Sum Of 8 Consecutive Numbers Is 124. Find The NumbersGive Breif Detail And Description This Question (2024)

The correct classification of DEF is a right-angled scalene triangle.

We are given three vertices D(-3, 2), E(-2, 3), and F(1, 0).The length of the side DE is √[(3-2)² + (-2-(-3))²] = √2.The length of the side EF is √[(0-3)² + (1-(-2))²] = 3√2.The length of the side FD is √[(2-0)² + (-3-1)²] = 2√5.The lengths of all the sides of the triangle are unequal.Thus, DEF is a scalene triangle.Apply the Pythagorean theorem.We notice that :DE² + EF² = FD²(√2)² + (3√2)² = (2√5)²2 + 18 = 2020 = 20Thus, DEF is also a right-angled triangle.Hence, DEF is a right-angled scalene triangle.

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Using a system of equations, the amounts of each coin that he has is given as follows:

Nickels: 12.Dimes: 27.Quarters: 36.

System of equations

The variables to the system of equations are given as follows:

Variable x: number of nickels.Variable y: number of dimes.Variable z: number of quarters.

Nicholas has nickels, dimes and quarters that total $12.30, hence, considering the value of each coin:

0.05x + 0.1y + 0.25z = 12.30.

The number of dimes is 3 more than twice the number of nickels, hence:

y = 2x + 3.

The number of quarters is three times the number of nickles, hence:

z = 3x.

Then we can solve for x as follows:

0.05x + 0.1y + 0.25z = 12.30.

0.05x + 0.1(2x + 3) + 0.25(3x) = 12.30.

x = 12. (nickels)

Then the other amounts are as follows:

y = 2x + 3 = 27(dimes).z = 3x = 36 (quarters).

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Answer:

y = 12

Step-by-step explanation:

y +2(y-5)=2y+2

y + 2y - 10 = 2y +2

3y - 10 = 2y +2

3y - 2y = 2 + 10

y = 12

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

check

12 + 2 * (12 - 5) = 2 * 12 + 2 (remember PEMDAS)

12 + 24 - 10 = 24 + 2

26 = 26

the answer is good

Highest possible whole number is 3.

What is properties of triangle?

A triangle has three sides, three angles, and three vertices, which are its characteristics. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property. Any two triangle sides can add up to a length that is longer than the third side.

Given Data

Sum of length of any two sides of a triangle is always equal to the third side.

For sides a, b and c

We must have, a + b > c

Sides of triangle are x, x +3 and 10cm

So,

x + x+ 3 > 10

2x > 10 - 3

2x> 7

x > [tex]\frac{7}{2}[/tex]

Possible values of x are 3.5, 3, and so on.

Highest possible whole number is 3.

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To prove ∠1 = ∠3.

What are parallel lines?

Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.

Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal). The parallel lines L1 and L2, which are divided by a transversal, can be seen in the following figure.

Given : [tex]l||k , m||n[/tex]

∠1= ∠2 {alternate interior angles}

∠2=∠3 {corresponding angles are equal because k is parallel to l }

Thus from the above two equations :

∠1 = ∠3

Hence, proved .

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Answer:

(x - 4) (2x - 1)(3x + 2)

Step-by-step explanation:

Dividing:

x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient

6x^3 -24x^2

x^2 - 6x

x^2 - 4x

-2x + 8

-2x + 8

6x^2 + x - 2

= 6x^2 - 3x + 4x - 2

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

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

The length of side BC, |BC|, is 2 units. The correct option is C. 2 units

Calculating length

From the question, we are to determine the length of side BC

First, we will determine the length of side BD

From Pythagorean theorem, we can write that

|BD|² = |AB|² + |AD|²

From the given information,

|AB| = 1

|AD| = 1

Thus,

|BD|² = 1² + 1²

|BD|² = 1 + 1

|BD|² = 2

|BD| = √2

Also, we can write that

|BC|² = |BD|² + |DC|²

From the given information,

|BD| = |DC|

Thus,

|BC|² = (√2)² + (√2)²

|BC|² = 2 + 2

|BC|² = 4

|BC| = √4

|BC| = 2

Hence, side BC is 2 units

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Answer:

7.5 or 7 1/2

Step-by-step explanation:

A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?​

3 × 2 1/2 can be written as 3 × 2.5 = 7.5 or 7 1/2

The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.

These are the x-values when y is equal to zero.

From the graph provided, the values of x when the graph cuts the x-axis are:

[tex]\begin{gathered} x=-3 \\ and \\ x=-1 \end{gathered}[/tex]

Therefore, the coordinates of the x-intercepts are:

[tex](-3,0)\text{ and }(-1,0)[/tex]

The answer type is "Two points".

Answer: The answer is x-y = -2

Answer: 26 degrees

Step-by-step explanation: Count from -15 to 11 or add them up.

The speed of the stream is 6 [tex]km/h[/tex]

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat

downstream = (18 + x) km/h.

The time is taken to go upstream = distance/speed

[tex]24/(18-x)[/tex] hours.

Similarly, the time is taken to go downstream =

[tex]24/(18+x)[/tex] hours.

According to the question,

[tex]24/(18-x) - 24/(18+x) = 1[/tex]

[tex]x^{2} +48x-324=0[/tex]

Using the quadratic formula, we get

[tex]x=\frac{-48+\sqrt{48^{2}+1296 } }{2}[/tex]

x = 6 or -54

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.

Hence the speed of the stream is 6 km/h.

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Answer:

p= -8

Step-by-step explanation:

[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]

The equation of parabola is (x − 3)² = −8(y − 2).

What is parabola?

A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax²+ bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Given:

Vertex = (3, 2)

Directrix, y =4

line of symmetry is the Y value in the vertex = 2

directrix, y= 2 - p

p = -2

and, a= 1/4p = -1/8

and, focus = (3, (2-2)) = (2, 0)

Now, equation of parabola

y= -1/8 (x- 3)² + 2

-8y = (x- 3)² + 2

(x − 3)² = −8(y − 2)

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The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt

What is the domain of a function?

The domain of the function is the set of input values of the graph

What is the range of a function?

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

How to determine the domain and the range?

The domain

On the graph of the function, we can see that:

The x values start from 0 and it extends indefinitely to the right

This means that the domain is x >= 0

The range

On the graph of the function, we can see that:

The y values extend indefinitely on all sides of the coordinate plane

This means that the range is -∝ < y < ∝

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A mathematical connection known as a function is one in which the values of one or more independent variables determine the values of a single dependent variable. Function implies that the independent variable affects the dependent variable (s).

Explain the functions and variables in mathematics? A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

We have seen that functions can be stored in variables, and we shall investigate this further later. In JavaScript, a value called an object is a container for additional data like integers, characters, functions, and other objects.

We can avoid repeatedly writing the same logic or code in a program by using functions. C functions can be called from anywhere in a program and at any number of times. When a large C program is broken up into several functions, we can simply track it.

The answer is -11

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By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

How to get the total number of children in the room?

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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The equation of the line passing through point P (0,1) = y=2x-1

What is Equation of line ?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

Rise over run = (y+1)/(x-0)

=(y+1)/x =-2

slope is (y+1)/(x-0) =(y+1)/x

=-2;

-2x=y+1, or

y+2x =-1, or

y=-2x-1

in the form of the slope intercept

The parallel line with the value of y=-2x+3 has been moved down by 4 units. The point at which this line crossed the y-axis was y=3. Now, with a 4 downshift, it crosses the y-axis at y=1.

Plugging the location (0,1) into the new equation:

y=2x-1 yields

1 = 2(0)-1

to validate the math.

Hence, the Equation of line passing through point P(0,1) is y=2x-1

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Answer: x = 3.3

Step-by-step explanation:

Based on the given conditions, formulate: 60,000 * 25% * x = 50,000

Multiply the monomials: 15000x = 50,000

Divide both sides of the equation by the coefficient of variable: x = 50,000

______

15,000

Cross out the common factor: x 10

3

Round the number: x = 3.3

Answer x = 3.3

The expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given that four students have rewritten the expression with rational exponent in radical form as shown.

As per Sammi's expression: VE

This is an incorrect expression

As per Malik's expression: √7³

This is an incorrect expression

As per Cassie's expression: √x⁵

This is the correct expression

As per Casey's expression: √T

This is an incorrect expression

Thus, the expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

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1. (-6, 8)

(x coordinate, y coordinate)

2. -2

This is the value of f(x) when x=3.

3. 4

When x=4, f(x) = -5.

The researchers use inferential statistics.

Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.

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The percentage of Americans who have diabetes and the reliability of the diagnostic. The percentage of those who do not have diabetes test negative is 56.8%.

Give that,

The percentage of Americans who have diabetes and the reliability of the diagnostic procedures now in use are listed in the table below.

There are 3 rows in a tables and 4 column.

1st row,

Diabetes---test positive---test negative---total

2nd row,

Have diabetes---36.1%---1.9%---38%

3rd row,

Do not have diabetes---5.2%---56.8%---62%

We have to find the percentage of those who do not have diabetes test negative for the disease.

See the 3rd row,

In that the percentage of those who do not have diabetes test negative is 56.8%.

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The zero of a function is the value of x of the point on which the value of y is equal to zero.

You can observe in the graph the such a point is the point (1,0).

Hence, the zero of the function is x = 0

The complement of the event is diamond, club or spade.

The complement of an event means " to not choose the mentioned one" .

That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.

In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.

Thus the complement of the event is diamond, club or spade.

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The estimates are used to construct the estimated regression equation:

ŷ = b0 + b1x.

What is the estimation of the regression function?Regression analysis is typically performed for one of two reasons: to estimate the influence of some explanatory variable on the dependent variable or to predict the value of the dependent variable for individuals for whom some information about the explanatory variables is available. Y = mX + b is the equation for simple linear regression, where X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept. An estimated regression equation is created using these estimates: ŷ = b0 + b1xA straight line is a good approximation to the relationship between y and x on the graph of the estimated regression equation for simple linear regression.

Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.

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Translating the given words into algebraic expression it becomes 2v(w-u) .

In the question ,

the word phrase is given as" double the difference of w and u, and then multiply the result by v "

for translating into algebraic expression , we proceed step by step

step 1 : difference of w and u

we get , (w - u)

step 2 : double the difference of w and u ,

we get , 2(w-u)

step 3 : then multiply the result by v ,

we get , 2(w-u)*v

= 2v(w-u)

Therefore , translating the given words into algebraic expression , the expression is 2v(w-u) .

The given question is incomplete , the complete question is

Translate the following word phrase into an algebraic expression , "double the difference of w and u, then multiply the result by v "

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Using the definition of the Laplace transform:

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]

Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,

[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]

or equivalently as

[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]

Then the Laplace transform is

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]

and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.

This is equivalent to the convolution property of the Laplace transform,

[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]

where

[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]

In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].

To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:

[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],

where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].

In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:

[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].

Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:

[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].

Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.