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Phoenix [80]
3 years ago
6

Solve using the substitution method. Show your work! Full credit will only be given if all steps are shown.

Mathematics
1 answer:
AnnyKZ [126]3 years ago
8 0

One of the ways to solve a system of equation is by using the substitution method

The values of x and y are -9 and 5

<h3>How to use the substitution method </h3>

The equations are given as:

2x + 6y = 12

x + y = -4

Make x the subject in the second equation

x = -4 - y

Substitute x = -4 - y in the first equation

2(-4 - y) + 6y = 12

Expand

-8 - 2y + 6y = 12

Add 8 to both sides

- 2y + 6y = 20

So, we have:

4y =20

Divide through by 4

y = 5

Recall that:

x = -4 - y

So, we have:

x = -4 - 5

x = -9

Hence, the values of x and y are -9 and 5

Read more about the substitution method at:

brainly.com/question/13476446

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O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
andriy [413]

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28°  ∠ACD=31°  &  line AB=AC .

According To the Question,

  • a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

  • b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

        thus , ∠ABC=76° .

  • c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°)  ⇔  104˚

   

  • d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre  

For Diagram, Please Find in Attachment  

4 0
3 years ago
A ball is hurled in the air such that its horizontal (x) and vertical (y) shifts are given by the functions x(t) = 20t and y(t)
Viefleur [7K]

x(t) = 20t

y(t) = 40t - 5t^2

Since we are only interested in comparing the two at time t = 5 seconds, we plug in 5 everywhere we see the variable t and then compare x and y

x(5) = 20(5) becomes x(5) = 100

y(5) = 40(5) - 5(5)^2 becomes y(5) = 200 - 125 and then y(5) = 75

The ratio of y to x can be expressed as: y/x, so we can say the ratio is equal to 75/100 or 0.75

Answer: 0.75

7 0
3 years ago
Michelle is making throw pillows to decorate her couch. She is going to make two square pillows that are each 2 feet by 2 feet a
lesantik [10]

ok so for the 2 ft pillows the perimeter would be 8 ft and for the 1 ft pillows the perimeter would be 3 ft. So you would need 8(2)+3(3)=16+9=25 so she needs 25 feet of trimming.

3 0
3 years ago
Mark save $258 more than Neil. In fact Mark saved $7 for every $4 Neil saved. How much money did Mark say?
olasank [31]

Let

x---------> amount of money saved by Mark

x---------> amount of money saved by Neil


we know that

x=y+258-------> equation 1

x/y=(7/4)-------> equation 2

substitute equation 1 in equation 2

(y+258) /y=7/4--------> 4*(y+258)=7*y------> 4y+1032=7y

7y-4y=1032--------> 3y=1032------> y=$344

x=344+258------>x=$602


the answer is

$602

6 0
3 years ago
You spend ​$25 on a meal including tax and want to leave a tip that is​ 20% of the ​$25. What is the total​ cost, with the​ tip?
Tems11 [23]
You mulitply 25 by .2 to get 5 and you add that to 25 to get $30
3 0
3 years ago
Read 2 more answers
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