QuestionSolve the system of linear equations by substitution.8x−13y=012x+3=y

Answer:

19/23, 50/23

Step-by-step explanation:

We can take the first equation and isolate the x:

x + 5y = 3 ⇒ -5y ⇒

x = 3 - 5y.

Then we can substitute the x in the first equation by this:

3y + 2 = 4(3-5y) ⇒

3y + 2 = 12 - 20y ⇒ +20y

23y + 2 = 12 ⇒ -2

23y = 10 ⇒ ÷23

y = [tex]\frac{10}{23}[/tex]

Then we can add the value of y into the equation equaling x we made:

x = 3 - 5([tex]\frac{10}{23}[/tex]) ⇒

x = 3 - [tex]\frac{50}{23}[/tex] ⇒

x = [tex]\frac{19}{23}[/tex]

Hope this helps! :)

Answer:

3.2 *10^-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{9.6*10^{-8}}{3*10^{-7}}==\dfrac{9.6}{3}*10^{-8-[-7]}\\\\\\= 3.2*10^{-8+7}\\\\\\=3.2*10^{-1}[/tex]

Answer:

2.83

Step-by-step explanation:

Answer:

1st =  13

2nd = 21

3rd = 36

Step-by-step explanation:

Let the first number be

f

The second of three numbers is 8 more than the first,

f + 8

third number is 3 less than 3 times the first.

3f - 3

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

the third number is 15 more than the second,

3f - 3 = (f + 8) + 15

3f - 3 = f + 23

Subtract f from both sides

2f - 3 = 23

add 3 to both sides

2f = 26

Divide both sides by 2

f = 13

f + 8 = 13 + 8 = 21

3f - 3 = 3(13) - 3 = 36

Answer:

1. Alternate exterior: None

2. Corresponding angles: None

3. Same side exterior angles: <1 and <5

4. Alternate interior: <3 and <4

5. Same side interior: <2 and <4

Step-by-step explanation:

Answer:

5. gross income of 10,000,000

When two or more lines are parallel to each other, this implies that they do not meet even extending them till infinity. So the statement justifies the construction because only one line through point C can be constructed to be parallel to AB.

When a parallel line is constructed through a point to a given line, this is the only parallel line that can be drawn to the given line. Parallel lines are lines that will not meet at any point. Thus, only one parallel line can be constructed through a point not to a given line.

The construction of a line through C that is parallel to line AB is justified by the given statement in the theorem since this is the only parallel line to line AB that can be drawn through the point C. Any other line through C would intersect or meet line AB at a point when extended, thus would not be parallel to the given line.

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Answer:  

a.  28.7 miles

b.  40 miles

Step-by-step explanation:

See attachment.

Convert minutes to hours and divide that into 1 1/2 miles to get a speed of 40 miles/hr (mph).  Multiply 40 mph by each of the two times (converted to hours) to find the miles travelled for the two times.

a.  28.7 miles

b.  40 miles

Answer:

The last one is the answer.

Answer:

Exponential Growth

Step-by-step explanation:

Answer: Profit

Step-by-step explanation:

1.  She made profit

2. She got 300 more than what she bought it for.

3. Her percentage was I think 25% more ( i am not sure on this one)

Answer:  

145°

Step-by-step explanation:  

[Finding the non-label angled in the triangle] 180° - 75° = 105°

Finding 3: (x = angle 3)  

[Sum of a triangle's angles] 105° + 40° + x (angle 3) = 180  

[combine like terms] 145° + x = 180°  

[subtracting 145 from both sides] 35° = x  

   () We can test that this is correct by adding 40 and 35 together, to get angle 1 as it is an exterior angle

Finding 4: (x = angle 4)  

180 - 35 = 145°

Have a nice day!  

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)  

- Heather

Answer:

the answer is 4276, hope this helps :)

Answer:

8

Step-by-step explanation:

it just makes sense, 5=10, therefore 4=8.

Step-by-step explanation:

a. (3 - 2/3) ÷ (4/3 x 7)

= [(3 x 3) / (1 x 3) - 2/3] ÷ 28/3

= (9/3 - 2/3) ÷ 28/3

= 7/3 x 3/28

= 21/84

= (21 x 1) / (21 x 4)

= 1/4

b. 2/3 ÷ 5/6 - 2/5

= 2/3 x 6/5 - 2/5

= 12/15 - 2/5

= (3 x 4) / (3 x 5) - 2/5

= 4/5 - 2/5

= 2/5

c. (- 3/4 + 1/2) ÷ (2/5 - 5/2)

= [- 3/4 + (1 x 12) / (2 x 2)] ÷ [(2 x 2) / (5 x 2) - (5 x 5) / (2 x 5)]

= (- 3/4 + 12/4) ÷ (4/10 - 25/10)

= 9/4 ÷ (- 21/10)

= 9/4 x - 10/21

= - 90/84

= (6 x - 15) / (6 x 14)

= - 15/14.

If you have any doubt, then you can ask me in the comments.

Answer:

You haven't explained the  time for account A - we will assume 12 months or the answer is obvious:

for Acct(A) :   I = 12.5 = A1  * .04           A1 =  $312.50

for Acct(B)     I = 11.25 = A2 * .03 * 5/4 = 300

Note that annual interest in B is .03 or I = .03 + .03 * 1/4 = .0375 for 15 mos.

11.25 = .0375 * A2     A2 = 300

Account A will have the greater principal

Answer:

d.

took the test

Step-by-step explanation:

Answer:

  13 refrigerators and 7 pianos will NOT overload the truck

Step-by-step explanation:

For x refrigerators, their total weight is 300x.

For y pianos, their total weight is 525y.

The total weight of both of these together must not exceed 7600, so the inequality is ...

  300x +525y ≤ 7600

__

The point (x, y) = (13, 7) lies in the solution area. The truck will not be overloaded.

__

Check

  300(13) +525(7) = 7575 . . . this is less than 7600

Answer:

Step-by-step explanation:

Represent the number of refrigerators by r and that of pianos by p.

Then the total weight in the truck bed is calculated and we determine whether or not this total is less than the truck capacity.

Find the total weight of the load consisting of 13 refrigerators and 7 pianos.   The inequality given above becomes:

w(r, p) = (300 lb)r + (525 lb)p ≤ 7600 lb

w(13, 7) = (300 lb)13 + (525 lb)7 ≤ 7600 lb becomes:

w(13, 7) = 3900 lb + 3675 lb = 7575 lb

Since 7575 lb is just under the truck's capacity (7600 lb), the truck will not be overloaded.

Answer:

0

Step-by-step explanation:

There is no gradient there.

[tex] \: \: \: \: \: [/tex]

step-by-step explanation

refer to the attachment

Answer:

[tex]-16 = \frac{m}{5} - 18\\2 = \frac{m}{5}\\10 = m\\[/tex]

Step-by-step explanation:

Given the equation [tex]-16 = \frac{m}{5} - 18[/tex] isolate [tex]m[/tex]

 1.  The first is sum both sides by 18

   [tex]-16 + 18= \frac{m}{5} - 18 + 18\\2 = \frac{m}{5}[/tex]

 2. The second is multiply both sides by [tex]5[/tex]

   [tex]5 \cdot 2 =5 \cdot \frac{m}{5}\\10 = m[/tex]

So of this way you can proof that [tex]m = 10[/tex]

Answer:

I dont know if this is right but... i tried XD

Step-by-step explanation:

Angle A is congruent to angle C.

A triangle in geometry is a polygon with three sides and three angles. The sum of the interior angles of a triangle is 180°.

If XYZ is a triangle, it is represented as ΔXYZ

Here, it is given that BD is the perpendicular bisector of AC.

Then by the definition of perpendicular bisector, B is the midpoint of AC.

Consider ΔABD and  ΔCBD

ΔABD and  ΔCBD are right triangles with  ∡ABD =  ∡CBD = 90°.

So,  ∡ABD ≅  ∡CBD   (∵ all right angles are congruent)

Now, by the reflexive property of congruence, every side or angles are congruent to itself.

So BD ≅ BD

Since B is the midpoint of AC, AB = BC.

Hence AB ≅ BC

By SAS theorem, if two sides and an angle of a triangle are congruent to two sides and angles of another triangle, then both triangles are congruent.

Hence ΔABD ≅ ΔCBD

So, Angle A is congruent to angle C.

Hence ∡A ≅ ∡C if BD is perpendicular bisector of AC.

To learn more about congruence of triangles, click:

https://brainly.com/question/10677854

#SPJ2

Step-by-step explanation:

4+(3+2)2

4+(5)2

4+10

14

Answer:

In mathematics, a set is a collection of elements. The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton.

Answer:

y = 2x-1

Step-by-step explanation:

I'm guessing gradient of 2 means slope of 2

if line passes through (2,3) and has a slope of 2, we can use the slope intercept equation

slope-intercept (y=mx+b)

m is the slope and b is the y-intercept (which we are trying to find)

so far, we have a point and a slope so we can fill in x,y, and m

(3) = (2)(2) + b

3 = 4 + b

3-4 = 4-4 + b (to undo addition, you use subtraction so I minus 4 from each side)

-1 = b

we found b so we just take the (2,3) out of the equation substitute the x,y back into the equation

y = 2x - 1

Answer:

14416

Step-by-step explanation:

youre welcome

Answer:

14416

Step-by-step explanation:

check the steps for answers

Answer:

x+4 x<5

8 5<_x<7

2x -1 7<_x<_10

Answer:

1+1???????? 1+1=2. :/

Answer:

Length=22 cm

Step-by-step explanation:

Perimeter=56 cm

let width=x

According to given condition:

length=4x-2 ...........(A)

Perimeter=2(length+width)

Substitute the values in above formula:

56cm=2(4x-2+x)

56cm=2(5x-2)

56cm=10x-4

(56+4)=10x

60 cm=10x

x=60cm/10

x=6cm

For the value of length :

Substitute the value of x in equation (A):

Length=4x-2

Length=4(6)-2 cm

Length=24-2 cm

Length=22 cm