13 5/8 + 9 1/5 in lowest terms

Step-by-step explanation:

f(-2)= -2^2-3= -7

f(4)= 4^2-3= 13

f(0)=0^2-3= -3

Answer:

Step-by-step explanation:

is an isosceles triangle, so 12 = x + 4

12 = x + 4

x = 12- 4

x = 8

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

check

12 = 8 + 4

12 = 12

the answer is good

Answer:

3960

Step-by-step explanation:

multiply 45 by the amount of feet in a mile (5280)

take that answer and divide in by how many minutes are in an hour

Answer:

32

...when you subtract five from 37

It is a pattern that goes:

-13

-11

-9

-7

and now -5 = 32

Answer:

Hallo, I will help you with the problem T^T

Step-by-step explanation:

3.75r + 2.75b = 22.25

3.75r = The amount a red can costs, MULTIPLIED BY the amount of red cans they bought!

2.75b = The amount a black can costs, MULTIPLIED BY the amount of black cans they bought!

So this means that they bought:

3 cans of red paint.

And 4 cans of black paint.

Now you may be thinking, how do you know?

If you multiply the COST 3.75, by 3 cans of red paint, you get 11.25

And then if you multiply the COST of the black paint (The cost for a can of black paint is 2.75) multiply that by 4, you get 11 :0

So add 11 + 11.25 and you get 22.25 :]

Comment if you have any questions, no matter how insignificant you think they may be, I will help you :]

[tex]\underline{\bf{Given \:equation:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex]

[tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex]

[tex]\sf We\:know,[/tex]

[tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex]

[tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex]

[tex]\underline{\large{\bf Identities\:used:-}}[/tex]

[tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex]

[tex]\boxed{\sf (√a)^2=a}[/tex]

[tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex]

[tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex]

[tex]\underline{\bf Final\: Solution:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex]

[tex]\bull\sf Apply\: Squares[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex]

[tex]\bull\sf Put\:values[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex]

[tex]\bull\sf Simplify[/tex]

[tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex]

[tex]\underline{\bf More\: simplification:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex]

[tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]

The value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Roots of a quadratic equation

Given the quadratic equation ax² + bx + c, the sum and product  of the roots are expressed as:

Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]

Taking the square of the expression will give:

Take the square root of both sides:

[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]

Substitute the product and the sum values into the expression to have:

[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Hence the value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Learn more on the roots of equation here: https://brainly.com/question/25841119

Answer:

65/13

650/130

Step-by-step explanation:

6.5/1.3

times 10: 65/13

times 100: 650/130

Answer:

$140

Step-by-step explanation:

90-(3x10)-20+100= 140

He started with $90: (90)

Then he wrote 3 checks of $10 each: -(3x10)

Then he withdrew $20: -20

Finally, he made a deposit of $100: +100

Thus, our equation would be: 90-(3x10)-20+100=

(You might want to simplify this expression; giving you 140)

Answer:

x=15

Step-by-step explanation:

the basic property is: AB/AD=BC/CD, for more info see the attachment.

Answer:

At least 5 times

Step-by-step explanation:

Number of balls to be selected for having assurance of at least three balls of the same colour is equals to 5 balls.

" Without replacement means if an item is drawn from the set of items it is not kept back which represents sample space is decrease by as per the number of selection is done in first draw."

According to the question,

Number of red balls in a box = 8

Number of black balls in a box =8

As per the condition of without replacement we get,

In this case worst selection case could be

Alternate balls are of different colour

Black →Red → Black → Red → fifth ball is either Red or Black

Hence, 5balls must be selected for assuring at least three balls of the same colour .

Learn more about without replacement here

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Answer:

A: 312  P: 80

Step-by-step explanation:

Answer:

A=120, P=60

Step-by-step explanation:

Here’s a small hint: “miles per hour”

Put the amount of miles over the amount of hours then calculate the amount from there! It’s either the 2nd option or the 4th one! Hope it’s helpful!

Answer:

i say its c

Step-by-step explanation:

Answer:

Use the table to complete the statements.

The x-intercepts shown in the table are  

(–2, 0)

and  

(2, 0

.

The y-intercept shown in the table is  

(0, –4)

.

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

look at comments

Answer:

yes

Step-by-step explanation:

For the sides to form a triangle , then the sum of any 2 sides must be greater than the third side

9 + 11 = 20 > 15

9 + 15 = 24 > 11

11 + 15 = 24 > 9

The 3 sides given will form a triangle

Note that

The length of any two sides must be greater than the third side

So

Yes it's a triangle

Answer:

10111

Step-by-step explanation:

10111

The equation of the line for the graph that has y-intercept (0, 6) and contains the point (2, 1) is; y = -2.5x + 6

The general form of the equation of a Line in Slope Intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are told that the graph has the points (0, 6) and (2, 1). Thus, the formula for slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 6)/(2 - 0)

m = -5/2

m = -2.5

Now, since the y-intercept is at (0, 6), then it means that;

c = 6

Thus, the equation of the line is; y = -2.5x + 6

Read more about slope intercept form at; https://brainly.com/question/1884491

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The percent of the purchase price that is the price of the warranty is: b. 19%.

Using this formula

Purchase price percent=Total cost-Purchase price/Purchase price

Where:

Total cost=$512

Purchase price=$430

Let plug in the formula

Purchase price percent=$512-$430/$430

Purchase price percent=$82/$430

Purchase price percent=0.19×100

Purchase price percent=19%

Inconclusion the percent of the purchase price that is the price of the warranty is: b. 19%.

Learn more about purchase price here:https://brainly.com/question/6076645

Answer: 0 = 96

Step-by-step explanation:

Answer:

The Answer is 0=96

Answer:

Step-by-step explanation:

The area of the square is 3 units by 3 units. because the area of a square is side length squared.

side length = 3

side length^2 = 3 * 3 = 9

The area of a circle is much harder to reason out. You could start with the area of a square and use the diameter is 3 units. But the corners are rounded and you don't know off hand what the area of one of them is, let alone all 4. You are given a formula for circles area, but you have no real idea what the formula actually means. Does it take the corner area into account? At the beginning levels, we don't know.

Answer:

The area of the square is 9 aka [tex]3^{2}[/tex]

You can find it easily by just counting the number of squares inside the square, or by counting the number of squares at its length then multiplying it by its width; so 3 x 3 = 9

It wouldn't be as easy to find the area of the circle because you don't have the radius, nor diameter, so basically, no quantitative values could be used to at least guess.

Answer:

Step-by-step explanation:

[tex] = \frac{ {6}^{4} . {6}^{3} }{ {6}^{5} } [/tex]

[tex] = \frac{ {6}^{(4 + 3)} }{ {6}^{5} } [/tex]

[tex] = \frac{ {6}^{7} }{ {6}^{5} } [/tex]

[tex] = {6}^{(7 - 5)} [/tex]

[tex] = {6}^{2} (ans)[/tex]

Step-by-step explanation:

remember, the general formula to solve a quadratic equation ax² + bx + c = 0 is

x = (-b ± sqrt(b² - 4ac))/(2a)

a)

I think there is a typo, and this should be

5x² - 7x = 72

5x² -7x - 72 = 0

x = (7 ± sqrt(49 - -1440))/10 = (7 ± sqrt(1489))/10

x1 = (7 + sqrt(1489))/10

x2 = (7 - sqrt(1489))/10

b)

x(x + 2) = 5

x² + 2x - 5 = 0

x = (-2 ± sqrt(4 - -20))/2 = (-2 ± sqrt(24))/2 =

= (-2 ± sqrt(4×6))/2 = (-2 ± 2×sqrt(6))/2 =

= -1 ± sqrt(6)

x1 = -1 + sqrt(6)

x2 = -1 - sqrt(6)

c)

3x² + 2x - 4 = 0

x = (-2 ± sqrt(4 - -48))/6 = (-2 ± sqrt(52))/6 =

= (-2 ± sqrt(4×13))/6 = (-2 ± 2×sqrt(13))/6 =

= (-1 ± sqrt(13))/3

x1 = (-1 + sqrt(13))/3

x2 = (-1 - sqrt(13))/3

The base and altitude of the triangular plot are [tex]42m[/tex] and [tex]21m[/tex] respectively.

The perimeter of the square plot having the same area as the triangular plot is [tex]84m[/tex]

a) Calculate the base and altitude of the triangular plot

The relationship between the Total cost of leveling the triangular plot, the cost per unit area, and the area of the triangular plot is

[tex]\text{unit cost}=\frac{\text{total cost}}{\text{area}}\\\\\text{area}=\frac{\text{total cost}}{\text{unit cost}}\\\\=\frac{\text{11025Rs.}\rupee}{25Rs./m^2}=441m^2[/tex]

The formula for calculating the area of a triangle, given the base and altitude is

[tex]\text{area of triangle}=\frac{1}{2}\text{base}\times\text{altitude}[/tex]

From the question

[tex]\text{base}=2\times\text{altitude}[/tex]

so

[tex]\text{area of triangle}=\frac{1}{2}\times 2\times\text{altitude}\times\text{altitude}\\\\\text{area of triangle}=\text{altitude}^2\\441=\text{altitude}^2\\\text{altitude}=\sqrt{441}=21m[/tex]

from this we can get the base

[tex]\text{base}=2\times\text{altitude}\\=2\times21m=42m[/tex]

b) Calculate the perimeter of a square plot having the same area

Since we found the area of the triangular plot to be [tex]441m^2[/tex], we will use this value for the area of the square plot, so that we can obtain the side

[tex]\text{area of square plot}=side^2\\441=side^2\\\sqrt{441}=side=21m[/tex]

Hence, the perimeter is equal to

[tex]perimeter=4\times side\\=4\times21=84m[/tex]

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Answer:

Domain[0, ∞). Range (-∞,4).

Step-by-step explanation:

domain is your lowest x (zero) to your highest x (infinity)

range is the lowest y (negative infinity) to your highest y (four)

Answer:

its b

Step-by-step explanation:

The party was attended by Karen, her mother, 4 other adults, and 110 of Karen's friends, for a total of $ 555.

Since Karen invited 150 friends to her 15th birthday party, but not everyone can attend, Karen's mother want one adult for every 25 of her friends, and the cost of food is $ 20 for every four of her friends, and the adults eat for free, if a total of 116 people (including Karen and her mother) go to the party, to determine how many are adults and how many are Karen's friends and how much will the food cost, the following calculations must be performed:

Therefore, the party was attended by Karen, her mother, 4 other adults, and 110 of Karen's friends, for a total of $ 555.

Learn more about maths in https://brainly.com/question/25865591

Answer:

Horizontal compression by a factor of 2 followed by a vertical shift by positive 3

Step-by-step explanation:

a*f(k(x-d))+c

k=2

c=3

Answer:

(2,1)

Step-by-step explanation:

The answer is (2,1)

Answer:

4/9

Step-by-step explanation:

I did the butterfly method to see which one is the bigger one

Answer:

4/9

Step-by-step explanation:

Answer:

Cost = 8 + 1.25x

Step-by-step explanation: