Solve the system of equations : 5x - 2y = -1 and -15x + 6y = 3

We use the slope equation to solve for the slope/gradient of a line:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We're given:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Plug in the given information:

[tex]-\dfrac{1}{6}=\dfrac{-6-y}{4-(-2)}\\\\-\dfrac{1}{6}=\dfrac{-6-y}{4+2}\\\\-\dfrac{1}{6}=\dfrac{-6-y}{6}[/tex]

Cross multiply (by multiplying the numerators by the opposite denominators):

[tex]-\dfrac{1}{6}=\dfrac{-6-y}{6}\\\\-1\times 6=6(-6-y)\\-6=-36-6y\\30=-6y\\y=-5[/tex]

y = -5

The length of the diagonal of the TV is 50 inches

Given that the TV is 30 inches tall and 40 inches wide.

So length of the TV, l = 30 inches

and Width of the TV = 40 inches

The angle between the length and width of the TV is right angle. So we can use Pythagoras Law here.

That is, square of the hypotenuse is equal to the sum of the squares of the base and altitude of the right triangle.

i.e., If 'd' is the diagonal of the TV, then,

    [tex]d^2 = l^2 +b^2 = 30^2+40^2 = 2500[/tex]

This implies that  [tex]d=\sqrt{2500}=50[/tex] inches.

So the diagonal of the TV is 50 inches long.

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Answer:

50 inches

Step-by-step explanation:

Hope this helps

The data in the given three questions can be considered as nominal, ordinal and ratio, respectively.

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Answer:

False

The perimeter of the trapezoid shown is 23 units

Step-by-step explanation:

Equation [tex]y=x^{2} +7x-11[/tex] has two real solutions.

Here are the coefficients:  a=1,b=7,c=11

The discriminating party is: [tex]7^{2}[/tex] -4(1)(-11)=93

Positive, so there are two viable options.

According to the discriminant:

[tex]y=-3x^{2} +x+12[/tex] has two real solutions.

[tex]y=2x^{2} -6x+5[/tex] has zero real solutions.

[tex]y=x^{2} +7x-11[/tex] has two real solutions.

[tex]y=-x^{2} -8x-16[/tex] has one real solution.

Quadratic functions occupy a special place in the academic curriculum. They are small improvements over linear functions and offer a major break from attachment to straight lines because their values may be readily derived from input values.

The discriminant informs you of the number of quadratic equation solutions or x intercepts for a parabola.

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Answer:

y=x=70

hope this helps

Step-by-step explanation:

In parallelogram the adjacent angles are supplementary

∠TBE+y=180

110+y=180

y=70

Also, opposite angles of a parallelogram are equal.

z=∠TSE=110

y=x=70

The lengths of the four sides of such a quadrilateral as indicated in the task content are; 26, 27, 28 and 29.

It follows from the task content that the length of the four sides of the quadrilateral in discuss be determined.

Since the lengths are consecutive integers, we can take.the lengths as;

x, (x+1), (x+2), (x+3).

Hence, the sum of the lengths is equal to 110 as follows;

x + (x+1) + (x+2) + (x+3) = 110

4x + 6 = 110

4x = 104

x = 26 which is the shortest of all sides.

Ultimately, the length of the four sides are; 26, 27, 28 and 29.

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Answer:

x = -7

Step-by-step explanation:

Solve for x:

5 - 4 x + 3 (3 x + 5) = -15

3 (3 x + 5) = 9 x + 15:

(9 x + 15) - 4 x + 5 = -15

Grouping like terms, 9 x - 4 x + 5 + 15 = (-4 x + 9 x) + (5 + 15):

((-4 x + 9 x) + (5 + 15)) = -15

9 x - 4 x = 5 x:

5 x + (5 + 15) = -15

5 + 15 = 20:

5 x + 20 = -15

Subtract 20 from both sides:

5 x + (20 - 20) = -20 - 15

20 - 20 = 0:

5 x = -20 - 15

-20 - 15 = -35:

5 x = -35

Divide both sides of 5 x = -35 by 5:

(5 x)/5 = (-35)/5

5/5 = 1:

x = (-35)/5

The gcd of -35 and 5 is 5, so (-35)/5 = (5 (-7))/(5×1) = 5/5×-7 = -7:

Answer: x = -7

Answer:

x = -7

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

Hope this helps!

Have a great day and God bless! :)

Answer:

35 dollars

Step-by-step explanation:

thats the answer

Answer:

it's C_67$-$(?9

Step-by-step explanation:

it's )3)384((3(# 920

Out of mixture of 3 pounds with cost $3.36 per pound ,pounds each kind of nuts used by Marina are almonds 2.1 and walnuts 0.9 pounds.

As given,

Cost per pound

Almonds=$3.00

Walnuts=$4.20

Total mixture=3 pounds

Cost of mixture=$ 3.36 per pound

Let x amount of almonds and y walnuts Marina use

According to condition,

x +y=3                           __(1)

3x +4.20y =3 ×3.36     __(2)

Multiply 3 to (1) and subtract from (2)

3x +4.20y=10.08

3x +3y= 9

      1.2y=1.08

⇒y=0.9

Substitute y=0.9 in (1),

x=2.1

Therefore, pounds of each kind of nuts used by Marina are almonds 2.1 and walnuts 0.9 pounds.

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The answer is B

since sqrt x = x ^1/2 one being the power of the x and two being the number of radical

in this case 7sqrt x^3 = x ^ 3/7 which is B

The expression is simplified to -33/4

Fractions are simply defined as the part of a whole set.

There are different types of fractions, which includes;

Given the expression;

15/4+(-4/1/3)

To simply the expression, we need to take the following steps;

First, we need to expand the bracket, we have;

15/ 4 - 4/ 1/ 3

Now, take the inverse of the divisor and multiply

15/ 4 - 4 × 3/ 1

15/ 4 - 12

Find the lowest common multiple

15 -  48/4

-33/4

Thus, the expression is simplified to -33/4

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Using the subtraction between two amounts, it is found that:

The difference between the longest and shortest measurement is of 33 cm.

The measurements are given as follows:

To find the difference between difference between the longest and shortest measurement, we have to subtracted the longest measurement by the shortest measures.

From the measurements given, we have that:

Hence, the subtraction is given as follows:

41 cm - 8 cm = 33 cm.

The difference between the longest and shortest measurement is of 33 cm.

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Answer:

1. 2p(2 + r + 3z)

2. x(a + b + c)

Step-by-step explanation:

1. The greatest common factor is 2p.

4p+2pr+6pz = 2p(2 + r + 3z)

2. The greatest common factor is x.

ax + bx + cx = x(a + b + c)

Answer:

28y - 4z

Step-by-step explanation:

Hey there!

In order to simplify this, we need to first distribute the numbers outside of the parentheses to the numbers inside the parentheses:

20y + 8z + 8z - 20z + 8y

Now we combine like terms:

28y - 4z

f

(

4

x

2

−

5

)

=

12

x

2

−

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Subtract:

Answer:

Step-by-step explanation:

49000/ 10 = 4900

the points will become from ( x , y ) to ( x - 5 , y + 2) and these has been plotted on the graph.

We are given the coordinates of the points:

A (3 , 2)

B (3 , 6)

C (5 , 4)

We need to plot them on the graph paper.

Now, we need to translate the points 2 units to the up and 5 units to the left.

So, the coordinates will change from ( x , y ) to ( x - 5 , y + 2)

So, we get that:

A (3 , 2) will become A' ( - 2 , 4)

B (3 , 6) will become B' ( - 2 , 8)

C (5 , 4) will become C' ( 0 , 6)

Therefore, we get that, the points will become from ( x , y ) to ( x - 5 , y + 2) and these has been plotted on the graph.

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Answer:

3x+15

Multiply the single term 33 by each term of the polynomial (x+5)

3x+15

To find the rate of change in a tablet the same process applies:

1. find the coordinates of the given points, it's optional to label them.

2. find the difference between the output values.

3. find the difference between the input values.

4. calculate the ratio between the change in y to the change in x: ∆y∆x.

That's the correct answer stated above.

The slope of a line is defined as the ratio of the difference between the y-coordinate and x-coordinate of the two points m= y₂-y₁/x₂-x₁

We have total spending = $15

So the equation of the budget line will be

PсQс+ PрQр = 15

Where, Pс and Qс is the price of unit candy and quantity of candy respectively. Pр and Qр is the price of unit peanuts and quantity of peanuts respectively.

Part A:Goods A B C D E F Candy Bars 0 4 8 12 16 20Bag of peanuts 10 8 6 4 2 0

Part B :Graph of Budget line

Budget line The slope of a budget is -2 i.e ratio of the prices.

Opportunity costs remain constant as each additional unit of the product is purchased.

The opportunity cost of one more candy bar is 0.5 bags of peanuts.

The opportunity costs of one more bag of peanuts are 2 candy bars.

Part C: No, it tells only what is possible.

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The coordinate of point B from the given coordinates is (6, -9)

The formula for calculating the midpoint of coordinates is expressed according to the formula:

M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the coordinate points M (2, -2) and A (-2, 1)

Substitute

2 = (x₁+x₂)/2

2 = -2+x₂/2

4 = -2 + x₂

x₂ = 6

Similarly;

Substitute

-2 = (1+y₂)/2

-4 = 1+x₂/2

-8 = 1 + y₂

y₂ = -9

Hence the coordinate of point B from the given coordinates is (6, -9)

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Answer:(6,-5)

Step-by-step explanation:deta math

Answer:

1/4

Step-by-step explanation:

If the system has infinitely many solutions, then

     [tex]\sf \boxed{\bf \dfrac{a_1}{b_1}= \dfrac{a_2}{b_2}= \dfrac{c_1}{c_2}}[/tex]

    ax + by = 12  ⇒ a₁ = a  ; b₁ = b ; c₁ = 12

    2x + 8y =60  ⇒ a₂ = 2  ; b₂ = 8 ; c₂ = 60

[tex]\sf \dfrac{a}{2}= \dfrac{b}{8}= \dfrac{12}{60}\\\\\\ \dfrac{a}{2}= \dfrac{12}{60}\\\\a = \dfrac{12}{60}*2\\\\a = \dfrac{2}{5}[/tex]

                         [tex]\sf \dfrac{b}{8}= \dfrac{12}{60}\\\\ b = \dfrac{12}{60}*8\\\\b = \dfrac{8}{5}\\[/tex]

[tex]\sf \dfrac{a}{b}= \dfrac{ \dfrac{2}{5}}{ \dfrac{8}{5}}\\\\[/tex]

    [tex]\sf = \dfrac{2}{5}* \dfrac{5}{8}\\\\ = \dfrac{1}{4}[/tex]

The rule of arithmetic progression is -15, -9, - 3, 3, 9, 15.

So, to find the rule:

Therefore, the rule is -15, -9, - 3, 3, 9, 15.

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The value of a is 3.

The value of b is -14.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The function of the graph is,

y = 2x² + ax + b

The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).

Now,

Since, The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).

Hence, The points must satisfy the graph of the function.

So, Points (-7/2, 0) and (2, 0) are satisfy the function y = 2x² + ax + b.

When point (-7/2, 0) satisfy the function y = 2x² + ax + b

Then,

0 = 2 × (-7/2)² + a × (-7/2) + b

0 = 49/2 - 7a/2 + b

7a/2 - b = 49/2 .... (i)

And, When point (2, 0) satisfy the function y = 2x² + ax + b

Then,

0 = 2 × (2)² + a×2 + b

2a + b = -8    .... (ii)

Add equation (i) and (ii) we get;

7a/2 - b + 2a - b = 49/2 + (-8)

11a/2 = 33/2

11a = 33

a = 3

And, 2a + b = -8

2 × 3 + b = -8

b = -8 - 6

b = -14

Hence, The value of a is 3.

The value of b is -14.

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