where it is divided into the ratio [tex]2:3[/tex] as shown in Figure 1 (attached in the end).

The above used steps are used to divide any line in the given ratio.

Therefore, the line [tex]\bf ab[/tex] can be divided into the ratio of [tex]2:3[/tex].

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Constructions

Keywords: Alexis, compass, partition, segment, ab, ratio, 2:3, constructions, line, ray, parallel, intersection, angle, acute, geometry, line segment, acute angle.

Answer:

it is decreasing in the time interval 0<x<2 hours.

Step-by-step explanation:

Graph of first line going through ordered pairs A(0, 40) and B(2, 10).

Graph of second line going through ordered pairs B(2, 10) and C(4, 10). Graph of third line going through ordered pairs C(4, 10) and D(7, 50).

When movement is from point A to B, change in x = 2 and change in y = -30

Hence change for unit x = -30/2 = -15 ... i

When movement is from point B to C, change in x = 2 and change in y = 0

Hence change for unit x = 0/2 = 0 ... ii

When movement is from point C to D, change in x = 3 and change in y = +40

Hence change for unit x = 40/7 = 5.71  .. iii

Hence from A to B it is decreasing, B to C it remains constant and C to D it is increasing.

x coordinate represents hours and y coordinate degrees.

Hence answer is it is decreasing in the time interval 0<x<2 hours.

Answer:

decreasing in the time interval 0<x<2 hours. or B

Step-by-step explanation:

We can let x and y represent cups of lemonade and numbers of lemon bars, respectively. Then the constraints are ...

A graph is shown in the attachment, with the ordered pairs plotted. It is not feasible to sell half cups of lemonade or half lemon bars, so the second and third choices must be excluded. The point (160, 110) falls outside the feasible region, so is not a correct choice.

The correct choices are ...

Final answer:

The only ordered pairs that meet the constraints of Larry's Lemons business situation are (150,200) and (180,100), as these combinations satisfy the conditions for revenue, expenses, and minimum amount of lemonade sold.

Explanation:

To find which ordered pairs (x, y) make sense in the context of Larry's Lemons' business situation, we need to consider the given conditions and set up inequalities to express the sales and expense constraints.

The conditions are:

Revenue Constraint:

For the revenue, we need to ensure that the seller made at least $500.

2x + 1.5y ≥ 500

Expense Constraint:

For the expenses, they should not exceed $100.

0.25x + 0.20y ≤ 100

Lemonade Sold Constraint:

Since at least 150 cups of lemonade were sold:

x ≥ 150

Now we check the given ordered pairs against these constraints:

Only the ordered pairs (150,200) and (180,100) satisfy all the conditions of the problem.

(1)

take out the common factor (y - 4 )

= (y - 4)(3x - 2)

(2)

factor by grouping (1/2 terms and 3/4 terms )

4y(5x - 1) + 7(5x - 1)

take out the common factor (5x - 1)

= (5x - 1)(4y + 7)

1.  Factor out the (y-4)

(y-4) (3x-2)

2.Factor by grouping

20xy -4y    +35x -7

4y(5x-1) +7(5x-1)

then factor out 5x-1

(5x-1)(4y+7)

The sum of interior angles of a triangle is 180°, and a linear pair is supplementary (adds to 180°). The appropriate choice is

... G. w = 105°, because ...

_____

In short, an exterior angle is equal to the sum of the opposite interior angles.

... w = 180 - (180 - (45 + 60)) = 180 -180 +45 +60

... w = 45 +60

Replace the variables with their values and do the arithmetic.

qxs = -30 +2(600) -4(60) = -30 +1200 -240

qxs = 930

930 of product x is produced.

Explanation of how to determine the quantity of product x produced when given specific prices, the quantity produced of product x is -150.

Supply Function: qxs = - 30 + 2px - 4pz

a. To determine the quantity produced when px = $600 and pz = $60, substitute these values into the supply function:

qxs = -30 + 2(600) - 4(60) = -30 + 120 - 240 = -150

Therefore, when px = $600 and pz = $60, the quantity produced of product x is -150.

Yes this is a Law of Detachment.

Multiplicity means multiple roots. So [tex](x + a)^n[/tex] means that the root [tex]-a[/tex] has multiplicity [tex]n[/tex].

Using the definition of multiplicity of roots, we deduce that we have:

(A) -2 with multiplicity 2, 4 with multiplicity 1, and  -1 with multiplicity 3.

Multiplicity of a polynomial means how many times a particular number is a zero for a given polynomial.

In the given polynomial :

[tex]f(x)=(x+2)^{2} (x-4)(x+1)^{3}[/tex]

The roots of the equation can be found by taking the factor =0.

x+2=0 or x=-2

x-4=0

or x=4

x+1=0

or x=-1

The roots of the polynomial are -2,4,-1.

The powers of the root denotes the multiplicity of the polynomial.

The root -2 occurs 2 times ,4 occurs once ,-1 occurs 3 times.

So we say :–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3.

Option A is the right option.

Answer:

Step-by-step explanation:

Apparently, your periodic rate is that used to compute the interest accrued each period. It seems to be the compound (annual) rate divided by the number of periods in a year: quarterly, 4; monthly, 12; daily, 365; biweekly, 26; semimonthly, 24.

_____

If you want the effective annual rate to be 18% in each case, the numbers are different. For n periods per year, those are calculated as

[tex]\sqrt[n]{1.18}-1[/tex]

A periodic rate of 0.04224664 will give an effective annual rate of 18%.

Periodic rates for a 18% compound rate compounded quarterly, monthly, daily, biweekly, and semimonthly are calculated as follows :

You will need to find the area of the rectangular shaped wooden floor and divide that area by 115 square feet.

46 x 35 = 1610

1610 square feet/115 square feet

= 14 cans of wood stain

Answer:

It should be 14

Step-by-step explanation: