solve the following system of equations
-2x+y=1
-4x+y=-1

The correct answer is [tex]$\sqrt{3}$[/tex]. Hence the correct option is d.

To find the value of [tex]$\tan 60^\circ$[/tex] using the unit circle, follow these steps:

Draw the unit circle, which is a circle with a radius of 1 unit centered at the origin (0,0) on the Cartesian coordinate plane.

Identify the point on the unit circle corresponding to [tex]$60^\circ$[/tex]. This point is located in the first quadrant and makes an angle of [tex]$60^\circ$[/tex]with the positive x-axis.

Since the unit circle has a radius of 1, the coordinates of the point corresponding to 60 are:

[tex]$x$-coordinate: $\cos(60^\circ) = \frac{1}{2}$\\$y$-coordinate: $\sin(60^\circ) = \frac{\sqrt{3}}{2}$[/tex]

Now, we'll use the definition of tangent to find [tex]$\tan(60^\circ)$[/tex]:

[tex]$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$\\Substitute the values of $\sin(60^\circ)$ and $\cos(60^\circ)$ into the formula:$\tan(60^\circ) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$[/tex]

Simplify the expression:

[tex]$\tan(60^\circ) = \left(\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{2}{1}\right)$$\tan(60^\circ) = \sqrt{3}$[/tex]

So, the correct answer is [tex]$\sqrt{3}$[/tex]. Hence the correct option is d.

Complete question:

Use the unit circle to find tan 60°.

a. square root 3/3

c. 2 square root 3/3

b. square root 3/2

d. square root 3

Answer:

Kiki has 0.03 cents more than Jordan.

Step-by-step explanation:

so first add 2.48 and 1.69= 4.17

Kiki's amount of money= $4.17

Add 3.05 and 1.09= 4.14

Jordan's amount of money= $4.14

subtract 4.17-4.14=0.03

After adding up the amounts for both Kiki and Jordan, it is determined that Kiki has more money by $0.03.

To find out who has more money, Kiki or Jordan, we need to add up the amounts that each person has in their respective locations and then compare the totals. First, let's calculate Kiki's total amount:

Adding these two amounts gives Kiki a total of $4.17.

Now let's calculate Jordan's total amount:

Adding these two amounts gives Jordan a total of $4.14.

By comparing the two totals, we see that Kiki has more money than Jordan. The difference in their amounts is $4.17 (Kiki's total) - $4.14 (Jordan's total) = $0.03. Therefore, Kiki has three cents more than Jordan.

In a complete sentence: Kiki has more money than Jordan by three cents.

Answer:

0.75

Step-by-step explanation:

Final answer:

To convert 75% to a decimal, divide 75 by 100 to get 0.75. This conversion is necessary to express the percent of free space on a computer in decimal form.

Explanation:

To convert the percent of free space on the computer to a decimal, you can follow these steps:

The decimal equivalent of 75% is 0.75. This means that 75% of the computer's storage capacity is free space.

Answer:

B 3*-3* -4/9

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

64[tex]x^{6}[/tex] + 144[tex]x^{4}[/tex] + 108x² + 27

Step-by-step explanation:

Using the formula for volume, V = s³, then

V = (4x² + 3)³

This may be expanded as

(4x² + 3)(4x² + 3)(4x² + 3) ← expand the first 2 factors using FOIL

= (16[tex]x^{4}[/tex] + 24x² + 9)(4x² + 3) ← distribute by 4x² and 3

= 64[tex]x^{6}[/tex] +96[tex]x^{4}[/tex] + 36x² + 48[tex]x^{4}[/tex] + 72x² + 27 ← collect like terms

= 64[tex]x^{6}[/tex] + 144[tex]x^{4}[/tex] + 108x² + 27

Answer:

[tex]64x^{6}[/tex] + [tex]144x^{4}[/tex] + [tex]108x^{2}[/tex] + 27

Step-by-step explanation:

Answer:10

Step-by-step explanation:

28-4-4=20

20÷2=10

10+10+4+4=28

Answer:

y=2x-6

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=2(x-1)

y+4=2x-2

y=2x-2-4

y=2x-6

Answer:

10.15 dollars is the answer...

Answer:

2/3 as a decimal is 0.6 recurring

Step-by-step explanation:

See above

Answer:

3.01 is a decimal and 2/3 as a decimal is .666666666666666666 it keeps going on

Step-by-step explanation:

Answer:

1 hour rate = 180 - 5 hour rate = 900

Step-by-step explanation:

To make the whole equation easy divide the number of people by the time.  

75 / 25 = 3

Now the number of people can be adjusted to any amount of time.  

For the hour rate multiply the number of people per minute by 60.

3 x 60 = 180

For the five hour rate use the same exact equation but multiply the 60 by 5 first.

3 ( 60 x 5 ) = 900

Hope this helped.

Answer:

 The standard deviation estimate by the Range Rule of Thumb = 18.3

Step-by-step explanation:

i) maximum = 96

ii) minimum = 23

iii) standard deviation [tex]\approx[/tex]  [tex]\frac{(maximum\hspace{0.1cm} - \hspace{0.1cm} minimum)}{4} = \frac{96 - 23}{4} = \frac{73}{4} = 18.25[/tex]

   The standard deviation estimate by the Range Rule of Thumb = 18.3

The required number would be 5/6 which subtracts from 35/6 to make 5.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

We have to determine the number which subtracts from 35/6 to make 5.

Let's assume that the required number would be x

As per the given question, the required solution would be as:

⇒ 35/6 - x = 5

Rearrange the terms in the above equation, and solve for x

⇒ x = 35/6 - 5

Take the LCM in the terms

⇒ x = (35 - 30)/6

Apply the subtraction operation in the terms

⇒ x = 5/6

Therefore, the required number would be 5/6.

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10 hours, none more, none less

Answer:

The money each boy had after buying his ticket is $2.50.

Step-by-step explanation:

Given:

Miguel and three of his friends went to the movies. They originally had a total of $40. Each boy had the same amount of money and spent $7.50 on a ticket.

Now, to find the money each boy had after buying his ticket.

Let the money each boy had after buying his ticket be [tex]x.[/tex]

Total number of boys = 4.

Total money they had = $40.

Money each boy spent = $7.50.

Now, to write an equation:

[tex]4(x+7.50)=40[/tex]

Now, to solve the equation for getting the money each boy had after buying his ticket:

[tex]4(x+7.50)=40[/tex]

[tex]4x+30=40[/tex]

Subtracting both sides by 30 we get:

[tex]4x=10[/tex]

Dividing both sides by 4 we get:

[tex]x=\$2.50.[/tex]

Therefore, the money each boy had after buying his ticket is $2.50.

The equation that I think you are looking for is:

c = 8h + 6

33°≤ t ≤ 35°

Step-by-step explanation:

The body temperature of a bee is given as 35°

When it sleeps, it drops by 2°

The sleeping temperature is therefore : 35°-2°=33°

The rage of body temperature is : 33°-35°

If t is  body temperature then the rage in body temperature is;

33°≤ t ≤ 35°

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Keywords : body, temperature, sleep,drop,range, variable

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Answer:

177° C

Step-by-step explanation:

substitute F = 350 into the formula

C = [tex]\frac{5(350-32)}{9}[/tex] = [tex]\frac{5(318)}{9}[/tex] = [tex]\frac{1590}{9}[/tex] ≈ 177 ( to the nearest degree )

Answer:

all work is pictured and shown

answer is b

Answer:

{x | x ≤ 2}

Step-by-step explanation:

Answer:

See attachment and explanation

Step-by-step explanation:

Assuming f(x) and its g(x) are the graphs shown in the attachment.

Then we have the base function to be

[tex]f(x) = {10}^{x} [/tex]

We can see from the graph that, f(x) has been shifted up 3 units to obtain g(x).

Hence the equation of g(x) is

[tex]g(x) = {10}^{x} + 3[/tex]

Answer:

g(x) = 10^x – 3 is the answer

\

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the question, apply BODMAS approach. that is solve the brackets, division, multiplication first before the addition and subtraction.

step 1: take the first bracket (4/7 + 8)

[tex]\frac{4}{7} + 8[/tex] is the same as (4/7)+ (8/1). The LCM is 7. multiply each term by the LCM and divide by the denominator.

[tex]\frac{4}{7} + 8[/tex] =  [tex]\frac{(4X1) + (8X7)}{7}[/tex] = [tex]\frac{4+56}{7}[/tex] = [tex]\frac{60}{7}[/tex]

step 2: consider the second bracket (3-(-4))

there is a sign multiplication in the terms. minus (-) x minus (-) = plus (+)

therefore the second bracket (3-(-4)) =  3 + 4 = 7

step 3: multiply both brackets.

(4/7 + 8) x (3-(-4)) = [tex]\frac{60}{7} X 7[/tex] = 60

The answer is 60

Answer:

0.625

Step-by-step explanation:

0.625 * 8 = 5

Answer: 0.625

Step-by-step explanation: When doing 5 divided by 8, you get 0.625

[tex](n-4)(n-6) = n^2-10n+24\\\\(a+5)(a-6) = a^2 -a-30\\\\(4b + 6)(b-4) = 4b^2 -10b-24[/tex]

Solution:

Multiplying polynomials:

Multiplying polynomials is same like multiplying numbers

First, multiply the first term in the first parentheses by all the terms in the second parentheses

Now we multiply the second term in the first parentheses by all terms in the second parentheses and add them to the previous terms

[tex]1)\ (n-4)(n-6)[/tex]

[tex](n-4) \times (n-6) = n^2 -6n -4n +24\\\\Simplify\\\\(n-4) \times (n-6) = n^2 -10n + 24[/tex]

Now let us multiply the second given option

[tex]2)\ (a+5)(a-6)[/tex]

Multiply them together

[tex](a+5)(a-6) = a^2 -6a + 5a - 30\\\\Simplify\ by\ combining\ the\ like\ terms\\\\(a+5)(a-6) = a^2 -a -30[/tex]

Now let us multiply the third given polynomial

[tex]3)\ (4b+6)(b-4)[/tex]

Multiply them together

[tex](4b+6)(b-4) = 4b^2 -16b + 6b - 24\\\\Simplify\ by\ combining\ the\ like\ terms\\\\(4b+6)(b-4) = 4b^2 -10b -24[/tex]

Thus the given polynomials are multiplied

The solution to the inequality 5x-3(x+1)<7 is x<5.

Step-by-step explanation:

Given inequality is;

5x-3(x+1)<7

Solving the inequality

[tex]5x-3x-3<7[/tex]

Adding 3 on both sides both sides of inequality  

[tex]5x-3x-3+3<7+3\\2x<10[/tex]

Dividing both sides of inequality by 2

[tex]\frac{2x}{2}<\frac{10}{2}\\\\x<5[/tex]

The solution to the inequality 5x-3(x+1)<7 is x<5.

Keywords: inequality, division

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The missing coordinate r is 11.

Solution:

Given points are (–15, 1) and (–7, r).

[tex]x_{1}=-15, x_{2}=-7, y_{1}=1 \text { and } y_{2}=7[/tex]

Slope (m) = [tex]\frac{5}{4}[/tex]

To find the missing coordinate r:

Slope formula:

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute the given values in the formula.

[tex]$\frac{5}{4}=\frac{r-1}{-7-(-15)}[/tex]

[tex]$\frac{5}{4}=\frac{r-1}{-7+15}[/tex]

[tex]$\frac{5}{4}=\frac{r-1}{8}[/tex]

Do cross multiplication.

[tex]8 \times 5=4(r-1)[/tex]

40 = 4r – 4

Add 4 on both side of the equation.

44 = 4r

Divide by 4 on both side of the equation.

11 = r

⇒ r = 11

Hence the missing coordinate r is 11.

Answer:

yes,in fact he can do it in just 4 minutes.

Step-by-step explanation:

number of words he can text per hour=1500

number of words he can text in a minute=1500÷60 (since there are 60 minutes in an hour,we are dividing 1500 by 60 to get the answer in minutes)

=25 words per minute

number of minutes he has=5.

now, we have to multiply the number of words he can type in a minute by the number of minutes he has,so 25×5=125.

he can type 125 words in 5 minutes.

Sao can text 25 words in a minute. Therefore, Sao can text a total of 125 words in 5 minutes. Thus, 85 words can be texted comfortably within this timeframe.

In this situation, we first need to determine how many words Sao can type in one minute. Since he can type 1500 words per hour, and there are 60 minutes in an hour, by dividing 1500 by 60, we determine that Sao can type 25 words per minute. Now, given that Sao has 5 minutes to type the message and he can type 25 words per minute, in 5 minutes, he should be able to type 125 words - 5 (minutes) * 25 (words). This means that if Sao has a message with 85 words, yes, he can complete the text in 5 minutes as 85 is less than 125.

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Answer:

4/3

Step-by-step explanation:

2 2/3=8/3

(8/3)(1/2)=8/6=4/3

Answer:

The second option, 0.3 is the probability.

Answer:

f(x) = x + 3  , if -3 ≤ x < -1

f(x) = 5       , if -1 ≤ x ≤ 1