Solve the system of equations.
3x +y = 3
x + y = 2

Answer:

[tex]x = - 4[/tex]

Step-by-step explanation:

[tex]4x - 2 = - 3 \times 2 + 3x[/tex]

Calculate the product:

[tex]4x - 2 = - 6 + 3x[/tex]

Rearrange the terms:

[tex]4x - 3x = - 6 + 2[/tex]

Combine like terms:

[tex]x = - 6 + 2[/tex]

Calculate:

[tex]x = - 4[/tex]

Answer:
x = 1/2
Step-by-step explanation:
Combine exponents
4x-x-2=-3^2+3xx
4x-x-2=-3x^2+3x^2
Combine like terms
4x-2=-3x^2+3x^2
4x-2=0
Add 2 to both sides
4x-2=0
4x-2+2=0+2
Simplify:
Add the numbers
4x-2+2=0+2
4x=0+2
Add the numbers again
4x=0+2
4x=2
Divide both sides by the same factor
4x=2
4x/4 = 2/4
Simplify:
Cancel terms that are in both the numerator and denominator
4x/4 = 2/4
X= 2/4
Divid the numbers
X= 2/4
X= 1/2
Solution/ Answer
x= 1/2

Hope this helps

Answer:

1536

Step-by-step explanation:

volume=baseareaxheight

. =32cmsquarex1.5cm

. =1536cm

If the answer is correct please vote



Answer:

16 blue, 11 yellow, and 4 red

Step-by-step explanation:

Answer:

Hey!!!!

the answers are 2, 6, 3, 12, 4, 1

Please read the explanation... it always helps..

Step-by-step explanation:

Alrighty... let's begin....

A factor is any number that you can multiply by another number to get a product

So choose the numbers you can mutiply by another number to get twelve... which are...  2, 6, 3, 12, 4, 1

if you are wondering why twelve well... 12 x 1 = 12

i hope this helps!!!!

The experimental probability is the number of cars with no defect/ total cars inspected: 988/100 = 0.988

multiply total cars by experimental probability

2500 x 0.988 = 2470

Answer:

98.8%; 2470 cars

Step-by-step explanation:

Answer:

25 gm

Step-by-step explanation:convert kg in gr

therefore

0.1 * 1000 = 100 gm

now take difference :-

100 - 75 = 25 gm

Answer:

(C) The largest possible profit the company can make is 7 million dollars

Step-by-step explanation:

Proverbs 3:5-6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Trust in the Lord with all your heart

   and lean not on your own understanding;

in all your ways submit to him,

   and he will make your paths straight.

_________________________________________________________

Have a blessed day!!

:)

Answer:

23:25

Step-by-step explanation:

Answer:

23/25 23 to 25   23:25

Step-by-step explanation:

Two boys  23 girls=25 children

girls=23

23/25

Answer:

m∈(-∞;-2]∪[6;+∞).

Step-by-step explanation:

1) Δ=b²-4ac, then

m²-4(m+3)≥0; ⇔m²-4m-12≥0; ⇔ (m-6)(m+2)≥0;

2) m∈(-∝;-2]∪[6;+∝).

Answer:

C and B

Step-by-step explanation:

Evaluate all the exponents

3^8: 6,561

8^3 = 512

(3 * 3) ^4 = 6,561

(3^4)^2 = 6,561

Options C and B would work.

Answer:

x = -2, -5

Step-by-step explanation:

x^2 + 7x + 10 = 0

The factors of 10 are as follows:

1, 10

2, 5

We can combine 2 and 5 to make 7

(x +2) (x + 5) = 0

One of these brackets must equal 0 to make the answer 0, as you are multiplying them together

If x + 2 = 0, x = -2

If x + 5 = 0, x = -5

Therefore, x = -2, -5

Hey there!

QUADRATIC EQUATION:

ax² + bx + c = 0 where a ≠ 0

The sign of the discrimant (b² - 4ac) determines the number of real-number solutions :

The solutions of the equation, also called roots, can be obtained with the QUADRATIC FORMULA :

[tex]x = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

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

▪️ x² + 7x + 10 = 0

(1) Substitute the letters in the general quadratic equation with their values in the given expression:

(2) Determine the sign of the discriminant:

[tex]{b}^{2} - 4ac \\ \\ \Longrightarrow {7}^{2} - 4(1)(10) \\ \\ \Longrightarrow 49 - 40 \: \: \: \: \: \: \: \: \: \\ \\ \Longrightarrow \red{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The discrimant is positive ; the equation has two real-number solutions.

(3) Determine the roots of the equation :

[tex]x_1 = \frac{ - b \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_1 = \frac{ - 7 - \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = \frac{ - 7 - 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{10}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \green{ \boxed{ \red{x_1 = - 5}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 7 + \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{ - 7 + 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{4}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \red{ \boxed{ \green{x_2 = - 2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, x = -5 or x = -2

▪️ Learn more about quadratic equations :

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Answer:

21/250

Step-by-step explanation:

Converting percentage to fraction :

Step-by-step explanation:

4x-1

x+-×+1=5

×-5

there are no terms like that

Answer:

line will be horizontal running through (0,2)

Step-by-step explanation:

6,2
1,2
2-2/1-6 = 0/-5 = 0 slope. 2 = 0x6+b, 2=b. line will be y=b , y=2.

Answer:

D

Step-by-step explanation:

cotangent = cos / sin        

                 = 4/3

using pythagorean theorem   4^2 + 3^3 = h^2      <=====  h = 5

      then cos = 4/5    sin = 3/5    

               then,  since    csc = 1/sin = 5/3

Answer:

1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2

S(x) = (  ) + (  ) =3

P(x) = (   )  *  (   ) =2

S(x) = ( 2 ) + ( 1 ) =3

P(x) = (  2 )  *  ( 1  ) =2

These numbers in bold will be coeficients of x.

Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2

So x²+3x+2 =x²+2x+1x+2

x² +2x+x+2   Put the x in evidence

x(x+2)+1(x+2)  Find the Maximum Common Divider

(x+1)(x+2)

2) x²+x-6=0

Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?

S(x) = ( 3  ) + ( -2  ) =1

P(x) = ( 3  )  * ( -2  ) =-6

Rewrite

x²+x-6

x²+3x-2x-6      Group them

x(x+3)-2(x+3)   Common Term

(x+3)(x-2)

3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0

Firstly multiply a*c, in this case -2 * 30 = -60

Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.

P(x)=  ( 10  )  *   ( - 6 )  = -60

S(x) = (  10 )  +  (  -6 )  = 4

Rewriting

-2x²+10x-6x+30   Group them

2x(x+5) -6(x+5)

(2x-6)(x+5)   Inserting the -1 to finally adjust

-1(2x-6)(x+5)

4) Explanation is the same principle as a≠1

3x²+4x-4=0

P(x) = ( 6  )  *  (-2  ) = -12

S(x) = (  6 ) +  ( -2  )  = 4

3x²+4x-4 = 3x²+6x-2x-4

3x²+6x -2x+4

3x(x+2)-2(x-2)

(3x-2)(x+2)

The other ones are just applications of these, above.

Step-by-step explanation:

The volume of the given cylinder.

First, we'll have to find the raduis.

[tex]d = 2r [/tex]

[tex]r = \frac{12}{2} [/tex]

[tex]r = 6 \: in [/tex]

Now, we can work out the volume.

[tex]V = \pi {r}^{2} h[/tex]

[tex]V = \pi \times {6}^{2} \times 13[/tex]

[tex]V = 1470.26536 \: {in}^{3} [/tex]

[tex]\large\boxed{\sf{V = 1470.3 \: {in}^{3}}}[/tex]

Hence, the volume of the given cylinder is 1470.3 cubic inches.

The car that travels for 7 hours and 50 minutes at an average speed of 130 km/h covered a distance of 1017.9 km.

The car travels for 7 hours and 50minutes at an average speed  of 130 km/h.

Therefore,

speed = distance / time

speed = 130 km/h

time = 7 hours 50minutes = 7 + 0.833333 = 7.83 hours

Therefore,

130 = distance / 7.83

cross multiply

distance = 7.83 × 130

distance = 1017.9 km

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Answer is 5

Slope is found by finding change in y over change in x

First I solved for Y, -15-3= -18

So I knew x had to be -9 for the slope to be 2

See picture for detailed math

10yx⁵w⁴ - w³v⁵ - 5x¹¹ - 6

Degree = biggest exponent = 11

Answer:

2^3 a^5 b^4

4b^2 c^3

2^(3-2) a^5 b^(4-2)

c^3

2a^5 b^2

2a^5 b^2 c^3

Answer:

44.415 degrees

Step-by-step explanation:

find the third side

49 - 25 = 24

square root of 24 =

2√6

law of cosines

missing angle = arccos ((a^2+b^2-c^2)/2ab))

Answer:

Step-by-step explanation:

We know that all angles are equal to 180.

The angle right next to the letter see is a Right Angle that equals 90 degrees.

To find the sum of angle A, we have to do some simple math.

180-90= 90

Then we have two angles left. We have to divide 90 in half.

90/2= 45

then to check your work: 90+45+45= 180

So angle A is 45 degrees.

Answer:

A, D, E

Step-by-step explanation:

AREA OF SQUARE

[tex](x - 1)(x - 1) = x^2 - 2x + 1[/tex]

AREA OF RECTANGLE

[tex]x(x - 2) = x^2 - 2x[/tex]

Using this we know that the difference is 1, so B is incorrect. We also know that D and E are correct because we solved for the area. C is also wrong, by the same reasoning. Now, all we need to see is if A is right. Plug in x = 2.

[tex](2)^2 - 2(2) + 1 \\= 4 - 4 + 1 \\= 1[/tex]

Because the area of the square is a square unit larger than the rectangle, the rectangle would have an area of 0, which is impossible, so A is correct.

The line given by the equation y = 2x + 3/2 have a slope (m) of 2 and y-intercept (b) of 3/2

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a line is:

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

The line given by the equation y = 2x + 3/2 have a slope (m) of 2 and y-intercept (b) of 3/2

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Answer: C

Step-by-step explanation: bcuz

Answer:

[tex]\textsf{A)} \quad f\left(-\dfrac{1}{2}x\right)[/tex]

Step-by-step explanation:

From observation of the given graph, function f has been reflected across the y-axis.  

When a graph is reflected across the y-axis, the y-coordinate stays the same while the x-coordinate is negated.

Therefore, replace y = f(x) with y = f(-x), so:

[tex]\implies g(x) = f(-x)[/tex]

It appears that the graph has also been stretched parallel to the x-axis.

When a graph is stretched parallel to the x-axis the x is multiplied by a constant.  If the constant is greater than 1, the graph is compressed.  If the constant is greater than zero and less than 1, the graph is stretched.

As the graph has been stretched, the constant is 0 < c < 1, so:

[tex]\implies g(x)=f\left(-\dfrac{1}{2}x\right)[/tex]