A triangle has a base of 4 units and a height of 3 units. Mark draws the triangle again but
doubles the height. How does the area of the triangle change?
The area increases by 3 square units.
The area increases by 6 square units.
The area increases by 12 square units.
The area does not change.

Answer: ASA

Step-by-step explanation:

The center of the sphere is (0, 0, 0) and its radius is √(4/3).

To find the center and radius of the sphere, we need to examine the equation of the sphere, which is given as\(3x^2 + 3y^2 + 3z^2\)+ x + y + z = 4. By comparing this equation with the standard equation of a sphere \((x-a)^2 + (y-b)^2 + (z-c)^2 = r^2\), we can determine the center and radius.

In this case, the coefficients of x, y, and z terms are all 1, which suggests that the sphere is centered at (a, b, c) = (0, 0, 0). This means that the origin, or the point (0, 0, 0), is the center of the sphere.

To find the radius, we can focus on the constant term in the equation. In this case, the constant term is 4. The radius (r) can be calculated using the formula r^2 = constant term / coefficient of the squared terms. In our equation, the coefficient of the squared terms is 3. Thus, the radius squared is 4/3, and the radius itself is the square root of 4/3, which simplifies to approximately 0.816.

In conclusion, the center of the sphere is (0, 0, 0), and the radius is approximately √(4/3) or 0.816.

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Answer:

C, 4.82

Step-by-step explanation:

add the given lengths and subtract it from the total lengths to get 4.82

Answer:

C

Step-by-step explanation:

The slope of the line segment AB will change from -3 to 1/3 after a 270 degree rotation of the line segment

information gotten from the question include

Points A' and B' are the images of points A and B after a 270 rotation

the slope of line segment AB is -3

Rotation is one of the movements that is under transformation it involves a movement about an axis.

With respect to the problem here, the axis of the rotation is the origin of the coordinates

The rotation will lead to formation of an image A'B' which is perpendicular to the preimage

The relationship between two slopes that are perpendicular to each other is

slope of line, m = -1/slope of the perpendicular line, m'

m' = -1/m

m' = -1/3

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Answer:

$352.80

Step-by-step explanation:

First, we need to find the area of the room.

A = L * W

A = 14 * 12

A = 168 ft²

Now, we need to find the cost.

168 ft² * $2.10 per ft² = $352.80

     It will cost $352.80 to carpet the room

Answer:

23. Congruent

24. Not congruent

Step-by-step explanation:

23. KJ and HL:

Since the side lengths are both 4 in, these segments are congruent.

24. EH and FG:

Since the side lengths are different numbers (0.45 cm and 0.5 cm), these segments are not congruent.

Answer:

x1= 100 x2=99.999

Step-by-step explanation:

\(x^{0.5\log _{10}\left(x\right)}=0.01x^2\)

\(0.5\log _{10}\left(x\right)\log _{10}\left(x\right)=\log _{10}\left(0.01\right)+2\log _{10}\left(x\right)\)

u=log(x)

\(0.5uu=\log _{10}\left(0.01\right)+2u\)

\(u=2+\sqrt{1.0E-15},\:u=2-\sqrt{1.0E-15}\)

\(x=10^{2+\sqrt{1.0E-15}},\:x=10^{2-\sqrt{1.0E-15}}\)

The features of the quadratic function are given as follows:

The quadratic function in the context of this problem is given as follows:

y = -0.25x² + 7.

The coefficients of the function are given as follows:

a = -0.25, b = 0, c = 7.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 0/0.5

x = 0.

The x-coordinate of the vertex gives the axis of symmetry of the function.

The y-coordinate of the vertex is given as follows:

y = f(0) = -0.25(0)² + 7 = 7.

As a < 0, y = 7 is the maximum value of the function.

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Answer:

GCF

Step-by-step explanation:

Each row will have the same number of plants.  So we want to know what's the biggest number we can divide 45, 81, and 63 by.  That means we need to find the greatest common factor.  In this case, it's 9.  Each row can have at most 9 seeds.

Answer:

-8x

Step-by-step explanation:

Answer:

2x + 9

Step-by-step explanation:

Monomial has only one term.

The required equation of the line is y = 3x + 2 in slope-intercept form.

To write the equation of a line in slope-intercept form, we need to know the slope of the line and the y-intercept. The slope of a line is defined as the change in y divided by the change in x for two points on the line.

According to the given graph, the required solution would be as:

For the given points (2, 2) and (4, 8),

So, the slope is : m = 8 - 2 / 4 - 2 = 6 / 2 = 3.

With the slope and y-intercept, we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the point (2, 2), the y-coordinate is the y-intercept, so the y-intercept is 2.

So, the equation is y = 3x + 2

Therefore, the required equation of the line is y = 3x + 2 in slope-intercept form.

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Answer:56

Step-by-step explanation:

Let ttt be the initial number of trees.

Hint #22 / 5

MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.

The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.

Hint #33 / 5

Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:

\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790

Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.

Hint #44 / 5

\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}

210(t−5)

210

210(t−5)

​

t−5

t−5+5

t

​

=41790

=

210

41790

​

=199

=199+5

=204

​

​

divide both sides by 210

add 5 to both sides

​

Hint #55 / 5

The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point

MacDonald's farm initially had 204204204 orange trees.

Related content

The true statement is that Jana has completed more than 75%

To determine the fraction of Jana's homework that she has completed, we need to add 1/4 and 2/3.

However, these fractions have different denominators, so we need to find a common denominator first.

A common denominator for 1/4 and 2/3 is 12.

To convert 1/4 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 3:

1/4 = (1 x 3)/(4 x 3) = 3/12

To convert 2/3 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 4:

2/3 = (2 x 4)/(3 x 4) = 8/12

Now we can add the fractions:

1/4 + 2/3 = 3/12 + 8/12 = 11/12

Therefore, Jana has completed 11/12 of her homework.

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The rate of increase of area when the diagonal of the square is 14 m is 4√2x m²/min.

Given, The length of the diagonal of a square is increasing at a rate of 4 m/min.The diagonal length of the square when the area is increasing is 14 m each.
Let the side of the square be 'x' units.Diagonal of the square = √2x
The area of the square = x²
From the above details, we can relate the diagonal and the area of the square in terms of 'x' units.
Diagonal of the square, d = √2x ... (1)
Area of the square, A = x² ... (2)
Now differentiate the equation (1) and (2) with respect to time t.
d/dt (d) = d/dt (√2x)4 = d/dt (√2x) => d/dt (d) = 2(√2) (dx/dt) ... (3)
Differentiating (2) with respect to time t, we get
d/dt (A) = d/dt (x²)=> d/dt
(A) = 2x(dx/dt) ... (4)
From equations (1) and (3), we get:
dx/dt = 4 / (2√2)dx/dt = 2√2 m/min
From equations (2) and (4), we get:
d/dt (A) = 2x(dx/dt)
d/dt (A) = 2(x) (2√2)
d/dt (A) = 4√2x
The area of the square is increasing at a rate of 4√2x m²/min when the diagonal length is 14 m each.

So, the rate of increase of area when the diagonal of the square is 14 m is 4√2x m²/min.

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To find the probability that the first ticket drawn is a 1, we need to consider the total number of tickets and the number of 1s in the box.

There are a total of 8 tickets in the box. Among them, there are 3 tickets with a value of 1.

When the first ticket is drawn, there are 8 possible outcomes. Out of these, 3 outcomes will result in drawing a ticket with a value of 1 (as there are 3 tickets with a value of 1).

Therefore, the probability of drawing a 1 as the first ticket is 3/8 or 0.375. This means that there is a 37.5% chance of drawing a 1 as the first ticket.

The probability is calculated by dividing the number of favorable outcomes (drawing a 1) by the total number of possible outcomes (drawing any ticket from the box).

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Answer:

4x-10

Step-by-step explanation:

The product of four and a number is the "4x"

Then the ten less is the "-10"

So, this gives you 4x-10.

Answer:

10-(4*x)

Step-by-step explanation:

Answer:

6 maybe I'm not sure jkeneekenene

Answer:

3x

Step-by-step explanation:

A rectangle is similar to a square, in the sense that opposite sides will always be the same. Because we are given the side of the length is 3x-3, this means that the other length will too be 3x-3. Now, we may add these:

(3x-3)+(3x-3)=6x-6

And because we are given our perimiter, simply subtract the lengths we do know:

(12x+6)-(6x-6)=6x

This is the perimetor we have left in our shape. Because we again know that opposing sides are the same length, simply dividing our answer by two will give us the length we need:

6x/2=3x

Based on this, our length of the indicated side is 3x!

Hope this helped!

If the initial population is 3800. The population of cockroaches after 3 years will be 1603.

Consider the function:

y = a(1 ± r)ⁿ

where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, there is exponential growth happening by r fraction or r%.

If there is a minus sign, there is exponential decay happening by r fraction or r%.

If the population is currently 3,800 cockroaches.

The expression is given as

y = 3800(0.75)ⁿ

The population of cockroaches after 3 years will be

y = 3800(0.75)³

y = 3800 x 0.4218

y = 1603.125

y ≅ 1603

Hence, the population of cockroaches after 3 years will be 1603.

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The complete question is:

Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.

Answer:

1.1%

Step-by-step explanation:

Original number = 92

New number = 93

increase in the value of number = 93-92 = 1.

Percentage increase in number is given by

increase in the value  / old value ) *100

= (Original number -New number)/ Original number)*100

= (93-92/92) *100 = (1/92 )* 100 = 1.0869 %

Percentage increase in number is 1.0869%

Percentage increase in number to nearest tenth is 1.1%

Answer:

30°, 60°, 90°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 3 = 6 parts

divide the sum of the angles in a triangle. 180° by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio , then

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

The 3 angles are 30°, 60° and 90°

Answer:

The desired quotient is 25/12.

Step-by-step explanation:

Rewrite 1 2/3 as an improper fraction:  5/3.

Then divide this 5/3 by 4/5:

 5

------ ÷ 4/5

  3

It's easier (but completely correct) to invert the divisor (4/5) and then multiply 5/3 by (5/4):

  5       5       25

----- *  ----- = ------

  3        4       12

Answer:

\(-5x^3 + 8\)

Step-by-step explanation:

See comment for complete question

Given

\(Degree \to 3rd\)

\(Constant \to 8\)

\(Type \to Binomial\)

Required

Which of the options is true

\(Type \to Binomial\)

This implies that the polynomial has just 2 terms

The above shows that (a), (b) and (c) are not true because they have more than 2 terms

\(Degree \to 3rd\)

This implies that the highest power of x is 3

\(Constant \to 8\)

The second term of the polynomial must be +8

Only (d) satisfy the above conditions

The function f(x) = x^3 - 6x^2 - 14x + 10 can be written in the form f(x) = (x + 2)q(x) + r, where k = -2. To demonstrate that f(k) = r, we evaluate f(-2) and compare it to the value of r.

To write the function f(x) = x^3 - 6x^2 - 14x + 10 in the desired form f(x) = (x + 2)q(x) + r, we need to divide the function by (x + 2) using synthetic division or polynomial long division. Performing the division, we find that q(x) = x^2 - 8x + 18 and r = -26.

Now, to demonstrate that f(k) = r, where k = -2, we substitute -2 into the function f(x) and compare the result to the value of r.

Evaluating f(-2), we have f(-2) = (-2)^3 - 6(-2)^2 - 14(-2) + 10 = -8 - 24 + 28 + 10 = 6.

Comparing f(-2) = 6 to the value of r = -26, we see that they are not equal.

Therefore, f(k) ≠ r for k = -2 in this case.

Hence, the function f(x) = x^3 - 6x^2 - 14x + 10 does not satisfy f(k) = r for k = -2.

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Counting numbers are another name for natural numbers. These are 1, 2, 3, and so forth.

Natural numbers plus zero are whole numbers.

Natural numbers, whole numbers, and the opposites of whole numbers are all considered integers. These numbers range from -3 through -2, -1, 0, 1, 2, 3, etc.

Integers, whole numbers, rational numbers, and numbers that may be expressed as fractions are all considered rational numbers. In this case, fraction \(\frac{a}{b}\), where; a and b must both be integers.

All non-rational numbers are categorized as being irrational. These figures cannot be expressed as fractions. This includes decimals like \(\pi\), \(\sqrt{2}\), and 3.2576352417942 that doesn't end or repeat.

The collection of all rational and irrational numbers, as well as their subsets, is known as the Real Number System.

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The number of ways the pet trainer can arrange 3 dogs, 2 cats, and 2 bear cubs to sit around in a circle such that all the dogs sit next to each other is 4 * 3! * 2! = 48.

To calculate the number of ways, we treat the pack of dogs as a single entity. So, we have 4 entities (pack of dogs, 2 cats, 2 bear cubs, and an empty seat) to arrange in a circle.

The pack of dogs can be arranged in 4 different ways (as a single entity): 1) Dog1-Dog2-Dog3, 2) Dog2-Dog3-Dog1, 3) Dog3-Dog1-Dog2, 4) Dog1-Dog3-Dog2.

Within the pack of dogs, the dogs can be arranged among themselves in 3! = 6 ways.

The cats can be arranged among themselves in 2! = 2 ways, and the bear cubs can be arranged among themselves in 2! = 2 ways.

Therefore, the total number of ways to arrange them in a circle, such that all the dogs sit next to each other, is 4 * 3! * 2! = 48.

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I believe the answer is A

Answer:

\((a+b-2)-(b-a+2)+(a-b+2) \\ a + b - 2-b+a -2+a-b+2 \\ collecting \: like \: terms \\ a + a + a + b - b - b - 2 - 2 + 2 \\ 3a - b - 2\)

The ranger who is closest to the fire is approximately 9.91 miles away.

Given that the west tower and east tower are 15 miles away from each other, and the fire is observed at angles of 41 degrees north of east and 56 degrees north of west, we can use trigonometry to determine the distances of the rangers from the fire.

Let's denote the distance from the west tower to the fire as x and the distance from the east tower to the fire as y. Using the tangent function, we can set up the following equations:

In the west tower triangle:

tan(41°) = x / 15

In the east tower triangle:

tan(56°) = y / 15

Solving these equations, we find:

x = 15 * tan(41°) ≈ 9.91 miles (rounded to the nearest hundredth)

y = 15 * tan(56°) ≈ 18.95 miles (rounded to the nearest hundredth)

Comparing the distances, we can conclude that the ranger in the west tower is closer to the fire, with a distance of approximately 9.91 miles.

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Answer:

32

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

4.5*3=13.5