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Desmos is Function Calculator is a great tool for this, the correct answer is z= 7/3

7/3= 2.333~ and so √(3*2.333~) + 2= 2.9999999833333~

Now 7- 2.9999999833333~= 4.0000000166667~ but I don't know the true infinate sign for this so thats why my numbers look a little werid, just plug (7/3) in for z and you will get 4, trust me

The root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation 7-[tex]\sqrt{3z+2}[/tex] = 4

Solving for z,

7-[tex]\sqrt{3z+2}[/tex] = 4

[tex]\sqrt{3z+2}[/tex] = 3

Squaring both sides,

3z + 2 = 9

3z = 9-2

3z = 7

z = 7/3

Hence, the root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3

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Answer:

Step-by-step explanation:

Given that a study shows that, over the course of a lifetime, the average salary of college graduates is greater than the average salary of people with only a high school diploma.

The results were published claiming that graduating from college ensures you will make more money over the course of your lifetime.

Only means should not be compared. variances of each sample should be ascertained and test for comparison of two means to be done to conclude that one mean is greater than the other.

Hence here problem is correlation and causality.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

       A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

     Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8   ----(eq 1)

x + 5y = 11     ----(eq 2)

      Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

    In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

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There are [tex]728000[/tex] possibilities  of different licence plates.

The License plate is consist of [tex]4[/tex] digits followed by [tex]2[/tex] uppercase letters, i,e,

We have [tex]6[/tex] digits so let's first check  the choices of letter or digits over that.

Consider [tex]1[/tex]st Digit , according so question it should be odd so the choices we have for [tex]1[/tex]st Digits are [tex]1,3,5,7,9[/tex] i.e, [tex]5[/tex] choices we have as repitition not allowed.

Now consider [tex]2[/tex]nd Digit , according so question it should be odd so the choices we have for [tex]2[/tex]nd Digits are [tex]4[/tex] because [tex]1[/tex] odd digits has been used in  [tex]1[/tex]st Digit.

[tex]3rd[/tex] digit - [tex]2[/tex] digits has been used in [tex]1[/tex]st and [tex]2[/tex]nd digits so [tex]8[/tex] choices left.

[tex]4th[/tex] digit - This is left with [tex]7[/tex] choices.

[tex]5th[/tex]- On this [tex]2[/tex] uppercase letters required so choices we have are [tex]26[/tex].

[tex]6th[/tex]- On this we have to use uppercase so [tex]25[/tex] choices are left as repitition not allowed.

So Possibility of different license [tex]5 \times 4\times\times 8\times 7\times26\times 25=728000[/tex]

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Pi is a very special number in math and it’s so special that it even gets its own symbol. Mathematicians found out that when you try to write down what pi is, the decimal points keep going and going. This means that it’s impossible to find all the digits of pi.

I will only write down some digits.

π = 3.1415926535897932384626

Answer:

Step-by-step explanation:

1.

[tex](c+9)^2=64=8^2\\[/tex]

c+9=±8

either c=8-9=-1

c=-8-9=-17

so c=-1,-17

D

2.

8x^2-3=2

8x^2=5

[tex]x^2=\frac{5}{8}=\frac{10}{16}[/tex]

[tex]x=±\frac{\sqrt{10}}{4}[/tex]

so A

3.

[tex]x^2+4x+4=18\\(x+2)^2=9*2\\x+2=3\sqrt{2} \\x=-2  ±3\sqrt{2}[/tex]

so D

or

The investment is worth $9,200 after 2 decades.

To find the value of the investment after 2 decades, we can substitute x = 2 into the function f(x) = 2300 * 2^x.

So, f(2) = 2300 * 2^2 = 2300 * 4 = 9200.

Therefore, the investment is worth $9,200 after 2 decades.

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In the given problem , missing number in the synthetic division is equal to [tex]10[/tex].

" Synthetic division is defined as simplified way of dividing a polynomial by another polynomial of first degree by writing its coefficient and changing usual subtraction into addition."

According to the question,

As shown in the given synthetic division,

[tex]4 + 20 = 24\\\\-2 + 6 = 4[/tex]

Therefore,

Missing number in the given synthetic division [tex]= 2+ 8[/tex]

                                                                                [tex]=10[/tex]

Hence, Option (C) is the correct answer.

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The best estimate for the solution of the system of equations is (-4.5, 1.5).

The system of equations given is:

y = -34x - 2

y = x + 6

To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.

Let's check each option:

For (-4.25, 1.5):

1.5 = -4.25 + 6

1.5 = 1.75 (not equal)

This is not a solution for the system.

For (-4.75, 1.75):

1.75 = -4.75 + 6

1.75 = 1.25 (not equal)

This is not a solution for the system.

For (-4.5, 1.5):

1.5 = -4.5 + 6

1.5 = 1.5 (equal)

This is a solution for the system.

For (-4.5, 1.75):

1.75 = -4.5 + 6

1.75 = 1.5 (not equal)

This is not a solution for the system.

Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).

Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]

We can use following formulas to solve this problem :-

1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]

2. sin(2∅) = 2·sin(∅)·cos(∅)

Solving the given equation :-

[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]

Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].

The point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.

The equation of the plane is defined as the plane has three variables. Having the coordinates in all three dimensions. The general form of the equation of the plane is ax + by + cz = d.

The given equation of plane is 2x + 7y + 3z = -25.

Check the point which satisfies the equation of the plane. Take the point ( -6,-4,5).

2x + 7y + 3z = -25.

2 ( -6 ) + 7(-4) + 3(5) = -25

-12 - 28 + 15 = -25

-40 + 15 = -25

-25 = -25

Therefore,  the point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.

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Answer:

Step 3

Step-by-step explanation:

By asking the participants how delicious chocolate B is, you can possibly create bias in the test.  It is a leading question; these should not be asked to avoid creating bias.

Answer:

graph c is the correct answer hope this helps you get an A.

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].

True. Overdraft protection is a service offered by banks to their customers. When your account does not have enough money to cover a transaction, overdraft protection allows the bank to loan you the necessary funds to complete the transaction.

If you make a purchase or withdrawal that exceeds your account balance, the bank will cover the shortfall by lending you the needed amount. This ensures the transaction goes through, but typically comes with fees or interest. While convenient, it can lead to extra costs if used frequently.

Overdraft protection may apply to debit card purchases, checks, or automatic bill payments, depending on the account settings. Some banks offer this service automatically, while others require customers to opt in. It's a useful safety net but should be used responsibly to avoid accumulating unnecessary charges.