Is quadrilateral ABCD a rectangle? Provide justification for your decision using the grid or by explanation.

Answer:

The last one on the right

Step-by-step explanation:

The others are 2 equations in x and y, while the last is one equation in x  only and another in y only

The solution is Option D.

The system of equations 3 = y + 1 and x = -6 are equations is one variable

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the system of equations be

y = 3x - 1   be equation (1)

y = 3x + 1   be equation (2)

Now , the equations are linear equations in 2 variables

b)

Let the system of equations be

-2x + y = 2   be equation (1)

-4x + 2y = 4   be equation (2)

Now , the equations are linear equations in 2 variables

c)

Let the system of equations be

y - 1 = 2 ( x + 4 )   be equation (1)

y + 3 = -5 ( x + 1 )   be equation (2)

Now , the equations are linear equations in 2 variables

d)

Let the system of equations be

3 = y + 1   be equation (1)

y = 2

x = -6   be equation (2)

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

So , the equation is linear equation is one variable

Hence , the equations y = 2 and x = -6 are equations in one variable

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Using  Pythagoras triple, the side lengths 6, 9 and 12 are not the sides of a triangle

Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

In this problem, we are going to determine is 6, 9 and 12 are Pythagoras triple.

Taking the largest number and assuming it's the hypothenuse of the triangle;

12² = 6² + 9²

144 = 117

144≠117

The side lengths 6, 9 and 12 can't form a right angle triangle.

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Answer:

z = 22

Step-by-step explanation:

Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).

Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:

2z = z + 22

Now, all we have to do is solve for z

2z = z + 22

-z   - z

z = 22

The completed statement obtained using the proportional relationship between the recipes and the number of bags of snack mix made are presented as follows;'

A proportional relationship is one in which the output variable is a constant multiple of the input variable.

The possible recipe to make 6 bags of snacks obtained froma similar question is presented as follows;

3 cups of granola

1 cup of raisins

1.5 cup of almonds

0.5 cup of cranberries

0.75 cup of chocolate chips

The evaluation of the possible statements in the question that requires completion using proportional relationships of the recipe, are presented as follows;

1. To make 18 bags of snack mix, Sherry needs ___ cups of almonds

18 = 3 × 6

Therefore, the amount ingredients required to make 18 bags of the snack mix is 3 times the amount of ingredients in the recipe, which indicates;

The number of cups of almonds Sherry needs = 3 × 1.5 = 4.5

2. Sherry needs 6 cups of granola to make ___ bags of the snacks

The number of granola required for 6 bags = 3 cups

6 = 2 × 3

The number of bags of the snack mix 6 cups of granola can make is twice the number made by 3 cups, of granola or 2 × 6 = 12 bags of snack mix.

3. If Sherry uses 1 cup of cranberries, she will need to use ___ cups of resins

The number of cups of cranberries in the recipe = 0.5 cups

Number of cups of resins in the recipe = 1 cup of resin

Therefore, 1 cup of resin is required for 0.5 cups of cranberries

2 × 1 = 2 cups of resins will be required for 2 × 0.5 = 1 cup of cranberries

4. The recipe will make ___ bags of snack mix if Sherry  uses only 1 cup of granola

3 cups of granola are required for 6 bags of snack mix

Therefore; 3/3 = 1 cup of granola will be required for 6/3 = 2 bags of the snack mix

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The mean can only be used with interval/ratio level data.

what is  ratio data ?

Ratio data is a form of quantitative (numeric) data. It measures variables on a continuous scale, with an equal distance between adjacent values. While it shares these features with interval data (another type of quantitative data), a distinguishing property of ratio data is that it has a 'true zero.

What are mean , median and mode?

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Hence, the mean can only be used with interval/ratio level data.

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The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.

The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.

Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.

Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.

N (# of periods) = 12 months

I/Y (Interest per year) = 11.99%

PV (Present Value) = $6,299.59

PMT (Periodic Payment) = $-350

Results:

FV = $3,009.15

Sum of all periodic payments = $3,850 ($350 x 11)

Total Interest = $559.57

The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)

The total amount paid in full in the first month = $6,299.59

Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)

Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.

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Answer: 12 miles

Step-by-step explanation:

Let y represent the cost and x represent the number of miles!

y = 1.25x + 3

Now put the $18 in for y

18= 1.25x + 3

15 = 1.25x

x = 12 miles

Answer:

Step-by-step explanation:

We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:

18 = 1.25x + 3

15 = 1.25x (subtracted 3 from both sides)

12 = x (divided each side by 1.25)

So, the trip was 12 miles

Answer:Antonio drove 24 miles west

Step-by-step explanation: 50-26=24

4x - 7y + 28 = 0,5y - 7x + 9 = 0 is the system of equation that has no solution.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

Dependent, Independent and inconsistent are the three types of system of equation.

If we solve this system of equation we will get complex roots that means it has no solution.

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By evaluating the function for 2f(a), we get 6a² + 6a -4.

We can evaluate the function, f(x) =3x² +3x -2 for 2 f(a) by using the following steps:

Firstly, we have to find f(a).

In order to find f(a) we need to substitute 'x' with 'a' in the given function.

So the f(a) would be equal to :

f(a) = 3a² +3a-2

Now in the second step in order to find 2f(a) we need to multiply the whole function of f(a) with 2.

So 2f(a) would be equals to:

2f(a) = 2(3a² + 3a -2)

2f(a) = 6a² +6a -4

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The exact length of the polar curve in this problem is given as follows:

320,597 units.

The definition of a polar curve is given as follows:

r(θ).

Then the length of the curve over an interval a ≤ θ ≤ b is given by the definite integral presented as follows:

[tex]L = \int_{a}^{b} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta[/tex]

The curve in this problem is given as follows:

[tex]r = e^{2\theta}[/tex]

The derivative is given as follows:

[tex]\frac{dr}{d\theta} = 2e^{2\theta}[/tex]

Then the arc length is given by the integral presented as follows:

[tex]L = \int_{0}^{2\pi} \sqrt{e^{4\theta} + 4e^{4\theta}} d\theta[/tex]

[tex]L = \int_{0}^{2\pi} \sqrt{5e^{4\theta}} d\theta[/tex]

[tex]L = \sqrt{5}(\int_{0}^{2\pi} e^{2\theta} d\theta)[/tex]

[tex]L = \frac{\sqrt{5}}{2}(e^{2\theta})|_{\theta = 0}^{\theta = 2\pi}[/tex]

Applying the Fundamental Theorem of Calculus to solve the double integral, the length of the arc is givena s follows:

[tex]L = \frac{\sqrt{5}}{2}(e^{4\pi} - 1)[/tex]

L = 320,597 units.

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Answer: The cost of a ticket for an adult is $12 while for children it is $10.

Step-by-step explanation:

Let's assume that cost for adults is A while for children it is C

Now,

2 adults and 4 children spend $64.

2A + 4C = 64

1 adult and 3 children spend $42.

A + 3C = 42

Multiply by 2

2A + 6C = 84

By subtracting equations

6C - 4C = 84 - 64

2C = 20

C = 10

A = 42 - 3(10)

A = 12

Hence "The cost of a ticket for an adult is $12 while for children it is $10".

Answer:

I'm pretty sure its 3500

Answer:

3,500 meters above the ground.

Step-by-step explanation:

The working is in the picture I attached to this response.

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The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R

Full question is:

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)

If we have a level surface, then it will give us

f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.

Now let us calculate the ∇ gradient of f at point (0,0,7):

∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)

= (1, 1, 1)

We get the equation for the tangent plane A:

A: 1(x−0) + 1(y−0) + 1(z−7)=0

This can also be written as:

x+y+z = 7 ------------------------------------------------------------------(a)

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)

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Answer:

Step-by-step explanation:

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Answer:

Correct answer is ([7],[5])

Step-by-step explanation:

For the vertex form of the parabola, y = a(x – h)2 + k, the coordinates (h, k) of the vertex are:

(h, k) = (-b/2a, -D/4a)

where,

a is the coefficient of x2,

b is the coefficient of x,

D = b2 – 4ac is the discriminant of the standard form y = ax2 + bx + c.

The probability that the ladybug will be at position 1 at time t+1 is ((1/2)*(12/50) + (1/2)*(16/50)) = 14/50 = 0.28.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

The probability is computed by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

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We can conclude that there is a statistically significant correlation between the two variables, a and b. The correlation coefficient is .10, which indicates a weak positive relationship.

A correlation coefficient of .10 indicates that there is a weak positive relationship between the two variables, a and b. A p-value of .01 indicates that the correlation between the two variables is statistically significant, meaning that it is unlikely to be due to chance. This suggests that there is a real relationship between the two variables, even though it is weak.

To calculate the correlation coefficient, you can use the formula  where x and y are the two variables in question. In this case, the correlation coefficient is .10. This can be determined by plugging in the values for x and y and doing the necessary calculations.

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The equation of the line in slope-intercept form is y = 0.5x + 1

From the question, we have the following parameters that can be used in our computation:

Points = (0, 1) and (-4, -1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = slope

This means that

c = 1

So, we have the following representation

y = mx + 1

At (-4, -1), we have

-1 = -4m + 1

This gives

-4m = -2

Divide by -4

m = 0.5

So, we have

y = 0.5x + 1

Hence, the equation  is y = 0.5x + 1

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Yes, it is possible for a line to be tangent to a circle at a point.

If a line is tangent to a circle at a point, it means that the line touches the circle at that point but does not intersect the circle at any other point. The line is perpendicular to the radius of the circle at the point of tangency.

In this case, the line QR is tangent to circle P at point Q. This means that the line QR touches the circle P at point Q, but does not intersect the circle P at any other point. The line QR is also perpendicular to the radius of circle P at point Q.

In below diagram QR is tangent to circle P at point Q. The line QR is perpendicular to the radius of circle P at point Q, indicated by the right angle at Q.

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The perimeter of the triangle ΔABC will be 21 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The perimeter of the triangle is determined by adding together all of its sides.

If d, e, and f are midpoints of the sides of ABC. A = 7, C = 8, and B = 6. Then the perimeter of the triangle is given as,

Perimeter = A + B + C

Perimeter = 7 + 6 + 8

Perimeter = 21

The perimeter of the triangle ΔABC will be 21 units.

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Answer:

1. using the formula (aX2/h)-22

17

Step-by-step explanation:

Take area multiply by 2

234x2=468

Divide answer by height which is 12 you get 39

39subtract 22 you get your answer as 17

The required graph of the inequality has been shown and the solution is; 8 Nickels  and 12 dimes.

Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).

Let the number of nickels be x and let the number of dimes be y,

We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;

x + y = 20

x = 20 - y - - - - (1)

0.05x + 0.10y ≤ 1.60 - - - -(2)

We are also told that no less than 4 of the coins are dimes. Thus;

x ≥ 4

From the graph, one solution is given as 8 Nickels and 12 dimes.

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The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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We know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.

The definition of equations in algebra is a mathematical statement that shows the equality of two mathematical equations.

For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Solve equations to find the equation which has no solution as follows:

(A) 4(x+3) + 2x= 6(x+2)

4(x + 3) + 2x = 6(x + 2)

4x + 12 + 2x = 6x + 12

6x = 6x

L. H. S = R. H. S

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

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

5 + 6 + 4x = x + 3x + 3

11 + 4x = 4x + 3

L. H. S ≠ R. H. S

(We got our answer and so we don't need to solve further options)

Therefore, we know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.

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Correct question:

Which equation has no solution?

a 4(x+3) + 2x= 6(x+2)

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

c 5(x+3) + x = 4 (x+3) + 3

d 4 + 6(2+x) = 2(3x+8)

The probability that Steph Curry makes the first 2 free throws and misses the last throw is 81/1000

Let A be the event that Steph Curry makes the free throw.

Let B be the event that Stech Curry does not make the free throw.

According to the problem,

P(A) = 90%

= 9/10

Since B is the complement of A,

P(B) = 1 - P(A)

= 1/10

Hee, Steph Curry gets 3 free throws. Hence, the probability that he makes the first 2 throws while he misses the third one is

P(A) X P(A) X P(B)

= 9/10 X 9/10 X 1/10

= 81/1000

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