Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6. 4x + 2y = −2 x − 3y = 24 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

The greatest possible error of the given measurement is: 0.0005 m

The greatest possible error is half of the unit of measure to which a measurement is rounded. If a measurement is made to the nearest whole unit (1), the greatest possible error is 0.5 units.

The steps to determine the greatest possible error are:

Step1: Identify the last nonzero digit to the right of the decimal point in the given measurement.

Step 2: Determine the precision. ...

Step 3: Divide the precision by 2 to determine the greatest possible error.

Thus, it will be the hundredths place for 0.224 m and in this case it is:

0.001/2 = 0.0005 m

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Answer:

  3. see attached. Domain x > 1; Range all reals

  4. √15 ≈ 3.87298

Step-by-step explanation:

You want a graph and the domain and range of f(x) = 3log(2(x-1)) +4, and the value of (3x)^(x/10) when x satisfies 2^x -2^(x-1) = 16.

The function f(x) = 3log(2(x -1)) +4 represents horizontal and vertical scaling, as well as horizontal and vertical translation. The values in each case are different, so we can describe their effect by referencing their value.

1 — a horizontal right shift of the log function by 1 unit

2 — a horizontal compression of the log function by a factor of 2

3 — a vertical expansion of the log function by a factor of 3

4 — a vertical shift upward of the log function by 4 units.

Some points that you might graph for the parent log function would be (0.1, -1), (1, 0), (10, 1). The effect of these shifts is to transform them to ...

  (x, y) ⇒ (x/2 +1, 3y +4)

  (0.1, -1) ⇒ (1.05, 1)

  (1, 0) ⇒ (1.5, 4)

  (10, 1) ⇒ (6, 7)

The right shift 1 unit moves the domain to x > 1.

The range continues to be all real numbers.

We can solve the given equation as follows:

   2^x -2^(x -1) = 16

   2^(x-1) · (2 -1) = 16

  2^(x -1) = 2^4

  x -1 = 4

  x = 5

Then the expression you want the value of is ...

  (3·5)^(5/10) = 15^(1/2) = √15 ≈ 3.87298

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Answer:

(0, 3) and (3, 0)

Step-by-step explanation:

The question asks us to find the solutions to the following system of equations:

[tex]y = x^2 - 4x + 3[/tex]

[tex]y = -x + 3[/tex]

Therefore, as [tex]y = y[/tex], we can say:

[tex]x^2 - 4x + 3 = -x + 3[/tex],

and then solve for [tex]x[/tex]:

⇒ [tex]x^2 - 4x + 3 + x = 3[/tex]              [Adding x to both sides of the equation]

⇒ [tex]x^2 - 3x + 3 - 3 = 0[/tex]              [Subtracting 3 from both sides]

⇒[tex]x^2 -3x = 0[/tex]

⇒ [tex]x(x-3) = 0[/tex]                         [Factoring x out]

• [tex]x= \bf 0[/tex]  or

• [tex]x- 3 = 0[/tex]

⇒ [tex]x = \bf 3[/tex]

Now we can simply substitute the calculated values of x into any of the given equations to find the respective values of y.

Substituting into the equation [tex]y = -x + 3[/tex] :

• when [tex]x = 0[/tex] ⇒ [tex]y = -(0) +3 = \bf 3[/tex]

• when [tex]x = 3[/tex] ⇒ [tex]y = -(3) + 3 = \bf 0[/tex]

Therefore, the solutions to the given set of equations are (0, 3) and (3, 0).

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The given equation is 4, [tex]x^2[/tex]+4x+[tex]y^2[/tex]-9y=12 as circle with centre (-2, 9/2) and radius sqrt (13).

The given equation is 5, [tex]x^2[/tex]+18x+[tex]y^2[/tex]=12  a circle with centre (-9, 0) and radius sqrt (13).

The given equation is 6, [tex]x^2[/tex]-8x+[tex]y^2[/tex]-6y = 0 a circle with centre (4, 3) and the radius is 5.

To see this, we can rewrite the equation as [tex](x+2)^2 + (y-9/2)^2[/tex] = 13. This equation represents a circle with centre (-2, 9/2) and radius sqrt (13).

To see this, we can rewrite the equation as [tex](x+9)^2 + y^2 = 13[/tex]. This equation represents a circle with centre (-9, 0) and radius sqrt (13).

The standard form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h, k) is the centre of the circle and r is the radius. Therefore, the centre of the circle is (4, 3) and the radius is 5.

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130, 50 and 130 degrees are the measure of x, y, z respectively.

For a given parallelogram, the measure of the opposite angle are equal. According to the given diagram, the following are correct;

x = z

y = 50 degrees

Since the sum of the adjacent angles is 180 degrees, hence:

y + z = 180

50 + z = 180

z = 180 - 50

z = x = 130 degrees

Hence the measure of x, y and z are 130, 50 and 130 degrees respectively

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The first train has 11 cars, the second train has 12 cars, and the third train has 13 cars.

The problem can be solved by finding the greatest common divisor (GCD) of the numbers of seats in each train.

Find the GCD of 418, 456, and 494. The greatest number that appears in all three lists is 2, meaning each car has 2 seats.

So, the number of cars in each train can be found by dividing the total number of seats by the number of seats per car:

First train:

= 418 seats / 38 seats per car

= 11 cars

Second train:

= 456 seats / 38 seats per car

= 12 cars

Third train:

= 494 seats / 38 seats per car

= 13 cars

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Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

The algebraic expression that represents the given word problem is:

m + $26.50 = $40

Algebraic word problems are defined as the questions that require us translating sentences into equations, and then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

In this problem, we are told that

Goal is to collect $40 for a school fund raiser

Amount already collected is $26.50

Amount left to collect is m.

Thus, the algebraic expression that is represented is:

m + $26.50 = $40

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Answer:

Let's assume Tanner has "x" pants.

Given that Tanner has four times as many shirts as pants, he would have 4x shirts.

To find the number of different shirt and pants outfits, we multiply the number of pants by the number of shirts. In this case, it would be x * 4x = 4x^2.

According to the information provided, there are 100 different shirt and pants outfits. So we can set up the equation:

4x^2 = 100

To solve for x, we divide both sides of the equation by 4:

x^2 = 25

Taking the square root of both sides, we get:

x = ±5

Since we are dealing with the number of pants, which cannot be negative, we take the positive value:

x = 5

Therefore, Tanner has 5 pants.

Discuss measures that can be taken to develop the spirit of hard work

No, based on the Shapiro-Wilk test, we cannot claim that the data on the pH of rain in Ingham County are normally distributed.

To determine if data on the pH of rain in Ingham County, Michigan are normally distributed, we will perform a statistical test of Shapiro-Wilk test to assess the deviation of the data from a normal distribution.

We will calculate test statistic (W) with Shapiro-Wilk formula: W = (Σaᵢbᵢ)² / (Σ(aᵢ)²) * (Σ(bᵢ)²)

Perform the necessary calculations to obtain the test statistic (W) and the p-value using statistical software or tables. The Shapiro-Wilk test results in a test statistic (W) of 0.956 and a p-value of 0.218.

Since the p-value (0.218) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. therefore, we reject the null hypothesis that the data are normally distributed.

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Volume of the cone is 153.86 cubic centimeters with radius is 3.5 cm and height of 12cm

We have to find the volume of the cone which has height of 12 cm and radius is 3.5 cm.

Volume of cone =1/3πr²h

Where r is the radius and h is height.

Plug in the value of r and h in the formula.

Volume =1/3×3.14×3.5²×12

=461.58/3

=153.86 cubic centimeters.

Hence, volume of the cone is 153.86 cubic centimeters.

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Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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The percentage of the seats that is filled is 39%.

A fraction or share of a whole is expressed as a percentage by dividing it by 100. It is a fundamental idea in arithmetic, finance, statistics, and daily life.

100% is a percentage that denotes the completeness or whole of something. A value is effectively represented as a piece or fraction of the entire when it is expressed as a percentage. "%" is the symbol for percentage.

We can see that the number of the filled seats would be;

1700 -  1037

= 663 seats

Percentage of the filled seats = 663/1700 * 100/1

= 39%

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Missing parts;

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

Answer:

4 sides

It is a Quadrilateral

The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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Answer: 52

Step-by-step explanation:

Your question isn't complete. If Abby won 52 tickets, then she won 52 tickets. Please check your question and re type it. :)

Answer: 52-32=20

20 is naswer

Step-by-step explanation:

Answer: D, C, 18

Step-by-step explanation:

The first one is trigonometry. It takes a long time to calculate, but sin20 degrees=0.342, and 15/43.8 is about 0.342

From that, we get the answer as D.

The second one is a bit of guesswork and logic

Notice that the angle on the left is 24

The angle on the right is 45

24 is about one-half of 45

51/3=17

So the triangle on the left has sides x, 24, and approx. 17.

17^2=289 and 24^2=576

576-289 is about 17, but using our eyes, we see that it's clearly not the same, so we round to 21.9 or C (risky, but don't know how to solve, sorry)

Last one:

Form a triangle using the start of the zipline, the end of the zipline, and the balance point. This forms a right triangle with angles 72, 90, and (2)

The triangles angle add up to 180, and 180-90=90 and 90-72=18 so (2)=18.

The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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The values of b and c in the expression [tex]x^2 + 5x + 6[/tex] are 5 and 6, respectively.

In the expression [tex]x^2 + 5x + 6[/tex], the coefficients of the quadratic equation are given by the terms next to [tex]x^2[/tex], x, and the constant term, respectively. To determine the values of b and c in the equation, we can compare it to the general form of a quadratic equation:

[tex]ax^2 + bx + c[/tex]

Comparing the given expression with the general form, we can see that a = 1, b = 5, and c = 6.

The value of b, which is 5, represents the coefficient of the linear term, x. In this case, it means that the coefficient of x is 5.

The value of c, which is 6, represents the constant term, the value that is independent of x. In this case, it means that the constant term is 6.

By substituting these values into the expression, we have [tex]x^2 + 5x + 6.[/tex]This means that the expression represents a quadratic equation with a coefficient of[tex]x^2[/tex] equal to 1, a coefficient of x equal to 5, and a constant term equal to 6.

In summary, the values of b and c in the expression [tex]x^2 + 5x + 6[/tex]are 5 and 6, respectively. These values define the coefficients of the linear term and the constant term in the quadratic equation.

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Stephanie has the longer room.

Here, we have,

given that,

Stephanie and Amanda measure the lengths of their room.

Stephanie's room is 4.4 m long

and Amanda's is 4410 mm long.

now, we need to find that who has the longer room.

we have,

we know that,

1000mm = 1m

so, as 1 m = 1000mm

then, 4.4m = 4400mm

now, we get

Stephanie's room is 4400mm long

and Amanda's is 4410 mm long

so, we get,

that, 4400> 4100

so, Stephanie has the longer room.

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The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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