Find the area of a rectangle with a base of 2 and a height of 6.

The logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

We are given the logarithm as:

log₃ 3 / 2 = 1 / 2 log₃ 3

We need to tell if it is true of not.

We get that, it is false as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

So, the statement given will be a false statement.

Therefore, we get that, the logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

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The congruent figures are given as follows:

Congruent figures are figures whose outer side lengths have the same measures. They may have different orientations, but the outer side lengths have to be the same.

Hence the congruent figures in this problem are given as follows:

They have different orientations(rotated), but same side lengths.

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The subtraction of the expression 10√27 - 4√12 is 22√3.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.

In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.

Consider the expression,

y = 10√27 - 4√12

Now, the number in the root can also be written as:

27 = 3 × 3 × 3

12 = 2 × 2 × 3

Therefore,

y = 10√27 - 4√12

y = 10[ √(3 × 3 × 3) ] - 4[ √( 2 × 2 × 3 ) ]

y = 10 × 3√3 - 4 × 2√3

y = √3 ( 10 × 3 - 4 × 2 )

y = √3 ( 30 - 8 )

y = 22√3

The value of the expression 10√27 - 4√12 is 22√3.

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Answer: 1. 0.937

2. 20.786

3. 35.001

Step-by-step explanation:

1. 0.9+0.03+0.007=

0.900+0.030+0.007=0.937

2. 20 +0.7 + 0.08 + 0.006=

20.000 +0.700 + 0.080 + 0.006=20.786

3. 35 + 0.01 - 0.009=

35.000 + 0.010 - 0.009=

35.010 - 0.009=35.001

The solution of the equation 3√2 x + 6 = 18 is 2√2.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

3√2 x + 6 = 18

Subtracting 6 from each side of the equation.

3√2 x + 6 - 6 = 18 - 6

3√2 x = 12

Dividing each side of the equation by 3.

( 3√2 x / 3 ) = ( 12/3 )

√2 x = 4

Dividing each side of the equation by √2.

( √2x/√2 ) = ( 4/√2 )

x = 2√2

Now checking the extraneous solution:

x = 2√2

[tex]3\sqrt{2}x + 6 = 18\\ 3\sqrt{2} \times 2\sqrt{2} + 6 = 18\\ 6(2) + 6 = 18\\ 18 = 18[/tex]

The solution for the equation is 2√2.

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The value of x is 2 and the value of y is -6.

The substitution method is one of the methods used to solve simultaneous equations. It entails making one of the variables the subject of the equation in one of the equations.

Then the variable is substituted for in the first equation:

3x-y=12

Second equation :

1Y=4x-14

Substitute for y in equation 1 using equation 2 :

3x - (4x - 14) = 12 3x -4x + 14 = 12

Combine similar terms:

14 - 12 = 4x -3x

Add similar terms;

2 = x

Substitute for x in equation:

2y = 4(2) - 14 y = 8 - 14 y = -6

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The value of x is 2 and the value of y is -6.

The substitution method is one of the methods that is used to solve for simultaneous equations. It entails making either of the variables the subject of the formula and then replacing for the variable in the other equation.

Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.

3x - y = 12 equation 1

Y= 4x - 14 equation 2

y is the subject of the formula in equation 2

Substitute for y in equation 1

3x - (4x - 14) = 12

3x -4x + 14 = 12

Combine similar terms together:

14 - 12 = 4x -3x

Add similar terms together

2 = x

In order to determine the value of y, take the following steps

Substitute for x in equation 2

y = 4(2) - 14

8 - 14

y = -6

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Answer:

B

Step-by-step explanation:

calculate the distance between A and B using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )

d = [tex]\sqrt{(x-1)^2+(-2-6)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+(-8)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+64}[/tex]

given AB = 10, then equating gives

[tex]\sqrt{(x-1)^2+64}[/tex] = 10 ( square both sides to clear the radical )

(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )

(x - 1)² = 36 ← take square root of both sides

x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )

x = 1 ± 6

then

x = 1 - 6 = - 5

x = 1 + 6 = 7

from the list then x = - 5 is a possible value

Step-by-step explanation:

when you use 3 por multiply the answer is 5×

(5×)+3

Answer:

No

Step-by-step explanation:

The correct answer is -406,726

A negative minus a negative is the same as a negative plus a positive

-621,044 + 214,318 = -406,726

The total amount earned when he waits 18 tables is $143

The total amount earned when he waits t tables is $35 + $6t

The equation that can be used to determine the total amount Carson earns is a linear equation. A linear equation is an equation that when drawn on a graph yields a straight line.

A linear equation increases by a constant amount. The highest power of a variable in a linear equation is 1.

The form of a linear equation is y = a + bx

Where:

Total amount earned = guaranteed wage + (tip per table x total number of tables he waits)

Total amount earned when he waits 18 tables: $35 + ($6 x 18)

$35 + $108 = $143

Total amount earned when he waits t tables: $35 + ($6 x t)

$35 + $6t

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Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

Answer:

10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

Step-by-step explanation:

Compute (10 x^3 - x^2 - 29 x - 30) ÷ (x^2 - x - 2) using polynomial long division:

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

To eliminate the leading term of the numerator, 10 x^3, multiply x^2 - x - 2 by 10 x to get 10 x^3 - 10 x^2 - 20 x. Write 10 x on top of the division bracket and subtract 10 x^3 - 10 x^2 - 20 x from 10 x^3 - x^2 - 29 x - 30 to get 9 x^2 - 9 x - 30:

| | | | | 10 x | |

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

To eliminate the leading term of the remainder of the previous step, 9 x^2, multiply x^2 - x - 2 by 9 to get 9 x^2 - 9 x - 18. Write 9 on top of the division bracket and subtract 9 x^2 - 9 x - 18 from 9 x^2 - 9 x - 30 to get -12:

| | | | | 10 x | + | 9

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

| | | -(9 x^2 | - | 9 x | - | 18)

| | | | | | | -12

The quotient of (10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) is the sum of the terms on top of the division bracket. The remainder is the expression that remains after the final subtraction step.

| | | | | 10 x | + | 9 | (quotient)

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30 |

| -(10 x^3 | - | 10 x^2 | - | 20 x) | | |

| | | 9 x^2 | - | 9 x | - | 30 |

| | | -(9 x^2 | - | 9 x | - | 18) |

| | | | | | | -12 | (remainder) invisible comma

(10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) = (10 x + 9) - 12/(x^2 - x - 2)

Write the result in quotient and remainder form:

Answer: 10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

The factors for given equation are -2/3 and -2.

Rewriting the equation firstly -

3x² + 8x + 4 = 0

ax² + bx + c = 0

Factorizing the equation as per mentioned two rules -

6 and 2 are the suitable factors for given expression -

3x² + 6x + 2x + 4 = 0

3x (x + 2) + 2(x + 2) = 0

(3x + 2) (x + 2) = 0

3x + 2 = 0

3x = -2

x = -2/3

x + 2 = 0

x = -2

So, the two factors of equation are -2/3 and -2.

To check the factors, we will keep the value of x in equation -

When x = -2/3

3x² + 8x + 4 = 0

3(-2/3)² + 8(-2/3) + 4 = 0

3(4/9) - 16/3 + 4 = 0

4/3 - 16/3 + 4 = 0

Multiplying the equation with 3/4

1 - 4 + 3 = 0

- 3 + 3 = 0

0 = 0

When x = -2

3x² + 8x + 4 = 0

3(-2)² + 8(-2) + 4 = 0

12 - 16 + 4 = 0

- 4 + 4 = 0

0 = 0

Since for both values of x, Left hand Side and Right Hand Side of equation is same, the two resultant factors are correct.

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the inequality to determine if a child's height satisfies the regulation is:

30in < h < 50 in.

Here we know that the allowed height of the child can be any value between 30 inches and 50 inches (not included, so we need to use the symbols > and <)

So, if we define h as the height, then h must be larger than 30 inches, so we can wrte:

h > 30 in

And h must be smaller than 50 inches, then:

h < 50 in.

If we write these two inequalities as one, we get:

30in < h < 50 in.

That is the inequality to determine if a child's height satisfies the regulation.

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The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.

The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:

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Answer:

option 4 and option 3

Step-by-step explanation:

(3)

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](x^{\frac{3}{2}) } ^{6}[/tex]

= [tex]x^{\frac{3}{2}(6) }[/tex]

= [tex]x^{9}[/tex]

(4)

using the rule of exponents/ radicals

[tex]x^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{x^m}[/tex] , then

7[tex]x^{\frac{2}{3} }[/tex]

= 7 × [tex]\sqrt[3]{x^2}[/tex]

= 7 [tex]\sqrt[3]{x^2}[/tex]

Answer: ab = 3a + 2b + c subtract 3a from both sides. ab - 3a = 2b + c factor the left side. a (b - 3) = 2b + c divide both sides by ( b - 3).

sorry but only one for then second screenshot :/

Hope this helps! :)

When the cool rock that is rolling down the side of the volcano is compared to the mass of hot lava that is slowly flowing, the rock has 2. less thermal energy and more mechanical energy.

The mechanical energy that an object has refers to the combination of kinetic and potential energy. The rock will have more mechanical energy than the hot lava as it is moving faster.

Thermal energy on the other hand refers to how much heat/ energy is in an object. The rock is cool as opposed to the hot lava which would have more thermal energy as a result of its heat.

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Based on theword problem, the inequality of the word problem is 7/2 + 4h >=  1

Inequalities are used to represent expressions that do not have equal values i.e. unequal expression

The word problem is given as

Half of 7 added to product of h and 4 is at least 1

At least 1 means greater than or equal to 1

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to product of h and 4 >=  1

The product of h and 4 means 4h

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to 4h >=  1

Half of 7 means 7/2

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 added to 4h >=  1

added to means +

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 + 4h >=  1

Hence, the inequality of the word problem is 7/2 + 4h >=  1

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Answer:

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

Step-by-step explanation:

[tex]1. \: y + 2 = 2x \\ 2. \: \frac{y + 2}{2} = x \\ 3. \: 1 + \frac{y}{2} = x \\ 4. \: x = 1 + \frac{y}{2} \\ \\ \\ 1. \: x = 4 - y \: or \: y = 4 - x[/tex]

The equation that best fits all the points on the graph is y = -2x + 3.

The line of best fit is a line that can be drawn to connect most of the points on the graph. In other words, it best fits the points.

Using a linear regression tool, input the coordinates that are on the graph including:

(-4, 10) (-2, 8) (-1, 5) (1, 3) (2, 0) (2, -3)

The formula you get for line of best fit would be:

y = -2.08564x + 3.01259

Rounding up gives:

y = -2x + 3

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It should be noted that the value of angle B in thee complementary angle is 60°.

It should be noted that the total angles on a complementary angle is illustrated as 90°.

Therefore, based on the information given, it should be noted that we will add the equation and equate them to 90°.

This will be:

5x + 8 + 6x + 4 = 90°

11x + 12 = 90°

11x = 90° + 12°

11x = 102°

Divide

x = 102° / 11

x = 9.27

Therefore the value of angle B will be:

= 6x + 4

= 6(9.27) + 4

= 55.6 + 4

= 59.6°

= 60° approximately

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Answer:

C. 40 times greater is the distance of Pluto from the Sun than the distance of Venus from the sun.

Answer: 1.29

Step-by-step explanation: 2/5 = 0.4.

1/9 = 0.1111...

So, 3-2 = 1.

0.4-0.1111 = .28888889 (its repeating so you are going to have a rounded number)

3-2= 1 --- .4 - .1111 = 2.8888889

= 1.288889 (The 8's are not exact as they keep repeating)

Round up to 1.29 and it will be correct.

Hope this helped:)

she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.

We are given that:

Jocelyn received 25 reward points just for signing up.

She earns 12.5 points for each visit that she makes to the movie theatre.

The free movie ticket is available when she has 170 points with her.

Points to be collected more for a free movie ticket will be:

Points = 170 points - 25 points = 145 points.

So, the number of visits she has to make to the movie theatre will be calculated with the help of division.

Number of visits = 145 points / 12.5 points

Number of visits = 11.6 visits that is 12 visits.

Therefore, she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.

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Answer:

m + n + p = a

Step-by-step explanation:

m - a = n- p

M = a - n - p

M + n = a - p

M + n + p = a

Answer:

$12.5xy

Step-by-step explanation:

y = how much the jobs pays

x = hours of work

25/2

= 12.5xy

The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given the trigonometry identity;

d=94 secθ.

If the object is sighted at an angle of  25°, then;

d=94 sec25

d = 94 × 1/cos25

d = 94 × 1.1033

d = 103.71feet

If the object is sighted at an angle of  55°, then;

d=94 sec55

d = 94 × 1/cos55

d = 94 × 1.7434

d = 163.88feet

Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

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