1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
soldier1979 [14.2K]
3 years ago
11

Please help me on this question I really need help. :,)

Mathematics
1 answer:
Kazeer [188]3 years ago
6 0

Answer:

a. (7, 27) Polly was incorrect.

b. (3, 1) Polly was correct.

Step-by-step explanation:

a.

y = 4x - 1

2x - y = -13

We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.

2x - y = -13

2x - (4x - 1) = -13

First distribute the negative sign across the parentheses.

2x - 4x + 1 = -13

Combine like terms.

-2x + 1 = -13

-2x = -14

Divide both sides by -2.

x = 7

Now that we know x, plug its value into one of our original equations.

y = 4x - 1

y = 4(7) - 1

Solve.

y = 28 - 1

y = 27

Our solution is (7, 27).

Let's check our answer by plugging both values into one of our original equations.

2x - y = -13

2(7) - 27 = -13

Solve.

14 - 27 = -13

-13 = -13

Your solution is correct.

Polly's solution was (-2, -9), which is incorrect.

b.

3x + 6y = 15

-2x + 3y = -3

Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.

We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.

-2x + 3y = -3

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

4x - 6y = 6

Write the equations together.

3x + 6y = 15

4x - 6y = 6

Now we can see that the y variable will cancel out.

Apply the elimination method.

3x + 6y = 15

4x - 6y = 6

________

7x = 21

Divide both sides by 7.

x = 3

Now that we know x, plug its value into one of our original equations.

3x + 6y = 15

3(3) + 6y = 15

Solve.

9 + 6y = 15

6y = 15 - 9

6y = 6

y = 1

Our solution is (3, 1).

Let's check our answer by plugging both values into one of our original equations.

-2x + 3y = -3

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

Solve.

-6 + 3 = -3

-3 = -3

Your solution is correct.

Polly's solution was (3, 1), so she was correct.

Hope this helps!

You might be interested in
Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)
Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

d_D_E=\sqrt{90}\ units

d_E_F=\sqrt{65}\ units

d_D_F=\sqrt{221}\ units

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}

d=\sqrt{(3)^{2}+(9)^{2}}

d_D_E=\sqrt{90}\ units

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

d=\sqrt{(5+3)^{2}+(-2+1)^{2}}

d=\sqrt{(8)^{2}+(-1)^{2}}

d_E_F=\sqrt{65}\ units

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

d=\sqrt{(5+6)^{2}+(-2-8)^{2}}

d=\sqrt{(11)^{2}+(-10)^{2}}

d_D_F=\sqrt{221}\ units

step 4

Classify the triangle by the measure of its sides

we have

d_D_E=\sqrt{90}\ units

d_E_F=\sqrt{65}\ units

d_D_F=\sqrt{221}\ units

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

6 0
3 years ago
While in transit, the antitoxin had to stay between 36ºF and 46ºF. The dogsled teams stopped along the route often to warm the a
eimsori [14]
Range is the difference between the largest and the smallest numbers in a given contest

Hence the range
= 46 - 36
= 10 °F
6 0
2 years ago
How do you write 70% as a fraction in simplest form ?
alexdok [17]
70% equals to 70/100 in fraction form.
But, you need to write it in simplest form. so, divide both of them from 10 'cause they both can divide completely by it.
70/100 = 7/10
so, your answer is 7/10
3 0
3 years ago
The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
3 years ago
What is the answer to 12x23
Triss [41]
The answer to 12x23 is 276
8 0
4 years ago
Other questions:
  • Kelly rode her bicycle for 35 minutes at a speed of 12 miles per hour at that speed how many miles did she ride
    7·1 answer
  • Xiao's teacher asked him to rewrite the sum 60+90 is the product of the GCF of the two numbers and the sum. Xiao wrote 3(20+30).
    11·1 answer
  • What order is greatest to least
    15·1 answer
  • What is the missing number in this array <br> A)5<br> B)6<br> C)7<br> D)8<br> E)9
    5·1 answer
  • Find the probability of its being a day of the week with a "T" in it remember to reduce your answer in simplest form is necessar
    8·1 answer
  • an achers arrow follows a parabolic patch. the height of the arrow, f(x), in feet, can modeled by the function f(x)=-0.07x^2+1.5
    14·1 answer
  • How fraction is less than 5/6 has a denominator of 8
    9·1 answer
  • A merchant surveyed 370 people to determine the way they learned about an upcoming sale. The survey showed that 170 learned abou
    14·1 answer
  • Josiah downloads 44 songs, including 16 songs by his favorite band.
    7·1 answer
  • -13 =\dfrac r9+8−13= <br> 9<br> r<br> ​ <br> +8
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!