Write an expression involving exponents to represent the shaded area in square inches of the diagram than use that expression to calculate the shaded area in squares inches of the diagram

The length of the new base is 26.56 inches or [tex]26\frac{14}{25}[/tex] inches. Using the area of a right triangle, the required base is calculated.

The area of the right triangle is given by

A = [tex]\frac{1}{2}[/tex] × b × h sq. units

Where A -area; b -base; h -height;

It is given that,

The right triangle has a base of length b = 8 1/2 = 8.5 inches and a height of length h = 12 1/2 = 12.5 inches.

So, its area is

A = [tex]\frac{1}{2}[/tex] × 8.5 × 12.5 = 53.125 sq. inches

When the height of the right triangle is reduced to 4 inches,

53.125 = [tex]\frac{1}{2}[/tex] × b × 4

⇒ b = 53.125/2

∴ b = 26.56 or [tex]26\frac{14}{25}[/tex] inches

Thus, the length of the new base is 26.56 or [tex]26\frac{14}{25}[/tex] inches.

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Answer:

b = 133, a = 47

Step-by-step explanation:

If the two lines are parallel, then angle b is equal to 180-47 = 133 (same side interior angles), and angle is equal to angle 0 (alternate interior angles)

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:a = \theta[/tex]

( by Alternate interior angle pair )

[tex]\qquad \therefore\: \sf \:a = 47 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \:b = 180 - \theta[/tex]

( by co - interior angle pair )

[tex]\qquad❖ \: \sf \:b = 180 - 47[/tex]

[tex]\qquad \therefore \: \sf \:b = 133 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \:a = 47 \degree[/tex]

and

[tex]\qquad❖ \: \sf \:b = 133 \degree[/tex]

Answer:

x = 48°

Step-by-step explanation:

Complementary angles

Angles that sum to 90°.

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Therefore, angle x is equal to the angle that is complementary to 42°.

To find x, subtract 42° from 90°:

⇒ x = 90° - 42°

⇒ x = 48°

Answer:

P(B) 7

Step-by-step explanation:

The answer is P (B)

Angle HEJ measures 15 degrees.

The answer is 492 feet.

If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.

cos 60° = x / 984

1/2 = x/984

x = 984/2

x = 492 feet

The time requires to catch up to him will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.

Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.

The time will be calculated as below:-

30 minutes = 0.5 hour

15x = 18(x - 0.5)

15x = 18x - 9

-3x = -9

x = 3 hours

Therefore, the time requires to catch up to him will be 3 hours.

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Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The side opposite to the largest angle is the longest side of a triangle.

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, we can conclude that longest side is e

( since it's opposite angle is the largest, i.e 86° )

Check the picture below.

[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]

Answer: 5 times

Step-by-step explanation: The distance from his house to school and back is 0.4 km. Since he traveled 2km in a week, we have to divide 2 by0.4. 0.4x5 = 2 so he went to school 5 times a week.

Answer:

false

Step-by-step explanation:

The converse of the statement is

This is false by definition.

0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out. This can be obtained by using the formula for probability.

Probability is the chance of occurrence of an event.

⇒ The formula for finding probability,

Probability = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Here it is given in the question that,

Therefore by using the formula of probability we get,

⇒ Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ events\ sold\ out}{Total\ number\ of\ events}[/tex]

Probability (Junior Athletics being sold out) = 5/7

⇒ Probability (Junior Athletics being sold out) = 0.7

Hence 0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out.

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Answer:

What is this?

Can't understand anything!

Answer : what is this question?

The solution to the equation as given in the task content is; x = -3.47.

It follows from the task content that the equation given is; (43/7÷ x+32/9) ÷25/6=4/3

(43/7÷ x+32/9) = 25/6 × 4/3

(43/7÷ x+32/9) = 100/18

x +32/9 = 43/7 ÷ 100/18

x + 32/9 = 774/700

x = 774/700 - 32/9

x = -3.47.

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Answer: 5 is the smaller number and 21 is the larger number

Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.

Answer:

84

Step-by-step explanation:

15+15+27+27

The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

We want to solve the algebraic fraction equation given as;

3a³ - 5b³ + (3/a) + b³

Rearranging the algebra to get;

(3a³ + (3/a)) + b³ - 5b³

Factorizing out 3/a and simplifying gives;

(3/a)(a⁴ + a) - 4b³

This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

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(i) The equation of the axis of symmetry is x = - 5.

(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.  

In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.

(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:

y = x² - 8 · x - 2

y + 18 = x² - 8 · x + 16

y + 18 = (x - 4)²

In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) Now here we must apply a procedure similar to what was in used in part (ii):

y = - 2 · (x² - 4 · x + 2)

y - 4 = - 2 · (x² - 4 · x + 2) - 4

y - 4 = - 2 · (x² - 4 · x + 4)

y - 4 = - 2 · (x - 2)²

According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.  

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We can write the integration domain as

[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]

so that the integral is

[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]

Answer:

5

Step-by-step explanation:

3 x |12 - x| - 4

3 x |12 - 15| - 4

3 x 3 - 4

9 - 4

5

Answer: Rational, Irrational, Rational, Natural, Natural, Integer

Step-by-step explanation:

-4.2 is a rational number as it can be converted into a fraction

3√5 is an irrational number as it can't be converted into a fraction

5/3 is a rational number as it is a fraction

9 is a natural number as it is a positive whole number

√16 is a natural number as despite the square root, √16 is 4 which is a natural number

-8/2 is an integer as -8/2 is -4 which is a negative whole number

Answer: -3/7

Step-by-step explanation:

The first step is to find the slope of the line

y = mx + c where m is the slope of the line
Rearrange the equation and we get

3y = 7x + 7
y = 7x/3 + 7/3

So the slope of the line 7x - 3y = -7 is 7/3

There is another rule that states: The product of the slopes of two lines perpendicular to each other is -1

So, the slope of the line perpendicular to 7x - 3y = -7 is -1/(7/3) = -3/7

Answer:

6 * (5 + n)

Explanation:

Sum = addition

Difference = subtraction

Product = multiplication

Quotient = division

Answer:

mLx = 144

mLy=154

Step-by-step explanation:

180-36=144

x=144

180-62=118

36+118=154

180-154=26

180-26=154

y=154

Answer:

154 degrees

Step-by-step explanation:

you can find measure of angle y, since it is the supplement of angle a, so

measure of angle y = 180 - measure of angle a, which is 144 degrees

you can find the measure of angle x, by finding its complement.

Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x

so, the supplement of angle x is 26 degrees, so x is 154 degrees

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:

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Answer: 111

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees, so:

[tex]121+58+70+x=360\\\\x=111[/tex]

Answer:

111

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 360:

121 + 58 + 70 + x = 360 add like terms

249 + x = 360 subtract 249 from both sides

x = 111 is the measure of the angle represented with x