The sum of two numbers is 15. Twice the large
number plus 4 times the smaller number is 24.
Find the large number.

The numeric value of the function f(x) = 3x² + 4x - 2 at x = x + 1 is obtained as follows:

f(x + 1) = 3x² + 10x + 3.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² + 4x - 2

The numeric value at x = x + 1 is found replacing both instances of x by x + 1, hence:

f(x + 1) = 3(x + 1)² + 4(x + 1) - 2

f(x + 1) = 3(x² + 2x + 1) + 4x + 4 - 4

f(x + 1) = 3x² + 6x + 3 + 4x

f(x + 1) = 3x² + 10x + 3.

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The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

Linearity is a property of equations with highest degree of 1. There isn't a single variable in it with an exponent greater than 1. The name "linear equation" comes from the fact that a linear equation always results in a straight line on a graph.

Linear equations in one variable and two variables are common in mathematics.

Two of lines' points on the plane are (1, 0)and (0, 9)

Lets put the value in the slope formula

y₂ - y₁ = m(x₂ - x₁)

9 - 0 = m(0 - 1)

9 = -m

m = -9

As we have the slope of the line lets put one of the values to get slope intercept form

y - y₁ = m(x - x₁)

y - 9 = -9(x - 0)

y = -9x + 9

Thus, The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

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the slope is -4

hope this helps!!

Answer:

the slope is -4

Step-by-step explanation:

The measure of all the angles are given as follows;

<XVR = 125°  [Sum of angle on a straight line]

<RVS = 55° [Angle on a straight line or Opposite Angles]

< WVS = 125° [Opposite Angles]

< RST = 125° [Angle on a straight line] Note that ΔRVS is an equilateral

< RSV = 55° [Equilateral Triangle]

<VSU = 125° [VSU and RST are Opposite angles]

<UST = 55° [Opposite Angles]

<TUS = 54° [Sum of angles in a Triangle.

A straight line's angles add up to 180°. Angles may also be calculated using this information.

Opposite angles are non-adjacent angles created by two intersecting lines, which is also a mathematical truth.

Angles that are opposite each other are congruent (equal in measure). They are also known as vertically opposing angles and are occasionally referred to as vertical ones. Because they are vertically opposing' at the same vertex, the two angles labeled 'a' are equal.

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Answer:1200

Step-by-step explanation:

Answer:

[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]

The balance of the account after 6 years is $175.64 (nearest cent).

Step-by-step explanation:

To write a function that represents the balance y (in dollars) of the investment account after t years, substitute the given values into the compound interest formula.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute these values into the formula:

[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]

[tex]\implies y=120\left(1.016\right)^{4t}[/tex]

To calculate the balance of the account after 6 years, substitute t = 6 into the function:

[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]

[tex]\implies y=120\left(1.016\right)^{24}[/tex]

[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]

[tex]\implies y=175.642753...[/tex]

Therefore, the balance of the account after 6 years is $175.64 (nearest cent).

The values of u and v in the table are directly proportional to each other with a constant k is 3.

When x increases, y increases; when x decreases, y decreases.

The opposite of direct is indirect. When x rises, y falls; when x falls, y rises.

If you said y is directly proportional to x,

it would be y/x=k or y=kx.

Here given that,

u = 0.25, 0.3, 0.1

v = 0.75, 0.9, 0.3

So here v = 3u

That is v = 3 x 0.25

v = 0.75

Hence u and v are directly proportional with a constant k = 3

When v = 2/5

To find u,

v = 3u

2/5 = 3u

u = 2/15

When u = 3/7

Then v = 3 x 3/7

v = 9/7

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The value of m from the given equation is 37.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The given equation is m+6=43

We need to find the value of m from the given equation.

The group of values used to replace the unknowns in an equation to make it true is known as the solution.

To solve given equation:

Transpose 6 to RHS of the equation, we get

m=43-6

Subtract 43 and 6 we get 37

So, m=37

Therefore, the value of m from the given equation is 37.

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Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.

The angle of elevation is defined in mathematics as "the angle created between the horizontal line and the line of sight when an observer looks upwards." It's always higher than the spectator, usually at a greater height. Angles of depression are created when a person looks downward, and they are the polar opposite of angles of elevation. While studying heights and distances in trigonometry, it is crucial to understand the angle of elevation and depression. Angle, horizontal line, and line of sight are the three general terms used to describe the angle of elevation.

To calculate the height of a tree using trigonometry, you would use the tangent function. Specifically, you would use the tangent of the angle of elevation (52° in this case) and the distance from the base of the tree to where you are standing (25 feet in this case).

The formula is:

height = distance * tangent(angle of elevation)

So, the height of the tree is approximately:

25 * tangent(52) = 25 * 1.19 = 29.75 feet

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The transformation that maps the quadrilateral into itself is [-1 0] and [ 0 -1] and the vertices of the quadrilateral is (-3,-4),(2,5),(-2,-5),(3,4)

a. A point symmetry about the origin is a transformation that maps a figure onto itself by reflecting it across the origin. This transformation is known as a central reflection or an isometry, and it is represented by the matrix (with respect to the standard basis)

[-1 0]

[ 0 -1]

b. To find the other two vertices of the quadrilateral, we can apply the transformation to the given vertices.

The transformation maps (2,5) to (-2,-5) and (-3,-4) to (3,4).

So, the other two vertices of the quadrilateral are (-2,-5) and (3,4)

So the quadrilateral will be (-3,-4),(2,5),(-2,-5),(3,4)

Note that a quadrilateral with point symmetry about the origin is called a kite.

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The greatest number of friends Gary can give shells and coins to is 8

friends. Each friend will receive 9 shells and 5 coins.

We have to find the factors of 72

72/ 2 = 36 / 2 = 18/ 2 = 9/ 3 = 3

72 = 2 * 2* 2 * 3

We would find the factors of 40

40 / 2 = 20 / 2 = 10 / 2 = 5

40 = 2 * 2 * 2 * 5

Then we would find the common factors they have

2 * 2 * 2 = 8

This is the number of friends that Gary can have

Then 72 / 8 = 9

40 / 8 = 5

The greatest number of friends Gary can give shells and coins to is 8

friends. Each friend will receive 9 shells and 5 coins.

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Answer:

[tex]\textsf{a)\;\;passes\;through\;$(-2, 18.75)$\;and\;$(1, 1.2)$}[/tex]

     [tex]\textsf{$a$-value:\;\;3 \quad $b$-value: \;\;0.4}[/tex]

     [tex]\textsf{Equation: \quad $y=3 (0.4)^x$}[/tex]

[tex]\textsf{b)\;\;passes\;through\;$(0, 6)$\;and\;$(2, 8.64)$}[/tex]

     [tex]\textsf{$a$-value:\;\;6 \quad $b$-value: \;\;1.2}[/tex]

     [tex]\textsf{Equation: \quad $y=6 (1.2)^x$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute both points into the exponential function formula to create two equations:

Divide the equations to eliminate a, then solve for b:

[tex]\implies \dfrac{18.75}{1.2}=\dfrac{ab^{-2}}{ab}[/tex]

[tex]\implies15.625=\dfrac{b^{-2}}{b}[/tex]

[tex]\implies15.625=b^{-2}b^{-1}[/tex]

[tex]\implies15.625=b^{-3}[/tex]

[tex]\implies15.625=\dfrac{1}{b^{3}}[/tex]

[tex]\implies b^{3}=\dfrac{1}{15.625}[/tex]

[tex]\implies b=0.4[/tex]

Substitute the found value of b into the second equation and solve for b:

[tex]\implies 1.2=0.4a[/tex]

[tex]\implies a=3[/tex]

Therefore, the exponential equation is:

[tex]y=3 (0.4)^x[/tex]

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

Given points:

Substitute point (0, 6) into the exponential function formula and solve for a:

[tex]\implies 6=ab^0[/tex]

[tex]\implies 6=a(1)[/tex]

[tex]\implies a=6[/tex]

Substitute the found value of a and point (2, 8.64) into the exponential function formula and solve for b:

[tex]\implies 8.64=6b^2[/tex]

[tex]\implies b^2=\dfrac{8.64}{6}[/tex]

[tex]\implies b^2=1.44[/tex]

[tex]\implies b=\sqrt{1.44}[/tex]

[tex]\implies b=1.2[/tex]

Therefore, the exponential equation is:

[tex]y=6 (1.2)^x[/tex]

To determine how long it will take for a ball to fall from the top of a building 74 ft tall to ground level, we can use the formula:

t = √(2*d/g)

where t is the time in seconds, d is the distance in feet, and g is the acceleration due to gravity (approximately 32.2 ft/s^2 on Earth).

Plugging in the values:

t = √(2*74 / 32.2)

t ≈ 3.63 seconds

So the ball will take approximately 3.63 seconds to fall to the ground level.

It's important to note that this calculation assumes that there's no air resistance and the ball is dropped vertically. In reality, air resistance and the ball's trajectory would affect the time it takes to fall.

Answer: 0.06 + 0.004

Exploring Base Ten Blocks : Measure 1 x 1 x 1 cm with units of "ones."

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

Our base ten number system is spatially represented by Base Ten Blocks. The four separate concrete representations known as "Base Ten Blocks" are generally used in middle school arithmetic after being introduced in elementary school.

Measure 1 x 1 x 1 cm with units of "ones."

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

When names are given based on shape rather than value, it is possible to rename the pieces as needed. For instance, a class learning decimals can use the flat to represent a unit and then determine the value of the other components.

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Answer:

13.389 = 13.4

Answer:

the answer to the question is 9.9 in the nearest tenth

Quadrilateral  ABCD is a Parallelogram can be proved by many postulates. The most important three Postulates are:-

1. The two opposite side pairs are parallel.

2. The two opposing side pairs are both congruent.

3. One set of opposite sides is parallel and congruent.

In geometry, you'll frequently be required to provide evidence that a particular shape actually exists. For instance, you can be asked to demonstrate that a quadrilateral is a parallelogram after being shown it. Do not forget that a quadrilateral is a flat, four-sided shape. A quadrilateral with two sets of opposing, parallel sides is referred to as a parallelogram.

A quadrilateral ABCD is a Parallelogram

The five approaches to demonstrate that a quadrilateral is a parallelogram will be discussed first, though. You'll employ one of these five methods, depending on the data you've got to work with.

1. Establish the parallelism of the two pairs of opposite sides.

This one is just the opposite of what a parallelogram is. If you can demonstrate that the quadrilateral satisfies the requirements for a parallelogram, then it is one.

2. Establish the congruence of both pairs of opposite sides.

There will always be two opposite pairs of parallel sides in a quadrilateral if both pairs of opposite sides are congruent. They measure similarly when objects are congruent.

3. Establish that one pair of opposing sides is parallel and congruent.

The previous procedure and this one are quite comparable. It simply presents the evidence in a different manner. Actually, four toothpicks will work for this experiment. Try it by aligning two toothpicks in a parallel but opposing direction. Now join these two toothpicks to the other two toothpicks at both ends. You'll see that your second pair of toothpicks will always be parallel, regardless of how you arrange your first set.

Hence, Quadrilateral establish parallelogram.

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A. The range of the sample data is 4 mi/gal.

B. The variance of the sample data is 0.98 mi/gal.

C. The standard deviation of the sample data is 0.99 mi/gal.

D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean (4 mi/gal is less than 2*0.99 mi/gal).

A. To find the range of the sample data, we need to find the difference between the largest and smallest values in the sample. In this case, the largest value is 4 mi/gal and the smallest value is 1 mi/gal. The range is the difference between these two values, which is 4 mi/gal - 1 mi/gal = 3 mi/gal.

B. To find the variance of the sample data, we first need to find the mean of the sample. The mean is calculated by summing all the values in the sample and dividing by the number of values in the sample. In this case, the mean is [tex]\frac{(2+1+2+1+3+3+4+2+2+2+2+2+2+2+2+3+2+2+2+2+2)}{20} = 2.05[/tex].

Next, we need to subtract the mean from each value in the sample, square the result, and divide it by the number of values in the sample. The variance is

[tex][(2-2.05)^2 + (1-2.05)^2 + (2-2.05)^2 + (1-2.05)^2 + (3-2.05)^2 + (3-2.05)^2 + (4-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (3-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2] = 19.6[/tex]

[tex]\frac{19.6}{20} = 0.98 mi/gal.[/tex]

C. To find the standard deviation, we take the square root of the variance. The standard deviation is  [tex]\sqrt{0.98} = 0.99 mi/gal[/tex]

D. The standard deviation measures the amount of variation or dispersion in the data. The standard deviation is used to determine how much the values in a sample differ from the mean. If a value is more than two standard deviations away from the mean, it is considered unusual. In this case, the value of 4 mi/gal is less than 2*0.99 mi/gal = 1.98 mi/gal away from the mean, so it is not considered unusual.

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Answer: This is a linear equation problem. The farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer. We can create two equations to represent this information:

Let x be the number of old packages

x(60) + y(65) = 1550 (long-term-growth supplement)

x(50) + y(45) = 1200 (weed killer)

Now we can use the system of equation to find the number of old and new packages:

x(60) + y(65) = 1550

x(50) + y(45) = 1200

We can use any method of solving system of equations like substitution, elimination or graphing to find the solution.

Example using substitution method:

x(50) + y(45) = 1200

x = (1200 - y(45)) / 50

x(60) + y(65) = 1550

(1200 - y(45)) / 50 * 60 + y(65) = 1550

We can then solve for y and then x by substituting the value of y back into the first equation

y = (1550- (1200 - y(45)) / 50 * 60 ) / 65

Finally, the number of old packages is x and the number of new packages is y.

Step-by-step explanation:

The number of old packages and the number of new packages is 15 and 10 respectively.

Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true.

Given that, the farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer.

We can create two equations to represent this information:

Let,

x = the number of old packages

y = the number of new packages

The system of equations that describes the situation is:

60x + 65y = 1550

12x+13y = 310......(i)

50x + 45y = 1200

10x+9y = 240......(ii)

Solving the equations,

Multiply the eq(i) by 10 and the eq(ii) by 12, and then subtract,

22y = 220

y = 10

Put y = 10 in eq(ii)

10x+90 = 240

10x = 150

x = 15

Hence, the number of old packages and the number of new packages is 15 and 10 respectively.

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Answer: 23,760 feet

Step-by-step explanation:

1 mile = 5280 feet

4.5 * 5280 = 23,760

Answer:

B

Step-by-step explanation:

Each floor, the rent is 3% more than the previous floor, so we multiply by 1.03.

Since we do this 17 times, the answer is [tex]1420 \cdot 1.03^{17}[/tex].

Answer: B

Step-by-step explanation:

You just need to find the formula, replace 17 with variable x and $2347.04 with y and graph. It will give you the right answer.

Answer: $32.60

Step-by-step explanation:

(4)(2.30) + (6)(3.90)

= 32.60

Answer:

for him it send 4 small packages it will cost 9.20

For him to send 6 large packages it will cost 23.40

23.40 + 9.20 = 32.60

Step-by-step explanation:

Formula: Quanity x Cost = Total

After Totals + Costs = Exact Total

If the APR on your credit card is current 31.2%. your monthly periodic rate is: 2.6%.

Using this formula to determine the monthly periodic rate

Monthly periodic rate = APR / 12 months

Where:

APR = Annual percentage rate = 31.2% or 0.312

Let plug in the formula

Monthly periodic rate = 0.312/12

Monthly periodic rate = 0.026 or 2.6%

Therefore we can conclude that the monthly periodic rate is 2.6%.

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The equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7). The solution has been obtained by using the simplification method.

What is simplification?

Simplifying in mathematics refers to the process of working with and understanding an equation in a way that makes it more understandable or transparent. The process of grouping similar terms together so that the problem can no longer be solved further is known as simplification.

We are given -2y + 3/2x + 7/4

In order to find which expression is equivalent to the given, we need to simplify the expressions.

a. -1/2xy+7/4

This is not the same expression as given.

b. 3/2x-2(y+7/2)

⇒ 3/2x - 2y - 7

This is not the same expression as given.

c. -1/4y+3/2 (y+x)

⇒ -1/4y + 3y/2 + 3x/2

This is not the same expression as given.

d. -2y+1/2(3x+7/2)

⇒ -2y + 3x/2 + 7/4

This is the same expression as given.

e. 1/4 (-8y+6x+7)

⇒-2y + 3x/2 + 7/4

This is the same expression as given.

Hence, the equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7).

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Area of given polygon is 39 unit².

As seen above, a polygon is a geometric shape that is described as "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, as well as the line segments joining the points."

A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. We can quickly determine the geometry of a polygon based on how many sides it has.

For the given polygon,

Below is the given image of partition,

We will calculate the area by dividing the figure in different portions,

triangle and rectangle,

Area of triangle = 1/2 × Base × Height

Base = 6 units

Height = 3 units

= 1/2 × 6 × 3 = 9 unit²

Area of rectangle = length × breadth

length = 5 units

breadth = 6 units

Area = 5 × 6 = 30 unit²

Total area = area of triangle + area of rectangle = 9 + 30 = 39 unit²

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The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;

Statements                                                        Reasons

Points A, B, and C form a triangle.        ⇒        Given

Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4             ⇒    alternate interior angle theorem.

m∠1 = m∠4 and m∠3 = m∠5  ⇒    congruent angles have equal measures.

m∠4 + m∠2 + m∠5 = 180°    ⇒    angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180°      ⇒  substitution

In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are congruent when the measure of their angles are equal.

This ultimately implies that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;

m∠1 = m∠4 and m∠3 = m∠5

By applying the Alternate Interior Angles Theorem to triangle ABC and line DE, we have the following:

∠3 ≅ ∠5 and ∠1 ≅ ∠4

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Option B : observed frequencies  are the frequencies obtained from the performance of an experiment for a goodness-of-fit test .    

The frequency, or outcomes, that are gathered during an experiment are known as observed frequencies. This is frequently the collection of data that is documented in mathematics. The distinction between an observed frequency and an expected frequency is described on the display poster. Counts derived from experimental data are known as observed frequencies. In other words, you really take measurements when the data is being collected. For instance, you might roll a die ten times and then tally the number of times each number appears. Following the experiment, the count is made. The observed frequencies are these numbers, and the sign for an observed frequency is O. There are k entries in the table. There are n total observed frequencies. Calculating predicted frequencies involves multiplying the probability.

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