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What is the unknown scale size?



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The Zero Product Property in mathematics states that if the product of two numbers is zero, then at least one of the numbers must be zero. You typically use this property when solving quadratic equations by setting each factored term equal to zero and then solving for every variable.

The Zero Product Property is an essential concept in algebra, particularly when it comes to solving quadratic equations. The Zero Product Property states that if the product of two numbers, terms, or factors is zero, then at least one of the factors must be zero. In simple terms, if a * b = 0, then a has to be zero, or b has to be zero, or both.

To use the Zero Product Property, you usually start by setting an equation equal to zero. For example, let's solve the quadratic equation x^2 - 5x = 0. First, you would factor the equation to (x)(x-5) = 0. Now, using the Zero Product Property, we can set each factor equal to zero and solve for x. This gives us x = 0 and x = 5.

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Answer:

(sin^2 w + 1) / cos w.

Step-by-step explanation:

Note: sec w = 1 / cos w and csc w = 1/ sin w.

So we have:

(sec w(1 + csc^2 w)) / (csc^2 w)​

= 1/cos w (  1 + 1/ sin^2 w)  /   (1 / sin^2 w)

= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w

=  sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)

= sin^2 w / cos w + 1 /  cos w

=  (sin^2 w + 1) / cos w.

Answer:

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen; When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

Step-by-step explanation:

In a binomial distribution, there are only two outcomes, or outcomes that can be reduced to 2.  In the first choice, we either draw a prime number or do not draw a prime number.  In the third choice, we either draw a 3 or do not draw a 3.

There must be a fixed number of trials.  In the first choice, we have 5 trials; in the third option, we have 6 trials.

The trials must be independent of each other.  Since the cards in the first and third options are drawn with replacement, the outcome of one trial does not influence the probability of the next trial.

The probability must be the same for every trial.  This is true of the first and third options.

Answer:

Prime And 3 is choosen

Step-by-step explanation:

Answer:

[tex]\large\boxed{M+T=-15r^2+2r+8}[/tex]

Step-by-step explanation:

[tex]M=-8r^2+11r-6\\T=-7r^2-9r+14\\\\M+T=?\\\\\text{Substitute:}\\\\M+T=(-8r^2+11r-6)+(-7r^2-9r+14)\\\\M+T=-8r^2+11r-6-7r^2-9r+14\qquad\text{combine like terms}\\\\M+T=(-8r^2-7r^2)+(11r-9r)+(-6+14)\\\\M+T=-15r^2+2r+8[/tex]

The expression that represents M + T is -15r^2 + 2r + 8

The equations for M and T are given as:

[tex]M=-8r^2 +11r -6[/tex]

[tex]T=-7r^2-9r+14[/tex]

The sum of M and T is represented as: M + T

This is then calculated as:

[tex]M+T=-8r^2 +11r -6-7r^2-9r+14[/tex]

Collect like terms

[tex]M+T=-8r^2 -7r^2+11r -9r-6+14[/tex]

Evaluate the like terms

[tex]M + T = -15r^2 + 2r + 8[/tex]

Hence, the expression that represents M + T is -15r^2 + 2r + 8

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Answer:

C) 0.70

Explanation:

:))

Answer:

[tex]an = 2.5 + (n - 1)(-5)[/tex]

Step-by-step explanation:

we know that

The explicit formula for the nth term of an arithmetic sequence is given by the formula

[tex]an = a1 + (n - 1)r[/tex]

where

a1 is the first term

n is the term number

r is the common difference

In this problem we have

[tex]a1=2.5, r=-5[/tex]

substitute

[tex]an = 2.5 + (n - 1)(-5)[/tex]

Answer:

Lucy reads 10 fewer pages that Carey

Step-by-step explanation:

The first sentence reads as Carey having more, so Lucy has fewer,

Rewriting it using fewer means that Lucy will be the main subject of the sentence, so Lucy reads 10 fewer pages that Carey is the sentence you want

Answer:

We can start solving this problem by first identifying what the elements of the sets really are.

R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.

Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).

W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.

W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.

R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.

0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.

∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are not an element of R).

{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).

-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.

Step-by-step explanation:

Certain elements and sets are examined for their relationships with the sets of real numbers, integers, and whole numbers; identifying which elements belong to which sets and if one set is a subset of another.

When comparing different sets of numbers, we analyze whether one set is a subset of another and whether certain elements belong to specific sets. The given question involves the sets R (real numbers), Z (integers), and W = {0, 1, 2, ...}, also known as the set of whole numbers or non-negative integers.

→ W ⊂ Z: This is true because all elements of W are non-negative integers, which are a subset of Z, the set of all integers including negative, zero and positive whole numbers.

→ R ⊂ W: This is false because the set of real numbers includes irrational numbers as well as negative numbers, which are not included in W.

→ 0 ∈ Z: This is true because zero is an integer and, therefore, is an element of Z.

→ ∅ ⊂ R: This is true because the empty set is a subset of all sets, including the set of real numbers.

→ {0, 1, 2, ...} ⊆ W: This is true because this set is exactly W itself, and a set is always a subset of itself.

→ -2 ∈ W: This is false because W contains only non-negative integers, and -2 is a negative number.

Answer:

Jody

Step-by-step explanation:

You can either convert 500 seconds to minutes or 8 minutes to seconds to compare. I'll do both.

There is 60 seconds in a minute. To find the total minutes of 500 seconds, divide 500 by 60 → 8.3, which means that Jody practiced for 8.3 minutes.

To find the total seconds of 8 minutes, multiply 60 seconds per minute by 8 minutes → 60 * 8 = 480 seconds which means that Bill practiced for 480 seconds.

Now you can compare. Jody practiced for 500 seconds, or 8.3 minutes. Bill practiced for 480 seconds, or 8 minutes. Jody practiced longer.

Answer: x = 1/5

//Hope it helps.

Answer:

[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]

Step-by-step explanation:

The given logarithmic expression is:

[tex]\log_2(\sqrt[5]{16} )[/tex]

We rewrite the radical as an exponent to obtain;

[tex]\log_2(\sqrt[5]{16} )=\log_2(16^{\frac{1}{5}} )[/tex]

Recall and use the power rule; [tex]\log_a(M^n)=n\log_a(M)[/tex]

[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(16 )[/tex]

We write 16 as an index number to base 2.

[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(2^4)[/tex]

We apply the power rule again;

[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}\log_2(2)[/tex]

We simplify to get;

[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}(1)[/tex]

[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]

Answer:

Step-by-step explanation:

The formula of regular polygon with n sides of length b and apothem a:

[tex]A=\dfrac{nba}{2}[/tex]

We have:

n = 6

b = 8

a = 6

Substitute:

[tex]A=\dfrac{(6)(8)(6)}{2}=144[/tex]

The perimeter:

[tex]P=6b\to P=(6)(8)=48[/tex]

Answer:

A) 90

Step-by-step explanation:

"The sum of two integers is 23" becomes

a + b = 23

"the positive difference of the same two integers is 13" becomes

a - b = 13        (difference means subtract)

Now solve the system..

a + b = 23

a - b = 13            *use addition or elimination method, since b has opposite coefficients...

2a = 36             ( we add the two equations together)

   a = 18             (divide by 2 on both sides)

Since a = 18,   18 + b = 23, gives us b = 5.     (18 + 5 = 23)

ab = (18)(5) = 90

Answer: A) 90

Let one integer is = x.

Sum of them is 23. So the other integer is (23 - x).

Given: Difference = 13.

So,

[tex]x-(23-x)=13\\ x-23+x=13\\ 2x=36\\ x=18[/tex]

So the other number is = 23 - x = 23 - 18 = 5.

So the product = 18*5=90

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Answer:

[tex]\large\boxed{\overline{QT}\cong\overline{AZ}}[/tex]

Step-by-step explanation:

[tex]\triangle QPT\cong\triangle ARZ\\\\\begin{array}{c|c}Q&A\\P&R\\T&Z\end{array}\Rightarrow\begin{array}{ccc}\overline{QP}\cong\overline{AR}\\\overline{PT}\cong\overline{RZ}\\\overline{QT}\cong\overline{AZ}\end{array}[/tex]

Answer:

First option.

Step-by-step explanation:

I drew the triangles to see it better. If two triangles are congruent the sides and the angles have the same length. Also, the order of the vertex is important. I put them as it is enunciated. So, watching the image the congruent sides are:

QT and AZ

QP and AR

PT and RZ

Then, the correct option is the first one.

Answer:

4. South Korea’s leadership arrested and killed thousands of

✔ alleged North Korean agents.

Step-by-step explanation:

got it right on edge 2021

Answer:

alleged North Korean agents.

Step-by-step explanation:

Edge 2022

Answer:

L8

Step-by-step explanation:

We turn that upside-down

86 '? '88 '89 '90 '9I

Then obviously we can tell that ? is to be replaced by 87

86 '87 '88 '89 '90 '9I

Then we turn it back right-side up again, and we have:

I6, 06, 68, 88, L8, 98

Answer: L8

Hope this helps ;)

The missing number in the sequence 16...06...68...88...?...98 is 78

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

16...06...68...88...?...98

When the number are flipped upside down, we have

91....90....89.....88......?.......86

In the above sequence, we can see that -2 is added to the previous term to get the new term

This means that the complete sequence is

91....90....89.....88......87.......86

When flipped, we have

16...06...68...88...78...98

Hence, the missing number is 78

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Answer:

  θ = 6.28k +3.14

Step-by-step explanation:

cos(θ) is -1 for θ = π and multiples of 2π added to that.

___

The answer above rounds π and 2π as requested by the problem statement. Those values are only valid for small values of k. (I suppose it might be reasonable to argue that no rounding is appropriate.)

Answer: This would equal the same distance

Explanation: Think of a clock if it rotates 90 degrees counter clockwise it would stop at the number 9. If it rotates 90 clockwise it would stop at 3, then rotate that hand clockwise by 90 degrees one more time it will stop at 6, then 9 at 270 degrees.

Answer:

sorry if im late but this is the answer:

Step-by-step explanation:

Yes, I think they are the same. One revolution is 360 degrees. A 180-degree clockwise rotation is the same as a 180-degree counterclockwise rotation. The sum of the measures is 360. So, moving in a clockwise direction for 270 degrees would end at the same place as moving 90 degrees in a counterclockwise direction.

Answer:

  Because point P is not the midpoint of OQ.

Step-by-step explanation:

The circle center is found at the intersection of the perpendicular bisectors of any two chords. Segment PC is perpendicular to OQ, but does not bisect it. Hence, point C cannot be the circle center.

Answer:

Selena lives 1/3 of a mile away from her school.

Step-by-step explanation: If the walk to her school AND back is 2/3 of a mile, then all you have to do is split 2/3 in half. Which is 1/3 of a mile.

Answer:

1/3 miles. 2/3 divided by 2 = 1/3.

Step-by-step explanation:

Answer:

The answer is ellipse; 23° to the nearest degree ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

- 9x² + 4xy + 5y² - 40 = 0

∵ A = 9 , B = 4 , 5 = 5

∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0

∴ B² - 4AC < 0

∴ If a conic exists, it will be either a circle or an ellipse.

* To find the type of the graph lets check;

- If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs and are not equal

∴ The graph is an ellipse

* If we have term xy ⇒ B ≠ 0

∴ The graph is rotate by angle Ф

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 9 , B = 4 , C = 5

∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1

∴ tan(2Ф) = 1

∴ 2Ф = 45°

∴ Ф = 22.5° ≅ 23° to the nearest degree

* The answer is ellipse; with angle of rotation = 23°

Answer:

x=3

Step-by-step explanation:

[tex]2x+3+5x=24\\7x+3=24\\7x=21\\x=3[/tex]

Final answer:

Jason can cut 12 pieces of sausage from the 6-inch roll, since dividing the roll's length by the thickness of each piece (6 inches ÷ 1/2 inch) yields 12 pieces.

Explanation:

To determine how many pieces of sausage Jason can cut from a roll that is 6 inches long, where each piece is 1/2 inches thick, one would perform a simple division.

The length of the sausage roll (6 inches) is divided by the thickness of each piece (1/2 inch) to find out how many pieces can be cut.

This is a basic fraction division problem that we solve by multiplying the length of the roll by the reciprocal of the thickness of the pieces to be cut.

Calculation

To calculate:
6 inches × 2/1 (which is the reciprocal of 1/2) equals 12.

So, Jason can cut 12 half-inch-thick pieces from the 6-inch roll.

[tex]\displaystyle\lim_{x\to0^+}x\ln x^3=\lim_{x\to\infty}\frac{\ln\frac1{x^3}}x=-3\lim_{x\to\infty}\frac{\ln x}x=\frac\infty\infty[/tex]

L'Hopital's rule tells us the limit is equal to

[tex]-3\displaystyle\lim_{x\to\infty}\frac{\frac1x}1=0[/tex]

Hence, the lakes' altitudes varied by 40 feet. To sum up: Average: around -26.3 feet, Average: -18 feet , Zero mode and 30 to 40 ft.

The mean, a statistic of central tendency in mathematics, is the average of a group of numerical values. It is also frequently known as the geometric average. A set of values' mean is calculated by adding up all of the values and dividing the result by the amount of values in the set. The mean can be determined, for instance, if the set of values is 3, 5, 7, 9, and 11, by multiplying the values together and dividing them by the total amount of numbers: Mean = (3 + 5 + 7 + 9 + 11) / 5 = 7 .As a result, 7 represents the set's mean value.

given

The median altitude of the lakes is -18 feet because the middle number is -18.

Mode: To identify the mode, we search the collection for the number that pops up the most often. There is no mode because no number appears more than once in this instance.

Range: To get the range, divide the largest by the smallest number:

Maximum number - smallest number equals the range (-9) - (-49) = 40

Hence, the lakes' altitudes varied by 40 feet. To sum up: Average: around -26.3 feet, Average: -18 feet , Zero mode and 30 to 40 ft.

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Answer:

B

Step-by-step explanation:

The function -x^4 + 1 is a polynomial graph. As such it has specific characteristics or behavior you can expect to see:

In conclusion, this graphs has ends which end the same direction and both face down.

Answer:

c. 105 yd^2.

Step-by-step explanation:

First find the slant height (h) of each of the triangular walls:

tan 60 = h /  3.1

h = 3.1 tan 60

= 5.369 yds.

Area of each side = 3.1* 5.369

= 16.645

Total surface area of the pyramid

= 4 * 16.645 + 6.2^2

= 105.02 yd^2.

Answer:

2 and -1

Step-by-step explanation:

y = x^2 -x-2

To find the x intercept, set y = 0

0 = x^2 -x-2

Factor

What 2 numbers multiply to -2 and add to -1

-2*1 = -2

-2 +1 = -1

0 = (x-2) (x+1)

Using the zero product product property

x-2 = 0    x+1 =0  

x=2          x=-1

Answer:

Answer is C (1/2)

Step-by-step explanation:

Answer:

Tthe area of the shaded region is [tex](x^{2}-3x+36)\ unit^{2}[/tex]

Step-by-step explanation:

we know that

To find the area of the shaded region (blue region), subtract the area of the smaller rectangle from the area of the larger square

so

Find the area of the larger square

[tex]A=(x+1)^{2}=(x^{2}+2x+1)\ unit^{2}[/tex]

Find the area of the smaller rectangle

[tex]A=5(x-7)=(5x-35)\ unit^{2}[/tex]

Subtract the polynomials

[tex](x^{2}+2x+1)-(5x-35)=(x^{2}-3x+36)\ unit^{2}[/tex]