A student wants to prove that she can solve a system of a system of equations by replacing one of the equations with two times that equation and adding the other equation. The original system was 12x +2y =30 and 10x+y = 26. The student claims that her first step is to add the two linear equations. Select the option that refutes the student claim

Answer:

The rectangle width is 5.5 cm. This should be the answer.

Step-by-step explanation:

Answer:

the width of the rectangle is 5.5 cm.

Step-by-step explanation:

Let's denote the width of the rectangle as "w".

According to the given information, the length of the rectangle is three times its width, which means the length is 3w.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

Substituting the values into the formula, we have:

44 = 2(3w + w)

Simplifying the equation, we get:

44 = 2(4w)

44 = 8w

Dividing both sides of the equation by 8, we find:

w = 44/8

w = 5.5

Answer:

false

Step-by-step explanation:

outliers can be neglected especially when working out the mean

Therefore, The statement that "outliers are extreme values above or below the mean that require special consideration" is True.

Explanation:
Outliers are extreme values that lie significantly above or below the mean. They have special considerations because they can affect the interpretation of the mean and standard deviation. For instance, if an outlier is included in the dataset, the mean will be different from when it is excluded, making the mean unreliable. Therefore, outliers should be examined carefully to determine if they represent a genuine value or an error.

Therefore, The statement that "outliers are extreme values above or below the mean that require special consideration" is True.

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Answer:

Solving the expression: \((6.2 - 3.51) \times (11.7 \times 0.3)\) we get 9.4419

Step-by-step explanation:

We need to solve the expression: \((6.2 - 3.51) \times (11.7 \times 0.3)\)

According to DMAS rules first we solve brackets and then we will multiply the results found after solving brackets

So,

\((6.2 - 3.51) \times (11.7 \times 0.3)\\=2.69 \times 3.51\\=9.4419\)

First we solved the terms (6.2-3.51) and get 2.69 and by solving (11.7 x 0.3) we get 3.51

Now, we will multiply 2.69 with 3.51 to get the final result.

The final result is 9.4419

So, solving the expression: \((6.2 - 3.51) \times (11.7 \times 0.3)\) we get 9.4419

Answer:

3 and 5.

Step-by-step explanation:

Let the 2 numbers be x and x + 2, then:

3(x + 2)^2 = 10x + 45

3x^2 + 12x + 12 - 10x - 45 = 0

3x^2 + 2x - 33 = 0

3x^2 - 9x + 11x - 33 = 0

3x(x - 3) + 11(x - 3) = 0

(3x + 11)(x - 3) = 0

x = 3, x = -11/3

We are only interested in the 3 as we are looking for an integer.

So, the answer is 3 and 3+2 = 5.

Answer:

26

Step-by-step explanation:

7w-x

\(7 \times 5 - 9\)

\(35 - 9\)

\(26\)

Answer:

$3250

Step-by-step explanation:

interest=deposit×simple interest×time

interest=5000×6.5%×10

5000×65/1000×10=3250

ans;$3250

The variance of the sample mean x = 7 is 18(option c).

Given table:

X          7  5  11   1   11

(x₁ - x)² 0  4  16 36 16​

n = number of observations = 5

Variance σ² = 1/n-1 Σ\(\ \ n} \atop {i=1} \right.\) (\(X_{1}\) - X)²

= 1/5-1 (0 +4 + 16 + 36 + 16)

= 1/4(72)

= 18

Therefore variance σ² = 18

Hence the variance of the sample mean x = 7 is 18.

so option c is correct.

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​

The value of 5/8 + 2/9 is equal to 61/ 72.

Here, we are given 2 fractions 5/8 and 2/9, we need to find their sums.

If we want to add two fractions, we first need to make sure that their denominators are equal.

The denominator of 5/8 is 8 and that of 2/9 is 9.

Now, the Least common multiple of 8 and 9 is 8 × 9 = 72

Thus, we multiply the denominator and numerator of 5/8 by 9-

5/8 × 9/9 = 45/ 72

Similarly, we multiply the denominator and numerator of 2/9 by 8-

2/9 × 8/8 = 16/ 72

Now, we can add the two-

45/ 72 + 16/ 72

= (45 + 16)/ 72

= 61/ 72

Thus, the value of 5/8 + 2/9 is equal to 61/ 72.

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Answer:gamble that,on average,will leave a person with the same amount of money.

Step-by-step explanation:

The equation of the graph shown can be written in factored form as follows:

y = a(x - h)(x - k)(x - m)

To find the equation, we need to identify the x-intercepts and the minimum point of the graph.

From the description, we know that the graph starts at the top left and continues down through the x-axis at x = -4. This means that one of the factors is (x + 4).

Next, the graph reaches a minimum around y = -2.8. This indicates that the graph touches the x-axis at this point, so another factor is (x + 2).

Moving forward, the graph goes back down to another minimum around y = -0.4. Again, this means the graph touches the x-axis at this point. So we have another factor, (x + 1).

Now we have all the necessary factors: (x + 4), (x + 2), and (x + 1). To determine the coefficient "a," we can use the fact that the graph goes up after crossing the x-axis at x = -2. This suggests that "a" must be positive.

Therefore, the equation of the graph in factored form is:

y = a(x + 4)(x + 2)(x + 1)

Please note that without specific points, it is not possible to determine the exact value of "a" or the precise shape of the graph. The equation provided represents a general equation that satisfies the given conditions.

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If BDFH is a parallelogram, then KN = MN. This is because KM is parallel to both BF and DH, and MN and KN are both half the length of BD and FH, respectively, which are equal since BDFH is a parallelogram.

Two pairs of parallel sides quadrilateral is known as parallelogram.

It is a four-sided planar figure with opposite sides that are parallel and congruent.

Since BDFH is a parallelogram, opposite sides are parallel and congruent. Therefore, BD is parallel and congruent to FH, and BF is parallel and congruent to DH.

Since KM is the line joining the midpoints of BD and FH, KM is parallel to BD and FH. Thus, KM is also parallel to BF and DH.

Let N be the intersection point of diagonals BD and FH, and let P and Q be the midpoints of BD and FH, respectively.

Since P and Q are midpoints of BD and FH, respectively, we have:

BP = PD, and FQ = QH.

By the midpoint theorem, we also have:

MN = 1/2 * BD, and KN = 1/2 * FH.

Since BDFH is a parallelogram, we have BD = FH, and therefore:

MN = 1/2 * BD = 1/2 * FH = KN.

Therefore, KN = MN.

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The null hypothesis must be rejected as there is enough evidence that the diameter differs from 0.5 inches.

Given values are

The population mean is  0.5 inches

The Null hypothesis is  : H₀ : μ = 0.5 inches

The Alternative hypothesis is  given by Hₐ : μ ≠ 0.5 inches

Now let us consider the parameter given:

sample size is  n =  15  

test statistics is  t =  1.66

The level of significance : α = 0.05

The degree of freedom: df = n-1 = 15 -1 =14

Calculating the critical value : \(t_\frac{\alpha}{2} ,df\) = 2.145

We are using the critical value of \(t_\frac{\alpha}{2}\) as the test is one-tailed .

Comparing the value of  t and \(t_\frac{\alpha}{2}\) we can see that : \(t < t_\frac{\alpha}{2}\)

Hence the null hypothesis can be rejected.

Given that the value of t does not fall within the range covered by (i.e., the range from -2.145 to the bottom of the normal distribution curve), we are unable to reject the null hypothesis.

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A- the area of the plot as a function of x. is 6 x^2 +10x-5

B- the perimeter of the plot as a function of x is 10x+8

A rectangle plot of land has a width of 3x+5 feet,

and a length of 2x-1 feet.

A) the area of the plot as a function of x is given by

A= length * width

  = ( 2x-1) * ( 3x+5)

  =6 x^2 +10x-5

B) the perimeter of the plot as a function of x

P = 2( l+ W)

  = 2 (( 2x-1) +( 3x+5))

  = 2( 5x +4)

  = 10x +8

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Answer:

1 foot

Step-by-step explanation:

1 meter = 3 feet

3 feet divided by 3 = 1 foot

The length of each section of the rope is 1 foot.

The piece of rope is 1m long.

Carter divided the ropes into three equal parts by tying up the knot.

1 meter = 3 foot.

Therefore, divide 3 by 3.

\(\frac{3}{3} =1\) foot.

Therefore, each section is 1 foot long.

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A ratio shows us the number of times a number contains another number. Caitlin is right.

A ratio shows us the number of times a number contains another number.

The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,

M/S = 2/5

M = 2S/5

After 8 years, their ages will be in the ratio 1:2, therefore,

(M+8)/(S+8) = 1/2

2M + 16 = S + 8

2M - S = -16 + 8

Substitute the value of M,

2(2S/5) - S = -8

-0.2S = -8

S = 40

Now, if we substitute the value of S in the first ratio,

M/S = 2/5

M/40 = 2/5

M = 16

Now, if we take the difference in their ages the difference will be 24(40-16).

Since the difference is 24, we can conclude that Caitlin is right.

Hence, Caitlin is right.

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Answer: G=4

Step-by-step explanation:

The area of a parallelogram, whose vertices are (−4,−2),(−2,6),(10,6) and (8,−2) is (c) 72.

To find the area of the parallelogram, we can use the formula A = base × height, where the base is the distance between two parallel sides and the height is the perpendicular distance between the base and the other parallel side.

We can take the vectors formed by the coordinates of the parallelogram's adjacent sides, then take the cross product of those vectors to find the area.

Using the coordinates given, the vectors formed are (-2+4, 6+2) = (2,8) and (8-10, -2-6) = (-2,-8). Taking the cross product of these vectors, we get |(2,-8,0) x (-2,8,0)| = 72.

Therefore, the area of the parallelogram is 72 square units.

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Answer:

Perpindicular is when two lines cross to form a 90 degree angle

Step-by-step explanation:

Answer:

A fourth degree polynomial:

\(2x^{4} + 10x^{3} + 21\)

The closure property in relation to addition of polynomials means that any polynomials added together will result in another polynomial. For example

(10x^2 + 12) + (x^2 + 6) = 11x^2 + 18

This demonstrates closure because 11x^2 + 18 is also a polynomial

Step-by-step explanation:

Part A: \(x^{4}+2x+20\) is a fourth degree polynomial with three terms and it proved that it is in standard form

Part B: Closure property has been proved in the addition of polynomials

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Part A

Example of fourth degree polynomial with three terms is

\(x^{4}+2x+20\)

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on

Hence, it is a standard form

Part B

The closure property in relation to addition of polynomials means that any polynomials added together will result in another polynomial

Example

(2x+6)+(5x+2)= 7x+8

Hence, the Closure property has been proved in the addition of polynomial

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She ran a total distance of 28 miles in 5 hours.

We can solve this problem by using the formula: distance = rate × time

First, we need to calculate the distance traveled during the first 3 hours at 6 mph. Using the formula, we have:

distance = rate × time

distance = 6 mph × 3 hours

distance = 18 miles

Next, we need to calculate the distance traveled during the last 2 hours at 5 mph. Using the same formula, we have:

distance = rate × time

distance = 5 mph × 2 hours

distance = 10 miles

Finally, we can add the distances traveled during the first 3 hours and the last 2 hours to get the total distance:

total distance = 18 miles + 10 miles

total distance = 28 miles

Therefore, the runner ran a total distance of 28 miles in 5 hours.

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Answer:

30 feet

Step-by-step explanation:

The scale factor is 1 inch = 3 feet

So 10 inches = 10 x 3 feet= 30 feet

Height of the lighthouse is 30 feet

The commission earned by jarrod ,the salesperson is = $44.8

7% of $640 is the commission earned by the salesperson Jarrold .

so therefore commission earned by the salesperson is 640   * 0.07 = $44.8

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Answer:

15

Step-by-step explanation:

If you do the Pythagorean theorem or use the right triangle triples, you’ll get 15 as your answer, hope this helps :)

Answer: (7.6) = 3.8

Step-by-step explanation: Hope this helped!

Answer:

70

Step-by-step explanation:

We have 7 blue marbles, and 20 total marbles. As a result, if we randomly chose one marble from the bag, the probability would be (number of favorable outcomes)/(number of total outcomes) = 7/20.

This means that for each 20 trials, we would expect to pull out a blue marble 7 times, as the probability does not change over time (because we put the marbles back, there are the same amount of each marble). Over 200 trials, we can simply make it out of 200 instead of 20. We can thus multiply 7/20 by 10/10 (10/10 is equal to 1, keeping the proportions equal) to get 70/200, so we can expect 70 blue marbles out of 200.

Answer:

11% i think maybe search in gogle

Step-by-step explanation:

65% means 65 out of 100, or 65/100.

65% of 90 is an unknown number, x.

65 is to 100 as x is to 90.

65/100 = x/90

Hope it helps.