.
Solve the system using elimination.
x-3y = -9
- x + 5y = 17
PRESENTER
THE
The solution is
(Simplify your answer. Type an ordered pair.)
help plz it’s systems of equations

Answer:

3/10 or 30%

Step-by-step explanation:

it is the number of pop songs in the list divided by all of the songs combined.

so 15 pop songs

over

12+13+10+15=50

15/50 is you answer

simplify and get

3/10

Answer:

383 children and 361 adults

Step-by-step explanation:

Let's say there are a adults and c children. Since the total number of people was 744, we can write:

a + c = 744

We also know that children's prices are $1.75 per child and adults' prices are $2 per adult. Since the total is $1392.25, we can write:

1.75c + 2a = 1392.25

Now we have a system of linear equations:

a + c = 744

1.75c + 2a = 1392.25

Multiply the first equation by 2:

2 * (a + c = 744)  ⇒  2a + 2c = 1488

Now subtract the second equation from this one:

    2a + 2c = 1488

-    2a + 1.75c = 1392.25

___________________

    0a + 0.25c = 95.75

c = 383

Plug this in to find a:

a + c = 744

a + 383 = 744

a = 361

There were 383 children and 361 adults.

Lets use some variables:

x = number of adults

y = number of children

744 total people used the public swimming pool and the number adults and children are unknown, so, we can write an equation like:

x + y = 744

Since $2 are for adults, we can write that as 2x. Since $1.75 are for children, we can write that as 1.75y. Since the total price is $1,392.25, that's what the equation should equal. Equation:

2x + 1.75y = 1,392.25

Now, we have a system of equations.

~Rationalize equations

x + y = 744, 2x + 7/4y = 5569/4

~Isolate x for [ x + y = 744 ]

x + y - y = 744 - y

x = 744 - y

~Substitute with x

2(744 - y) + 7/4y = 5569/4

~Isolate y for [ 2(744 - y) + 7/4y = 5569/4 ]

2(744 - y) * 4 + 7/4y * 4 = 5569/4 * 4

8(744 - y) + 7y = 5569

5952 - 8y + 7y = 5569

5952 - y = 5569

5952 - 5952 - y = 5569 - 5952

-y = -383

-y/-1 = -383/-1

y = 383

~Substitute y with 383 in [ x = 744 - y ]

x = 744 - 383

x = 361

Therefore, there are 361 adults and 383 children.

Best of Luck!

The area of a sector with a radius of 5 inches and a 180-degree arc is half the area of the full circle, resulting in 39.27 square inches when rounded.

The area of a sector of a circle with radius 5 inches that is bounded by a 180-degree arc can be found by first calculating the area of the entire circle and then taking half of that area, since 180 degrees is half of the full 360 degrees of a circle. The formula to calculate the area of a circle is A = πr². For a radius (r) of 5 inches, the entire circle's area would be A = π(5 inches)².

Thus, the entire circle area is A = 3.1415927 × (5 inches)² = 78.53981633974483 square inches. Since the sector is half of the circle, the area of the sector would be 39.269908169872415 square inches, or when rounded to two decimal places, 39.27 square inches.

Answer:

144 ft^2

Step-by-step explanation:

6 inches to feet (comparison based on scale) would make each side 12 feet long (6x2). 12 times 12 is 144.

Answer:

144

Step-by-step explanation:

Final answer:

Perpendicular lines on a coordinate plane intersect to form right angles, which are precisely 90°. The slopes of perpendicular lines are negative reciprocals of each other.

Explanation:

When two lines on a coordinate plane are described as being perpendicular, this means they intersect to form right angles, which are angles of 90°. It's important to recognize that perpendicular lines have slopes that are negative reciprocals of each other. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2. These slopes ensure that the angles formed between the lines are exactly 90 degrees.

In geometry and physics, this concept is further explored with orthogonal vectors, which are two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors. Their importance lies in various applications, such as breaking down a force into components acting along perpendicular axes.

Answer:

i believe it is 185 feet

Answer:

a cross section is the intersection of a solid and a plane.

Step-by-step explanation:

The correlation show in the scatter plot There is no positive or negative correlation

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

Given:

The positive linear correlation shows a line which is Diagonally rising.

and, The negative linear correlation shows a line which is Diagonally falling.

So, the graph we have no Correlation because it does not any falling and rising line.

Learn more about Correlation here:

https://brainly.com/question/28898177

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Answer:

On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

A function [tex]f^{-1}[/tex] is the inverse of f if whenever y =f(x) and [tex]x =f^{-1}[/tex]

To find the  inverse of f(x) = [tex]x^{3}[/tex] - 5, we use the following steps:

y = [tex]x^{3}[/tex] - 5

<=> [tex]x^{3}[/tex]  = y + 5

<=> x = [tex]\sqrt[3]{y+ 5}[/tex]

[tex]f^{-1}(y) =\sqrt[3]{y+5}[/tex]

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

Let Calculate 3 points on f(x)

x = 0 => y = -5

x = 1  => y = -4

x = 2 => y = 3

Let Calculate 3 points on [tex]f^{-1}[/tex] (x)

x = -5 => y = 0

x = -4  => y = 1

x = 3 => y = 2

Yes, the inverse is correct because:

Answer:

  20°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  ∠C = 180° -∠E = 180° -160°

  m∠BCD = 20°

Answer:

Step-by-step explanation:

Heaat

Answer:

I = 94.2 ft

Step-by-step explanation:

The formula for circumference is

[tex]2\pi r[/tex]

if the radius is 15 all you need to do is plug it in and solve

[tex]2\pi 15[/tex]

multiply 2 and 15

30

multiply 30 and pi

94.2

add units and you're done

(if you use the symbol for pi in the calculator it gives you 94.25 but it said to use 3.14 for pi. If you use the symbol pi it's way more than just 3.14)

Known :

Perimeter = 160 ft

length = 50 ft

Asked :

Area = ...?

Answer :

Find the width first :

Perimeter = 2 (length + width)

160 = 2 (50 + width)

width = (160 ÷ 2) - 50

width = 80 - 50

width = 30 ft

Now, let's find the Area :

Area = length × width

= 50 × 30

= 1.500 ft²

So, the area of the playground is 1.500 ft²

Hope it helpful and useful :)

Answer:2 in.

Step-by-step explanation:

Given

Dimension of photo frame is [tex]20\ in.\times 24\ in.[/tex]

If the photo cover an area of [tex]320\ in.^2[/tex]

Suppose x be the width of border

Therefore dimension of frame without border is

[tex]A'=(20-2x)(24-2x)[/tex]

And [tex]A'[/tex] must be equal to [tex]320\ in.^2[/tex]

So,

[tex]\Rightarrow (20-2x)(24-2x)=320[/tex]

[tex]\Rightarrow (10-x)(12-x)=80[/tex]

[tex]\Rightarrow 120-10x-12x+x^2=80[/tex]

[tex]\Rightarrow x^2-22x+40=0[/tex]

[tex]\Rightarrow x^2-20x-2x+40=0[/tex]

[tex]\Rightarrow (x-2)(x-20)=0[/tex]

Thus there are two values of x out of which [tex]x=20\ in.[/tex] is not valid because it is not feasible

thus width of border is [tex]x=2\ in.[/tex]

The gross margin percentage after packaging costs would be a) 30%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Danielle had planned her gift basket to be priced at $50 with a 40% gross margin.

let, The original price be 'x'.

Therefore, $50 is 140% of 'x' which is,

(140/100)×x = 50.

1.4x = 50.

x = 50/1.4.

x = 35.71.

Now, The packaging cost is $3 which makes the cost of the product 38.71.

So, (50/38.71)×100.

= 29% gross margin.

learn more about percentages here :

https://brainly.com/question/24159063

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Answer:

(a)x=100

(b)Maximum Height, h=53 Units

(c)x=200 Units

Step-by-step explanation:

Given the equation which describes the path of the baseball

[tex]h = -0.005x^2 + x + 3[/tex]

(a)Equation of the axis of symmetry

For a quadratic function of the form [tex]y=ax^2+bx+c[/tex], its equation of the axis of symmetry is determined by the equation:

[tex]x=-\dfrac{b}{2a}[/tex]

In the function given: a=–0.005, b=1

Therefore:

[tex]x=-\dfrac{1}{2*-0.005}=\dfrac{1}{0.01}\\\\x=100[/tex]

Equation of the axis of symmetry, x=100

(b)Maximum height reached by the baseball

The maximum height reached by the baseball occurs at the line of symmetry.

Therefore, when x=100

Maximum Height, [tex]h = -0.005(100)^2 + 100 + 3[/tex]

=53 Units

(c)When the height =3 feet, we want to determine the value of x.

[tex]h = -0.005x^2 + x + 3\\3 = -0.005x^2 + x + 3\\-0.005x^2 + x=0\\x(-0.005x + 1)=0\\-0.005x + 1=0\\-0.005x =-1\\$Divide both sides by -0.005\\x=200 Units[/tex]

Final answer:

The equation of the axis of symmetry is x = -100, the maximum height reached by the baseball is 103 feet, and to find the specific distance traveled when caught at 3 feet would require solving the quadratic equation given.

Explanation:

The equation h = –[tex]0.005x^2[/tex]+ x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.

a. What is the equation of the axis of symmetry?

The equation of the axis of symmetry for a quadratic equation in the form of [tex]ax^2 + bx + c[/tex] is given by x = –b/2a. Hence, for our equation, the axis of symmetry is x = –(1)/(2×–0.005) = –100.

b. What is the maximum height reached by the baseball?

The maximum height can be found by substituting the x-value of the axis of symmetry into the original equation. So, h = –[tex]0.005(100)^2[/tex] + 100 + 3 = 103 feet.

c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?

To find the horizontal distance when h is 3, we set the equation equal to 3: –[tex]0.005x^2 + x + 3 = 3.[/tex] Simplifying gives x values where the ball is at 3 feet off the ground. After simplification, one possible solution would be the distance before the ball reaches its peak. However, solving this particular quadratic may require a calculator for precise roots, implying the distances at which the ball is 3 feet high.

Answer:

its the second, third, and fifth one

Step-by-step explanation:

Answer:

C. -0.34

Step-by-step explanation:

We have that for a normal distribution, the value of z can be calculated using the following formula:

z = (x - m) / sd

where x is the value to evaluate, m the mean and sd the standard deviation, we have those values x = 16.3, m = 17.4 and sd = 3.2

if we replace we have:

z = (16.3 - 17.4) /3.2

z = -0.3437

if we round to 2 decimal places, it would be -0.34, that is, the answer is C.

The z-score for a fish measuring 16.3 cm, with a mean length of 17.4 cm and a standard deviation of 3.2 cm, is -0.34.

The score of the length of the fish, also known as the z-score, is calculated by subtracting the mean from the observed value and then dividing by the standard deviation. Using the provided data, we have a mean (μ) of 17.4 cm and a standard deviation (σ) of 3.2 cm. The fish in question measures 16.3 cm.

To find the z-score, the calculation is as follows:

Z = (X - μ) / σ

Z = (16.3 cm - 17.4 cm) / 3.2 cm

Z = -1.1 cm / 3.2 cm

Z = -0.34 (rounded to two decimal places)

Therefore, the z-score for a fish that is 16.3 cm long is -0.34, which corresponds with answer option C.

The ratio of similarity between the two trapezoids  is 2:1, which means that the linear dimensions of the larger trapezoid are twice those of the smaller one.

To find the ratio of similarity between two similar trapezoids with areas of 180 [tex]cm^2[/tex] and 45 [tex]cm^2[/tex], we use the principle that the ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions. In other words, if the ratio of similarity (scale factor) between the linear dimensions of two similar figures is 'k', then the ratio of their areas is '[tex]k^2[/tex]'.

Let the ratio of similarity be 'k'. Then we have 180/45 = k^2. Simplifying this, we get 4 = [tex]k^2[/tex] and thus, k = 2. This means the linear dimensions of the larger trapezoid are twice those of the smaller one.

Therefore, the ratio of similarity between the two trapezoids is 2:1.

Answer:150.

Step-by-step explanation:

Answer:

73.72

Step-by-step explanation:

Using law of Sines in area:

A(triangle) = S1 * S2 * sin(theta) /2

A(triangle) = 12 * 15 * sin(55) / 2 = about 73.72 when rounded

ANSWER: 73.72

Answer: B

Step-by-step explanation:

Using 6 decimals for pi = 3.141592

[tex]Formula: C= \pi d\\[/tex]

[tex]C=(3.141592)(24in)\\C=75.398223in[/tex]

Answer:

1/72

Step-by-step explanation:

Answer:

1/72

Step-by-step explanation:

1/8 divided by 9 = 1/8 times 1/9.

We have ti flip 9/1 so we get 1/9

You multiply 9 by 8 you get 72

so the answer is 1/72

Answer:

a, c, b, a

Step-by-step explanation:

Answer:

Situation 1 is exponential decay. Situation 2 is linear. Situation 3 is exponential growth.

Step-by-step explanation:

Situation 1 is exponential decay because it declined in a non linear way.

600-480=120 480-364=116

Situation 2 is linear because when it declined it has a dependent to another.

400-340=60 340-280=60

Situation 3 is exponential growth because is increases.

Answer:

92 i believe .

Step-by-step explanation:

Answer:

2 1/2 bars each.

Step-by-step explanation:

That would be 15/6.

Answer: c. 18.3

Step-by-step explanation: 100 times .6 equals 60 so if you divide 11 by .6 you get 18.3

Answer:

here you go

Step-by-step explanation:

add them all together = 60

+ 40 = 100

4 boxed

40 divided by 4 = 10

add 10 onto each number

red = 21%

silver = 34%

grey = 26%

black = 19%

all of them added together = 100%

Answer:

-6x-5

Step-by-step explanation:

Answer:

6x^2-10

Step-by-step explanation:

(5x^2+2)-(-4x^2+7)+(-3x^2-5)=

5x^2+2+4x^2-7-3x^2-5=

5x^2+4x^2-3x^2+2-7-5=

9x^2-3x^2-5-5=

6x^2-10