Practice writing and evaluating powers.AssignmentUse the expression to complete the statements.(0.5)10(0.5)10 is the(0.5) is theof (0.5)1010 is the✔ of (0.5) 10A power is another way to writeThe choices for 1,2 and 3 are:BaseExponent PowerThe choices for the last one are: Repeated addition,repeated division,repeated multiplication,repeated subtraction

Based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

To determine the distance between Houston, TX and Dallas, TX using the given scale, we can set up a proportion using the distances on the map and the actual distances.

Let's denote the distance between Houston and Dallas as "x" (in miles).

According to the scale provided, 2.3 centimeters on the map represents a distance of 348 miles. This can be expressed as:

2.3 cm / 348 miles = 1.6 cm / x miles

To find the value of "x," we can cross-multiply and solve the equation:

(2.3 cm) * (x miles) = (1.6 cm) * (348 miles)

2.3x = 556.8

Divide both sides by 2.3 to isolate "x":

x = 556.8 / 2.3

x ≈ 242.0869565

Therefore, based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

Please note that this is an approximation based on the given scale and the assumption that the scale is linear and consistent throughout the map. Actual distances may vary and should be verified using more accurate measurements or reliable sources.

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Answer:

9 kilograms

Step-by-step explanation:

The amount more in income tax that Cho pays than Helen each month would be £56.

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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The number of hamburgers sold on Saturday is 108

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Given that:

1. The combined total of hamburgers and cheeseburgers is 432.

2. The number of cheeseburgers sold was three times the number of hamburgers sold

Let h and c represent hamburgers and cheeseburgers respectively

1st sentence can be written as:

h + c = 432   .... (1)

2nd sentence can be written as:

c = 3h   .... (2)

Substitute (2) into (1):

h + 3h = 432

4h = 432

h = 432/4 = 108

Therefore, 108 hamburgers were sold on Saturday

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

the answer is d=g³/(H+4M)

Step-by-step explanation:

Hd+4Md=g³

d(H+4M)=g³

divide both sides by (H+4M)

d=g³/(H+4M)

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Given:

Formula:

so :

The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

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Answer:

∠BCA = 59

x = 2

∠B = 83

Step-by-step explanation:

Properties of a parallelogram:

Opposite angles are congruent

Opposite side lengths are congruent

That being said lets find x, ∠B and ∠BCA

First x

Segment AD and segment CD are parallels which are congruent

Knowing that we create an equation

6x = 12

step 1: Divide each side by 6

6x/6=x

12/6=2

we're left with x = 2

For ∠B

∠D and ∠B are opposite angles of a parallelogram

meaning that ∠D≅∠B

So if ∠D=83 then ∠B also = 83

For ∠BCA

∠BCA and ∠DAC happen to be opposite angles ( like stated previously opposite angles are congruent.)

Because ∠DAC = 59 ∠BCA also = 59

Answer:

the father is 45 and the son is 15

Answer:

$153

Step-by-step explanation:

323/17=19

19x7=153

The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

50°

Step-by-step explanation:

90-40= 50° ............

Answer:

Terms: \(10x^2, -y, 12\ and\ -3x^2\)

Like Terms: \(10x^2\ and\ -3x^2\)

Step-by-step explanation:

Given

\(10x^2 - y + 12 - 3x^2\)

Required

List out the terms and like terms

The terms of a mathematical expression:

\(a + b - c + d\) are a, b, c and d

Using the same yardstick as above;

The terms of \(10x^2 - y + 12 - 3x^2\) are

\(10x^2, -y, 12\ and\ -3x^2\)

To get the like terms, we look for terms with the same variable

\(10x^2\ and\ -3x^2\) have the same variable of x^2

Hence, they are like terms

Answer:

A = 50 + 0.02x

Step-by-step explanation:

Let the fixed amount be m

Let the charge for each cubic ft used be c

Let the amount of cubic ft of water used be x.

Let the total cost per month be A

Now, for the first household, they used 1500 cubic feet in a month and were billed $80.

This means, x = 1500 ft³ and A = $80

Since, we are told they are charged a fixed amount plus a fee per cubic ft consumed. We can say that;

m + cx = A

Thus,

m + 1500c = 80 - - - - (eq1)

For 2nd household:

They used 2100 cubic feet was billed $92.

Thus;

m + 2100c = 92 - - - - (eq 2)

Let's subtract eq1 from eq 2 to get;

2100c - 1500c = 92 - 80

600c = 12

c = 12/600

c = 0.02

Putting 0.02 for C in eq1 gives;

m + 1500(0.02) = 80

m + 30 = 80

m = 80 - 30

m = 50

From m + cx = A, we can say that;

50 + 0.02x = A

The algebraic expression "difference of 4 and a number" where the number is letter x is represented as 4 - x.

Algebra is an elementary branch of mathematics that deals with the numbers and the basic mathematics operations of addition, subtraction, division and multiplication. Algebraic expression involves arithmetic where the use of unknown quantities along with numbers.

From the question, we have the mathematical statement "difference of 4 and a number" and the number is "a number" is represented with the letter x.

the word difference in mathematics implies Subtraction (-)

Therefore, the mathematical statement "difference of 4 and a number" is represented as 4 - x.

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Answer:

The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.

Step-by-step explanation:

If the meat should be no more than two days old on average when used, the stock of hamburguer in the refrigerator has to be at most the equivalent to 2 day of sales.

The "2 days old" represents the inventory turnover.

If we use all the hamburguers in the refrigerator and refill inmediatly, the average inventory is:

\(\bar I=\dfrac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\\\\\\bar I=\dfrac{2*3,500+0}{2}=3,500\)

The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.

Answer:

Angle 145 degrees

Step-by-step explanation:

Hope it can help you lovelots

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▹ Answer

x₁ = -5

x₂ = 7

▹ Step-by-Step Explanation

x² - 2x - 35 = 0

x² + 5x - 7x - 35 = 0

x(x + 5) - 7x - 35 = 0

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

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

x + 5 = 0 → 0 - 5 = -5

x - 7 = 0 → 0 + 7 = 7

x₁ = -5

x₂ = 7

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

Step-by-step explanation:

\( {x}^{2} - 2x - 35 = 0\)

Write -2x as a difference

\( {x}^{2} + 5x - 7x - 35 = 0\)

Factor out X from the expression

\(x(x + 5) - 7x - 35 = 0\)

Factor out -7 from the expression

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

Factor out x+5 from the expression

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

When the product of factors equals to 0, at least one factor is 0

\(x + 5 = 0\)

\(x - 7 = 0\)

Either,

\(x + 5 = 0\)

\(x = 0 - 5\)

\(x = - 5\)

Or,

\(x - 7 = 0\)

\(x = 0 + 7\)

\(x = 7\)

Hope this helps...

Best regards!!

Answer:

7

Step-by-step explanation:

7

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of a/b  

where a and b are integers.

Irrational numbers are those real numbers which are not rational numbers.

Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

A composite number is a number divisible by another number than 1 and the number itself.

To find example, a sum of two composite numbers, which is not a composite number, is needed.

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.

Hence so the correct option is D.

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Answer:

\( \rm \displaystyle y' = 2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} \)

Step-by-step explanation:

we would like to figure out the differential coefficient of \(e^{2x}(1+\ln(x))\)

remember that,

the differential coefficient of a function y is what is now called its derivative y', therefore let,

\( \displaystyle y = {e}^{2x} \cdot (1 + \ln(x) )\)

to do so distribute:

\( \displaystyle y = {e}^{2x} + \ln(x) \cdot {e}^{2x} \)

take derivative in both sides which yields:

\( \displaystyle y' = \frac{d}{dx} ( {e}^{2x} + \ln(x) \cdot {e}^{2x} )\)

by sum derivation rule we acquire:

\( \rm \displaystyle y' = \frac{d}{dx} {e}^{2x} + \frac{d}{dx} \ln(x) \cdot {e}^{2x} \)

Part-A: differentiating $e^{2x}$

\( \displaystyle \frac{d}{dx} {e}^{2x} \)

the rule of composite function derivation is given by:

\( \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)\)

so let g(x) [2x] be u and transform it:

\( \displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x\)

differentiate:

\( \displaystyle {e}^{u} \cdot 2\)

substitute back:

\( \displaystyle \boxed{2{e}^{2x} }\)

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

\( \displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)\)

let

substitute

\( \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \frac{d}{dx}( \ln(x) ) {e}^{2x} + \ln(x) \frac{d}{dx} {e}^{2x} \)

differentiate:

\( \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }\)

Final part:

substitute what we got:

\( \rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }\)

and we're done!

Answer:

Product Rule for Differentiation

\(\textsf{If }y=uv\)

\(\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v\dfrac{du}{dx}\)

Given equation:

\(y=e^{2x}(1+\ln x)\)

Define the variables:

\(\textsf{Let }u=e^{2x} \implies \dfrac{du}{dx}=2e^{2x}\)

\(\textsf{Let }v=1+\ln x \implies \dfrac{dv}{dx}=\dfrac{1}{x}\)

Therefore:

\(\begin{aligned}\dfrac{dy}{dx} & =u\dfrac{dv}{dx}+v\dfrac{du}{dx}\\\\\implies \dfrac{dy}{dx} & =e^{2x} \cdot \dfrac{1}{x}+(1+\ln x) \cdot 2e^{2x}\\\\& = \dfrac{e^{2x}}{x}+2e^{2x}(1+\ln x)\\\\ & = \dfrac{e^{2x}}{x}+2e^{2x}+2e^{2x} \ln x\\\\& = e^{2x}\left(\dfrac{1}{x}+2+2 \ln x \right)\end{aligned}\)

Answer:

The total number of apples is 550

Step-by-step explanation:

12% - Turn into a fraction of 12/100

12/100

X = total number of apples

*Make another fraction of x the denominator and the 66 that are in good condition as the numerator*

12/100 = 66/X

Cross multiply

12 * X = 12x

66 * 100 = 6600

Divide

6600/12 = 12x/12 - cancel

6600/12= 550

X = 550