Solve the system of one linear- one Quadratic equations algebraically.
x-y=3
x^2-3y=19

If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

Consider the first odd integer as x

Then the next consecutive odd integer = x+2

The 6 times the second integer=  6(x+2)

= 6x+12

Sum of an integer and 6 times the next consecutive odd integer is 61

Then the equation will be

x + 6x+12 = 61

Add the like terms in the equation

(1+6)x + 12 = 61

7x +12 = 61

Move 12 to the right hand side of the equation

7x = 61-12

7x = 49

x = 49/7

x = 7

The second number is

x+2 = 7+2

= 9

Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

Learn more about equation here

brainly.com/question/28741857

#SPJ1

Step-by-step explanation:

Meow island get's their population multiplied by 3 per year

Purr island get's and additional 4 cats per year

The population of cats on each island in the mathematical form is:

Meow island:

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

y = 4x + 2

Where x is the number of years from x = 0, 1, 2, 3 ,,,,

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

We will make ordered pair of number of years x and number of cats y as

(x, y).

Meow island:

We see that the number of cats is increasing 3 times the previous number of cats.

So,

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

(0, 2), (1, 6), (2, 10), (3, 14) ....

The equation for the table.

y = mx + c

m = (6 - 2) / (2 - 1) = 4/1 = 4

(0, 2) = (x, y)

2 = 4 x 0 + c

c = 2

Now,

y = 4x + 2

Thus,

The population of cats on each island in mathematical form is given above.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

100000000000000000000000000000

Step-by-step explanation:

we know that

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y

so

In this problem

The domain is the interval {-1,3}

so

The range is the interval {-4,5}

so

answer Option A

The distance between the ordered pairs is 4 units

What is distance formula?

Distance formula calculates the distance between two coordinates. it calculates the straight line distance between two points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2}+(d-b)^{2} }[/tex] for the coordinates (a, b) (c, d)

We are given the ordered pair (w+2,m) and (2t,c-3)

We are given the value w = 6, m = 3, t = 4 and c = 10.

Substituting the values in the pairs

We get,

(6+2,3),(2(4),10-3)

(8,3),(8,7)

We use distance formula to find the distance

[tex]d=\sqrt{(8-8)^{2} +(7-3)^{2} }\\ d=\sqrt{4^{2} }\\ d=4[/tex]

Hence the distance between the ordered pairs is 4 units.

To learn more about distance formula please refer

https://brainly.com/question/27262878

#SPJ13

Given that

Caleb predicted player would score 27 points.

But he scored 23 points.

so percentage error,

Answer:

area of trapezium → 1/2 × Sum of parallel sides × Distance between them.

Area → 15in² {given}

B1 → 4in

B2 → 6in

15 = 1/2 × ( 4+6 ) × h

h = 15 × 2 ÷ 10

h = 3in

I hope it's helpful

Answer:

i wouldd but likee

Step-by-step explanation:

i didnt pay a single second of attention in math

The equation of line is y = -x + 6

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

The given point are (5, 1) and (7, 11)

We know, the equation of line is,

y = mx + b

where, m = slope

            b = y-intercept

First, find slope i.e m

we know the formula of slope (m) = (y2 - y1) / (x2 - x1)

The points, (x1, x2) = (5, 1) and,

                   (y1, y2) = (7, 11)

put these values in slope formula,

m = (11 -7) / (1 - 5)

   = 4 / -4

m = -1

we get the slope is -1

Next, find y-intercept i.e 'b'

for that, take any one point I'm taking (5, 1) and put these in equation ,

y = mx + b

1 = -1 * 5 + b

1 = -5 + b

b = 6

Now, put slope (m) and y-intercept (b) value in ,

y = mx + b

we get,

y = -x + 6

Hence, the equation of line is y = -x + 6

To read more about Equation of line.

https://brainly.com/question/18831322

#SPJ9

Answer:

[tex] \csc(θ) = \frac{1}{ \sin(θ) } [/tex]

Answer:

(a)

[tex] log_{2}(7) + log_{2}(3) = log_{2}(21) [/tex]

(b)

[tex] log_{9}(7) - log_{9}(8) = log_{9}( \frac{7}{8} ) [/tex]

(c)

[tex] log_{2}( \frac{1}{9} ) = - 2 log_{2}(3) [/tex]

The ratio of the pole's height to its shadow is 1:4.

So, the ratio of height:shadow:

The ratio will be:

Therefore, the ratio of the pole's height to its shadow is 1:4.

Know more about ratios here:

https://brainly.com/question/2328454

#SPJ13

Answer:

realto, hindi ako sure eh

Step-by-step explanation:

tama yan

The result of the expression given as 6x/(-2) is -3x

From the question, the expression is given as

6x/(-2)

The above expression is a quotient expression

So, we start by rewritting it as a product

This is represented as

6x/(-2) = 6x * 1/(-2)

Remove the bracket

So, we have the following equation

6x/(-2) = 6x * 1/-2

Evaluate the product

6x/(-2) = -3x

Hence, the value of the expression is -3x

Read more about expression at

https://brainly.com/question/20662459

#SPJ1

Answer:

£94

Step-by-step explanation:

24+ (14×5) = £94

p.s pls give brainliest answer :)

The perimeter of the triangle ABC is equal to 36 centimeters. (Correct choice: A)

Triangles are close figures with three sides and three internal angles. Two triangles are congruent when they share sides with same lengths and angle and side distributions, then AC ≅ XZ, BC ≅ YZ and AB ≅ XY. The perimeter is the sum of the lengths of the three sides of the figure, then:

p = 10 cm + 12 cm + 14 cm

p = 36 cm

The perimeter is equal to 36 centimeters.

To learn more on perimeters of triangles: https://brainly.com/question/21506745

#SPJ1

Two triangles are congruent if all of their sides are the same. Perimeter of triangle ABC is 36cm.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are congruent if all of their sides are the same.

By data triangle ABC and triangle XYZ are congruent.

In triangle ABC, AB = 12 cm and AC = 14

In triangle XYZ,  YZ = 10 cm and XZ = 14

As ABC and XYZ are congruent then the other side of triangle ABC has 10cm.

Perimeter of triangle=Sum of three sides

=10+12+14

=36

Hence perimeter of triangle ABC is 36cm.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

Answer:

70

Step-by-step explanation:

Proportional means in a ratio.

Picking any L/W from the table works. Set that equal to 42/W.

[tex]\frac{6}{10} =\frac{42}{W}[/tex]

Solve for W.

6W = 42 * 10

6W=420

W=70

An inscribed circle is the largest circle contained in the polygon (triangle):

• Bisects two angles of the triangle.

• The angle bisector will intersect at the intercenter.

Procedure

To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.

Let

y ----> total cost in dollars

x -----> number of miles

we have that

Option B

y=50

Option A

Find out the slope

take two points from the graph

(0,20) and (150,50)

m=(50-20)/(150-0)

m=30/150

m=1/5=$0.20 per mile

therefore

y=0.20x+20

Part A

For x=75 miles

Option A -----> y=0.20(75)+20=$35

Option B ------> y=$50

therefore

Option A costs less

Find out the difference

$50-$35=$15

Cost $15 less than the other option

Part B

Looking at the graph

For x=150 miles

Both options cost the same

If David drives more than this amount option B costs less

The equation will be used for solving the retail price is y = 1.8x

Given,

The equation will be used for solving the retail price is y = 1.8x

A local shoe store buys shoes at a wholesale price.

and mark up 80%

The table is:

Quantity                                              Wholesale Price

0-20 pairs                                                  $25.00

21-40 pairs                                                 $23.00

41-60 pairs                                                 $21.00

61-80 pairs                                                 $19.00

81 or more pairs                                         $17.00

To find the retail price for each range.

Now, According to the question:

An equation will be used :

the equation for all of them would be :

y = new price

x = wholesale price

y = 1.8x

Quantity of :0 - 20 pairs.

= 25 x 1.80

= $45.00

Quantity of: 21 - 40 pairs

= 23 x 1.80

= $41.40

Quantity of: 41 - 60 pairs

= 21 x 1.80

= $37.80

Quantity of: 61 - 80 pairs

= 19 x 1.80

= $34.20

Quantity of: 81 or more pairs

= 17 x 1.80

= $30.60

Hence, The equation will be used for solving the retail price is y = 1.8x

Learn more about Equations at:

https://brainly.com/question/10413253

#SPJ1

The next three terms for the pattern will be 12, 48, 192 and 768.

It is important to note that a pattern is used to show the sequence of events.

In this case, the first term of a pattern is 12 and the pattern follows the rule "multiply by 4."

This will be:

First term = 12

Second term = 12 × 4 = 48

Third term = 48 × 4 = 192

Fourth term = 768

Learn more about pattern on:

brainly.com/question/27033681

#SPJ1

Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]

The perimeter of the given triangle is the sum of the following segments:

Perimeter = PD + DO + OP

based on the given graph, you have that the coordinates of the points PDO are:

P: (1,-6)

D: (4,3)

O: (7,-6)

use the following formula for the distance in between two points:

d = √((x2 - x1)²+(y2 -y1)²)

where (x1,y1) and (x2,y2) are two points on the cordinate system.

For segement PD you have:

PD = √((1-4)²+(-6-3)²) = √(100) = 10

For segemtn DO:

DO = √((4-7)²+(-6-3)²) = √(100) = 10

For segment OP:

OP = √((1-7)²+(-6+6)²) = √36 = 6

then, the perimeter of the triangle is:

perimeter = 10 + 10 + 6 = 26

Answer:

3rd option

Step-by-step explanation:

the factors of 48 are

1 , 2, 3, 4, 6, 8, 12, 16 , 24 , 48

the factor pairs are

1 × 48 , 2 × 24 , 3 × 16 , 4 × 12 , 6 × 8

Answer:

1: figures a and b

2: figures a and b

3: figure a

Step-by-step explanation:

2 & 3:

all squares are rectangles, but not all rectangles are squares

Hope this helps!

SOLUTION

The equation of the parabola is defined using

Since the vertex is at the origin the equation becomes

Since the directrix is y=5

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix

It follows

Thus the equation becomes

Therefore the equation of the required parabola is

Answer: Y=-1/20x^2

Step-by-step explanation:

Step-by-step explanation:

lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer

Answer:

His commission is 104$.

Step-by-step explanation:

1. Find 20% of 520$, which is 104$.

That's the answer! Please mark me as the brainliest!

We are given a set of coordinates which are;

And the slope which is;

The equation of a line in slope-intercept form is;

Note that in this equation, the variable m is the slope (that is, the coefficient of x). we can now substitute for x, y and m into the equation above and we'll have;

We now have the values of the slope and the y-intercept as

The equation now can be written as;

ANSWER: