In square QRST, ST = 8x + 9 and QR = 73, what is x?

The area of land inside the fence is 7600 square feet.

What is the area of the triangle?

If the height of the triangle is 'h' and the base is 'b', then the area of the triangle can be computed by using the formula,

           Area = 1/2 * base * height

To find the area of the land inside the fence, we can use the formula for the area of a right triangle:

Area = (1/2) * a * b

where a is the length of one of the legs of the triangle and b is the length of the hypotenuse.

We are given that the length of fence b is 130 feet and that the measure of angle A is 42°. Since the triangle is right, angle A is complementary to angle 90°, so the measure of angle A is 90° - 42° = 48°. Since the measure of angle A is 48°, the other leg of the triangle (which we will call "a") is the side opposite angle A.

We can use the sine function to find the length of side a:

a = b * sin A

= 130 * sin 48°

= approximately 117.3 feet

Substituting these values into the formula for the area of a right triangle gives:

Area = (1/2) * 117.3 feet * 130 feet

= approximately 7600.5 square feet

Rounded to the nearest square foot, the area of land inside the fence is 7600 square feet.

To learn more about area of the triangle, visit:

https://brainly.com/question/17335144

#SPJ1

Answer:

12 notches from both left and right of 0

you want the absolute value of (-12). all that means is how far is the number away from 0. in this case it's just 12

Answer:

$9

Step-by-step explanation:

20*45/100=9

So Ally should tip $9

Answer

$9.00

Reason

(45 * 0.20) = 9.

Answer:

Step-by-step explanation:

One of the Answers is C

The measure of the diagonal brace of the rectangular painting is 69.5 inches.

A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.

The diagonal of the brace and the length of one side and width of one side form a right-angled triangle and by Pythagoras we have

diagonal^2 = length(L)^2 + width(W)^2

diagonal^2 = 60^2 + 35^2

diagonal^2 = 3600 + 1225

diagonal^2 = 4825

diagonal = [tex]\sqrt{4825}[/tex]

diagonal = 69.5 inches

In conclusion the diagonal of the brace is 69.5 inches

Learn more about rectangles: https://brainly.com/question/24438517

#SPJ1

Answer:

10L + 21t = 188

t = 4L

Step-by-step explanation:

Let L be the number of hours spent lifeguarding and t be the number of hours spent tutoring. Kayla earned $188 total, so 10L+ 21t = 188(the number of hours spent lifeguarding/tutoring times how much she gets paid every hour). We also know that she spent 4 times longer tutoring than lifeguarding, so t = 4L. These are our systems of equations.

Answer: A 2/1

Step-by-step explanation:

Determine the slope of the line by finding 2 points

(2,-1),(4,3)

use slope formula

y2-y1/x2-x1

plug in and solve

3+1/4-2

4/2

2

the slope is 2 or 2/1

Answer:

W = width

L = length = 2W + 3

P = 36 = 2W + 2L = 2W + 2(2W + 3) =

6W + 6 = 36

6W = 30

W = 5

L = 13

The quotient that represents the fraction 15/3 is given as follows:

5.

A fraction has the standard notation given as follows:

Fraction = x/y.

In which the terms have the technical names given as follows:

Then the quotient is obtained as the division of the numerator by the denominator.

In this problem, the fraction is given as follows:

15/3.

Then the numerator and the denominator are given as follows:

Then the quotient is given as follows:

15/3 = 5.

As the division of 15 by 3 has a result of 5.

More can be learned about quotients and fractions at https://brainly.com/question/25714370

#SPJ1

The given exponents simplified as 2.89. Therefore, option C is the correct answer.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Given that, one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.

Now, ((1.7)⁶÷(1.7)⁵)²

= (1.7)²

= 2.89

The given exponents simplified as 2.89. Therefore, option C is the correct answer.

To learn more about an exponents visit:

https://brainly.com/question/15993626.

#SPJ1

Answer: 4^3 * 5^3

Step-by-step explanation: 4 repeats itself 3 times and 5 repeats itself 3 times

4^3 * 5^3

Put the numbers in numerical order

4 comes before 5

Answer:

[tex] { 4}^{3} \times {5}^{3} [/tex]

Step-by-step explanation:

I'd assume your x's stand for multiplication, so using that logic there are three fours and three fives. Each being multiplied by itself, so the simplified/exponential version of the equation is:

[tex] {4}^{3} \times {5}^{3} [/tex]

Make sure you put in numerical order (4 goes before 5).

Answer:

30

Step-by-step explanation:

Substitute and multiply :))

f(3)=10(3)

f(3)=30

Answer: Total angles on the 4

Step-by-step explanation:

The sum of the marked angles = Total angles on the 4 straight lines – Sum of the interior angles of the quadrilateral. Sum of interior angles of polygon of 4 sides = (4 – 2) *1800 =3600

Hence, sum of the marked angles = 4 * 180° – 360° = 720° – 360° = 360°

Representative fraction is a form of scale that can be used to change the size of an object to form an image. The required length is 32 inches.

A scale is a fraction of numbers that can be used to either increase or decrease the size of a given object. It is majorly referred to as representative fraction in scale drawing.

Representative fraction = [tex]\frac{length on drawing}{original length}[/tex]

In the given question, we have;

12 inches = 1 feet

x inches = 30 feet

So that:

x = 30 x 12 inches

  = 360 inches

representative fraction = [tex]\frac{2 inches}{360 inches}[/tex]

                             = 5.56 x [tex]10^{-3}[/tex]

Thus, given that the length of the Alamo Mission is 480 feet long. Then:

480 feet = 480 x 12 inches

              = 5760 inches

So that,

the required length in inches = 5760 x 5.56 x [tex]10^{-3}[/tex]

                                             = 32 inches

Therefore the expected length of the Alamo Mission is 32 inches.

Learn more about scale drawing at https://brainly.com/question/23209981

#SPJ1

flips a fair coin five times, 5/16 is the probability that there are 3 heads in a row somewhere in the sequence of five flips.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability.

The number of positive outcomes may be expressed by x for an experiment with n number of outcomes.

The following equation can be used to determine an event's probability:

Probability(Event) = Favorable outcomes / Total Outcomes = x/n

Considering a fair coin, after 5 flips, there are [tex]2^5[/tex] = 32 different arrangements of heads and tails.

To get exactly 3 heads,

[tex]^5C_3[/tex] = 5! / (5 - 3)! 3!

     = 5!/ 3! 2!

     = 10 ways

P(exactly 3 heads) = 10/32 = 5/16

Therefore, the probability of exactly 3 heads is 5/16.

To know more about probability refer to:

https://brainly.com/question/24756209

#SPJ4

Answer:

Step-by-step explanation:

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:((x1 + x2)/2, (y1 + y2)/2)Substituting the coordinates of points P and Q into the formula, we get:((2 + (-7))/2, (4 + (-2))/2) = (-2.5, 1)The coordinates of the midpoint of segment PQ are (-2.5, 1).To verify that this point is on the line through P and Q, we can find the slope of the line using the coordinates of points P and Q:slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-7 - 2) = -6/-9 = 2/3We can then use the point-slope form of a linear equation to write the equation of the line through points P and Q:y - y1 = m(x - x1)

y - 4 = (2/3)(x - 2)We can substitute the coordinates of the midpoint (-2.5, 1) into this equation to see if it is a solution:1 - 4 = (2/3)(-2.5 - 2)

-3 = -10/3The equation is true, so the midpoint (-2.5, 1) is on the line through points P and Q.To show that this point is just as far from P as it is from Q, we can use the distance formula to find the distance from the midpoint to points P and Q:distance = √((x2 - x1)^2 + (y2 - y1)^2)distance from (-2.5, 1) to (2, 4) = √((2 - (-2.5))^2 + (4 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4distance from (-2.5, 1) to (-7, -2) = √((-7 - (-2.5))^2 + (-2 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4. Since the distance from the midpoint to points P and Q is the same, the midpoint is just as far from P as it is from Q.

The height of the right triangle if the area of the triangle is 150 square units = 30 units

In this question, we have been given a right triangle's height is 3 times the length of its base.

We need to find the height of the right triangle if the area of the triangle is 150 square units.

Let h be the height and b is the base of the right triangle.

A right triangle's height is 3 times the length of its base.

So we get an equation,

h = 3b              ............(1)

Using the formula of area of right triangle,

A = 1/2 * b * h

150 = 1/2 * b * 3b                  .........(from equation (1))

300 = 3b^2

b^2 = 100

b = 10

Subatitute above value of b in equation (1),

h = 3 * 10

h = 30 units

Therefore, the height of right triangle is 30 units

Learn more about area of right triangle here:

https://brainly.com/question/22176005

#SPJ4

Answer:

Step-by-step explanation:

The unit rate is 400 square feet per gallon.

What is unitary method ?

Unitary method is a mathematical way of deriving a single unit and then finding the required unit by multiplying.

A graph is shown in the diagram and two points are given x co-ordinate represents paint used per gallon and y co-ordinate represents wall painted in square feet.

Given (1/4,100) implies 1/4th of a gallon paint is needed to pain 100 square feet of wall.

∴ In 1 gallon (100)÷1/4 square feet of wall can be painted which is 400 square feet.

And the unit rate is 400 square feet per gallon.

The angles,  x = 11 and y = 3,if l ll m,

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

A transversal intersects the parallel lines marked by the letters "l" and "m.

The two suplementary angles have the radii (13x - 19°) and (17y + 5)°, respectively.

Thus, (13x - 19)° plus (17y + 5)° equals 180°.

13x + 17y = 180 + 14

13x + 17y = 194 ————(1) (1)

The comparable angles are (9x + 25) and (13x - 19).

Consequently, (9x + 25) = (13x - 19)

9x - 13x = -19 - 25

-4x = -44

x = 11

By changing equation's value for 'x' (1),

13x + 17y = 194

13(11) + 17y = 194

17y = 194 - 143

17y = 51

y = 3

As a result, the solution will be x = 11 and y = 3.

learn more about angles click here:

brainly.com/question/25716982

#SPJ1

The values needed for the box plot that Adams wants to display are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

Given the following data that represents the records of the increase in the height of a plant for 10 weeks, 4.5, 3.2, 8.0, 9.1, 10.2, 6.8, 7.2, 9.5, 10.0, 8.8, in order to draft a box plot, the following steps are what Adams should take to find each of the values needed.

Step 1: Order the data set from least to the greatest.

3.2, 4.5, 6.8, 7.2, 8.0, 8.8, 9.1, 9.5, 10.0, 10.2

Step 2: Find the median.

The median is the middle of the data set = (8.0 + 8.8)/2 = 16.8/2 = 8.4

Step 3: Find the lower quartile which is the center of the first part of the data that is divided by the median.

Lower quartile = 6.8

Step 4: Find the upper quartile which is the center of the second part of the data that is divided by the median.

Upper quartile = 9.5

Therefore, the values that Adam needs for his box plot are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

Learn more about the median and quartiles on:

https://brainly.com/question/3876456

#SPJ1

11.4 centimeters is the radius of the cylinder .

What does volume mean in plain terms?

The capacity of a solid shape is determined using volume, a three-dimensional quantity.

                     It implies that a closed figure's volume determines how much three-dimensional space it can fill.

The volume of a cylinder is given by

   v = πr²h

The total volume of the two hemispheres is given by

   v' = 2× 2/3 πr³

    v' = 4/3 πr³

Now, the total volume of the solid is given by:

  [tex]V_{T}[/tex] = πr²h + 4/3 πr³

  Now, substitute the value of the total volume in the above expression and then solve for h.

       12 = πr²h + 4/3 πr³

        h = 12/πr² - 4r/3

Now, the surface area of the curved surface is given by:

        A = πrh

Now, the surface area of the two hemispheres is given by

      A' = 2 × (2πr² )

      A' = 4πr²

Now, the total area is given by

    [tex]A_{T}[/tex] = 2πr ( 12/πr² - 4r/3) + 4πr²

 Simplify the above expression.

  [tex]A_{T} =[/tex]  24/r + 4πr²/3

Now, differentiate the total area with respect to 'r'.

      [tex]\frac{dA_{T} }{dr}[/tex] = -24/r² + 8πr/3

Now, equate the above expression to zero.

     0 = -24/r² + 8πr/3

Simplify the above expression in order to determine the value of 'r'.

        8πr³  =  60

         r =  11.4

Learn more about volume

brainly.com/question/13338592

#SPJ4

The equation of the line in slope-intercept form is y = -2x+8

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Given the table, pick any two points in order to find the slope:

point 1: x₁ = 0, y₁ = 8

point 1: x₂ = -2, y₂ = 12

slope (m) =  (y₂-y₁) / (x₂-x₁)

slope (m) = (12-8)/(-2-0) = 4/(-2) = -2

Using y = mx+b and x₁ = 0, y₁ = 8:

8 = -2(0) + b

b = 8

y = -2x+8

Thus, the equation of the line is y = -2x+8

Learn more about equation of a line on:

brainly.com/question/12626026

#SPJ1

Answer:

B) 18 ft

Step-by-step explanation:

The scale is 1 in. model : 6 ft real.

6/1 = 6

To go from model size to real size, multiply the model size by 6 and change from inches to feet.

3 in. model = 3 × 6 ft = 18 ft

Answer:

19

Step-by-step explanation:

replace x with 10

f(10)=9+10

f(10)=19

hopes this helps please mark brainliest

Hypothesis test for µ1 – µ2 can be used to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications.

The Independent Samples t Test analyses the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. Independent Samples t Test is known as parametric test.

The population means are deemed to be different if the two-sample means are sufficiently dissimilar from one another.

The null and alternative hypothesis for the programs is

H0: μ1 - μ2=0

H1: μ1 - μ2  ≠0        

To learn more about hypothesis refer here

https://brainly.com/question/29519577#

#SPJ4

The length of the hypotenuse is 6.71

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:

[tex]{\displaystyle a^{2}+b^{2}=c^{2},}[/tex]

Given ,

Pythagorean therum

a^2 + b^2 = c^2....a and b are ur legs and c is the hypotenuse

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2...take the sqrt of both sides....this eliminates the ^2

sqrt 45 = c

6.708 rounded = 6.71 = c

Therefore the length of the hypotenuse is 6.71

To learn more about Pythagorean theorem refer to :

https://brainly.com/question/343682

#SPJ1

The depth of the dugout is less than 24.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

[tex]2\frac{1}{4}d < -54[/tex]

Where d is the depth of the dugout.

We have to find the depth of the dugout.

Now to simplify the inequality.

[tex]2\frac{1}{4}d < -54[/tex]

convert improper fraction into a fraction.

[tex]2\frac{1}{4} = \frac{9}{4}[/tex]

⇒ 9/4d < -54

Multiply both sides by 4/9

⇒  d < -54 x 4/9

    d < -6 x 4

    d < -24

Hence, the depth of the dugout is less than 24.

To know more about inequality, click on the link

https://brainly.com/question/24372553

#SPJ1

Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

Ms. Flores using to add these numbers in this order is follow Commutative Property of Addition.

What is Commutative Property of Addition?

No matter what sequence the addends are in when we add two or more integers, the result is always the same. This characteristic may be expressed as A + B Equals B + A. In this case, 2+4=4 + 2 = 6. Due to the fact that the total of both phrases is 6, 2+4 is equivalent to 4+2. The Commutative Property of Addition refers to this.

On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12=44.

Ms. Flores decides to add 18 and 12 to get 30

18+12= 30

And then adds 14

30+14=44

To learn more about Commutative Property of Addition visit:https://brainly.com/question/778086

#SPJ1