2
If x and y vary directly and y=32 when x=18, then which of the following equations correctly represents
the algebraic relationship between x and y?
(c) x + y = 50
16
(a) y=x
(b) y=x+14
(d) y=-x/16

a) Jeffrey needs an extra amount of $40,357.5 for buying a car.

b) After 20 years fund is worth $1364.

c) After 20 years $1200 interest had been earned.

a) P = $500

r = 12% = 12 ÷ 100 = 0.12

n = 12 because it was compounded 12 times in a year.

t = 5 years

Therefore,

A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]

A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]

A = 500 × 1.285

A = $ 642.5

Jeffrey needs an extra $40,357.5 for buying a car.

b) P = $500

r = 12% = 12 ÷ 100 = 0.12

n = 12 because it was compounded 12 times in a year.

t = 20 years

Therefore,

A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]

A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]

A = 500 × 2.728

A = $1364

After 20 years fund is worth $1364.

c) Simple interest = P × R × T ÷ 100

Simple interest = 500 × 12 × 20 ÷ 100

Simple interest = $1200

After 20 years $1200 interest had been earned.

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Answer:

2. 14.42

3. 17.69

6. 12.8

9. 10.29 (I cant see your answer)

Rest is correct ;D

Step-by-step explanation:

Answer: 1665

Step-by-step explanation:

Prime factorization of the numbers:

15 = 3 × 5

45 = 3 × 3 × 5

37 = 37

LCM(15, 45, 37)

= 3 × 3 × 5 × 37

= 1665

Hope this helps!

Answer:x squared = 60

Step-by-step explanation:

x2-6=54, first you have to cancel out the 6 on the left side by adding 6 to -6 after doing that you are left with

x2-(-6+6)=54

but since you did +6 on the right side you have to do +6 on the left so after that you are left with

x2=54+6

now you just do 54+6=60 so after all of that you get

x2=60

(you can use a calculator to find the square root of 60)

Answer: The answer could be 28 but I need to know what is the length and what is the height.

Step-by-step explanation:

I will just name the points for simplicity:

A - (3, -5)

B - (7, -5)

C - (7, 2)

D - (3, 3)

A to B - 4

B to C - 7

C to D -  4.1231

***

Distance (d) = √(3 - 7)^2 + (3 - 2)^2

= √(-4)^2 + (1)^2

= √17

= 4.1231056256177

***

D to A - 8

4 * 7 = 28

Taking into account the definition of a system of linear equations, a small pizza and a regular pizza cost £7 and £11 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.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This mieans thar systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

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

2r + 3s= 43

8r + 9s= 151

Of the several methods to solve a system of equations. it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "r" from the first equation:

2r= 43 - 3s

r= (43 -3s)÷2

r= 43/2 - 3/2s

Replacing this expression in the second equation:

8×(43/2 - 3/2s) + 9s= 151

Solving:

8×43/2 - 8×3/2s + 9s= 151

172 -12s + 9s= 151

-12s + 9s= 151 - 172

-3s= -21

s= (-21)÷ (-3)

s= 7

Remembering that r=43/2 - 3/2s you get:

r=43/2 - 3/2×7

r= 11

Finally, a small pizza cost £7 and a regular pizza cost £11.

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Answer: 2.5.02

Step-by-step explanation:

Answer:

The rectangles length is 2 times as much as its width.

Step-by-step explanation:

8 x 10⁴ = 80,000

4 x 10⁴ = 40,000

40,000 x 2 = 80,000

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}[/tex]

Answer:

Step-by-step explanation:

(12 nights)($184) = $2208

(9 nights)($6) = $54

(6 taxi rides)($27) = $162

$2208 + $54 + $162 = $2424

We will use a ratio to calculate American dollars to pounds

2424/x = 1.83/1

Cross multiply

1.83x=2424

Divide

= ~£1324.59

£1324.59 + £1600 = £2924.59

The answer is ~2924.59 pounds

The total cost of the flights, the hotel room, the wifi, and 6 taxi journeys for Tony's holiday in Canada is approximately £2925.13.

Given that Tony is vacationing in Canada, his flight cost is £1600, he stayed for 12 nights, his hotel cost $184 per night, Tony used wifi for 9 days. Wifi cost $6 per day. Tony took a taxi 6 times costing a mean average of $27 per taxi journey.

The exchange rate was $1.83 to £1.

We need to find the total cost his spend in the vacation.

To calculate the total cost of Tony's holiday, we need to convert all the expenses to pounds and then sum them up.

Flights cost: £1600

Hotel cost per night: $184

Hotel cost for 12 nights: 12 nights x $184/night = $2208

Wifi cost per day: $6

Wifi cost for 9 days: 9 days x $6/day = $54

Taxi cost per journey (mean average): $27

Total taxi cost for 6 journeys: 6 journeys x $27/journey = $162

Now, we need to convert the costs from dollars to pounds using the exchange rate of $1.83 to £1.

Flights cost in pounds: £1600

Hotel cost in pounds: $2208 / $1.83 = £1207.10

Wifi cost in pounds: $54 / $1.83 = £29.51

Taxi cost in pounds: $162 / $1.83 = £88.52

Finally, we can calculate the total cost in pounds:

Total cost = Flights cost + Hotel cost + Wifi cost + Taxi cost

Total cost = £1600 + £1207.10 + £29.51 + £88.52

Total cost = £2925.13

So, the total cost for Tony's holiday in Canada is approximately £2925.13.

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Answer:

870,000

Step-by-step explanation:

Ten thousand is 10,000.

The ten thousand value here is 6

The thousand value here is 7.

Using rounding rules, 5 and up goes up therefore the ten thousand value becomes 7.

867,000 --> 870,000

Hope that helps

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products.

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products. A factored form can represent any logic function, and every factored form represents some logic function.

1a)The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)Area = length × width

To estimate the algebraic expressions for length and width

Area = (7x + 3)(4x - 2) = 28x² - 14x + 12x - 6 = 28x² - 2x - 6

Area = 28x² - 2x - 6

Given x = 10,

Let the equation be 28 x² - 2x - 6

substitute the value of x, in the above equation, we get

= 28(10)² - 2(10) - 6

= 2774

Area = 2774 sq . m

2. We can group the first two terms and next two terms:

xy - 4y + 7x - 28 = (xy - 4y) + (7x - 28)

simplifying the above equation, we get

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

Therefore, the equation is in factored form.

The complete question is:

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow change. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length that is three more than seven times x and the width is four times x minus 2.a.) What are the dimensions of your mowing plot? (2 points)

Length: ______________________________________

Width: ______________________________________

b.) What is the area of your plot (remember area = length x width)? (2 points)

Area: _________________________________________

c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)

Area: _________________________________________

2.) Factor by grouping: (4 points)

xy − 4y + 7x − 28

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Answer:

Step-by-step explanation:

The required two odd numbers are 3 and 5.

We have to determine,  It is a factor of 30 and a multiple of 3 what are 2 numbers.

To obtain the factor of 30 and 2 numbers is calculated in the following steps.

The Factors of 30 are,

30 = 2 , 3 , 5 ,

And multiply the terms by 2,

After multiply by 2 all the term become even.

Then,

The 2 odd numbers are: 3, 5

Hence, The required two odd numbers are 3 and 5.

Both figures 1 & 2 are similar

Point S in figure 1 corresponds to Point P in fugure 2

The reasons that proves the congruency of the triangles are;

2.7 [tex] \Delta EDF \cong \Delta FGE[/tex] by SSS congruency postulate

2.8 [tex] \Delta AOB \cong \Delta COB[/tex], by SAS congruency rule

[tex] \Delta AOB \cong \Delta COB[/tex], by ASA congruency rule or postulate

The rules that proves two triangles to be congruent is if they satisfy any of the 5 rules of congruency, which are; Side–side–side, or SSS, side–angle–side, or SAS, side–angle–angle, or SAA, angle–side–angle, or ASA, and right angle–hypotenuse–side, or RHS

2.7 The given parameters of the two triangles are;

DE = GF, and DF = GE

Required;

To prove that

[tex] \Delta EDF \cong \Delta FGE[/tex]

Solution;

From the given diagram, we have;

[tex]EF \cong FE[/tex]

Reflexive property

Therefore;

[tex] \Delta EDF \cong \Delta FGE[/tex]

Side–Side–Side, SSS rule of congruency

The Side–Side–Side congruency postulate states that if the three sides of one triangle are congruent to three sides of another triangle, then both triangles are congruent.

2.8 The circle information are;

The midpoint (center) of the circle = Point O

Segment OB is perpendicular to segment AC, [tex] OB \perp AC [/tex]

OB bisects AC

Required;

To prove that [tex] \Delta AOB \cong \Delta COB[/tex]

Solution;

Segment OA and OC are the radius of circle O

Therefore;

[tex] OA \cong OC[/tex] by the properties of the radius of a circle

The angle [tex] \angle OAB \cong \angle OCB [/tex] ; Base angles of isosceles triangle ∆OAC

[tex] AB \cong BC[/tex], Segments formed by the perpendicular bisector OB

Given that AB, [tex] \angle OAB [/tex] and OA in [tex] \Delta AOB [/tex] are congruent to BC, [tex] \angle OCB [/tex] and OB in [tex] \Delta COB [/tex], we have;

Second proof;

Given that OB is the perpendicular bisector of AC, we have;

[tex] \angle OBA \cong \angle OBC = 90^{\circ} [/tex], definition of angles formed by perpendicular lines

[tex] AB \cong BC[/tex]

Therefore;

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Answer:

[tex]f(x)=x^4(x-a)(x-b)^2[/tex]

Step-by-step explanation:

The graph of a polynomial function will:

The zero at the origin (0, 0) touches the x-axis and so it has an even multiplicity (exponent).  Therefore, we can immediately discount the first two answer options as both have x as a zero (x = x¹ so its exponent is odd).

The end behavior of the graphed function means the leading coefficient is positive and the degree of the polynomial is odd.

The sum of the multiplicities is the degree of the polynomial function.

[tex]f(x)=x^4(x-a)(x-b)^2 \implies \textsf{Sum of multiplicities}: 4+1+2=7[/tex]

[tex]f(x)=x^2(x-a)^5(x-b) \implies \textsf{Sum of multiplicities}: 2+5+1=8[/tex]

Therefore, the only function that could represent the given graph is

[tex]\boxed{f(x)=x^4(x-a)(x-b)^2}[/tex]

as its degree is odd and it has a zero at the origin with even multiplicity.

The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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The probability that fewer than 3 women will deliver prematurely is 1/20.

So, 10% of 20:

Therefore, the probability that fewer than 3 women will deliver prematurely is 1/20.

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The correct question is given below:

A large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. what is the probability that fewer than 3 of them will deliver prematurely?

Answer:

16 and -16

Step-by-step explanation:

Answer: D. 16 and -16

Step-by-step explanation: I dont think you need an explanation because it is multiple choice.

Based on the number of people who are engineers and those who are chemical engineers, the percentage who are chemical engineers is 2.01%

To find the percentage of something out of the total number, the formula is:

= Number of selected variables / Total number of variables x 100%

The selected variable here is chemical engineers so the percentage of chemical engineers out of the total number of engineers is:

= Number of chemical engineers / Total number of engineers x 100%

= 27,860 / 1,326,800 x 100%

= 2.01%

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Answer:

Domain: { -5, -1, 1, 3, 4}
Range: { -2, 1, 5}

Step-by-step explanation:
Domain = X-Values

Range = Y-Values

Every possible X-Value is the domain, and likewise with the Range.

Meaning if it was a line that went on forever through Y-1 the the Domain would be X = {-[infinity], +[infinity]} and the range would be Y = {1}

Hope this helps.

Answer: Yes, 6.20

Step-by-step explanation:

1/5 is equal to 0.20, so 6 1/5 equals 6.20

Answer:

19

Step-by-step explanation:

The square value of the measure of hypotenuse is equal to the square measure of sum of two legs.

Let x represent the missing leg:

[tex] {20}^{2} = {7}^{2} + {x}^{2} [/tex]

400 = 49 + x^2 subtract 49 from both sides

351 = x^2 find the root for both sides

The root of 351 is between 18 and 19 but it is closer to 19 since 19×19 = 361 and since we are asked to round to the nearest tenth the answer is 19.

The greatest common factor of the given terms is 2a⁴b

From the question, we are to determine the greatest common factors of the given terms

The given terms are

18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7

That is,

18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷

We will express each of the given terms as a product of their factors

18a⁴b⁹c² = 2 × 3 × 3 × a⁴ × b⁸ × b × c²

34a⁶b⁵ = 2 × 17 × a⁴ × a² × b⁴ × b

22a⁸bc⁷ = 2 × 11 × a⁴ × a⁴ × b × c⁷

Hence, the GCF is 2 × a⁴ × b = 2a⁴b

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Answer: r

Step-by-step explanation:

The figures are symmetrical about line r.

Answer:

I think the first number is 45 and the second number is 81.

Step-by-step explanation:

45 > 42 but 45 < 55       81 > 80 but 81 < 89