Solve and CHECK the following: 2(a−3)/3=4

Answer:

y>9x+6

Step-by-step explanation:

y-9x+(9x)>6+(9x)

y>9x+6

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

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Answer:

Hey there!

The two lines in this graph are: y=-1/5x+2, and y=3x-2

Since y=-1/5x+2 is a dotted line, we know that we use the < or > symbols.

Since y=3x-2 is a straight line, we use the ≤ and ≥ symbols.

Thus, for area z, we have y<-1/5x+2, and y≥3x-2

Hope this helps :)

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4x – 3y = 24

Convert the equation from standard form to slope-intercept form. Then we have

4x – 3y = 24

3y = 4x - 24

y = (4/3)x - 24 / 3

y = (4/3)x - 8

The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

More about the linear equation link is given below.

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Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

r = radius

h = r+12 = height, 12 more than the radius

[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]

ANSWER: SECOND OPTION

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Answer:

30

Step-by-step explanation:

4/5 (x-20)=8

4/5x-4/5*20=8

4/5x-16=8

4/5x=24

x=(24*5)/4

x=30

hope it helps..

Answer:

140 toy cars

Step-by-step explanation:

The ratio of Ed's toy car to Pete's toy car is initially given as 5:2

Ed gave Pete a total number of 30 cars

Let x represent the greatest common factor that exists between both number

Number of Ed's car is represented as 5x

Number of Pete car is represented as 2x

Since they each have an equal number of cars which is 30 then we can solve for x as follows

5x-30=2x+30

Collect the like terms

5x-2x= 30+30

3x= 60

Divide both sides by the coefficient of x which is 3

3x/3=60/3

x=20

Ed's car is 5x, we substitute 20 for x

5(20)

= 100 cars

Pete car is 2x,we substitute 20 for x

2(20)

= 40 cars

Therefore, the total number of cars can be calculated as follows

= 100+40

= 140 toy cars

Hence they have 140 toy cars altogether

Answer:

140

Step-by-step explanation:

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.

  Tan = Opposite/Adjacent

  tan(T) = SU/ST

  tan(T) = (5√51)/(5√17) = √3

Now, the arctangent function is used to find the angle whose tangent is √3.

 T = arctan(√3) = 60°

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4

Answer:

x-intercept → (-5, 0)

Step-by-step explanation:

Let the equation of the line having pairs given in the table is,

y - y' = m(x - x')

m = slope of the line

(x', y') is a point lying on the line.

From the given table,

Two points (33, -22) and (52, -33) lie on the line.

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                        m = [tex]\frac{-33+22}{52-33}[/tex]

                        m = [tex]-\frac{11}{19}[/tex]

Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,

y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]

For x-intercept y = 0,

0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]

-38 = x - 33

x = -38 + 33

x = -5

Therefore, x-intercept of the line is (-5, 0).

Answer:

-5,0

Step-by-step explanation:

khan academy

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]

[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

Learn more about graph here:

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Answer:

y=2 or y-2=0

Step-by-step explanation:

to find the equation first find the slope m points (-1,2) and (5,2)

m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0

y=mx+b  the slope is zero then y=b=2

Answer:

See my explanation

Step-by-step explanation:

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22          <- this is wrong in question writing as x = 22

so, x = -22

Answer:

(5, 11) and (2, 2)

Step-by-step explanation:

y = (x-2)² + 2

y + 4 = 3x

(x-2)² + 2 + 4 = 3x

x² - 4x + 4 + 6 = 3x

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

x - 5 = 0, x = 5

x - 2 = 0, x = 2

y = (5-2)² + 2 = 11

(5, 11)

y = (2-2)² + 2 = 2

(2, 2)

Answer:

[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We want to solve this system of equations.

[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]

This is equivalent to (subtract 4 from the second equation).

[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]

Then, we can write y = y, meaning:

[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]

[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]

For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)

So the solutions are (2,2) and (5,11)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]\frac{9}{4}/\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].

[tex]-\frac{2}{3}[/tex] can stay put.

The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.

In addition, when two negatives are put together the answer must always be positive.  

Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].

Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer:

-5 ≤ x≤ 3

Step-by-step explanation:

The domain is the values for x

x starts and -5 and includes -5 since the circle is closed

and goes to 3 and  includes 3 since the circle is closed

-5 ≤ x≤ 3

Answer:

first option

Step-by-step explanation:

The domain are the values from the x- axis that can be input into the function.

The closed circles at the ends of the graph indicate that x can equal these values.

left side value of x = - 5 and right hand value of x = 3, thus

domain is - 5 ≤ x ≤ 3

Answer:

B

Step-by-step explanation:

C is too little and D is too much

Answer:

[tex]\frac{7}{12}[/tex] of the cake

Step-by-step explanation:

add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]

c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]

You are left with [tex]\frac{7}{12}[/tex] of the cake.

Answer:

k= l/3 - 14/3j

Step-by-step explanation:

l = 14j + 3k

Solve for k

l = 14j + 3k

Subtract 14j from both sides

l - 14j =14j + 3k - 14j

l - 14j = 3k

Divide both sides by 3

l - 14j / 3=3k / 3

k= l/3 - 14/3j

Or

1/3(l - 14j) = k

Answer:

Which expression is equivalent to ‐10

k

‐

10

?

Step-by-step explanation:

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

Construction II

Step-by-step explanation:

Construct 3 perpendicular bisectors of the triangles sides; where they intersect is the point of concurrency. The distance from the point of concurrency to one of the vertices is the radius.

Answer:

1/4

1/2

3/4

Step-by-step explanation:

Given:

Types of colors in the spinner

Yellow 1

Red 2

Blue 1

Total:4

Successful outcome of Yellow:1

Successful outcome of Red:2

Successful outcome of Blue:1

Required:

Probability of the

Formula:

Probability= successful outcome ÷ possible outcome

Solution

Probability=1 ÷ 4

Probability= 2÷4

Probability= 3÷4

Hope this helps ;) ❤❤❤

Answer:

28.142m

Step-by-step explanation:

area of rectangle=width x lenght

so; (rotating the formula with what is given)

area of rectangle/width=lenght

197/7=lenght

28.142m =lenght

Answer:

Length is 18 m and width is 11 m

Step-by-step explanation:

So based on the information given length is seven cm more than your width, and since we don’t know the values of these, we can plot this information into a formula that looks like this: (x+7)(x)=198, which is basically how you take the area of the plot of land.

If you multiply your values, you will get a quadratic equation that looks like this x²+7x-198. If you follow the quadratic formula to solve this equation, the positive result you will get for x is 11, this is your width. And since length exceeds by 7, you just add 7 to 11 to find the length, which ends up being 18.

to verify, you can simply multiply these two values

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation: