Express the given function

Step-by-step explanation:

15. \(f(2+h) = (2 + h)^2 - (2 +h) + 1\)

\(\:\:\:\:\:\:\:= 3 + 3h + h^2\)

\(f(2) = (2)^2 - (2) + 1 = 3\)

Therefore,

\(\dfrac{f(2+h) - f(2)}{h} = \dfrac{3h + h^2}{h}\)

\(\:\:\:\:\:\:\:= 3 + h\)

16. \(f(x + h) = 5(x + h) - (x + h)^2\)

\(\:\:\:\:\:\:\:= 5x + 5h - x^2 - 2hx - h^2\)

Therefore,

\(\dfrac{f(x+h) - f(x)}{h} = \dfrac{5h - 2hx - h^2}{h}\)

\(\:\:\:\:\:\:\:= 5 - 2x - h\)

Answer:

1. D

2. Is A $0.87 for each song

Step-by-step explanation:

12 x $0.87 = $10.44

$10.44 + $5.04 = $15.48

I hope this helped you

The sample space is (R, G, P, Y).(OB)

What is sample space?

A sample space is a collection  of possible outcomes of a random experiment. The sample space is represented by the symbol, “S”.  A sample space may contain a  finite number of outcomes which depends on the experiment.

You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1

yellow (Y).

So here is 4 sections

Red(R), Green (G), Purple (P), Yellow(Y)

So there are 4 sections in sample space

The sample space for one spin of the spinner is  (R, G, P, Y).

Hence, the sample space is (R, G, P, Y).

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A linearly independent set that generates the subspace of diagonal matrix in M2x2(F) is {[1,0;0,0], [0,0;0,1]}.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a, b∈F.

A linearly independent set of vectors that generate this subspace is {[1,0;0,0], [0,0;0,1]}. Any diagonal matrix can be written as a linear combination of these two vectors.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a,b∈F. This means that all the diagonal entries in the matrix must be non-zero. To find a linearly independent set that generates this subspace, we can start by considering the simplest form of a diagonal matrix, which is [1,0;0,0]. This vector is linearly independent, as it cannot be expressed as a linear combination of any other vector in the space. Similarly, [0,0;0,1] is also linearly independent, as it can't be expressed as a linear combination of any other vector.

These two vectors form a linearly independent set that generates the subspace of diagonal matrices in M2x2(F). Any diagonal matrix can be written as a linear combination of these two vectors. For example, the matrix [2,0;0,3] can be expressed as 2[1,0;0,0]+3[0,0;0,1]. Thus, this set of vectors is sufficient to generate the entire subspace.

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Answer:

I don't know answer what is

Answer: Part 1: 1/52 Part 2: 15/26 Part 3: 1/26

Step-by-step explanation:

A ace of hearts is only 1 card

a 8 or a diamond a 8 is a 4/52 chance and a diamond is a 26 / 52 chance

26 + 4 = 30

30/52 simplifies to 15/26

A red 7 has a 4/52 chance for a 7 and half of that for a red card so 2/52 then 1/26

Answer:

1. Expression: y = 235x

Answer: 1,175

2. The cost of the shirts is 5 dollars. Alex has 15 dollars in his wallet. He wants to buy 3 shirts. Write an expression that represents this problem.

Step-by-step explanation:

5. 235 per second

5 x 235 = 1,175

Expression: y = 235x

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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On solving the provided question, we can say that  -   sine of x = arcsin 39/74 = 31.8 degrees

The hypotenuse of a right triangle is its longest side, while its "opposite" and "adjacent" sides are those that are across from and next to the same angle, respectively. For the sides of right triangles, we have unique terminology. A right triangle's hypotenuse is always the side that faces away from the right angle.

The hypotenuse of a right triangle is its longest side, while its "opposite" and "adjacent" sides are those that are across from and next to the same angle, respectively. For the sides of right triangles, we have unique terminology. A right triangle's hypotenuse is always the side that faces away from the right angle.

Here the sine of x = ( / (hypotenuse) = 39/74.  Using a calculator with the inverse trig functions built in, we find

arcsine 39/74 = 31.8 degrees

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

Step-by-step explanation:

The answer to your question is the second one 78/9, 45 , and 97

Answer:

1. 1/4

2. -3

3. 3

4. -3/2

5. -2

6. -3/4

Answer:

60 and -60

Hope this helps! :)

Answer:

7:01

29%

Doyan of low

Shiman 1-R-1

Flous 1-1 Gambe 1-4-20

12 dual purpose

Martins 1-2-3 Flores 1-2, 1-3, 14

Gamba 2-1-5

Custand 1-4, 2-1

Conditions " humanitarian groups Salahiel 1-1-1, 1-1-2, 1-2-3 1-R-5, 2-L-2, 2-L-3, 2-14, 2-1-5, 2-RI

Flores 1-30

Munting 1-2-4

Gumbon 1-1-3 CDP 1-1-3

Status oppose ending 742 Montoya 1-1, 1-2, 1-3

federal courts challenge

Gamboa 1-R-2 Custom 1-7

CDP 1-L-36, 1-2-4

de Vogue 1-2-1, 2-1-5, 2-L-6

7 expulsions at boders

root causes textul Amer.

Cop 1-L-34, 1-1-2, 1-R-4

Border Report 1-2

CDP 1-R-2, 1-R-3 Montoya 1-8

Custarda 2-2

=

CLOSE

Hopes this helps :)

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )

A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

Suppose  λ and  μ are 2 distinct values of matrix  A.

For the matrix to be Symmetric,

                 ( Ax,y)=(x,Ay)

 condition needs to be satisfied.

Here, ( x,y) is dot product between vectors  x and  y

                 λ (u,v) = (λu,v)

 where  u,v are eigen vectors for eigen values  λ and  μ

             λ(u,v) = (Au,v)

             λ(u,v) = (u,Av)

             λ(u,v) = μ(u,v)

             λ(u,v) = μ(u,v)

but  λ≠μ

                             ∴ (u,v) = 0.

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The complete question is :

If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.

The included angle of one triangle are congruent to the corresponding parts of the other triangle. Since the sides AD and BE are congruent, as well as the included angle DAB and CBA, then △ADE≅△BCE.

By the Side-Angle-Side (SAS) congruence theorem, if two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent. In this proof, the given statements provide that the sides AE and EB are congruent, as well as the angles DAB and CBA. This means that the two corresponding sides of the triangles △ADE and △BCE are congruent, and the included angles of the triangles are also congruent. Therefore, according to the SAS congruence theorem, the two triangles are congruent, and thus △ADE≅△BCE.

The SAS congruence theorem applies to any two triangles, regardless of the size or shape of the triangles. The congruence of the sides and angles is sufficient to prove that two triangles are congruent. This theorem can be used to prove other theorems, such as the Triangle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees. To prove this theorem, one could use the SAS congruence theorem to show that two right triangles are congruent, and then use the congruent angles to prove that the sum of the angles in a triangle is 180 degrees.

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Answer:

yes

Step-by-step explanation:

the length of the diagonal of the suitcase is 30 in.

pythagorean theorem: a^2+b^2=c^2

(the length times the height=the diagonal)

So, 24^2 + 18^2=something

24^2=576

18^2=324

576+324= 900

square root of 900=30

so, c equals 30

therefore the diagonal =30 , so there's plenty of space to put the umbrella because it's less long than the diagonal

Answer:

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability that a sophomore non-Chemistry major

Out of 92 students, 9 are non-chemistry major sophomores. So

\(P(A) = \frac{9}{92}\)

Then a junior non-Chemistry major are chosen at random.

Now, there are 91 students(1 has been chosen), of which 10 are non-chemistry major juniors. So

\(P(B) = \frac{10}{91}\)

What is the probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random

\(P = P(A)*P(B) = \frac{9}{92}*\frac{10}{91} = \frac{9*10}{92*91} = 0.0108\)

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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In the picture there is a parallel line with the intersection line. ∠5=91° and ∠2=(8x+1)°and x value is 11.

Given that,

In the picture there is a parallel line with the intersection line.

We have to find the x value.

Given ∠5=91° and ∠2=(8x+1)°

We know that if there are 2 parallel line and 1 line is intersecting to the parallel line then the corresponding angles are equal.

∠1=∠5

So, ∠1=91°

Now,

We can write as ∠1+∠2=180° because the ∠1 and ∠2 are on 1 line.

91+8x+1=180

8x+92=180

8x=180-92

8x=88

x=88/8

x=11

Therefore, x value is 11.

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The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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Answer:

0

Step-by-step explanation:

combine the same variables

Answer: Infinite Solution

Step-by-step explanation: 2.5x+0.25=2.5x+0.25, since the equations are equal, any number you plug in will be the same.

The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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