Mike mixes paint at a hardware store. A certain shade of orange paint is made by
mixing white, red, and yellow paint in a ratio of 4 to 3 to 2. If Mike wants to make 3
gallons of paint that is this shade of orange, how many gallons of red paint will he
need?

Answer:

B

Step-by-step explanation:

given the graph of y = 0.5x

Then any point on the line satisfies y = 0.5x

consider the points given

x = 1 then y = 0.5 × 1 = 0.5 ⇒ (1, 0.5 ) is on the line

x = 4 then y = 0.5 × 4 = 2 ⇒ (4, 2 ) is on the line

The solution of the given equation is -6 and 1.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given equation:

  (x+2)(x+3) = 12

 x(x+3)+2(x+3) = 12

 x² + 3x + 2x + 6 = 12

 x² + 5x + 6 - 12 = 0

 x² + 5x - 6 = 0

 x² + 6x - x - 6 = 0

 x(x+6) -1(x+6) = 0

 (x+6)(x-1) = 0

Now, x + 6 = 0      or      x - 1 = 0

        x = -6           or      x = 1

Thus, the solution of the given equation is -6 and 1.

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The expression which is equal to the expression [tex]x^{2} yx^4} y^{3} xy^{2}[/tex] is as [tex]x^{7} y^{6}[/tex].

Given Expression   [tex]x^{2} yx^4} y^{3} xy^{2}[/tex] and we have to find the expression equal to this.

Two variables are present in the given expression x and y but both are in different form or powers.

x is having power 2 , 4 and 1 so because the base is same for all and they are in multiplied form so we will add the powers to form [tex]x^{4+2+1}\\[/tex]

=[tex]x^{7}[/tex]

Now y is having 1,3,2 powers so because the base is same for all and they are in multiplied form so we will add all the powers to form [tex]y^{6}[/tex]

Now multiply both to get the required expression which is [tex]x^{7} y^{6}[/tex].

Hence the expression which is equal to the given expression is [tex]x^{7} y^{6}[/tex].

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The length of the rectangle is 60 feet and the width of the rectangle is 45 feet.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L×W square units

A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length.

L = W + 15

Then we have

2700 = W(W + 15)

W² + 15W - 2700 = 0

W² + 60W - 45W - 2700 = 0

(W + 60)(W - 45) = 0

W = 45, -60

Then the dimension of the rectangle will be

W = 45 feet

L = W + 15

L = 45 + 15

L = 60 feet

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In the given triangle, it should be noted that ADC is the same as BCD due to SAS congruence.

From the information given,

AD = BC

BCD = ADC.

This depicts the concept of SAS. In this case, the two-sided will be equivalent.

Also, it should be noted that DAC and CBD are equal according to the vertical angle theorem.

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Answer:

see picture ....

Step-by-step explanation:

[tex]\tan(90^{\circ}-A)\\ \\ =\frac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}\\ \\ =\frac{\cos A}{\sin A}\\\\=\boxed{\frac{1}{\tan A}}[/tex]

Answer:

D is the answer for you.

Answer:

1. the possible outcomes are any of the seven days of the week

2. 1/7 chance of choosing Wednesday

3. 2/7 chance of choosing Saturday or Sunday

[tex]\mathbb{PROBLEM:}[/tex]

[tex] \\ [/tex]

A day is chosen from a week.

1. What are the possible outcomes?

2. What is the chance of choosing Wednesday?

3. Find the probability of selecting weekends.

[tex] \\ [/tex]

=======================================

[tex]\mathbb{SOLUTION:}[/tex]

[tex] \\ [/tex]

1. What are the possible outcomes?

2. What is the chance of choosing Wednesday?

[tex]\tt\underline\red{ \: \: \frac{1}{7} \: \: }[/tex]

3. Find the probability of selecting weekends.

[tex]\tt\underline\red{ \: \: \frac{2}{7} \: \: } [/tex]

=======================================

♥️

Answer:

y = 90 -5/2 x

Step-by-step explanation:

The angle on the left equals x+3x+x = 5x

The angle on the right equals 2y

The two angles are same side interior angles which are supplementary because the lines are parallel

5x+2y = 180

Solving for y

2y = 180-5x

Divide by 2

2y/2 = 180/2 -5x/2

y = 90 -5/2 x

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The two lines are parallel, henceforth we can apply Angle pair rules.

[tex]\qquad \tt \rightarrow \:(x + 3x + x) + 2y = 180[/tex]

[ Co - interior angles ]

[tex]\qquad \tt \rightarrow \:5x + 2y = 180[/tex]

[tex]\qquad \tt \rightarrow \:2y = 180 - 5x[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{180 - 5x}{2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{180 }{2} - \cfrac{5x}{2} [/tex]

[tex]\qquad \tt \rightarrow \:y = 90 \degree - \cfrac{5x}{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3

Step-by-step explanation:

Factors of 15 are 1, 3, 5, 15

Factors or 6 are 1, 2, 3, 6

HCF = 3

Step-by-step explanation:

s.i= P×T×R/100

=2000×0.25×2/100

= 1000/100

= 10

Answer:

$10

Step-by-step explanation:

[tex]2000 \times .02 \times \frac{1}{4} = 10[/tex]

Answer:

a = 11, b = 7

Step-by-step explanation:

See picture

Answer:

x^2 + 7x + 12

Step-by-step explanation:

This is a product of two binomials.  There's a formula:  

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

Therefore, (x + 3)(x + 4)​ = x^2 + 3x + 4x + 12  =  x^2 + 7x + 12

All the parts shown in the figure are solved.

A mathematical technique that is used to determine the possible arrangement of the objects when the sequence of selection does not matter.

Part 1

(a) When two dices are rolled the basic outcomes will be =?

Each dice has 6 outcomes and therefore 6* 6 =36

Therefore total 36 basic outcomes.

(b) Yes both the events are equally likely .

Part 2

(a) There can be 11 types of sum from 2 -12 obtained when two dices are rolled

Sum

2 1+1                                                  

3 1+2, 2+1                                          

4 1+3, 2+2, 3+1                                  

5 1+4, 2+3, 3+2, 4+1                            

6 1+5, 2+4, 3+3, 4+2, 5+1                    

7 1+6, 2+5, 3+4, 4+3, 5+2, 6+1          

8 2+6, 3+5, 4+4, 5+3, 6+2          

9 3+6, 4+5, 5+4, 6+3                          

10 4+6, 5+5, 6+4                                  

11 5+6, 6+5                                          

12 6+6    

(b) They are not equally likely as the sum obtained is dependent on both the dice rolling.

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Answer:

False

Step-by-step explanation:

m∆A+m∆C=180°

110°+110°=180°

220°(/=) 180°

A circle can be circumscribed about the given quadrilateral, the answer is true.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the the circumference of the circle.

Opposite angles of a circumscribed polygon are supplementary.

Therefore, a circle can be circumscribed about the given quadrilateral is true

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Answer:

Step-by-step explanation:

Buford should use 7.5 pounds of the 50% corn bag.

A system of linear equation is an equation containing two different equations with variables and the coefficient.

From the given information, let:

Sp, we can a system of a linear equation that says:

x + y = 30

0.5x + 0.9y = 0.8(30)

Using elimination method

x + y = 30

-

x - 1.8y = -48

0 - 0.8y = -18

y = 18/0.8

y = 22.5

From x + y = 30

x = 30 - 22.5

x = 7.5

Therefore, we can conclude that he should use 7.5 pounds of the 50% corn bag.

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Answer:

x=3.5

Step-by-step explanation:

x × 2 = 7

   ÷2     ÷2

    x=3.5

Answer: Add the equations to eliminate k

Step-by-step explanation:

Adding the equations, you get 2b=18, which you can solve for b. Afterward, you can substitute this value of b back into either equation to solve for k.

Answer:

4 more wrenches than screwdrivers

Step-by-step explanation:

6+8=14

14-10=4

therefore there are 4 more wrenches than screwdrivers.

:)

Answer:

14

Step-by-step explanation:

solution

Screwdrivers- 10

wrenches- 6

if bella adds 8 more wrenches.

= 6 + 8

=14

Now, there are 14 wrenches in the box

The ordered pair of the given equation will be ( 3, 6 ) and ( -3, 18).

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The given functions are:-

F(x) =x²-2x+3

F(x) = -2x + 12

When we plot the graph of the function we will see that the line -2x +12 cut the parabola at points ( -3, 18 ) and ( 3, 6 ) so these are the ordered pairs of the two functions. The graph of the functions is also attached with the answer.

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line is y=-(7/5)x + (56/5).

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

Given two points of the line AB, where the coordinates of point A are (8,0) and the coordinates of point B are (3,7). Now, the slope of the equation can be written as,

m = (0-7)/(8-3) = -7/5

Substitute any one of the points in the equation,

y = -(7/5)x + c

7 = -(7/5)3 + c

7 = -21/5 + c

76/5 = c

Hence, the equation of the line is y=-(7/5)x + (56/5).

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The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.

Given equation;

y + 2 = (x+2)

Rearrange the equation;

y + 2 = x+ 2

y=x

The standard equation for the straight line is;

y = mx + c

Where c is the intercept and m is the slope

After comparing the given equation with the standard equation we get;

m = 1

c =0

Hence,the graph is plotted and attached in the attachment.

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Sarah charges $6.00 for one bracelet.

We know that a collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics.

Let Sarah charges $x and $y for one bracelet and one ring respectively.

Since her first customer spends $48 on 3 bracelets and 10 rings, we can write it as

3x + 10y = 48 ...(1)

Since her second customer spends $54 on 7 bracelets and 4 rings, we can write it as

7x + 4y = 54 ...(2)

Now, we have to solve this system of linear equations.

Multiplying (1) by 2, 6x + 20y = 96 ...(3)

Multiplying (2) by 5, 35x + 20y = 270 ...(4)

Subtracting (3) from (4), 35x + 20y - 6x - 20y = 270 - 96

i.e. 29x = 174

i.e. x = 174/29 = 6

Therefore we can conclude that Sarah charges $6 for one bracelet. Option B is correct.

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The equation of the directrix of the parabola given is x = 6, Option D is the correct answer.

A parabola is a U shaped curve whose all point are at same distnace from a  point called as focus and a line called as Directrix .

The equation of the parabola given is

y² = -24x

When the standard equation of parabola is

 (y - k)² = 4p (x - h),

where the focus is (h + p, k) and the directrix is x = h - p.

here h = 0

p = -24/4 = -6

x =  0 - (-6)

x = 6

Therefore Option D is the correct answer.

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Answer:

0 is the answer to the question

Answer:

The reference atomic mass is carbon-12 when calculating atomic masses.

Step-by-step explanation:

The one-twelfth mass of an atom of carbon-12 is known as an atomic mass unit.

Because no other nuclide has a mass that is exactly a whole number in this scale except for carbon-12.

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A function assigns the values. The half life of the substance is 6.25 days.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function for the substance as [tex]N= N_o e^{-kt}[/tex], therefore, the half life of the substance can be written as,

[tex]N= N_o e^{-kt}\\\\\dfrac{N}{N_o}= e^{-kt}[/tex]

Since we need to find the half life, therefore, the ratio of the initial mass and the mass after half-life will be 1/2.

[tex]\dfrac12= e^{-kt}\\\\\ln (0.5) = -kt[/tex]

Given the value of k is 0.1109, therefore,

[tex]\ln (0.5) = -kt\\\\\ln (0.5) = -(0.1109)t\\\\t = 6.25[/tex]

Hence, the half life of the substance is 6.25 days.

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Answer:

3 and -3

Step-by-step explanation: