For each diagram, write and solve an inequality for x.
7.
2x - 5
X

2ab + c²

(a+b)² and a² + 2ab + b²

2ab

1) Examining that picture, we can state the following about that:

The shaded triangles area:

Note that the area of the triangle is 1/2 the product of the base by its height.

The area of that white inner square is given by c² since the Area of a square is equal to the side length raised to the 2nd powe.

2) Then

The expression 2ab + c² represents the area...

The equivalent expressions (a+b)² and a² + 2ab + b² use the length of the figure (a square) raised to the 2nd power. As explained above.

For the last statement let's calculate it:

2ab + c² = (a+b)²

a² +2ab + b² = 2ab +c² Subtracting 2ab

a² +b² = c²

3) Hence, the answers are:

2ab + c²

(a+b)² and a² + 2ab + b²

2ab

Notice that triangles QRS and YRZ are similar, therefore:

Substituting YZ=x+2, QS=3x-8, and solving for x we get:

Answer: Option C).

We are given the expression below:

To find the solution to the expression, we would make use of PEDMAS to other our steps on finding the solution. PEDMAS implies

The order of PEDMAS would then be utilized in finding the value in the question.

Therefore, the answer is

The right option is option C

We will investigate how to determine one of the indicator dimensions of a regular figure.

We have a rectangular fish tank which can be modeled as a cuboid. The indicator lengths of a cuboid or a rectangular fish tank are as such:

One of the indicator lengths of the rectangular fish tank Length ( L ) is unknown. Howver, we are given the total amount of water that the fish tank can withold as follows:

We will use the conversion factor between milliLiters and centimeter cube as follows:

Therefore,

The amount of water a fish tank can hold is equivalent to the volume of the fish tank. We have modeled our rectangular fish tank as a cuboid. The volume ( V ) of a cuboid can be expressed in terms of its indicator dimensions as follows:

We can use the above volume expression to determine one off our missing indicator dimension of length ( L ). We plug in the respective quantities and evaluate:

Therefore, the length ( L ) of the fish tank must be:

As given by the question

There are given that the inside edge is 4 in.

Now,

Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube

So,

Then,

Volume of the sphere is given by:

And,

The volume of a cube is:

Then,

The volume of the space between the sphere and cube = 64-33.5 = 30.5.

Hence, the answer is 30.5 cube inches.

The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.

The probability of getting exactly three robberies in a day is 0.1607.

The Poisson distribution is a discrete probability distribution used in probability theory and statistics to express the likelihood that a given number of events will occur within a specified time or space interval if they occur at a known constant mean rate and regardless of the interval since the last event.

The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.

In the poison distribution a discrete random variable X has the following probability mass function,

[tex]$P(X=x)=\frac{e^{-\lambda} \cdot \lambda^x}{x !}$[/tex], where [tex]$\lambda$[/tex] is the mean of the distribution and [tex]$x=0,1,2,3 \ldots \ldots$[/tex]

Given that [tex]$\lambda=1.8$[/tex]

The required probability, [tex]$P(X=3)=\frac{e^{-1.8} .(1.8)^3}{3 !}=0.1607$[/tex]

Therefore, the probability of getting exactly three robberies in a day is = 0.1607.

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To find the distance between her home and her latest position:

According to the question, the diagram is,

Consider the right triangle,

AB=120 km

BC=50 km

To find AC:

Using Pythagoras theorem,

Hence, the distance between the new position and her home is 130 km.

The plant food should Miguel add to 7 cups of water is 336 plant food

What is Algebra?

One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.

To feed his plants, Miguel combines water and plant food. According to the directions on the plant food, you should add 1 teaspoon to every 4 cups of water. To demonstrate the relationship between cups of water (w) and teaspoons of plant food (f), create an equation.

48 teaspoons = 1 cup.

1 teaspoon = plants food

4 cups =  water.

= 48 teaspoons x 4.

= 192 teaspoons

The formula is:

water in cups = w

Teaspoon of nourishment for plants equals f

The mixture = 192w + f

The relation between  f and w is f = kw.

1 teaspoon = plant food

7 cups = water.

= 48teaspoon x 7

= 336teaspoon

The formula is:

water in cups = w

Teaspoon of nourishment for plants equals f

The mixture = 336w + f

Hence, 336 plant food  should Miguel add to 7 cups of work

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ANSWER :

Triangles UWY and UXZ are similar

EXPLANATION :

Two triangles are similar if the ratio of their corresponding sides is the same.

We can try UW/UX, WY/XZ, and UY/UZ

Since the ratios are the same, then the triangles are similar.

Answer:

11/12

Step-by-step explanation:

hopes this helps, I am sorry if I am wrong

5 1/2 ÷ 6

11/2 ÷ 6

11/2 × 1/6

11/12

The cost of the two shipping options be the same when B. a package that weighs 7 pounds will cost $17 for both options.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The cost, y, can be represented by the equation: y = 3 + 2x,

x = the amount of pounds of the package

Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.

The equation will be equated together.This will be:

3 + 2x = 17

Collect like terms

2x = 17 - 3

2x = 14

Divide

x = 14 / 2

x = 7

The weight is 7 pounds.

In conclusion, the correct option is B.

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Answer:

Explanations:

From the question, we are to use synthetic division to divide x - 1 by the polynomial function -3x^3 - 2x^2 - 1

Next is to use the synthetic division to carry out the operation as shown below;

From the calculation above, we can conclude the following;

Answer:

y = 0

Step-by-step explanation:

The function has a horizontal asymptote at y = 0 where y is the value of the car

[tex]\text{Since the equation for the value of the car is }[/tex]  [tex]23000(1-0.15)^t[/tex]

As [tex]t \rightarrow \infty, \text{the term } (1-0.15)^t \rightarrow 0 \\[/tex]

This is because the term (1-0.15) is < 1 and a nˣ approaches 0 as x → ∞ since the values get smaller and smaller with increasing powers of x

So the equation for the horizontal asymptote is y = 0

Provided graph to illustrate

The true statements are,

The range for the distribution of the number of absences is larger for

class D.

The IQR for the distribution of the number of absences is larger for class C.

The interquartile range serves as a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where the majority of the values lay, whereas a range measures where a set's start and finish are.

Given, Are 2 dot plots titled class absences.

Arranging the data set For class D,

0, 1, 2, 3, 3, 4, 7, 11.

So, The range of the data set D is 11 - 0 = 11.

The IQR for the absences for class D is Q₃ - Q₁ = 7 - 1 = 6.

Arranging the data set For class C,

0, 1, 1, 1, 1, 2, 3, 4, 5, 8, 10, 10.

So, The range of the data set C is 10 - 0 = 10.

The IQR for the absences for class C is Q₃ - Q₁ = 8 - 1 = 7.

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Answer:

20.36

Step-by-step explanation:

72.60 cuando se divide por 100 se obtiene 1% o 0.73x8=5.84
entonces 72.60/10=7.26x2=20% o 14.52

14.52+5.84=20.36

To make 12 pancakes we need 100 g flour, 2 eggs, 300 ml milk

Abdul has 175 g flour, 4 eggs and 500 g milk

The ration between Abdul's amount of each ingredient and the total needed to make 12 pancakes is: (175/100) = 1.75 flour, (4/2) = 2 eggs, (500/300) = 1.67 milk.

So, the total amount of pancakes that Abdul can make is determined by the amount of the less abundant ingredient (milk): 1.67*12 = 20 pancakes

Doing the same steps for Beckie, we got that her less abundant ingredient is milk, with a ratio of 400/300 = 1.33. Then, she can make 1.33*12 = 16 pancakes.

For Cynthia, her less abundant ingredient is flour, with a ratio of 150/100 1.5. Then, she can make 1.5*12 = 18 pancakes.

And for Douglas, his less avundant ingredient is egg, with a ratio of 3/2 = 1.5. Then, he can make 1.,5*12 = 18 pancakes.

Therefore, Abdul is the one who can make the most pancakes

The x intercepts of the quadratic function are the points where the graph of the parabola intersects with the x axis.

In the given graph, the parabola intersects the x axis at points with coordinates (-1, 0) and (3, 0).

Therefore, the x intercepts of the quadratic are:

(-1, 0) ; (3, 0).

Remember that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent

Verify the proportionality between corresponding sides

so

that means

The triangles are not similar

Reason:

There aren't any repeated items in the domain. Each x input goes to exactly one y output. This is why we have a function.

The y values can repeat, but the function wouldn't be one-to-one (i.e. injective).

(g o f)(-8) = 36

For f(x) = 2x + 12 and g(x) = 2x² + 2x + 12 the value of (g o f)(-8) is 36.

Given that f(x) = 2x + 12, g(x) = 2x² + 2x + 12.

to locate (g o f) (-8),

To find (g o f)(-8), we must first find g(f(x)) and then substitute x = -8.

Find g(f(x)) by substituting f(x) into g. (x)

= g(f(x))  = 2( 2x +12)² + 2( 2x + 12) + 12

x = -8 so,

g( f( - 8) ) = 2( 2(-8) +12)² + 2( 2(-8) + 12) + 12

g( f( - 8) ) = 2( -16 +12)² + 2( -16 + 12) + 12

g( f( - 8) ) = 2(-4)² + 2( -4 ) + 12

g( f( - 8) ) = 2 x 16 -8 + 12

g( f( - 8) ) = 32 - 8 + 12

g( f( - 8) ) = 36

So (g o f)(-8) = 36

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Find the area of the triangle;

The area of the triangle is 14 square units

**Please Note; The instruction is to type in a whole number, so you may exclude "Square Units" from your answer

Answer:

x>0

Step-by-step explanation:

any number less than or equal to zero does not give a negative solution and you need a negative solution so x must be greater than 0

A(-5,7)

B(4,4)

The segment is reflected over the line y =4

The line y=4 is a horizontal line, coordinate in x doesn't change after reflection.

To find coordinate y after reflection:

Find the distance of each point from y=4

As y=4 is below the point A, the point A' will have a coordinate y of: 4-3=1

As point B is on line y=4 the point B' will have a coordinate y of 4-0:4

then rotated 90° CW:

Rule for a rotation 90º CW:

Then, you get the next coordinates for A'' and B'':

The answer to g(f(x)) expressed as a polynomial in Standard form is x² + 6x + 13.

Given the composition of functions g(f(x)),

For which f(x) = x + 5, and g(x) = x² - 4x + 8.

Considering f(x) as input we substitute it in g(x) in place of x.

g(f(x)) = (x+5)²- 4(x+5) + 8

         = x² + 25 + 10x - 4x -20 + 8

        = x² + 6x + 13

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Answer:

range = 16

Step-by-step explanation:

The total of all the numbers = mean x number of values = 6 x 12 = 72

The ratio of the numbers is

1: 1: 1: 1:2 :3

The sum of the ratios is 9

So the numbers in the ratio of 1 must be 1/9 x 72 = 8

The number with a ratio of 2 must be 2 x 8 = 16

and finally the number with the ratio of 3 = 3 x  = 24

The range of the numbers is 24-8 = 16

4.5 = 45/10 Using GCF

9/2

Answer:

A = (1, 1i)

B = (-7, 3i)

C = (-4, -7i)

Step-by-step explanation:

Complex numbers makes the x axis the "real" axis and the y axis the "imaginary" axis. Therefore, your "y" coordinates will have an "i" attached to them to signify that they are imaginary.

She made 12 bracelets with pastel colors

Here, we want to get the number of bracelets she made with pastel colors

From the question, we are told that for every 4 bracelets she makes with neon colors, she has 3 bracelets made with pastel colors

So the ratio of neon to pastel color bracelets is 4 to 3

For the 16 neon bracelets, let the number of pastel colored bracelets made be x

Thus, we have;

Answer: 12

Step-by-step explanation: