How long is the hypotenuse of a right triangle 24 square inches in area and with one leg 6 inches long? A. 24 inches B. 18 inches C. 12 inches D. 10 inches​

The angles which makes 45° and 90° in square are shown below.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

ABCD is a square,

The angles which are 45°,

∠ CAD, ∠ CAB, ∠ DBA, ∠ DBC, ∠ ACB, ∠ ACD, ∠ BDA, ∠ BDC

The angle which are 90°,

∠ DAB, ∠ ABC, ∠ BCD,  ∠ ADC

And central angles also make 90°,

∠ AEB, ∠ BEC, ∠ CED, ∠ DEA

In square there is no angle that neither makes 45° nor 90°.

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Angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and

∠ABC = ∠AED = 90° respectively.

Square is a polygon which has 4 sides. All four sides of square are equal length and perpendicular to each other that means the angle between two adjacent side is 90°.

Given that ABCD is a square surface. And diagonal of square creates two isosceles triangles.

So the ∠ABC = ∠BCD = ∠CDA = DAB = 90°

Here, BD and AC are two diagonals of a square ABCD and E is the intersection point of diagonals.

Diagonals cut each other perpendicular.

So, ∠AED = 90°  and ∠EAD = ∠EDA = 45°

Now to find ∠BAC;

we have ∠ABC = 90° so from the property of isosceles triangle

∠BAC = ∠BCA = 45°

In isosceles triangle BCD,

∠BCD = 90° and ∠DBC = ∠BDC = 45°

Therefore, the angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and ∠ABC = ∠AED = 90° respectively.

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Answer: Sale price: $254.15 , Discount: $44.85

Step-by-step explanation:

15% off indicates that the stereo will now cost 85% of what it did originally:

$299(100% – 15%) = $299(85%)

Decimalizing the percentage results in = $299(0.85) = $254.15

Discount= $299 - $254.15 = 44.85

Answer:

12

Step-by-step explanation:

He is running 12

Answer:

A.) [tex]\frac{1}{5^6}[/tex]

Step-by-step explanation:

To simplify [tex](5^2)^3[/tex], use the exponent rule that states [tex](a^m)^n=a^{mn}[/tex]

So,

[tex](5^2)^3=5^{2*3}=5^6[/tex]

Use the same exponent rule to begin simplifying [tex](5^4)^{-3}[/tex]:

[tex](5^4)^{-3}=5^{4*(-3)}=5^{-12}[/tex]

To further simplify [tex]5^{-12}[/tex], use the exponent rule that states [tex]a^{-m}=\frac{1}{a^m}[/tex]

So,

[tex]5^{-12}=\frac{1}{5^{12}}[/tex]

Then multiply the two new expressions as indicated in the original problem:

[tex](5^6)(\frac{1}{5^{12}})=\frac{5^6}{5^12}=\frac{1}{5^6}[/tex]

Alternatively, you could use the exponent rule that states [tex]a^m*a^n=a^{m+n}[/tex]

where

[tex]a^m=5^6\\a^n=5^{-12}[/tex]

So,

[tex](5^6)(5^{-12})=5^{6+(-12)}=5^{-6}=\frac{1}{5^6}[/tex]

The slope of the line y = 14x – 1 is 14.

To find the slope of a line, we need to know two points on the line. We can choose any two points, as long as they are not the same. For example, we can choose the points (0, -1) and (1, 13):

y = 14x – 1

y = 14(0) – 1 = -1 when x = 0

y = 14(1) – 1 = 13 when x = 1

The slope of the line is the change in y divided by the change in x between these two points. In this case, the change in y is 13 – (-1) = 14, and the change in x is 1 – 0 = 1. Therefore, the slope of the line is 14/1 = 14.

We can also write the slope as a simplified fraction. In this case, 14 is already a simplified fraction, so we don't need to simplify further. Therefore, the slope of the line y = 14x – 1 is 14.

Answer:

13.0434782609%

Step-by-step explanation:

200000 - 230000

-----------

230000

x 100% = 13.0434782609% - 100 = 86.9565217

86.9565217 x 230,000 = 200,000

Answer:

the value of x is 1

Step-by-step explanation:

2x+3(4x-3)=8-3x

2x+12x-9=8-3x

2x+12x+3x=8+9

17x=17

17x/17=17/17.......... divide both side by 17 to get the value of x

x=1......so, the value of x is 1

A two-column method be that can used to prove that segment QR is parallel to segment PS is presented as follows;

Statement                      [tex]{}[/tex]                 Reasons

1. [tex]\overline{QP}[/tex] ≅ [tex]\overline{RS}[/tex]                                     1. Given

2. [tex]\overline{QP}[/tex] ║ [tex]\overline{RS}[/tex]   [tex]{}[/tex]                                 2. Given

3. ∠PRQ ≅ ∠RPS [tex]{}[/tex]                          3. Alt. int. angles theorem

∠QPR ≅ ∠PRS    [tex]{}[/tex]                      

4. ∠PRQ = ∠RPS        [tex]{}[/tex]                    4. Definition of congruency

∠QPR = ∠PRS

5. ∠QRS = ∠PRQ + ∠PRS [tex]{}[/tex]            5. Angle addition postulate

∠QPS = ∠QPR + ∠RPS

6. ∠PRQ + ∠PRS = ∠QPR + ∠RPS [tex]{}[/tex] 6. Substitution property

7. ∠QRP = ∠QPS   [tex]{}[/tex]                          7. Transitive property

8. [tex]\overline{PR}[/tex] ≅ [tex]\overline{PR}[/tex]             [tex]{}[/tex]  [tex]{}[/tex]                    8. Reflexive property

9. ΔQRP ≅ ΔSPR  [tex]{}[/tex]                        9. ASA congruency rule

10. ∠PQR ≅ ∠PSR  [tex]{}[/tex]                       10. CPCTC

11. ∠PQR = ∠PSR [tex]{}[/tex]                          11. Definition of congruency

12. QRSP is a parallelogram [tex]{}[/tex]       12. Parallelogram opp. int. ∠s theorem

13. [tex]\overline{QR}[/tex] ║ [tex]\overline{PS}[/tex]              [tex]{}[/tex]                   13. Properties of a parallelogram

A parallelogram is a quadrilateral that has opposite parallel sides.

The details of the reasons used to prove that the segment [tex]\overline{QR}[/tex] is parallel to segment [tex]\overline{PS}[/tex] are as follows;

Alt. int. angles theorem

The alternate interior angles theorem states that the alternate interior angles formed between two parallel lines and their common transversal are congruent

Definition of congruency

Two geometric figures are congruent if they have the same measurements.

Angle addition postulate

The angle addition postulate states that the measure of an angle ∠A, which is formed by two adjacent angles ∠B and ∠C, is the same as the sum of the measures of the two angles, ∠A = ∠B + ∠C

Substitution property

The substitution property of equality states that if a variable, a = another variable, b, a = b, then b can be plugged into expressions and equations to substitute for a and the values of the expressions and sides of equations remain the same.

Transitive property

The transitive property of equality states that if a = b, and b = c, then a = c

Reflexive property

The reflexive property of congruency states that a geometric figure is congruent to its self

ASA congruency rule

The Angle-Side-Angle congruency rule states that if two angles and the included side of one triangle are congruent to the two angles and included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

Parallelogram opp. int. ∠s theorem

The parallelogram opposite interior angles theorem states that the opposite interior angles of a parallelogram are congruent.

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Answer:

Step-by-step explanation:

4y=3x+7

divide both sides by 4

y= 0.75x+1.75

or in fraction

y=3/4x+7/4

The quotient of the given division is (x + 9).

What is synthetic division?

Synthetic division is a technique for performing manual Euclidean division of polynomials in algebra that requires less writing and calculation than long division. Although it is typically taught for division by monic linear polynomials, the technique can be applied to division by any polynomial.

Given:  x^2 - 81 / (x - 9)

We have to find the quotient for the given division.

We can find the quotient using synthetic division.

                       x + 9

                 [tex]\sqrt[x-9]{x^2-81}[/tex]

                 -    x^2 - 9x

              _______________

                            9x - 81

                       -    9x - 81

                 _____________

                                    0

Hence, the quotient of the given division is (x + 9).

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Answer:

[tex]\huge\boxed{\sf y = \pm 13}[/tex]

Step-by-step explanation:

Given that,

y² = 169

Take sq. root on both sides

√y² = √169

So,

y = 13    OR    y = -13

[tex]\rule[225]{225}{2}[/tex]

Answer:

b) y = + 13

Step-by-step explanation:

Now we have to,

→ find the required value of y.

The problem is,

→ y² = 169

Let's solve the problem,

→ y² = 169

→ y = √(169)

→ [ y = + 13 ]

Hence, the answer is + 13.

The graph of the quartic function f(x) = -x⁴ + 1 is attached below with points at (-1 ,0), (0, 1) and (1, 0)

Quartic polynomials are continuous curves like the cubic polynomials. This means that you can draw the graph of the quartic without lifting your pencil from the page. There are no holes or jumps in the curve but, unlike the cubic graph, a graph of the quartic looks like a W or an M.

The general form of quartics of this form is y = a(x − h)⁴ + k The turning point is at (h, k). When sketching quartic graphs of the form y = a(x − h)⁴ + k, first identify the turning point. To add further detail to the graph, the x-axis and y-axis intercepts are found.

In this function given;

f(x) = -x⁴ + 1

This quartic function has points at (-1 ,0), (0, 1) and (1, 0)

Kindly find the attached graph below

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Answer:

-19

Step-by-step explanation:

Use a calculator

The required measures of the angle are given as,
∠JKL = 72°      ∠MLK = 108°      ∠JMK = 36°
∠MJL = 54°       ∠KNL = 90°

Given that.
The measure of the rhombus is given, we have to determine the measure of the angles,

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as angle.

Here,
∠JKL= 2 × ∠JKM  = 72°
∠MLK = 180 - 2 × ∠JKM =  108°
∠JMK = ∠JKM = 36°
∠MJL = ∠MLK/2 =  54°
The diagonal of the rhombus bisect each other at an angle of 90°
So,
∠KNL = 90°

Thus, all the measure of the angles is shown above.

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The required circumference of the pool is given as 95.1 feet.

Perimeter is the measure of the figure on its circumference. where the circumference of the circle is given as 2πr.

Here,
The Linton family has a swimming pool as of the circular profile.
The radius of the circular swimming pool is 15 feet
π = 3.17

Now,
Circumference of the swimming pool is given as,
= 2πr

Substitute the value in the above formula,
Circumference of the swimming pool = 2 × 3.17 × 15
                                                         = 95.1 feet.

Thus, the circumference is 95.1 feet.

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For both the experienced bricklayer and her apprentice working together it will take 2 hours to complete the work.

This is type of combined rate or time and work problem. Here, the experienced bricklayer takes 3 hours and apprentice take 6 hours to complete the job. So the experienced bricklayer completes 1/3rd of work in an hour and her apprentice completes 1/6th of work in an hour.        

Let us consider they would take x hours to complete the work together. The work done is the summation of product of time taken by each person to do the work and the rate of work done by each person.

x (1/3 + 1/6) = 1

x = 1/(1/3 + 1/6)

=18/9

=2

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When we say, "a system of linear equations works" it means that the linear equations share one or more ordered pairs (x,y) when graphed.

In many practical applications in daily life, linear equations are a crucial tool in science. They enable scientists to, among other things, make predictions, compute rates, and characterize relationships between two variables in the physical world. In order to see trends, linear equations are often graphed.

Slope intercept form, direct variation, point slope form and standard form are four types of linear functions.

When we have a system of linear equations and when we solve them simultaneously we get one or more ordered pair depending upon the variable in system.

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Answer:

£990

Step-by-step explanation:

£11000 * 2.25% * 4 = £990

If Two signs that scores are significantly different then (a) the error bars of group will not overlap

Error bars are graphical representations of data variability that are used to indicate the error or uncertainty in a reported measurement on graphs.

The estimated error in a measurement is indicated by error bars. In other words, an error bar represents the degree of uncertainty in a value.

When the standard deviation error bars overlap significantly, it is an indication that the difference is not statistically significant. To reach a conclusion, you must conduct a statistical test.

When the standard deviation error bars overlap even less, it indicates that the difference is unlikely to be statistically significant.

For significantly different group , we also have p-value greater than 0.05

So, Option (b) is incorrect.

Hence, (a) The error bars of the groups will not overlap is correct

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Answer:

12x -7

Step-by-step explanation:

According to the angle of incidence, the angle of reflection will also be 36°

Angle of incidence:

In math it means the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.

Given,

Here we need to find the If light strikes a plate mirror at a 36° angle of incidence, then what would you expect the resulting angle of reflection to be.

Here we know that, the incident ray, the reflected ray and the normal ray at the point of incidence all lies in the same plane.

Then the angle of incidence is equal to the angle of reflection

And it can be written as,

=> Angle of incidence = angle of reflection

As per the 2nd law given above, we say that if a light ray incident at 45°, then the reflected angle will also be 45°

Here we know that the value of,

=> Angle of incidence = 36°

Therefore, the Angle of reflection = 36°

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The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times then the table 4 represents a linear function.

An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx + b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The slope-intercept form of the equation for a linear function. As a result, it is written as f(x) = mx + b, where b is the line's y-intercept and m is the slope. Tables with a constant rate of change are represented by linear functions.

Table 4 represents a linear function

From the given tables, only table 4 represent a linear function.

As x's values change by 1, the matching y's values change by 5. This is why.

The table exists represented as:

x     y

1     -5

2     0

3     5

4     10

Therefore, table 4 represents a linear function.

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Safety net policies like food assistance, housing assistance, and family tax credits keep millions of Americans from poverty each year and reduce hardship for millions more.

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If according to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. The number of those households that owned a pet is:  200,588.

We would be making use of the given data to find the number of household that owned a pet.

Using this formula

Number of household with pet = Percentage of household × Number of household

Let plug in the formula

Number of household with pet = 72% × 278,595

Number of household with pet = 200,588 household

Therefore the Number of household with pet  is 200,588.

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Answer:

X <-2 or X > 5

Step-by-step explanation:

The inequality model of given problem is |5x-4|≤80.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. In mathematics, an inequality depicts the connection between two non-equal values in an algebraic expression. Inequality signs can indicate that one of the two variables is larger than, greater than or equal to, less than, or less than or equal to another value. An inequality is a mathematical connection between two expressions that is represented by one of the following symbols:: "less than or equal to": "less than": "not equal to"

Here,

The provided problem's inequality model is |5x-4|≤80.

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Answer:

Step-by-step explanation:

2a + 4b = 12c

4b = 12c - 2a

b = 3c - 1/2a

or

b = (6c - a)/2

Answer:

21°

Step-by-step explanation:

Answer: If a1 = 16 and a2 = -8, then we can write a recursive formula for the nth term of the sequence as follows:

an = a(n-1)/2

This formula states that the nth term of the sequence is equal to the previous term (n-1) divided by 2. For example, if n = 3, then a3 = a(3-1)/2 = a2/-8/2 = 4.

We can also write this formula in terms of the initial values of the sequence as follows:

a(n) = (-1)^(n-1) * 8

This formula states that the nth term of the sequence is equal to (-1) raised to the power of (n-1), multiplied by 8. This formula will always give the correct value for the nth term of the sequence, regardless of the initial values of the sequence.