find the solution of this system of equations. -x - 5y= 30, 10x + 5y= -75

Answer:

y = x² + 2x + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here the vertex = (- 1, 4), thus

y = a(x + 1)² + 4

To find a substitute (0, 5) a point on the graph into the equation

5 = a(0 + 1)² + 4

5 = a + 4 ( subtract 4 from both sides )

a = 1, thus

y = (x + 1)² + 4 ← expand and simplify

  = x² + 2x + 1 + 4

  = x² + 2x + 5

The quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

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

The graph of the quadratic function is given in the picture.

As we know,

(y - h)² = 4a(x - k)

(h, k) is the vertex of the parabola:

Or

y = a(x - h)² + k

From the graph:

Here the vertex = (- 1, 4)

y = a(x + 1)² + 4

Plug x = 0, and y = 5 to find the value of a

5 = a(0 + 1)² + 4

a = 1

y = (x + 1)² + 4

f(x) = x² + 2x + 5

Thus, the quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

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Answer:

Part B is 271!!!

Step-by-step explanation:

a9=54

S9=9/2(6+54)=270

270+1

=271

By plugging in the ring number, 9, in the equation for the number of

cells in a ring, gives 54.

Response:

A. The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

B. The number of cells in the ninth ring are 54 cells

Given;

The type of sequence = Arithmetic sequence

From the possible drawing of the question obtained from a similar question, we have;

Number of cells in the first ring that goes around the first cell = 6

Number of cells that go around the second ring = 12

A. The common difference of the arithmetic sequence = 12 - 6 = 6

We have that the nth term of an arithmetic sequence is; aₙ = a + (n - 1)·d

Taking the first ring as the first term, we have;

a = 6

Which gives;

The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

Where;

n = The ring number

B. In the ninth ring, we have;

a₉ = 6 + (9 - 1) × 6 = 54

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4 hours and 45 minutes

The number of miles increasing each hour is 16, 16 times 4 is 64, and to get to 76, you add an extra 3/4 of an hour, which is 45 minutes.

The distance between Antony and Lily will be 76 miles after 4.75 hours.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Antony and Lily started moving in opposite directions from the same point at the same time.

Speed of Antony = 12 mph

Speed of Lily = 4 mph

Let x be the distance traveled by Antony.

Then the distance traveled by Lily = 76 - x

Time will be the same, let it be t.

t = x /12 and t = (76 - x) / 4

x/12 = (76 - x) / 4

4x = 12 (76 - x)

4x + 12x = 912

16x = 912

x = 57

t = 57/12 = 4.75 hours

Hence the time is 4.75 hours.

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Answer:

Angle C is 101 degrees

Step-by-step explanation:

Given triangle ABC,

Side BC =3

Side AB =16

Angle A=20

Also, Angle C is an obtuse angle.

To find Angle C:

As shown in figure,

By using basic trigonometry,

Angle A =20 and AB=13

BD =13sin20 and AD = 13cos20

Now, AD=AC+CD

CD=13cos20-3

CD=2.30506

And BD =13sin20=11.86828

In triangle BDC,

Tan(BCD) = [tex]\frac{BD}{CD}[/tex]

Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]

Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]=5.1487

Angle BCD = 79.00

Therefore, Angle BCA =180-Angle BCD=180-79=101.

Angle C is 101 degrees

The measure of angle C in triangle ABC is approximately 150.8° when rounded to the nearest tenth of a degree.

To find the measure of angle C, we can use the fact that the sum of the angles in any triangle is 180°. Given that angle A is 20° and angle C is obtuse, we can set up the following equation:

[tex]\[ \angle A + \angle B + \angle C = 180 \][/tex]

Since angle A is 20°, we can substitute this value into the equation:

[tex]\[ 20 + \angle B + \angle C = 180 \][/tex]

To find the measure of angle B, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle:

[tex]\[ \frac{a}{\sin(\angle A)} = \frac{b}{\sin(\angle B)} = \frac{c}{\sin(\angle C)} \][/tex]

We can use the sides AB and BC to find angle B:

[tex]\[ \frac{16}{\sin(20)} = \frac{3}{\sin(\angle B)} \][/tex]

Solving for[tex]\(\sin(\angle B)\)[/tex]:

[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \][/tex]

Now, we calculate the value of [tex]\(\sin(\angle B)\)[/tex]:

[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \approx \frac{3}{16} \cdot 0.3420 \approx 0.0649 \][/tex]

Taking the inverse sine [tex](sine) of \(\sin(\angle B)\)[/tex] gives us the measure of angle B :

[tex]\[ \angle B = \sin(0.0649) \approx 3.7 \][/tex]

Now we have the measures of angles A and B, so we can find angle C :

[tex]\[ 20 + 3.7 + \angle C = 180 \] \\[/tex]

[tex]\[ \angle C = 180 - 20 - 3.7\] \\[/tex]

[tex]\[ \angle C = 180 - 23.7 \] \\[/tex]

[tex]\[ \angle C = 156.3 \][/tex]

Since angle C is obtuse, we do not need to consider any other solutions for angle B that might be less than 90°. Therefore, the measure of angle C is approximately 156.3°, which rounds to the nearest tenth of a degree as 150.8°.

Answer:

Adrian needs to pay $5 for all the fruit.

Step-by-step explanation:

Consider the provided information.

Grapes cost  $2.35 per pound, oranges cost $0.99 per  pound, and apples cost $1.65 per pound.

In order to find how much Adrian needs to pay we need to add $2.35, $0.99 and $1.65.

[tex]\$2.35 + \$0.99 + \$1.65=\$4.99[/tex]

Now round $4.99 to the nearest whole number.

[tex]\$4.99\approx\$5[/tex]

Hence, Adrian needs to pay $5 for all the fruit.

Answer:

2/3d=h

Step-by-step explanation:

2/3 is the amount it grows (in inches)

d represtenst the days

h represents height

2/3*6 = 4

Answer: 2/3

Step-by-step explanation: 2/3 is the amount it grows (in inches)

D= THE DAYS

H= THE HEIGHT

So... 2/3x6= 4

                   = 2/3

The price of senior citizen ticket is $8 and that of children ticket is $14          

Let the price of ticket for senior citizen be ‘s’ and for child be ‘c’

Given that on the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38

So, an equation can formed which is as follows:

3s + c = 38  ---- eqn 1

On the Second day of ticket sales the school sold 3 senior citizen and 2 child ticket for a total of $52

3s + 2c = 52  ---- eqn 2

Multiply eqn 1 by 2

6s + 2c = 76 ---- eqn 3

Now subtract eqn 2 from eqn 2

6s + 2c = 76

(-) 3s + 2c = 52

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

3s = 24

s = 8

Plug in s = 8 in eqn 2,

24 + 2c = 52

2c = 28

c = 14

Hence, the price of senior citizen ticket is $8 and that of children ticket is $14                      

Answer:

Option 4 - [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]

Step-by-step explanation:

To find : Which set of rational numbers is arranged from least to greatest?

Solution :

The set of rational numbers are

[tex]3,\ \frac{1}{5},\ -1.4,\ -\frac{1}{2}[/tex]

Writing all number in one form,

[tex]\frac{1}{5}=0.2[/tex]

[tex]-\frac{1}{2}=-0.5[/tex]

Now, -1.4<-0.5<0.2<3

From least to greatest the set of natural numbers are

[tex]-1.4<\ -\frac{1}{2}<\frac{1}{5}<\ 3[/tex]

So, [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]

Therefore, option 4 is correct.

Answer:

Option 4

Step-by-step explanation:

Answer:

1.8=100x+b

Step-by-step explanation:

The formula y = mx + b sometimes appears with

different symbols.

For example, instead of x, we could use the

letter C. Instead of y, we could use the letter F.

Then the equation becomes

F = mC + b.

All temperature scales are related by linear

equations. For example, the temperature in

degrees Fahrenheit is a linear function of degrees Celsius.

Water freezes at: 0°C, 32°F

Water Boils at: 100°C, 212°F

Answer:

0.7

Step-by-step explanation:

7 millimiters equals 0.7 centimeters

Answer:

0.7 cm

Step-by-step explanation:

1 mm=0.1 cm

7 mm=0.1*7=0.7 cm

Answer:

x=2

Step-by-step explanation:

2x+4=8

2x=8-4

2x=4

x=4/2

x=2

Answer:

  x = 2

Step-by-step explanation:

The equation shown is a perfectly good equation.

___

Look at what is being done to the variable. It is multiplied by 2, and 4 is added to the product.

To find the value of the variable, we reverse these operations, in reverse order. We undo the addition by adding the opposite of 4 (to both sides of the equation).

  2x +4 -4 = 8 -4

  2x = 4 . . . . . simplify

We undo the multiplication by multiplying by the inverse value, 1/2 (to both sides of the equation).

  (1/2)(2x) = (1/2)(4)

  x = 2 . . . . . simplify

_____

The rules of equations are pretty simple: whatever you do to one side, you must also do to the other side.

_____

Comment on this equation

You may notice that all of the numbers in this equation are divisible by 2. Another way to solve it is to start by dividing (both sides!) by 2:

  x + 2 = 4

Now, you have a 2nd-grade problem in addition facts: what added to 2 gives 4? Since you know your addition facts, you know the answer is 2. In algebra, we solve this by subtracting 2 (from both sides!).

  x = 2

The given expressions are solved and matched

To match the given expressions we need to solve the expressions with the given values of g and h and find their value.

Given that g = -7 and h = 3

[tex]\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}[/tex]

The expressions are evaluated by substituting g = -7 and h = 3 into each one. After calculation, the matching values are found for each expression.

To evaluate each expression for g = -7 and h = 3, we'll substitute these values into the equations and perform the operations step by step.

Then, you can match each expression to its corresponding value that has been calculated:

The pair (2, -1) is the solution the system of equations.

The given system equations are 2a+b = 3 and a - 3b = 5.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

2a+b = 3 --------(1) and a - 3b = 5 --------(2)

Multiply equation (1) by 3

6a+3b=9 --------(3)

Add equation (2) and (3), we get

a - 3b+6a+3b = 5+9

⇒ 7a = 14

⇒ a = 2

Put a=2 in the equation (1), that is

2(2)+b=3

⇒ b=-1

Therefore, the pair (2, -1) is the solution the system of equations.

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Final answer:

The correct pair (a,b) that solves the given system of equations 2a + b = 3 and a - 3b = 5 is (2, -1), which is option J.

Explanation:

To find which pair (a,b) is the solution to the system of equations 2a + b = 3 and a - 3b = 5, we can use substitution or elimination. Here's a step-by-step explanation using the elimination method:

Therefore, the correct solution to the system of equations is (2, -1), which corresponds to option J.

Answer:

378

Step-by-step explanation:

            She has 9 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 9 (she can pick any one of them).

            She has 7 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 7 (she can pick any one of them).

            She has 3 designs of first-class stamps out of which she has to chose only 1.

The number of ways of doing this is 3 (she can pick any one of them).

            She has to pick the color of pen and she has 2 to choose from.

The number of ways of doing this is 2 (she can choose any one of them).

She has to do Work 1 and Work 2 and Work 3 and Work 4.

∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378

The perimeter of Jake window is 16x - 2 inches

Given that height of Jake window is 5x - 3 inches

Also given that width is 3x + 2 inches

To find: perimeter of Jake window

We know that, in general a window is of rectangular shape

The perimeter of rectangle is given as:

Perimeter of rectangle = 2(length + width)

Substituting the values we get,

Perimeter of rectangle = 2(5x - 3 + 3x + 2)

Perimeter of rectangle = 2(8x - 1) = 16x - 2

Hence, the perimeter of the window is 16x – 2 inches

Answer:

B

Step-by-step explanation:

18.00 MOP equals to 2.26 US Dollars.

Step-by-step explanation:

Cost of taxi ride = 18.00 MOP

It is given that;

1 US Dollar = 7.98 MOP

It can also be written as,

7.98 MOP = 1 US Dollar

Therefore,

1 MOP = [tex]\frac{1}{7.98}\ US\ Dollars[/tex]

Now,

18.00 MOP = [tex]\frac{1}{7.98}*18.00\ US\ Dollars[/tex]

[tex]18.00\ MOP=\frac{18.00}{7.98}\ US\ Dollars\\18.00\ MOP= 2.26\ US\ Dollars[/tex]

18.00 MOP equals to 2.26 US Dollars.

Keywords: conversion, division

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Answer:

The answer is 225 cm

Step-by-step explanation:

15×15=225

Answer:

5 or 3

Step-by-step explanation:

Answer:

the third side is 40 m long

Step-by-step explanation:

The perimeter of the triangle is the sum of its three sides, and they give you what that value in meters is (120 m)

Your are given the length of two of them: 30 m and 50 m, and need to find the third one (let's call it "x" for this unknown side)

Now set the following equation:

Perimeter = side 1 + side 2 + side 3   --> replace these with the info you know

120 m = 30 m + 50 m + x   --> add 30 m and 50 m obtaining 80 m

120 m = 80 m + x  --> now solve for x (isolate the x on one side) by subtracting 80 m from both sides

120 m - 80 m = x  --> perform the subtraction 120 m - 80 m = 40 m

40 m = x

Which tells us that the third unknown side has a length of 40 m

Answer:

The third side is 40 meters long

Step-by-step explanation:

From the question, we were told that a triangular courtyard has a perimeter of 120 meters, we are to find the length of the third side if the other two sides are 30 and 50 meters.

First, we need to know that perimeter is the distance around a polygon.

Let the third side = side c, let the two sides be side A and side B

Perimeter = side A + side B + side c

side A = 30 meters

side B = 50 meters

side C = ?

Perimeter = 120 meters

We can now proceed to insert the values in the equation above

Perimeter = side A + side B + side c

      120    = 30 + 50 + side c

      120 = 80 + side c

Subtract 80 from both-side of the equation

120 - 80 = 80 - 80 + side c

40 = side c

side c = 40 meters

Therefore, the third side is 40 meters long

The division of 3.78 by 0.9 equals 4.2 after rounding to the nearest tenth. The given problem is an arithmetic division question typically encountered in mathematics. The keyword 3.78 is the number being divided by 0.9.

The division question posed: 3.78 divided by 0.9, is a simple arithmetic problem. To solve, we will perform the division calculation directly. First, we divide 3.78 (the dividend) by 0.9 (the divisor). This yields a quotient of approximately 4.2. Thus, 3.78 divided by 0.9 equals 4.2 when rounded to the nearest tenth. This division problem would be typically encountered in arithmetic, a branch of mathematics that deals with numbers and numerical computation.

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Answer:

19.5

is the correct answer

Answer:

The answer is 19.5

Step-by-step explanation

Have an amazing day :)

Answer:

Step-by-step explanation:

Equation 1:  3a + 1o =5     3(1) + 1(2) = 5

Equation 2:  1a + 1o =3      2(1) + 1(2) = 3

Solution: apples are $1.00 each and oranges are $2.00 each

Answer:

21(2x+1)

Step-by-step explanation:

42x+21=21(2x+1)

Answer:

-4x

Step-by-step explanation:

Answer:

w<=16

Step-by-step explanation:

600-25w>=200

25w>=600-200

25w>=400

w>=400/25

w>=16

w<=16

Answer:

It is.

Step-by-step explanation:

1. Multiply 2x *x and 2x* -3 ;

2. Multiply 1*x and 1*(-3) ;

You should get: 2x^2 -6x +x -3 = 2x^2 -5x -3;

3. Add -6x +x;

In the end you get : 2x^2 -5x -3=2x^2 -5x -3

Answer:

Step-by-step explanation:

Use FOIL:

(a + b)(c + d) = ac + ad+ bc+ bd

(2x + 1)(x - 3)

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

= 2x² - 6x + x - 3          combine like terms

= 2x² + (-6x + x) - 3

= 2x² - 5x - 3

Answer:

4$

Step-by-step explanation:

in 2000, ticket price is 75% of 8$ that is 6$. in 2005, money spent is increased by 50% of 8$ that is 12$ with same ticket price(6$). so non ticket price is increased from 2$(in 2000) to 6$(in 2005).

Answer:

4

Step-by-step explanation:

6(2005) - 2(2000) = 4

Easier to read then the one above, like its addition

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

c = 7/5

Decimal Form:

c = 1.4

Mixed Number Form:

c = 1/2/5

Edit: I answered this on Jan 7th, 2021.