Select the correct answer.
Which graph represents the solution to this system of inequalities?
x+y<4
2x-3y²12
O A.
-10
y 10
-5
10

2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.

3) The coordinates after dilation are: (5.4, 27)

2) The coordinates transformed points after dilation are completed as:

B(2, 4) → B'(3, 6)

K(4, -4) → K'(6, -6)

N(-6, 0) →N'(-9, 0)

The scale factor is same because using the ratio of the x coordinates gives:

3/2 = 1.5

6/4 = 1.5

-9/-6 = 1.5

3) The point W of the vertex of the polygon has coordinates as (2, 10)

Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:

(2*2.7, 10*2.7) = (5.4, 27)

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Answer:

128

Step-by-step explanation:

To translate the sentence into an equation, we can use the following formula: number / 8 = 16. This equation shows that we are dividing a number by 8 and getting a result of 16. To solve for the number, we can multiply both sides of the equation by 8. This gives us the equation number = 16 x 8, which simplifies to number = 128. Therefore, the solution to the equation is 128.

Answer:

128

Step-by-step explanation:

got it right on edge

The graph is a function: A. yes

The domain of this function is: E. x ≥ -3.

The range of this function: G. all real numbers.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.

Range = {-∞, ∞} or all real numbers.

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Answer:

2k+16

Step-by-step explanation:

Kevin: k

Ben: 8 years older than k, k+8

Hannah: 2 times Ben's age, 2(k+8)=2k+16

Answer:

Step-by-step explanation:

A = length x width = (2w + 5)(w) = 2w² + 5w

P = 2(2w + 5) + 2w = 6w + 10

To graph:  sorry, Brainly doesn't have graphing tools so I'll just have to describe it

A:  parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)

P:  straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)

FYI, the 2 graphs intersect at 2 points:  (-2, 2) and (2.5, 25)

The area of the circular pateo is 50.24 square yards.

Remember that for a circle of radius R, the area is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:

R = 4yd/2

R = 2 yd

Replacing that in the area formula we will get:

A = 3.14*(2yd)²

A = 50.24 yd²

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Answer:

BD = 3 units

Step-by-step explanation:

since AB is a tangent to the circle, then the angle between the tangent and the radius at the point of contact A is 90°

Then Δ ABC is right

using Pythagoras' identity in the right triangle

BC² = AC² + AB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

BC = [tex]\sqrt{56.25}[/tex] = 7.5

now CD is a radius of the circle = 4.5

Then

BD = BC - CD = 7.5 - 4.5 = 3 units

The solution to the system of equations in this problem is given as follows:

(0.6, 2.4).

The system of equations in the context of this problem is defined as follows:

Equaling the two equations, we can obtain the value of x, as follows:

4x = -x + 3

5x = 3

x = 3/5

x = 0.6.

Substituting the value of x into the second equation, we obtain the value of y as follows:

y = -0.6 + 3

y = 2.4.

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Answer:

Step-by-step explanation:

Using trigonometric relations we can see that:

6) θ = 30°

7)   θ = 60°

We can see a right triangle where we want to find the value of θ, we know the hypotenuse and the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opp cath)/hyp

Replacing what we know:

sin(θ) = 6/12 = 1/2

Then we know that θ = 30°

For the second one we know the adjacent cathetus and the hypotenuse, here we need to use the cosine relation:

cos(θ) = 5/10

cos(θ) = 1/2

then θ = 60°

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Answer:

a) Utilizando la fórmula para el tamaño de muestra, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).

Sustituyendo los valores, obtenemos:

n = (1.96 * 9 / 2)^2 ≈ 77

Por lo tanto, se debe tomar una muestra de al menos 77 familias.

b) De manera similar, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).

Sustituyendo los valores, obtenemos:

n = (2.58 * 9 / 1.5)^2 ≈ 261

Por lo tanto, se debe tomar una muestra de al menos 261 familias.

Step-by-step explanation:

Answer:

0.1 oz

Step-by-step explanation:

1000=10 oz

10 drops

1000/100=10

10/100=O.1 oz

The area of the triangle with base of 5 ​inches and a height of 10 inches is 25 square inches. The correct answer is C.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base, and h is the height. Using this formula, we can calculate the area of the triangle in question.

Given that the base of the triangle is 5 inches and the height is 10 inches, we can plug these values into the formula and solve for A:

A = 1/2 * b * h

A = 1/2 * 5 * 10

A = 25

Therefore, correct answer is C.

The height of a triangle is the perpendicular distance between the base and the opposite vertex. The base is the side of the triangle on which the height is measured.

By multiplying the base and the height and dividing the result by 2, we can find the area of a triangle. This formula works for all types of triangles, regardless of their size or shape.

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Complete question is:

Find the area of a triangle with base of 5 ​inches and a height of 10 inches.

A 100 square inches

B 50 square inches

C 25 square inches

D 12.5 square inches

Beth could not join the club because the highest age which is allowed here is only 55 years

Since, A statistical expression obtained from a list of data that refers an abnormal gap from other values.

The statistical rules that instruct us to divides the data or observation values into four parts.

After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.

the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.

hence, Beth did not join the club because her age was above the highest age that allowed in this club.

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the answer to your math problem is 2000

The value of the radius of the cone is, 5 inches

We have to given that;

The volume of a cone is 35π cubic inches.

And, the height is 4.2 inches.

Now, We know that;

Volume of cone is,

V = πr²h/3

Hence, We get;

35π = π × r² × 4.2 / 3

105 = 4.2r²

r² = 105/4.2

r² = 25

r = 5 inches

Thus, The value of the radius of the cone is, 5 inches

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Answer: 20

Step-by-step explanation:

because Juanita has a aquarium that is 5 feet LONG, 4 feet WIDE, and 2 feet DEEP, in part b it asks what if the water is 1 foot DEEP so what they're trying to say is what if you replace the original 2 feet DEEP with 1 foot DEEP?

so it would be length x width x depth

5x4x1=20

so the volume is 20ft^3

After two years, Brooklyn will have more money in her savings account than Matthew.

Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

a.

[tex]A = P(1 + r/n)^{nt}[/tex]

where A is the final amount, P is the initial principal (or net pay), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

For Brooklyn saving account,

P = $625, r = 0.025, n = 12 (monthly compounding), and t = 2.

A = $625(1 + 0.025/12)^(12*2) = $686.71

For Matthew saving account,

P = $446, r = 0.04, n = 4 (quarterly compounding), and t = 2.

A = $446(1 + 0.04/4)^(4*2) = $506.84

b.

To graph Brooklyn's equation and Matthew's equation on the same graph, we can use the following equations:

Brooklyn's equation: A = 625(1 + 0.025/12)^(12t)

Matthew's equation: A = 446(1 + 0.04/4)^(4t)

Now,

The resulting graph will show the growth of each saving account over time.

The points of intersection on the graph represent the times when the two savings accounts have the same amount of money.

From the graph, we can see that the two accounts intersect at around 11 months and 23 months.

We can say that Brooklyn's savings account grows at a slower rate than Matthew's initially, but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

Thus,

After two years, Brooklyn will have more money in her savings account than Matthew.

Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

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The matching table is given in the image below:

A scatter plot, an undeniably essential chart for visualizing the correlation between two variables, is constructed by putting one variable on the x-axis and another one alongside the y-axis, with each individual data point symbolizing both associated values.

Scatter plots are not only indispensable when inspecting trends and peculiarities in a given set of data but can likewise be applied to examine the relationship or link between the two components.

Essentially imperative to fields such as economics, engineering, and statistics, these diagrams are efficiently drawn up through popular software applications like Excel or Python.

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The number of people who ate at neither McDonald's or Wendy's is given as follows:

D) 30.

Before obtaining the number of people who ate at neither place, we must obtain the number of people who ate at least one place, as follows:

At least one = McDonald's + Wendy's - (McDonald's and Wendy's).

Replacing the values given in this problem, we have that:

At least one = 55 + 35 - 20

At least one = 70.

Considering that 100 students were surveyed, the number of students who ate at neither place is given as follows:

Neither = 100 - At least one

Neither = 100 - 70

Neither = 30 students.

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You can use functions to complete the table as follow:

x   f(g(x))

4      2

10     4

20    6

34    8

52   10

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

f(x) = √(x+1)

g(x) = 2x - 5

When x = 4:

f(g(x)) = f(g(4))

f(g(4)) = f(2*4 - 5)

f(g(4)) = f(3)

f(g(4)) = √(3+1)      [Remember f(x) = √(x+1)]

f(g(4)) =  2

When x = 10:

f(g(10)) = f(2*10 - 5)

f(g(10)) = f(15)

f(g(10)) = √(15+1)

f(g(10)) = 4

When x = 20:

f(g(20)) = f(2*20 - 5)

f(g(20)) = f(35)

f(g(20)) = √(35+1)

f(g(20)) = 6

When x = 34:

f(g(34)) = f(2*34 - 5)

f(g(34)) = f(63)

f(g(34)) = √(63+1)

f(g(34)) = 8

When x = 52:

f(g(34)) = f(2*52 - 5)

f(g(34)) = f(99)

f(g(34)) = √(99+1)

f(g(34)) = 10

Thus, fill the values into the table to complete it.

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The objective of the above task to to check your ability to compute various parts of a parallelogram given various inputs. See the solution attached.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

Note that the corners angles (AB,C,D)are derived as follows;

A = C = θ

B = D = Φ

A + B = 180° = π radians

for a parallelogram that is not a rectangle or square,

0 < A< 90° (0 < A < π/2),

90° < B < 180° (π/2 < B < π)

The diagonals are derived as follows:

Diagonals: d, c

d = √( a² + b² - 2ab cos(A) ) = √( a² + b² + 2ab cos(B) )

c = √( a² + b² + 2ab cos(A) ) = √( a² + b² - 2ab cos(B) )

d² + c² = 2(a² + b²)

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The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

For Container A, the radius is half the diameter, or 16 feet. So the volume of Container A is:

V_A = π(16 ft)^2(16 ft) = 8,192π cubic feet

For Container B, the radius is half the diameter, or 15 feet. So the volume of Container B is:

V_B = π(15 ft)^2(18 ft) = 12,735π cubic feet

To find the volume of water that was transferred from Container A to Container B, we can subtract the volume of Container A from the volume of both containers combined:

V_water = V_A + V_B - V_A = V_B

V_water = 12,735π cubic feet

To find the volume of water remaining in Container A, we can subtract the volume of water that was transferred from the volume of Container A:

V_remaining = V_A - V_water

V_remaining = 8,192π - 12,735π

V_remaining ≈ -3,543.7 cubic feet

However, a negative volume doesn't make sense in this context, so we know that there must be no water remaining in Container A after the transfer. Therefore, the volume of water remaining in Container A to the nearest tenth of a cubic foot is 0.

The area of the following composite figures is 78 square units.

The area of the square is computed as 36 (length x width) or 2(Length).

The area of the triangle is computed as (base x height) ÷ 2.

The areas of the composite figures are added to determine the total area.

Line AD = 6

Line DC = 6

Line AB = 20

Base of the triangle = 14 (20 - 6)

Area of triangle = (h x b) ÷ 2

= (6 x 14) ÷ 2

= 42

Area of square portion = 36 (6 x 6)

Total area = 78 square units

Thus, we can conclude that the area of the composite figures are 78 square units.

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Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2

From the question, we have the following expression that can be used in our computation:

-2 square root of 2r +5=6

Express properly

So, we have

-2√(2r + 5) = 6

Divide by -2

√(2r + 5) = -3

So, we have

2r + 5 = 9

Subtract 5 from both sides

2r = 4

Divide

r = 2

Hence, the solution is 2

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Answer:

The measure of angle E is 56°.

The surface area of the triangular prism is 108 km².

Given is a triangular prism we need to find the surface area of the prism,

SA = perimeter × length

= (3 + 4 + 5) × 9

= 12 × 9

= 108

Hence, the surface area of the triangular prism is 108 km².

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Answer: D

Step-by-step explanation:The option that is statistical question that can result in numerical data is D) What is the height of the tallest player on a team?

What is a statistical question?

A statistical question is one that can be answered by gathering varying amounts of data. A statistical question is one that may be answered by gathering data and for which the data will vary. Questions answered with a single data point are not statistical questions since the data utilized to answer the question is not variable.

If u= (-10,-3) and v= (4,8) . Proj vu is  is (640/109, 192/109).

Using this formula to determine the projection of v onto u (proj vu)

proj vu = ((v dot u) / (||u||)^2) × u

Where:

v dot u = dot product of v and u

||u|| = magnitude of u

First step is to find  the dot product of v and u:

v dot u = (-104) + (-38)

v dot u = -40 - 24

v dot u = -64

Second step to to calculate the magnitude of u:

||u|| = √((-10)^2 + (-3)^2)

||u|| = √(100 + 9)

||u|| = √(109)

Let plug in the formula

proj vu = ((-64) / (√(109))^2)× (-10,-3)

proj vu = (-64 / 109) × (-10,-3)

proj vu = (640/109, 192/109)

Therefore  the correct option is A.

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