Solve each system by graphing. Y=x-4 and y=-x

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A:

16a^2-24a+9

16a^2-12a-12a+9

4a(4a-3)-3(4a-3)

(4a-3)(4a-3)

(4a-3)^2

(4a-3)^2

B: Use difference of squares method

(3a+5b)(3a−5b)

Part A: The length of each side of the square is (4a - 3) units.

Part B: The dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).

Part A:

The area of a square is given by the formula A = s^2, where "s" is the length of each side of the square. In this case, the area is (16a² - 24a + 9) square units.

To determine the length of each side of the square, we need to factor the area expression completely and set it equal to (s^2).

The area expression is a quadratic trinomial: 16a² - 24a + 9.

To factor the trinomial, we look for two binomials that, when multiplied together, give us the original trinomial. The binomials will have the form: (ma ± b)(na ± c).

To factor 16a² - 24a + 9, we look for two numbers whose product is 16 * 9 = 144, and whose sum is -24 (the middle coefficient).

The two numbers are -12 and -12 because (-12) * (-12) = 144 and (-12) + (-12) = -24.

Now, rewrite the middle term (-24a) using -12a - 12a:

16a² - 12a - 12a + 9

Group the terms and factor by grouping:

(16a² - 12a) - (12a - 9)

Now, factor out the greatest common factor (GCF) from each group:

4a(4a - 3) - 3(4a - 3)

Now, notice that we have a common binomial factor of (4a - 3):

(4a - 3)(4a - 3)

Since both binomials are the same, we can rewrite it as (4a - 3)^2.

Now, set (4a - 3)^2 equal to (s^2):

(4a - 3)^2 = s^2

To find the length of each side (s), take the square root of both sides:

√((4a - 3)^2) = √(s^2)

4a - 3 = s

Therefore, the length of each side of the square is (4a - 3) units.

Part B:

The area of a rectangle is given by the formula A = length * width. In this case, the area is (9a² - 25b²) square units.

To determine the dimensions of the rectangle, we need to factor the area expression completely and identify the length and width.

The area expression is a difference of squares: 9a² - 25b².

To factor a difference of squares, we use the formula: a² - b² = (a + b)(a - b).

In this case, a = 3a and b = 5b:

9a² - 25b² = (3a + 5b)(3a - 5b)

Therefore, the dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).

To know more about  square:

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Answer:

50 seconds

Step-by-step explanation:

because 5÷0.1=50 50×1sec=50 seconds

Answer:

Formula for volume of hemisphere;

V = 2/3 * π * [tex]r^{3}[/tex]

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * [tex]r^{3}[/tex]

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.

q = 12.5

hope it helps..!!!

Answer:

12.5

Step-by-step explanation:

u dont need it lol

[tex]2.5x = 15[/tex]

[tex]x = \frac{15}{2.5} = 6[/tex]

Answer:

or Also

[tex] \frac{5}{2} x = 15 \\ 5x = 15 \times 2 \\ 5x = 30 \\ 5x \div 5 = 30 \div 5 \\ x = 6[/tex]

Step-by-step explanation:

2 m corresponds to 0.4 cm on a blueprint.

so,

2 m / 0.4 cm = 200 cm / 0.4 cm

our fun the point of view of the blueprint

0.4 cm / 200 cm

the scale on a map or blueprint is usually normed to one unit on the blueprint :

0.4/200 × f/f = 1/(200×f)

0.4 × f = 1

f = 1/0.4 = 2.5

so, our scale is

(0.4 × 2.5) / (200 × 2.5) = 1 / 500

that means 1 cm on the blueprint corresponds to 500 cm or 5 m in reality.

The function p(t) for the number of visitors over 1-year is an exponential function

The function is given as:

p(t) = 119 + (t-83)e^0.02t

Start by plotting the graph of the function p(t).

From the graph (see attachment), we have the parameters to be:

Hence, the function has no critical point

Read mroe about critical points at:

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Answer:

ok so 5/10ths is also 3/6ths or 2/4ths or 1/2

Step-by-step explanation:

Answer:

0864

Step-by-step explanation:

The answer is 0864.

Hope it helps!

Study well!

Answer:

Step-by-step explanation:

The volume of a sphere can be found using the formula ...

  V = 4/3πr³ . . . . . where r is the radius

__

The figure points to a diameter line and indicates 2.2 m. The arrowhead is in the middle of a radius line, making it easy to interpret the dimension as the radius of the sphere.

If 2.2 m is used as the radius, the volume is computed to be ...

  V = 4/3π(2.2 m)³ ≈ 44.58 m³

This agrees with your friend's volume, suggesting the diameter was used in place of the radius in the computation.

__

The correct volume, using 2.2 m as the diameter, is ...

  V = 4/3π(1.1 m)³ ≈ 5.57 m³

The major axis, which is horizontal, is of the length [tex]2\sqrt{7.29} = 5.4[/tex] ft, the miror axis, which is vertical, is of the length [tex]2\sqrt{6.25} = 5[/tex] ft.

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:

[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1[/tex]

For the considered case, the equation of the considered ellipse is:

[tex]\dfrac{x^2}{(\sqrt{7.29})^2} + \dfrac{y^2}{(\sqrt{5.4})^2} =1[/tex]

Thus, the major axis, which is horizontal, is of the length [tex]2\sqrt{7.29} = 5.4[/tex] ft,

the miror axis, which is vertical, is of the length [tex]2\sqrt{6.25} = 5[/tex] ft.

Learn more about ellipse here:

https://brainly.com/question/19910594

Answer:

The mirror has a vertical orientation and is 5.4 ft tall.

Step-by-step explanation:

Got it right. The major axis is vertical (the ellipse has a vertical orientation) because the y^2 term comes first. It is 5.4 ft tall because if you take the square root of the number under the y^2 term (square root of 7.29), it is equal to 2.7. This is only the distance from the center to one vertex on the major axis, and so twice 2.7 is 5.4, and the mirror is 5.4 ft tall.

Also I know I am weeks late, but maybe this will help others at some point. Sorry I didn't get here in time!

Answer:

Step-by-step explanation:

I'll work on the left triangle first:

tan 20 = x /10

x = 10tan 20 = 3.64

cos 20 = 10/y

y = 10/cos20 = 10.64.

tan 70 = 12/x

x = 12/tan 70 = 4.37.

sin 70 = 12/y

y =  12/sin70 = 12.77.

Answers:

AREA OF A CIRCLE = pi x r^2

5m circle:

when it says 5 i think it means diameter so divide by 2 for radius

5/2 = 2.5

3.14 x 2.5^2=

3.14 x 6.25=

19.625m^2

50mm circle:

50/2= 25

3.14 x 25^2=

3.14 x 625=

1962.5mm^2

40in circle:

40/2= 20

3.14 x 20^2 =

3.14 x 400=

1256in^2

7ft circle:

7/2= 3.5

3.14 x 3.5^2=

3.14 x 12.25=

38.465ft^2

21mm circle:

21/2= 10.5

3.14 x 10.5^2=

3.14 x 110.25=

346.185mm^2

70cm circle:

70/2=35

3.14 x 35^2=

314 x 1225=

3846.5cm^2

Hope that helps :)

Answer:

a) exponential growth   b) 8000  c) 1.02  d) f(x) = 8000(1+.05/4)^(4)(5)   e)  $11887.58

Step-by-step explanation:

This situation is exponential growth because the money will be increasing over time.  The initial amount is the amount invested in the beginning so in this case 8000.  The growth factor is found by 1+r/n where r is the rate and n is the number of compounds per year so 1 + .08/4 where the r is expressed as a decimal and compounding quarterly means 4 times per year.  The function is modeled by f(x) = P(1 +r/n)^nt.  Evaluating the function gives f(x) = 8000(1 + .08/4)^(4*5).

Answer:

1. -39/50

2. -0.77777

3. square root of 92

4. 9.73

[tex] = (3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

3/6 ⇒ 9/12⇒ 15/18

Step-by-step explanation:

To put the following lists 3/6,9/12, 15/18 in order from least to greatest we can turn the fraction into decimal..

3/6 = 0.5

15/18 = 0.83333333333

9/12= 0.75

Hence from least to greatest:

0.5,0.75, 0.83333333333

Also know as:

3/6,9/12,15/18

~lenvy~

Answer:

Order 3/6, 9/12, and 15/18 from least to greatest.

First, we must simplify these fractions as much as possible then find a possible common denominator.

3/6 simplifies to 1/2

9/12 simplifies to 3/4

15/18 simplifies to 5/6

Now we have fractions of 1/2(3/6), 3/4(9/12), and 5/6(15/18).

If we look at these fractions, we can see that they have a common denominator of 12. So let's convert these fractions into having a denominator of 12;

1/2 x 6/6 = 6/12

3/4 x 3/3 = 9/12

5/6 x 2/2 = 10/12.

So now we have the fractions 6/12(3/6), 9/12(9/12), and 10/12(5/6).

These are already ordered from least to greatest.

So therefore, this'll be ordered;

3/6, 9/12, and 15/18.

Answer:

TRUE

Step-by-step explanation:

Answer:

(b1+b2)h divided by 2 is the formula for a trapezoid

Step-by-step explanation:

ANSWER: 468 ft (squared?)

Answer:

sin M = [tex]\frac{12}{13}[/tex], tan M = [tex]\frac{12}{5}[/tex], cos M = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of an angle is equal to [tex]\frac{opposite}{hypotenuse}[/tex].  The opposite (opposite from the angle) side is 12 and the hypotenuse is 13.

The tangent of an angle is equal to [tex]\frac{opposite}{adjacent}[/tex].  The opposite side is 12 and the adjacent (next to the angle) side is 5.

The cosine of an angle is equal to [tex]\frac{adjacent}{hypotenuse}[/tex].  The adjacent (next to the angle) side is 5 and the hypotenuse is 13.

Let the number to be added be A

Now,

[tex]\begin{gathered}\implies\quad \sf −5x^3 + 4x − 3 + A = x^2 − x − 1 \\\end{gathered} [/tex]

Transposing (−5x³+ 4x − 3 ) to other side-

[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 -( −5x^3 + 4x − 3) \\\end{gathered} [/tex]

Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket

[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 + 5x^3 - 4x + 3\\\end{gathered} [/tex]

Putting like terms together -

[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 - x -4x +3 -1 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 -5x +2 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

⇒ 5w + 3g = 109.9

Given:

⇒ w + 4g = 75.7

Rewrite  w + 4g = 75.7  to make w the subject:

⇒ w = 75.7 - 4g

Substitute into  5w + 3g = 109.9  and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

Step-by-step answer:

If there are 40% students that are girls , and the rest are 250 boys. Then that must mean there are 60% boys. Because that is the compliment.

i)

Because we know that 60% of the people in the group are boys, and that the amount of boys amounts to 250, we can model an equation like this.

[tex]Total * 0.6 = 250[/tex].

[tex]Total = 250/0.6[/tex]

[tex]Total = 417[/tex]

There are 417 students

ii)

Because we know that the total amount is 417, we can find the amount of girls there are by multiplying the total by the percentage.

[tex]417 * 0.4 = 167[/tex]

There are 167 students that are girls.

Answer:

m= 15

Step-by-step explanation:

[tex] \frac{m}{9} + \frac{2}{3} = \frac{7}{3} [/tex]

To solve for m, start by moving the constants (numbers that are not attached to any variable) to the other side of the equation.

[tex] \frac{m}{9} = \frac{7}{3} - \frac{2}{3} [/tex]

Simplify:

[tex] \frac{m}{9} = \frac{5}{3} [/tex]

Multiply both sides by 9:

[tex]m = \frac{5}{3} \times 9[/tex]

Crossing out 3 from the denominator and from 9:

m= 5(3)

m= 15

Answer:

P=141,300(1+0.05)^6

Step-by-step explanation:

r = rate = 5/100 = 0.05

a = starting amount = 141,300

t = time = 6 years

% growth formula:

a(1+r)^t

141,300(1.05)^6

Answer:

P=141,300(1+0.05)^6

Step-by-step explanation:

r = rate = 5/100 = 0.05

a = starting amount = 141,300

t = time = 6 years

% growth formula:

a(1+r)^t

141,300(1.05)^6

Answer:

Here!!

Step-by-step explanation:

Here are a few ratios that are equivalent to  4 : 11  . . . . .

8 : 22

12 : 33

20 : 55

400 : 1100

308 : 847

4 billion : 11 billion

Answer:

∠ SOU = 138°

Step-by-step explanation:

the opposite angles of a tangent kite are supplementary, sum to 180° , so

∠ SOU + ∠ STU = 180° , that is

∠ SOU + 42° = 180° ( subtract 42° from both sides )

∠ SOU = 138°