which of the following would be an acceptable first step in simplifying the expression?

Given:

Amount of chocolate chips needed = 1 1/2 times as much floor.

Amount of floor used = 3 1/2 cups.

Let's find the quantity of chocolate chips that would be needed according to the recipe.

To find the amount of chocolate chips used, we have:

Amount of chocolate chips

From the image, we are asked the number of sides a polygon can have to form a regular tesselation.

The first step is to understand what a regular tessellation is;

A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.

This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).

From the given options we can clearly see that 3 sides is the only available option.

ANSWER: Option B

In this problem we have that

mso

the formula to calculate the interior angle is equal to

msubstitute the given values

m

therefore

SOLUTION:

Case: Rectangles

Method:

The sum is:

w + w + 2w + 5 = 89

4w + 5 = 89

4w = 89 - 5

4w = 84

w = 84/ 4

w= 21 feet

The length, l

l = 2w + 5

l = 2( 21) + 5

l = 42 + 5

l = 47 feet

Final answer:

length of the patio, l = 47 feet

width of the patio, w= 21 feet

The result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1

The function is

f(p) = [tex]p^2[/tex] + 3p + 1  

The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.

The values of p = -2

Substitute the value of p in the function and find the solution

f(p) = [tex]p^2[/tex] + 3p + 1  

f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1

f(-2) = 4 - 6 + 1

f(-2) = -1

Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1

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From the given figures in the 2 triangles XYZ and ABC

mXZ = AC

m

Since we have two equal angles and the sides between them are equal, then

The 2 triangles are congruent using ASA postulate

The answer is C

Apply difference of two square

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the growing rate of the first tree

Tree 1 is growing 1.5 inches every week

STEP 2: Calculate the growing rate of the second tree

This implies the slope and is calculated using the formula;

By substitution,

The slope of 1 means that Tree 2 is growing at a rate of 1 inch per week

Hence, the tree that is growing faster is Tree 1 with a rate of 1.5 inches per week

ANSWER:

Tree 1

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

For the given question.

Line m is the line along which reflection of point P is taken.

Then, line m is called the "perpendicular bisector" of line PP'.

P is the object and P' will be the image of the point P.

Thus, the complete definition of the reflection is given as-

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

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Solution

The functions that define the region in consideration are given below:

The Washer Method:

- Plotting these functions would help us visualize the question better. This is done below:

- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:

-

We can represent the region bounded by the function by rearranging the functions as follows:

Recall that in a Fibonacci-like sequence, the sum of two consecutive terms yields the third term.

Mathematically,

Since we are given the first two terms, we can find the third term and so on...

F₁ = 0

F₂ = 3

Answer:

Th

Explanation:

Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;

Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.

Okay, here we have a Combination Problem, we need just multiply to get the answer, of this mode:

She can wear 315 outfits.

SOLUTION

We are trying to get the equation for the horizontal line passing through the point (-6,-6).​

( x1 , y 1 ) = ( 0, 0 )

( x2 , y2 ) = ( -6 , -6 )

Gradient, m = ( y2 - y1 ) / ( x2 - x1 )

m = ( -6 -0 ) / ( -6 - 0 )

m = -6 / - 6

m = 1

Then, using the equation of a line;

y - y 1 = m ( x - x 1 )

y - 0 = 1 ( x - 0 )

y = x

Answer:

The First one (1.7,3.1)

Step-by-step explanation:

3x-2=-0.5x+4

3.5x=6

x=12/7

x≈1.7

sub x back into to find y

y≈3.1

2 - 3

the correct answer is letter C

If we follow the rules of the exponents, the power is negative so we change the negative sign writing the numerator in the denominator,

We were given the equation:

We will proceed to graph this equation as shown below:

We will proceed to plot these ordered pairs on a graph, we have:

The vertical angle theorem states that the opposite angles formed by two lines that intersect each other are always equal to each other.

Then, if we apply this to the figure shown we can say that by the vertical angle theorem

The total area under the normal distribution curve is 1. z-scores are indicated in the horizontal axis below this curve. This means that the sum of areas under the curve at the left and at the right of a certain z-score must be equal to 1.

Then if the area at the right of the z-score that we are looking for is 0.04 the area at its left must be equal to 1-0.04=0.96. The area at the left of z is important because z-score tables usually show the areas at the left of several z-scores. Then the only thing that we have to do is look for the z-score associated with 0.96 in one of these tables. In your case the table that you should use is the one named "Normal Table -∞ to z". That table should look like this one:

As you can see the value 0.96 is associated with the row 1.7 and the column .05 which means that the z-score that meets that the area under the curve at its right is 0.04 is z=1.7+0.05=1.75.

Then the answer is 1.75

Right Triangles

A right triangle is recognized because it has an interior angle of 90°.

In right triangles, the Pythagora's Theorem is satisfied.

Being a and b the shorter sides (also called legs) of the triangle, and c the longer side (called hypotenuse), then:

The triangle shown in the image has the two legs of values a=15 and b=8. The hypotenuse is c=x, thus:

Operating:

Solving for x:

x = 17

Answer:

Explanation:

Answer:

<A=32°

Explanation:

<BEC = 90° because it has the red half square and we know that <DCE = 42°. <ACB= 2x because <ACD and <DCB both =x. The equation we would set up is

90+(42+x) +2x=180

We get x=16.

Since <ACB = 2x we multiple 16 by 2

16*2=32

So <ACB =32°

The value of S in the expression 5/8-3/8 S = two minus S is 2 1/5.

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

In this case, this is illustrated thus:

5/8 - 3/8S = 2 -S

Collect like terms

-3/8S + S = 2 - 5/8

5/8S = 1 3/8

Divide

S= 1 3/8 ÷ 5/8

S = 11/8 × 8/5

S = 11/5

S = 2 1/5

This illustrates the concept of expression.

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• Chord: ,a line segment connecting ,any two points, in a curve (circle).

• Diameter: ,a chord passing ,through the center ,of the figure.

• Radius: ,a line segment going ,from the center, to any point in the circumference.

The difference between them is that the chord is any two points touching the circumference, the diameter has to go through the center to any two points, and the radius goes from the center to just one point in the circumference.

Then, the line segment that meets the requirements of being the diameter in circle F is segment CD as it passes through the center.

The radius could be CF, DF, and EF. While a chord could be AB.

Answer: CD

Answer:

The correct answer is:

The ordered pair (2, 3) is not a solution to the system.

Explanation:

The system given is:

If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.

In the first equation;

We can see that this result is not true, as 27 is not equal to 1.

In the second equation:

Once again, a false result.

To see in the system has equations, let's solve for x in the second equation:

Now, we can use substitution in the first equation:

And solve for y:

Now, we can find the value of x:

The solution to the system is (-2, 1)

Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"

The answer in polar form:

19 in

1 yd

2ft

32 in

First, we have to convert all the length into a unique unit:

For example, inches:

Since

1 ft = 12 inches

2 ft = 2 x12 = 22 inches

1yd = 36 inches

Now, we have to order from least to greatest:

19 in-22in -32in-36in

In the original units:

19 in , 2ft, 32in ,1yd

We are told that a 7% tax is applied to the original sales price, in order to determine the tax amount we just have to multiply the original price ($46.85) by the tax percentage (0.07 as 7% in decimal form), then we get:

Tax amount = 0.07×46.85 ≈ 3.28

By adding the tax amount to the original price we should get the final price, like this:

Total purchase price = 46.85 + 3.28 = 50.13

Then, the total purchase price after tax is $50.13

The solution to the inequalities will be,

( 5 ) y ≥ 2

( 6 ) x < 3

( 7 ) No solution.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The given inequalities will be calculated as:-

-4 ≤ 4( 6y - 12 ) - 2y

-4 ≤ 24y - 48 - 2y

-4 ≤ 22 y - 48

22y ≥ 44

y ≥ 2

4x + 3 < 3x + 6

4x - 3x < 6 - 3

x < 3

-5r + 6 ≤ -5( r + 2 )

-5r + 6 ≤ -5r - 10

No solution

Therefore, the inequalities are solved above.

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-1 3/4, 14/8, 1.125 and -0.875 correspond to points 1, 8, 6 and 4 respectively on the number line.

Looking at the number line, there are 8 divisions between two points e.g 0 to 1.  

To know the value of  1 division, we divide the value of the distance between two points by the number of divisions:

= 1/8 = 0.125

To find the locations, we just divide the value of the locations with the value of 1 division:

-1 3/4 / 0.125 = -14  (Count 14 divisions to the left of 0) = point 1

14/8  / 0.125 = 14  (Count 14 divisions to the right of 0) = point 8

1.125/ 0.125 = 9 (Count 9 divisions to the right of 0) = point 6

-0.875 / 0.125 = -7  (Count 7 divisions to the left of 0) = point 4

Therefore, the positions of -1 3/4, 14/8, 1.125 and -0.875 on the number line are points 1, 8, 6 and 4 respectively.

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