Find the length of the three missing sides in the rhombus below.
x=

y=

z=

Answer:

x=2

Step-by-step explanation:

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x=-26

x=2

a) The error first appears between Steps 2 and 4.

b) The value of the expression is given by: 5^(-4) = 1/625.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The numerator is simplified as follows:

25^(-4) = 5²^(-4) = 5^(2 x -4) = 5^(-8).

The denominator is given as follows:

5²^(-2) = 5^(-4).

When two terms have the same base and different exponents and are divided, we keep the base and subtract the exponents, hence:

5^(-8)/[5^(-4)] = 5^(-8 - (-4)) = 5^(-4) = 1/(5^4) = 1/625.

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The formula for V0 from the expression given will be V0 = V1 - at

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, the formula for V0 will be found thus:

a = V1 - V0 / t

Cross Multiply

at = V1 - V0

Subtract V1 from both sides

-V0 = at - V1

V0 = V1 - at

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A Pythagorean triple using Euclid's rule is (3, 4, 5).

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

Pythagorean triples consist of the three positive numbers a, b, and c, where a²+b² = c².

The symbols for these triples are (a, b, c).

Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

The example of triplets is (3,4,5).

Therefore, the example of triplets is (3,4,5).

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There would be 40,320 different types of burgers.

If each burger must have all of the ingredients listed (cheese, lettuce, tomato, pickles, onions, mayo, catsup, and mustard), and the order of the ingredients is important, then the number of different types of burgers would be 8! (8 factorial), which is the number of permutations of 8 items.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

So there would be 40,320 different types of burgers that can be made with all of the ingredients and the order of placement is important.

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There is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

To calculate the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school, you would need to follow these steps:

Calculate the mean of the sample by adding up all the hours of sleep reported and dividing by the sample size (n).

Calculate the standard deviation (σ) of the sample by taking the square root of the sum of squares of the differences between the sample values and the mean divided by n1.

Calculate the standard error (SE) by dividing the standard deviation by the square root of n.

Calculate the margin of error (ME) by multiplying the standard error by the critical value of 1. 96.

Calculate the confidence interval by adding and subtracting the margin of error from the mean. This will give you the lower and upper bounds of the confidence interval.

Therefore, the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school is (6. 73, 7. 67). This means that there is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

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Answer:

5

Step-by-step explanation:

The domain of each function is given as follows:

11. All real values except x = -2 and x = 4.

12. All real values except x = -1 and x = 1.

13. All real values except x = -2.

The domain of a function is the set that contains all the possible input values for the function.

The functions in this problem are rational functions, meaning that all the values of x that make the denominator zero are excluded from the domain.

Then the excluded values are obtained as follows:

11. x² - 4 = 0 -> x = -2 and x = 2.

12. x² - 1 = 0 -> x = -1 and x = 1.

13. x + 2 = 0 -> x = -2.

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The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c2.

Given here : Two special triangles

1) Clearly the given triangle is a right isosceles triangle as  a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

Thus x=y

Now using pythagoraes theorem we get

[tex]x^2+x^2=30^2\\2x^2=900\\x^2=450\\x=15\sqrt{2}[/tex]

Thus x=y=15√2

2) Again the given triangle is an isosceles triangle and thus x=√10

[tex]\sqrt{10}^2+\sqrt{10}^2 =y^2\\y^2=20\\y=2\sqrt{5}[/tex]

Hence,  The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)

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Answer:

X < 4

Step-by-step explanation:

3rd one.

The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.

The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them. So a total of m+n comparisons are required in the worst case scenario.

This can be visualized by using a formula: n + m = m+n. This formula can be used to calculate the total number of comparisons required.

For example, if m = 10 and n = 15, then 10 + 15 = 25. This means that 25 comparisons would be required in order to sort the two lists.

Thus, the merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them.

The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.

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Answer:

x ≥ 1

Step-by-step explanation:

The filled in circle means the inequality includes 1

Hope this helped!

Answer:

0, 1, 2, and 3

Step-by-step explanation:

make a number line -5 to 5, mark the spots -1 and 4. the numbers in between are your answer!

The speed of the car is 0.8 miles per hour when the skid mark is 100 feet.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The speed of a car in miles per hour is √(20)L, Where 'L' is the length in feet of its skid mark.

We know, 1 mile is equal to 5280 feet.

So, The speed of the car is √(20)×(L/5280) miles.

Therefore, The speed of the car when the skid mark is 100 feet is,

=  √(20)×(100/5280) miles.

= √20×0.019 miles.

= 0.8 miles per hour.

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Answer: 3 2/3

Step-by-step explanation:

Remeber that the formula is A=(b*h)/2

2 times 3 2/3 = 7 1/3

7 1/3 halved is 3 2/3

Therefore, the answer is 3 2/3

Answer: Jan 11

Step-by-step explanation:

You subtract two weeks (14 days) from Jan 25.

25-14=11

The last pay day was January 11.

C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school.

C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school. The domain for X consists of all students in the school and the domain for Y consists of all classes being offered. To explain this statement further, firstly it should be noted that the statement is saying that a student (X) is enrolled in a class (Y). Secondly, the term “domain” refers to the set of all possible values that can be used for a given variable. In this case, the domain for X consists of all students in the school, while the domain for Y consists of all classes being offered at the school. Therefore, the statement C(X,y) is saying that a student from the school is enrolled in one of the classes offered by the school.

The complete question: Let C(X,Y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being

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Answer:

Option B)

Step-by-step explanation:

The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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The total amount that he will owe after the loan period of 25 weeks is; $806.25

The formula to calculate simple interest is;

I = PRT/100

Where;

P is principal

R is rate

T is time

We are given;

P = $780

R = 7%

T = 25 weeks = 25/52 years

Thus;

I = (780 * 7 * 25/52)/100

I = $26.25

Total payoff = $780 + $26.25

= $806.25

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The required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
y = 1/5x + 6,
4x + 5y = 5

Graph the given equation on the coordinate plane,
As we can see both lines intersect each other at (-5, 5), which is the solution of the system of the equation given.

Thus, the required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).

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Lainey cannot descend for more than 3 minutes.

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

Given:

We know that she first descends 22 feet, and then she descends at a rate of 22 feet per minute. Basically, we have 22 feet which have to me summed with 22x, which expresses the ratio per minute, where x is minutes, and these terms cannot be more than 93 feet, so there are equal or less than 93 feet.

The expression would be

22 + 22x ≤ 93

If we solve this, we have,

22 + 22x ≤ 93

22x ≤ 93 - 22

22x ≤ 71

x ≤ [tex]\frac{71}{22}[/tex]

Therefore, She cannot descent for more than 3 minutes.

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If x must be a number. The same outcome is obtained by increasing x by 20% as well as by decreasing that product of four with x by 5. x has the value of 25/14.

Let's look up an expression for raising x by 20%. This might be shown as x + 20%. x = x + 0.2x = 1.2x = 6x/5.

The two expressions must now be set to be equal to each other.

6x/5 = 4x - 5

Add 6x/5 to both sides and subtract. To make 4x and 6x/5 have a similar denominator, we can rephrase 4x as 20x/5.

0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5

0 = 14x/5 - 5

We can now increase both sides by five.

5 = 14x/5

Now that we have the reciprocal of 14/5, 5/14, we may multiply either sides by this number.

5(5/14) = (14x/5)(5/14) = x

25/14 = x

Thus, the solution is 25/14.

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Option C. A random sample of attendees would be a group of attendees selected in a systematic and unbiased manner, such that each attendee has an equal chance of being selected to participate in the survey.

This ensures that the opinions represented in the survey are representative of the opinions of the entire attendee population. For example, the organizers could randomly select every 10th attendee, or they could use a random number generator to select a certain number of attendees. The important thing is that the selection process is not influenced by any extraneous factors and is done in a way that ensures each attendee has an equal chance of being selected.

Finally, it is also important to ensure that the survey questions are clear, unbiased, and relevant to the topic being studied. This will help ensure that the responses obtained are meaningful and accurately reflect the opinions of the attendees.

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The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a random sample of attendees?

A. The organizers form groups of 20 attendees based on the day the attendees registered. Then, the organizers randomly choose 4 groups and select all of the attendees in these groups.

B. The organizers select the first 80 attendees who register for the conference because these attendees are easily accessible.

C. The organizers assign each attendee a different number. Using a random number table, the organizers draw 80 of those numbers at random. Then, organizers select the attendees assigned to the drawn numbers. Every set of 80 attendees is equally likely to be drawn using the random number table.

Answer:

47500

Step-by-step explanation:

5 x 19=95

95 x 25=2375

2375 x 4=9500

9500 x 5= 47500

hope this is correct :)

The answer is [tex]L = 624 cm^2; S = 944 cm^2[/tex]  where L is the lateral area and S is the surface area of a right rectangular prism.

The lateral area of a right rectangular prism is given by the formula:

[tex]L = 2(lw + bh)[/tex]

where l and b are the length and width of the base, and h is the height of the prism.

The surface area is given by the formula:

[tex]S = 2(lb + bh + lh)[/tex]

For the given prism with a base of 12 cm by 10 cm and a height of 16 cm, the lateral area is:

[tex]L = 2((12 cm)(10 cm) + (12 cm)(16 cm)) \\= 2(120 cm^2 + 192 cm^2)\\= 2(312 cm^2)\\= 624 cm^2.[/tex]

The surface area is:

[tex]S = 2((12 cm)(10 cm) + (10 cm)(16 cm) + (12 cm)(16 cm))\\ = 2(120 cm^2 + 160 cm^2 + 192 cm^2) \\ = 2(472 cm^2) \\ = 944 cm^2.[/tex]

So the answer is [tex]L = 624 cm^2[/tex] ; [tex]S = 944 cm^2[/tex] .

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Answer:

The correct answer is L=704 cm^2 ; S-944 cm^2

Step-by-step explanation:

p=2l+2w

P=2(12)+2(10)=24+20=44cm

L=(44)(16)=704 cm^2

So the lateral area is 704 cm^2

B=(12)(10)=120cm^2

S=704+2(120)=704+240=944cm^2

So the surface area is 944 cm^2

Answer: $480

Step-by-step explanation:

Calculators=$80 per 12 calculators

Calculators=$25 for 3 Calculators

80 x 6= 480

the price at each level of demand can be calculated by p = D(q) = 28 - 2.25q.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, Given a function that defines the price for a certain model of a youth wristwatch is related by p = D(q) = 28 - 2.25q.

Thus,

A) The demand function is p = 28 - 2.25q.

When demand q is 0,

price is p = 28 - 2.25*0 = $28

B) When demand q is 400,

price is p = 28 - 2.25*4 = $19.

C) When the price is 10,

we have 10 = 28 - 2.25q or 2.25q = 18.

This gives q = 800 or 8 in hundreds

D) Graph of the demand function will have a vertical intercept of 28 (When q = 0, the value of p is 28) and a horizontal intercept of 12.44.

Here the first graph in part A is correct because it fits the intercepts

E) Supply function is p = 1.25q.

When the price is 0,

the quantity supplied is 0.

F) When the price is 17,

quantity supplied is 17 = 1.25q or q* = 13.6 of 1360 in hundreds

G) The vertical intercept is 0.

The graph will be similar to the one in option A because it matches both demand and supply equations.

H) Equilibrium occurs when demand and supply are equal

28 - 2.25q = 1.25q

28 = 3.5q

q* = 28/3.5 = 8 or 800 watches

price is p = 1.25*8 = $10.

therefore,  the price at each level of demand is solved above.

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Complete question:

Answer:

Trina

Step-by-step explanation:

Trina is 85.6 below sea level

Jessie is 87.9 above

distance wise 85.6 is shorter

The equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.

The equation in Exploration 4.1.1 problem 3 is an identity because it was derived from the general quadratic equation [tex](ax^2 + bx + c = 0)[/tex]. Therefore, it always works when given the coefficients of a quadratic equation. This is demonstrated by using the formula for the quadratic equation, which is [tex]x = (-b ±√(b^2 - 4ac))/2a[/tex]. Plugging in the coefficients of a quadratic equation, the result is always the zeros of the quadratic equation. For example, for the equation[tex]6x^2 - 4x + 3 = 0[/tex], the zeros are found by plugging in a = 6, b = -4, and c = 3 into the formula. This gives us[tex]x = (-(-4) ±√((-4)^2 - 4(6)(3))/2(6) = (4 ±√(16 - 72))/12 = (4 ±√(-56))/12 = (4 ±√(7i))/12[/tex]which corresponds to the two zeros of the equation,[tex]x = -2 ± 3i[/tex]. This demonstrates that the equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.

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