how to simplify -7 ( 3x - 7y) ?

The simplest radical form of the hypotenuse of the given right-angled triangle is therefore discovered to be [tex]6\sqrt{2}[/tex] units.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.

The given right angled triangle has sides 6 units each.

We need to determine the hypotenuse using the Pythagorean theorem.

Hypotenuse = [tex]\sqrt{(side 1)^{2} + side 2)^{2} }[/tex]

                      [tex]=\sqrt{6^{2} + 6^{2} } \\\\= \sqrt{72}\\ \\= 6\sqrt{2}[/tex]

Therefore, the hypotenuse of the given right angled triangle is found to be [tex]6\sqrt{2}[/tex]  units which is the simplest radical form.

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Answer:

[tex]D=\sqrt{29}[/tex]

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

We have in total 432 students.

8.

We know that 23% of the students want to be a teacher, this means that:

99 students want to be a teacher.

9.

We know that 13% of the students want to be doctor or nurses, this means that 26% of them want to be one of those, then:

112 students want to be doctor or nurses.

10.

Since 9% of the students want to be lawyers, this means that 91% of them did not want to be lawyers, then:

393 students does not want to be lawyers.

Answer:

393 students do not want to be lawyers.

Step-by-step explanation:

The correct description regarding each table is given as follows:

1. Rate of change of 4, linear.

2. Rate of change of -2/3, linear.

3. Rate of change of 1/4, linear.

4. Rate of change of -1, linear.

5. Not linear.

6. Rate of change of 3, linear.

A linear function has the definition presented as follows:

y = mx + b.

In which:

A data-set will only be classified as linear if the rate of change is constant.

Hence the tables in this problem are classified as follows:

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group of friends have $150 to spend on the amusement park admission and parking.

150 - 13.50 = 136.50

136.50 / 22.75 = 6

x = 6

13.50 + 22.75x = 150

13.50 + 22.75(6) = 150

22.75 * 6 = 136.50

136.50 + 13.50 = 150

Answer:

Step-by-step explanation:

Use a distributive property.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

First, expand by distributive property from multiply the numbers from left to right.

-9j=-9(j-20)

-9(j-20)

-9*j=-9j

9*20=180

=-9j+180

-9j=-9j+180

Add by 9j from both sides.

-9j+9j=-9j+180+9j

Solve.

0=180

No solution.

Therefore, the correct answer is A. no solution.

I hope this helps, let me know if you have any questions.

Using the Fundamental Counting Theorem, it is found that Samantha has 24 different outfits to choose from.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with n1 ,n2 , n3, ..... nn ways to be done, each thing independent of the other, the number of ways they can be done is:

N= n1*n2*n3.....nn

In this problem:

For the pants, there are 2 options,  hence n1=2 .

For the t-shirts, there are 2 outcomes, hence n2=2.

For the shoes, there are 9 outcomes, hence  n3=6.

Thus, the total number of outfits is given by:

N = 2 x 2 x 6 = 24.

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The answer of the given question of radicals is -1.

What is radicals?
A surd or radical is an unresolved root, particularly one that employs the radical symbol. A radical expression is any expression that contains a radical, whether it is a square root, a cube root, or a higher root, while an algebraic expression is any statement that does not contain any transcendental functions or transcendental numbers. The root test is used to determine the radius of convergence of a power series. The nth roots of 1 are known as roots of unity, and they play an important role in many areas of mathematics, including number theory, equation theory, and the Fourier transform.

Given, ∛-1

if we evaluate this radical then,

∛-1 = -1

because 1 perfect cube.

Hence, the answer is option(a) i.e, -1

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A unit rate is the amount of a quantity at the rate of one.

The number of hours per week to earn approximately 190 is

22 hours 45 minutes

A unit rate is the amount of a quantity at the rate of one.

It is written as a ratio with a denominator of one. 

Example:

If 3 miles in 3 minutes then 1 mile in 1 minute.

We have,

The amount earned per hour = 8.35

This can be written as:

1 hour = 8.35

Multiply 190/8.35 on both sides.

190/8.35 x 1 hour = 190/8.35 x 8.35

22.75 hours = 190 ____(1)

1 hour = 60 minutes

0.75 hour = 45 minutes

From (1) we get,

22 hours 45 minutes = 190

Thus,

The number of hours per week to earn approximately 190 is

22 hours 45 minutes.

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The graph of the inequality is attached below to represent the solution.

To solve this problem, we can simply plot the graph of the inequality using a graphing calculator. To do this, we can simply input the value of both inequalities and then plot the values.

In the graph below, the the red broken line represents the first equation which is "<" or less than and the second equation which is the straight blue line which represents the ">" or greater than sign.

Kindly find the attached image below.

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The possible values of X are that if n is even X can takes even integers from [-n, n], and if n is odd, X can takes odd integers from [-n, n]

To solve this question, we can use X to represents the difference between the number of heads and the number of tails obtained when a coin is tossed X times, the possible values of X are now obtained below:

Let H be the no. of heads and T be the no. of tails, since the coin is tossed n times, we have:

H+T=n

now, X = H-T ,

X=H-(n-H)

X=2H-n

Now,

H takes values {0,1,2,3 ......,n-2, n-1,n}

2H takes values {0,2,4,6,.....,2n-4,2n-2,2n}

2H - n takes values {-n,-(n-2),-(n-4), -(n-6),.............,n-4, n-2,n}

X takes values {-n,-(n-2), -(n-4),-(n-6),.............,n-4, n-2, n}

therefore, if n is even X can takes even integers from [-n, n]

and, if n is odd, X can takes odd integers from [-n, n]

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Answer: You Welcome

Step-by-step explanation:

12.6 Repeating Decimal = 12 2/3 as a Fraction

Answer:

no, it not

Step-by-step explanation:

It's not a repeating decimal because

A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is not the case here, which means that our answer is as follows:

12/6

= no.-repeating

Answer: I think the answer is 6.70$ or 6.66666667

Step-by-step explanation:6.70 x 3 = 20.1

But You Multiply 6.66666667 x 3 = 20

Answer:

p>-1/3

Step-by-step explanation:

-3p-4<6

+4 +4

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

-3p<10

Divide -3 on both sides and you get something like p>-1/3 because you have to flip the sign.

Using LCM, Ramya and Deepika will exercise together after 8 days.

Step 1: Use the repeated division method to identify the prime factors of the supplied numbers.

Write the numbers in exponent form in step two. Only those prime factors' product with the highest power should be sought.

Step 3: The LCM of the provided numbers is the product of these factors with the highest powers.

Factors of 8 = 2 × 2 × 2

Factors of 4 = 2 × 2

LCM of 8 and 4 = 8

∴ Ramya and Deepika will exercise together after 8 days.

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Correct Question -

Ramya exercises every 8 days and Deepika every 4 days • Ramya and Deepika exerised today. After how many days they exercise together again?​

Answer:

3 seconds

Step-by-step explanation:

The height of the rocket when it hits the ground will be zero meters.

Therefore, set the equation to zero and solve for t by using the quadratic formula.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Given equation:

[tex]-4.9t^2+14t+2.1=0[/tex]

Therefore:

[tex]a=-4.9, \quad b=14, \quad c=2.1[/tex]

Substitute the values into the quadratic formula:

[tex]\implies t=\dfrac{-14 \pm \sqrt{14^2-4(-4.9)(2.1)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-14 \pm \sqrt{196+41.16}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-14 \pm \sqrt{237.16}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-14 \pm15.4}{-9.8}[/tex]

Therefore:

[tex]\implies t=\dfrac{-14 +15.4}{-9.8}=\dfrac{1.4}{-9.8}=-\dfrac{1}{7}[/tex]

[tex]\implies t=\dfrac{-14-15.4}{-9.8}=\dfrac{-29.4}{-9.8}=3[/tex]

As time is positive, t = 3 s only.

Therefore, it will take 3 seconds for the rocket to hit the ground.

Answer:

(9, 1 )

Step-by-step explanation:

a translation 2 units right means add 2 to the x- coordinate

a translation of 1 unit up means add 1 to the y- coordinate.

(7, 0 ) → (7 + 2, 0 + 1 ) → (9, 1 )

Answer:

1: missing: x values are 4 and 2. missing y values are 20.

2: missing: x values are 12. missing y values are 5 and 3.

3: missing x value is 18. missing y value is 2 and 5.

4: missing x values are, 5, 8, and 12

fill in answers are going from in order left to right

The inequality statement comparing m and n is m > n.

The inequality is true because m is further along the number line than n

It should be noted that an inequality is simply used to express the information given hat aren't equal.

Based on the number line that's drawn we came we that is close to 3 and n is close to 1.

Therefore, this shows that m is greater than n.

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The amount she earned this week is £325

Shirley earns £52 for an 8 hour shift at a call centre.

Therefore,

8 hours = £52

1 hour = ?

cross multiply

1 hour earning = 52 / 8

1 hour earning = £6.5

Therefore,  In one week, Shirley works fifty hours at the call centre. The amount she earns during the week is as follows:

Hence,

amount she earns this week = 6.5 × 50

amount she earns this week = £325

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Answer:

x = 3

Step-by-step explanation:

[tex]{ \rm{5x + 2 = 7x - 4}}[/tex]

- First, using equality order by collecting like terms of x together and constants together;

[tex]{ \rm{(5x + 2) { \green{- 2}} + = (7x- 4){ \green{ - 2}}}} \\ { \rm{5x = 7x - 6}}[/tex]

[tex]{ \rm{5x - { \blue{7x}} = (7x - 6) - { \blue{7x}}}} \\ { \rm{ - 2x = - 6}}[/tex]

- Using division property of equality, by dividing -2 on both sides;

[tex]{ \rm{ \frac{ - 2x}{ \orange{ - 2}} } = \frac{ - 6}{ \orange{ - 2}} } \\ \\ { \rm{x = 3}}[/tex]

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: \: creed}}}[/tex]

Answer:

Step-by-step explanation:

What’s x??

Solve for x

5x+2=7x-4

2 + 4 = 7x - 5x

6 = 2x

x = 6 : 2

x = 3

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

check

5 * 3 + 2 = 7 * 3 - 4

17 = 17

The license plate can be made in 1,757,600,000 ways

For the license plate, we need 3 letters out of 26 letters of the English alphabet and 5 digits out of 0-9

For the alphabet:

So, the first letter can be chosen in 26 ways

The second letter can be chosen in 26 ways

The third letter can be chosen in 26 ways

For the digits:

The first number can be chosen in 10 ways

The second number can be chosen in 10 ways

Similarly, the remaining three numbers can be chosen in 10 ways each

So, total ways = 26*26*26*10*10*10*10*10 = 1,757,600,000

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Answer:

5

Step-by-step explanation:

If he wants to cut it into 3/5 meters long then each rope is 0.6 meters long.

3/0.6 = 5

The quadratic equation in standard form is y = 3 · x² + 2 · x - 1. (Correct choice: C)

In accordance with the fundamental theorem of algebra, a quadratic function can be found by knowing three distinct points. Quadratic functions are polynomials of the form, known as standard form:

y = a · x² + b · x + c

Where a, b, c are real coefficients.

If we know that (x₁, y₁) = (- 3, 20), (x₂, y₂) = (0, - 1) and (x₃, y₃) = (2, 15), then the coefficients of the polynomial are found by numerical methods:

9 · a - 3 · b + c = 20

c = - 1

4 · a + 2 · b + c = 15

The solution to the system of linear equations is (a, b, c) = (3, 2, - 1). The equation is y = 3 · x² + 2 · x - 1.

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The solution of the equation 4 = 13 – 3x is x = 3 which is the correct answer would be an option (B).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given an equation as

4 = 13 – 3x

Rearrange the terms non-variables and variables,

3x = 13 - 4

Apply the subtraction operation,

3x = 9

x = 9/3

Apply the division operation, and we get

x = 3

Therefore, the correct answer would be an option (B).

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Answer:

Step 2

Step-by-step explanation:

In basic algebra, if one side is positive then you must subtract on both sides, and if one side is negative then you must add on both sides to isolate the x variable.

Answer: 3.5 batches is correct.

Step-by-step explanation: Take 28 and divide that by 8 and that equals 3.5

Hope this helps!

The number of batches of cookies that can be made using 28 ounces of chocolate chips is 3.5 batches.

The correct answer option is option a

Equation:

y = 8x

Where,

If there are 28 ounces of chocolate chips:

y = 8x

28 = 8 × x

28 = 8x

x = 28/8

x = 3.5 batches

So therefore, the

So therefore, 3.5 batches of cookies can be made using 28 ounces of chocolate chips.

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