please help me i have a test and i did not study.

The value of (x,y) is ( 6, -6) (optionA)

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14, 4x − 4y = 4. 6a + b = 18, 4a + b = 14.

6x+4y = 12 equation 1

-6x +6y = -72 equation 2

add equation 1 and 2

10y = - 60

y = -60/10

y = -6

substitute -6 for y in equation 1

6x +4(-6) = 12

6x -24 = 12

6x = 12+24

6x = 36

x = 36/6 = 6

therefore the value of (x,y) = ( 6, -6)

learn more about Simultaneous equation from

https://brainly.com/question/148035

#SPJ1

The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /) that represents a value or a calculation. It can contain variables, which are placeholders for unknown or changing values, and can be simplified or evaluated using mathematical rules and operations. Examples of expressions include 3x + 5, (a + b) / 2, and √(16 - 3y).

The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

where x is the unknown number.

Therefore, the mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

To know more about expressions visit :

https://brainly.com/question/1859113

#SPJ1

The scale factor using in that dilation of the dashed triangle would be = 3:1

A scale factor is defined as the ratio that exists between an original size of an object and the new formed size of the same object.

The formula that can be used to calculate the scale factor ;

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Using the base of the triangle from the centre of origin in the graph;

The dimension of the new shape = 18

The dimension of the original shape = 6

scale factor = 18/6 =3

That is, the scale factor = 3:1

Learn more about scale factor here ;

https://brainly.com/question/28339205

#SPJ1

The measure of angle 1 would be equal to 59 degrees.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We have been given the angles as 31 degrees and 90 degree

We know that the sum of angle of triangle is 180 then the angle 1 will be;

31 + 90 + m∠1 = 180

m∠1 = 180 - 90 - 31

m∠1 = 59

Hence, m∠1 = 59

Learn more about parallelograms;

https://brainly.com/question/28854514

#SPJ1

let's convert all mixed fractions to improper fractions, let's add all berries and then see how many times 1/2 go into that sum or namely division.

[tex]\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} ~\hfill \stackrel{mixed}{4\frac{1}{2}} \implies \cfrac{4\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ strawberries }{\cfrac{13}{4}}~~ + ~~\stackrel{ blueberries }{\cfrac{9}{2}}\implies \cfrac{(1)13~~ + ~~(2)9}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{13+18}{4}\implies \cfrac{31}{4} \\\\\\ \stackrel{\textit{now let's divide that sum by }\frac{1}{2}}{\cfrac{31}{4}\div \cfrac{1}{2}}\implies \cfrac{31}{4}\cdot \cfrac{2}{1}\implies \cfrac{31}{2}\implies {\Large \begin{array}{llll} 15\frac{1}{2} \end{array}}[/tex]

The change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

What is the basic arithmetic operations?

The four basic arithmetic operations are Addition, subtraction, multiplication, and division.

To calculate Rachel's change, we first need to determine the sale price of the sweater after the discount and then subtract it from the $10 bill.

Let's say the original price of the sweater was $30, and it was discounted by 50% to $15. Rachel's coupon gives her an additional 25% off the sale price, so she can get the sweater for 75% of the sale price.

To calculate the final price Rachel will pay, we can multiply the sale price by 0.75:

Final price = $15 * 0.75 = $11.25

Rachel pays with a $10 bill, so her change will be:

Change = $10 - $11.25 = -$1.25

Hence, the change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

To learn more about basic arithmetic operations , Visit

https://brainly.com/question/20628271

#SPJ1

After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.

You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.

Let's write the coordinates of the original figure,

A = (1, -5)

B = (6, -2)

C = (6, -5)

D = (1, -8)

Now, if we rotate it 90 degrees counterclockwise, the coordinates are:

A' = ( 5, 1)

B' = (2, 6)

C' = (5, 6)

D' = (8, 1)

Now if we rotate it again 90 degrees counterclockwise, the coordinates are:

A'' = ( -1, 5)

B'' = (-6, 2)

C'' = (-6, 5)

D'' = (-1, 8)

Now from the figure, let's write the coordinates.

A' = ( -1, 5)

B' =  (-6, 2)

C' = (-6, 5)

D' =  (-1, 8)

This is the same as the coordinates of the second 90 degrees counterclockwise rotation.

Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.

Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

To learn more about the rotation of figures, follow the link.

https://brainly.com/question/13286537

#SPJ1

The relationship between ∠8 and ∠4 include the following: A. corresponding angles.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines l and m, we have the following:

8 ≅ ∠4

3 ≅ ∠7

Read more on parallel lines here: brainly.com/question/16959398

#SPJ1

The factors of the form (x - c) are (x - 2) and (x² + 49).

To factor the polynomial f(x) = x³ - 2x² + 49x - 98 into factors of the form (x - c), we can use synthetic division with the given zero of 2.

2 | 1 -2 49 -98
  |     2  0  98
    1  0 49   0

The result of the synthetic division gives us the quotient (x² + 49) and a remainder of 0, confirming that 2 is indeed a zero of the polynomial.

Now we can write the polynomial as the product of (x - 2) and the quotient (x² + 49):

f(x) = (x - 2)(x² + 49)

Since the quadratic factor (x² + 49) cannot be factored further using real numbers, the final factorization of the polynomial is:

f(x) = (x - 2)(x² + 49)

Learn more about factorization here: https://brainly.com/question/25829061.

#SPJ11

The octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V.

An octagon is a two-dimensional shape with eight sides and eight angles. It is a polygon which means it is a closed, two-dimensional shape with straight sides. Octagons are used in architecture and design and are commonly seen in stop signs and floor tiles. The angles of an octagon are all equal and each side is the same length.

The regular octagon has eight equal sides and angles. The angles of an octagon are all of the same size, which is 135°. If the octagon is rotated clockwise about its center, then the vertex at T is moved to V. This means that the octagon will have rotated 45° in order to move T to V.

To calculate the angle of rotation, we can use the formula: angle of rotation = (360°/number of sides). Therefore, the angle of rotation for this octagon will be (360°/8) = 45°.

To confirm this, we can use a protractor to measure the angle between the two lines. The angle between the two lines is 45°. This confirms that the octagon has rotated by 45° as the vertex at T has been moved to V.

Therefore, the octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V. This can be confirmed by using a protractor to measure the angle between the two lines.

For more questions related to polygon

https://brainly.com/question/26583264

#SPJ1

Therefore , the solution of the given problem of  expression comes out to be 480 fluid ounces = 15 quarts further answer given below.

Mathematical processes like multiplying, dividing, adding, and now even deleting are required. If they were merged, the following claim would be made: An equation, some statistics, and a mathematical formula Values, components, and mathematical processes like additions, variables subtractions, reversals, algebraic formulas, and divisions make up a statement of truth. Words and phrases can be rated and analysed.

Here,

=>118 pints = 36 cups

=> 25 pounds = 400 ounces

=> 6 pounds 15 ounces = 111 ounces

=> 2 1/4 hours = 8100 seconds

=> 5 gallons = 20 quarts

=> 220000 pounds = 110 tons

=> 150 tons = 300000 pounds

=> 30 yards = 90 feet

=> 6 feet 4 inches = 76 inches

=> 2 feet = 24 inches

=> 480 fluid ounces = 15 quarts

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The first runner is covering a mile in 9.25 minutes and the second runner is covering a mile in 18.5 minutes the first runner is traveling at a greater speed.

Travel is the movement of people between distant geographical locations for any purpose. It can be done by foot, bicycle, car, boat, bus, train, or plane. Travel can also include relatively short stays between successive movements, such as in the case of tourism or business travel. Travel can be for leisure, recreational, or business purposes, and can be one way or round trip. It may involve travel to different places within the same country, or to another country altogether.

The first runner is traveling at a greater speed because their time to complete each mile is less than the second runner.
For example, the first runner takes 18.5 minutes to complete 2 miles, while the second runner takes 37 minutes to complete the same distance.
This means that the first runner is covering a mile in 9.25 minutes, while the second runner is covering a mile in 18.5 minutes.
Therefore, the first runner is traveling at a greater speed.

To learn more about travel
https://brainly.com/question/24283318
#SPJ1

Answer: Runner 1

Jonson family I think  sorry if im wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

idrk

The altitudes of a triangle are the angle bisectors of the orthic triangle is true because the orthic triangle is formed by the feet of the altitudes of the original triangle. The circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle is true because circumcircle of a triangle passes through all three vertices.

To prove the first statement, we can use the fact that the altitudes of a triangle are perpendicular to the sides and intersect at the orthocenter. The orthic triangle is formed by the feet of the altitudes of the original triangle.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Since AD is an altitude, ∠ADB and ∠ADC are right angles.
3. Similarly, ∠BEC and ∠BFC are right angles.
4. Therefore, ∠BDC and ∠EDF are supplementary angles, meaning they add up to 180 degrees.
5. Since ∠BDC and ∠EDF are supplementary and they share a common side, they are also the angle bisectors of the orthic triangle DEF.
6. The same logic can be applied to the other two altitudes to show that they are also angle bisectors of the orthic triangle.

To prove the second statement, we can use the fact that the circumcircle of a triangle passes through all three vertices.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Let O be the circumcenter of the original triangle ABC.
3. Since the circumcircle passes through all three vertices, OD, OE, and OF are all radii of the circle.
4. Since all radii of a circle are equal, OD = OE = OF.
5. Therefore, the circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle, as they are all equidistant from the center of the circle.

Learn more about triangle at https://brainly.com/question/30069772

#SPJ11

Answer: 19

Step-by-step explanation: The formula for the area of a quadrilateral is length x width.

Here, we have the width missing. So our equation would be,

12x=228.

dividing both sides by 12 gives us x=228/12.

solving this, we get x=19.

So, your answer will be 19.

Answer:

The width of the rectangle is 19 feet

Step-by-step explanation:

The formula for the area of a rectangle is length times width which can be expressed as

[tex]A=lw[/tex]

We can rearrange the equation and solve for the width.

Divide both sides of the equation by [tex]l[/tex].

[tex]\frac{A}{l}=w[/tex]

Now we have an equation to evaluate the width.

Numerical Evaluation

Substituting our values into the equation yields

[tex]\frac{228}{12}=w[/tex]

[tex]w=19[/tex]

To restrict the domain of the function f so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. This means that for every value of x in the restricted domain, there is exactly one value of f(x).

Once we have restricted the domain, we can find the inverse function f-1 by switching the x and y values in the original function and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

For example, consider the function f(x) = x^2. This function is not one-to-one because for every value of x, there are two values of f(x) (one positive and one negative). However, if we restrict the domain to x ≥ 0, the function becomes one-to-one and we can find the inverse function.

The restricted function is f(x) = x^2 for x ≥ 0. The inverse function is f-1(x) = √x for x ≥ 0. The domain of f is x ≥ 0 and the range is f(x) ≥ 0. The domain of f-1 is x ≥ 0 and the range is f-1(x) ≥ 0.

In general, to restrict the domain of a function so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. Once we have restricted the domain, we can find the inverse function by switching the x and y values and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

To know more about domain and range refer here:

https://brainly.com/question/29452843

#SPJ11

The value of x in the equation 8+4=2(x-1) is 7

To solve for x in the equation 8+4=2(x-1), we can follow these steps:

Simplify the left-hand side of the equation by adding 8 and 4 to get 12:

8 + 4 = 12

Simplify the right-hand side of the equation by distributing the 2 to the expression inside the parentheses:

2(x-1) = 2x - 2

Set the left-hand side and the right-hand side equal to each other:

12 = 2x - 2

Add 2 to both sides of the equation:

12 + 2 = 2x

14 = 2x

Divide both sides of the equation by 2:

14/2 = x

x = 7

Therefore, the value of x in the equation 8+4=2(x-1) is 7.

To learn more about equation

https://brainly.com/question/10413253

#SPJ4

A. The amount of aspirin in the dose is 22.066 milligrams.

B. ƒ (60) = 7.483 milligrams
This means that 60 hours after ingesting a dose of 22.066 milligrams of aspirin, the amount of aspirin in the person's blood will be 7.483 milligrams.

C. The aspirin level will be less than 10 milligrams after approximately 45.06 hours.

a. The initial amount of aspirin in the dose can be found by evaluating f(0):

f(0) = 300 * (1/2)^(1/30) ≈ 22.066

Therefore, there are approximately 22.066 milligrams of aspirin in the dose.

b. We can find f(60) by substituting t = 60 into the equation:

f(60) = 300 * (1/2)^(1/30 * 60) ≈ 7.483

Therefore, there are approximately 7.483 milligrams of aspirin in the person's blood 60 hours after ingesting the dose. This is significantly less than the initial amount of 22.066 milligrams, indicating that the aspirin is being metabolized and eliminated from the body over time.

c. We want to solve for t when f(t) < 10:

300 * (1/2)^(1/30t) < 10

Dividing both sides by 300:

(1/2)^(1/30t) < 1/30

Taking the natural logarithm of both sides:

ln[(1/2)^(1/30t)] < ln(1/30)

Using the properties of logarithms:

(1/30t)ln(1/2) < ln(1/30)

Simplifying:

-0.6931t < ln(1/30)

Dividing both sides by -0.6931 (which is ln(1/2)):

t > ln(1/30) / (-0.6931)

t > 45.06

Therefore, the aspirin level will be less than 10 milligrams after approximately 45.06 hours.

Learn more about aspirin at https://brainly.com/question/20877853
#SPJ11

Answer: a. The distribution of X is a binomial distribution with n = 3 and p = 1/4. That is, X ~ Binomial(3, 1/4).

b. The cdf of Y is given by F_Y(y) = P(Y <= y) = P(Y < y) + P(Y = y). Since Y is the middle one of the three points, we can write P(Y < y) as P(X >= 2, Z <= y) where Z is the smallest one of the three points. Similarly, we can write P(Y = y) as P(X = 1, Z = y). Therefore, the cdf of Y is given by:
F_Y(y) = P(X >= 2, Z <= y) + P(X = 1, Z = y)
= P(X >= 2)P(Z <= y) + P(X = 1)P(Z = y)
= (3/64)(y^3) + (9/64)(y^2)(1-y)

c. The pdf of Y is given by the derivative of the cdf with respect to y. That is,
f_Y(y) = dF_Y(y)/dy
= (3/64)(3y^2) + (9/64)(2y)(1-y) + (9/64)(y^2)(-1)
= (9/64)(y^2 - y^3)

Therefore, the pdf of Y is f_Y(y) = (9/64)(y^2 - y^3) for 0 <= y <= 1.

You can read more about binomial distribution at https://brainly.com/question/30049535#:

#SPJ11

Answer:

Step-by-step explanation:

8×-4

The solver for this expression is x = -5/2, 5/2, 2, -1/3, 1, 2.

To solve this expression, we will first need to factor the numerator and denominator of each fraction.

For the first fraction, we can factor the numerator as follows:
[tex]25 - 4x^2 = (5 + 2x)(5 - 2x)[/tex]

The denominator can be factored as follows:
[tex]6x^2 + 9x - 15 = (2x + 5)(3x - 3)[/tex]

For the second fraction, the numerator can be factored as follows:
[tex]6x^2 - 2x - 4 = (2x - 4)(3x + 1)[/tex]

The denominator can be factored as follows:
[tex]2x^2 - x - 10 = (2x + 5)(x - 2)[/tex]

Now we can simplify the expression by canceling out any common factors:
[tex](5 + 2x)(5 - 2x)/(2x + 5)(3x - 3) * (2x - 4)(3x + 1)/(2x + 5)(x - 2)[/tex]
[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(2x + 5)(3x - 3)(2x + 5)(x - 2)[/tex]

[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(3x - 3)(x - 2)[/tex]

Since the expression is equal to 0, we can set each factor equal to 0 and solve for [tex]x[/tex]:

[tex]5 + 2x = 0 \\5 - 2x = 0 \\2x - 4 = 0 \\3x + 1 = 0 \\3x - 3 = 0 \\x - 2 = 0 \\[/tex]

Solving for x, we get the following solutions:
[tex]x = -5/2 \\x = 5/2 \\x = 2 \\x = -1/3\\ x = 1 \\x = 2 \\[/tex]

Therefore, the solver for this expression is [tex]x = -5/2, 5/2, 2, -1/3, 1, 2[/tex].

See more about equations at: https://brainly.com/question/22688504

#SPJ11

Lee's gross pay is $472.

First, we need to calculate the commission Lee earned. To do this, we take her total sales and multiply it by her commission rate.

Commission = Total Sales x Commission Rate

Commission = $4,000 x 0.04

Commission = $160

So, Lee earned $160 in commission.

Next, we need to calculate her base pay. To do this, we multiply her hourly rate by the number of hours she worked.

Base Pay = Hourly Rate x Hours Worked

Base Pay = $8.00 x 39

Base Pay = $312

Now that we have calculated her commission and base pay, we can add them together to find her gross pay.

Gross Pay = Base Pay + Commission

Gross Pay = $312 + $160

Gross Pay = $472

This means that before any deductions (such as taxes), Lee would earn $472 for working 39 hours and making $4,000 in sales.

To know more about gross pay here

https://brainly.com/question/14690804

#SPJ4

Answer:

P(4, tail) = 1/12

Step-by-step explanation:

The probability of a particular outcome when all possible outcomes are equaly likely, is the number of "desired" oucomes divided by the total number of possible outcomes.

In your case, there are 12 possible outcomes (you can count them, or calculate 6 for the dice times 2 for the coin). Only one of them is "desired", namely the combination of 4 and a tail. Hence 1 divided by 12.

Answer:

Step-by-step explanation:

When calculating this equation you simply insert the x value into the equation given, in this case (x-2)^2

for example you are given 4 to 4 which is achieved by the method previously described, like this (4-2)^2 = (2)^2 = 4

so the answers would be

6 -> 16 (6 - 2 = 4 and 4^2 is 16)

10 -> 64 (10 - 2 = 8 and 8^2 is 64)

Step-by-step explanation:

3 - (1/4)×(8/3 × 9)

3 - (1/4)×(8×9/3)

3 - (1/4)×(8×3)

3 - (1/4)×24

3 - 24/4

3 - 6 = -3

The value of Y is not independent of the value of X, and so X and Y are not independent.

Let X be a random variable with EXP <∞ and let Y = [X]. Since X has a Lebesgue density symmetric about 0, we know that E[X] = 0. Therefore, E[XY] = E[X[X]] = E[X²] = Var[X] + E[X]² = Var[X].

Since X and Y are uncorrelated, we have E[XY] - E[X]E[Y] = 0, which implies that E[XY] = E[X]E[Y] = 0*E[Y] = 0. Therefore, X and Y are uncorrelated.

However, X and Y are not independent because the value of Y depends on the value of X. For example, if X = 1.5, then Y = 1, but if X = -1.5, then Y = -2. Therefore, the value of Y is not independent of the value of X, and so X and Y are not independent.

Lear more about Random variable

brainly.com/question/17238189

#SPJ11

We can conclude that the number of defective products

To test the hypothesis that the number of defective products follows the binomial distribution, we need to calculate the expected frequency for each category and compare it with the observed frequency using the chi-square test.

First, let's calculate the expected frequency for each category:

E(0) = 200 * (0.95)^20 = 7.64

E(1) = 200 * 20 * (0.95)^19 * (0.05)^1 = 32.15

E(2) = 200 * 190 * (0.95)^18 * (0.05)^2 = 67.53

E(3) = 200 * 1140 * (0.95)^17 * (0.05)^3 = 90.71

E(4) = 200 * 4845 * (0.95)^16 * (0.05)^4 = 85.64

E(5) = 200 * 15504 * (0.95)^15 * (0.05)^5 = 61.29

E(6) = 200 * 38760 * (0.95)^14 * (0.05)^6 = 34.71

Next, we calculate the chi-square test statistic:

X^2 = (28-7.64)^2/7.64 + (44-32.15)^2/32.15 + (37-67.53)^2/67.53 + (48-90.71)^2/90.71 + (30-85.64)^2/85.64 + (9-61.29)^2/61.29 + (4-34.71)^2/34.71 = 84.31

Since we have 7 categories, the degrees of freedom for the chi-square distribution is 7-1=6. The critical value for alpha=1% and df=6 is 16.81. Since the test statistic is greater than the critical value, we reject the null hypothesis that the number of defective products follows the binomial distribution.

Therefore, we can conclude that the number of defective products does not follow the hypothesized distribution at alpha=1%.

Learn more about products

https://brainly.com/question/25243865

#SPJ11

Step By Step Explanation

Filled jar = ?

How much poured or (x) = 350ml × 8 glasses

=2800 ml

How much left or (y) = 200ml

Capacity = How much poured + How much left

Capacity = x + y

Capacity = 2800 ml + 200 ml

Capacity = 3000ml

Give answer in litres

1 litre = 1000 millilitre

So 3000ml = 3000 ÷ 1000

So 3000 ml = 3 litres

Capacity = 3 litres