State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Similar solids have exactly the same shape, but not necessarily the same size.

Answer: 3 ft

Step-by-step explanation:

l=length. w=width. h=height. V=volume

V=l*w*h

24=4*w*2

24=8*w

8w=24

w=3 ft

Answer:

561

Step-by-step explanation:

168/3=56 (10 percent of armandos pull ups)

56 x 10 = 560 (100 percent of armandos pull ups)

Now it is equal. We are looking for greater than armando. You would need 561 pull ups to have more

The interval using two different representations are (-∝, 11) ∪ (0, ∝) and {x | x < −11 or x > 0}

The interval is given as

x < −11 or x > 0

Inequalities like < and > are represented using the parenthesis ( and )

Also, the term "or" mean union and it is represented using ∪

So, one representation of the interval can be represented as

(-∝, 11) ∪ (0, ∝)

Another representation of the interval is {x | x < −11 or x > 0}

Hence, the interval using two different representations are (-∝, 11) ∪ (0, ∝) and {x | x < −11 or x > 0}

Read more about inequalities at

https://brainly.com/question/25275758

#SPJ1

The solution to the logarithmic equation is - 10 / 3.

Logarithms are examples of trascendent functions, that is, function that cannot be described in algebraic terms. Herein we must take advantage of logarithm properties to solve for x in the expression given. The complete procedure is shown below:

㏒₃ (3 · x - 2) - ㏒₃ (x + 2) = 2                        Given

㏒₃ [(3 · x - 2) / (x + 2)] = 2                             Logarithm of a division of functions

(3 · x - 2) / (x + 2) = 3²                                    Definitions of power and logarithm

(3 · x - 2) / (x + 2) = 9                                      Definition of power

3 · x - 2 = 9 · (x + 2)                                        Definition of division / Compatibility with multiplication / Existence of the multiplicative inverse / Associative and modulative properties

3 · x - 2 = 9 · x + 18                                         Distributive property

- 20 = 6 · x                                                       Compatibility with addition / Existence of the additive inverse / Associative, commutative and modulative properties

6 · x = - 20                                                       Symmetric property

x = - 20 / 6                                                       Definition of division / Compatibility of multiplication / Existence of the multiplicative inverse / Associative, commutative and modulative properties

x = - 10 / 3                                                        Simplification of fractions / Result

To learn more on logarithmic properties: https://brainly.com/question/12049968

#SPJ1

The ratio of trick-or-treaters who were not dressed as snow white last Halloween is 5/9

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two or more ratios.

example: a : b = c : d

If four out of every nine trick-or-treaters that came to your house last Halloween were dressed as snow white, then the rest were not dressed as snow white.

9 - 4 = 5

If five out every nine trick-or-treaters that came to your house last Halloween were not dressed as snow white, we can express the ratio as

5 out of 9 or 5 : 9 or 5/9

To know more about ratio, visit brainly.com/question/13513438.

#SPJ4

Answer: 1st option

Step-by-step explanation:

Black to Red is the transformation

C to C'

I to I'

Q to Q'

G to G'

1st, graph is moved up by 1 unit(+1 in x direction)

Then, graph is moved to right by 5 units(+5 in y direction)

(1, 5) is the change ==> 1st option

A geometric series exist as the totality of an infinite number of terms that contain a constant ratio between consecutive terms.

The sum of the infinite series is 1/4.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Given: a(first term) = 1/3

r(common  ratio) = a2/a1

= (-1/9)/(1/3) = -1/3

Since | r | ∠ 1, the infinite series converges.  

The sum of infinite geometric series is:

S∞ = a/(1 - r); -1 ∠ r ∠1

S∞ = (1/3) / (1+(1/3)) = 1/4

The sum of the infinite series is 1/4.

To learn more about infinite geometric series, refer to:

https://brainly.com/question/27350852

#SPJ4

Answer:

Hello,

Step-by-step explanation:

Do you remember the formula

[tex]\boxed{a^3-b^3=(a-b)(a^2+ab+b^2)}\\\\\\27x^6y^9-64=(3x^2y^3)^3-4^3\\\\=(3x^2y^3-4)((3x^2y^3)^2+(3x^2y^3*4)+4^2)\\\\\\=(3x^2y^3-4)(9x^4y^6+12x^2y^3+16)\\[/tex]

cot(55°) = 0.70021 ... cot(58°) = 0.62487 ... cot(77°) = 0.23087 ... cot(80°) = 0.17633

(1+cot55)(1+cot80)(1+cot77)(1+cot58).

In trigonometry, the cot or cotangent is one of the six trigonometric ratios. In a right triangle, the lattice of angles is equal to the ratio of the adjacent and opposite sides of the angle. Cot x is also equal to the reciprocal of tan x.

Therefore, the cotangent of the angle α of a right triangle is equal to the length of the adjacent side b divided by the opposite side a. To remove the crib, simply enter the length of the adjacent and opposite sides, then remove it. This formula can be very similar to the formula used to calculate the tangent.

Learn more about cot at

https://brainly.com/question/25472035

#SPJ9

Answer:

B.  -2  <  x  <  4

Step-by-step explanation:

The function is (x +2)/(x-4) and we are asked to determine the x interval when the inequality (x +2)/(x-4) < 0 is satisfied

1. Find the critical points

The critical points are

x = - 2 when the numerator becomes -2 + 2 = 0, and f(x) = 0

and

x = 4 when the denominator becomes 4 - 4 = 0 and (x + 2)/0 is undefined

So critical points are -2 and 4

2. Use these critical points to divide the number line into intervals
The intervals are -∞ < x < -2, -2 < x < 4 and 4 < x < ∞
these can be re-written as x < -2, -2 < x < -4 and x > 4

3. For each  of these intervals take a test point and see if it satisfies that inequality
(a) -∞ < x < -2    Take x = -3 which is less than -2
We get f(-3) =  (-3 + 2)/(-3 -4) = -1/-7 which is + 1/7 and does not satisfy the (x+2)/(x-4) < 0 inequality.

So we can discard this interval
(b) For interval -2 < x < 4, Let's take x = 0
(0+2)/(0-4) = 2/(-4) = -1/2 = -0.5 which does satisfy the inequality
(x+2)/(x-4) <0, so this is a valid interval

(c) For interval x > 4, take x = 5
(x+2)/(x-4 ) = (5 + 2)/(5-4) = 7/1 = 7 and does not satisfy (x+2)/(x-4 ) < 0

So the interval which satisfies the inequality is -2 < x < 4

Answer:

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

Reason:

In the first graph, it is possible to draw a single vertical line through more than one point on the blue graph. For instance, draw a vertical line through 1 on the x axis.

Because this happens, we consider the graph to "fail the vertical line test". This leads to the graph not being a function.

A function is only possible if any input in the domain leads to exactly one and only one output.

The input x = 1 leads to multiple outputs y = 3 and y = -3 simultaneously.

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

On the other hand, the second graph doesn't have this issue happening. It's impossible to draw a single vertical line through more than one point on the blue graph.

Therefore, this graph passes the vertical line test and it is a function. Whatever x input you pick, it leads to one y output only.

Answer:

100 m/s

Step-by-step explanation:

divide by 3.6 to get km/h to m/s, multiply by 3.6 to get m/s to km/h!

By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

Given,

The algebraic expression = 7b-(3a-8b)

Expand the expression

7b-(3a-8b)= 7b-3a+8b

Rearrange the terms and combine like terms

7b-3a+8b= -3a+7b+8b

=-3a+(7+8)b

=-3a+15b

Hence, By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

Learn more about algebraic expression here

brainly.com/question/19245500

#SPJ4

                         Expression                               Property used

Step 1   1 x 3/2 x (-5) x 3 x (-4)        Inverse Property of Multiplication

Step 2  1 x (-4) x 3/2 x (-5) x 3        Associative Property of Multiplication

Step 3  1 x [ (-4) x 3/2 ] x (-5) x 3  Commutative Property of Multiplication

Step 4  1 x [-6] x (-5) x 3                Identity Property of Multiplication

Step 5  -6 x (-5) x 3

The inverse property of multiplication refers to multiplying a number with it's reciprocal. This is applied while transforming from division to multiplication as division is the inverse of multiplication.

Associative property of multiplication is applied while multiplying several values, Hence rearranging the terms will still give same answer.

This property has it that the order of the multiplication do not matter, hence multiplication can start with any order.

This property refers to multiplication of a value with one, such multiplication usually return same value as the product.

Read more on properties of multiplication here: https://brainly.com/question/23843546

#SPJ1

The estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

It follows from the task content that the estimated thickness of paper such that it is written using a single digit and a power of 10 as required in the task content is to be determined.

Given;

Thickness of sheet = 0.0013.

By rounding to one significant digit; the digit is considered and rounded down to zero which is added to 1 so that we have;

= 0.001.

On this note, since the number, 0.001 can be written via the laws of indices as;

= (1/1000)

= 1/10³

And ultimately, we have

= 1 × 10-³.

Ultimately, the estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

Read more on rounding off;

https://brainly.com/question/26754942

#SPJ1

Determine whether each infinite geometric series diverges or converges.The series converges.

If the series converges, state the sum. 1-1+1- . . . .

The sum of the infinite series is 1/2

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=1\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{-1}{1}=-1[/tex]

Since  [tex]\vert r\vert < 1[/tex] , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{1}{1+1} =\frac{1}{2}[/tex]

The sum of the infinite series is 1/2

What is an infinite geometric series?

To learn more about infinite geometric series, refer:

brainly.com/question/27350852

#SPJ4

Answer:

perimeter=4l then multiply with how many square are there

then area = l²

multiple with how many square are there

Answer:

Q= ( -4 -9)

Step-by-step explanation:

Using the midpoint formula

X1 + X2 Y1 + Y1

----------, ---------

2. 2

The midpoint QR = (2, -5) and R = (-8, 1) Q =>(x, y)

= x + 8. y - 1

------------ = 2 and -------- = -5

2 2

=> (4 = x + 8) and( -10= y-1)

=> 4 -8 = x and -10+1= y

Q(x, y) = (-4, -9)

Answer: x = 5, 7

Step-by-step explanation:

       This equation is already factored for us, so we can split it into two separate equations set equal to 0 and solve for x.

Given:

(x - 7)(x - 5) = 0

Equation #1:

x - 7 = 0

x = 7

Equation #2:

x - 5 = 0

x = 5

Solution:

x = 5, 7

Answer:

x = 5, x = 7

Step-by-step explanation:

(x - 7)(x - 5) = 0 ← in standard factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x - 5 = 0 ⇒ x = 5

The 32th term of the arithmetic sequence AP is found to be -146.

An arithmetic progression (AP) is a succession in which each successive term has the same distinctions.

Now, to answer the question;

The given sequence of the numbers is-

9,4,-1,-6,-11, ...........

There are total 32 terms in the series for which we have to find 32nd number.

Let the first term be 'a₁' = 9.

Let the second term be 'a₂' = 4

Let the third term be 'a₃' = -1.

The common difference of between the two consecutive terms is equal of an AP is 'd'.

d = a₂ - a₁  

Substitute the values in the above equation;

d = 4 - 9

d = -5

Now, the 32th term is calculated by the nth term formula;

Now, substitute all the value in the formula,

a₃₂ = a + (n - 1) d

a₃₂ = 9 + (32 - 1)(-5)

a₃₂ = 9 - 160 + 5

a₃₂ = -146.

Therefore, the 32nd term of the arithmetic sequence is estimated as -146.

To know more about the arithmetic sequence, here

brainly.com/question/6561461

#SPJ4

ΔPRQ ≅ ΔTRS under both (side-side-side) SSS condition and (angle-side-angle) ASA condition.

So,

Given: ∠P ≅ ∠T, ∠S ≅ ∠Q, TR ≅ PR, RP ≅ RQ, RT ≅ RS, PQ ≅ TS

To Prove: Δ PRQ ≅ ΔTRS

So, ΔPRQ ≅ ΔTRS under both SSS condition and ASA condition.

Therefore, ΔPRQ ≅ ΔTRS under both SSS condition and ASA condition.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

#SPJ4

The value for x = -2,0,1 and 4 is -5,1,4,13 respectively.

To "solve for x" is to determine the value of x that would result in the equation being true. Think about the following equation: x plus 1 = 3. You would have to figure out a value for x such that it produces three when one is added in order to try to solve it.

For x = -2,

3x+1

= 3(-2)+1

= -6 +1

= -5

For x = 0

3x+1

= 3(0) + 1

= 1

For x = 1

3x+1

= 3(1) + 1

= 4

For x = 4

3x+1

= 3(4) + 1

= 13

To learn more about solving for x from given link

https://brainly.com/question/27990748

#SPJ4

Based on the scale of the drawing, and the actual width, the width of a park in a drawing would be 14 inches.

A single inch of the width of a park in a drawing, is 5 yards of the width of the actual park.

This means that a single inch equates to 5 yards.

If there were therefore 70 yards in the actual park, the width of the drawing is:
= 70 / 5

= 14 inches

Find out more on scale drawings at https://brainly.com/question/25324744

#SPJ1

Option D is the correct answer.

Triangle Inequality Theorem states that the sum of two side lengths of a triangle is always greater than the third side.

If this is true for all three combinations of three combinations of side lengths.

i.e., a + b > c , b + c > a and c + a > b then the length form a triangle.

(A) 10 + 11 = 21 > 20

And 11 + 20 =31 > 10

And, 20 + 10 = 30 > 11

So, it forms a triangle

(B) 14 + 16 = 30 >28

And 16 + 28 = 44 >14

And 28 + 14 = 42 > 16

So, it forms a triangle

(C) 35 + 45 = 80 > 75

And 45 + 75 = 120 > 35

And 75 + 35 = 110 > 45

So, it forms a triangle

(D) 41 + 55 = 96 < 98

It does not form a triangle

because sum of two sides lengths is less than the third side length.

Hence, Option D is the correct answer

Learn more about Sides of triangle at:

https://brainly.com/question/19124013

#SPJ4

Answer:

2(x + 6) = 38

Step-by-step explanation:

First, we choose a variable to represent the unknown number.

1. Let x = the unknown number.

Then, we translate the sentence into an equation using the variable we chose.

"Twice the sum of six and a number is 38."

We do it piece by piece:

"the sum of six and a number":                        x + 6

"Twice the sum of six and a number":              2(x + 6)

"Twice the sum of six and a number is 38.":    2(x + 6) = 38

Now we have an equation that represents the sentence.

2(x + 6) = 38

The direct variation equation between x and y is 4x = y.

Here, we are given that x and y are in direct variation. In other words, this means that x and y are directly proportional to each other.

Thus, if k is a constant term, then the relation between x and y can be represented as-

x = ky

Now, we are given that if y = 12, x = 3

⇒ 3 = 12k

12k = 3

k= 3/12

k= 1/4

Thus, we found the value of k, the relation will become-

x = y/4

or 4x = y

Thus, the direct variation equation between x and y is 4x = y.

Learn more about proportionality here-

brainly.com/question/24868934

#SPJ9

Answer:

Step-by-step explanation:

58 + 66(x-1) + 50 = 1428cents

66(x-1) + 108 = 1428

66(x-1) =1320

x-1 = 20

x = 21 mins

The local grocery store mixed 13 oz of planters mixed nuts with 19.5 oz of emerald mixed nuts to get 32.5 oz bags of mixed nuts that contain 56% peanuts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of planters mixed nuts and y represent the amount of emerald mixed nuts, hence:

x + y = 32.5   (1)

Also:

0.5x + 0.6y = 0.56(32.5)       (2)

From both equations:

x = 13, y = 19.5

The local grocery store mixed 13 oz of planters mixed nuts with 19.5 oz of emerald mixed nuts to get 32.5 oz bags of mixed nuts that contain 56% peanuts.

Find more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

I want to say False.

Step-by-step explanation:

I would think that the opposite of 4 would be -4.

Good luck! :)

Answer:

True

Step-by-step explanation:

4 = 4/1 1/4 is the reciprocal or the opposite of 4