Which statement and reason are missing in step 4?

Select the two correct answers

Answer:

b) (3x + 5)(3x + y)

Step-by-step explanation:

First, we can factor out a common factor of 3x from the first two terms:

9x^2 + 3xy = 3x(3x + y)

Now, we can factor out a common factor of 5 from the last two terms:

15x + 5y = 5(3x + y)

Putting it all together, we get:

9x^2 + 3xy + 15x + 5y = 3x(3x + y) + 5(3x + y) = (3x + 5)(3x + y)

the area of the square is 100 square units if its side is 10 units.by using area formula of square we can get answer

what is  square ?

A square is a shape with four equal sides and four right angles. It is a regular polygon with four sides, and all of its interior angles measure 90 degrees. In geometry, a square is often represented by the symbol "□"

In the given question,

If the side of a square is 10 units, then the area of the square can be calculated as:

Area of square = Side x Side

Area of square = 10 x 10

Area of square = 100 square units

Therefore, the area of the square is 100 square units if its side is 10 units.

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Answer: A

Step-by-step explanation:

sqrt(10x^2) sqrt(5x)

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(10x^2 * 5x)

sqrt(50x^3)

sqrt(2*25 *x^2 *x)

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(25) sqrt(x^2) sqrt(2x)

5x sqrt(2x)

In a direct variation, y=9 when x=3. A direct variation equation that shows the relationship between x and y is y=3x

What do you mean by direct variation?

Direct variation is a type of proportionality when one quantity changes right away in reaction to a change in another variable. This implies that if one number rises, the other will follow suit in a comparable manner. Similar to the last illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.

Given,

In a direct variation, y=9 when x=3.

Formulate an equation based on the conditions stated: y=kx

We put the value of the y and x in this equation

9=k*3

Subtract the coefficient of the variable from both sides of the equation

k= 3

We can write the equation of the function by putting the value of k:  y=3x

Hence the correct answer is y=3x

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In the prοbability,

1) B) Unlikely

2) F) Likely.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here The prοbability οf a randοmly-selected persοn being left-handed is

=> 1/10 = 0.1

Then , the given event οccurring rate is less than 0.5. Then,

Therefοre, a randοmly-selected persοn being left-handed is B) Unlikely.

Nοw , The prοbability οf rοlling a standard pair οf dice οnce and getting a sum greater than 5 is 0.7 .

Then the given event οccurring rate is greater than 0.5. Then,

Therefοre, this event is F) Likely.

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Answer:

Step-by-step explanation:

we can use the data points to write a system of equations to solve for the values of a and b in the general exponential function of the form f(x) = a(b)^x.

Using the data points, we get:

f(-1) = 1/3 = a(b)^(-1)

f(0) = 1/2 = a(b)^0 = a

f(1) = 3/4 = a(b)^1 = ab

Solving for a and b, we get:

a = 1/2

b = 3/4a = 3/4(1/2) = 3/8

Therefore, the exponential function that matches the given data points is:

f(x) = (3/8)^x + 1/2

Now we can evaluate the statements:

   The base of the exponential function is 3/8. (True)

   The function is decreasing. (False - since the base is between 0 and 1, the function is actually increasing)

   The y-intercept of the function is (0, 1/2). (True)

   The function passes through the point (2, 9/16). (False - the function is only defined for x = -1, 0, 1)

   The function is concave up. (True)

the only value of c that satisfies the conclusion of Rolle's Theorem is c = 2.we can use rolls theorem to solve this one

what is rolls theorem  ?

Rolle's Theorem is a fundamental theorem in calculus named after Michel Rolle, a French mathematician who lived in the 17th century. It states that if a function f(x) is continuous on a closed interval [a,b], differentiable on the open interval (a,b), and f(a) = f(b), then there exists at least one point c

In the given question,

To verify that the function satisfies the three hypotheses of Rolle's Theorem, we need to check the following:

f(x) is continuous on [0,4]

f(x) is differentiable on (0,4)

f(0) = f(4)

f(x) is a polynomial function and hence it is continuous on [0,4].

f'(x) = 2x - 4 is also a polynomial function and hence it is differentiable on (0,4).

f(0) = 8 and f(4) = 8, so f(0) = f(4).

Therefore, all three hypotheses of Rolle's Theorem are satisfied on [0,4].

Now, by Rolle's Theorem, there exists at least one value c in (0,4) such that f'(c) = 0. Solving f'(c) = 0, we get:

2c - 4 = 0

c = 2

Thus, the only value of c that satisfies the conclusion of Rolle's Theorem is c = 2.

Therefore, the value of c is 2.

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In interval notation, the number provided would be [57,555, 57,555].

Interval notation is used to represent a range of values between two endpoints using square brackets [ ] or parentheses ( ) depending on whether the endpoints are included or excluded.

Interval notation is a way to represent a range of values. However only one value was provided, I = 57,555.

To represent this single value using interval notation, you can simply express it as an interval with the same starting and ending points:

[57,555, 57,555]

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The interquartile range of the given data is 20 and last option is the correct choice.

The  interquartile range is difference of upper quartile and lower quartile.

We have been given the 5-number summary of a box plot that represents Coins in Collection. The five-number summary from left to right is 7, 16, 30, 36, 38.

We are asked to find the inter-quartile range of the given data.

The 5-point summary represents the lower data point, lower quartile, median, upper quartile and upper data point respectively.

We can see from our given 5 point-summary that lower quartile is 16 and upper quartile is 36.

interquartile range= upper quartile- lower quartile

interquartile range= 36 - 16

interquartile range = 20

Therefore, the interquartile range of the given data is 20 and last option is the correct choice.

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Step-by-step explanation:

Lucia is right. Faye is wrong.

because

3y³(7 - 3y) = +21y³ - 9y⁴

that is different to

-21y³ - 9y⁴

they have to remember : the outward sign (and factor in general) then applies to all terms inside the brackets when doing the multiplication.

so, if we need only negative terms as result, we need either a negative outward sign and all inward signs are positive, or we have a positive outward sign, and all inward signs must be negative.

mixing things up will not work for this goal.

Answer:

Without repetition: 6 numbers

With repetition: 27 numbers

Step-by-step explanation:

Given:

Numbers: 2;3;4 (3 numbers in total)

Without repetition (in the first place you can write all 3 out of 3 numbers, in the 2nd place two, since you cannot repeat the 1st number and so on)

Multiply the choice options:

3 × 2 × 1 = 6 (we don't divide it by the factorial of 3, because the order of forming numbers is important)

.

With repetition (in all three places you can write all 3 given numbers, since you can repeat them)

Multiply the choice options:

3 × 3 × 3 = 27 (the order is important)

Answer: 92 cm

Step-by-step explanation:

Your first step should be to solve for variables. Usually when finding unknown lengths or widths for perimeter, we use L & W to solve for length and width. You're already given 16 for the width of the rectangle. Perimeter: (L+L+W+W). Now we solve for length. Do 34 squared - 16 squared to get the missing length. 1156-256=900. Find the square root of 900 and now you have your length (30). Now you just add all the values up. 30+30+16+16=P. Therefore, the perimeter should equal 92. :)

Answer:

The coefficients are 6 and -4. The exponents are 3 and 1.

The amount of square feet that would be lined with extra padding is equal to 1,044 ft².

In Mathematics and Geometry, the lateral surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

SA = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the lateral surface area of a rectangular prism, we have the following;

SA = 2(24 × 12 + 6.5 × 12 + 6.5 × 24)

SA = 2(288 + 78 + 156)

SA = 2(522)

SA = 1,044 ft².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

[tex]h^-1[/tex] is the inverse of h, we can also express this relationship as: h([tex]h^-1[/tex](5)) = h(1) = 5.

A function that "undoes" the result of another function is called an inverse function. Formally speaking, if a function f maps input values from a set A to output values in a set B, then its inverse function, [tex]f-1[/tex], is a function that reverses the mapping, returning output values from B to the original input values in A.

If the function h has an inverse, it means that it is a one-to-one function, which implies that every input value has a unique output value and every output value has a unique input value.

Given that [tex]h^-1[/tex](5) = 1, we know that the inverse of h maps the input value of 5 to the output value of 1. In other words, if we input 5 into [tex]h^-1[/tex], we get 1 as the output:

[tex]h^-1[/tex](5) = 1

Since [tex]h^-1[/tex] is the inverse of h, we can also express this relationship as:

h([tex]h^-1[/tex](5)) = h(1) = 5

Therefore, we know that h(1) = 5, which is the output value that results when the input value of 1 is applied to the function h.

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Required ratios that represent the number of cars to the number of bicycle are 2:1, 5:2,8:3.

What is ratio?

A ratio is a mathematical comparison of two quantities or values, typically expressed as the quotient of one divided by the other. It is a way of expressing the relationship between two numbers or quantities, and is often used to make comparisons or to express the relative size or proportion of different things.

A ratio can be expressed in several ways, such as with a colon (:) or as a fraction. For example, the ratio of the number of apples to the number of oranges in a basket can be expressed as "3:2" or "3/2", meaning there are three apples for every two oranges. Ratios can be simplified or reduced to their simplest form, such as by dividing both sides of the ratio by their greatest common factor.

Ratios are used in many fields, including mathematics, finance, and science, to compare and analyze data, make predictions, and solve problems

Here we need to write three ratios that represent the number of cars to the number of bicycle.

So we can take following ratios,

2:1 (for every 2 cars, there is 1 bicycle)

5:2 (for every 5 cars, there are 2 bicycles)

8:3 (for every 8 cars, there are 3 bicycles).

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Correct question is "Write three ratios that represent the number of cars to the number of bicycle."

Answer:

Step-by-step explanation:

Answer:

The appropriate form for this problem is:

(Amount of Type A per bag) + (Amount of Type B per bag) = Total weight per bag

Using the given information, we can fill in the blanks:

(3 kg) + (___ kg) = (36 kg) ÷ (4 bags)

Simplifying the right side:

(36 kg) ÷ (4 bags) = 9 kg/bag

Substituting back into the equation:

3 kg + (___ kg) = 9 kg/bag

Solving for the blank:

___ kg = 9 kg/bag - 3 kg

___ kg = 6 kg/bag

Therefore, there are 6 kilograms of type B in one bag of the blend.

The volume of a rectangular prism is equal to length*width*height. In this case, we have V = 243 and H = 3.

243 = LW(3), so LW = 81, where L & W are whole numbers greater than 1. There are only 3 possible pairs of values for this: 27 x 3, 9 x 9, and 3 x 27 (we cannot use 1 x 81 or 81 x 1, since we need dimensions > 1).

Part A: This could be true if Length = 9 in and Width = 9 in, as 9 x 9 = 81.

Part B: The claim could be false if Length = 27 in and Width = 3 in, as 27 x 3 = 81, but 27 is not equal to 3.

Note that the width cannot be longer than the length.

Answer:

318 cm^2.

Step-by-step explanation:

Area of triangular sides = 2 * 1/2 * 5 * 6 = 30 cm^2.

Area of the rectangular sides = 2 * 6.5 * 16 = 208  + 5*16 = 288

Total area = 318 cm^2

Answer:

1). Equation: S= 60w + 750

2). $1470

Step-by-step explanation:

S= 60w + 750
S =60 x 12 + 750

S= 720 + 750

S = 1470

Answer:

15. (B) 47 degrees

16. (A) A square is always a parallelogram

17. (A) 17

18. (C) 16

19. (A) 2

Step-by-step explanation:

15. In a rhombus, all sides are the same length. If we draw a diagonal through it, then the two triangles that are left will be isosceles. Therefore, ADB and ABD are the same angle.

16. A square is always a parallelogram, but not vice versa (a parallelogram is always a square)

17. To find the median of a trapezoid, the equation is b = (a + c)/2, where a and c are the bases. Therefore, the answer is A.

18. This is an isosceles trapezoid, meaning WZ and XY are the same length. That means that WY and XZ are the same, allowing us the create the equation 3a + 7 = 7a - 5. Solve and find the answer.

19. Using the median formula b = (a + c)/2, we can solve the equation.

As a result, the size of the polygon created by placing the three cards in this manner is smaller than the sum of the three card's areas.

The volume of space contained by a polygon is its area. Depending on the type of polygon, a polygon's area can be calculated using a specific formula. For instance, multiplying a rectangle's length and breadth yields the area of the shape.

The formula to get the area of a regular polygon with n sides is:

A = (1/2) × n× s × a

where A is the polygon's surface area, n is its number of sides, s is each side's length, and an is its apothem (the distance from the center of the polygon to the midpoint of any side).

The three rectangular cards can be arranged by Isabella into a triangle shape, with two cards serving as the base and the third card sitting on top of them.

A larger rectangle with the measurements 4 inches by 10 inches will result from doing this.

The shortest perimeter that can be created by the three cards without overlapping is 28 inches, which is the perimeter of this rectangle.

rectangle=4×10=40square inches

This rectangle has a surface area of 40 square inches.

The three cards' aggregate surface area is 60 square inches. As a result, the size of the polygon created by placing the three cards in this manner is smaller than the sum of the three card's areas.

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Correct option is C. Hence,12.5% percentage of the volunteers from the second Saturday signed up to continue helping with community out reach service day once a month.

On the first Saturday, 80 volunteers showed up, and on the second Saturday, 60% of them did the same . The quantity of volunteers who showed up again on the second Saturday :

60% of 80 = 0.6 x 80 = 48

6 of these 48 volunteers agreed to continue offering their services once a month. So,the percentage of volunteers from the second Saturday 

(6/48) x 100% = 12.5%

As a result, 12.5% of the volunteers from the second Saturday agreed to continue participating in the monthly community outreach work day.

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The surface area in the image is 416 cm^2

Surface area is the measurement of the total area that the surface of a three-dimensional object occupies. It is typically measured in square units, such as square meters, square centimeters, or square feet. The surface area of an object can be calculated by finding the sum of the areas of all its faces or surfaces.

surface area = (2*0.5*12*8) + (2*10*10) + (12*10)

= 96 + 200 + 120

= 416 cm^2

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For each statement for triangle SQP and SQR, Q is the midpoint of PR: No, ∠P ≅ ∠R: No, ∠PSQ ≅ ∠RSQ: Yes, m∠P = 33°, m∠RSQ = 57°: No, ∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes.

What is triangle?

A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. Triangles are one of the basic shapes studied in geometry and are used in a wide range of applications, from construction to computer graphics.

Here are the answers to whether each statement provides enough information to prove that △SQP ≅ △SQR:

Q is the midpoint of PR: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the angles or sides.

∠P ≅ ∠R: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠SQP is a right angle, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-side (AAS) congruence criterion.

∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-angle (AAA) congruence criterion.

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Answer:

-by-step explanation:

The result:

1. 1 3/4 = 7/

4

= 1 3/

4

= 1.75

2. is 4

Using probability we know that the correct option is (C) Events A and B are distinct from one another because their occurrence has no bearing on it.

The probability of occurrence is a metric used in science to determine how likely an event is to occur.

When expressed as a percentage, it is written as a number between 0 and 1, or between 0% and 100%.

The higher an event's probability, the more likely it is to occur.

By computing the ratio of favorable outcomes to all outcomes, a probability calculator can determine the chance of an event.

So, in the given situation:

Event A and Event B are independent.

Then, thus occurrence of 1 does not affect the occurrence of others.

Therefore, using probability we know that the correct option is (C) Events A and B are distinct from one another because their occurrence has no bearing on it.

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The equation of the parabola y = 2x² - 8x + 13 in vertex form is y = 2(x - 2)² + 5.

An equation is a formula that links two statements and uses the equals sign (=) to indicate that the statements are equivalent. A mathematical statement proving the equality of two algebraic expressions is called an equation. For instance, the equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14. The relationship between the two sentences that appear on opposing sides of a letter is expressed mathematically. The single variable and the symbol are typically the same. Like 2x - 4 Equals 2, for example.

To write the equation of a parabola in vertex form, we use the formula:

y = a(x - h)² + k

Where (h,k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola. To convert the equation y = 2x² - 8x + 13 to vertex form, we need to complete the square.

First, let's factor out the leading coefficient of 2:

y = 2(x² - 4x) + 13

Next, we need to add and subtract a constant inside the parentheses to complete the square. To determine this constant, we take half of the coefficient of x, square it, and add it inside the parentheses:

y = 2(x² - 4x + 4 - 4) + 13

y = 2((x - 2)² - 4) + 13

Now we can simplify and write the equation in vertex form:

y = 2(x - 2)² - 8 + 13

y = 2(x - 2)² + 5

Therefore, the equation of the parabola y = 2x² - 8x + 13 in vertex form is y = 2(x - 2)² + 5.

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The complete question is:

The equation of the parabola is y = 2x² - 8x + 13. Its vertex form is ______________.