Solve y=x+5 and 2x-3y=4

Answer:

Step-by-step explanation:

The angles labeled with 2x, 4x, and 3x are on a straight line so their sum is equal to 180

2x + 4x + 3x = 180 add like terms

9x = 180 divide both sides by 9

x = 20

The angle represented with 3x - 30 and the angle represented with 2x + 10 are alternate and their measurement is same

3x - 30 = 2x + 10 export like terms to same side of the equation

3x - 2x = 10 + 30

x = 40

to find the angles replace x with the value found for each.

Answer:

last option, x = -1

Step-by-step explanation:

[tex]x^{2} + 2x + 1 = 0\\x_{1} = \frac{-2 + \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{2} = \frac{-2 - \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{1} = \frac{-2 + \sqrt{0} }{2}\\x_{2} = \frac{-2 - \sqrt{0} }{2}\\x = \frac{-2}{2} \\x = -1[/tex]

The value of x by using the Quadratic Formula is,

⇒ x = - 1

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Equation is,

⇒ x² + 2x + 1

Now, We can use the Quadratic Formula for x as;

⇒ x² + 2x + 1

⇒ x = - 2 ± √2² - 4×1×1 / 2

⇒ x = - 2 ± √4 - 4 / 2

⇒ x = - 2 / 2

⇒ x = - 1

Thus, The value of x by using the Quadratic Formula is,

⇒ x = - 1

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Answer:

The solution set is {-6, -2}.

Step-by-step explanation:

x^2 + 8x + 15 = 3

x^2 + 8x = -12

Completing the square:

(x + 4)^2 - 16 = -12

(x + 4)^2 = 4

Taking square roots of both sides:

x + 4 =  +/- 2

x = 2 - 4 = -2  or x = -2-4 = -6.

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.

First, we determine the length of each side:

[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]

[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]

[tex]RS = \sqrt{13}[/tex]

[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]

[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]

[tex]ST = \sqrt{65}[/tex]

[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]

[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]

[tex]RT = \sqrt{80}[/tex]

Now we calculate the area of the triangle by Heron's formula:

[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]

s ≈ 10.306

[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]

A ≈ 14.525

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

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Answer:

Length: 18 inches

Width: 6 inches

Step-by-step explanation:

l+w=24

l=3w    w=1w

3w+w=24

       w=6

Length: 3*6=18 inches

Width: 6 inches

Answer:

  2973.5 liters

Step-by-step explanation:

You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.

__

The available area is ...

  ($100) / ($10/m²) = 10 m²

The area of a sphere with diameter d is ...

  A = πd²

Then the diameter for the given area is ...

  10 m² = πd²

  (10/π) m² = d² . . . . . divide by π

  √(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere

The volume of a sphere is given by ...

  V = 4/3πr³ = (π/6)d³

For the diameter found above, the volume of the sphere will be ...

  V = (π/6)(1.78412 m)³ ≈ 2.97354 m³

There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...

  2.97354 m³ × (1000 L/m³) = 2973.54 L

The largest amount of water the container can hold is about 2973.5 liters.

Answer:

Step-by-step explanation:

The problem is concerned with angles 4 and 5, which lie between the lines given as parallel. They are on opposite sides of the line cutting across those parallel lines (the transversal), so they are ...

__

Being congruent angles, their measures are ...

_____

Additional comment

For questions like this, there are many descriptions that are true. It would be helpful to know the possible answer choices.

Answer:

[tex]2\sqrt{61\pi }[/tex]

Step-by-step explanation:

Let's find c by using the Pythagorean Theorem: [tex]10^2 + 12^2 = c^2[/tex] so [tex]c = \sqrt{10^2 + 12^2}[/tex]. I'm going to leave c like this so it is easier to multiply by [tex]\sqrt{\pi }[/tex]. [tex]c\sqrt{\pi } = \sqrt{10^2 + 12^2}\sqrt{\pi } = 2\sqrt{61\pi }.[/tex]

Hope this helped! :)

Answer: Correct me if I am wrong, but this is how I think you should solve it.

Step-by-step explanation:

1. Simplify 8×5 to 40.

−2×(40+9)−6×7

2. Simplify 40+9 to 49.

−2×49−6×7

3. Simplify −2×49 to −98.

−98−6×7

4. Simplify 6×7 to 42.

−98−42

5. Simplify

−140

Your all done! Hope this helps.

Answer:

-1 - 4 i

Step-by-step explanation:

5 - (2 * i) - (2 * (3 + i)) =

-1 - 4 i

[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]

Expression 3200(1.06)^t represents the enrollment of a high school t years after 2000 will increase by 6%.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

The given expression is as follows:-

=  3200 ( 1.06 ) [tex],^t[/tex]

Here when the time has increased the percentage is also increased by 6%.

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Answer:

m = 60

Step-by-step explanation:

log is another way to write an exponent.

Example:

exponent form:

7^2 = 49

log form:

log_7 (49) = 2



In your question, we need to change to exponent form, from log form.

log_5 (2m+5)=3

5 is the base. 3 is the exponent.

Now it can be solved.

5^3 = 2m+5

125 = 2m + 5

120 = 2m

60 = m

Answer:

Yes

Step-by-step explanation:

So we know the second child was a boy however if the first child was a boy, the probability of getting a second boy would be 7/17 since one boy is missing and one person is missing from the total.

However, if a girl was chosen as the first child, the probability of getting a boy second would be 8/17 since no boys would be missing but one person would be missing from the original total.

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

Reason:

If the linear scale factor is 5, then the volume scale factor is 5^3 = 125

Meaning we'll multiply the old volume by 125 to get the new volume

new volume = 125*(old volume)

new volume = 125*(24)

new volume = 3000

---------------

A more in-depth look:

Consider a 2 by 2 by 2 block. Its volume is 2*2*2 = 8

Now multiply each dimension by 5, so we now have a 10 by 10 by 10 block. The new larger volume is 10*10*10 = 1000

The volume ratio is 1000/8 = 125, which matches with the value found earlier.

Since we multiplied each piece by 5, and did so three times, we're really multiplying the volume by 5*5*5 = 125.

Answer:

"quotient" indicates division

999 ÷ c = ?

Find Q

Not safe

Apply Pythagorean theorem

PR²=4²+15²=16+225=241

Answer:

a) not safe

b) 15.5 ft (nearest tenth)

Step-by-step explanation:

Tan trig ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula and solving for x:

[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]

[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]

[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]

As 14.9° is not between 18° and 27°, the roof is not safe.

-------------------------------------------------------------------------------------------------

Pythagoras’ Theorem

[tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting the given values into the formula and solving for PR:

[tex]\implies \sf 15^2+4^2=PR^2[/tex]

[tex]\implies \sf 225+16=PR^2[/tex]

[tex]\implies \sf PR^2=241[/tex]

[tex]\implies \sf PR=\sqrt{241}[/tex]

[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

The circular pizza requires the same amount of dough as the square pizza.

Area of the square pizza =40 cm * 40 cm

                                         = 1600 [tex]cm^{2}[/tex].

Area of circle= [tex]\pi\; r^{2}[/tex]

        1600     = 3.14 *[tex]r^{2}[/tex]

         [tex]r^{2}[/tex] = 510

        r= 22.58

       r = 23 cm approx.

Area of circle= [tex]\pi\; r^{2}[/tex]

                     = [tex]3.14 * (23)^{2}[/tex]

                     = 1661.06 squared cm

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

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Answer:

7 things an investor should consider when picking stocks:

Trends in earnings growth.

Company strength relative to its peers.

Debt-to-equity ratio in line with industry norms.

Price-earnings ratio as an indicator of valuation.

How the company treats dividends.Effectiveness of executive leadership.

Step-by-step explanation:

Answer:

2(a+b)

Step-by-step explanation:

Answer:

P(A) = 13/18

P(B) = 7/18

Step-by-step explanation:

A) Sum greater than 5

If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.

There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.

B) Sum divisible by 4 or 6

The sum ranges from 2 to 12, there are two methods to calculate this:

B1) Method 1: Calculate the frequency one by one

The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.

B2) Method 2: Use the rule of not mutually exclusive events

Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.

The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.

P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12

P(A) = (3+5+1) / 36 = 9/36 = 1/4

P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12

P(B) = (5+1) / 36 = 6/36 = 1/6

P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12

P(A) = 1 / 36 = 1/36

Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18

Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.

Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3

Answer:

answer is a

Step-by-step explanation:

u just look at 6 and 6.60 thats 1 and 10 every eraser but for 3 its 1.30

Answer:

The first job pays more

Step-by-step explanation:

950 x 3 = One month pay = 2,850

2,859 x 12 = One year = 34,308 Per Year

Comparing them both

$45,000 One Year, First Job

$34,308 One Year, Second Job

Answer:

The mean is greater than median

Step-by-step explanation:

Option D

Answer:

it should be C I did something very very similar to this but different questions

Answer:

 a) {-6, 2}

 b) -12

 c) minimum: -16

Step-by-step explanation:

I find a graphing calculator to be a big help. Its graph is attached.

a) The function can be factored as:

 f(x) = (x -2)(x +6)

The factors are zero at the x-intercepts: x = 2, x = -6.

b) The y-intercept is the function value when x=0. That is the constant in the function. The y-intercept is -12.

c) The leading coefficient of the function is positive, so its graph opens upward. The extreme value is a minimum. It is found on the axis of symmetry, at the x-value that is halfway between the x-intercepts: x = (2-6)/2 = -2. The function value there is ...

f(-2) = (-2-2)(-2+6) = -4(4) = -16

The minimum is f(-2) = -16.

Answer:

[tex]\frac{93458}{19435}[/tex] ≈ 4.81

Step-by-step explanation:

[tex]\frac{93458}{19435}[/tex] can not be simplified

Answer:

3x +18+4x+15=180

7x+33=180

7x=180-33

7x=147

7x÷7=147÷7

x=21

Answer:

[tex]\boxed{\bf x = {21}^{o} }[/tex]

Step-by-step explanation:

We know that the sum of angles of a linear pair is always equal to 180°, they are also known as supplementary angles.

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