Does (-2,0 ) make the equation y=x true ?

[tex]\bf \begin{cases} 4x-2y=5\\ \boxed{y}=2x+10 \end{cases}~\hspace{7em}\stackrel{\textit{substituting \boxed{y} in the 1st equation}}{4x-2\left( \boxed{2x+10} \right)=5} \\\\\\ 4x-4x-20=5\implies -20\ne 5[/tex]

which makes no sense, our variable went poof, but that is a flag that this system has no solution, let's quickly solve both for "y" to put them in slope-intercept form,

[tex]\bf 4x-2y=5\implies 4x-5=2y\implies \cfrac{4x-5}{2}=y\implies ~\hfill \stackrel{\stackrel{m}{\downarrow }}{2}x-\cfrac{5}{2}=y \\\\\\ ~\hfill y=\stackrel{\stackrel{m}{\downarrow }}{2}x+10[/tex]

so, notice, the slopes(m) are exactly the same for both, whilst the y-intercept differs, meaning both lines are parallel and therefore never touch each other, thus, no solution.

the untrue equation of -20 = 5, is another way to say, "no solution".

[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=1.5 \end{cases}\implies SA=2\pi (1.5)(1.5+1.5) \\\\\\ SA=3\pi (3)\implies SA=9\pi[/tex]

Answer:

a=4

Step-by-step explanation:

ax − 4 = 2y

We need to get the equation is slope intercept form  y= mx+b.

Lets solve for y

Divide each side by 2

a/2 x - 4/2 = 2y/2

a/2 x -2 = y

or y=a/2 x -2

The slope is a/2 and the y intercept is -2

We want a slope of 2  so a/2 =2

a/2=2

Multiply each side by 2

a/2 * 2 =2*2

a =4

Answer:

6.6 stone

Step-by-step explanation:

We will use conversions to change kilograms to stones

1 kilogram= 2.2 pounds,

1 stone= 14 pounds

42 kilogram          2.2 lbs           1 stone

---------------       * -------------   * ---------------

                           1 kg                 14 lbs

All the units cancel except stone

(42*2.2)/14  stone

6.6 stone

Final answer:

The missing factors in the expression 3x³+12x²-9x are obtained by factoring out the common term 3x and then factoring the quadratic expression x²+4x-3. The final factorization is 3x(x+6)(x-1).

Explanation:

To find the missing factors in the expression 3x³+12x²-9x, we first factor out the common term, which is 3x.

So, the expression becomes 3x(x²+4x-3). Next, we need to find two numbers that multiply to -3 and add to 4. These numbers are 6 and -1, so we can further factor the quadratic as 3x(x+6)(x-1). In conclusion, the missing factors of the given expression are x+6 and x-1.

Answer:

55

Step-by-step explanation:

Given that a circle and inside two chords with same arc length.

We are to find the angle between the two chords.

Given that two arcs subtend angle 125 degrees at the centre.

Let us join the two ends of chords to make the figure as a triangle inside a circle.

The triangle is isosceles as two arcs and hence chords are equal.

By central angle theorem we have the two equal angles as 1/2 (125) = 62.5

Hence we have a triangle with two equal angles 62.5 and another angle 1.

By triangle sum of angles theorem

angle 1+62.5+62.5 = 180

Hence angle A = 180-62.5-62.5 = 55 degrees.

Answer:

7.25

Step-by-step explanation:

4 times 2 is 8 so then add another half and you will get 10 so multiply 2.5 times 2.5

Kellan should use 6.25 cups of water to make a batch of lemonade with 10 scoops of lemonade powder.

To determine how much water should be used, we can set up a proportion using the lemonade powder to water ratio. Since 4 scoops of lemonade powder are used for every 2.5 cups of water, we can write the proportion as:


4 scoops / 2.5 cups = 10 scoops / x cups

To solve for x, we can cross-multiply and divide:


4x = 10 * 2.5

4x = 25

x = 6.25 cups

Therefore, Kellan should use 6.25 cups of water to make a batch of lemonade with 10 scoops of lemonade powder.

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Answer:

4+y = -36

y = -40

The definition of a rational number is the ratio of two integers

Lets rewrite .57 as a fraction

.57 = 57/100

Both 57 and 100 are integers and 57/100 is the ratio of integers so .57 is rational.

Step-by-step explanation:

4+y = -36

Subtract 4 from each side

4+y-4 = -36-4

y = -40

The definition of a rational number is the ratio of two integers

Lets rewrite .57 as a fraction

.57 = 57/100

Both 57 and 100 are integers and 57/100 is the ratio of integers so .57 is rational.

Answer:

See below.

Step-by-step explanation:

The slope of the line is (5-1) / (3 - -3)

= 4/6  = 2/3

Point slope form:

y - y1 = m(x - x1)

Plugging in m = 2/3 and the point (-3,1):-

y - 1 = 2/3(x + 3) (answer)

Slope-intercept form:-

y - 1 = 2/3(x + 3)

y = 2/3x + 2 + 1

y = 2/3x + 3 (answer)

Standard Form:-

y = 2/3x + 3

Multiply through by 3:-

3y = 2x + 9

-2x + 3y = 9  (answer).

Answer:

19800

Step-by-step explanation

5 * 60 =300

5 hrs is 300 minutes

300 + 30 = 330

5hrs and 30 min is 330 min

330*60= 19800

5hrs and 30 min is 19800 sec

Answer:

If x is an exponent in all those functions, then the function that grows the fastest is D, because it has the highest base 5 which is raised to x.

Step-by-step explanation:

The function  [tex]f(x) = 2\times5^x[/tex]  grows fastest. The correct answer is option D.

Given that the following functions:

[tex]f(x) = 5\times2^x[/tex]                      (1)

[tex]f(x) = 4\times3^x[/tex]                        (2)  

[tex]f(x) = 3\times4^x[/tex]                        (3)

[tex]f(x) = 2\times5^x[/tex]                       (4)

To determine which exponential function grows the fastest, compare the bases of the functions. The base of an exponential function determines how quickly it grows.

Let's compare the bases:

(1) The base is 2.

(2) The base is 3.

(3) The base is 4.

(4) The base is 5.

Since the base determines the rate of growth, conclude that  [tex]f(x) = 2\times5^x[/tex]  grows the fastest among the given options because 5 is the largest base.

In other words, as x increases, the function  [tex]f(x) = 2\times5^x[/tex]  will have the steepest increase in value compared to the other options.

Hence, the function  [tex]f(x) = 2\times5^x[/tex]  grows fastest.The correct answer is option D.

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D) feet

A tree 1.5 x 10^3 is 1500 centimeters. That's about 300 inches, which would better be measured in feet.

You can use the fact that normally people use those measurements which are whole numbers or not elongated decimal number mostly and not much big numbers.

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

Normally people use those measurements which are whole numbers mostly and if not, then not too much long after decimal and not much big numbers.

A tree is measured suitably if we use feet. It is because the normal tree height is from few feet to few hundred feet.

If you measure tree height in centimetres, then as you can see in the question, the number before cm unit is quite big to handle by normal people.

If you measure in too big unit like kilometres, then the height would be expressed mostly like 0.some digits.

That's why we choose feet.

Since 1 cm = 0.0328 feet

thus, height of specified tree in feet would be

[tex]\rm 0.0328 \times 1.5 \times 10^{3} = 49.2 \: feet[/tex]

See the number before feet. Its not too big nor too small, and easy to remember and converse. That's why feet is appropriate.

Thus,

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

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Answer:

630.8 for the nearest tenth, and 631 for a whole number.

Step-by-step explanation:

Answer:

It would take 675.2809 days or 675.3 days

Step-by-step explanation:

first you simplify your equations if possible which you can here.

6.01×10^8=601,000,000        8.9×10^5=890,000

Then you are going to divide 601,000,000 by 890,000 or you cancel the zeros and then divide (your choice)

601,000,000/980,000

You can cancel out the zeros that both share so you'll be left with

60,100/89

then you divide and you get

675.2809

or you can round to the nearest tenth and you get

675.3

Answer:

18

Step-by-step explanation:

Let the side of the triangle be a and that of the new one be a'.

a'/a = 3/1      Insert the value of a

a'/6 = 3        Multiply each side by 6

  a' = 18

The measure of a side of the new triangle is 18.

Answer: 18 units.

Step-by-step explanation:

Given : An equilateral triangle is dilated by a scale factor of 3.

[Note an equilateral triangle has all its side-lengths are equal.]

Side-length of the original triangle = 6 units

Then, the measure of a side of the new triangle = Scale factor x Original side-length

= 3 x 6 = 18 units

Hence, the measure of a side of the new triangle = 18 units.

24 = 2 · 2 · 2 · 3

36 = 2 · 2 · 3 · 3

GCF(24, 36) = 2 · 2 · 3 = 12

24 = 12 · 2

36 = 12 · 3

Answer:

24 + 36 = 12 · 2 + 12 · 3 = 12 · (2 + 3)

Step-by-step explanation:

Answer:

your answer would be C

Step-by-step explanation:

follow the numbers up the graph

Answer:

C. After 6 minutes, Sam is 60 meters from the dock.

Step-by-step explanation:

Answer:

the answer is -20/8 or A

Step-by-step explanation:

Answer:

4.

a. base angle

b. leg

c. vertex

d. leg

e. base

f. base

5. You have 3 pairs of corresponding congruent sides, so the property that proves the triangles are congruent would be SSS.  

Answer:

-75.77

Step-by-step explanation:

finding the difference is just finding the distance between two points

your two points are 66.830 and 142.6

so subtract 66.830 from 142.6 and you will get -75.77 depending on the question it could be positive or negative.

Answer:

75.77

Step-by-step explanation:

[tex]y+8=-11\qquad\text{subtract 8 from both sides}\\\\y+8-8=-11-8\\\\\boxed{y=-19}[/tex]

The values of x and y that satisfy the system of equations are x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

The equations 3x − 1 + 2y = 0 and 3x2 − y2 + 4 = 0

Now,

To find the corresponding values of y, we can plug these values of x into the expression for y that we found earlier:

[tex]y = -1/2(3x - 1). For x = (1/3 + i√(19))/1, we get: y = -1/2(3(1/3 + i√(19))/1 - 1) = -1/2(i√(19) - 2) = (i√(19) + 2)/2. For x = (1/3 - i√(19))/1, we get: y = -1/2(3(1/3 - i√(19))/1 - 1) = -1/2(-i√(19) - 2) = (-i√(19) + 2)/2.[/tex]

These are the values of y that satisfy the system of equations.

Therefore, by quadratic equations the answer will be x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

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Answer:

15

Step-by-step explanation:

4g(3)+2[g(2)]²

4((3+4)/√7(3)-5)+2[(2+4)/√7(2)-5]²

=15

Answer:

Answer is option c. (15)

Answer:

3/8

Step-by-step explanation:

The height is 9 in the drawing and the statue is 24

We want the scale factor from drawing to statue

The ratio is 9/24

Divide the top and bottom by 3

3/8

Answer:

100:1

Step-by-step explanation:

To solve this, you must divide the two.

287 / 2.87 = 100

The scale factor of the model is 100:1.

The scale factor between a real building that is 287 feet tall and a model that is 2.87 feet tall is 0.01, or 1:100. This means that each unit on the model corresponds to 100 units on the actual building.

The subject here is regarding scale factor in mathematics. The scale factor is the ratio between the corresponding sides of two similar figures. In this case, the two figures are the actual capital building and its model. To calculate the scale, divide the height of the model by the height of the actual building. So, if an actual building is 287 feet and its model is 2.87 feet, then the scale is given by 2.87 / 287, which is 0.01.

So, the scale of the model to the building is 1:100, because for every one unit on the model, there are 100 units on the actual building. Remember this scale when considering the height and other dimensions of the model or the building.

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Answer:

They would be going at 56 miles per hour.

Step-by-step explanation:

You just take the miles they traveled (1,750) and divide it by the hours it took to get ther (31) the equation qould look like this 1,750 / 31 = 56  

miles per hour is measured by how far you go and how long it takes to get there!

Answer: The answer is 56 miles per hour

Step-by-step explanation:

you divide 1,750 by the time it took which  was 31

you would get 56.4516129032 then you round to the nearest whole number which is 56

i hope this helps- brycefoster

Answer:

Ask away

Step-by-step explanation:

Answer:

Ill do the math

Step-by-step explanation:

Answer:

88 percent because to get to 25*4 is 100 so whatever you do on the bottom you do on the top and you get 88

Step-by-step explanation:

Answer:

0.88

Step-by-step explanation:

this is easy!

divide 22 by 25.

the line between the numbers mean to divide

so you take the top number and put it outside the box then put the bottom on the inside of your box