solve using the substitution method x = 10 y = 2x- 6

Answer:

20

Step-by-step explanation:

Let t represent the number of toddlers in the class.  Then 15% of t = 3.

In other terms, 0.15t = 3, and t = 3/0.15 = 20.

There are 20 toddlers in the class.

A percent equation representing the problem is 0.15x = 3. Solving this equation reveals that there are 20 toddlers in the total class.

This problem can be solved by expressing the information given in mathematical form.

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Answer:

1. f(x)= [tex]\left \{ {{1/xWHEN x<1 ANDx\neq 0} \atop {\sqrt[3]{x}WHEN x\geq 1}} \right.[/tex]

2. yes this graph represents a polynomial, this line is of the form y=mx+b; there are no turning points as it is a polynomial of degree 1.

Step-by-step explanation:

For problem 1:

as can be seen in the given graph, the graph of 1/x is ended at the value of x=1 and for all the values of x>1.

so the condition x<1 and x[tex]\neq[/tex]0 applies here

then for graph [tex]\sqrt[3]{x}[/tex], the graph starts from (1,1) and there is no extension of it beyond the value of x=1.

so the condition x[tex]\geq[/tex]1 applies here.

For Problem 2:

the given graph is a linear line which is represent by polynomial y=mx+b

and the polynomial y=mx+b is a polynomial of degree 1.

As the given graph is a graph of straight line represented by y=mx+b there are no turning points.

!

Answer:

x = 4 in

Step-by-step explanation:

scale factor of reduction is

[tex]\frac{6}{18}[/tex] = [tex]\frac{1}{3}[/tex], thus

x = [tex]\frac{1}{3}[/tex] × 12 = 4

Answers

Part a: Opposite

Part b: cos

Part c: Adjacent

Explanation

If you doing sine, cosine, and tangent, just remember SOHCAHTOA.

Answer:

D.) 6 and 2

Step-by-step explanation:

Supplementary angles are two angles which sum up to 180°.

Answer:

B. [tex]\angle 2\text{ and }\angle 5[/tex]

Step-by-step explanation:

We have been given an image of intersecting lines. We are asked to find the pair of angles that must be supplementary.

We know that two angles are supplementary when they add up-to 180 degrees.

Upon looking at our given image, we can see that the measure of angle 2 and measure of angle 5 is 90 degrees. So these angles will add up-to 180 degrees, therefore, option B is the correct choice.

Answer:

B.) [tex]1\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{4} -\frac{2}{3}

Then multiply 4 by 2, then add 1.

frac{9}{4} - \frac{2}{3} \\[/tex]

Then find the Least Common Denominator(LCD); simply just multiply 4 by 3 to get 12; then multiply using the opposite number.

[tex]\frac{3}{3} *\frac{9}{4} - \frac{4}{4} * \frac{2}{3}[/tex]

to get: [tex]\frac{27}{12} - \frac{8}{12}[/tex].

now the denominators is the same on both sides, just subtract the numerator.

27 - 8 = 19

Now simply: [tex]\frac{19}{12} = 1\frac{7}{12}[/tex].

Your final answer is 1\frac{7}{12}[/tex].

Answer:

Step-by-step explanation:

That 7 in the 4th position of the given decimal is greater than 5 and thus indicates that we must round that 4 up:

25.0347 → 25.035.  This is "to 3 decimal places" accuracy.

The number 25.0347 rounded to 3 decimal places is 25.035.

The question is asking to round the number 25.0347 to 3 decimal places. As it is, the number 25.0347 already has 4 decimal places. Rounding it to 3 decimal places means you should retain up to the thousands place (3 digits after the decimal point) and adjust the last digit based on the digit that comes after it. If the 4th digit after the decimal point is 5 or more, you round up. If not, you just drop it.

In the number 25.0347, the fourth digit after the decimal point is 7, which is greater than 5. Therefore, we round up the third digit (4) by 1. So, the number 25.0347 rounded to 3 decimal places is 25.035.

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I believe it’s D or B

50% is ur answer your welcome

Answer:

The lighthouse is 424 feet away.

Step-by-step explanation:

There is no other way to do this but to use one of the 6 trigonometry functions.

Drawing

Draw a dotted horizontal line.

judge an angle that could be 23o. Let it slant downward from the left side of the dotted line.

Draw another horizontal line that represents sea level.

Join the left side of the dotted line to the last line you drew. The angle on your right is also 23o.

Function

You have 6 trig functions to choose from. You have the lighthouse height (180 feet) the angle on your right, and the length on the horizontal representing the distance from the lighthouse base to the boat.

You have an angle

You have an opposite side

You have a horizontal line (the adjacent side)

You want to use the tangent function.

Tan(23) = opposite / ad

Tan(23) = 180 / adjacent     Multiply both sides by the adjacent

adjacent*Tan(23)= 180        Divide by Tan(23)

adjacent = 180/Tan(23)

adjacent = 180 / 0.42447

adjacent = 424 feet.

Answer: A. 1 foot

Step-by-step explanation:

Since 1 cm= 2.5 feet, then o.5 cm= half of 2.5 feet.

2.5/2= 1.25 which is closest to 1 foot.

Answer: 1/6

Step-by-step explanation:

1/6+1/6+16 hope this helps!

Answer:

The dependent variable is the rate (3 meters per second) and the independent variable is m (the amount of meters he runs). This is because the rate changes based on the amount of meters he runs.

Answer:

The seconds are independent and the meters are dependent

Answer:

9. ∠A ≅ ∠R

10. SI ≅ GH

11. MN ≅ RN

12. FE ≅ TU

Step-by-step explanation:

Look at the reason identifier: A means "angle"; S means "side". The order is important. AAS means two adjacent angles with only one of them next to the corresponding sides. SAS means the angle is between two corresponding sides.

9. Sides CS and TS correspond and are congruent. The vertical angles at S are congruent, so the AAS identifier means you're looking for angles A and R to be congruent. (Using angles C and T would invoke the ASA identifier.)

__

10. Sides HI are congruent; the angles at H and I are congruent. The SAS identifier means you're looking for the sides on the other side of those angles to be congruent: sides SI and GH.

__

11. SSS means you're claiming all three sides are congruent to their corresponding sides. The common side is congruent to itself; the marked sides are congruent. So, you need the unmarked sides to be congruent to each other.

__

12. HL means you're claiming the hypotenuse and one leg of the right triangle are congruent. One leg is already marked, so you need the hypotenuses to be congruent.

Answer:

214

Step-by-step explanation:

set bc = to cd and solve for x

then substitute x into one of the equations and solve --> you should get 73

multiply 73 by 2 and then subtract that from 360

you should get 214

Answer:

Vertical asymptotes: x=-9 and x=3

Slant asymptote: y=5x-1

Step-by-step explanation:

Given

f(x)=(5x^3+29x^2-140x+21)/(x^2+6x-27)

For vertical asymptote, the denominator is put equal to zero,so

x^2+6x-27=0

Factorizing

x^2+9x-3x-27=0

x(x+9)-3(x+9)=0

(x+9)(x-3)=0

So,

x=-9 ;x=3

As the degree of the numerator is greater than the denominator the function will not have horizontal asymptote but it will have a slant asymptote which will be calculated by long division.

After dividing 5x^3+29x^2-140x+21  by x^2+6x-27  we get

Quotient: 5x-1

Remainder: x-6

We only need the quotient for the slant asymptote,

So the slant asymptote is y = 5x -1  ..

Answer:

Vertical asymptotes: x=-9 and x=3

Slant asymptote: y=5x-1

Step-by-step explanation:

Answer: B

Step-by-step explanation: Got it right on edge

Answer:B

Step-by-step explanation:I did it

Answer:

D. 13 cm

hope it helps

Answer:

13d

Step-by-step explanation:

Answer:It is 100

Step-by-step explanation:

0.75x = 60

You can also make it easier by using fractions:

3x/4 = 60

Multiply both sides by 4:

3x = 240

x = 80

For this case we must simplify the following expression:

[tex]\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}[/tex]

We rewrite:

[tex]64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3[/tex]

So:

[tex]\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}[/tex]

Answer:

Option B

Answer:

The measures of angles of this Δ are 23° , 67° , 90°

Step-by-step explanation:

* Lets talk about some facts in the circle

- An inscribed angle is an angle made from points sitting on the

 circle's circumference

- A central angle is the angle formed when the vertex is at the center

 of the circle

- The measure of an arc of a circle is equal to the measure of the

 central angle that intercepts the arc.

- The measure of an inscribed angle is equal to 1/2 the measure of

 its intercepted arc

- An angle inscribed across a circle's diameter is always a right angle

- The triangle is inscribed in a circle if their vertices lie on the

  circumference of the circle, and their angles will be inscribed

  angles in the circle

* Now lets solve the problem

- Δ ABC is inscribed in a circle

∵ its side AB is a diameter of the circle

∵ Its vertex C is on the circle

∴ ∠C is inscribed and across the circle's diameter

∴ ∠C is a right angle

∴ m∠C = 90°

∵ The measure of arc BC = 134°

∵ ∠A is inscribed angle subtended by arc BC

∵ The measure of an inscribed angle is equal to 1/2 the measure

   of its intercepted arc

∴ m∠A = 1/2 × 134° = 67°

∵ The sum of the measures of the interior angles of a triangle is 180°

∵ m∠A = 67°

∵ m∠C = 67°

∵ m∠A + m∠B + m∠C = 180°

∴ 67° + m∠B + 90° = 180°

∴ 157° + m∠B = 180° ⇒ subtract 157 from both sides

∴ m∠B = 23°

* The measures of angles of this Δ are 23° , 67° , 90°

Answer:

13.64%

Step-by-step explanation:

The increase, from 132 to 150, is 18.

Comparing 18 to the original 132, we get 18/132 = 0.1364

Rewriting this as a percentage change, we get 0.1364, or 13.64%.   The percentage increase from 132 to 150 is 13.64%.

Answer: z = -3 , y = 2 , x = 2

The solution to the system of equations is: x - y + 9z = -27 , 2x - 4y - z = -1 , 3x + 6y - 3z = 27 is

x = 2

y = 2

z = -3

Given the system of equations:

1. x - y + 9z = -27

2. 2x - 4y - z = -1

3. 3x + 6y - 3z = 27

We'll use the method of elimination to solve this system.

Step 1: Eliminate y from equations (1) and (2):

Adding equations (1) and (2):

(x - y + 9z) + (2x - 4y - z) = -27 + (-1)

x + 2x - y - 4y + 9z - z = -27 - 1

3x - 5y + 8z = -28

Step 2: Eliminate y from equations (2) and (3):

Multiplying equation (2) by (3) and equation (3) by (2):

6x - 12y - 3z = -3  (from equation 2)

6x + 12y - 6z = 54 (from equation 3, after multiplying by 2)

Adding these two equations:

(6x - 12y - 3z) + (6x + 12y - 6z) = -3 + 54

6x + 6x - 12y + 12y - 3z - 6z = 51

12x - 9z = 51

Now, we have two equations:

1. 3x - 5y + 8z = -28

2. 12x - 9z = 51

From equation (2), let's solve for (x):

12x - 9z = 51

12x = 51 + 9z

x = (51 + 9z) ÷ 12

Now, we'll substitute this expression for (x) into equation (1) to solve for (z):

3x - 5y + 8z = -28

[tex]\[ 3\left(\frac{51 + 9z}{12}\right) - 5y + 8z = -28 \][/tex]

[tex]\[ \frac{153 + 27z}{12} - 5y + 8z = -28 \][/tex]

Next, we'll isolate (z):

153 + 27z - 60y + 96z = -336

249z - 60y = -489

Now, let's solve for (z):

249z = -489 + 60y

z = (-489 + 60y) ÷ 249

Now, we'll substitute the expression for (z) back into equation (2) to solve for (y):

[tex]\[ 12x - 9\left(\frac{-489 + 60y}{249}\right) = 51 \][/tex]

[tex]\[ 12x - \frac{-489 + 60y}{27} = 51 \][/tex]

[tex]\[ 12x = 51 + \frac{-489 + 60y}{27} \][/tex]

[tex]\[ x = \frac{51 + \frac{-489 + 60y}{27}}{12} \][/tex]

[tex]\[ x = \frac{51\times27 + -489 + 60y}{12\times27} \][/tex]

[tex]\[ x = \frac{1377 - 489 + 60y}{324} \][/tex]

[tex]\[ x = \frac{888 + 60y}{324} \][/tex]

[tex]\[ x = \frac{148 + 10y}{54} \][/tex]

Now, we'll substitute the expressions for (x) and (z) into equation (1) to solve for (y):

x - y + 9z = -27

[tex]\[ \frac{148 + 10y}{54} - y + 9\left(\frac{-489 + 60y}{249}\right) = -27 \][/tex]

The least common multiple of (54) and (249) is (54 × 249).

⇒ (148 + 10y) × 249 - 54 × 249 × y + 9 × 54 × (-489 + 60y)  = -27 × 54 × 249

⇒ 36752 + 2490y - 133146y - 233640 + 29160y = -1458 × 249

⇒  2490y - 133146y + 29160y + 36752 - 233640 = -1458 × 249

⇒ -106496y - 197888 = -362682

⇒ -106496y = -164794

⇒ y = (-164794) ÷ (-106496)

y ≈ 1.547

y ≈ 2

Now that we have found (y = 2), we can substitute this value back into the expressions for (x) and (z) to find their values.

For (x):

[tex]\[ x = \frac{148 + 10(2)}{54} = \frac{168}{54} = 2 \][/tex]

For (z):

[tex]\[ z = \frac{-489 + 60(2)}{249} = \frac{-369}{249} = -\frac{3}{1} = -3 \][/tex]

So, the solution to the system of equations is:

x = 2

y = 2

z = -3

Answer:

the answer is b

Step-by-step explanation:

ANSWER

The mean absolute deviation is 1.75

EXPLANATION

The given date set is 2, 2, 5, 6, 8, 4, 8, 5

The mean is

[tex]\bar X = \frac{2 + 2 + 5 + 6 + 8 + 4 + 8 + 6}{8} = 5[/tex]

The mean absolute value deviation is given by:

[tex] =\frac{ \sum |x -\bar X| }{n} [/tex]

[tex] = \frac{ | 2 - 5| + |2 - 5|+ |5- 5|+ |6 - 5|+ |8 - 5| + |4 - 5|+ |8- 5|+ |5 - 5| }{8} [/tex]

[tex]= \frac{ 3 + 3+ 0+ 1+ 3 + 1+3+ 0}{8} [/tex]

[tex] = \frac{14}{8} [/tex]

[tex] = 1.75[/tex]

ANSWER

[tex]( \sin(x) + 2)( \sin(x) - 1)[/tex]

EXPLANATION

The given trigonometric function is:

[tex] \sin^{2} x + \sin(x) - 2[/tex]

This is a quadratic trinomial in sinx

We split the middle term to obtain:

[tex]\sin^{2} x + 2 \sin(x) - \sin(x) - 2[/tex]

[tex] \sin \:x ( \sin(x) + 2 ) - 1( \sin(x) + 2)[/tex]

The factors are:

[tex]( \sin(x) + 2)( \sin(x) - 1)[/tex]

the answer would be -3,1,2

Hello!

From Least To Greatest Your Numbers Would Be

Answer:

B

Step-by-step explanation:

Using the law of sines, we can make a proportion.

But first, we'll need to solve for the unknown angle.

We add up the two known angles and subtract that by 180.

90 + 41 = 131

180 - 131 = 49

So the unknown angles is 49.

Then, we can use the law of sines.

Make the equation.

sin(90)/55 = sin(49)/x

Simplify this using a calculator and you get around 41.51 or option B.

The correct option is B. [tex]41.51[/tex] The value of [tex]\( x \)[/tex] to the nearest hundredth

To find the value of [tex]\( x \)[/tex] to the nearest hundredth, we need to use the trigonometric functions for the right triangle given.

We are given:

The hypotenuse [tex](\( 55 \))[/tex]

An angle [tex](\( 41^\circ \))[/tex]

We need to find the adjacent side[tex](\( x \))[/tex]

We can use the cosine function, which is defined as:

[tex]\[\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\][/tex]

Substituting the given values:

[tex]\[\cos(41^\circ) = \frac{x}{55}\][/tex]

Solving for \( x \)

[tex]\[x = 55 \times \cos(41^\circ)\][/tex]

Using a calculator to find \(\cos(41^\circ)\)

[tex]\[\cos(41^\circ) = 0.7547\][/tex]

Now, multiplying:

[tex]\[x = 55 \times 0.7547 = 41.5085\][/tex]

To the nearest hundredth, \( x \) is:

[tex]\[x = 41.51\][/tex]

The complete Question is

To the nearest hundredth, what is the value of x?

A.36.08

B. 41.51

C. 47.81

D. 72.88

Answer:

x1= 14/4 and X2 = -2

Step-by-step explanation:

To find the values of "X" for which when the function is evaluated gives 19 we need to equal the function to 19, as follows:

2x^2+3x+5 = 19

2x^2+3x+5-19=0

2x^2+3x-14=0

Then, solving for "x" we need to use the quadratic formula (Attached), where a, b, and c, are the following:

a: 2 b: 3 c: 14

Using the quadratic formula, we get:

x1= 14/4 and X2 = -2