Can someone pls tell me how to do this?
My papers are coming really soon and my maths teacher didnt teach us this lesson ​

The properties of the function are

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

y = x² - 5

The vertex of the above function is

(0, -5)

The axis of symmetry is the x-coordinate of the vertex

So, we have

x = 0

The y-intercept is when x = 0

So, we have

y = -5

Because the leading coefficient is positive, the function has a minimum vertex

From the graph, we have the x-intercepts to be

x = ±2.236

The domain is the set of all real values, and the range is (-5, ∞)

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Mary's total payment last month can be calculated by adding her basic salary to her overtime payment. Mary received a total payment of $4,625 last month.

Her basic salary was $3,700.
To find out the amount of her overtime payment, we need to calculate 25% of her basic salary.
25% of $3,700 can be found by multiplying $3,700 by 0.25 (since 25% is equivalent to 0.25).
So, 25% of $3,700 is $925 ($3,700 x 0.25 = $925).
Now, we can find Mary's total payment by adding her basic salary and her overtime payment.
$3,700 + $925 = $4,625

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Answer:

A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.

Answer:

The answers are (-10, -4) and (0, 1)

Step-by-step explanation:

The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.

Hope this helps!

Answer:

∠A = 120° (180°-60°)

∠W = 60° (b/c ∠W=∠X)

∠Y = 100° (b/c 180°-80°)

∠X = 60° (180°-120°)

∠Z = 120° (180-60°)

Step-by-step explanation:

im unsure about A and W

Answer:

Work Shown:

\(a^2 + b^2 = c^2\\\\40^2 + 75^2 = c^2\\\\1600 + 5625 = c^2\\\\7225 = c^2\\\\c^2 = 7225\\\\c = \sqrt{7225}\\\\c = 85\\\\\)

I used the pythagorean theorem with a = 40 and b = 75. The order of the 'a' and b doesn't matter, as long as c is the largest side.

The 40-75-85 pythagorean triple is the scaled up version of the 8-15-17 triple (multiply each piece by 5).

Answer:

85 yd

Step-by-step explanation:

We know that

\(\pmb{\bf H^2=P^2+B^2}\)

Here,

H = c, P = 75 yd, B = 40 yd

\( \begin{gathered} \: \sf \implies \: {c }^{2} = (75) {}^{2} + {(40)}^{2} \\ \sf \implies {c}^{2} = 5625 + 1600 \\ \sf \implies \: {c}^{2} = 7225 \\ \sf \implies \: c = \sqrt{7225} \\ \sf \implies \: c = 85 \: yd \end{gathered}\)

Answer:

8/50

Step-by-step explanation:

2/10 x 4/5 = 8/50

Hope that helps!

The area of the floor required to cover using carpet is equal to 24 square yards .

To calculate the area of the room in square yards,

convert the dimensions from feet to yards and then find the product of the length and width.

1 yard (yd) = 3 feet (ft)

Room length in yards

= 18 feet / 3 feet/yd

= 6 yards

Room width in yards

= 12 feet / 3 feet/yd

= 4 yards

Now, find the area of the room in square yards:

Area = Length × Width

Area = 6 yards × 4 yards = 24 square yards

Therefore,  24 square yards of carpet area required to cover the floor of the room.

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The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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Answer:

3

Step-by-step explanation:

substitute x = 4 , y = 6 into the expression

y - (5 - (x - y))

= 6 - (5 - (6 - 4))

= 6 - (5 - 2))

= 6 - 3

= 3

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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An SAT-M score in the 98th percentile is approximately 734.55 or higher.

According to the College Board website,

The scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and a standard deviation of 111. Assume that SAT-M scores follow a normal distribution. To gain admission to a particular engineering school, a requirement is to obtain an SAT-M score in the 98th percentile, indicating that the score is among the top 2% of scores.

For getting the actual SAT-M score, we need to find the corresponding z-score for the 98th percentile.

Using the Inverse Normal Distribution Calculator, we get a z-score of 2.05 for the 98th percentile.

So, the formula for finding an actual SAT-M score is:

x = μ + zσ

Where x is the actual SAT-M score,

μ is the mean = 507,

z is the z-score = 2.05,

σ is the standard deviation = 111

x = 507 + (2.05)(111)

x = 507 + 227.55

x = 734.55

The actual SAT-M score for the 98th percentile is approximately 734.55 (rounded to the nearest hundredth).

Therefore, an SAT-M score of 734.55 or higher is required for admission to the engineering school.

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Answer:

Step-by-step explanation:

First, we need to look at the simpler equation. We see that the top equation is the simpler one.

y=-2x + 6

Now we plug that equation with the other one.

6x + 3(-2x + 6) = 18

6x -6x + 18 = 18

18 = 18

Since we see that 18 = 18. We know that this equation is a true equation. We can plug the y-variable in first and it will still be a true statement.

Obtaining assessment results from the previous year for students entering the fourth-grade class allows the teacher to gain valuable insights into their academic strengths and weaknesses.

By reviewing the assessment results from the previous year, the fourth-grade teacher can obtain a clear understanding of each student's individual academic performance. This information helps the teacher tailor their instructional strategies to meet the specific needs of each student. For students who excelled in certain areas, the teacher can provide enrichment activities or more challenging assignments to keep them engaged and motivated. On the other hand, for students who struggled in certain subjects, the teacher can offer targeted interventions and additional support to help them catch up.

Furthermore, the assessment results can guide the teacher in identifying any learning gaps or misconceptions that need to be addressed early on in the school year. Overall, utilizing the previous year's assessment results allows the teacher to create a more personalized and effective learning experience for their fourth-grade students, fostering growth and academic success.

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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer:

  12.6 pounds

Step-by-step explanation:

You want to find the total weight of rocks when one 6-lb rock is 47.5% of the total weight.

If w represents the weight of all of the rocks, then the fraction of that whole weight is ...

  6 = 47.5% × w

Dividing by the coefficient of w gives ...

  w = 6/0.475 ≈ 12.6

The weight of all of the rocks is about 12.6 pounds.

The simplification of the expression 3y(2) are 6y or 3y^2

The expression 3y(2) is ambiguous and can be interpreted in two ways depending on the intended meaning.

If the expression is intended to mean "3 times the product of y and 2", then the correct answer is 6y, which can be obtained by applying the distributive property of multiplication:

3y(2) = 3y x 2 = 6y

On the other hand, if the expression is intended to mean "3 times y squared", then the correct answer is 3y^2

3y(2) = 3y^2

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Answer:

I got 20 when calculating this

Answer: \(1536\ m^3\)

Step-by-step explanation:

Given

Box A has a volume of \(24\ m^3\)

Box B is similar to box A such that box A dimension is multiplied by 4 to get the box B

So, each length is 4 times the box A and volume is the cube of the side.

Thus, the volume of box B is \(4\times 4\times 4\) the volume of box A

The volume of box B is  

\(=4\times 4\times 4\times 24\\=1536\ m^3\)

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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Answer:

Square root of 100.  

Step-by-step explanation:

Step-by-step explanation:

We can write 10 as a fraction 10/1, therefore,\(\sqrt{}\)100   is a rational number.

Part A : A rational no. between 5.2 and 5.5 is 5.3.  

It is rational because it can be expressed in the form  

p/q where p and q are integers and q is not equal to 0, which is 53/10

Part B: A rational no. between 5.2 and 5.5 is 5.29150262213

An irrational number between 5.2 and 5.5 is 5.29150262213. It is irrational because there is no pattern that repeats and it cant be written as a fraction of two whole numbers.

Answer:

Step-by-step explanation:

Square root of all prime numbers is irrational.

97 is an prime number. So √97 is an irrational number.

√98 = \(\sqrt{2*7*7}=7\sqrt{2}\)  is an irrational number.

\(\sqrt{99}=\sqrt{3*3*11} =3\sqrt{11}\) is an irrational number

√100 = 10 is a rational number.

Part A:

5.3 is a rational number.

Rational can be written in p/q form and when divided the result will either terminating decimal or non terminating repeating decimal

Part B:

5.3020050......

Irrational numbers are non terminating non repeating numbers

The number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882 is 106, making option D the right choice.

The sum of an arithmetic series with the first term a, the common difference d, and the number of terms d, is given as:

S = (n/2)(2a + (n - 1)d).

In the question, we are asked to find the number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882.

The first term of the series, a = -13.

The common difference of the series, d = -9 - (-13) = 4.

The sum of the series, S = 20882.

We assume the number of terms to be n.

Putting all the values in the formula for the sum of an arithmetic series, we get:

20882 = (n/2)(2(-13) + (n - 1)4),

or, 41764 = n(4n - 30),

or, 4n² - 30n - 41764 = 0,

or, 2(2n + 197)(n - 106) = 0,

which gives, either n = 106 or, n = -197/2 = -98.5, which is not possible, as n is the number of terms, which cannot be negative.

Thus, n = 106.

Thus, the number of terms in the arithmetic series -13, -9, -5, ...., with the sum of the series being 20882 is 106, making option D the right choice.

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The cross-tabulation analysis is the analytical technique that assesses the statistical significance of categorical variable relationships.

If you are doing research analysis and want to compare the results of one or more variables with the results of another variable, there is only one solution i.e. cross-tabulation or crosstab.

For reference, a crosstab is a two (or more) dimensional table that records the number (frequency) of respondents with certain characteristics described in the table cells. Crosstabs provide a wealth of information about relationships between variables.

Cross-tabulation analysis has its own terminology, using terms such as 'banner', 'stub', 'chi-square statistic', and 'expected value'.

Cross-tabulation analysis (also cross-tabulation or crosstabs) is one of the most useful analytical tools and a workhorse in the market research industry.

Cross-tabulation analysis, also called contingency analysis, is most commonly used to analyze categorical (nominal measurement scale) data.

A cross-tabulation analysis is basically just a table of data that shows the results for an entire group of respondents and the results for a subgroup of respondents. This allows you to explore relationships in your data that aren't immediately apparent by just looking at the overall survey responses.

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The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.

Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website

We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)

The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)

Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612

Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.

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Answer:

The answer is a.) 6.75

Explanation:

I got it right on my quiz :)

Answer:

x = 16 units

Step-by-step explanation:

∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.

If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.

Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.

Since side BC is part of BCD.

Side opposite of 90° [∆BCD] = BC = 32.

Since x is opposite of 30° [∆BCD].

x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.

Answer:

True.

Step-by-step explanation:

The Han era was when paper and porcelain was invented. It was a time of peace when China could build up.

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The pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.

Thus, we get:

\(n = \dfrac{Ln}{L} = \dfrac{Wn}{W}\\\\or\\\\\text{Ratios of corresponding dilated sides are equal}\)

For the given cases, checking all the given pairs:

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{8} = \dfrac{1}{2}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{4} = \dfrac{1}{2}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{6} = \dfrac{2}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{3} \\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{2} \\\\\\Thus, \dfrac{L_1}{L_2} \neq \dfrac{W_1}{W_2}\)

Pair given are not dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{2} = \dfrac{2}{1}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{1.5} = \dfrac{2}{1}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Thus, the pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

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Answer:

c

Step-by-step explanation: