A dealer gained a 10% profit by selling an article for Birr 330.00. what was original price of the article​

Answer:

x = 2

Step-by-step explanation:

The triangle shown in the image is a right triangle.

a√2 = √8

a = √4

Remember we said a represents legs, in the image x represents the legs so the answer is:

x = √4 and √4 = 2, therefore the answer is 2.

The complete statement is ∠M = 40°

If the only difference between two triangles is their size (and perhaps the need to rotate or flip one), but not their shape, then they are similar.

In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

If ΔABC and ΔXYZ are similar triangles then

∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z  

Here we have

ΔXYZ and ΔLMN are similar triangles

=> ∠X = ∠L,  ∠Y = ∠M, and  ∠Z = ∠N    

From the given figure,

=> ∠X = ∠L = 25°

=> ∠Y = ∠N = 115°

=> ∠Z = ∠M    

From ΔLMN      

=> ∠L + ∠M + ∠N = 180°  

=> 25° + ∠M +115° = 180°    

=> ∠M = 180°- 115° - 25°  

=> ∠M = 40°    

Therefore,

The complete statement is ∠M = 40°

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The answer is 10 minutes

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2

                                              =15 gallons per day

Thus to fill 150 gallons the time required is 150/15=10 mins

Hence, The answer is 10 minutes

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The equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.

The fundamental form of an equation is the linear equation in standard form. Below is shown the standard form of a linear equation with two variables and more than two variables.

Here, a, b, (A)1, (A)2, (A)3,........ (A)n are referred to as the coefficients, and x, y, or (x)1, (x)2, (x)3,.... represent the variables. Constants are the numbers that appear after the equals to sign.

ax + by = c

A quadratic equation's standard form is a second-degree equation with a variable, coefficients, and constant term. X is a single variable of degree 2 in this situation. A quadratic equation has the following standard form.

ax² + bx + c = 0

We have given that:

[tex]$\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$[/tex]

Lets solve

[tex]$P_0(2,-1)$[/tex]

[tex]$d^2=10^2+6^2$[/tex]

[tex]$r=\frac{d}{2}=5.831$[/tex]

[tex]$r^2=34$[/tex]

[tex]$(x-2)^2+(y+1)^2=34$[/tex]

Thus, the equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.

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The tortoise travelled the maximum distance of 9 m estimated from the time graph journey of a tortoise.

Distance-time graphs demonstrate how a moving object's distance travelled varies over time.

For the stated time graph of the journey of tortoise.

On x axis - time taken.

On y axis - distance covered by the tortoise.

Thus, the maximum distance is covered by the tortoise is 9 m at the time of 3 minutes.

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A system of linear inequalities represented by the graph are;

Inequality 1: y ≤ 3x - 3

Inequality 2: y ≥ ¹/₂x - 3

Inequalities that use < or > symbols are usually plotted with a dashed line that shows us that the line is not included in the region. Meanwhile, Inequalities that use ≤ or ≥ symbols are normally plotted with a solid line that shows us that the line is included in the region.

The general formula of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, the graph that rises to the right side in the first quadrant has;

Slope = (3 - 1)/(3 - 2)

Slope = 3

the y-intercept is at y = -3

Thus, equation is;

y ≤ 3x - 3

Thus, the graph that rises to the left side in the second quadrant has;

Slope = (1 - 0)/(2 - 0)

Slope = 1/2

the y-intercept is at y = 1

Thus, equation is;

y ≥ ¹/₂x - 3

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Therefore , the solution of the given problem of expression comes out to be as a result, we can minimize the radical statement by doing the actions listed below.

the value of an object  variable is represented by collections of numbers, signs, and procedures (like + and).Examples: The equation is 5+7. 3 x/2 is an alternative formula. An expression lacks the equals symbol.

Here,

To simplify a radical expression, use the Product Property.

1) Determine the radical's largest factor, which is also the index's precise power. Use that factor to rewrite the radicand as the intersection of two factors.

2) Apply the product rule to the radicals to rewrite them as the outcomes of two additional radicals.

3. Decompose the root of the ideal power.

Therefore, by taking the methods outlined above, we may simplify the radical expression.

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Answer:

Consolidation

Step-by-step explanation:

Maths is a great way to get a job and then you can give it a try for a few days and then again you can give it a try for a few days and then again you can give it a try for a few days

Answer:

Corp donates

Step-by-step explanation:

Consolidation is a great way to get a job and then she can u me a little more about it and let me know if

Answer:

10:15

Step-by-step explanation:

fsd

Answer:

Alexander made $825 in commission last week. If he averaged the same amount each week, he would have made $42,900 in commission in 2011.

Step-by-step explanation:

$7,500 x 0.11 = $825 (Last Week's Commission)

$825 x 52 (weeks in a year) = $42,900 (2011 Commission)

Answer:

30

Step-by-step explanation:

n^2-9n-6

(-3)^2-9(-3)-6

(-3)(-3)+27-6

9+27-6

36-6

30

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{n^2 - 9n - 6}[/tex]

[tex]\mathsf{= -3^2 - 9(-3) - 6}[/tex]

[tex]\mathsf{= -3(-3) - 9(-3) - 6}[/tex]

[tex]\mathsf{= -9 - (-27) - 6}[/tex]

[tex]\mathsf{= -9 + 27 - 6}[/tex]

[tex]\mathsf{= 18 - 6}[/tex]

[tex]\mathsf{= 12}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The solution of the expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ [tex]\frac{5^{6x + 5} }{125^{3x - 1} } = 5^{-5x + 2}[/tex]

Now, Solve the equation by rule of exponent as;

⇒ [tex]\frac{5^{6x + 5} }{5^{5 (3x - 1)} } = 5^{-5x + 2}[/tex]

⇒ [tex]\frac{5^{6x + 5} }{5^{15x - 5} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5} } * {5^{- (15x - 5)} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5} } * {5^{-15x + 5} } = 5^{-5x + 2}[/tex]

⇒ [tex]{5^{6x + 5- 15 x+ 5} }= 5^{-5x + 2}[/tex]

⇒ [tex]{5^{-9x + 10} } = 5^{-5x + 2}[/tex]

By comparing, we get;

⇒ - 9x + 10 = - 5x + 2

⇒ 10 - 2 = 9x - 5x

⇒ 8 = 4x

⇒ x = 8/4

⇒ x = 2

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For the students collecting the data, it would be very difficult to select a random sample from this population.

The term Simple random sample, also known as an SRS, which is also a subset of people chosen at random from a larger group of people, all with the probability which is same. In this method samples are chosen at random. Each and every subset of k people in SRS has the equal opportunity of getting selected for the sample just like some other subset of k people.

An objective sampling strategy is a straightforward random sample. Simple random sampling is the most basic category of sampling that can be used in combination with other, more sophisticated sampling techniques.

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Answer:113.1 square feet

Step-by-step explanation:

The value of the $110 annuity given annual compounding is $9983.338.

The value of the annuity can be determining using this formula: amount deposited x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

n = number of years

r = interest rate

here, we have,

Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years

now,

r=4.5%/2

 =0.0225

n= 25*2 = 50

using the formula, we get,

the value of the annuity =$9983.338

hence, The value of the $110 annuity given annual compounding is $9983.338.

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Therefore , the solution of the given problem of triangle comes out to be triangle FUN and CAR is congruent thus it is proved that  m∠HAT = 50°

A triangle is a polygon since it has three parts and three vertices. It is a fundamental geometric figure. A triangle with the corners A, B, & C is referred to as triangle ABC. A single planar and triangle are found in geometric shapes when four elements are not collinear. Due of its three sides and top right corner, triangles are classified as polygons.

Here.

Triangle FUN is congruent with CAR , hence

then,

∠F equals ∠C

∠U is equivalent to ∠A.

∠N  equals ∠ R

and,

FN is equivalent to line CR

NU  is identical to line RA

UF  is equivalent to line AC

Cpct was used to resolve this.

congruent triangle's matching triangle segments

Therefore , the solution of the given problem of triangle comes out to be FUN is congruent with CAR .

For

m∠HAT = 50°

Thus triangle FUN and CAR is congruent thus it is proved that

m∠HAT = 50°

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Point A has coordinates (x1, y1). The x-coordinate, x1, is the horizontal distance from the origin, while the y-coordinate, y1, is the vertical distance from the origin.

Coordinates in math refer to a pair of numbers that indicate the position of a point on a two-dimensional graph or in a three-dimensional space. The two numbers are usually referred to as the x-coordinate (or abscissa) and the y-coordinate (or ordinate). In three-dimensional space, the third number is referred to as the z-coordinate (or applicate). A point located at (3, 4) on a two-dimensional graph would be located 3 units along the x-axis and 4 units along the y-axis. Similarly, a point located at (3, 4, 5) in three-dimensional space would be located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.

Both coordinates indicate the exact location of Point A in a coordinate system. For example, if Point A is located at (2, 4), it means that the x-coordinate of Point A is 2, which is 2 units away from the origin in a horizontal direction, and the y-coordinate of Point A is 4, which is 4 units away from the origin in a vertical direction. The origin is usually located at (0, 0) in a coordinate system.

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The required, complete truth table has been shown, where (P→ Q) and (¬Q → ¬P) are logically equivalent.

A truth table is a table used in logic and mathematics to show the truth or falsehood of propositional statements or logical expressions. It lists all the possible combinations of the truth values of the variables in the expression and the resulting truth value of the entire expression for each combination.

Here,
Using the fact to construct a truth table,
For the implication P → Q only T → F = F or else T,
And ¬T = F, ¬F = T

The complete table has been shown in the image attached below,

In the table column for P → Q and (¬Q → ¬P) have the same truth values.

Thus, (P→ Q) and (¬Q → ¬P) are logically equivalent.

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The final velocity of the car is given as follows:

25 m/s.

The velocity function is a linear function, modeled as follows:

v(t) = v(0) + at.

In which:

The parameter values for this problem are given as follows:

v(0) = 5, a = 2.

Hence the velocity function is given as follows:

v(t) = 5 + 2t.

At a time of 10 seconds, the velocity is given as follows:

v(10) = 5 + 2(10)

v(10) = 25 m/s.

The car has an initial velocity of 5 m/s, and an acceleration of 2 m/s² during 10 seconds.

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Answer:

Height = 557.1 to 1dp.

Step-by-step explanation:

Surface area of the given prism

= 2(12*3 + 12*10 + 10*3)

= 7272

The new prism must have surface are 2*7272 = 14544.

Let the new height be h, then:

2(3h + 10h + 30) = 14544

6h + 20h = 14544 - 60

26h = 14484

h = 14484/26

  = 557.1 cm.

The standard error of the estimate measures the vertical spread of the data points around the regression line.

The standard error of the estimate, a measurement of the average deviation of errors, is the difference between the y-values predicted by the multiple regression model and the y-values in the sample. This illustrates the precision of the regression model as well as the range of variation surrounding the estimated regression line.

The standard error of the estimate can be used to produce a confidence interval for the actual regression coefficient. The standard error is calculated by multiplying the standard deviation by the square root of the sample size. The standard deviation of the errors/residuals is the standard error of the estimate for the regression model.

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Based on the scatter plot shown, the correlation coefficient that best represents the scatter plot is r = 0.98.

Several dots are placed on a horizontal and vertical axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences called variables.

The scatter plot shown shows a highly positive correlation between the data. Hence, the value of the correlation coefficient is very nearly 1.

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Question 23

Using the alternate interior angles theorem, [tex]m\angle BCA=20^{\circ}[/tex].

Question 24

[tex]\overline{AD} \cong \overline{DC}[/tex] by the definition of a rhombus. This means that [tex]\triangle ADC[/tex] is isosceles. It follows that [tex]m\angle ACD=20^{\circ}[/tex]. Using the angle sum of a triangle, [tex]m\angle CDA=140^{\circ}[/tex].

Question 25

All rhombi are parallelograms, and diagonals of parallelograms bisect each other. This means that [tex]AC=2(4)=8[/tex].

There were 10 hours of daylight on that particular day

Total number of hours in a day= 24

If the ratio of daylight to darkness is 5:7, the number of hours of daylight is 5x and that of darkness is 7x

Then, 5x + 7x= 24

=> 12x = 24

=> x= 2

Thus, 5x= 5×2= 10

Therefore, there were 10 hours of daylight on that particular day

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Answer:

using the knowledge from the chapter similarity we can find how the two triangles are similar

Step-by-step explanation:

Triangle ABC and DEF

A B=DE

AC=DF

BC=EF

AB/DE=AC/DF=BC=EF

Answer:

22,256

Step-by-step explanation:

If the speedometer reading is 60, your actual speed is miles. miles per hour. Since the value of k = 1.1128 for the two tires in comparison, 1.1128 (20,000) = 22,256 miles (actual) and 1.1128 (60) = 66.768 miles per hour (actual). The percent error is 11.28% for both readings.