The first two steps in determining the solution set of the system of equations, y = x2 - 2x - 3 and y = -x +3, algebraically are
shown in the table.
Step
Equation
Step 1 XP-2x-3--x+3
Step 2
0=x2-X-6
Which represents the solution(s) of this system of equations?
(3.0) and (-2,5)
(-6, 9) and (1, 2)
(-3,6) and (2, 1)
(6.-3) and (-1.4)

The length of h in the given composite figure will be 4, i.e. option B.

Composite geometric figures are made from two or more geometric figures.

We have,

A composite figure,

Now,

From the figure -- (dash) marked lines are equal , and all dashed marked lines are equal to 1.

Now,

h of the given composite figure consists of two dashed marked lines and 2m.

i.e.

h = 1 + 1 + 2

So,

h = 4 m

So,

The length of h is 4m.

Hence, we can say that the length of h in the given composite figure will be 4, i.e. option B.

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Answer:

A

Step-by-step explanation:

Let d be the total number of computer desks and c be the total number eof single drawer file cabinets.

1. A computer desk weighs 50 pounds, then d computer desks weigh 50d pounds. A single drawer file cabinet weighs 30 pounds, then c cabinets weigh 30c pounds. In total, a train car can hold 1500 pounds of cargo, so

50d+30c=1500

2.  A computer desk occupies a space of 4 cubic feet, then d computer desks occupy 4d cubic feet. A single drawer file cabinet occupies a space of 3 cubic feet, then c cabinets occupy 3c cubic feet. In total, a train car can hold 138 cubic feet of space, so

4d+3c=138.

Thus, we get a system of two equations:

[tex]\left \{ {{50d+30c=1500} \atop {4d+3c=138}} \right.[/tex]

Answer:

x<11

Step-by-step explanation:

To solve this inequality, we must isolate the x. To do that, we divide both sides by 5. This gives us x<11. So all numbers less than eleven belong to the solution set of the inequality.

Answer:

All number less than 11.

Step-by-step explanation:

5x < 55

We just isolate x by dividing both sides by 5:

5x / 5 < 55/5

x < 11.

Ans.

7/12 , 2/3 , 5/6

Why:

If we give all the fractions the same denominator then the fractions are, 8/12 , 10/12 , 7/12. We then can easily see what is the order. Once ordered correctly, just simplifiy.

Answer:

7/12 , 2/3 , 5/6

Step-by-step explanation:

Firstly, give them a common denominator.

What do 3,6 and 12 all have in common? 12

So what we do to the bottom, we do to the top.

Multiply the 2/3 by 4 (3x4=12) to make 8/12.

Multiply the 5/6 by 2 (2x6=12) to make 10/12

7/12 already has 12 as the denominator.

Now order them.

7/12 , 8/12, 10/12.

Change them back to the original sums.

7/12 , 2/3 , 5/6

Answer:

= 10 rs

Step-by-step explanation:

C.P. - 120

S.P. - 130

cp < sp

120 < 130

so , profit = sp - cp

= 130-120

= 10 rs.

hope it helps !

To find the profit for selling eggs, subtract the cost price from the selling price, resulting in a profit of Rs. 10 per dozen.

To calculate the profit or loss from buying and selling eggs, we need to follow a series of steps. First, we find the cost of buying the eggs, which is Rs. 120 per dozen. Then, we find the revenue from selling the eggs, which is Rs. 130 per dozen. The difference between these two amounts will give us the profit or loss made on each dozen of eggs sold.

The calculation is as follows:

Selling Price (SP) per dozen = Rs. 130

Cost Price (CP) per dozen = Rs. 120

Profit per dozen = SP - CP

Profit per dozen = Rs. 130 - Rs. 120 = Rs. 10

Therefore, for each dozen of eggs sold, there's a profit of Rs. 10.

Answer:

Step-by-step explanation:

Good evening ,

_______________

a) p(rat)=1-(0,35+0,4+0,1)

b) p(cat ∪ hamster)=0,35+0,1

c) p(dog then dog)= (0,4)²

:)

Answer:

a=0.15

b=0.45

c=0.16

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle.

So

[tex]85-25=60[/tex]

[tex]\frac{60}{2}=30[/tex]

Answer:

From top to bottom:

3

7

6

12

Step-by-step explanation:

You just simply add the number in the top row and the number in the column together.

2 + 1 = 3

4 + 3 = 7

2 + 4 = 6

6 + 6 = 12

Area = Length x width and is given as square units.

The book is 1 ft x 5/8ft

Area = 1 x 5/8 = 5/8 square ft.

The answer would be D) 5/8 ft^2

Answer: 10 bags

Step-by-step explanation:

First we must calculate the field area. Assuming it is a rectangle then its area equals the product of its length times its width

[tex]A =360*160\\\\A = 57600 ft^2[/tex]

You use 8 pounds of fertilizer per 1,000 square feet

So the amount of fertilizer you should use is:

[tex]57,600 ft^2 * \frac{8\ pounds}{1,000\ ft^2} = 460.8\ pounds[/tex]

As the fertilizer comes in bags of 50 pound then you need

[tex]460.8\ pounds * \frac{1\ bag}{50\ pounds} = 9.2\ bags[/tex]

Since you can not buy 9.2 bags then we round up to the next whole number.

Finally you need 10 bags of fertilizer

Answer:

D. She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

Step-by-step explanation:

Find the rate of change between first two ordered pairs and the second two ordered pairs:

1. Points (2,4) and (3,9). Rate of change:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-4}{3-2}=\dfrac{5}{1}=5[/tex]

2. Points (3,9) and (4,16). Rate of change:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{16-9}{4-3}=\dfrac{7}{1}=7[/tex]

The rate of change for the linear function must the same for each two points on the graph of the function. In this case, the reate of change differs, so this function is not linear and correct option is D.

Answer:

its D

Step-by-step explanation:

The correct question is

 What value of b will

cause the system to have an infinite number of solutions?

For

y = 6x – b   and  -3x+(1/2)y=-3

 we have that

y = 6x – b   ---------> equation

1

-3x+(1/2)y=-3--------->  -6x+y=-6------ > -2x+y=-3------- > y=6x-6

y=6x-6------>

equation 2

 we know that

For the system to have an infinite number of solution,

equation 1 must be equal to equation 2

so

6x – b=6x-6-------> 6x-6x=b-6---------> b=6

 the answer is b=(6)

The value of b will cause the system to have an infinite number of solutions is 6

For the system of equations to have an infinite number of solutions, the system of equations must be similar

Given the system of equations:

y = 6x – b   and  -3x+(1/2)y= -3

y = 6x – b .................... 1

From the secind equation;

-3x+(1/2)y=-3

-6x+y=-6

-2x+y=-3

y=6x-6

y=6x-6

Equate with equation 1 to have:

6x - 6 = 6x - b

b = 6

Hence the value of b will cause the system to have an infinite number of solutions is 6

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False

why would it be true if its not.

Answer:

False

Step-by-step explanation:

Hope it helps.

Answer:

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

Step-by-step explanation:

It is given that the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to.

[tex]\begin{bmatrix}0 & 5 & 15\\ 5 & 0 & 35\\ 15 & 35 &0 \end{bmatrix}[/tex]

Here first element of first row represents the distance in miles from city 1 to city 1.

[tex]C_1\Rightarrow C_1=0[/tex]

Second element of first row represents the distance in miles from city 1 to city 2.

[tex]C_1\Rightarrow C_2=5[/tex]

Third element of first row represents the distance in miles from city 1 to city 3.

[tex]C_1\Rightarrow C_3=15[/tex]

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

Answer:

g(4) = 12

Step-by-step explanation:

We need to find the value the function g(x) when x = 4, that is;

g(4)

In the first definition of the function, the value of x is strictly less than 4. Consequently, we shall use the second definition of the function to evaluate g(4)

In the second definition, g(x) is given as;

Q(x) = 0.5x + 10

plug in x = 4 and simplify;

Q(4) = 0.5(4) + 10

Q(4) = 12

Answer:The equation of the line that has a slope of -1/2 and a y-intercept of -2 is: y=-1/2x-2. All you really have to do here is replace m with -1/2, which is the slope you gave, and replace b with -2, the y-intercept you gave, in the equation y=mx+b. 

If this helped, please mark me brainliest, thank you and if you need more help, feel free to message me .

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

edge

For this case we must find an equation equivalent to:

[tex]\sqrt {x ^ 2 + 81} = x + 10[/tex]

We square both sides of the equation to eliminate the root:

[tex]x ^ 2 + 81 = (x + 10) ^ 2[/tex]

We have by definition that:

[tex](a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2[/tex]

So, rewriting the right side of the equation we have:

[tex]x ^ 2 + 81 = x ^ 2 + 2 * 10 * x + 10 ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x + 100[/tex]

ANswer:

Option D

Given line: y =3x - 7

Slope-intercept form is y = mx + b where m is slope and b is the y intercept

To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)

the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]

This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]

This is the current formula you found:

[tex]y=\frac{-1}{3} x + b[/tex]

To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b

-1 = [tex]\frac{-1}{3}[/tex](2) + b

-1 = [tex]\frac{-2}{3}[/tex] + b

[tex]\frac{-1}{3}[/tex] = b

That means that the equation perpendicular to y = 3x - 7 is...

y = [tex]\frac{-1}{3} x - \frac{1}{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y =3x - 7

Step-by-step explanation:

Answer:

y= 1/2 x +6

Step-by-step explanation:

y-8= 1/2 (x-4)

y-8= 1/2 *x - 1/2*4

y= 1/2 *x - 1/2*4 +8

y= 1/2 *x - 2 +8

y= 1/2 *x +6

Answer:

6 units²

Step-by-step explanation:

The area (A) of a triangle is

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 3 and h = 4, hence

A = 0.5 × 3 × 4 = 0.5 × 12 = 6

Answer:

A. 7 red candles, 1 silver candle

Step-by-step explanation:

6 red candles * $3 each = $18

2 silver candles * $7 each = $14

$18 + $14 = $32 (the total cost)

Answer:

B. 6 red candles, 2 silver candle

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-\dfrac{1}{2}(2n-4)+6=-9+4(2n+1)\qquad\text{use the distributive property}\\\\\left(-\dfrac{1}{2}\right)(2n)+\left(-\dfrac{1}{2}\right)(-4)+6=-9+(4)(2n)+(4)(1)\\\\-n-2+6=-9+8n+4\qquad\text{combine like terms}\\\\-n+(-2+6)=8n+(-9+4)\\\\-n+4=8n-5\qquad\text{subtract 4 from both sides}\\\\-n=8n-9\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-9n=-9\qquad\text{divide both sides by (-9)}\\\\n=1[/tex]

Answer:

B y=55

Step-by-step explanation:

The sum of the angles of a triangle a 180 degrees

40 + y + (y+30) = 180

Combine like terms

70 + 2y = 180

Subtract 70 from each side

70-70 +2y = 180-70

2y = 110

Divide by 2

2y/2 = 110/2

y = 55

Answer:

2 real solutions

Step-by-step explanation:

To determine the nature of the solutions use the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real solutions

• If b² - 4ac = 0 the 2 real and equal solutions

• If b² - 4ac < 0 then no real solutions

Given

x² + 9x + 20 = 0 ← in standard form

with a = 1, b = 9, c = 20, then

b² - 4ac

= 9² - (4 × 1 × 20 ) = 81 - 80 = 1

Since b² - 4ac > 0 then there are 2 real solutions

Answer:

18

Step-by-step explanation:

a + 7b + 4c = 2,

Multiply this equation by 9

9( a + 7b + 4c) = 2*9

9a + 63b +36c = 18

Rearrange the order

36c +9a +63b = 18

Answer:

18

Step-by-step explanation:

36c+9a+63b= collecting 9:

=9*(4c+a+7b)

so it is 4 times the given a+7b+4c which in the definition is equal to 2; so:

=9*(4c+a+7b)=9 * 2=18

If we are given the equation y = -27x + 577 and that

x = weeks

y = money left in account

Then you must replace 145 (the money) for y and solve for x (the weeks)

145 = -27x + 577

145 - 577 = -27x + 577 - 577

-432 = -27x

-432/-27 = -27x/-27

16 = x

This means that after 16 weeks Alma will have $145 left in her account

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

b

Step-by-step explanation:

Answer:

x=20

Step-by-step explanation:

Since this is a right angle, it is equal to 90 degrees

x + 3x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10 from each side

4x+10-10 =90-10

4x=80

Divide by 4

4x/4=80/4

x = 20