solve the following simultaneous linear equations by the substitution method.
3x + 4y = 1
2x + 3y = 1​

Answer:

equation A and equation c

Answer:

Equation A and Equation C

Answer:

The tank is 10cm high

Step-by-step explanation:

Given

[tex]L=60cm[/tex] -- length

[tex]W=60cm[/tex] -- width

[tex]x = \frac{1}{5}[/tex] --- water lever

[tex]Addition = 24L[/tex]

Required

The height of the tank

Let y represents the remaining fraction before water is added.

So:

[tex]y + x = 1[/tex]

Make y the subject

[tex]y = 1 - x[/tex]

[tex]y = 1 - \frac{1}{5}[/tex]

Solve

[tex]y = \frac{5 - 1}{5}[/tex]

[tex]y = \frac{4}{5}[/tex]

Represent the volume of the tank with v

So:

[tex]y * v = 24L[/tex]

Make v the subject

[tex]v = \frac{24L}{y}[/tex]

Substitute: [tex]y = \frac{4}{5}[/tex]

[tex]v = \frac{24L}{4/5}[/tex]

[tex]v = 30L[/tex]

Represent the height of the tank with h;

So, the volume of the tank is:

[tex]v = lwh[/tex]

Make h the subject

[tex]h = \frac{v}{lw}[/tex]

Substitute values for v, l and w

[tex]h = \frac{30L}{60cm * 50cm}[/tex]

Convert 30L to cm^3

[tex]h = \frac{30*1000cm^3}{60cm * 50cm}[/tex]

[tex]h = \frac{30000cm^3}{3000cm^2}[/tex]

[tex]h = 10cm[/tex]

(x - [3])² + (y- [2])² = 16

Answer:

y = -5

o = 35 degrees

Step-by-step explanation:

If you replace y with -5, the statement  7y = 4y - 15 is correct. You get -35 =  -35. Hope this helped!

Given:

A figure of a circle.

To find:

The value of x.

Solution:

First label the given figure as shown below.

In triangle ABO,

[tex]OA=OB[/tex]                                          (Radii of same circle)

[tex]\Delta ABO[/tex] is an isosceles triangle.      (By the definition of isosceles triangle)

[tex]\angle OAB\cong \angle OBA[/tex]                               (Base angles of an isosceles triangle)

[tex]m\angle OAB=m\angle OBA[/tex]

[tex]42^\circ=m\angle OBA[/tex]

In triangle ABO,

[tex]m\angle AOB+m\angle OAB+m\angle OBA=180^\circ[/tex]      (Angle sum property)

[tex]m\angle AOB+42^\circ+42^\circ=180^\circ[/tex]

[tex]m\angle AOB=180^\circ-42^\circ-42^\circ[/tex]

[tex]m\angle AOB=96^\circ[/tex]

Now,

[tex]m\angle AOB+m\angle BOC=180^\circ[/tex]         (Linear pair)

[tex]96^\circ+x=180^\circ[/tex]

[tex]x=180^\circ-96^\circ[/tex]

[tex]x=84^\circ[/tex]

Therefore, the value of x is 84 degrees.

Answer:

(0,-3)

Step-by-step explanation:

Step-by-step explanation:

the sum of angels of a triangle is 180°

130+ ? + (180-160) = 180

130+ ? +20= 180

150+ ? = 180

? = 30°

the missing angle is 30°

Answer:

d∅/dt = √2/5 Rad/sec

Step-by-step explanation:

According to the Question,

Solution,

Let x be the Distance between the base of the wall and the bottom of the ladder.

and let ∅ be the angle between the top of the ladder and the wall.

Then, Sin∅ =x/10  so, x=sin∅ *10

Differentiating with respect to time t we get,

dx/dt = 10 * cos∅ * d∅ /dt

Now, Put these value we get

2 = 10 *(cos(π/4))* d∅/dt

2 = 10/√2 * d∅/dt

d∅/dt = √2/5 Rad/sec

Answer:

C

Step-by-step explanation:

What you wrote is not the same thing as what the question is, or at least I don't think so. I'll answer the printed question.

First of all, the 13 is what separates each of the terms. In other words 7 is the first term. 13 must be raised to the n - 1 power.

It is written like this

an = 7 * 13^(n - 1)

you want a1 to be 7. The only way that can happen is if 13^0 which gives you 1.

So the correct answer is C

Answer:

B

Step-by-step explanation:

Let divide g(x) by f(x)

[tex] \frac{ {x}^{2} - 9 }{2 - x {}^{ \frac{1}{2} } } [/tex]

The domain of a rational function cannot equal zero so let set the bottom function to zero.

[tex]2 - x {}^{ \frac{1}{2} } = 0[/tex]

[tex]x {}^{ \frac{1}{2} } = 2[/tex]

Square both sides

[tex]x = 4[/tex]

Also we can simplify the bottom denomiator into a square root function

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

The domain of a square root function is all real number greater than or equal to zero because a square root of a negative number isn't graphable.

So we must find a answer that

five I think I am not sure

Answer:

Step-by-step explanation:

C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1

Answer:

sum of five and 3 is divided by n

Answer:

just draw a circle that connects all of the 10's on the graph.

a circle is NOT a function

Step-by-step explanation:

Answer: here is a picture of all of them I hope this helps :). This picture will clearly show the answers for 1 and 2

Step-by-step explanation:

Answer: The b-value is the middle number, the number next to the X

Answer:

[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]

Step-by-step explanation:

Given

[tex](\frac{-3}{4})^3[/tex]

Required

Evaluate

The expression can be represented as:

[tex](\frac{-3}{4})^3 = (\frac{-3}{4})*(\frac{-3}{4})*(\frac{-3}{4})[/tex]

So, we have:

[tex](\frac{-3}{4})^3 = \frac{-3*-3*-3}{4*4*4}[/tex]

[tex](\frac{-3}{4})^3 = \frac{-27}{64}[/tex]

Rewrite as:

[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]

Answer:

B  -27/64

Step-by-step explanation:

Answer:

Step-by-step explanation:

Following is the sample space for all the possible outcomes when 2 standard 6-sided dice are rolled simultaneously:

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,4 3,4 3,5 3,6

4 4,1 4,2 4,3 4,4 4,5 4,6

5 5,1 5,2 5,3 5,4 5,5 5,6

6 6,1 6,2 6,3 6,4 6,5 6,6

Therefore the sample space for the multiplication of the two values in each possible outcome:

elements of the set are:

1*1=1

1*2=2

1*3=3

...........

2*1=2

2*2=4

2*3=6

.............

so on...

Therefore the complete set:

S={ 1, 2, 3, 4, 5, 6, 2, 4, 6, 8, 10, 12, 3, 6, 9, 12, 15, 18, 4, 8, 12, 16, 20, 24, 5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36 }

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

Answer:

[tex]x=0, \\x=\pi[/tex]

Step-by-step explanation:

Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].

Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:

[tex]2\sin x\cos x=2\sin x[/tex]

Subtract [tex]\sin x[/tex] from both sides:

[tex]2\sin x\cos x-2\sin x=0[/tex]

Factor out [tex]2\sin x[/tex] from both terms on the left:

[tex]2\sin x(\cos x-1)=0[/tex]

We now have two cases:

[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]

Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:

[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]

Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].

Step-by-step explanation:

???????? what is easy??

Answer:

fractions larger than 14 and one-half

decimals larger than 14 and one-half

whole numbers larger than 14 and one-half

Step-by-step explanation:

Which numbers are solutions to the inequality x greater-than 14 and one-half? Check all that apply.

Given that the inequality is represented by [tex]x>14\frac{1}{2}[/tex], i.e. x > 14.5

This inequality represent all the set of real numbers which are greater than 14.5. Whereas numbers including 14.5 and below are not involved. Hence the numbers that are a solution to this inequality are:

fractions larger than 14 and one-half

decimals larger than 14 and one-half

whole numbers larger than 14 and one-half

Answer:

0.4476

Step-by-step explanation:

Answer:

[tex]\displaystyle y=\frac{1}{2}x+5[/tex]

Step-by-step explanation:

We want to find the slope in slope-intercept form of a line that is parallel to:

[tex]\displaystyle y=\frac{1}{2}x-2[/tex]

And passes through the point (-8, 1).

Recall that parallel lines have equivalent slopes.

Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.

We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:

[tex]\displaystyle y-(1)=\frac{1}{2}(x-(-8))[/tex]

Since we want the equation in slope-intercept form, we can isolate y. Distribute:

[tex]\displaystyle y-1=\frac{1}{2}x+4[/tex]

Therefore, our equation is:

[tex]\displaystyle y=\frac{1}{2}x+5[/tex]

Answer:

0.125

Step-by-step explanation:

It could be a lot of things, but if you mean the decimal form then it would be 0.125. Just divide 1 by 8.

Answer:

the smaller number is 15 and the larger number is 35

Step-by-step explanation:

x+y=50

x=smaller number y=larger number

y=x+20

x+(x+20)=50

2x+20=50

2x=30

x=15

smaller number=15

larger number= 15+20=35

Answer:

Smaller: 15

Larger: 35

Step-by-step explanation:

Larger: y

Smaller: x

[tex]x+y=50[/tex]

[tex]y=20+x[/tex]

[tex]x+20+x=50\\2x=50-20\\2x=30\\x=15[/tex]

[tex]15+y=50\\y=50-15\\y=35[/tex]

x=15; y=35

Hope this helped! Please mark brainliest :)

Answer:

RQ = 9 units

Step-by-step explanation:

Answer:

A) 45=x

B) Yes, since both A and B are 90°

6x+90=360

6x=270

x=45

No lines are not parallel

Answer: Approximately 5.22%

========================================================

Work Shown:

A = true value = 13.4 seconds

B = measured value (erroneous value) = 14.1 seconds

C = percent error

C = [ (B-A)/A ] * 100%

C = [ (14.1-13.4)/(13.4) ] * 100%

C = 0.0522 * 100%

C = 5.22%

This value is approximate.