find the area of the semicircle

The dimensions of the bulletin board could be as follows:

length = 5 ft.

width = 3 ft.

[tex]A = l\times w[/tex]

where, 'l' represents the length of the rectangle

and 'w' represents the width of the rectangle

"If multiplying two whole numbers gives us a number, then the numbers we are multiplying are the factors of the product number."

For given example,

An area of the rectangular bulletin board is 15 sq. ft.

⇒ A = 15 sq. ft.

⇒ l × w = 15

Given that, the width and length of the bulletin board are whole

numbers.

Factors of 15 are,

15 = 5 × 3

15 = 15 × 1

From given figure we can say that he could use the dimension 5 ft. × 3 ft. for the bulletin board.

This means, the length of the bulletin board could be 5 ft. and the width  could be 3 ft.

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Answer:

9

Step-by-step explanation:

the range is the difference between the lowest and the highest number on the series

here the range is 3 two members have size 6 different from 6 and 3 which range its 3

Answer: 12 km\h north

Step-by-step explanation:

I actually have good guesses

Velocity = 12 km/h

-

Velocity can be defined as the division between distance traveled and the time it took for that distance to be traveled:

Velocity = Distance / Time

With the above information in mind, we can calculate the velocity of the bicycle:

Velocity = 18 km / 1.5 h

Velocity = 12 km/h

Thus the velocity of the bicycle is 12 kilometers per hour.

Answer:

Step-by-step explanation:

55 times 25, making Angel attempt 1375 free throws

Answer:

Step-by-step explanation:

Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.

Given,

A snail is moving away from a rock.

The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.

The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.

Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.

For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.

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Answer:

B) 7^2 x 7^3

Step-by-step explanation:

B is 7^5 , everything else is 7^4

Given:

Length of escalator = 26 ft

Angle of depression = 41 degrees

To find:

The horizontal distance x the escalator covers to the nearest tenth of a foot.

Solution:

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

Using this formula for the given triangle, we get

[tex]\cos 41^\circ=\dfrac{x}{26}[/tex]

[tex]26\cos 41^\circ=x[/tex]

[tex]26(0.7547)=x[/tex]

[tex]19.6222=x[/tex]

Round the value to the nearest tenth.

[tex]x\approx 19.6[/tex]

Therefore, the escalator covers 19.6 ft horizontally.

Answer:

Angle K is 1/2 the measure of arc JL, so JL = 228.  Add arc KL to arc JL to get 268 and subtract from 360. 360 - 268 = 92. 8x - 36 = 92. X = 16.

Step-by-step explanation:

The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C

from the question we have:

2400 = 7500(10)⁻ˣ

we would have to transform the equation that we have here into the logarithm form.

This is written as:

[tex]\frac{2400}{7500}=10^-^x[/tex]

from here we are to reduce the division

hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]

-x = log₁₀8/25

then

[tex]x = -log_{10} \frac{8}{25}[/tex]

option c is correct

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Answer:

?  We don't see any graphs to choose from

Step-by-step explanation:

[tex]y>\frac{1}{2}x-1[/tex]  Graph a dotted line (to show it's not included) with y-intercept 1 and slope 1/2.  Test the origin (0, 0) in the inequality:

[tex]0 > \frac{1}{2}0 - 1 = -1[/tex]  This is true, so shade the side of the line that the origin is on (above the line).

Next inequality...

[tex]y \le x+1[/tex]  Graph a solid line with y=intercept 1 and slope 1.  Test the origin.

[tex]0 \le 0+1=1[/tex]  True! Shade the side of the line the origin is on (below the line).  See image2, attached.

[tex]y>-2x-1[/tex]  Graph a dotted line with y-intercept -1 and slope -2.  Test the origin (0, 0).

[tex]0>-2(0)-1=-1[/tex]  True, so shade the side the origin is on (above the line).

The solutions are located where all the shadings intersect.  See image3.  The solutions are above the red line, above the green line and below the blue line.

Answer:

what does x mean, like what number does it represent in this situation

Answer:

x = 27

Step-by-step explanation:

I made '3' into 9/3

x/3 - 9/3 = x/9 + 9/3

convert terms to fractions with a denominator of 9

x/3 = 3x/9

9/3 = 27/9

3x/9 - 27/9 = x/9 + 27/9

(3x-27)/9 = (x+27)/9

since each denominator equals 9 we can set the numerators equal to each other:

3x - 27 = x + 27

3x = x + 54

2x = 54

x = 27

The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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Answer:

The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.

Step-by-step explanation:

We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.

First, we calculate the length of the oblique line, that is:

[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]

[tex]l_{O} = \sqrt{34}[/tex]

Second, we determine the length of the vertical line by direct observation, that is:

[tex]l_{V} = 12[/tex]

Lastly, the perimeter is determined by the following formula:

[tex]p = 2\cdot (l_{O}+l_{V})[/tex]

[tex]p = 24+2\sqrt{34}[/tex]

The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.  

Answer: 35.7

(This is the answer squared by the way)

Step-by-step explanation:

Answer: 3√13

Step-by-step explanation:

To find the length of AC we need to use the Pythagorean theorem.

Which is AC^2 = BC^2 + AB^2

AC^2 = 6^2 + 9^2

AC^2 = 36 + 81

AC^2 = 117

AC = √117

Answer:

2,138 in^3

Step-by-step explanation:

I know this is old but other people can find this helpful

In question 1;

The student multiplied without flipping the second expression.

In second question;

The negative should only be distributed to the numerator.

In third question,

3/2 should be remove from the x - value which make the expression undefined.

In fourth student;

Neither student is correct.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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

In question 1;

The expression is,

⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)

= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)

Cleary, The student multiplied without flipping the second expression.

In question 2;

⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)

⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)

Clearly, The negative should only be distributed to the numerator.

In Question 3;

The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''

In fourth student;

Neither student is doing correct solution.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

5⁻³

This can be written as 1/5³ which is equal to 1/125

-5⁻³

This can be written as -1/5³ which is equal to -1/125

(-5⁻³)⁻¹

We have an exponential property

[tex](x^{a} )^{b} =x^{ab}[/tex]

So (-5⁻³)⁻¹=(-5)³=-125

(-5⁻³)⁻¹  equivalent expression is -125

(-5⁻³)⁰

=(-5)⁰=1

Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

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Answer:

7

Step-by-step explanation:

So the log thingy is loga(b) = c

a^c = b

So in this one, a = a

b = 7

c = 4

a^4 = 7

The direction cosines of a vector are the cosines of the angles between the vector and the three mutually perpendicular axes of a coordinate system.

The direction cosines of a vector [tex]$\mathbf{a}$[/tex] are denoted by l, m and n. Mathematically, the relation between these direction cosines is given by:

[tex]$$\mathbf{a}=l\mathbf{\hat{i}}+m\mathbf{\hat{j}}+n\mathbf{\hat{k}}$$[/tex]

where i,j and k  are unit vectors along the three axes of the coordinate system.

To calculate the direction cosines of a given vector [tex]$\mathbf{a}$[/tex] with components [tex]$a_x$, $a_y$ and $a_z$[/tex], we can use the following formula:

[tex]$$l = \frac{a_x}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]

[tex]$$m = \frac{a_y}{\sqrt{a_x^2+a_y^2+a_z^2}}$$ \\ $$n = \frac{a_z}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]

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Answer:

I used desmos to make the graph

Step-by-step explanation:

Hopefully this helps!

With an accuracy of within $0.01, the student will be able to recognize

and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.

TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.

The TEKS are used to guide the development of curriculum and instruction in Texas schools.

The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."

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Growth that is slower than the Nuttall Oak growth rate is h=5t.

An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.

This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.

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Answer:

298.24 mph at an angle of 89 degrees

Step-by-step explanation:

[tex]v_p[/tex] = Velocity of plane = 300 mph at 50 degrees

[tex]v_j[/tex] = Velocity of jet stream = 200 mph at 160 degrees

The velocity of the plane in component form is

[tex]v_p=300\cos50^{\circ}\hat{i}+300\sin50^{\circ}\hat{j}[/tex]

The velocity of the jet stream in component form is

[tex]v_j=200\cos160^{\circ}\hat{i}+200\sin160^{\circ}\hat{j}[/tex]

Resultant velocity is given by

[tex]v=(300\cos50^{\circ}+200\cos160^{\circ})\hat{i}+(300\sin50^{\circ}+200\sin160^{\circ})\hat{j}\\\Rightarrow v=4.9\hat{i}+298.2\hat{j}[/tex]

Magnitude is given by

[tex]|v|=\sqrt{4.9^2+298.2^2}\\\Rightarrow |v|=298.24\ \text{mph}[/tex]

Angle is given by

[tex]\theta=\tan^{-1}\dfrac{298.2}{4.9}=89^{\circ}[/tex]

The velocity of the plane is 298.24 mph at an angle of 89 degrees.

Answer:

H 40%

Step-by-step explanation:

29+27+24=80

32/80=0.4

Answer:

Step-by-step explanation:

32/80 x 100 = 40%

Answer:

Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.

The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.

Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.

She wants to buy biking outfits that cost $45.35 each.

We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:

45.35o <= 372.81

This inequality can be solved by dividing both sides by 45.35:

o <= 8.24

Therefore, Gianna can purchase 8 biking outfits while staying within her budget.

Step-by-step explanation:

The amount of money that the business will receipt is $44.

given:

Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt

From the above question:

24oz of Lemonade = 1 bottle

528 oz of Lemonade = x

Cross Multiply

24 × x = 528

x = 528/24

x = 22 bottles

We are told that: they sell each bottle for $2

Hence:

1 bottle = $2

22 bottles = y

Cross Multiply

y = 22 × $2

y = $44

Therefore, the amount of money that the business will receipt = $44

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Answer:

$1,591.67

Step-by-step explanation:

The computation of the balance after 5 years is shown below:

Given that

Accumulated Balance on Credit Card = P = $2,300

r = Monthly interest amount = 17% ÷ 12 = 1.41666667%

M = Minimum payment = 2%

Now  

Balance on Credit Card after t year = P × (1+r) ×(1-M)

= $2,300 × (1+1.41666667%)^t × (1 - 2%)^t

= $2,300 × (0.993883337)^t

SO,

Balance on Credit Card after 5 years is

= $2,300 × (0.993883337)^60

= $2,300 × 0.692029437

= $1,591.66771

= $1,591.67