Add the two expressions,
--4.25r +3 and 2.5r- 6
Enter your answer in the box

The correct statement about the system of equations y = x - 6 and y = -x - 2 is that the equations are independent because the lines intersect at one point, as they have different slopes.

The student is asking which statement about the system of equations is correct. The equations given are:

Let's analyze both equations:

Since the two lines have different slopes, they are not parallel and will intersect at a single point, making the system consistent and independent. Therefore, the correct answer is:

A. The equations are independent because the lines intersect in one point.

Answer:

0.0925 miles per second

Step-by-step explanation:

Answer:

16.9 seconds in 1 mile

Step-by-step explanation:

213miles => 3600s

1 mile => X

X=1*3600/213

X=16.9s

Answer: [tex]5\frac{3}{10}[/tex]

We first write them as improper fraction.

[tex]1\frac{7}{10}=\frac{17}{10}[/tex]

[tex]3\frac{3}{5}=\frac{18}{5}[/tex]

Then we find the LCM of the denominators. That is 10.

Using LCD we find the sum:

[tex]1\frac{7}{10}+3\frac{3}{5}\\=\frac{17}{10}+\frac{18}{5}\\=\frac{17}{10}+\frac{36}{10}\\=\frac{53}{10}\\=5\frac{3}{10}[/tex]

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The sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

To find the sum of the fractions [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \)[/tex], let's first convert them to a common denominator.

The least common denominator for 7, 3, and 5 is 105 (since it's the smallest number divisible by all three denominators).

So, we need to express each fraction with a denominator of 105:

[tex]- \( \frac{1}{7} \) becomes \( \frac{15}{105} \) (multiplied by 15)[/tex]

[tex]- \( \frac{10}{3} \) becomes \( \frac{350}{105} \) (multiplied by 35)[/tex]

[tex]- \( \frac{3}{5} \) becomes \( \frac{63}{105} \) (multiplied by 21)[/tex]

Now, we add these fractions:

[tex]\( \frac{15}{105} + \frac{350}{105} + \frac{63}{105} = \frac{15 + 350 + 63}{105} = \frac{428}{105} \)[/tex]

So, the sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]

Answer:

i) [0,4)

ii) [-2,-10]

iii) (-6,-4)

Step-by-step explanation:

i) the interval notation shown in the figure for the first option is [0,4) . Square bracket is used when an end value is included in the range as indicated by the black circle and a normal bracket is used to indicate when the end value is not included in the range as indicated by the white circle.

ii) the interval notation for the second option is given as [-2, 10].

iii) the interval notation for the third option is given by (-6, -4)

Answer:

25422

Step-by-step explanation:

The measure of angle y in the heptagon is 145 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

To find the measure of angle y in a heptagon, we can use the formula for the sum of the interior angles of a polygon, which is:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon.

For a septagon (a polygon with seven sides), we can substitute n=7 into the formula:

Sum of interior angles = (7-2) x 180 degrees = 5 x 180 degrees = 900 degrees

We can now find the value of angle y by adding up the measures of all the given angles and subtracting the sum from the total sum of the interior angles:

y = 900 - (129 + 116 + 120 + 130 + 135 + 125) = 145 degrees

Therefore, the measure of angle y in the Heptagon is 145 degrees.

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Complete question:

Answer:

To find the y-intercept of a line you need to first put it into the equation y=mx+b

x+3y=14 (minus x from each side)

3y=-x+14 (divide both sides by 3)

y=-1/3x+14/3

Your y-intercept is the b in the formula above, so your y-intercept would be 14/3

Hope this helps ;)

Answer:

West Painting can paint, on average, 1 7/8 rooms per gallon of paint

Complete statement and question:

At West painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job Will take. If they average painting 3/4 of a room with 2/5 of a gallon of paint, then they can paint, on average ______ rooms per gallon.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of paint needed to paint 3/4 of a room = 2/5 of a gallon

2. They can paint, on average how many rooms per gallon?

Let's use the Rule of Three Simple to answer this question, this way:

Paint                 Rooms

2/5 gallon          3/4

1 gallon               x

x = Number of rooms on average painted with one gallon of paint

x * 2/5 = 3/4 * 1

x = 3/4 / 2/5

x = 3/4 * 5/2 = 15/8 = 1 7/8

West Painting can paint, on average, 1 7/8 rooms per gallon of paint

Answer:

I would use cubic meters :)

Step-by-step explanation:

Final answer:

The capacity of a backyard pool is commonly measured in gallons in the United States, or liters and kiloliters in countries using the metric system, due to the large volume of water pools can hold.

Explanation:

When considering the capacity of a backyard pool, we're dealing with a fairly large volume of water that needs to be measured. In the United States, the most common unit of measure for this purpose would be gallons, as it is a large unit for capacity suitable for measuring significant amounts of liquid like the volume of water in a swimming pool. Elsewhere, where the metric system is more common, one would likely use liters or kiloliters to quantify the capacity of a backyard pool.

For example, a typical backyard pool may contain about 15,000 gallons of water, which is significantly larger than quantities we would measure in smaller units such as milliliters or ounces. When discussing such large volumes, it's essential to use a unit of measure that appropriately represents the size of the container or space, hence gallons or liters are most suitable for the situation.

They can not, there are only 2 sides and they probably flipped it different ways. They got 'lucky'.

Final answer:

Flipping a coin 100 times and getting 73 heads suggests a potential unbalanced coin. A chi-square statistical test is needed to determine if the deviation from the expected 50-50 ratio is significant. The large deviation in this scenario does suggest bias, but only a hypothesis test can confirm if the coin is unbalanced.

Explanation:

Intuitively, we might accept variations in coin flips as part of chance when the number of trials is small. However, as the number of trials increases, the expected 50-50 ratio of heads and tails should emerge. In the case where a person flipped a coin 100 times and obtained 73 heads, one could suspect an unbalanced coin, but to conclusively determine this, a statistical test, such as a chi-square, should be conducted to assess the significance of the deviation from the expected 50-50 ratio.

Flipping a coin 100 times should result in approximately 50 heads and 50 tails, according to the law of large numbers. A result of 73 heads is quite far from the expected outcome. The empirical observation suggests that there might be a bias towards heads, which indicates that the coin could be unbalanced.

To determine whether the coin is truly unbalanced or whether this was a fluke, one would perform a hypothesis test at a specified significance level to see if the observed results significantly differ from what is expected by random chance alone. If the results show a statistically significant difference, we could conclude that there is evidence to support the claim that the coin is unbalanced.

Answer:

B

Step-by-step explanation:

In the picture above

Hope this helps.

Answer:

Option B is correct.

Step-by-step explanation:

Paul was asked to use the elmination to find the solution to the system of linear equations

What are the missing steps in his work below?

So, the step missing is multiplying equation 1 by 2 i.e

So, Option B is correct.

Answer:

6

Step-by-step explanation:

20-8=12

12÷2=6

6x6=36

Answer:

Step-by-step explanation:

Answer:

  (c)  10 cm, 9 cm, 9 cm

Step-by-step explanation:

You want to identify the set of side lengths that can form a triangle.

The triangle inequality requires a + b > c, for any assignment of a, b, c to side lengths. In effect, the sum of the two shortest sides must exceed the length of the longest side.

  6+6 = 12 < 15 . . . . not a triangle

  6+7 = 13 . . . . . . . . not greater; not a triangle

  9+9 = 18 > 10 . . . . forms a triangle

  4+8 = 12 < 14 . . . . not a triangle

The set of sides that will make a triangle is {10 cm, 9 cm, 9 cm}.

__

Additional comment

The semiperimeter (half the sum of side lengths) is always greater than any side length in a triangle. For example, if the perimeter is 20, the longest side must be less than 10.

By applying the Triangle Inequality Theorem, we find the only set of sides that could make a valid triangle is 10 cm, 9 cm, 9 cm.

The question is asking to identify which set of given lengths could make a valid triangle. To answer this question, it's important to remember the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this concept to each option.

Therefore, the only set of lengths that could make a valid triangle is 10 cm, 9 cm, 9 cm.

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Step-by-step explanation:

Given,

The area of the yard = 6,756 square yards and

The width of the yard (b) = 12 yards

To find, the length of the yard (l) = ?

We know that,

Area of the rectangle =  Length(l) × Breadth(b)

⇒ l × 12 = 6,756

⇒ l =[tex]\dfrac{6,756}{12}[/tex]

⇒ l = 563 yards

Thus, the length of the yard was 563 yards.

Answer:

Therefore the Length of the yard is 563 yards.

Step-by-step explanation:

Consider  the yard as a Rectangle

Area of the Yard = 6756 square yards

Width of the yard = W = 12 yards

To Find :

Length of the yard = L =?

Solution:

WE know that

[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]

Substituting the values we get

[tex]\textrm{Area of Yard}=L\times W=L\times 12\\6756=L\times 12\\\\W=\dfrac{6756}{12}=563\ yard[/tex]

Therefore the Length of the yard is 563 yards.

Answer is 30

Step-by-step explanation:

1.5 of X = 30

1.5*X = 30

X = 30/1.5

= 20

Answer:

20

Step by step explanation:

30/1.5

=20

Answer:

[tex]y=(x-6)^2+4[/tex]

Step-by-step explanation:

Vertex Form Of The Parabola

The equation of a parabola can be expressed in either standard or vertex form. The standard form is

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

and the vertex form is

[tex]y=a(x-h)^2+k[/tex]

Where (h,k) it the vertex of the parabola

Transforming one into the other form is easily achieved by applying simple algebra .

Our function is

[tex]y=x^2-12x+40[/tex]

Completing squares, we have

[tex]y=x^2-12x+36+40-36[/tex]

Reducing

[tex]\boxed{y=(x-6)^2+4 }[/tex]

The vertex of the parabola is the point (6,4)

Final answer:

To convert the quadratic equation y = x^2 - 12x + 40 into vertex form, the completing the square method is employed, resulting in y = (x - 6)^2 + 4, showing the vertex at (6, 4).

Explanation:

Converting a Quadratic Equation to Vertex Form

The question asks how to convert the quadratic equation y = x2 - 12x + 40 into its vertex form. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation into vertex form, we'll use completing the square method.

This shows the quadratic equation in vertex form with the vertex at (6, 4).

It snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

Solution:

Given that, At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today

From given information,

[tex]\text{Snowed yesterday } = \frac{1}{2} \text{ foot }\\\\\text{Snowed today } = \frac{1}{5} \text{ foot }[/tex]

To find: how much more did it snow yesterday than today

So we have to find the difference between snowed yesterday and today

[tex]\text{Difference} = \text{Snowed yesterday } - \text{ snowed today }\\\\\text{Difference} = \frac{1}{2} - \frac{1}{5}\\\\\text{Difference} = \frac{1 \times 5}{2 \times 5}-\frac{1 \times 2}{5 \times 2}\\\\\text{Difference} = \frac{5}{10}-\frac{2}{10}\\\\\text{Difference} =\frac{3}{10}[/tex]

Hence it snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today

Answer:

see attached work shown

Answer:

Step-by-step explanation:

1. animals - rabbit

2. plants - moss, flowers etc .

3. fungi - mushroom

4. protista - giant kelp

5. eubacteria - thermus

6. archaebacteria - euryarchaeota

Answer:

320

Step-by-step explanation:

87 1/2% (same as 87.5%) " of " the total jackets " is" 280

let j represent the total jackets

turn ur percent to a decimal....87.5% = 0.875

" of " means multiply , " is " means equals

0.875j = 280

j = 280 / 0.875

j = 320 <====== ur answer

Final answer:

The workers at the clothing factory were expected to make a total of 320 jackets for the week, as 280 jackets represented 87.5% of their weekly target.

Explanation:

To find the total number of jackets the workers were expected to make for the week, we'll set up a proportion where 87.5% corresponds to the 280 jackets they had made by Thursday. We know that 87.5% can also be expressed as the fraction 7/8. Therefore, if 7/8 of the total is 280 jackets, we need to divide 280 by 7 and then multiply by 8 to find the total number of jackets.

First, calculate the number of jackets corresponding to 1/8 of the total:

280 jackets
7 (parts) = 40 jackets

Next, multiply the value of 1/8 of the total by 8 to get the full 100%:

40 jackets
8 (parts) = 320 jackets

So, the workers were expected to make a total of 320 jackets for the week.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (1, -4) and (-2, 5).

Substitute:

[tex]m=\dfrac{5-(-4)}{-2-1}=\dfrac{5+4}{-3}=\dfrac{9}{-3}=-3[/tex]

Substitute the value of a slope and the coordinates of the point (1, -4) to the equation of a line:

[tex]-4=-3(1)+b[/tex]

[tex]-4=-3+b[/tex]            add 3 to both sides

[tex]-4+3=-3+3+b[/tex]

[tex]-1=b\to b=-1[/tex]

Finally:

[tex]y=-3x-1[/tex]

Answer:

6x+9

Step-by-step explanation:

add like terms

5x+x=6x

7+2=9

5x+7+x+2=6x+9

Answer:

4/5

Step-by-step explanation:

Because slope=rise/run.

Answer: slope = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

The formula for finding slope is given by

slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

From the graph give :

[tex]x_{1}[/tex] = -3

[tex]x_{2}[/tex] = 3

[tex]y_{2}[/tex] = 4

[tex]y_{1}[/tex] = -1

substituting into the formula , we have

slope = [tex]\frac{4-(-1)}{3-(-3)}[/tex]

slope = [tex]\frac{4+1}{3+3}[/tex]

slope = [tex]\frac{5}{6}[/tex]

QP=24 cm

RS=11.25 cm

QS=18.75 cm

Explanation:

Given that TQ bisects <RTP

[tex]therefore <QTP=<QTR\\[/tex](1)

consider ΔRQS and ΔRPT

QS||PT,RP and RT are transversals

[tex]<SQT=<QTP[/tex](alternate angles)(2)

comparing (1) and (2)

[tex]<SQT=<STQ[/tex] and triangle SQT is isocelus

Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle)

Therefore <RQS=<RPT(corresponding angles)

<RSQ=<RTP(corresponding angles)

therefore by AA criterion for similarity

ΔRQS~ΔRPT

According to the property of similar triangles

[tex]RQ/RP=RS/RT=QS/PT[/tex][tex]9/RP=X/30=QS/50\\9/RP=X/30=(30-X)/50\\X/30=(30-X)/50\\50X=30(30-X)\\50X=900-30X\\50X+30X=900\\80X=900\\X=900/80=11.25\\RS=11.25 cm\\QS=30-X=30-11.25\\QS=18.75 cm\\9/RP=X/30\\9/RP=11.25/30\\9*30/11.25=RP\\RP=24 cm[/tex]

Answer:

u = 40° , v = 40° and x = 100°

Step-by-step explanation:

i) from the rule of triangle we know that the sum of all three angles = 180°

ii) 100° + 40° + y = 180°. Therefore y = 40°. where y is the angle adjacent to v.

iii) from theorem on parallel lines we can say that u = y =40°

iv) from the properties of parallel lines we get v = 40° as interior alternate angles are equal.

v) again from the properties of parallel lines we get u = 40°

vi) using the triangle property as in i) we can see that u + v + x =180° therefore 40° + 40° + x = 180°. Therefore x = 100°.

vii) Therefore u = 40° , v = 40° and x = 100°

there is no acute angle.......

Answer:

angle CPB is an acute angle cause it's measure is less than 90°

Answer:

p = (218-6)/4

Step-by-step explanation:

218-6 is in parenthesis because you want to remove the 6 people driving from the population you're dividing first, since they wont be on the buses. The divide that number by 4 to figure out how many people are on each bus. The answer to that is 53. There are 53 people on each bus.

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Answer:

the answer is 55

Step-by-step explanation:

Answer: g(x) = -(x - 6)² + 4

Step-by-step explanation:

g(x) = -x² + 12x - 32

g(x) = -(x² - 12x) - 32

g(x) = -(x² - 2 × x × 6 + 6² - 6²) - 32

g(x) = -[ (x - 6)² - 36 ] - 32

g(x) = -(x - 6)² + 36 - 32

g(x) = -(x - 6)² + 4

Here, (6,4) is vertex.