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10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Answer:

x= 95/2  or  x=47.5  or   47 1/2

Step-by-step explanation:

3x + 10 = 5(x - 17)

First Step:

multiply and combine the right side (parentheses)

5 times x = 5x         5 times -17 = -85

3x + 10 = 5x -85

Second Step:

Add like terms ----> which is: 3x and 5x -----10 and -85

BUT since you only want one x on one side, you combine x first.

3x + 10 = 5x -85

-5x         -5x

-2x + 10 = -85

NOW

Third Step:     Add the integers---> 10 and -85

you want to get 10 on the same side as the -85, so you subtract it from BOTH sides.

which brings you:

-2x + 10 = -85

       -10    -10

NOW that we've subtracted -10 from -85 it's technically just adding 85 and 10 then putting a negative sign on it.

so now we have:

-2x = -95

Step Four:

divide -2 from each side to get X alone

-2x = -95

-2      -2

ANSWER:

x=47.5

Step-by-step explanation:

They are basically saying that you have to multiply the exponent law cited from exponents laws. this results in 5 times 3 in the exponent. Therefore you get 2^15.

1.9/10. 2.22 3.64. 4.3.15. 5.160. 6.81

Answer:

(2, -3)

Step-by-step explanation:

These are the steps I used:

(6x+2y=6) x3 -> 18x+6y=18

(7x+3y=5) x2 -> 14x+6y=10

When you subtract the equations you get:

4x=8

x=2

The solution to the system of equations is -3 and -2

The correct option is A

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one.

6x+2y=6 is equation (1)

7x+3y=5 is equation (2)

Multiplying equation (1) by (3)

18x+6y=18 is equation(3)

By multiplying (2) by 2

14x+6y=10 is equation (4)

Substrate equation (4) from (3)

4x=8 Now, divide both sides by 4

X=2

Substitute x=2 in (1)

6(2)+2y=6

12+2y=6

Substrate 12 from LHS and RHS

2y=-6

Divide both sides by 2

y=-3

Hence x=2 and y=-3

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Using different mathematical operations, the price of a slice that is all vegie is calculated to be $1.25.

What are arithmetic operations?

Arithmetic operations are a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics.

Given, Cost of the pizza = $10

and number of slices = 8 (half pepperoni and half veggie)

So, number of slices containing veggies = 8/2 = 4

and cost of 4 slices containing all veggie= 10/2 = $5

Therefore, value of a slice containing all veggie = 5/4 = $1.25

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Answer:

32

Step-by-step explanation:

2x2x2x2x2

Answer:

32

Step-by-step explanation:

The way exponents work, the little number represents how many times you multiply the big number by itself.

For example, 2^2 is 2 x 2 = 4 (the little ^ means the next number is an exponent)

2^3 is 2 x 2 x 2 = 8  (there is a little 3, so that means there are three 2's)

2^4 is 2 x 2 x 2 x 2 = 16  (there is a little 4, so there are four 2's)

So, 2^5 is 2 x 2 x 2 x 2 x 2

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 2 = 32

2^5 = 32

Repeated-measures design would require the smallest number of subject

Repeated-measures design: Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods. For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed

given that, a researcher conducts an experiment comparing two treatment conditions and obtains 20 scores in each treatment

Repeated-measures design would require the smallest number of subjects

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Answer:

B.

Step-by-step explanation:

Between 10 and 20 because there is a huge jump from 180 to 500.

Answer:

B

Hope this helps you!

the measurement of the couch in the scale drawing would be 15 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:

1/4 inch = 2 feet

This means that every 1/4 inch in the drawing represents 2 feet in real life.

To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.

First, we can convert the actual size of the couch to feet:

10 ft = 10 ft x 12 inches/ft = 120 inches

Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:

1/4 inch = 2 feet

1 inch = 8 feet (multiplying both sides by 4)

So, 120 inches in real life is equal to:

120 inches / 8 feet per inch = 15 inches in the drawing

Therefore, the measurement of the couch in the scale drawing would be 15 inches.

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Answer: x=3

Step-by-step explanation: This is a porportion, meaning that the numbers are set equal to each other. Look at your denominators, 4 and 8? What do they have in common? In this case, they have a factor of 2 in common, and 8 is 4x2. So then we look at the numerators now. What times 2 equals to 6? Your answer then becomes 3.

train A speed = 95 mph

train B speed = 105 mph

they are travelling towards each other

so effective speed = 200 mph.

distance = 360 miles

t= d/r

t=360/200

time = 1.8 hours they will meet

Answer:

A translation 3 units to the right and a 90-degree clockwise rotation

Step-by-step explanation:

s = 7 is the only solution of the equation.

We have to give that,

An expression to simplify,

\(s = 4 + \sqrt{s + 2}\)

Now, Simplify the expression as,

\(s = 4 + \sqrt{s + 2}\)

Subtract 4 on both sides,

\(s - 4 = \sqrt{s + 2}\)

Taking square root on both sides,

\((s - 4)^2 = s + 2\)

\(s^2 + 16 - 8s = s + 2\)

Combine like terms,

\(s^2 - 9s + 14 = 0\)

Apply factorization method,

\(s^2- 7s - 2s + 14 = 0\)

\(s (s - 7) - 2 (s - 7) = 0\)

\((s - 7) (s - 2) = 0\)

This gives two solutions,

\(s - 7 = 0\)

\(s = 7\)

And,

\(s - 2 = 0\)

\(s = 2\)

Put s = 7 in the above equation,

\(s = 4 + \sqrt{s+ 2}\)

\(7 = 4 + \sqrt{7+ 2}\)

\(7 = 4 + \sqrt{9}\)

\(7 = 4 + 3\)

\(7 = 7\)

Hence, 7 is the solution of the equation.

Put s = 2;

\(s = 4 + \sqrt{s+ 2}\)

\(2 = 4 + \sqrt{2+ 2}\)

\(2 = 4 + \sqrt{4}\)

\(2 = 4 + 2\)

\(2 = 6\)

Which is not possible.

Therefore, s = 7 is only the solution.

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Answer:

A rational number is any number that can be expressed as a whole number, a fraction, or as a non repeating decimal. Otherwise, it is an irrational number.

19/5: it is a rational number because it is in fraction form

√12: this is an irrational number

√49: this is a rational number because when you simplify this you will get the answer 7, that is a whole number.

0.3425563758:  This is a decimal, hence, this is rational.

4/25 :  it is a fraction so it is a rational number.

√1/8: this is an irrational number

√0.6¯: this is an irrational number

Answer:

The correct answer is 15.

Step-by-step explanation:

We are given that the original sides BC is 5.  To find the length of B'C' we take the side of BC and multiply it by the scale factor.

5 (original BC) x 5 (the given scale factor) = 15

Answer:

15

Step-by-step explanation:

correct on edge 2023

Answer:

y = 2x + 8

Step-by-step explanation:

  Parallel lines have same slope.

 y = 2x - 4

Slope = 2

Point (-2 ,4)

Equation of line in point-slope form:

         y - y₁ = m(x - x₁)

        y - 4  = 2(x - [-2] )

       y - 4   = 2(x + 2)

       y -4   = 2x + 4

             y = 2x + 4 + 4

        \(\sf \boxed{y = 2x + 8}\)

Answer:

176°

Step-by-step explanation:

Answer:

y = -½x + 4

Step-by-step explanation:

Equation of any line in slope-intercept form is y = mx + b, where,

m = slope = change in y/change in x

b = y-intercept = the point on the y-axis intercepted by the line.

Let's find m and b.

✔️Using two points on the line, (0, 4) and (2, 3),

Slope (m) = change in y/change in x = (3 - 4)/(2 - 0)

m = -1/2 = -½

✔️The line intercepts the y-axis at y = 4.

Therefore,

b = 4

✔️To write the equation of the line, substitute m = -½ and b = 4 into y = mx + b.

Thus,

y = -½x + 4

Answer:

B

Step-by-step explanation:

Option B is the set of range

The y-intercept of the graph of y = f(x) is (0, -5).Given a quartic polynomial with zeros at r = 1 (double), r = 3, and r = -2.Plugging in the values, we find that f(0) = -24.

Since (-1, -8) is on the graph of y = f(x), we know that f(-1) = -8.

We are given that f(x) is a quartic polynomial with zeros at r = 1 (double), r = 3, and r = -2. This means that the polynomial can be written as f(x) = \(a(x - 1)^2(x - 3)(x + 2)\), where a is a constant.

To find the y-intercept, we need to determine the value of f(0). Plugging in x = 0 into the polynomial, we have f(0) = \(a(0 - 1)^2(0 - 3)(0 + 2)\) = -6a.

We know that f(-1) = -8, so plugging in x = -1 into the polynomial, we have f(-1) = \(a(-1 - 1)^2(-1 - 3)(-1 + 2)\) = -2a.

Setting f(-1) = -8, we have -2a = -8, which implies a = 4.

Now we can find the y-intercept by substituting a = 4 into f(0) = -6a: f(0) = -6(4) = -24.

Therefore, the y-intercept of the graph of y = f(x) is (0, -24).

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Answer:

Step-by-step explanation:

The answer is 3, if you did 4-7 it would be -3, but since both -4-(-7) are negative it's a positive 3.

Ignore the parentheses, is just there so you don't mix the negative sign up with the subtraction sign.

Answer:

Step-by-step explanation:

According to the graph, the y-intercept is the point (0, 3), it is the point of intersection of the parabola with the y-axis.

Step-by-step explanation:

in general, a linear function is always of the structure

y = ax + b

"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

"b" is the y-intercept (the y-value when x = 0).

so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :

2 = a×1 + b = a + b

1 = a×2 + b = 2a + b

now we can simply subtract the first equation from the second and get

1 = 2a + b

- 2 = a + b

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

-1 = a + 0

a = -1

1 = 2×-1 + b = -2 + b

b = 3

and the equation is

y = -x + 3

therefore, when the input is n (that means f(n))

y = output = -n + 3

Answer:

3x + 75° = 90° , x = 5

Step-by-step explanation:

As we can see it is a right angled triangle so

3x + 75° + 90° = 180° ( being sum of angles of triangle)

we can write even

3x + 75° = 90° , x = 5

Answer:

12

Step-by-step explanation:

The average rate of change in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ 2, 4 ]

f(b) = f)4) = 32 ← from table

f(a) = f(2) = 8 ← from table

Then average rate of change is

\(\frac{32-8}{4-2}\) = \(\frac{24}{2}\) = 12