Use what you know about the properties of operations to rewrite the expression.

3(5-2)=

. 0.587 in scientific notation is 5.87 x 10^-1.

Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.

For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.

Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.

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We can say that the new area is given by 1600 square feet and the garden gets enlarged by 400 square feet.

The rectangular garden is 60 feet long and 20 feet wide.

To enlarge the garden while using the same fence, its shape is changed to a square.

The area of the rectangular garden is given by;

A = l × w

Where;

l = 60 feet

w = 20 feet

A = 60 × 20 = 1200 square feet.

To find the new area of the garden when it's changed to a square, we need to determine the length of one side of the square.

Since the square is formed by using the same fence that enclosed the rectangular garden, the perimeter of the square should be equal to the perimeter of the rectangular garden. Therefore;

Perimeter of rectangle = 2(l + w)

= 2(60 + 20)

= 2(80)

= 160 feet.

Perimeter of square = 160 feet.

Let s be the length of one side of the square. Then;

Perimeter of square = 4s

= 160 feet.

Divide both sides by 4;

4s/4 = 160/4

s = 40 feet.

New area of the garden is given by;

A = s²

= (40)²

= 1600 square feet.

The new area is 1600 square feet.

The garden enlarges by 1600 - 1200 = 400 square feet.

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a. The simple interest for 4 years would be $960.

b. The amount at the end of the 4 years would be $2160.$

A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.

a. For calculating simple interest for the 4 years

We have been given data as:

Principal (P) = $1200

Rate of Interest (R) = 20%

Time (T) = 4 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

The simple interest for 4 years would be:

⇒ 1200 x 20% x 4 = 960

b. For calculating the amount at the end of the 4 years

The amount at the end of the 4 years would be:

1200 + 960 = 2160

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The inverse of (a) is If she did not go to the party, then she will not finish her homework.

The inverse of (b) is If he did not finish the race, then he will not have trained for the race.

The inverse of (c) is If she has no side effects then the patient will not take the medicine.

The converse of (a) is if she finished her homework, then she went to the party.

The converse of (b) is if he trained for the race, then he finished the race.

The converse of (c) is if the patient took the medicine, then she had side effects.

The contrapositive of (a) is if she did not finish her homework, then she did not go to the party.

The contrapositive of (b) is if he did not train for the race, then he will not finish the race.

The contrapositive of (c) is if the patient did not take the medicine, then she will not have side effects.

Converse: By swapping the hypothesis and the conclusion, a statement can be made to mean the converse. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel."

Inverse: Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."

Contrapositive: a statement or theorem created by swapping out the hypothesis and conclusion, or the subject and predicate, of a given statement or theorem. The opposite of "if A then B" is "if not-B then not-A."

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Answer:

1) Find the equation of the line that is parallel to the line y = 3x - 4 and

passes through the point (-4, 6).*

O y = 3X-8

y=3x + 18

y = (1/3) x + 18

Option 4

y = 3x-18

Answer

-11/3>x>7/3

Step-by-step explanation:

|3*7/3+2|=9

|7+2|=9

|9|=9

9=9

therefore, x must be > 7/3

|3*-11/3+2|=9

|-11+2|=9

|-9|=9

9=9

therefore, x must be < -11/3

The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).

Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.

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Answer:

\(x=\sqrt{48}\)

Step-by-step explanation:

h^2=8^2-(8/2)^2

h^2=64-4^2

h^2=64-16

h^2=48

Square root both sides

\(h=\sqrt{48}\)

Hopes this helps please mark brainliest

There is only one possible outcome where the first card is odd and the second card is even: {3,2}.

We are dealing with a shuffled deck of three cards: 2, 3, and 4. There are three possible outcomes when dealing one card, and two possible outcomes when dealing the second card (since one card has already been dealt). Therefore, there are a total of 3x2=6 possible outcomes when dealing two cards, and 3x2x1=6 possible outcomes when dealing all three cards.

(a) What is P(E2 | E1), the probability the second card is even given that the first card is even?

There are two ways the first card can be even: 2 or 4. If the first card is 2, there are two possible outcomes for the second card: 3 or 4. If the first card is 4, there is only one possible outcome for the second card: 2. Therefore, there are three possible outcomes where the first card is even and the second card is even: {2,3}, {2,4}, and {4,2}. The probability of the second card being even given that the first card is even is therefore:

P(E2 | E1) = number of outcomes where E1 and E2 occur / number of outcomes where E1 occurs

P(E2 | E1) = 2 / 3

(b) What is the conditional probability that the first two cards are even given that the third card is even?

There is only one way the third card can be even: 2. If the third card is 2, there are two possible outcomes for the first card: 2 or 4. If the third card is 2 and the first card is 2, there is only one possible outcome for the second card: 4. If the third card is 2 and the first card is 4, there are two possible outcomes for the second card: 2 or 3. Therefore, there are three possible outcomes where the third card is even and the first two cards are even: {2,4,2}, {2,2,4}, and {4,2,4}. The probability that the first two cards are even given that the third card is even is therefore:

P(E1E2 | E3) = number of outcomes where E1 and E2 and E3 occur / number of outcomes where E3 occurs

P(E1E2 | E3) = 3 / 6 = 0.5

(c) Let Oi represent the event that the ith card dealt is odd numbered. What is P(E2 | O1), the conditional probability that the second card is even given that the first card is odd?

If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. The probability that the second card is even given that the first card is odd is therefore:

P(E2 | O1) = number of outcomes where O1 and E2 occur / number of outcomes where O1 occurs

P(E2 | O1) = 1 / 3

(d) What is the conditional probability that the second card is odd given that the first card is odd?

If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. Therefore, the conditional probability that the second.

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The slopes of lines DE and BC are the same, proving that the lines are parallel.

Parallel lines have an equal slope. The slope of parallel lines is equal because they are all equally inclined with respect to the positive x-axis. If m1 and m2 are the slopes of two parallel lines, then m1 = m2 is the result.

Given:

coordinates of A = (4, 6)

coordinates of B = (2,-2)

coordinates of C = (-2,-4)

Now we calculate the midpoints of AB and AC

the midpoint of AB:

x = ( x₁ + x₂) / 2

  = ( 4 + 2 ) / 2

  = 3

y =  ( y₁ + y₂) / 2

  = ( 6 - 2 ) / 2

  = 2

The coordinates of D are (3,2).

the midpoint of AC:

x = ( x₁ + x₂) / 2

  = ( 4 - 2 ) / 2

  = 1

y =  ( y₁ + y₂) / 2

  = ( 6 - 4 ) / 2

  = 1

The coordinates of E are (1, 1).

To prove lines DE and BC are parallel,

Slope of CB = y₂ - y₁ / x₂ - x₁

                   = 2 - (-4) / 2 - (-2)

                  = -2 + 4/ 2 + 2

                  = 2/4

                 = 1/2

Slope of ED = y₂ - y₁ / x₂ - x₁

                   = 2 - 1 / 3 - 1

                   =  1/2

The slopes of lines DE and BC are the same hence the lines are parallel.

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Answer:

6j^2 - 2j = 9

j^2 -(2/6)j = 9/6

j^2 - (2/6)j + 1/36 = 9/6 + 1 /36

(j - 1/6)^2 = 55/36

j - 1/6 = √55/36

j = (√55/36) + 1/6

j = 1.40

Step-by-step explanation:

step 1 transpose 9 and it becomes positive.

step two divide everything by 6 so that j^2 has a coefficient of 1.

step 3 make a perfect square.

Then it's just simple calculations to get the answer

Answer:

The second one is wrong, so select the rest

the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.

In this question we accept two angles is given that is:

two triangles ∠ABD and

In this, an angle is common that is,

AD = AD

AB = CD

∠A is equal = ∠A (which is given)

That is the reason the SAS rule is right.

SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.

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the complete question is:

Which congruency theorem can be used to prove

that ABD =DCA?

a. SAS

b. Not enough information

c. SSS

d. AAS

The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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A function gif g(x)

= f(x + 4) + 8 is a translated version of function f(x) by 4 units in the negative direction of the x-axis (shifted left by 4 units) and the entire graph of function f(x) is shifted 8 units upwards.

The 3 main features of a graph of the function gif g(x)

= f(x + 4) + 8 are: Translation (Shift) in x-axis: The entire graph of f(x) is shifted left or right by a distance of c units. If c is negative, the graph is shifted to the right; if c is positive, it is shifted to the left. Translation (Shift) in y-axis: The entire graph of f(x) is shifted upwards or downwards by a distance of k units. If k is positive, the graph is shifted upwards; if k is negative, it is shifted downwards. Affected Points: Every point on the graph of f(x) is shifted left or right by a distance of c units and up or down by a distance of k units to form the graph of the transformed function g(x).In this particular case, f(x) has been shifted 4 units to the left and then the entire graph has been shifted 8 units up.

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Answer:

67

Step-by-step explanation:

.__. that it

Answer:

4 = 90°

Step-by-step explanation:

If a box is drawn, that means it is 90 degrees exactly.

Angle 4 has that same box drawn, so that means it is 90°

I Hope That This Helps! :)

Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

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Answer:

A.

Step-by-step explanation:

Answer:

I call this angle chasing or angle hunting. The answer is 60°.

Step-by-step explanation:

\(m \: bad = 25 \\ m \: bcd = 70 \: therefore \\ m \: adc \: = 180 - (70 + 25) = 85\)

since ∆ BAD is an isosceles triangle m BDA = m BAD = 25°

\(m \: adc \: - m \: adb = 85 - 25 = 60 \\ x = 60 \: degrees\)

Answer:

The perimeter of square will be 18 units

Step-by-step explanation:

We are given that the coordinates of three vertices of a square A (-2 1/2 , 1 1/2), B (-2 1/2 -3), and C (2,1 1/2 )

When point D is placed on this perimeter.

We have to find the perimeter of the square.

First we have to find the side of square by using the distance formula

Distance formula

\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Coordinates of A=(-5/2,3/2)

Coordinates of B=(-5/2,-3)

Length of side AB=\(\sqrt{(-5/2+5/2)^2+(-3-3/2)^2}\)

Length of side AB=\(\sqrt{0+(-9/2)^2}\)

Length of side AB=9/2 units

Now, the perimeter of square=4 (side)

Using the formula

Perimeter of square=4(9/2)=18 units

The solutions of the equation are x = 15 and x = -20

The equation is given as:

the absolute value quantity two fifths times x plus 1 end quantity minus 7 equals 0

Rewrite the equation properly as:

|2/5x + 1| - 7 = 0

Add 7 to both sides

|2/5x + 1| = 7

Remove the absolute bracket

2/5x + 1 = 7 and 2/5x + 1 = -7

Subtract 1 from both sides

2/5x = 6  and 2/5x = -8

Solve for x

x = 15 and x = -20

Hence, the solutions of the equation are x = 15 and x = -20

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Answer:

B. x = -20 and x = 15

Step-by-step explanation:

Good luck! Hope this helped :)

8 students made 4 mistakes or more

Answer: 330,000

Step-by-step explanation: yes

Answer:

True

Step-by-step explanation:

True

Answer:

It is True

Step-by-step explanation:

If I got you it correct please give me brainliest, and if a right triangle have one acute angle then the other have to have it since it is a right triangle and a right triangle is isosceles. The right angle is the only part the others are acute.

Hope this helps!