Aldo's scores on four tests are 88, 85, 100, and 86. What must the score be on the fifth test for her average to be 90?

Answer:

If the line RS has been rotated 90 degrees, then VU will be perpendicular to RS and the two slopes must be opposite and reciprocal, i.e. product of the two slopes will equal -1.

As a verification, we find the locations of V and U from rotations of R & S.

(actually, the triangle had been rotated -90°, 90 ° clockwise)

Step-by-step explanation:

Slope RS, m1:

Slope VU, m2

Hence m1*m2=1*-1=-1, meaning that m1 and m2 are opposite (in sign) and are reciprocal to each other, as expected

The lines RS and VU have the opposite and reciprocal slopes because                               Slope of QRS is 1, where as Slope of TVU is -1

Slope of a triangle represents the angle that are formed between positve X-axis moving anticlockwise towards y-axis.

RQ=3

SQ=3

 slope (Tan∅)=\(\frac{perpendicular}{base}\)

                       =RQ/SQ

                        =3/3 =1

           TanФ=45°

UT=3

VT=-3

 slope (Tan∅)=\(\frac{perpendicular}{base}\)

                       =UT/VT

                        =3/-3 =-1

           TanФ=135°

Slope of QRS is 1, where as

Slope of TVU is -1

∴ RS and VU have the opposite and reciprocal slopes.

Learn more about slope here: https://brainly.com/question/3493733

#SPJ2

The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

Know more about equation here:

https://brainly.com/question/29657983

#SPJ11

(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.

Let us pull out the critical elements

Population: Normally distributed with mean of 2870

population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180

As population sigma is known, we do not have apply any corrections

P(xbar < $2500) = ?    

Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.

Ztest = (2500-2870 )/ 180  or -370/180 = -2.055

As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma  being 95.44% to get a close estimate.   If the area between -2 and 2 sigma = .9544 then the area outside = .0456.  Half of this (the amount under the curve LESS THAN -2) would be .0228

Using a calculator or computer for an exact answer we find (using a TI-83/86):

nmcdf(-9E6,2500,2870,180) = .0199

Learn more about Standard Deviation here:

https://brainly.com/question/14650840

#SPJ4

The differential equation is a mathematical equation that relates a function to its derivatives.

Differential equations are of two types: ordinary differential equations (ODEs) and partial differential equations (PDEs).

Ordinary differential equations (ODEs) deal with the functions of a single variable and its derivatives.

Partial differential equations (PDEs) are equations that involve partial derivatives of functions of multiple variables. Linear Differential Equation: If the dependent variable and its derivatives occur in the differential equation linearly, then it is called a linear differential equation.

Nonlinear Differential Equation: A differential equation is nonlinear if it is not a linear equation.

Homogeneous Differential Equation: A homogeneous equation is a type of differential equation in which all the terms have the same degree of the dependent variable and its derivatives. Non-Homogeneous Differential Equation: A differential equation is non-homogeneous if it is not a homogeneous equation.

\(The differential equation dx2 d2y/dx2 - 6dy/dx + 13y = 0\) given is the Ordinary Linear Homogeneous Differential Equation of the Second Order.

Therefore the order of the given Differential Equation is 2. y=e3xcos(2x) can be verified as a solution to the given differential equation dx2 d2y/dx2 - 6dy/dx + 13y = 0 as follows: Given, y = e3xcos(2x)Let us differentiate y twice:dy/dx = 3e3xcos(2x) - 2e3xsin(2x)And, d2y/dx2 = 9e3xcos(2x) - 12e3xsin(2x) - 12e3xsin(2x) - 4e3xcos(2x)

\(Hence the differential equation can be verified by substituting y=e3xcos(2x)\)

\(Putting the values we getdx2 d2y/dx2 = -13e3xcos(2x)\) and \(-6dy/dx = -6(3e3xcos(2x) - 2e3xsin(2x))= -18e3xcos(2x) + 12e3xsin(2x)And 13y = 13e3xcos(2x)\)

\(By substituting the values, we getdx2 d2y/dx2 - 6dy/dx + 13y = -13e3xcos(2x) + 18e3xcos(2x) - 12e3xsin(2x) + 13e3xcos(2x)=0\)

Therefore the indicated function y=e3xcos(2x) is a solution to the given differential equation.

To know more about the word substituting visits :

https://brainly.com/question/27759377

#SPJ11

The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

To know more about critical points, visit:

https://brainly.com/question/33412909

#SPJ11

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

The term "average" in statistics refers to a measure that summarizes the central tendency of a data set. Another term that could be used in place of "average" is "mean.  Average plays a crucial role in statistics as it provides a summary measure of central tendency.

The term "average" in statistics refers to a measure that represents the central tendency of a data set. It is commonly used to summarize and describe the typical value or typical level of a particular variable within a population or sample.

The role of the term "average" is to provide a single value that represents the collective information of the data set. It helps in simplifying and summarizing complex data by providing a measure that is representative of the entire distribution. It allows for comparisons, analysis, and inference based on a single value rather than considering each individual data point.

However, it's important to note that depending on the context and the nature of the data, alternative measures of central tendency may be more appropriate than the "average." For example, if the data set contains outliers or is heavily skewed, the median or mode might be better indicators of the typical value.

In summary, the term "average" plays a crucial role in statistics as it provides a summary measure of central tendency. However, it is important to consider the specific characteristics of the data set and potentially use alternative measures when necessary.

For more questions on statistics

https://brainly.com/question/15525560

#SPJ8

The volume of the cylindrical fish tank is given by the equation

V = 282.74 inches³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the radius of the cylindrical fish tank r = 3 inches

The height of the cylindrical fish tank h = 10 inches

The volume of fish tank = πr²h

Substituting the values in the equation , we get

Volume of Cylindrical fish tank V = π x ( 3 )² x 10

On simplifying the equation , we get

Volume of Cylindrical fish tank V = 90π inches ³

Volume of Cylindrical fish tank V = 282.74 inches³

Therefore , the value of V is 282.74 inches³

Hence , the volume of cylindrical fish tank is 282.74 inches³

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ2

Answer:

apple music

depending on how much spotify is monthly. Apple music would be signficantly cheaper in the long run and they both offer the same things.

Answer:

x = 0.75 and or x = -0.38

Step-by-step explanation:

If the minus sign after the x was on purpose or if you accidentally put the addition sign after the minus or the other way around basically I have no idea if the solution I provided is correct so here's the solution to both possible equations you might have meant to type instead (and if this was intentional then awesome):

1. 2x - 6x = -3 and 2. 2x + 6x = -3

Let's do 1. first!

\(2x-6x=-3\)

Simplify 2x-6x to -4x

\(-4x=-3\)

Divide each side by -4

\(x=\frac{-3}{-4}\)

And as you know, two negatives equal/make a positive

\(x=\frac{3}{4}\) or \(x=0.75\)

Now! Let's solve for 2.

\(2x+6x=-3\)

Simplify 2x+6x to 8x

\(8x=-3\\\)

Divide both sides by 8

\(x=\frac{-3}{8}\)

\(x=-\frac{3}{8}\) or \(x=-0.375\)

The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are  6 and -10.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point Q( -1, a )

Point P( 3, -2 )

To find the numerical value of a, plug the given coordinates into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

Square both sides

( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²

( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²

( 4√5 )² = ( 4 )² + ( -2 - a )²

80 = 16 + ( -2 - a )²

80 - 16 = ( -2 - a )²

64 = ( -2 - a )²

( -2 - a )² = 64

Expand the parenthesis

( -2 - a )( -2 - a ) = 64

a² + 4a + 4 = 64

a² + 4a + 4 - 64 = 0

a² + 4a - 60 = 0

solve for a

( a - 6 )( a + 10 ) = 0

a - 6 = 0, a + 10 = 0

a = 6, a = -10

Therefore, the values of a are 6 and -10.

Learn more about the distance formula here: brainly.com/question/24509115

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

$4.20 Per month = $4.2/1month

Step-by-step explanation:

1 year = 12 months

Proportions:

12 months ⇒ $48.24

1 month ⇒ $P

P = 48.24*1/12

P = $4.2

a. The relation R defined on the set S = {1, 2, 3, ..., 18, 19} is an equivalence relation. It is reflexive, symmetric, and transitive, b. The equivalence class of 1, denoted [1], consists of the perfect squares in S: {1, 4, 9, 16}, c. The equivalence classes with more than one element are [1], [2], [3], ..., [18], and [19]. Each equivalence class represents a set of numbers that are squares of integers.

a. To show that the relation R is an equivalence relation, we need to demonstrate that it is reflexive, symmetric, and transitive.

i. Reflexive: For R to be reflexive, every element in S must be related to itself. Since the square of any integer is still an integer, xRx holds for all x in S, satisfying reflexivity.

ii. Symmetric: For R to be symmetric, if xRy holds, then yRx must also hold. Since multiplication is commutative, if xy is a square of an integer, then yx is also a square of an integer. Hence, R is symmetric.

iii. Transitive: For R to be transitive, if xRy and yRz hold, then xRz must also hold. Since the product of two squares of integers is itself a square of an integer, xz is also a square of an integer. Thus, R is transitive.

b. To find the equivalence class of 1, denoted [1], we determine all elements in S that are related to 1 under R. In this case, [1] consists of the perfect squares in S: {1, 4, 9, 16}.

c. The equivalence classes with more than one element are [1], [2], [3], ..., [18], and [19]. Each equivalence class represents a set of numbers that are squares of integers. The equivalence class [1] includes all perfect squares in S, while the other equivalence classes consist of a single element, which are non-square integers.

To know more about equivalence relation, click here: brainly.com/question/30956755

#SPJ11

Answer:

2,000,000

Step-by-step explanation:

If you have a right triangle, then you have 2 legs and 1 hypotenuse. The hypotenuse is the longest side across from the 90 degree angle. Pythagoras came up with the theorem for right triangles that states that the sum of the squares of the 2 legs is equal to the hypotenuse squared.

Answer:

1. A

2. D

Step-by-step explanation

You can see in the first one it continuously goes up and in the second one it continuously goes down.

Answer:

x = -16

Step-by-step explanation:

\(7(x-5) =9x-3 \\7x -35 = 9x - 3\\3- 35 = 9x - 7x\\-32 = 2x\\x = \frac{-32}{2}\\\huge \red{\boxed{x = -16}}\)

Answer:

x = -16

Step-by-step explanation:

We are presented with the equation 7( x - 5 ) = 9x - 3 and we are asked to find the value of x. The first thing to do with equations with brackets is expand them out to make solving the equation easier. Then you want to collect all the 'x' terms to one side and all the numerical values to the other so we can make solving the equation easier.

→ 7( x - 5 ) = 9x - 3

⇒ Expand out the brackets

→ 7x - 35 = 9x - 3

⇒ Minus 9x from both sides to collect the 'x' terms

→ -2x - 35 = -3

⇒ Add -35 to both sides to isolate -2x

→ -2x = 32

⇒ Divide both sides by -2 to isolate x

→ x = -16

Answer:

C = -D - B

Step-by-step explanation:

Step 1: Write out equation

B + C = -D

Step 2: Subtract B on both sides

C = -D - B

Answer:

3 acute angles with different measures and 1 right angle and 2 acute angles with same measures

Answer:

1 1/2

Step-by-step explanation:

1+1= 2.

1/2+1/2= 1.

So add those up and you get 3. Please mark me brainliest?

Answer:

78 nickels and 22 dimes

Step-by-step explanation:

Nickels = n, Dimes = d

Number of coins = 100

Total sum in the piggy bank = $6.60

Consider the first equation in the second:

Answer: nickels 78 and dimes 22

Answer:

78 nikes and dimes 22

solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11

Step-by-step explanation:

Answer:

A,C,D and F i think

Step-by-step explanation:

I plotted them on mines

Answer:

Step-by-step explanation:

-8(z+2)-15+4z

First solve bracket

-8z-16-15+4z

Arrange them

-8z+4z-16-15

Answer: —4z - 31

Step-by-step explanation:

1. Distribute:

-8(z + 2) -15 + 4z

—8z — 16 — 15 + 4z

2. Subtract:

—8z — 16 — 15 + 4z

—8z — 31 + 4z

3. Combine like terms:

—8z — 31 + 4z

—4z - 31

So your answer will be —4z - 31

(a) An example of a matrix A for which the number of solutions to Ax = b is 0 or 1, depending on b, is a 2x2 matrix with either a nonzero determinant or a zero determinant and a nonzero nullspace.

(b) An example of a matrix A for which the number of solutions to Ax = b is ∞, regardless of b, is a matrix with a zero determinant and a nonzero nullspace.

(c) An example of a matrix A for which the number of solutions to Ax = b is 0 or ∞, depending on b, is a 2x2 matrix with a zero determinant and a nonzero nullspace.

(d) An example of a matrix A for which the number of solutions to Ax = b is 1, regardless of b, is a matrix with a nonzero determinant and a nullspace of zero.

If the determinant of A is nonzero, then there is only one solution to Ax = b, regardless of b.

This type of matrix is known as a singular matrix. The nullspace of such a matrix is nonempty, and since any vector in the nullspace is a solution to Ax = b, there are infinitely many solutions.

If the right hand side of the equation b is orthogonal to the nullspace of A, then the equation Ax = b has no solutions. However, if b lies in the nullspace of A, then the equation Ax = b has infinitely many solutions.

A matrix A for which solutions to Ax = b is 1, regardless of b, is a matrix with a nonzero and a nullspace of zero. This type of matrix is known as a nonsingular matrix, and in this case there is only one solution to Ax = b, regardless of the value of b.

know more about matrix here

https://brainly.com/question/28180105#

#SPJ11

Answer:

A

Step-by-step explanation:

The slope is

\(\frac{3-2}{4-2}=\frac{1}{2}\)

Substituting into point-slope form,

\(y-3=\frac{1}{2}(x-4) \\ \\ y-3=\frac{1}{2}x-2 \\ \\ y=\frac{1}{2}x+1\)

Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

<95141404393>

The graph the represents the function is graph 3.

A graph is a visual representation of data that conveys information about the relationships between variables in mathematics and statistics. It consists of a set of points, lines, curves, and other geometric structures. Graphs are frequently used to demonstrate patterns and trends in the data as well as to provide numerical data in a more intelligible and accessible format.

There are many different kinds of graphs, including pie charts, histograms, scatter plots, bar graphs, and line graphs. Different sorts of data are represented by several types of graphs, each of which has its own special characteristics.

For the given function y=-(x+1)² - 3 we observe that the parabola has negative values.

Also the x intercept us at the point:

y = - (0 + 1)² - 3

y = -1 - 3 = -4

Now for x = -1 we have:

y = - (-1 + 1)² - 3

y = - 0 - 3 = -3

The graph that satisfies this condition is the third graph.

Hence, the graph the represents the function is graph 3.

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ1