How many solutions does the system have?
x=y-2
-3x+3y=6

Answer:

The slope is dy/dx= -1/2

Step-by-step explanation:

Y-3= -1/2(X -2)

Y= -1/2x +2/2 +3

Y= -1/2x +1+3

Y= - 1/2x +4

The slope dy/dx= -1/2

Answer:

y=-1

Step-by-step explanation:

-5y+8=-3y+10

-5y-(-3y)+8=10

-5y+3y=10-8

-2y=2

y=2/-2

y=-1

Answer:

y=-2x-2

Step-by-step explanation:

y-4=-2(x+3)

y=-2x-6+4

y=-2x-2

Answer:

b. 2005

Step-by-step explanation:

(apex)

300=150(1.07)^x

1.07^x=2

x=ln 2/ln 1.07

=10.24

1995 plus ten years = 2005

hope this helps

Answer:

B. 2005

Step-by-step explanation:

We have been given that population of deer in a certain national park can be approximated by the function [tex]P(x)=150(1.07)^x[/tex], where x is the number of years since 1995. We are asked to find the year in which population will reach 300.

To solve our given problem, we will equate [tex]P(x)=300[/tex] and solve for x as:

[tex]300=150(1.07)^x[/tex]

[tex]\frac{300}{150}=\frac{150(1.07)^x}{150}[/tex]

[tex]2=(1.07)^x[/tex]

Now, we will take natural log on both sides as:

[tex]\text{ln}(2)=\text{ln}((1.07)^x)[/tex]

[tex]\text{ln}(2)=x\text{ln}(1.07)[/tex]

[tex]x=\frac{\text{ln}(2)}{\text{ln}(1.07)}[/tex]

[tex]x=10.2447[/tex]

[tex]x\approx 10[/tex]

Now, we will find 10 years after 1995 that is [tex]1995+10=2005[/tex].

Therefore, the population will be 300 in year 2005 and option B is the correct choice.

Answer:

Point T

Step-by-step explanation:

The only point that is right across from (-3,-5) is point T. If you reflect across the Y-axis, you get (3,-5)

Answer:

this photo should be it

Answer:

three hundred and ninety three billion, two hundred and thirty four million, and thirty four.

Step-by-step explanation:

billion is any digit that has seven to nine digits behind it

Answer:

Three hundred and ninety three billion, two hundred and thirty four million and thirty four.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

To subtract 3x2 + 4x – 5 from 7x2 + x + 9, we will take the difference of the two polynomials to have;

7x2 + x + 9 -(3x2 + 4x – 5)

= 7x²+x+9-3x²-4x+5

= 7x²-3x²+x-4x+9+5

= 4x²-3x+14

Further subtracting 4x²-3x from the resulting polynomial will give us;

4x²-3x+14 - (4x²-3x)

= 4x²-3x+14-4x²+3x

= 4x²-4x²-3x+3x+14

= 14

Therefore the final answer is 14

Subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9 yields the polynomial 4x^2 - 3x + 14. The difference polynomial is 4x^2 - 3x + 14.

When subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9, you need to subtract the coefficients of like terms.

Starting with 7x^2 + x + 9 - (3x^2 + 4x - 5), you subtract the corresponding coefficients:

(7x^2 - 3x^2) + (x - 4x) + (9 + 5)

This simplifies to:

4x^2 - 3x + 14

So, the resulting polynomial is 4x^2 - 3x + 14 after subtracting.

In this polynomial, the highest degree term is 4x^2, the linear term is -3x, and the constant term is 14. The difference is a quadratic polynomial with a leading coefficient of 4, a linear term with a coefficient of -3, and a constant term of 14.

This polynomial represents the result of subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9.

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Answer:

x-=13

Step-by-step explanation:

9x+2=119

subrtact 2 from both sides

9x=117

divide 9 from both sides

x=13

Answer: x=13

Step-by-step explanation:

Since alternate interior angles are congruent so

9x+2=119

9x=119-2

9x=117

x=117/9

x=13

Answer:

17

Step-by-step explanation:

Answer: 56

Step-by-step explanation:

difference goes up by 2 each time.

Answer:

Explanation:

1. First, calculate the number of hits had during the month, by difference:

2. Round the result to obtain an approximation = 43,000 hits

3. Multiply by the time that each lasted:

Hence, the answer is the option A.

Ranking the three from best to worst will be: point, line, plane. The justification is that, the starting concept determines the next one.

Step-by-step explanation:

The connection can be described by starting with the fundamental concept,procedure or strategy that give rise to the others. In this case, to form a line, you need to have points that join to extend infinitely in different directions. This means the point, is the fundamental concept, that will give the line.A plane is an infinite set of points that form a connected flat surface extending infinitely far in all direction. So here again, the plane exist where there is a set of points. However, a plane is named by three points that are in the plane but not in the same line. Hence, before naming a plane, the concept of a line should be considered. Ranking the three from best to worst will be: point, line, plane. The justification is that, the starting concept determines the next one.

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Keywords : Rank, mathematical concepts, connection, procedures, strategies,

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Answer: 21

Step-by-step explanation:

28-(28/100)*25=28-7=21

Final answer:

To find the value of d in the equation 749/d ∙ d/749 = 1, we can simplify the equation and solve for d. Canceling out the like terms and cross multiplying leads us to the solution: d = 1.

Explanation:

To find the value of d in the equation 749/d ∙ d/749 = 1, we need to simplify the equation and solve for d.

We can start by canceling out the like terms: 749 and d. Multiplying the numerators and denominators gives us:
(749/d) ∙ (d/749) = (749 ∙ d) / (d ∙ 749)

Since the two fractions are equal to 1, we can set up the equation:
(749 ∙ d) / (d ∙ 749) = 1

Next, we can cross multiply:
749 ∙ d = d ∙ 749

Now, we can divide both sides of the equation by 749:
d = d ∙ 749 / 749

Simplifying further:
d = 749 / 749

Finally, we arrive at the solution:
d = 1

Answer:

Area of the path is 475 m².

Step-by-step explanation:

Let us first draw the diagram for the given question.

Here rectangle ABCD represents a park whose length is 55 m and breadth is 35 m. The shaded portion shows the path all around the park whose width is 2.5 m.

Now, length of rectangle ABCD, l = 55 m

breadth of rectangle ABCD, B = 35 m

Now, width of the path = 2.5 m

So, length of rectangle PQRS, L = 55 + 2.5 + 2.5 = 60 m

breadth of rectangle PQRS, B = 35 + 2.5 + 2.5 = 40 m

Now, to calculate the area of shaded portion or the area of the path, we will subtract the area of the park or area of rectangle ABCD from the area of rectangle PQRS.

Now, area of rectangle PQRS, A₁ = L × B = 60 × 40 = 2400 m²

Area of rectangle ABCD, A₂ = l × b = 55 × 35 = 1925 m²

So, area of the path = A₁ - A₂ = 2400 - 1925 = 475 m²

Hence the area of the path is 475 m².

Answer:

A. 3 cm

Step-by-step explanation:

The smallest face has the sides 4 cm and 8 cm. If the water is 4 cm from its top, then the height of the water is [tex]16-4=12[/tex] cm and the volume of the water is

[tex]V_{water}=4\cdot 8\cdot 12=384\ cm^3[/tex]

The largest face has the sides 8 cm and 16 cm. If the container is placed on its largest face, then the volume of the water is

[tex]V_{water}=8\cdot 16\cdot h \ cm^3,[/tex]

where h is the height of the water.

Equate volumes of the water:

[tex]8\cdot 16\cdot h=384\\ \\h=\dfrac{384}{8\cdot 16}=3\ cm[/tex]

Therefore, the water is 3 cm from the bottom.

Answer:

[tex]\frac{9}{4}\ or\ 2\frac{1}{4}\ square feet[/tex]

Step-by-step explanation:

On the first day the moss covered

                              [tex]=1\frac{1}{2}\ square feet[/tex]

                         [tex]=\frac{3}{2}\ square\ feet[/tex]

One the second day the moss covered [tex]=3\frac{3}{4}[/tex] square feet

                                                      [tex]=\frac{15}{4}\ square\ feet[/tex]

Extension of moss cover on second day

= Moss covered second day - Moss covered first day

[tex]=\frac{15}{4}-\frac{3}{2}\\=\frac{15}{4}-\frac{3\times2}{2\times2} \\=\frac{15}{4}-\frac{6}{4}\\=\frac{9}{4} \\=2\frac{1}{4}\ square\ feet[/tex]

Answer:

168.67 lbs

Step-by-step explanation:

given that a 3 foot section of cable weights 2 lbs, i.e

3 feet ---> weighs 2 lbs

1 foot (i.e unit weight) -----> weighs 2/3 lbs

253 feet ------> weighs (2/3) x 253 = 168.67 lbs

To find the temperature in Boxerville at 4:00 p.m. after a drop of 18 degrees by 7:00 p.m. (with a 7:00 p.m. temperature of 64 degrees), we add the dropped degrees back to find the original temperature was 82 degrees.

The question asks to find the temperature at 4:00 p.m. in Boxerville given that it dropped 18 degrees by 7:00 p.m., and the temperature at 7:00 p.m. is 64 degrees. To solve this, we simply need to add the 18-degree drop back to the 7:00 p.m. temperature to find the original temperature at 4:00 p.m.

To find the temperature at 4:00 p.m., we calculate:

Temperature at 7:00 p.m.: 64 degrees

Temperature drop: 18 degrees

Original temperature at 4:00 p.m.: 64 degrees + 18 degrees = 82 degrees

Therefore, the temperature at 4:00 p.m. was 82 degrees.

Answer:

see the explanation

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

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

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

In this problem we have

[tex]y=25x+50[/tex]

This is the equation of a line in slope intercept form

so

Is a linear equation (the graph is a line)

The slope is positive and is equal to [tex]m=25[/tex]

The y-intercept is the point (0,50) (y-intercept is the value of y when the value of x is equal to zero)

The value of b is [tex]b=50[/tex] (y-coordinate of the y-intercept)

The x-intercept is the point (-2,0) (x-intercept is the value of x when the value of y is equal to zero)

The linear function is a increasing function (the slope is positive)

Answer:

The diagonals ZX and YW are perpendicular to each other.

Step-by-step explanation:

We have to prove diagonal ZX is perpendicular to diagonal YW.

Now, the coordinates of Z(0,b), and X(2a,b)

Hence, slope of ZX is m = [tex]\frac{b - b}{2a - 0} = 0[/tex]

Therefore, ZX is parallel to x-axis.

Now, the coordinates of Y(a,0) and W(a,4b)

Hence, slope of YW is n = [tex]\frac{4b - 0}{a - a} = \infty[/tex]

Therefore, YW is parallel to y-axis.

Hence, the diagonals ZX and YW are perpendicular to each other. (Proved)

Answer:

[tex]\frac{3}{8} or\ 0.375\ km[/tex]

Step-by-step explanation:

Given: Chandler walk 1/16 km every 10 minutes.

First, lets find how many 10 minutes in one hours or convert minutes in hours.

∴ Time= [tex]\frac{60}{10} \ h[/tex]

Now, finding kilometres travelled in 1 hour.

Distance travelled= [tex]\frac{1}{16} \times \frac{60}{10} = \frac{1}{16} \times 6[/tex]

Distance travelled = [tex]\frac{3}{8}[/tex]

Converting [tex]\frac{3}{8} \ km[/tex] into decimal will have 0.375 km.

∴ [tex]\frac{3}{8} or\ 0.375\ km[/tex] will chandler walk in 1 hour.

Answer:

y=3x+6

Step-by-step explanation:

Parallel means same slope.

y-y1=m(x-x1)

y-9=3(x-1)

y=3x-3+9

y=3x+6

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y=3x+6.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

Since the line is parallel to y=3x+2, the slope of the line will be the same as this line, therefore, will be equal to 3. The equation of the required line will be,

y = 3x + c

Now, the value of constant, c can be found by substituting the point in the equation of the line, therefore,

9 = 3(1) + c

9 = 3 + c

c = 6

Hence, the equation of the line will be y=3x+6.

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Two different non-vertical lines in the same plane with the same slope are parallel to each other. The slope determines the angle of the line with respect to the x-axis, and lines with the same slope do not intersect if they have different y-intercepts.

When making a conjecture about two different non-vertical lines in the same plane that have the same slope, one can conclude that these two lines are parallel to each other. This is because the slope of a line represents the steepness and direction of the line, and lines with the same slope will never intersect and are hence parallel. The slope is determined by the ratio of the rise (change in y) over the run (change in x), and as illustrated in Figure A1, the slope is consistent along the entire length of a straight line. If two lines have the same slope but different y-intercepts, they will maintain the same angle with respect to the x-axis but will be positioned at different locations in the plane.

An example is given in Figure A1, where a line has a y-intercept of 9 and a slope of 3. The slope and y-intercept are represented by the 'm' and 'b' terms in the linear equation y = mx + b. Therefore, even if two lines have the same 'm' value, if their 'b' values are different, the lines will be parallel but not coincident (overlapping).

Answer:

y=-2x

Step-by-step explanation:

Parallel means same slope.

y-y1=m(x-x1)

y-(-8)=-2(x-4)

y+8=-2x+8

y=-2x+8-8

y=-2x

Answer:

24

Step-by-step explanation:

she sold 12 glasses of lemonade in one our times by two and you get 24

Missy could have sold between 14 and 24 glasses of lemonade in two hours, given that she sold between 7 and 12 glasses per hour.

To find out the range of glasses Missy could have sold in two hours, we need to calculate the minimum and maximum number of glasses sold per hour and then find the totals for two hours:

Step-by-Step Explanation

Hence, Missy could have sold between 14 and 24 glasses of lemonade in the two hours.

Answer:

B. FOR SURE !!!

Step-by-step explanation:

Answer: B

Step-by-step explanation: