The graph of a system of inequalities shown

The number of red car altogether is 34

The number of blue cars altogether is 36

The  number of silver car altogether 70

The car manufacturer has parked some cars in 2 car parks .

The first car park has 60 cars.

In the ratio 1 :2:3

Therefore,

red car = 1 / 6 × 60 = 10 cars

blue car = 2 / 6 × 60 = 20 cars

Silver car = 60 - 30 = 30 cars

The second car park has 80 cars.

The ratio are

In the ratio 3:2 5

Therefore,

red cars = 3 / 10 ×80 = 24

blue cars = 2 / 10 × 80 = 16

silver cars = 5 / 10 × 80 = 40

Therefore,

The number of red car altogether is 24 + 10 = 34 red car

The number of blue cars altogether is 20 + 16 = 36 blue cars

The  number of silver car altogether is 30 + 40 = 70 silver cars

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Answer:

yeheheehejehejejejjejjejejejejje

Answer:

x=4

Step-by-step explanation:

We are given that the triangles are congruent.

Specifically, the order of the letters gives that the angles ∠DAB and ∠CBA are corresponding parts of the two congruent triangles.  Since corresponding parts of congruent triangles are themselves congruent, ∠DAB ≅ ∠CBA.  Thus, m∠DAB = m∠CBA.

Given the expressions for the two angles, we can substitute into the equation, and solve for the requested variable.

[tex]m\angle DAB=m\angle CBA\\(35)=(8x+3)\\(35)-3=(8x+3\!\!\!\!\!\!\!\!\!\!{--})-3 \!\!\!\!\!\!\!\!\!\! {--}\\32=8x\\\dfrac {32}{8}=\dfrac {8x\!\!\!\!\!\!\! {-}}{8\!\!\!\! {-}}\\4=x[/tex]

Answer:

Closer to 30.

Step-by-step explanation:

To answer this first find 40% of 90.

90*0.4=36

0.4 is the same as 40%

Hope this helps!

If not, I am sorry.

Answer:

21% of 456 = 0.21 x 400 + 0.21 x 50 + 0.21 x 6 = 95.76

Step-by-step explanation:

Answer:

10hr/m because the average velocity is divided by number

Answer:

4^3x=4^(4x+4)

Step-by-step explanation:

You can eliminate the first 2 options since those don’t make sense already, and the last option changed 64 to 2^6 which is correct, but when they changed the other side. They should have multiplied 8 to both x and 1 which would have made the whole term 2^(8x+8) and not 2^(8x+1). Left with the third option, 4 to the power of 3 is 64 so the left side makes sense, 4^3x=64^x, on the right side, 4^4 equals 256, so the whole exponent should multiply by 4 so from 256^(x+1) you get 4^4(x+1) giving 4^(4x+4) making the third choice the right answer.

Answer:

Rational.

Step-by-step explanation:

[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]

Answer:

The only methods allowed are

-  "Subtract equation 2 from equation 1,"  and "Multiply equation 1 by 2. Then add the new equation to equation 2"

-

Step-by-step explanation:

Subtract Eq 2 from Eq 1:

3x-2y=7

-3x-4y=-17

-6y = -10

y = (5/3)

Use y =(5/3) to solve for x in both equations.

x=(31/9)

Subtract the left side of equation 2 from the left side of equation  No, this is not a legal operation.  

Multiply equation 1 by 2. Then add the new equation to equation 2  Yes, this works.  Instead of solving for y first, this method solves for x, which can then be used to find y:

2(3x-2y=7)

  6x-4y=14

  3x+4y=17    

   9x = 31    (y is eliminated)

x = (31/9)

Now use this to find y in either equation:

3x-2y=7

3x-2(31/9)=7

y = (5/3)

Answer: None of the choices

Step-by-step explanation:

1. It couldn't be integers (whole numbers positive or negative), because a cube couldn't have a negative volume.

2. It could be natural numbers, but the problem is, that a volume could have decimal values, for example, 3.62 meters cubed which a natural number doesn't support.

3. Set of whole numbers is the same as integers, so it can't be that.

4. None of the choices, which in my opinion is the correct one.

I'm not sure it is correct, but I hope I helped you!

Answer:

Summer is incorrect

Step-by-step explanation:

It definitely matters which side is side "c".  Side "c" must be the hypotenuse (the side across from the right angle).

The other two sides are the legs (sides touching the right angle), and either leg can be "a" or "b", but the hypotenuse must be "c".

Take the equation, a² + b² = c², and subtract c² from both sides:

[tex]a^{2} +b^{2} -c^{2} =0[/tex]

It won't matter which leg is "a" or "b", because of the commutative property of addition.  Note that "a²" and "b²" are added together, and due to the commutative property of addition, we can add in either order and get the same result.

However, since the c² term is connected by subtraction, and subtraction doesn't have a commutative property, it can't be subtracted in any order.  Meaning which side it is is important.

The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

From the question, we are to determine the equation of the circle

The equation of circle is given by

(x - h)² + (y - k)² = r²

Where (h, k) is the center

and r is the radius

From the given information,

The two circles are concentric

∴ (h , k) = (4, 6)

But the other circle has a radius that is twice as large

∴ r = 2 × 2

r = 4

Thus,

The equation of the circle becomes

(x - 4)² + (y - 6)² = 4²

(x - 4)² + (y - 6)² = 16

Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

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Answer:

x=3

Step-by-step explanation:

we first write both equations:

[tex]3x + 4y = 12 \\ 9x - 4y = 24[/tex]

then we add the Left hand sides from both, and compare to the Right hand sides from both:

[tex]3x + 4y + 9x - 4y = 12 + 24 \\ 3x + 9x = 36 \\ 12x = 36 \\ x = 3[/tex]

Step-by-step explanation:

I am not sure what your problem here is.

you understand the inequality signs ?

anyway, to get

6×f(-2) + 3×g(1)

we can calculate every part of the expression separately, and then combine all the results into one final result.

f(-2)

we look at the definition.

into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?

is -2 < -2 ? no.

is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.

so, we have to use

1/3 x³

for x = -2 that is

1/3 × (-2)³ = 1/3 × -8 = -8/3

g(1)

again, we look at the definition.

into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?

is 1 > 2 ? no.

is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.

so we have to use

2×|x - 1| + 3

for x = 1 we get

2×0 + 3 = 3

6×f(-2) = 6 × -8/3 = 2× -8 = -16

3×g(1) = 3× 3 = 9

and so in total we get

6×f(-2) + 3×g(1) = -16 + 9 = -7

Step-by-step explanation:

here I have done you can check it out

Answer:

y=0.5(x−1)

Step-by-step explanation:

Explanation: To find the inverse of a function, you have to substitute y for x in the equation and simplify to get a normal equation again. In this case, f(x) is y.

y=2x+1

x=2y+1

2y+1=x

2y=x−1

y=0.5(x−1)

Answer

[tex]y=\frac{x-1}{2}[/tex]

Step-by-step explanation:

To find the inverse of a function  [tex]f(x)=2x+1[/tex] , we substitute x and y for each other and then solve for y to get a new function.

We rewrite the original function as:

[tex]x=2y+1[/tex]

And then we solve for y:

[tex]x-1=2y[/tex]

[tex]y=\frac{x-1}{2}[/tex]

This is our answer.

The first part is half of the second part. The first part is 16 and the second part is 8.

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Let the first part is x, y os the second part, and the no of half times is z then the equation is;

x × y = z

16×(1/2) = 8

Hence,the first part is half of the second part. The first part is 16 and the second part is 8.

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Answer:

2x + 3.

Step-by-step explanation:

x + x + 3

= 2x + 3.

Answer:

2x+3

Step-by-step explanation:

x+x+3=2x+3

sum means to add both expression together and we can see there are 2 x's so we can add them and get 2x+3

5) 2x + 8 - 4y - 1 = 2x - 4y + 7

6) -5x(3x² - 2x - 1) = -15x³ + 10x² + 5x

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

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The pair of functions are inverse of each other is, [tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex].Option C is correct.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

On checking the function one  by one we get that option c satisfies the conditions;

[tex]\rm f(x)=5x-9[/tex]

Change the coefficient;

y=f(x) as x=f(y)

The function is written as;

y=5x-9

x=5y-9

Simply the function;

[tex]\rm y = \frac{x+9}{5} \\\\ y=g(x) \\\\\ g(x) = \frac{x+9}{5}[/tex]

The pair of functions are inverses of each other is,[tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex]

Hence option C is correct.

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The figures Сone Z and Cylinder Y have the same volume.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Similarly, the volume of a cylinder can be calculated by using this formula:

V = πr²h

In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.

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

Answer:

Using the concepts of coordinate system and equation of line, we find that y ≥ (1/3)x + 3 and 3x-y > 2 are represented by the graph.

Step-by-step explanation:

Equation of line passes through points (a, b) and (c, d) is given by:

y-b = [(d-b) / (c-a)] / (x-a)

Given that the first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).

y-3 = [(4-3) / (3-0)] / (x-0)

y-3 = x / 3

y - (1/3)x = 3

Also, everything above the line is shaded, i.e. the inequality represents the first graph: y ≥ (1/3)x + 3

The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).

y+2 = [(1+2) / (1-0)](x-0)

y+2 = 3x

3x-y = 2

Everything to the right of the line is shaded.

i.e. inequality represents the second graph: 3x-y > 2

Hence, the system of linear inequalities is represented by the graph :

y ≥ (1/3)x + 3

3x-y > 2

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Answer:

D

Step-by-step explanation:

Got it right on edge 2022

Answer:     [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]

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

Work Shown:

[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]

The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.

The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.

Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.

Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.

Answer:

48 : 72

Step-by-step explanation: