What is one of the solutions to the following system of equations?
x² + y² = 25
y - 3x = -5

Answer:

x = 27, y = 6

Step-by-step explanation:

x - 2y = 15

x - 4y = 3 (rearranged the orginal equation)

  x - 2y = 15

-  x - 4y = 3

___________

2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

x and y of the simultaneous equation are 27 and 6 respectively.

Given,

x - 2y = 15

x - 3 = 4y

Here,

Equations:

x - 2y = 15

Rearranged the original equation

x - 4y = 3

Now subtract both equations,

x - 2y = 15

x - 4y = 3

⇒2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

Thus the solution of system of equation is x = 27 and y = 6.

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Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]

Step-by-step explanation:

Setting the equations equal to each other.

[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).

Hence, the correct option is B.

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The sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have a sandbox:

The length of the sandbox = 4 feet

The width of the sandbox = 6 feet

The height of the sandbox = 2 feet

Amount of sand can hold = volume of the sandbox

= 4×6×2

= 48 cubic feet

Thus, the sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

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Functions which are polynomials are y=[tex]5x^{4} +x^{2} -8[/tex] ,y=[tex]7x^{3}[/tex] and y=[tex]6^{x}[/tex]

Given Functions : 1) y=[tex]-x^{2} +1/1-2x[/tex] 2)y=[tex]5x^{4} +x^{2} -8[/tex]. 3) y=[tex]7x^{3}[/tex]and g(x)=[tex]6^{x}[/tex].

We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .

First function is y=[tex]-x^{2} +1/1-2x[/tex]

The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.

Second function is y=[tex]5x^{4} +x^{2} -8[/tex]

The above function is a polynomial as it has a variable having power and it is not in fraction also.

Third function is  y=[tex]7x^{3}[/tex]

The above function is also a polynomial for the same reason.

Fourth function is g(x)=[tex]6^{x}[/tex].

The above function is also a polynomial.

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The table that correctly identifies the sample of spinning the spinner and then selecting a card is Option A.

A sample is a random element that belongs to a population. Another way to state it is that, it is a set of all the outcomes that are possible from a given set of events.

Table A accurately depicts each potential result. Along the column on the left is where you'll see the card outcomes.

The spinner's output is shown along the top row. The intersection of the left and top results appears in each cell.

For instance, row 1, and column 3 include "red, purple" to show that you received a card with the color "purple" and the color "red" on the spinner.

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Answer:

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x ( x + 7 ) -3 ( x + 7 ) = 0

( x - 3 ) ( x + 7 ) = 0

∴ x - 3 = 0              or              x + 7 = 0

  x = 0 + 3                               x = 0 - 7

  x = 3                                      x = -7

Answer:

Amount in Blank total = $160

Amount of money Daniel’s agent made = $40

Amount of money Daniel and the agent made

from the show  = $160

Step-by-step explanation:

this question is based on the calculation of percentages

so,

it is is given in the question that -

Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show.

After paying the agent, Daniel takes home =  $120

so,

let 'x' is the total amount of money that Daniel earned form the show

it is also given that Daniel promised to give 25 % to his agent from what he earned from the show

so, percentage of money left to the Daniel is

100-25 = 75%

therefore according to the question,

75percent of the x = $120

75/100×(x)   =  120

  3/4×(x)   =  120

     3x   =   120×4

     3x  =  480

       x  =  $160

so the total amount of money Daniel earned from the show is $160

Now we know that Daniel’s agent made 25% of the total amount of money earned from the show

therefore

25percent of 160 = Daniel’s agent made

     25/100 ×160  = Daniel’s agent made

             $40 =  Daniel’s agent made

so the amount of money earned by Daniel’s agent made is $40

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Answer: Daniel’s agent made

✔ $40

Daniel and the agent made a total of

✔ $160

from the show.

.

Step-by-step explanation:

Answer:

A) 37, 34, 22, 28, 19, 25

E) 55, 43, 49, 61, 58, 54

Step-by-step explanation:

The range of a set of data is the largest number minus the smallest number

A) 37, 34, 22, 28, 19, 25

37 - 19 =18

Range is 18

B) 34, 22, 18, 19, 31, 33

34 - 18 =16

Range is 16

C) 95, 79, 83, 88, 81, 99

95 - 81 =14

Range is 14

D) 17, 26, 17, 18, 26, 31

31-17 =14

Range is 14

E) 55, 43, 49, 61, 58, 54

61 - 43 =18

Range is 18

By following the pattern the next image in the pattern is (b) since the correct option is (b).

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers is arranged in a particular way, the arrangement is referred to as a pattern.

From the pattern given: In pattern one, the first column contains 2 blocks and the second column contains 1 block. In pattern second, the first column contains 3 blocks, the second column contains 2 blocks and the third column contains 1 block. In pattern third, the first column contains 4 blocks, the second column contains 3 blocks, the third column contains 2 blocks and the fourth column contains 1 block.

∴ You can observe that block the ks are arranged in descending numbers.

Hence, option (b) is correct.

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The inequality is 100*[tex]3^{t}[/tex]≤ 656100.

The correct option is (B).

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

From the table attached below:

a=300, r= 900/300 = 3

As, it is GP

Now,

f(t) = [tex]ar^{t-1}[/tex]

f(t) = [tex]300*3^{t-1}[/tex]

f(t) = 300/3 *[tex]3^{t}[/tex]

f(t) = 100*[tex]3^{t}[/tex]

Inequality is used to determine greater than or equal to 656100

100*[tex]3^{t}[/tex]≤ 656100

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Answer:

a

Step-by-step explanation:

The value of the WZ will be 28.18. The given figure is quadrilateral.

It is concerned with the geometry, region, and density of various 2D and 3D shapes.

In ΔZXY

∠Z+∠X+∠Y=180

∠Z+34°+90°=180°

∠Z = 56°

In Δ WZY

sin Θ = WZ/ZY

sin 56° = WZ/34

WZ= 28.18

Hence, the value of the WZ will be 28.18.

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The side WZ = 30.4.

The angles which lie on the alternate side of the line between two parallel lines.

Given a geometry in which ZY = 34, WY = 38, and ∠ZXY = 34°

In this geometry, opposite sides are equal.

WZ = XY and WX = ZY.....................(1)

The diagonal are perpendicular to each other.

∠XVY = 90°

Diagonal form four right angle triangles. Take ΔXVY

VY = WY/2

VY = 38/2

VY = 17

Using trigonometric property,

sin X° =  VY / XY

sin 34° = 17/XY

XY = 30.4

From equation 1, we have

WZ = 30.4

Thus, the value of WZ is 30.4.

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Usando proporciones, en conjunto con multiplicación cruzada, encontra-se que el valor de p es de 6.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, relación es dada por:

[tex]\frac{p}{p+2} = \frac{6}{8}[/tex]

Aplicando multiplicación cruzada:

8p = 6(p + 2)

8p = 6p + 12

2p = 12

p = 12/2

p = 6.

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Answer:

A five units right and three units up

Step-by-step explanation:

take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place

The degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.

The degree of the polynomial is defined as the highest power of the variable of the given polynomial or it is the maximum power of the polynomial.

The degree of the given expressions are shown as follows:-

(x-9)                 →  degree 1,

(-4x²-6x+9)      → degree 2,

(x²-2x+9)         → degree 2,

(-3)                   → degree 0,

(3x-2)               → degree 1,

(6x+2)              → degree 1

(5)                    → degree 0.

Therefore the degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.

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33333333333333333333333333333333333

The measure of angle XYZ in the parallelogram is: 71°.

In a parallelogram, the angles that are opposite each other are congruent.

Find m∠XWZ using the triangle sum theorem:

m∠XWZ = 180 - m∠WXZ - m∠WZX

m∠XWZ = 180 - 81 - 28

m∠XWZ = 71°

m∠XWZ = m∠XYZ [opposite angles are congruent]

m∠XYZ = 71°

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Answer:

71°

Step-by-step explanation:

I got it right on Edmentum

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The molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

From the question, we are to determine the molarity of the resulting solution

From the given information,

Number of moles = 5.99 × 10⁻⁶ mol

Volume = 1.50 × 10⁻² L

Using the formula,

Molarity = Number moles / Volume

∴ Molarity = (5.99 × 10⁻⁶) / (1.50 × 10⁻²)
Molarity = 3.99 × 10⁻⁴ M

Hence, the molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

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Answer:

The answer is 3.99 × 10–4 M

Step-by-step explanation:

I just did the assignment on Edge :)

Answer:

1. 3/14

2. 2/7

3. 1/7

4. 5/14

5. 11/14

6. 9/14

Step-by-step explanation:

first get the total number of pens

3 red pens + 4 blue pens + 2 black pens + 5 green pens =

14 total number of pens

1. What is the probability that the pen chosen red?

3 red pens out of a total of 14 pens = 3/14

2. What is the probability that the pen chosen is blue?

4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7

3. What is the probability that the pen chosen is black?

2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7

4. What is the probability that the pen chosen is green?

5 green pens out of a total of 14 pens = 5/14

5. What is the probability that the pen chosen is NOT red?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

4 blue pens, 2 black pens and 5 green pens are NOT red

4 blue pens + 2 black pens + 5 green pens =

11 total number of pens that are NOT red

11 total number of pens that are NOT red out of a total of 14 pens = 11/14

6. What is the probability that the pen chosen is NOT green?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

the 3 red pens, 4 blue pens, 2 black pens are NOT green

3 red pens + 4 blue pens + 2 black pens =

9 total number of pens that are NOT green

9 total number of pens that are NOT green out of a total of 14 pens = 9/14

gathmath.com

Given :-

>> Total no. of outcomes = 3 + 4 + 2 + 5

>> Total no. of outcomes = 3 + 4 + 7

>> Total no. of outcomes = 10 + 4

>> Total no. of outcomes = 14

Solution 1 :-

We know,

As there are three red pens. Therefore,

Solution 2 :-

We know,

As there are four blue pens. Therefore,

Solution 3 :-

We know,

As there are two black pens. Therefore,

Solution 4 :-

We know,

As there are five green pens. Therefore,

Solution 5 :-

We know,

As there 11 pens that are not red (Green + black + blue).

Solution 6 :-

We know,

As there are 9 pens that are not green (Red + blue + black).

The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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The question was incomplete. Below you will find the missing content.
The square root function f(x) is x <= 7

Options are :

A. 7 is subtracted from the x-term inside the radical.
B. The radical is multiplied by a negative number.
C. 7 is added to the radical term.
D. The x-term inside the radical has a negative coefficient.

Option D is correct, which is : The x-term inside the radical has a negative coefficient.

Given, the domain of the square root function f(x) is x <= 7
Consider the function y = √x.
The domain of this function is x ≥ 0 and the range is y ≥ 0.
The expression inside the radical must be greater than or equal to zero.
Now, if x ≤ 7
x - 7 ≤ 0
7 - x ≥ 0
And the function y = √(7-x) will have the domain x ≤ 7.
This implies that the x-term inside the radical has a negative coefficient.
Therefore, the statement that the x-term inside the radical has a negative coefficient must be true.

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Answer:

y=2x-8

or

f(x)=2x-8

Step-by-step explanation:

To write in slope-intercept form using this information, first use the point slope formula.

y-y1=m(x-x1)

m is slope.

y+4=2(x-2)

Use distributive property on the right side.

y+4=2x-4

Now, subtract 4 from both sides.

y+4-4=2x-4-4

y=2x-8

Written using function notation:

f(x)=2x-8

Hope this helps!

If not, I am sorry.

The probability that a red ace is drawn first and then a black ace is mathematically given as

x=1/4

Where

Sample mean=(x,y)\, x, y \in \{h,d,c,s\}

If we want a player to draw two cards of the same color from their deck, the following combinations of cards are appropriate choices:

[tex](h,h),\ (h,d),\ (d,h),\ (d,d),\ (c,c),\ (c,s),\ (s,c),\ (s,s)[/tex]

Generally, 8 possible pairings above 16. This indicates that the likelihood of a player drawing two cards of the same color is 8/16, which is equivalent to a probability of half.

In conclusion, In a similar vein, the following pairs of cards illustrate the likelihood of obtaining a black ace after having drawn a red ace in the previous round:

[tex](h,c),\ (h,s),\ (d,c),\ (d,s)[/tex]

Giving

x=4/16

x=1/4

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Answer:

1/4

Step-by-step explanation:

Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.

A linear function is modeled by:

y = mx + b

In which:

Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:

C(n) = 1200 + 45n.

Now, we have to solve for n when C(n) = 4800, hence:

1200 + 45n = 4800

45n = 3600

n = 3600/45

n = 80.

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Answer:

I think it's 1.17 - -3.85

If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.

Given 95% confidence level, standard deviation=0.05.

We know that margin of error is the range of values below and above the sample statistic in a confidence interval.

We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data  near the mean are more frequent in occurence than data far from mean.

We know that margin of error for a confidence interval is given by:

Me=[tex]z/2* ST/\sqrt{N}[/tex]

α=1-0.95=0.05

α/2=0.025

z with α/2=1.96 (using normal distribution table)

Solving for n using formula of margin of error.

[tex]n=(z/2ST/Me)^{2}[/tex]

n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]

=96.4

By rounding off we will get 97.

Hence the sample size required will be 97.

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The given question is incomplete and the full question is as under:

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?