solve for
 (6x + 9)/3 =​

Step-by-step explanation:

[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]

Answer:

The interest for the two years is 144.

Step-by-step explanation:

Hallar the interest produced by a capital of /240 to an annual interest rate of 30% provided for a period of 2 years

Principal, P = 240

Interest, R = 30 %

Time, t = 2 years

The simple interest is given by

[tex]I = \frac{P\times R\times T}{100}\\\\I = \frac{240\times 30\times 2}{100}\\\\I = 144[/tex]

Answer:

[tex]y_1 = -2[/tex] and [tex]y_2 = 4[/tex]

Step-by-step explanation:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

Move the constant to the right-hand side and change their sign.

[tex] \sqrt{10y + 24} = y + 1 + 3 [/tex]

combine like terms

[tex] \sqrt{10y + 24} - 3 = y + 4[/tex]

Square both side to remove square brackets.

10y + 24 - 3 = y²+ 8y + 16

Move the expression to the left-hand side and change its sign.

10y + 24 - y² - 8y - 16 = 0

Combine like terms

10y - 8y + 24 - 16 - y² = 0

2y + 8 - y² = 0

Use commutative property to reorder the terms.

-y² + 2y + 8 = 0

Change the sign of expression.

y² -2y -8 = 0

split -2y

y² + 2y - 4y - 8 = 0

Factor out y from the first pair and -4 from the second equation.

y ( y + 2 ) - 4 ( y + 2 ) = 0

Factor out y+2 from the expression.

( y + 2 ) ( y - 4)

When the products and factors equals 0, at least one factor is 0.

y + 2 = 0

y - 4 = 0

Solve for y

y = -2

y = 4

When we plug the both solution as y we found that both is true solution of this equation.

This equation has two solutions which are -2 and 4.

Answer:

Solution given:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

keep the constant term in one side

[tex] \sqrt{10y + 24} =y+1+3[/tex]

solve possible one

[tex]\sqrt{10y+24}=y+4[/tex]

now

squaring both side

[tex](\sqrt{10y+24})²=(y+4)²[/tex]

10y+24=y²+8y+16

taking all term on one side

10y+24-y²-8y-16=0

solve like terms

8+2y-y²=0

doing middle term factorisation

8+4y-2y-y²=0

4(2+y)-y(2+y)=0

(2+y)(4-y)=0

either

y=-2

or

y=4

y=-2,4

Answer:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Step-by-step explanation:

This is the fibonacci sequence with each term times x.

Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.

That is:

1x+1x=2x

1x+2x=3x

2x+3x=5x

3x+5x=8x

So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.

f(1)=1x since first term of f is 1x

f(2)=1x since second term of f is 1x

Yes, I'm naming the sequence f.

So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...

Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.

So in general f(n)=f(n-1)+f(n-2).

So the full recursive definition is:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Answer:

d

Step-by-step explanation:

vertical angles are congruent , so

∠ B = ∠ A  = 43°

Answer:

Exact surface area = 500+20pi square cm

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

Explanation:

All areas mentioned are in square cm, which can be abbreviated to cm^2.

Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.

Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.

The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is

LSA = 2*pi*r*h

but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.

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

In summary we have these six areas for the faces

Add up those sub areas to get the full surface area of this particular 3D solid.

120+84+84+(70-2pi)+(70-2pi)+(72+24pi)

(120+84+84+70+70+72)+(-2pi-2pi+24pi)

500+20pi

This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2

Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2

In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).

Answer:

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get

6.5 > –2.4b – 8.1

Correct

Luis started by subtracting 4.8b from both sides to get

2.4b + 6.5 < – 8.1

Incorrect

Shauna started by subtracting 6.5 from both sides to get

7.2b > 4.8b – 14.6

Correct

Clarence started by adding 8.1 to both sides to get

7.2b + 14.6 > 4.8b

Correct

Luis’s is incorrect because he flipped the inequality sign when he subtracted

Answer:

D) 144π sq. units

Step-by-step explanation:

The formula for finding the surface area of a sphere is 4π

Substitute 6 in for r.  4π = 144π

Answer:

144π sq. units

Step-by-step explanation:

The formula to determine the surface area of a sphere is: 4πr^2

But there’s no digit of pi given. Therefore we will use the formula but ignoring pi:

4πr^2

= 4r^2

= 4(6^2)

= 4(36)

= 144

Surface area is measured in square units.

Therefore the answer is 144π. The answer will be the true answer surface area once we know what π to use. For now, π will be just a variable next to 144 and will be later multiplied to it.

I hope you understand this! Hope I helped!

Answer:

Step-by-step explanation:

x is greater than minus 3. You have everything right but the graph. The arrowhead goes the other way. Around -3 is as small as x gets.

0====0====0====0====0

-3       -2      -1        O       1

O------------------------------->

Let's replace x with -4 and simplify

y = (x/4) + 7

y = (-4/4) + 7

y = -1 + 7

y = 6

This means x = -4 and y = 6 pair up together.

So 6 goes in the box under the -4

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

Repeat those steps for x = 0

y = (x/4) + 7

y = (0/4) + 7

y = 0 + 7

y = 7

So 7 goes in the box under the 0

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

Let's repeat those steps for x = 4

y = (x/4) + 7

y = (4/4) + 7

y = 1 + 7

y = 8

So 8 goes in the box under the 4

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

Lastly, for x = 8, we get

y = (x/4) + 7

y = (8/4) + 7

y = 2 + 7

y = 9

9 goes in the box under the 8

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

The y outputs we got were: 6, 7, 8, 9

Notice how each time y increases by 1, x goes up by 4.

This means slope = rise/run = 1/4

We can think of x/4 as (1/4)x to help see that the slope is 1/4.

A function assigns the values. The value of the y in the given table should be 6, 7, 8, and 9, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

The function of the x and y is given y=(x/4)+7, use this function to find the value of y for the given values of x. Thus,

x = -4

y = (-4/4)+7

y = -1+7

y = 6

x = 0

y = (0/4)+7

y = 7

x = 4

y = (4/4)+7

y = 8

x = 8

y=(8/4)+7

y = 9

Hence, the value of the y in the given table should be 6, 7, 8, and 9, respectively.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ2

Answer:

30.44 pounds.  

Step-by-step explanation:

to find the answer you have to subtract 45.33 and 14.89

so 45.33-14.89= 30.44

so now you would have to round. the number after the decimal is NOT greater then 5 so Therefore, we simply remove the 4 an d the the whole number as: 30

SO your answer ROUNDING wise is 30

Hope this helps

Answer:

48 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

D)

y = - x + 1

y = -1/4 +2

Step-by-step explanation:

The equation of a linear graph: y = mx + b

The red graph is going down, so it would mean the m value is negative (-). This cancels options A) and C). The red graph also moves one unit up the y-axis which means the b is one (1). So the equation would be y = - x + 1.

The blue graph is also going down, so it would mean the m value is negative (-). This means it could be options B) or D). But, the blue graph also moves two units up the y-axis, which means the b is two (2).  So the equation would be y = - 1/4x + 2.

Answer:

Step-by-step explanation:

Given:

Perimeter = 46 cm

Length = 12 cm

To Find:

Width = ?

Solution:

Perimeter of Rectangle = 2( l + b)

We know the value of length

So, we can express this as a linear equation,

[tex]2(l + b) = 46 \\ 2(12 + b) = 46 \\ 24 + 2b = 46 \\ 2b = 46 - 24 \\ 2b = 22 \\ b = \frac{22}{2} \\ b = 11[/tex]

So therfore, the width/breadth of the rectangle is 11.

The function f(x)=3/4 (x) -3 is a straight line,

so the range of the function is (-∞,∞)

Answered by GAUTHMATH

Answer:

[tex] \blue{b = \dfrac{2A}{h}} [/tex]

Step-by-step explanation:

[tex] A = \dfrac{1}{2}bh [/tex]

Step 1. Switch sides.

[tex] \dfrac{1}{2}bh = A [/tex]

Step 2. Since the fraction 1/2 multiplies b, multiply both sides by the reciprocal of 1/2 which is 2.

[tex] 2 \times \dfrac{1}{2}bh = 2 \times A [/tex]

[tex] bh = 2A [/tex]

Step 3. Since h is multiplying b, and you want b alone, divide both sides by h.

[tex] \dfrac{bh}{h} = \dfrac{2A}{h} [/tex]

Answer:

[tex] b = \dfrac{2A}{h} [/tex]

Check this link: https://brainly.com/question/12053038

The same question is explained here :).

Hope it helps.

Answer:

(-0.5,2.5)

Step-by-step explanation:

The given equations are ,

[tex]\implies x + y - 2 = 0 [/tex]

[tex]\implies 3x - y +4 = 0 [/tex]

The point of intersection will be the solution of the given system of equations. Adding both , y will get cancelled . So that ,

[tex]\implies 4x +2 = 0 [/tex]

Now solve for x , we have ,

[tex]\implies 4x = -2 \\\\\implies x =\dfrac{-2}{4}\\\\\implies x = -0.5 [/tex]

Now put this value in any equation and solve out for y , we have ,

[tex]\implies -0.5 + y - 2 = 0 \\\\\implies y = 2.5 [/tex]

Therefore , the point of intersection will be ,

[tex]\implies\underline{\underline{ Point = (-0.5,2.5 ) }}[/tex]

10a+46-(3a+2b)

= 10a + 46 - 3a - 2b

= 7a - 2b + 46

Answer:

Difference between average day temperature and average night temperature = 70°

Step-by-step explanation:

Given;

Average day temperature = 43° C

Average night temperature = -30° C

Find:

Difference between average day temperature and average night temperature

Computation:

Difference between average day temperature and average night temperature = Average day temperature - Average night temperature

Difference between average day temperature and average night temperature = 43 - (-30)

Difference between average day temperature and average night temperature = 70°

Step-by-step explanation:

180-(90° +32°)

180- 122= 58

triangle =180°

180° - (58° +58°)

180° - 116°= 64°

Answer:

x=64

Step-by-step explanation:

∠A = 180-(90°+32°)

=> ∠A=180-122= 58

Angle sum property in Triangle=180°

=> x = 180° - (58°+58°)

=> x = 180° - 116°= 64°

Answer:

Step-by-step explanation:

sorry bout the poor drawing but it should be legible

What is mean: A mean is the simple mathematical average of a set of two or more numbers. To solve for it add all numbers together then divide by how many numbers are there. (Its best to put them in order)

$40 + $40 $60 + $80 + $100= $320/5= $64 is the mean

what is median: The median is the value separating the higher half of a data sample

40,40,60,80,100 (i like to cross it out so 40 and 100 cancle each other, another 40 and 80 cancel each other) now that you are left with only 1 number which is 60 that is the median.

What is Mode: the number that repeats the most

Mode is 40 because 40 repeats twice

Answer:

A

Step-by-step explanation:

The domain is all real numbers and the range is all real numbers greater than zero

The domain is {x| all real numbers} and the range is {y| y > 0}

The domain of a function is the set of inputs that we can use in the function. To find it, we initially assume that it is the set of all real numbers, and then remove the problematic values of x.

For example, a problematic point would be a value of x that causes the denominator to be equal to zero.

In this particular case, we can see that the variable is in the exponent, thus it can take any real value and it will not cause any problem, so the domain is the set of all real numbers.

The range is the set of possible outputs. Because in this case, the base is a positive number, the outcomes will only be positive, then the range is given by:

y > 0.

So the correct option is A.

If you want to learn more about range and domain, you can read:

https://brainly.com/question/1770447

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

Answer:

in 90 minutes he ran 30 laps

there is 60 minutes in a hour so the fraction would be

2/3 so we have to multiply this by 30

2/3*30=20

He can run 20 laps in a hour

Hope This Helps!!!

Answer:

Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.

Step-by-step explanation:

We have to take into consideration three things:

For each household, there are only two possible outcomes, either they own stocks, or they do not.

The probability of a household owning stock is independent of any other household, that is, for any household, the probability of someone owning stocks is 28%.

There is a fixed number of trials.

Is this experiment a binomial experiment?

Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.

Answer:

(x,y) right arrow (negative x , y)

Step-by-step explanation:

Mathematically, when we reflect a point over the x-axis; we have a result

The result is that the x- coordinate of the point reflected takes up a negative value

so what we have here is that;

(x,y) becomes (-x,y) once reflected over the y-axis

So, traditionally, we add the arrow

So our answer is thus;

(x,y) right arrow (negative x , y)

Answer:

A.

Step-by-step explanation: