Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill Two years ago she has been at the hospital for twice as long How long has each been at r=the hospital

[tex]\\ \rm\Rrightarrow \dfrac{6}{x^2-3x}=\dfrac{12}{x}+\dfrac{1}{x-3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6}{x(x-3)}=\dfrac{12}{x}+\dfrac{1}{x-3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6}{x(x-3)}=\dfrac{12(x-3)+x}{x(x-3)}[/tex]

[tex]\\ \rm\Rrightarrow 6=12x-36+x[/tex]

[tex]\\ \rm\Rrightarrow 6=13x-36[/tex]

[tex]\\ \rm\Rrightarrow 13x=42[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{42}{13}[/tex]

Step-by-step explanation:

[tex] log_{5}(x + 9) = log_{5}(x + 5) + 1[/tex]

[tex] \frac{ log(x + 9) }{ log(5) } = \frac{ log(x + 5) }{ log(5) } + 1[/tex]

[tex] log(x + 9) = log(x + 5) + log(5) [/tex]

[tex] log(x + 9) = log(5x + 25) [/tex]

[tex]x + 9 = 5x + 25[/tex]

[tex]x = - 4[/tex]

If we plug it in, it is true

For the given linear system equations, the value for the variables are: x=-2, y=4, and z=-5 - Option C.

System of Linear Equations

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

2x+y-5z=4 (1)

x+3y+z=5  (2)

3x-y-4z=-11 (3)

First, you should sum equations 1 and 2. The results will be:

3x+4y-4z=9 then you have a new equation (4).

3x-y-4z=-11 (3)

3x+4y-4z= 9(4)

Now, you should multiply equation (3) by -1, then you will have:

-3x+y+4z=+11 (3)

3x+4y-4z=9 (4)

After that, you should sum the previous equations: (3) and (4).

5y=20

y=4

For find z, you should multiply equation 2 by -2. After that, you should sum equations 1 and 2.

2x+y-5z=4 (1)

-2x-6y-2z=-10  (2)

Thus, you will have:

-5y-7z=-6, like y=4 you have

-5*4-7z=-6

-20-7z=-6

-7z=14

z=-2

If z=-2 and y=4 from equation 2, you can find x.

x+3y+z=5

x+3*4-2=5

x+12-2=5

x+10=5

x=5-10

x=-5

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Answer:

8

Step-by-step explanation:

I am good at math

Answer:

E. 22

Step-by-step explanation:

Hello!

We know that b>6, and we are asked to find the possible values for 3b + 3.

Let's directly substitute 6 for b:

Now, because b is greater than 6, and not equal to 6, any value greater than 21 will work.

The correct option is E. 22.

[tex] \frac{1}{ \sqrt{1 - {(x - 1)}^{2} } } [/tex]

Answer: 10

Step-by-step explanation:

It appears that [tex]\overline{AC} \perp \overline{BC}[/tex], so to check if this is the case, we can use the slope formula.

[tex]m_{\overline{AC}}=\frac{3-1}{6-2}=\frac{1}{2}\\m_{\overline{BC}}=\frac{3-7}{6-4}=-2[/tex]

Since these slopes are negative reciprocals, we can see that this is the case. So, we can take [tex]\overline{AC}[/tex] as the base of the triangle and [tex]\overline{BC}[/tex] as the height of the triangle, and then use the formula [tex]A=\frac{1}{2}bh[/tex].

Using the distance formula,

[tex]AC=\sqrt{(6-2)^{2}+(3-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(4-6)^{2}+(7-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]

So, the area is [tex]\frac{1}{2}(2\sqrt{5})(2\sqrt{5})=\boxed{10}[/tex]

Answer:

I have no clue, cant lie to you. God Bless you though.

Step-by-step explanation:

Answer:

D is the right ans after solving eqn we get two value of x and they are 1 and 3

The value of y based on the values given ib the equilateral triangle will be 4.

From the information given, MN is one of the sides of the equilateral triangle. Therefore, side MR will be:

= 1/2 × 8 = 4

In the above, it should be noted that MR was calculated since it's half of the value of MN which is 8.

Here, value of y based on the values given ib the equilateral triangle will be 4.

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Answer:

Step-by-step explanation:

4

Answer:

5.5

Step-by-step explanation:

The longest string length is 12 3/4 (12.75)

The two shortest string lengths are 3 and 4 1/4 (4.25)

combine the length of the tow shortest string by adding them together,

3 + 4.25 = 7.25

to find how much longer the longest string you subtract the two numbers,

12.75 - 7.25 = 5.5

Step-by-step explanation:

that means that in 5 ml there are 250mg.

and that means that in 1 ml there are 250/5 = 50 mg.

and now we can find out the mg in 7 ml (by multiplying everything by 7) :

7 ml = 50 × 7 = 350 mg

Answer:

4500

Step-by-step explanation:

all of them were admitted.

[tex]|\Omega|=48\\A=\{24,48\}\\|A|=2\\\\P(A)=\dfrac{2}{48}=\dfrac{1}{24}\approx4.2\%[/tex]

Answer:

x = 10

Step-by-step explanation:

rewrite this equation with x on the left and numbers on the right

2x - 3x = 5 - 15

-x = -10

x=10

give brainliest, please!

hope this helps :)

The value of x is x = 10

To solve a first degree equation, first: we add or subtract like terms. Finally, we split the terms of both equalities.

- In this equation, we're going to subtract the like terms -- and on the other side of the equation, we're going to also subtract the real terms.

15 + 2x = 5 + 3x

2x - 3x = 5 - 10

-1x = -10

x = 10

So, the correct value is x = 10

Answer:

D

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 2[tex]\sqrt{2}[/tex]

Answer:

11.25

Step-by-step explanation:

6 3/4 + 4 1/2

Answer:

The answer is [tex]x > 2[/tex]

Step-by-step explanation:

to solve this inequality:

[tex]5x+7 > 17[/tex]

Put "-7" on both sides

[tex]5x+10[/tex]

divide by 5 on both sides

your answer should be 2.

If we need to turn this into a mathematical expression:

Answer: (x + y) - 9

Step-by-step explanation:

    9 less than the sum of x and y

    (the sum of x and y) - 9

    (x + y) - 9

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Answer:

14/29

Step-by-step explanation:

14/29 is the answer

Using the vertically opposite angles theorem and corresponding angles theorem, we have proven that alternate exterior angles are congruent

From the question, we are to prove that alternate exterior angles are congruent.

In the given diagram, examples of alternate exterior angles are

∠1 and ∠8

∠2 and ∠7

Now, we will prove that ∠1 = ∠8

In the diagram, we can observe that

∠1 = ∠4 (Vertically opposite angles theorem)

and

∠4 = ∠8 (Corresponding angles theorem)

Then,

By the substitution property of equality

∠1 = ∠8

Hence, alternate exterior angles are congruent

Here is the complete and correct question:

Consider parallel lines cut by a transversal. Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

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Answer:

Step-by-step explanation:

Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.

Use the diagram to complete the statements.

Angles 1 and 5 are

✔ congruent

because they are

✔ corresponding

angles.

Angles 4 and 6 are

✔ supplementary

because they are

✔ same-side interior

angles.

well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]

Answer:

5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.

Step-by-step explanation: Also pls answer by question

Answer: 30

Step-by-step explanation:

(Assuming the line is a tangent)

So

Hence

Option A

Answer:

Option A

Step-by-step explanation:

y=4x+10

So

Put x ax 12°C

Hence

y=4(12)+10

y=48+10

y=58

The equation of the line about which the quadrilateral is reflected will be y = x.

It is the image of the point which is located in the opposite direction of a given point.

The rule of the refection is given will be

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

First, draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral.

Vertex Preimage Coordinates                  Vertex Image Coordinates

          A (-3,-2)                                                           A' (-2,-3)

          B (-2,-1)                                                            B' (-1,-2)

          C (-1,-2)                                                            C' (-2,-1)

          D (-1,-4)                                                            D' (-4,-1)

The diagram is given below.

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