Solve by elimination
-5x+8y=-27
-8x+7y=-20

Answer:

all work is pictured and shown

Final answer:

The equation of a line with a slope of 1 that passes through the point (2,5) in slope-intercept form is y = x + 3.

Explanation:

To write the equation of a line in slope-intercept form (y = mx + b), you need to know the slope (m) and the y-intercept (b). Since the slope is given as 1 and the line passes through the point (2,5), we can use the point-slope formula to find the y-intercept.

The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in the values we have:

y - 5 = 1(x - 2) → y - 5 = x - 2 → y = x + 3

So, the equation of the line in slope-intercept form is y = x + 3.

Answer: 672 cars will have defective engine mounds

Step-by-step explanation: 25% of 2,688 is 672

Answer:

Step-by-step explanation:

Steps:

1. Let x = #

2. "Five less than six times a number" can be written as: 6x - 5

3. "is at least" is the same as "greater than or equal to" and can be written as: >=

4. "nine subtracted from two times that number" can be written as: 2x - 9

5. the equation is: 6x - 5 >= 2x - 9

6. solve for x by grouping the x variable terms on one side and the constants on the other side:

6x - 5 >= 2x - 9

-2x +5 -2X +5

4x >= -4

7. divide each side by 4, and you get: x = -1

The solution according to the given statement is "x = -1".

According to the question,

The equation will be:

By adding "5" both sides, we get

→ [tex]6x - 5+5 \geq 2x - 9+5[/tex]

→             [tex]6x \geq 2x-4[/tex]

By subtracting "2x" form both sides, we get

→     [tex]6x-2x \geq 2x-4-2x[/tex]

→             [tex]4x \geq -4[/tex]

→               [tex]x \geq -\frac{4}{4}[/tex]

→               [tex]x = -1[/tex]

Thus the above answer is appropriate.

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Answer:

273

Step-by-step explanation:

8736÷32=273

273×32=8736

7 is the prime number.

7 × 1000 = 7000

Answer:

1, 2, 3, 4, 6, 8, 9

The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.

The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.

To determine if a number is divisible by another, we check if the remainder is 0 when dividing the number being tested by the potential divisor. In this case, for example, if we divide 3456 by 2, we get no remainder, so it is divisible by 2.

Similarly, if we divide 3456 by 3, 4, 6, or 8, we get no remainder in each case, so it is also divisible by these numbers.

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Answer:

1.  0.8 cm

2.  1.6 cm

Step-by-step explanation:

1.

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

[tex]\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8[/tex]

Hene, 0.8 centimeters would be the distance in 2nd map

2.

A scale of 1:50 means 1 cm equal 50 cm

So, 0.8m would be

0.8 * 100 = 80 cm

Hence, 80 cm would be represented by 80/50 on the map, that is:

[tex]\frac{80}{50}=1.6[/tex]

That is 1.6 centimeters

Answer: [tex]2,412.74\ cm^2[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Total surface area of a solid hemisphere:

[tex]SA_{total}=3\pi r^2[/tex]

Where "r" is the radius.

 Since you cut a styrofoam ball in half, the total surface areas are equal.

The exercise gives you the diameter. Observe in the figure that this is:

[tex]d=32\ cm[/tex]

Since the radius is half the diameter, you know that:

[tex]r=\frac{d}{2}\\\\r=\frac{32\ cm}{2}\\\\r=16\ cm[/tex]

Finally, you can substitute the radius into the formula:

 [tex]SA_{total}=3\pi (16\ cm)^2=2,412.74\ cm^2[/tex] (Of each half of the styrofoam ball)

You can use the fact that along with the surface area of hemisphere, you need to add the surface area of the circle that's on the top of each hemisphere.(hemisphere means half of sphere)

The surface area of each half of the styrofoam ball is [tex]3\pi r^2 \: \rm unit^2[/tex]

Surface area of sphere = [tex]4 \pi r^2[/tex] sq. units where r is radius of sphere.

Since hemisphere is half of the sphere, thus,

Surface area of hemisphere = [tex]2\pi r^2[/tex] sq. units.

Since the foam ball is not hollow, if we slice it in half, each of the half piece is having surface = outer half sphere's surface + that circle which is formed due to slicing the ball

Thus, surface area of each half of the Styrofoam ball is calculated as

Surface area = Surface area of hemisphere + area of circle

Let the ball had radius r, then we have the needed surface area as:

[tex]S = 2\pi r^2 + \pi r^2 = 3\pi r^2 \: \rm unit^2[/tex]

S is surface area of each half of the styrofoam ball.

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Answer: He burned 800 calories per hour playing basketball.

Step-by-step explanation:

Let be "b" the amount of calories  per hour Jason burned playing basketball and "c" the amount of calories  per hour Jason burned canoeing.

Set up a system of equations:

[tex]\left \{ {{b+2c=1,400} \atop {2b+3c=2,500}} \right.[/tex]

You can apply Elimination Method:

Therefore, you get:

[tex]\left \{ {{-3b-6c=-4,200} \atop {4b+6c=5,000}} \right.\\.............................\\b=800[/tex]

Answer:

22

Step-by-step explanation:

The slope of the given line is:

                        [tex]\dfrac{4}{5}[/tex]

We know that if a line is represented in the slope intercept form i.e.

             [tex]y=mx+c[/tex]

then m represents the slope of the line and c represents the y-intercept of the line.

Here we are given a equation of a line as follows:

                [tex]y=\dfrac{4}{5}x-3[/tex]

i.e. on comparing the equation with  the slope-intercept form of the line we have the slope  of the line is:

             [tex]m=\dfrac{4}{5}[/tex]

Final answer:

The slope of the equation y=4/5x-3 is 4/5, which represents the consistent rise over run for the line.

Explanation:

The slope of the line is represented by the equation [tex]y = \frac{4}{5}x - 3 is \frac{4}{5}.[/tex] In the standard form y = mx + b, where m is the slope and b is the y-intercept, and the coefficient of x represents the slope of the line.

Therefore, by comparing the given equation to the standard form, the number 4/5 in front of x is the slope of the line. The slope indicates a rise of 4 units on the vertical axis for every increase of 5 units on the horizontal axis. The slope of a line remains constant along the entire length of the line.

tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,

[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}[/tex]

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

7 is rmthe correct answer as it's value is 3 the answer is on no 7.

Answer:

A. [tex]R=1,500+6x,\ x\le 800[/tex]

B. 584

Step-by-step explanation:

A band is performing at an auditorium for a fee of $1500.

In addition to this fee, the band receives 30% of each $20 ticket sold. Let x be the number of tickets sold, then these x tickets cost $20x. Calculate 30% of 20x:

[tex]20x\cdot 0.3=6x[/tex]

A. The total cost is

[tex]R=1,500+6x[/tex]

The maximum capacity of the auditorium is 800 people, so x≤800.

B. The band needs $5,000 for new equipment so

[tex]1,500x+6x\ge 5,000\\ \\6x\ge 3,500\\ \\x\ge \dfrac{3500}{6}\\ \\x\ge 583.333...[/tex]

So, it is enough 584 tickets to be sold.

The band's revenue equation is R = 1500 + 0.30 * 20 * x. To earn $5000 for new equipment, the band needs to sell at least 584 tickets, considering their fixed fee and the additional revenue from ticket sales.

Calculating Revenue for a Band's Performance

The band's total revenue (R) when x tickets are sold can be calculated using the equation: R = 1500 + 0.30 *20* x. This equation includes their fixed fee of $1500 plus the variable amount obtained from ticket sales, which is 30% of the ticket price ($20). For every ticket sold, the band adds $6 (30% of $20) to their revenue.

For the band to afford new equipment costing $5000, we need to determine how many tickets need to be sold. The equation becomes:

R = 1500 + 0.30 * 20 * x

$5000 = 1500 + 6 * x

$5000 - 1500 = 6 * x

$3500 = 6x

x = $3500 / 6

x = 583.33

Since the band cannot sell a fraction of a ticket, they would need to sell at least 584 tickets to meet their goal of $5000.

Answer:

f(x) = 4x − 12

Step-by-step explanation:

It's not quadratic.  It's linear.  Each time x increases by 1, f(x) increases by 4.  So the slope is 4.  The y-intercept (when x=0) is -12.  The equation of the line is therefore:

f(x) = 4x − 12

The next number in the sequence is 36.

Starting from 1, the number increases by 3, 1 + 3 = 4. But the next number, the number it's being increased by increases by 2. 3 + 2 = 5, 4 + 5 = 9. And again, 5 + 2 = 7, 7 + 9 = 16. And again. 7 + 2 = 9, 16 + 9 = 25. Therefore, it is increased to + 11, and the next number is 36.

I hope this helped, and you have a great day!

Answer:

36

Step-by-step explanation:

Answer:

y = 2x - 16

Step-by-step explanation:

Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes]:

-½ → 2

-4 = 2[6] + b

-16 = b

y = 2x - 16 >> Perpendicular Line in Slope-Intercept Form

I am joyous to assist you anytime.

The equation of the line that is perpendicular to y = -1/2x - 5 and passes through the point (6, -4) is y = 2x - 16. This is found using the concept of negative reciprocals and the point-slope form of the line equation.

The equation of the original line given is y = -1/2x - 5. The slope of this line is -1/2. Since a line perpendicular to this line will have a slope which is the negative reciprocal of -1/2, the slope of the line we're seeking is 2 (because -1 divided by -1/2 is 2).

We also know from the question that the line we're seeking passes through the point (6, -4). Using the slope-intercept form of the equation of a line (y = mx + b), where m is the slope and b is the y-intercept, we substitute the slope and the coordinates of the point into the equation to solve for 'b': -4 = 2*6 + b. Solving this equation gives us b = -16.

Therefore, the equation of the line that is perpendicular to y = -1/2x -5 and passing through the point (6, -4) is y = 2x - 16.

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Answer:

(40-y)^3

Step-by-step explanation:

Make the unknown y

(40-y)^3

Answer:

The difference can be expressed as

y=x³+120x²-4800x+64000

Or

y=(40-x)³

Step-by-step explanation:

Step one

To solve the problem problem let us first initialize the number to be x

By breaking the statement into component parts and implementing

Step two

1. The difference between 40 and the number

=(40-x)

2. The cube of the difference

= (40-x)³

Let us equate the expression to y

y=(40-x)³

Step three

Expanding the expression we have

y= (40-x)(40-x)(40-x)

Opening bracket we have

y=(1600-40x-40x+x²)(40-x)

y=64000-1600x-

1600x+40x²-1600x+40x²+40x²-x³

y=x³+120x²-4800x+64000

Answer: -39g + 9

Step-by-step explanation:

PEMDAS states that multiplication must be performed before addition & subtraction

  (6g × 7) - (3²g × 9) + 3³

=     42g   -     81g     + 9

=           -39g             + 9

Answer:

10

Step-by-step explanation:

Answer:

53

Equation:

y = -2(6) + 65

y = -12 + 65

y = 65 - 12

y = 53

Answer:

53

Stp-by-step explanation:

Answer:

Step-by-step explanation:

move x to the right making the equation 5y=-9x-1 then divide both sides by 5 to get y= -9/5x-1/5. the slope of a perpendicular line is the opposite reciprocal of the slope from the og eq. so the slope of the new line is 5/9x and the y-intercept stays the same so the equation should be y=5/9x-1/5

Answer:

A, C, and D are correct

Step-by-step explanation:

A. (0.32)(-2)

(0.32)(-2) = -0.64

Correct.

B. 1.6(-4)

1.6(-4) = -6.4

Wrong.

Divide by 10.

[tex]\dfrac{-6.4}{10} = \mathbf{-0.64}[/tex]

C. 0.64(-1)

0.64(-1) = -0.64

Correct.

D. (1.28)(-0.5)

(1.28)(-0.5) = 0.64

Correct.

E. (-4)(-0.16)

(-4)(-0.16) = 0.64

Wrong.

Multiply by -1.

(0.64)(-1)= -0.64

Answer:

a = -5

Step-by-step explanation:

(5 - 3)/(5 - a)

2/(5 - a)

perpendicular of 2/(5 - a) = -(5 - a)/2

(a - 0)/(1 - 0) = -(5 - a)/2

a/1 = -(5 - a)/2

2a = -5 + a

a = -5

Final answer:

A cube with a 5-inch edge has square-shaped faces, an area per face of 25 square inches, a total surface area of 150 square inches, and a volume of 125 cubic inches.

Explanation:

The question relates to the properties of a cube with an edge length of 5 inches. Here are the answers to each part:

b. Each face of the cube is a square shape.

c. The area of each face is 5 inches × 5 inches = 25 square inches.

d. The surface area of the cube is 6 × (area of one face) = 6 × 25 square inches = 150 square inches.

e. The volume of the cube is the cube of the side length, so 5 inches × 5 inches × 5 inches = 125 cubic inches.