What is the solution to the system of equations?

2x + 4y = 12
y = 1/4x - 3

A. (–1, 8)
B. (8, –1)
C. (5, 1/2)
D. (1/2, 5)

Answer:

Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.

Step-by-step explanation:

Equivalent fractions =  two or more than two fractions are said to be equal if both results the same fraction after simplification.

For example, consider the fraction 1/3

Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6

Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9

Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12

Therefore, we can conclude that,

1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.

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Answer: 2 and 6/8

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

DE/AB = EF/BC = FD/CA

15/45 = 9/27 = 8/24 = 1/3

hope this will help u

Answer:

8

Step-by-step explanation:

let the ratio constant be 'x'

=> 2x:3x

sum = 2x + 3x = 5x

Total number of boys

=>(2x/5x)20 = 8

The ratio of boys and girls in a classroom is 2 : 3 respectively. If the total number of children is 20. How many boys are there in the class ?

In this question we are provided with the ratio of boys isto girls that is 2 : 3 it is also given that total number of children are 20. We are asked to calculate number of boys.

[tex] \green{ \small \pmb{\tt{ First \: we \: will \: form \: an \: equation }}}[/tex]

Let us assume the number of girls as 3x and number of boys as 2x.

Total number of children = 20

3x + 2x = 20

[tex] \orange{\small \pmb{\tt{ Now \: we \: will \: solve \: this \: equation }}}[/tex]

[tex] \small\frak{ 3x + 2x = 20}[/tex]

[tex] \small\frak{ 5x = 20}[/tex]

[tex] \small\frak{ x = \dfrac{20}{5} = 4}[/tex]

[tex] \small \underline{ \boxed{\pmb{x = 4} }} \large \: \star[/tex]

Boys = 2 × 4 = 8

Girls = 3 × 4 = 12

[tex] \tiny \tt{spbankingandsscseries}[/tex]

According to no. of terms it's binomial since it has two terms , according to the power it's cubic function since the power of X is 3

PLEASE GIVE BRAINLIEST

The area of the shaded sector must be 144π units².

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

We know that the angle measurement of central angle QRS is less than π radians.

for r = 18 units

The area of the circle = π18² = 324π  units²

The area of ​​the half of a circle = 324π /2 = 162π units²

The area of ​​a quarter of a circle = 324π /4 = 81π  units²

so

The area of the shaded sector < 162π  units²

and

The area of the shaded sector > 81π  units²

Hence the answer must be 144π units²

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Answer:

DE

Step-by-step explanation:

a tangent is a straight line that only touches the circle at one point.

Answer:

The correct option is k(x) = 5x - (5-x)

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given functions are;

g(x) = 5x                  h(x) = 5 - x

Now,

        k(x) = (g - h)(x)

        k(x) = g(x) - h(x)

        k(x) = 5x - (5 - x)

Thus, the correct option is k(x) = 5x - (5-x).

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Answer:

5.1% (nearest tenth)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for r:

[tex]\implies \sf 2209=2000\left(1+r\right)^{2}[/tex]

[tex]\implies \sf \dfrac{2209}{2000}=(1+r)^2[/tex]

[tex]\implies \sf 1.1045=(1+r)^2[/tex]

[tex]\implies \sf \sqrt{1.1045}=1+r[/tex]

[tex]\implies \sf r = \sqrt{1.1045}-1[/tex]

[tex]\implies \sf r = 0.05095194942...[/tex]

[tex]\implies \sf r = 5.095194942...\%[/tex]

Therefore, the annual interest rate is 5.1% (nearest tenth)

Answer:

-2.5 < x < 71

Step-by-step explanation:

I don't see a 'z' here, so I'll use x from the picture.

You would line up your values as such:

0 < 2x+5 < 71

You have a zero at the beginning because even without having an x value, your outcome would still be 5.

Subtract 5 from all sides.

-5 < 2x < 66

You now divide by two on both sides.

-2.5 < x < 33.

Which is your final answer.

You cannot go over 33, since 71 is your largest angle, and having something like say, 34, would give you 73.

-2.5 is your lowest value since if you went lower, you would have a negative angle, which isn't possible.

The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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It should be noted that the volume of the pyramid will be 14.8 unit³.

From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².

The height of the pyramid is also 6 units.

Therefore, the volume of the pyramid will be

= 1/3 × Area of the base × height

= 1/3 × 7.4 × 6

= 14.8 units³

In conclusion, the volume of the pyramid is 14.8 unit³.

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The probability that exactly 5 out of the first 10 customers buy a magazine is 0.00126.

Given suspicion of 9.7% that buy a magazine is correct.

We have to find the probability that exactly 5 out of the first 10 customers buy a magazine. Probability is the chance of happening an event among all the events possible.

The binomial distribution is the probability of exactly x successes on n repeated trials and X can only have two outcomes.

[tex]P(X=x)=C_{n,x}p^{x} (1-p)^{n-x}[/tex]

In which [tex]C_{n,x}=n!/x!(n-x)![/tex]

And P is the probability of happening of X.

In the question 9.7% of his customers buy a magazine.

So the value of P=0.097

This can be calculated by :

P(X=5) when n=13

[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]

[tex]P(X=5)=C_{10,5} (0.097)^{5} (1-0.097)^{10-5}[/tex]

=[tex]P(X=5)=C_{10,5} (0.097)^{5} (0.903)^{5}[/tex]

[tex]=10!/5!5!*0.0000085*0.600397[/tex]

=252*0.00000510

=0.001286

Hence the probability that exactly 5 out of the first 10 customers buy a magazine is 0.001286.

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When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. The correct option is A.

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. Investors buy stocks in firms they believe will increase in value. If this occurs, the value of the company's shares rises as well.

For a 70-year-old investor, selling a weak stock at a loss may be a smart move to avoid potential additional future losses.

Hence, the correct option is A.

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Answer:

-282

Step-by-step explanation:

Any altitude below sea level would have a negative sign in front of it.

Answer:

2

Step-by-step explanation:

[tex]a+b=-5[/tex]

[tex]-(a+b)=-a-b=5[/tex]

[tex]\frac{|-5| + 5}{|5|}[/tex]

[tex]\frac{5+5}{5}[/tex]

[tex]2[/tex]

Answer:

2

Step-by-step explanation:

Given:

To find -a - b  

Factor out the common term -1:

⇒ -a - b = -(a + b)

Substitute a + b = -5:

⇒ -a - b = -(-5)

Apply rule -(-x) = x:

⇒ -a - b = 5

Therefore:

[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]

Note:  |-x| = x

[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]

Answer:

Step-by-step explanation:

Just took the test:

6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=

2sqrt15/5 cis (5pie/6)

answer: t=2

steps:

16-2t = 3/2t+9

7 = 3/2t + 2t

2 is 4/2

7 = 3/2t + 4/2t

7 = 7/2t

7/2t = 7

(2/7)7/2t=7(2/7)

t=7(2/7)

t=2

Answer:

Step-by-step explanation:

there is no root in denominator so I think it is rationalised

Graph C represents the following system of inequalities. For clarification refer to the attachment.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

Given relations;

x < - 2x + 4

y < x + 3

x < 3

Hence graph C represents the following system of inequalities.

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Answer:

x is 48 and y is 100

Step-by-step explanation:

Angle y = 100 degree

Angle x = 48 degree

Answer:

The sum of the polynomials is a 7th degree polynomial.

The difference of the polynomials is a 7th degree polynomial.

Step-by-step explanation:

Janie's polynomial is a 3rd degree with only x terms. Maybe she wrote:

f(x) = x^3

or maybe she was fancy and wrote:

f(x) =

x^3 + 2x^2 - 7x + 4

could be anything really, but the biggest exponent is 3.

Then Max does like:

g(x) = x^7

or

g(x) = x^7-x^4-3x+2

Whatever he made up, but the biggest exponent is 7.

So if they add or subtract their two polynomials, there's no x^7 in Janie's to add with the x^7 in Max's. MAYBE Max put some x^3 or x^2 or x or constants that might combine with the terms in Janie's.

Either way, anything that Max put in his polynomial that is a bigger power than 3 (4th, 5th, 6th, or 7th power) is just going to end up in the sum or difference.

Answer:

D. 115

Step-by-step explanation:

because if Angle 6 is 115 then so is Angle is 4 due to AIA (alternate Interior Angles)

Answer:

-3

Step-by-step explanation:

The points (3,-4) and (1,2) lie on the line.

m = (-4-2)/(3-1) = -3

Answer:

-1/5

Step-by-step explanation:

What are parallel lines?

Lines that are parallel never touch. They can extend infinitely and they will still never touch. In order for this to happen the slope of the two lines must be the same. So if we want to find the slope of every line that is parallel to the line on the graph, we simply find the slope of the line of the graph.

Finding the slope

We can find the slope using the following formula:

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

Where the x and y values are derived from any given points on the line (x1,y1) and (x2,y2)

Here the given points are (-5,-1) and (0,-2)

So we have (x1,y1) = (-5,-1) meaning x1 = -5 and y1 = -1

We also have (x2,y2) = (0,-2) meaning x2 = 0 and y2 = -2

Now we plug these values into the formula

Recall formula : [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

==> Plug in x1 = -5 , y1 = -1 , x2 = 0 and y2 = -2

[tex]Slope=\frac{-2-(-1)}{0-5}[/tex]

==> simplify numerator and denominator

[tex]slope = \frac{1}{-5}[/tex]

So the slope of the line is -1/5

This means the slope of any parallel line to that line would also have a slope of -1/5

Answer:

B.

Step-by-step explanation:

if x is 3 then you just substitue every instance of x as 3. 2(x-4) + 3x - x^2 =

2(3 - 4) + 3(3) - 3^2 =

6-8 + 9 - 9 =

-2

Answer:

6x^2 + 17x + 5

Step-by-step explanation:

(2x + 5)(3x + 1)

= 6x^2 + 2x + 15x + 5

= 6x^2 + 17x + 5

The expression (2x+5)(3x+1) is a product of two binomials. To expand this product, we multiply each term in the first binomial by each term in the second binomial, using the distributive property of multiplication.

When we multiply 2x by 3x, we get 6x^2.

Then we multiply 2x by 1, which gives us 2x.

Next, we multiply 5 by 3x, which gives us 15x.

Finally, we multiply 5 by 1, which gives us 5.

Putting these terms together gives us the expanded form of the expression:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying, we can add the 2x and 15x terms to get 17x, giving us the final simplified expression:

(2x+5)(3x+1) = 6x^2 + 17x + 5.

Answer:

putting the values of coordinates in equation to check for the solution.

For A

2x + y < 10

2(-5) + 4 < 10.

-10 - 4 < 10

-14 < 10 ( true)

2x - 4y > 8

2(-5) - 4(4) > 8

-10 - 16 > 8

-26 > 8

false..

it is not the solution of the equation.

similarly we can find for other coordinates.

E is the solution

Answer:

the answer is d........