A system of equations is shown on the graph below.


On a coordinate plane, 2 lines intersect at (negative 1, 2).

How many solutions does this system have?

Answer:150?

Step-by-step explanation:

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

Answer:

7/2x

Step-by-step explanation:

Well first we need to put,

2x + 7y = 5,

into slope intercept

-2x

7y = -2x + 5

Divide y to all numbers

y = -2/7x + 5/7

So the slope for the given line is -2/7,

the slope of the line that is perpendicular to it is its reciprocal.

Meaning the slope of the perpendicular line is 7/2.

Thus,

the slope of the perpendicular line is 7/2x.

Hope this helps :)

Answer:

The slope of the perpendicular line is 7/2

Step-by-step explanation:

2x+7y=5

Solve for y to find the slope

2x-2x+7y=5-2x

7y = -2x+5

Divide by 7

7y/7 = -2/7 x +5/7

y = -2/7x + 5/7

The slope is -2/7

The slope of perpendicular lines multiply to -1

m * -2/7 = -1

Multiply each side by -7/2

m * -2/7 *-7/2 = -1 * -7/2

m = 7/2

The slope of the perpendicular line is 7/2

The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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Answer:

7 in by 6 in

Step-by-step explanation:

divide 28 and 24 by 4

Answer: A

because slope are

Answer: The value of \((g - f)(x)=4 .\)

Step-by-step explanation:

Given functions :  \(f(x) = x + 4\) and \(g(x) = x + 7\)

To find : \((g - f)(x)\)

Difference between two functions: \((u-v)(x)=u(x)-v(x)\)

Then, \((g-f)(x)=g(x)-f(x)\)

\(=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3\)

Hence, the value of \((g - f)(x)=4 .\)

Answer:

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

So the answer is f(x) = 2x2

Thank you and please rate me as brainliest as it will help me

The function f(x) = 2x² is the quadratic function while the other functions are not the quadratic function. The first option is the correct one.

A quadratic function is a polynomial with degree 4.

f(x) = 2x² is a quadratic function as the degree of the function is 2.

g(x) = 5x³ is a cubic function as the degree of the function is 3.

k(x) = -x is a linear function as the degree of the function is 1.

\(b(x) = -9x^4\) is a quartic function as the degree of the function is 4.

So, among all options, f(x) = 2x² is the quadratic function. The correct option is the first one.

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Answer:

51

Step-by-step explanation:

if there isn't such an answer tell me so that I can try again.goodbye

Answer:

6/24.

Step-by-step explanation:

24 = 4 * 6 so we:

multiply by 6/6:

1 * 6

------  =    6 / 24.

4 * 6

Answer:

b

Step-by-step explanation:

10x6=60

<3

Answer:

The answer is B.

Answer:

question unclear

Step-by-step explanation:

Clock strikes once at 1 twice at 2, thrice at 3 and so on. But it only strikes 12 times at most. And then it repeats. So,

No. Of times clock strikes = 2 x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)

= 2 x 78

No. Of times clock strikes = 156 times

Therefore, the answer is 156 times.

1. The probability that the point is on the triangle is 2/15

2. The probability that the point is in the circle is 1/15

3. The probability that the point is in the circle or triangle is 3/15

4. The probability that the point is not triangle is 13/15

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it is equivalent to 100% in percentage.

Probability = sample space / Total outcome

sample space is the area of the shapes

Area of triangle = 1/2 bh

= 1/2 × 3 × 4

= 3 × 2 = 6cm²

area of circle = πr²

= 3.14 × 1² = 3.14

= 3( to whole number)

Total outcome is the area of rectangle

= l× w = 9 × 5 = 45 cm²

1. The probability that the point is on the triangle is 6/45 = 2/15

2. The probability that the point is in the circle is

= 3/45 = 1/15

3. The probability that the point is in the circle or triangle = 1/15 +2/15 = 3/15 = 1/5

4. The probability that the point is not triangle is

= 1-2/15 = 13/15

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Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.

The exact value of sin(pi/3) can be determined using trigonometric properties and identities.

First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.

To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.

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The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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Answer:

B and D represent a proportioonal relationship.

Step-by-step explanation:

In order for an equation to be proportional, it must be in the form of y = kx.

Answer:

51ft^2

Step-by-step explanation:

Given data

Side of square patio= 9ft

Area= 9*9= 81 ft^2

New length = 9+3= 12ft

New Widht = 9+2= 11ft

New Area= 12*11

New Area= 132ft^2

Hence the area added is

=132-81

=51ft^2

The 51 square feet area will be added to the patio if the length is increased by 3 feet and the width is by increased  2 feet, Option fourth is correct.

It is given that steve has a square patio with a side length of 9 feet he plans to enlarge it to a rectangular patio by increasing the length by 3 feet and the width by 2 feet.

It is required to find how many square feet in the area will be added.

In mathematics, the area is the space occupied by the 2-dimensional figure or surface.

We know the formula for finding the area of square 'A'

\(\rm A= a^{2}\)  where a is the length of the side.

We have a = 9 feet

\(\rm A= 9^2\\\rm A= 81 \ Feet^2\)

Increasing the length by 3 feet and the width by 2 feet respectively, wet get:

L =  9+3  ⇒ 12 Feet

W = 9+2 ⇒ 11 Feet, Where L is the length and W is the width of the rectangle.

Area of rectangle = L×W

Area of rectangle = 12×11

Area of rectangle = 132 \(\rm Feet^2\)

The area which will be added = (Area of rectangle) - (area of square)

The area which will be added = (132) - (81)

The area which will be added = 51 \(\rm Feet^2\)

Thus, the 51 square feet area will be added to the patio.

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Answer:

0.35

Step-by-step explanation

6 ) 2.1 (  0.35   <------- Quotient.

     18  

       30

       30

        ...

9514 1404 393

Answer:

  19. wrong multiplier was used, and used incorrectly; x = -324

  20. wrong multiplier was used, and used incorrectly; y = 5

Step-by-step explanation:

In each case, the equation was multiplied by the coefficient of the variable, instead of divided. In each case, the square of the coefficient was evaluated incorrectly (so the error wasn't noticed).

__

19) As described above.

  (-36)(9) = (x/9)(9)

  -324 = x

__

20) In addition to the errors described above, the variable was changed from y to x.

  15/3 = (3y)/3

  5 = y

Step-by-step explanation:

100% = $27.50

1% = 100%/100 = $27.50/100 = $0.275

the extra amount paid (for the tip) was

$32.45 - $27.50 = $4.95

to know how many percent that is, we need to see how often 1% fits into that amount.

so,

4.95 / 0.275 = 18

therefore the tip was 18%.

FYI - in real life the tip percentage (and corresponding amount) is calculated based on the net bill (the amount before sales tax).

Given:

Angle IHG formed by two rays.

To find:

The rays that form the sides of ∠IHG.

Solution:

From the given diagram it is clear that the initial point of both rays is point H.

First ray passes through the point I with initial point H, so the name of first ray is \(\overrightarrow{HI}\).

Second ray passes through the point G with initial point H, so the name of second ray is \(\overrightarrow{HG}\).

The rays \(\overrightarrow{HI}\) and \(\overrightarrow{HG}\) form the sides of ∠IHG.

Therefore, the correct options are E and F.

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

\(P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)\)

And we can find the probability with the complement rule and the normal standard distirbution and we got:

\(P(z>0.6875)=1-P(z<0.6875)= 1-0.7541= 0.2459\)

Step-by-step explanation:

Let X the random variable that represent the time spent reading of a population, and for this case we know the distribution for X is given by:

\(X \sim N(49,16)\)  

Where \(\mu=49\) and \(\sigma=16\)

We are interested on this probability

\(P(X>60)\)

And we can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we got:

\(P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)\)

And we can find the probability with the complement rule and the normal standard distirbution and we got:

\(P(z>0.6875)=1-P(z<0.6875)= 1-0.7541= 0.2459\)

Answer:

s=-2

Step-by-step explanation:

Answer:

-2/3 or -0.666667

Step-by-step explanation:

first distribute- 2s+4=4s+8

than combine factors- -4=6s

divide by 6-   s= -4/6

simplify to -2/3

if you need the decimal it is- -0.66666 repeating

Answer:

72x^7+24x^3  (finding the derivative using the chain and power rules)

Step-by-step explanation:

Answer:

the answer is 8

Step-by-step explanation: