Estimate the solution to the following system.

Answer:

4.5 birds, 7.5 mice

Step-by-step explanation:

We know that birds have 2 legs and mice have 4. Furthermore, birds have 1 head as well as mice.

If b represents the amount of birds and m represents the amount of mice, because there are only birds and mice here, the total amount of birds and mice (b + m) must equal 12.

b + m = 12

Next, to find the total amount of bird legs, we must add 2 legs for each bird. Another way of putting this is to multiply 2 by the amount of birds, or b * 2. Similarly, the amount of mice legs is equal to m * 4. The total amount of legs is equal to 39, so

2b + 4m = 39

Our two equations are thus

b + m = 12

2b + 4m = 39

One way to solve this is to solve for m in the first equation and plug that into the second. We have

b + m = 12

subtract b from both sides

m = 12-b

substitute that into the second equation

2b + 4(12-b) = 39

2b + 48 - 4b = 39

-2b + 48 = 39

subtract 48 from both sides to isolate the b and its coefficient

-2b = -9

divide both sides by -2 to isolate b

b = 4.5

Therefore, there are 4.5 birds on the ground (there is somehow a half of a bird!)

Plugging that into m = 12-b, we have m = 12-4.5 = 7.5

Answer:

The required sum is 392

Step-by-step explanation:

Given the sum as shown;

[tex]\sum \left \77} \atop {a=1}} \right. (3a^2-4)[/tex]

When n = 1

f(1) = 3(1)²-4

f(1) = 3 - 4

f(1) = - 1

When n = 2

f(2) = 3(2)²-4

f(2) = 12 - 4

f(2) = 8

When n = 3

f(3) = 3(3)²-4

f(3) = 27 - 4

f(3) = 23

When n = 4

f(4) = 3(4)²-4

f(4) = 48 - 4

f(4) = 44

When n = 5

f(5) = 3(5)²-4

f(5) = 75 - 4

f(5) = 71

When n = 6

f(6) = 3(6)²-4

f(6) = 108 - 4

f(6) = 104

When n = 7

f(7) = 3(7)²-4

f(7) = 147 - 4

f(7) = 143

Taking their sum

Sum = f(1)+f(2)+(3)+f(4)+f(5)+f(6)+f(7)

Sum = -1 + 8 + 23 + 44 + 71 + 104 + 143

Sum = 392

Hence the required sum is 392

Answer:

this is this because of PTI

Step-by-step explanation:

pto explain it to me on Monday and Friday Saturday morning

Answer:

[tex]2x^2+5x[/tex]

[tex]=2xx+5x[/tex]

[tex]=x\left(2x+5\right)[/tex]

Hope it helps u

Answer:

Oxygen; 34.01°C

Step-by-step explanation:

The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:

-218.79 - (-252.8)

= 252.8 - 218.79

= 34.01

Answer:

Step-by-step explanation:

Answer:

Shannon

Step-by-step explanation:

Cuando se habla de lo que uno tiene, podemos usar números positivos.

Por ejemplo:

Pedro tiene 10 manzanas.

Para el caso de deudas, utilizamos números negativos, por ejemplo:

Pedro tiene -10 manzanas

Lo cual significa que Pedro debe 10 manzanas a alguien.

Entonces si le diéramos a Pedro 12 manzanas, el ahora tendría:

-10 + 12 = 2

Pedro tiene 2 manzanas, porque tuvo que entregar 10 de las 12 que le dimos para pagar su deuda.

Ahora vamos a resolver el problema:

La cuenta de Sally tiene un saldo de:

S = -$200.90

El signo negativo quiere decir que Sally tiene una deuda de $200.90

La cuenta de su amiga Shannon tiene un saldo de:

S' = -$240.55

De vuelta, el signo negativo quiere decir que Shannon tiene una deuda de $240.55

Con esto ya podemos concluir que la deuda de Shannon es mayor, por lo tanto Shannon es la que tiene más deuda.

Answer:

$30

Step-by-step explanation:

Let the ratios be 6x and 7x

Then 65 = 6x + 7x

65 = 13x

x = 65/13

x=5

6x = 6 x 5 = $30

7x = 7 x 5 = $35

Answer From Gauth Math

Answer:

brackets stand for multiplication therefore this means multiply 5.9 by 1.102..

I hope this helps and sorry if it's wrong

Answer:

x=2

y=-3

Step-by-step explanation:

2x+y = 1

3x+2y = 0

Multiply the first equation by -2

-4x-2y = -2

Add this to the second equation

-4x-2y = -2

3x+2y = 0

-------------------

-x = -2

Multiply by -1

x = 2

Now find y

2x+y = 1

2(2) +y = 1

4 +y = 1

Subtract 4 from each side

y = 1-4

y = -3

Answer: y = -2x + 1

Solution to the system: (2,-3)

Step-by-step explanation:

2x + y = 1

3x + 2y = 0

We can solve this using substitution

The first thing that we're going to want to do is solve for y in the first equation

Solve for y

2x + y = 1

Subtract 2x from both sides

y = 1 - 2x

We now have the two equations

y = -2x + 1 and 3x + 2y = 0

The next step in solving the system is to plug in the expression of y ( -2x + 1) into the second equation

3x + 2y = 0

Substitute -2x + 1 for y

3x + 2(-2x + 1) = 0

Now solve for x

Distribute the 2 to the -2x and 1

2 * -2x = -4x

2 * 1 = 2

We now have 3x - 4x + 2 = 0

Combine like terms

-x + 2 = 0

Add x to both sides

2 = x

Now to find the value of y we substitute the value of x into one of the equations and solve for y

2x + y = 1

x = 2

2(2) + y = 1

Multiply

4 + y = 1

Subtract 4 from both sides

y = -3

The solution to the system is (2,-3)

And we are done!

Answer:

38318

Step-by-step explanation:

Break the numbers into prime factors

46 = 23*2

49 = 7*7

17 = 17*1

The least common multiple is

23*2*7*7*17 = 38318

Answer:

So the greatest common factor 85 and 95 is 5.

Step-by-step explanation:

We will now calculate the prime factors of 85 and 95, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85 and 95.

We will first find the prime factorization of 85 and 95. After we will calculate the factors of 85 and 95 and find the biggest common factor number .

Prime factors of 85 are 5, 17. Prime factorization of 85 in exponential form is:

85 = 5^1 × 17^1

Prime factors of 95 are 5, 19. Prime factorization of 95 in exponential form is:

95 = 5^1 × 19^1

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17

We found the factors and prime factorization of 85 and 95. The biggest common factor number is the GCF number.

So the greatest common factor 85 and 95 is 5.

Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:

[tex]6=a(6-4)^2+5[/tex] and

[tex]6=a(2)^2+5[/tex] and

6 = 4a + 5 and

1 = 4a so

[tex]a=\frac{1}{4}[/tex] and the equation is

[tex]y=\frac{1}{4}(x-4)^2+5[/tex]

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← is in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = 3 + c ⇒ c = 4 - 3 = 1

y = - [tex]\frac{3}{2}[/tex] x + 1 ← equation of line

Answer:

B) ΔABC and ΔA′B′C′ are congruent.

Step-by-step explanation:

Given

See attachment for [tex]\triangle ABC[/tex] and [tex]\triangle A'B'C'[/tex]

Required

Determine the relationship between both triangles

The single line on all sides of both triangles implies that the sides of the triangles are equal

i.e.

[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- sides

Similarly, the same mark on the three angles of both triangles means that the angles of the both triangles are equal

i.e.

[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- angles

Hence, both triangles are congruent

Answer:

B) ΔABC and ΔA′B′C′ are congruent.

Step-by-step explanation:

Answer:

i think yes!!!

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Yes, you did this correctly.

By subtracting the volume of the cylinder from the volume of the rectangular solid, you accurately acquired the volume of the remaining figure.

And yes, your calculations are correct.

Answer:

90

Step-by-step explanation:

To solve this problem we need to set up an expression

35x+20

35 is the cost per hour, and 20 dollars is the visit fee.

x is the amount of hours the CT can work

So if we plug in the amount for the number of hours from the problem we get

35(2)+20

Which becomes 70+20 which is 90.

Hope thsi helps!

The computer technician works for 2 hours will take total charges equal to $90 .

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7

According to the question

The computer technician charges $20 per visit plus $35 per hour.

i.e

Let hours he work = x

therefore,

Total charge of computer technician in equation = 20 +  35x  

Now,

As the computer technician works for 2 hours the cost will be

By using equation

Total charge of computer technician in dollars  = 20 + 35x  

where x = 2

so,

= 20 +  35*2  

= $90  

Hence, the computer technician works for 2 hours will take total charges equal to $90 .  

To know more about equation here:

https://brainly.com/question/10413253

#SPJ2

Answer:

Yes, both equations are equivalent

Step-by-step explanation:

Simplifying [tex]10x - 3 + 2x - 5[/tex] by combining "like terms" gives us [tex]12x-8[/tex].

Now, to solve "four (3X - 2)", we need to use the distributive property. Doing [tex](4\cdot3x)-(4\cdot2)[/tex] gives us [tex]12x-8[/tex] again.

Therefore, [tex]10x - 3 + 2x - 5[/tex] and four (3X -2) are equivalent!

(Hope this helped you! If any part of the explanation doesn't make sense, or the answer is incorrect/not the answer you we're looking for, then please tell me and I will try to fix my answer as soon as possible)

Answer:

c

Step-by-step explanation:

come on ! you can literally see that in the chart.

how many parts of the gray 3/8 are covered by the gray 1/4 ?

2 parts = 2/8 are clearly covered by 1/4.

2/8 is what part of 3/8 ?

it is the same question as "2 is what part of 3" ?

is 2 a quarter (1/4) of 3 ? no, 1/4×3 = 3/4 and not 2.

is 2 one third (1/3) of 3 ? no, 1/3 of 3 = 1/3×3 = 1 and not 2.

is 2 two thirds (2/3) of 3 ? ah, 2/3 × 3 = 2. that is correct !

is 2 three quarters (3/4) of 3 ? no, 3/4×3 = 9/4 and not 2.

once you have the same denominator, you can easily compare the numerators and ignore the denominators for such problems.

Answer:

900°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7 , then

sum = 180° × 5 = 900°

Answer:

She used 1/8 or 12.5% more flour than sugar

Step-by-step explanation:

flour: 5/8

sugar: 1/2 = 4/8

[tex]\frac{5}{8} - \frac{4}{8} = \frac{1} {8} = 0.125[/tex]

0.125 = 12.5%

Answer:

552

Step-by-step explanation:

I'm almost certain this is correct. Only one step is rounded.

Answer:  942 - 225*sqrt(3)

This is roughly equivalent to 552.29

The unit for the area is in square cm, or cm^2.

The two area values above are based on pi = 3.14, so they are approximations.

============================================================

Explanation:

The radius of the circle is r = 30 because OA = 30.

The full circle has area A = pi*r^2 = 3.14*30^2 = 2826 cm^2 approximately

However, we only want 120/360 = 1/3 of this full area to get the area of the pizza slice. So the area of the pizza slice is approximately (1/3)*2826 = 942 cm^2

This is not the final answer, but helps get us there.

What we just calculated was the approximate area of the entire figure: the yellow area plus the white triangle.

If we can find the area of the white triangle, and subtract it off, then we'll find just the area of the yellow region only.

-----------------------

The SAS (side angle side) area formula for a triangle is

Area = 0.5*p*q*sin(R)

where p,q are the sides and angle R is between those sides.

Here we have p = q = 30, which are sides OA and OB, and we have R = 120 degrees as the central angle.

So the area of triangle AOB is...

Area = 0.5*p*q*sin(R)

Area = 0.5*30*30*sin(120)

Area = 450*sqrt(3)/2

Area = 225*sqrt(3)

This value is exact.

-----------------------

The area of the yellow region is therefore

(area of full figure) - (area of triangle)

(942) - (225*sqrt(3))

942 - 225*sqrt(3)

This is approximate because we used pi = 3.14 as an approximation earlier.

You could then use your calculator to say

942 - 225*sqrt(3) = 552.288568

This rounds to 552.29

Answer:

x^2-3x

pls mark me brainliest

Step-by-step explanation:

4x(x+2)-x(3x+5)

4x^2+8x-3x^2-5x

x^2-3x

Answer:

$399.45

Step-by-step explanation:

all you gotta do is

11.25×35.5

Answer:

look at the explanation

Step-by-step explanation:

Write an equation:

Trash a way : $25 + 0.25x

Garbage No More : $45 per month

so to make them equal we need to have enough trash in Trash A Way that it equals $45

25  + 0.25x =45

0.25x = 20

x = 80

So, you need to have 80 pounds of trash to make them equal

hope this helps!

please vote and heart!

Answer:

Step-by-step explanation:

1) 76*.67 = 50.9

   73 * .33 = 24.1

75% = C

2) .3 * 71 + .3*77+ .4*98=

  21.3+23.1+39.2 = 83.6

83.6 = B

3) 73.24  vs.  68.55

hw   88 22 13.2

cp   84 8.4 8.4

test  59 23.6 35.4

fe  77 19.25  11.55

             tats      ester

totals = 73.24    68.55

Step-by-step explanation:

it will not represent the equation of a line since there's no slope

9514 1404 393

Answer:

  no

Step-by-step explanation:

The equation becomes 0 = 0. This is a truism, valid for any variable values.

It is not the equation of a line.

Answer:

x=y=z=106

Step-by-step explanation:

The upper line is a straight line, so x+74=180, x=106.

y and x are equal in measure as it's a pair of parallel lines and z=y as they are alternate interior angles

Answer:

A)

Step-by-step explanation:

Volume of a Rectangular Prism Formula: L x W x H

6 yd x 3 yd x 4 yd = 72 yd^3