pls, help me!!!
and can you show how you got to answer?
Kevin is 6 years older than Timothy. 4 years ago, Kevin was twice as old as Timothy. Find their present ages.

Answer:

y = - 9x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = \(\frac{-31-50}{5-(-4)}\) = \(\frac{-81}{5+4}\) = \(\frac{-81}{9}\) = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

Answer:

Step-by-step explanation:

Given

Find a₁

Use the nth term equation of AP

Apply to the given case and solve for a₁

Answer:

\(a_1=4\)

Step-by-step explanation:

Arithmetic sequence

General form of an arithmetic sequence: \(a_n=a+(n-1)d\)

where:

Given:

Therefore:

\(\implies a_7=-2\)

\(\implies a+(7-1)(-1)=-2\)

\(\implies a-6=-2\)

\(\implies a=4\)

Therefore:

\(\implies a_1=4\)

Answer:

i believe their proportional

Step-by-step explanation:

cause they have a linear function

An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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The correct answer is 14 because distance from center of dilation to point on pre-image is 14 times the distance from center of dilation to corresponding point on image

We can solve this problem using the formula of the scale factor of dilation which is given below:

Scale factor of dilation = (image distance)/(pre-image distance)

In the above formula, the image and pre-image distances are measured from the center of dilation.

Let us assume that the scale factor is x.

The vertices of the two triangles are labeled as follows:

Pre-image triangle vertices: A(-2,2), B(-1,3), and C(-3,3)

Image triangle vertices: A′(10,-14), B′(6,-10), and C′(14,-10)

Now, we can calculate the image and pre-image distances using the distance formula and the Pythagorean theorem.

Pre-image distance between A(-2,2) and B(-1,3) is

AB = √[(3 - 2)^2 + (-1 + 2)^2]

= √2

Pre-image distance between A(-2,2) and C(-3,3) is

AC = √[(3 - 2)^2 + (-3 + 2)^2]

= √2

Pre-image distance between B(-1,3) and C(-3,3) is

BC = √[(3 - 3)^2 + (-1 + 3)^2]

= 2

Pre-image perimeter of the triangle ABC is

P₁ = AB + AC + BC

= √2 + √2 + 2

= 2√2 + 2

The image distances are measured between the center of dilation (1,-1) and the vertices of the image triangle.

We can calculate the image distance between two points (x1,y1) and (x2,y2) using the formula below:

Image distance between (x1,y1) and (x2,y2) = x2 - x1 or y2 - y1

Let us calculate the image distances between the center of dilation and the vertices of the image triangle.Image distance between (1,-1) and A′(10,-14) is

10 - 1 = 9

Image distance between (1,-1) and B′(6,-10) is

6 - 1 = 5

Image distance between (1,-1) and C′(14,-10) is

14 - 1 = 13

Image perimeter of the triangle A′B′C′ is

P₂ = A′B′ + B′C′ + C′A′

=  √(9² + 13²) + √(5² + 9²) + √(13² + 5²)

= 39.25 + 10.3 + 14.42

≈ 64.97

Scale factor of dilation = (image distance)/(pre-image distance)

= P₂/P₁

= 64.97/(2√2 + 2)

≈ 14.

Hence, the correct option is 14.

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Her dexterity improved due to Increased myelination of the central nervous system.

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A reflection across the y-axis.

A translation transformation rule describes how to move an object in the plane without changing its shape, size, or orientation. A reflection transformation rule describes how to flip an object across a line or plane. A scaling transformation rule describes how to change the size of an object by multiplying its coordinates by a scalar factor. A rotation transformation rule describes how to rotate an object around a fixed point by a certain angle.

From the graph, we can see,

The coordinates of the figure A are (-2, 0), (-2, 3) and (-5, 2)

The coordinates of the figure A' are (2, 0), (2, 3) and (5, 2)

The reflection across the y-axis, according to the rule is: \((x, y)\) → \((-x, y)\)

We can see, the y-coordinates stay the same values, while the x-coordinates will have the opposite values.

Therefore, the reflection across the y-axis.

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The angle of inclination of the Earth's axis with its orbital plane is approximately 23.5 degrees.

The Earth's axis of rotation is an imaginary line that runs through the North and South Poles. This axis is tilted with respect to the plane of the Earth's orbit around the Sun. The angle of inclination between the Earth's axis and its orbital plane is known as the axial tilt or obliquity of the Earth. Currently, this tilt is approximately 23.5 degrees.

The axial tilt of the Earth is responsible for the changing seasons experienced in different parts of the world throughout the year. As the Earth orbits the Sun, different parts of the planet receive varying amounts of sunlight. During the summer solstice, which occurs around June 21st in the Northern Hemisphere, the North Pole is tilted towards the Sun, resulting in longer days and warmer temperatures.

Conversely, during the winter solstice around December 21st, the North Pole is tilted away from the Sun, leading to shorter days and colder temperatures. The axial tilt also affects the distribution of sunlight, which influences climate patterns and weather conditions on Earth.

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The Area of the gable is 0.9 m²

Prudence's statement is not valid.

1. Convert 500 cm to meters:

Since 1 meter is equal to 100 centimeters,

So, 500 cm ÷ 100 = 5 meters

2. The formula for the area of a rectangle is Area = Length x Width.

Given the dimensions:

Length = 1.2 m

Width = 1.4 m

Area of one window = 1.2 m x 1.4 m = 1.68 m²

3. Calculate the area of the vent:

The formula for the area of a circle is Area = π x r².

Radius = (2.6 m) / 2 = 1.3 m

Area of the vent = 3.142 x (1.3 m)² ≈ 5.309 m²

4. Length = 1.1 m

Width = 1.6 m

Area of the rectangular part of the wall = 1.1 m x 1.6 m

= 1.76 m²

5. Calculate the area of the gable:

Given the dimensions:

Base = 0.6 m

Height = 1.8 m

Area of the gable = 0.5 m x 1.8 m = 0.9 m²

Prudence states that the area of the wall that must be painted is 14.42 m².

So, Area of the rectangular part of the wall + Area of the gable

= 1.76 m² + 0.9 m² = 2.66 m²

Therefore, Prudence's statement is not valid.

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Solution

Given that the Perimeter is: 340 yards. Lenght is 91 yards

Since P = 2(L + W)

where L is the Length

W is the width

=> 340 = 2(91 + W)

=> 340 = 182 + 2W

=> 158 = 2W

Dividing both sides by 2

=> W = 79

Hence, the width is 79 yards

Answer: it would be 79yards

Step-by-step explanation: 91•2=182

340-182=158

158/2=79yards

False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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For problem 1, (a) F′(x) = ∫0 u² cos(u) du, (b) F′(x) = x√(x² - 1), (c) 6∫3 L′(t) dt represents the total change in horn length between t = 3 and t = 6. (d)

The units of the definite integral are the units of the integrand (in this case, cm/year) multiplied by the units of the variable of integration (in this case, years), so the units of r(t) (cm/year) and t (years) are reflected in the units of the definite integral.

In (c), the integral represents the total increase in horn length between t=3 and t=6, which can also be expressed as the change in L(t) between these values.

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Answer:

a

Step-by-step explanation:

Answer:

\(\frac{7}{16}\)

Step-by-step explanation:

=> \(\frac{13}{16}-\frac{3}{8}\)

LCM = 16

=> \(\frac{13-6}{16}\)

=> \(\frac{7}{16}\)

Answer:

7/16

Step-by-step explanation:

13/16 - 3/8

Lowest common multiple is 16.

= 13/16 - 6/16

Subtract the fractions.

= (13-6)/16

= 7/16

Answer:

I'm not sure if its A or C but C sounds like it could be the right answer

Step-by-step explanation:

Answer: Planting vegations near riverbanks

Step-by-step explanation:

because everything else is harmful to the earth .-.

Answer:

Sale Price = $36

Step-by-step explanation:

To find the sale price, you need to find what 10% of the original price is. 10% of $45 is $4.50. Now we need to find what 20% is, 20% is double 10% so we multiply the answer we got by 2. This equals to $9. The question is asking for the sale price, to find it you have to subtract $9 (the discount) from $45 (regular price). The answer you should get is $36.

Equation:
$45 ÷ 10 = $4.50
$4.50 × 2 = $9
$45 - $9 = $36

The rank of matrix A is 2, and a basis for its column space is given by the vectors [1; 0; 1] and [1; 1; 0].

To find the rank and a basis for the column space of matrix A, we can perform row reduction (Gaussian elimination) on the matrix and analyze the resulting row-echelon form.

Given matrix A = [1 1 1; 0 1 3; 1 0 -2], we can start by performing row reduction:

1. Swap rows R1 and R3: [1 0 -2; 0 1 3; 1 1 1]

2. Subtract R1 from R3: [1 0 -2; 0 1 3; 0 1 3]

3. Subtract R2 from R3: [1 0 -2; 0 1 3; 0 0 0]

The resulting row-echelon form shows that the last row consists of all zeros. This indicates that the rank of matrix A is 2, as there are only 2 nonzero rows.

To find a basis for the column space of A, we can select the corresponding columns of the original matrix A that correspond to the pivot columns in the row-echelon form.

In this case, the first and second columns (corresponding to the pivot columns) form a basis for the column space of A. Therefore, a basis for the column space of A is:

Basis = { [1; 0; 1], [1; 1; 0] }

These two vectors are linearly independent and span the column space of matrix A.

In summary, the rank of matrix A is 2, and a basis for its column space is given by the vectors [1; 0; 1] and [1; 1; 0].

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The secοnd statement is wrοng, because the PQRS form is a kite. And the first statement is true because cοnnected it Will be quadrilateral

The statement  the diagonals οf quadrilateral qrst are perpendicular is cοrrect and qrst must be either a square or a rhοmbus is wrong.

Word problems are οften described verbally as instances where a problem exists and one or more questions are pοsed, the solutions to which can be fοund by applying mathematical operations to the numerical information provided in the prοblem statement. Determining whether twο provided statements are equal with respect to a collection of rewritings is known as a word prοblem in computational mathematics.

Here the given qrst quadrilateral is Kite.

We knοw that diagonal of kite bisect each other at 90°.

Then. the qrst quadrilateral diagοnals are perpendicular.

Then secοnd statement is wrοng , because it qrst is kite.

Hence the first statement is cοrrect.

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Answer:

Question 16 = 22

Question 17 = 20 cm²

Step-by-step explanation:

Concepts:

Area of Square = s²

Area of Triangle = bh/2

Diagonals of the square are congruent and bisect each other, which forms a right angle with 90°

Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Question # 16

Step One: Find the total area of two squares

Large square: 5 × 5 = 25

Small square: 2 × 2 = 4

25 + 4 = 29

Step Two: Find the area of the blank triangle

b = 5 + 2 = 7

h = 2

A = bh / 2

A = (7) (2) / 2

A = 14 / 2

A = 7

Step Three: Subtract the area of the blank triangle from the total area

Total area = 29

Area of Square = 7

29 - 7 = 22

-----------------------------------------------------------

Question # 17

Step One: Find the length of PT

Given:

PT = PR + RT [Segment addition postulate]

PT = (4) + (6)

PT = 10 cm

Step Two: Find the length of S to PT perpendicularly

According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Three: Find the area of ΔPST

b = PT = 10 cm

h = S to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Four: Find the length of Q to PT perpendicularly

Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Five: Find the area of ΔPQT

b = PT = 10 cm

h = Q to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Six: Combine area of two triangles to find the total area

Area of ΔPST = 10 cm²

Area of ΔPQT = 10 cm²

10 + 10 = 20 cm²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2x - 6 = 8.

Step-by-step explanation:

To simplify the equation 7x - 6 - 5x = 8, we combine the like terms. Like terms are those that have the same variable raised to the same power. In this equation, the like terms are 7x and -5x because they both have the variable x raised to the power 1.

When we combine 7x and -5x, we subtract the coefficients (7 - 5 = 2) and keep the variable x unchanged. So we have 2x.

The other terms, -6 and 8, are constants and remain as they are in the equation.

Thus, after combining the like terms, we get the simplified equation 2x - 6 = 8.

The probability of getting heads twice in a row at some point during three coin flips is 1/8.

Given info;

Assume that a fair coin has an equal chance of coming up heads or tails.

What is the likelihood that three coin flips will result in two consecutive heads at any point?

There is a three-coin flip. The potential results are;

(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)

1 is the number of successful results.

Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8

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Answer: Addition.

Step-by-step explanation:

The word descended gives you a hint to use subtraction.

The span of {u, v} represents a plane in three-dimensional space. w is not in the span of {u, v}. the span of {u, v, w} is the entire three-dimensional space.

(a) The span of {u, v} represents a plane in three-dimensional space. Geometrically, this plane can be visualized as a flat surface extending infinitely in all directions. It includes all possible vectors that can be obtained by scaling and adding u and v. Any vector lying on this plane can be expressed as a linear combination of u and v.

(b) To determine if w is in the span of {u, v}, we need to check if w can be expressed as a linear combination of u and v. We can write w as follows:

w = a*u + b*v

Solving the system of equations formed by equating corresponding components, we have:

-2 = 3a - 2b

2 = -a + 2b

6 = -2a - 6b

Solving this system, we find that there are no values of a and b that satisfy all three equations simultaneously. Therefore, w is not in the span of {u, v}.

(c) The span of {u, v, w} is the entire three-dimensional space. To justify this, we consider the matrix A whose columns are u, v, and w:

A = [u v w] = [1 3 -2; -1 1 2; -2 -6 6]

We can row-reduce matrix A to its echelon form:

[1 3 -2; -1 1 2; -2 -6 6] -> [1 3 -2; 0 4 0; 0 0 0]

The echelon form shows that the columns of A are linearly independent, and they span the entire three-dimensional space. Therefore, any vector in three-dimensional space can be expressed as a linear combination of u, v, and w, indicating that the span of {u, v, w} is the entire three-dimensional space.

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Answer: I can't find JL and m∠NLK.

Step-by-step explanation:

Answer:

I'm not sure, but maybe try

\((1, -\frac{3}{4} ) or (2,- \frac{3}{2})\)

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<Jayla>

Answer:

The answer to y=3x+5 is Only(2,110

Answer:

54 monthly payments

Step-by-step explanation:

the total number of payments = 4.5 years x 12 payments per year = 54 monthly payments

each monthly payment = loan / PV annuity factor

monthly payment = $19,000 / 45.6139 = $416.54

The measure of location most likely to be influenced by extreme values in the data set is given as follows:

d) Mean

The three measures of location in a data-set are given as follows:

From the three definitions above, we can see that the mean is the only measure that is influenced by all observations, hence it is the most affected by outliers, and thus option d is correct.

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The two different factorizations of 4 into irreducibles in ZI√51 are (1 + √51)(1 - √51) and (2 + √51)(2 - √51). We can establish that 3 + 2√5 and −56 +25√5 are associates in ZI√51 by showing that one can be obtained from the other by multiplication with a unit. If P is a prime in Z such that p=N(y), some a € Z|√5| (so if y = a +b√5, N(y) = (a+b√5)(a − b√5) = a² - 5b²), then p=I mod10. To factorize both 11 and 19 into irreducibles in Z[√5], we use the equations N(2+ √5) =11 and N(4+ √5) =19.

a) Two different factorizations of 4 into irreducibles in ZI√51 are:

4 = (1 + √51)(1 - √51)

4 = (2 + √51)(2 - √51)

Both factorizations are different because they involve different irreducible elements 1.

b) To establish that 3 + 2√5 and −56 +25√5 are associates in ZI√51, we need to show that one can be obtained from the other by multiplication with a unit. Let’s define the unit u = 7 + 4√5. Then:

(3 + 2√5) * u = (-56 +25√5)

Therefore, 3 + 2√5 and −56 +25√5 are associates in ZI√51 2.

c) Suppose P is a prime in Z, and p=N(y), some a € Z|√5| (so if y = a +b√5,N(y) = (a+b√5)(a − b√5) = a² - 5b² prove that p=I 1 mod10.

Let’s assume that p is not equal to I mod10. Then p can be written as either I mod10 or -I mod10. In either case, we can write p as: p = a² - 5b²

where a and b are integers. Since p is prime, it cannot be factored into smaller integers. Therefore, we know that either a or b must be equal to I mod10. Without loss of generality, let’s assume that a is equal to I mod10. Then: a² - 5b² ≡ I mod10

This implies that: a² ≡ b² + I mod10

Since b is an integer, b² is either congruent to I or 0 mod10. Therefore, a² must be congruent to either 6 or 1 mod10. But this contradicts our assumption that a is congruent to I mod10. Therefore, p must be equal to I mod10 3.

d) To determine a particular p++/- 1 mod 10 and a BEZ[√5] with N(B)=+/-p² and use it to deduce that Z[√5] is not a UFD (unique factorization domain), we need more information about the problem.

e) To factorize both 11 and 19 into irreducibles in Z[√5], we can use the following equations:

N(2+ √5) =11

N(4+ √5) =19

Therefore,

(2+ √5)(2- √5) =11

(4+ √5)(4- √5) =19

Both equations give us the irreducible factorization of the numbers 1.

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Approximately 16.28 cm

1) We can sketch out this triangle to better figure out:

2) So now, let's resort to the Pythagorean Relation:

Note that the hypotenuse is always on the left, in the Pythagorean Theorem.