A straight line passes through the point (-1,2) and (2,8). Find the equation of the
straight line.

The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree

The equation of curve 1, which is in the shape of a parabola is, when represented in general form

[tex]y = -2x^2 - 4x + 12\\\\y = -2(x^2 - 2x + 6)\\\\\dfrac{y}{-2} = (x^2 - 2x + 6)\\\\\dfrac{y}{-2} +7=(x+1)^2[/tex]

So,

x+1=0

x= -1

and,

y = 14

Therefore, the Coordinate of a vertex is (-1,14).

The x-coordinate of the vertex of the function [tex]y = -2x^2 - 4x + 12[/tex] is equal to -1.

The equation of curve 2 , which is in the shape of a parabola is , when represented in general form

[tex]y = x^2 - 4x + 3\\\\y =( x-2)^2-1\\\\y+1 =( x-2)^2[/tex]

So,

x-2=0

x= 2

and, y+1=0

y= -1

Therefore, the Coordinate of a vertex is (2,-1).

The x-coordinate of the vertex of the function [tex]y = x^2 - 4x + 3[/tex] is equal to 2.

The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

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answer is 31 dimes, 11 nickels

see picture attachment for the math

equation is .05N + .10D = 3.65

value of nickels and dimes

using D + N = 42

change to find value of N = 42 - D

plug value of N into the equation and solve

The probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total outcomes = 4×8 = 32  (because 4 cards of 8 design)

The probability of selecting a card with a sunflower or butterfly design:

= 4/32  +  4/32

= 8/32 = 1/4

The probability of selecting a card with a lily, daisy, puppy, or bird design:

= 4(4/32)

= 1/2

The probability of selecting a card with a landscape design:

= 4/32 = 1/8

The probability of selecting a card with a dolphin, sunflower, or landscape design:

= 3(4/32)

= 3/8

Similarly, we can calculate the rest of the probability.

Thus, the probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.

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Answer:

13(1+2)

Step-by-step explanation:

13(1)+13(2)=13+26

The GCF of 13, 26 is 13.

Answer:

  3

Step-by-step explanation:

To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.

__

  1/3(-6) +5 = -2 +5 = 3

For x = -6, the value of the expression is 3.

Answer:

y = 6

1/3 indicates that we may have to multiply the number by 3 to get the whole number. Multiply 3 by the part given, 2.

3 × 2 = 6

Answer:

Step-by-step explanation:

next multiply 12 and 35. and get 420

finally subtract the two and get 345

The selection of a random number from 1 - 72 is an illustration of probability, and the probability of selecting a multiple of 9 is 1/8

The sample size is given as:

n = 72

There are 8 multiples of 9 from 1 to 72.

So, the probability that a multiple of 9 is selected is:

P(Multiple of 9) = 8/72

Simplify

P(Multiple of 9) = 1/9

Hence, the probability of selecting a multiple of 9 is 1/8

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Use the general formula for decay substance

[tex]\\ \rm\Rrightarrow N=N_o(1-r)^t[/tex]

For our equation r=62%=0.62

So

function becomes

[tex]\\ \rm\Rrightarrow N=650(1-0.62)^t[/tex]

[tex]\\ \rm\Rrightarrow N=650(0.38)^t[/tex]

Change for a year

[tex]\\ \rm\Rrightarrow N=650(0.38)[/tex]

[tex]\\ \rm\Rrightarrow N=247g[/tex]

Amount decayed=650-247=403g

Daily decay

Percentage decay

[tex]\\ \rm\Rrightarrow \dfrac{1.1}{650}\times 100[/tex]

[tex]\\ \rm\Rrightarrow 0.169[/tex]

[tex]\\ \rm\Rrightarrow 16.9\%[/tex]

Answer:

70

Step-by-step explanation:

Just do it backwards.

94 - 12 = 82.

82 + 6 = 88.

88 - 18 = 70.

Answer: y = -2x - 4

Step-by-step explanation:

This question asks that you give your answer in slope-intercept form, which is written as y = mx + b, where m is the slope, and b is the y-intercept.

In order to write an equation for this line in slope-intercept form, you need to find the slope and the y-intercept. You can find the slope by selecting any two clear points on the graph and finding the [change in y] ÷ [change in x].

For example, I’ll use (-3, 2) and (-2, 0):

Change in y: 2 - 0 = 2

Change in x: -3 - (-2) = -1

Change in y ÷ Change in x = 2 ÷ (-1) = -2

So, the slope, m, is -2. Finding b, or the y-intercept is a lot more straightforward; you just find where the line intercepts the y-axis, or when x = 0. Looking at the graph, we can see that the y-intercept is -4, so b = -4.

Now, we can put these together in an equation.

y = mx + b, where m = -2 and b = -4

y = -2x -4

Answer:

x-2

x+9

Step-by-step explanation:

Answer:

[tex]\frac{x-2}{x+9}[/tex]

Step-by-step explanation:

Factorizing Fraction 1

Factorizing Fraction 2

Now, multiply the fractions :

Answer:

B) 1/4 gallon

Step-by-step explanation:

There is 5/8 in a jug

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

There are 3 jugs containing (1/8). To these jugs 1/8 of the juice from (5/8) is poured.

So, now all the jugs will have (2/8) = 1/4

Answer:

294 yd²

Step-by-step explanation:

a cube has 6 congruent square faces.

the area of 1 face = 7 × 7 = 49 yd²

then surface area = 6 × 49 = 294 yd²

Area

= 3 cm

[tex] \frac{1}{2} BH = 7,5 \\ \\ (\frac{1}{2} \times5)H=7,5 \\ \\ 2,5H = 7,5 \\ \\ H=7,5 \div 2,5 \\ H=3 \: cm[/tex]

Answer:

[tex]\left[\begin{array}{ccc}38&28&66\\22&12&34\\60&40&100\end{array}\right][/tex]

Step-by-step explanation:

70% of 40 is 28, with that number you can obtain the other data.

What I got is in the image below.

I got the rest of the numbers by subtracting and adding. I also managed to find the 70% by multiplying 40 (I subtracted 60 and 100 to get the total number of people who don't watch sports) by 0.7, getting that 28 of people who don't watch sports liked pop music. From there, getting the rest of the numbers is just a whole lot of adding and subtracting. I subtracted 60 and 34 to get the number of people who watch sports and like pop, which is 26. I also added 26 and 28 to get the total of people who like pop, which is 56. To get 46 for total number of people who don't like pop, I subtracted 40 and 28 which equals 12 (number of people who don't watch sports but don't like pop), then added 34 + 12 to get 46.

Answer:

3

Step-by-step explanation:

75% is equal to 3/4

The easiest way to do this is to divide 12 by 4.

12/4 = 3

Now multiply this by three to get 3/4 of 12.

3 x 3 = 9

9 dogs left the shelter.

12 - 9 = 3

There are three dogs left.

Answer:

5, 18, 44, 96, 200

Step-by-step explanation:

Given

First term : 5

Second term : a₂ = 2(a₁ + 4)

Third term : a₃ = 2(a₂ + 4) = 2(18 + 4) = 2(22) = 44

Fourth term : a₄ = 2(a₃ + 4) = 2(44 + 4) = 2(48) = 96

Fifth term : a₅ = 2(a₄ + 4) = 2(96 + 4) = 2(100) = 200

Hence, the first 5 terms of the sequence are :

Answer:

5, 18, 44, 96, 200

Step-by-step explanation:

[tex]\textsf{Given sequence}: \quad a_n=2(a_{n-1}+4)[/tex]

[tex]\textsf{Given first term}: \quad a_1=5[/tex]

[tex]\implies a_1=5[/tex]

[tex]\implies a_2=2(a_{1}+4)=2(5+4)=2(9)=18[/tex]

[tex]\implies a_3=2(a_{2}+4)=2(18+4)=2(22)=44[/tex]

[tex]\implies a_4=2(a_{3}+4)=2(44+4)=2(48)=96[/tex]

[tex]\implies a_5=2(a_{4}+4)=2(96+4)=2(100)=200[/tex]

The reasoning used here is coding and decoding.

Coding is a portion of the logical reasoning element that is used to encrypt words, numbers, or codes utilizing specified rules and regulations. The process of decoding patterns into their original forms from supplied forms is known as decoding.

We have an expression:-

a = b and c = d, then a − c = b − d

Therefore the reasoning used here is coding and decoding.

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                                    _____

Step-by-step explanation:

[tex] \frac{5x}{2} + \frac{9}{5} = 25 \\ \frac{25x + 18}{10} = 25 \\ 25x + 18 = 250 \\ \frac{250 - 18}{25} = x \\ x = \frac{232}{25} [/tex]

hope it helps

Please refer to the attachment

Answer:

V≈25.13in³

Step-by-step explanation:

Answer:

a) Yes

b) Not a right triangle

Step-by-step explanation:

The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.

7 + 8 = 15 > 9

7 + 9 = 16 > 8

8 + 9 = 17 > 7

Therefore, a triangle with side lengths 7, 8 and 9 can be made.

To determine if the triangle is a right triangle, use Pythagoras' Theorem:

a² + b² = c² (where a and b are the legs, and c is the hypotenuse)

The hypotenuse is the longest side, therefore:

Substituting these values into the formula:

⇒ a² + b² = c²

⇒ 7² + 8² ≠ 9²

⇒ 113 ≠ 81

As  7² + 8² ≠ 9²  then the triangle is not a right triangle.

Answer:

12 cakes.

Step-by-step explanation:

There are 21/3 = 7 slices  from each cake.

84 / 7   = 12.

The Cost of Carl's first item is 3.95. The Cost of his second item is 4.95. To find the total amount we need to add these two numbers together.

3 plus 4 is 7

95 cents plus 95 cents is 1.90

7+1.90 is 8.90

The total cost is $8.90

Hope this helps!

Answer:

20 miles

Step-by-step explanation:

This is a Pythagorean Theorem Problem

1. We know that one side of the triangle is 6 miles. And we know that another side is 19 miles.

2. We use the pythagorean Theorem to solve. We get

[tex]19^2+6^2=C^2[/tex]

Where C is the distance.

Solving that we get that 20 miles is the answer.

[tex]\text{Given that,}\\\\\theta =\tan^{-1} \left(\dfrac y x \right)\\\\\\\dfrac{\partial \theta}{\partial x} = \dfrac{\partial }{\partial x} \tan^{-1} \left(\dfrac yx \right)\\ \\\\~~~~~~=\dfrac{1}{1 +\tfrac{y^2}{x^2}} \cdot y \dfrac{\partial }{\partial x} \left(\dfrac 1x \right)\\\\\\~~~~~~=\dfrac{yx^2}{x^2 +y^2} \cdot (-1)x^{-2}\\ \\\\~~~~~~=-\dfrac{yx^2}{x^2(x^2 +y^2)}\\\\\\~~~~~~=- \dfrac{y}{x^2 +y^2}\\\\\\[/tex]

[tex]\dfrac{\partial^2\theta}{ \partial x^2} = -\dfrac{\partial }{ \partial x} \left( \dfrac{y}{x^2+y^2} \right)\\\\\\~~~~~~=-y\dfrac{\partial}{\partial x} \left(\dfrac 1{x^2 +y^2} \right)\\\\\\~~~~~~=y (-1)(-1) (x^2 +y^2)^{-2} \dfrac{\partial }{\partial x}(x^2 +y^2)\\\\\\~~~~~~=\dfrac{y}{(x^2 +y^2)^2} \cdot (2x+0)\\\\\\~~~~~~=\dfrac{2xy}{(x^2 +y^2)^2}[/tex]

[tex]\text{Similarly,}~~\\ \\\dfrac{\partial \theta}{\partial y }= \dfrac{x}{x^2 +y^2}\\\\\\\dfrac{\partial^2 \theta}{\partial y^2 } = -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\\text{Now,}\\\\\dfrac{\partial^2 \theta}{\partial x^2 }+\dfrac{\partial^2 \theta}{\partial y^2 }\\\\\\=\dfrac{2xy}{(x^2 +y^2)^2} -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\=0[/tex]

[tex]\sf \large \boxed{110 ^\circ}[/tex]