If side a measures 30 feet and side b measures 40 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work.

Answer:

Step-by-step explanation:

Let he have Rs . 1

spent on transport  =  17/35

spent on sweet  =  5/6 of  18/35

                   =  3/7

The area of sector in the given circle is 275π/6 square meters.

We have to find the area of sector which measures 165 degrees and radius of circle is 10m.

Area = (θ/360)πr²

where θ is the angle in degrees, π is the mathematical constant pi (approximately 3.14159), and r is the radius of the circle.

In this case, the angle is 165 degrees and the radius is 10 meters. Plugging these values into the formula, we get:

Area = (165/360)π(10)²

Area = (11/24) × π × 100

Area =1100/24π

=275π/6 square meters.

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Answer: 48

Step-by-step explanation: median of list of consecutive integers is the mean of the endpoints. (31+65)/2

The circumference of the circle is 88 units given the radius 14 units

Circumference of a circle is the measurement of the boundary of the circle or the path or the boundary that surrounds the shape. It is also called Perimeter of a circle.

Howto determine this

Given the radius of the circle = 14

Circumference of a circle = 2πr

Where π = 22/7

Circumference of circle = 2 * 22/7 * 14

Circumference of circle = 44/7 * 14

Circumference of circle = 616/14

Circumference of circle = 88 units

Therefore, the Circumference of circle is 88 units

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This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

Answer:

hello

the answer to (a) is:

y = kx ----> y = (1/8)x

and the answer to (b) is:

if x = 7

y = (1/8) × 7 = 7/8 or 0.875

UIF at 1% of the basic salary is R234.

The actual dimension of the kitchen on the floor is 0.036 meters.

2.2.1. UIF stands for Unemployment Insurance Fund.

2.2.2. To calculate UIF at 1% of the basic salary, we multiply the basic salary by 1%:

UIF = 1% of Basic Salary

= 1/100 x Basic Salary

Given that the Basic Salary is R23,400, we can calculate UIF:

UIF = 1/100 x 23,400

= 234

Therefore, UIF at 1% of the basic salary is R234.

2.2.3. One benefit of contributing UIF by the employee is that it provides financial protection against unemployment. If an employee becomes unemployed, they may be eligible to receive UIF benefits, which can provide temporary financial support during the period of unemployment.

2.2.4. Unfortunately, the values of B and C are not provided in the given information. If you provide the values, I can assist you with determining them.

3.1.1. The scale used is 1:100.

3.1.2. If the dimension (length) of the kitchen on the plan is 3.6 cm, to determine the actual dimension in meters, we need to scale it up by the scale factor:

Scale factor = 1/100 (since it's a 1:100 scale)

Actual dimension = Dimension on the plan x Scale factor

= 3.6 cm x (1/100)

= 0.036 meters

Therefore, the actual dimension of the kitchen on the floor is 0.036 meters.

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By completing squares we will get the expression:

(x + 7)² = -4

Here we have the quadratic equation:

x² + 22x = 8x - 53

First, move all the terms to the left side, then we will get:

x² + 22x - 8x + 53 = 0

x² + 14x + 53  =0

Now, remember the perfect square trinomial:

(a + b)² = a² + 2ab + b²

Then we can rewrite our expression as:

x² + 2*7*x + 53  =0

Now we can add and subtract 7², then we will get.

x² + 2*7*x + 7² - 7² + 53  =0

(x + 7)² - 7² + 53 = 0

(x + 7)² - 49 + 53 = 0

(x + 7)² + 4 = 0

(x + 7)² = -4

That is the expression we wanted.

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Pam will use 27/50 cups of apple juice.

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

To get how many cups of apple juice Pam will use, we must calculate 3/5 of 9/10 cups.

The 3/5 of 9/10 is:

= (3/5) * (9/10)

= (3 * 9) / (5 * 10)

= 27/50

Therefore, Pam will use 27/50 cups of apple juice.

Translated question:

A recipe calls for 9/10 cups of apple juice. Pam is preparing 3/5 of the recipe. How many cups of apple juice will Pam use?​

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Answer:

13 pints

Step-by-step explanation:

quarts times 2.

6.5•2=13

Answer:

13 pints.

Step-by-step explanation:

The conversion rate from pints to quarts is 1:2 meaning every 1 pints will result in 2 quarts. Therefore with this formula, (6 1/2)*2 brings the result to 13.

You're welcome!

The true comparisons are:

B. 3.114 > 3.112: In this case, the number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1).

D. 0.541 > 0.145: Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1).

E. 0.141 < 0.19: In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).

Option A is not a true comparison because 32.03 is actually less than 32.3. The digit in the hundredth place is 0 in both numbers, and the digit in the thousandth place is 3 in 32.03, while it is 0 in 32.3.

Option C is also not a true comparison since 4.003 is greater than 3.996. The digit in the thousandth place (4) is greater than the corresponding digit in 3.996 (3).

Answer: -D) 0.541 > 0.145

-B) 3.114 > 3.112

-E) 0.141 < 0.19

explanation: The number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1). Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1). In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).

Based on the ratio of the digit in its hundred places compared to the same digit in its hundredth place, the number of times the value of the digit in the hundred places is greater than the value of the digit in the hundredth place is 10,000.

The ratio is the relative size of one value, number, or quantity compared to another.

The ratio is computed as the quotient of one quantity divided by another.

We can express a ratio as a fraction, decimal, percentage, or in its standard form (:).

For instance, using the digit 4 in its hundred places will give 400.  The same digit in its hundredth place gives 0.04.

The ratio of 400 to 0.04 = 10,000 (400 ÷ 0.04)

Thus, in this instance, we can conclude that 400 is 10,000 times greater than 0.04.

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The length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

Given is a triangle with angles 64° and 32°, and side 21.1 and 30, we need to find the third side,

So, according to the angle sum property of triangle,

Third angle = 180° - (64° + 32°)

Third angle = 84°

To find the length of the third side, which is opposite the angle of 84°, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.

Let's label the triangle with angles A, B, and C, and sides a, b, and c, respectively.

In this case, angle A is 84°, angle B is 64°, and angle C is 32°. Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.

Using the Law of Sines, we have the following equation:

sin(A) / a = sin(B) / b = sin(C) / c

We want to find the length of side a, so we can rearrange the equation as follows:

sin(A) / a = sin(B) / b

Now we can substitute the given values:

sin(84°) / a = sin(64°) / 30

To find side a, we can solve for it algebraically:

a = (sin(84°) × 30) / sin(64°)

Calculating this expression, we get:

a ≈ 30.1

Therefore, the length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

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The actual area of logo 2 would be = 45ft²

The area of logo 2 would be = 2.5in²

To determine the actual area of logo 2, the given dimensions are first converted to ft and the formula for the area of square is used. That is

Actual area of logo 2 = a²

a = 1/2 in (convert to ft)

But 1 in = 6 ft

1/2in = 3ft

Then divide the logo 2 in various squares to get 5 equal squares.

Area = 5(a²)

= 5×3×3

= 45ft²

The area of the logo 2 model = 5(0.5) = 2.5in²

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Answer:

Step-by-step explanation:

Ok so, as given in the table, the cost of the 3rd tank is 800$, we can thus determine the cost of 1 cubic inch for a tank and use that to determine the cost of the other tanks.

[tex]volume =L\times W\times H\\=24\times 24\times 24\\=13824 in^3[/tex]

thus, to compute the cost of one cubic inch, we can divide the cost by the volume of the 3rd tank (in cubic inches)

[tex]\frac{800}{13824}=0.0579[/tex] [tex]usd/in^3[/tex]

now, we can determine the dimensions of the second tank that will make it cost 150$

[tex]0.0579\times 18\times W\times 24=150[/tex]

[tex]W=\frac{150}{0.0579\times 18\times 24} =6 in.[/tex]

Now to determine the cost of the first tank, we can multiply its volume by the cost per cubic inch:

[tex]cost=0.0579\times36\times 36\times 36=2700[/tex]$

As of question B, the cost will increase as the width increases.

For Question C, we can find the volume of the sphere by the formula:

[tex]volume=\frac{4}{3}\pi r^3 =\frac{4}{3}\pi \times 24^3=57905 in^3[/tex]

To find the cost of that tank, we just multiply its volume by the cost per unit volume:

[tex]cost=57905\times 0.0579=3352[/tex]$ (roughly)

Answer:

[tex]\displaystyle \frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]

Step-by-step explanation:

[tex]\displaystyle \int x^5\sqrt{2-x^3}\,dx\\\\=\int x^5(2-x^3)^{\frac{1}{2}}\,dx\\\\=\int x^3x^2(2-x^3)^{\frac{1}{2}}\,dx[/tex] <-- Breaking up [tex]x^5[/tex] into [tex]x^3x^2[/tex] helps us later

Let [tex]u=2-x^3[/tex] and [tex]du=-3x^2\,dx[/tex] so that [tex]2-u=x^3[/tex] and [tex]\displaystyle -\frac{1}{3}du=x^2dx[/tex]:

[tex]\displaystyle -\frac{1}{3} \int (2-u)u^{\frac{1}{2}}\,du\\\\=-\frac{1}{3} \int 2u^{\frac{1}{2}}-u^{\frac{3}{2}}\,du\\\\=-\frac{1}{3}\biggr(\frac{4}{3}u^{\frac{3}{2}}-\frac{2}{5}u^{\frac{5}{2}}\biggr)+C\\\\=-\frac{1}{3}\biggr(\frac{4}{3}(2-x^3)^{\frac{3}{2}}-\frac{2}{5}(2-x^3)^{\frac{5}{2}}\biggr)+C\\\\=-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+\frac{2}{15}(2-x^3)^{\frac{5}{2}}+C\\\\=\frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]

hello

the answer to the question is:

volume of sphere = ⁴⁄₃πr³

4.5π = ⁴⁄₃πr³ ----> r³ = 3.375 ----> r = 1.5 cm

1)

Surface area of rectangular prism:

SA = 2( hw + lw + lh )

h= height of prism .

w = width of prism .

l = length of prism .

Substitute the values,

h= 4m

w=1.2 m

l= 13.4 m

SA = 2(4*1.2 + 13.4*1.2 + 13.4*4)

SA = 148.96 m²

2)

Surface area of triangular prism:

SA = (S1 +S2 + S3)L + bh

h= height of prism .

b = base of prism .

S1 , S2 , S3 = sides of triangle .

Substitute the values,

SA = (3+ 4 + 0.5)4 + 0.5*3

SA = 31.5 in²

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Answer:

6.98

Step-by-step explanation:

5.9454+1.03 =6.9754 which is rounded to 6.98

The volume of the  triangular prism is determined as 2,520 yd².

The volume of the  triangular prism is calculated by applying the following formula as follows;

V = ¹/₂bhl

where;

The volume of the  triangular prism is calculated as;

V =  ¹/₂  x 12 yd x 14 yd x 30 yd

V = 2,520 yd²

Thus, the volume of the  triangular prism is calculated by applying the following formula for volume of  triangular prism.

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The perimeter of the triangle is √34 + √65 + √101, and the area is 2.5.

We have,

To calculate the perimeter and area of a triangle, we need to know the coordinates of its vertices.

Let's calculate the perimeter and area for the given triangles.

a) Triangle with vertices A(2,2), B(7,-1), C(3,-8)

To calculate the perimeter, we need to find the lengths of the three sides of the triangle and sum them up.

Side AB:

Length AB = √((x2 - x1)² + (y2 - y1)²)

= √((7 - 2)² + (-1 - 2)²)

= √(5² + (-3)²)

= √(25 + 9)

= √34

Side BC:

Length BC = √((x2 - x1)² + (y2 - y1)²)

= √((3 - 7)² + (-8 - (-1))²)

= √((-4)² + (-7)²)

= √(16 + 49)

= √65

Side AC:

Length AC = √((x2 - x1)² + (y2 - y1)²)

= √((3 - 2)² + (-8 - 2)²)

= √(1² + (-10)²)

= √(1 + 100)

= √101

Perimeter = AB + BC + AC

= √34 + √65 + √101

To calculate the area, we can use the formula for the area of a triangle:

Area = 1/2 x base x height

We can consider any side of the triangle as the base and find the height corresponding to that base.

Let's consider side AB as the base.

Height h = distance between point C and the line AB

Using the formula for the distance between a point (x0, y0) and a line Ax + By + C = 0:

h = |(Ax0 + By0 + C)| / √(A² + B²)

Equation of line AB:

(x2 - x1) (y - y1) - (y2 - y1)(x - x1) = 0

(7 - 2)(y - 2) - (-1 - 2)(x - 2) = 0

5(y - 2) + 3(x - 2) = 0

5y - 10 + 3x - 6 = 0

5y + 3x - 16 = 0

Plugging in the coordinates of point C (3, -8):

h = |(53 + 3(-8) - 16)| / √(5² + 3²)

= |-5| / √(25 + 9)

= 5 / √34

Area = 1/2 x AB x h

= 1/2 x √34 x (5 / √34)

= 1/2 x 5

= 2.5

Therefore,

The perimeter of the triangle is √34 + √65 + √101, and the area is 2.5.

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The complete question.

Calculate the perimeter and area of ​​the triangles whose vertices are a) A(2,2) B(7,-1) ((3,-8) ​

The equation of the circle with a center at (-4, 6) and a point on the circumference at (-2, 9) is (x + 4)² + (y - 6)² = 13.

Given:

Center of the circle: (-4, 6)

Point on the circumference: (-2, 9)

The center of the circle (h, k) is given as (-4, 6), which means h = -4 and k = 6.

The formula for the distance between the center and the point on the circumference can be used to determine the radius (r).

The formula for distance is provided by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) is the center (-4, 6), and (x₂, y₂) is the point on the circumference (-2, 9).

Putting in the values:

d = √((-2 - (-4))² + (9 - 6)²)

= √((2)² + (3)²)

= √(4 + 9)

= √13

So, the radius (r) is √13.

Now, we can substitute the values of h, k, and r into the general equation of the circle:

(x - h)² + (y - k)² = r²

(x - (-4))² + (y - 6)² = (√13)²

(x + 4)² + (y - 6)² = 13

Therefore, the equation of the circle is (x + 4)² + (y - 6)² = 13.

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Answer:

  2

Step-by-step explanation:

You want to know the mode of a dot plot that could be represented as ...

  1 | x x

  2 | x x x x x

  3 | x x x

  4 | x x x x

  5 | x x

The mode is the data element that appears most often in the data set.

The 5 xs above the 2 is the largest number of xs that appear anywhere, so 2 is the mode.

<95141404393>

The value of x that is measure of angle R from the given triangle PQR is 60°.

In the given triangle PQR, angle P is right angle and measure 90°, angle Q measures 30° and angle R measures x.

We know that, sum of the interior angles of triangle is 180°.

Here, ∠P+∠Q+∠R=180°

90°+30°+∠R=180°

120°+∠R=180°

∠R=180°-120°

∠R=60°

Therefore, the value of x that is measure of angle R from the given triangle PQR is 60°.

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DC and DE are tangents to the circle at C and E respectively A is the centre of the circle B lies on the circle and BAE is a straight line L N

7.2.1: AABC is parallel to ADEC (AABC|||ADEC).

7.2.2: This completes the proof of both statements:

AABC|||ADEC and AE · EC = BC · DE.

To prove that AABC is parallel to ADEC, we can make use of the properties of tangents and alternate angles.

Proof:

AABC|||ADEC

DC and DE are tangents to the circle at C and E, respectively.

BAE is a straight line.

To prove AABC|||ADEC, we need to show that the alternate interior angles are congruent.

First, let's consider angle AED and angle ABC.

These angles are alternate interior angles formed by transversal AE intersecting the lines DE and BC.

Since DE is a tangent to the circle at E, angle AED is a right angle (90 degrees).

We know that a tangent to a circle is perpendicular to the radius at the point of tangency.

angle AED = 90 degrees.

Let's consider angle ABC. Since DC is a tangent to the circle at C, angle ABC is also a right angle (90 degrees).

Again, this follows from the property that a tangent is perpendicular to the radius at the point of tangency.

Since both angle AED and angle ABC are right angles, they are congruent:

angle AED = angle ABC.

By the alternate interior angle if two lines are intersected by transversal and the alternate interior angles are congruent, then the lines are parallel.

AABC is parallel to ADEC (AABC|||ADEC).

7.2.2 Showing that AE · EC = BC · DE

To prove that AE · EC = BC · DE, we can use the fact that AABC is parallel to ADEC.

Since AABC is parallel to ADEC, we can apply the intercept theorem or the proportionality theorem.

According to the intercept two parallel lines intersect a set of parallel lines, then the segments formed on one transversal are proportional to the corresponding segments formed on any other transversal.

Using the intercept theorem, we can write the following proportion:

AE/BC = DE/EC

To find AE · EC, we can cross-multiply the proportion:

AE · EC = BC · DE

We have shown that AE · EC is equal to BC · DE.

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The container is indeed big enough to store 560 sugar cubes.

To determine if the container is big enough to store 560 sugar cubes, we need to calculate the volume of the container and compare it to the total volume occupied by the sugar cubes.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

In this case, the dimensions of the container are:

Length (l) = 6 inches

Width (w) = 4 inches

Height (h) = 3 inches

Using the formula, the volume of the container is calculated as follows:

V = 6 inches * 4 inches * 3 inches

V = 72 cubic inches

Now, let's calculate the volume occupied by a single sugar cube:

The side length of a sugar cube is 0.5 inches, so the volume of a single sugar cube is:

V_cube = 0.5 inches * 0.5 inches * 0.5 inches

V_cube = 0.125 cubic inches

To determine the number of sugar cubes that can fit in the container, we divide the volume of the container by the volume of a single sugar cube:

Number of sugar cubes = V_container / V_cube

Number of sugar cubes = 72 cubic inches / 0.125 cubic inches

Number of sugar cubes = 576

Since the number of sugar cubes that can fit in the container is 576, which is greater than the required 560 sugar cubes, we can conclude that the container is indeed big enough to store 560 sugar cubes.

Therefore, the container can comfortably accommodate the desired quantity of sugar cubes while providing a tight seal to keep ants away.

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The decimal equivalent to the fraction of a cup of flour added to each case is approximately 0.923.

To find the decimal equivalent of the fraction of a cup of flour added to each case, we can divide the total amount of flour (36 cups) by the number of cases (39).

Decimal equivalent = Total amount of flour / Number of cases

Decimal equivalent = 36 cups / 39 cases

Calculating this division:

Decimal equivalent ≈ 0.923

Therefore, the decimal equivalent to the fraction of a cup of flour added to each case is approximately 0.923.

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Answer:

Set your calculator to degree mode.

[tex]x = {cos}^{ - 1} \frac{3.9}{8.5} = 62.7 \: degrees[/tex]

Angle x measures about 62.7°.

The case are appropriate with the given:

(x-3)² = 8(y-4)

y² = 4²x

(y-2)² = 4(x-3)

Analyze each given equation to determine the appropriate case and find the vertex, focus, opening of the graph, directrix, and latus rectum.

1. (x-3)² = 8(y-4)

This equation represents a parabola with its vertex form given by (h, k) = (3, 4).

Case 1: The coefficient of (y - k) is positive, indicating an upward-opening parabola.

Vertex: The vertex is (3, 4).

Focus: The focus can be found using the formula (h, k + 1/4a), where a = coefficient of (y - k). In this case, the focus is (3, 4 + 1/4 × 8) = (3, 6).

Directrix: The directrix is a horizontal line located at y = k - 1/4a. In this case, the directrix is y = 4 - 1/4 × 8 = 2.

Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 8 = 32 units.

2. y² = 4²x

This equation represents a parabola with its vertex form given by (h, k) = (0, 0).

Case 2: The coefficient of x is positive, indicating a right-opening parabola.

Vertex: The vertex is (0, 0).

Focus: The focus can be found using the formula (h + 1/4a, k), where a = coefficient of x. In this case, the focus is (0 + 1/4 × 4, 0) = (1, 0).

Directrix: The directrix is a vertical line located at x = h - 1/4a. In this case, the directrix is x = 0 - 1/4 × 4 = -1.

Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 4 = 16 units.

3. (y-2)² = 4(x-3)

This equation represents a parabola with its vertex form given by (h, k) = (3, 2).

Case 3: The coefficient of (x - h) is positive, indicating a right-opening parabola.

Vertex: The vertex is (3, 2).

Focus: The focus can be found using the formula (h + 1/4a, k), where a = coefficient of (x - h). In this case, the focus is (3 + 1/4 × 4, 2) = (4, 2).

Directrix: The directrix is a vertical line located at x = h - 1/4a. In this case, the directrix is x = 3 - 1/4 × 4 = 2.

Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 4 = 16 units.

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