A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.

A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 7 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.

What is the area of the tile shown?

58 cm2
44 cm2
74 cm2
70 cm2

The exact value of the expression tan(π/6) sin(5π/3)⋅cos(-3π/4) is -√3/2.

We have tan(π/6). The angle π/6 is equivalent to 30 degrees. The tangent of 30 degrees is √3/3.

We have sin(5π/3). The angle 5π/3 is equivalent to 300 degrees. In the unit circle, the sine value at 300 degrees is -√3/2.

Finally, we have cos(-3π/4). The angle -3π/4 is equivalent to -135 degrees. In the unit circle, the cosine value at -135 degrees is -√2/2.

Multiplying these values together, we have (√3/3) * (-√3/2) * (-√2/2). Simplifying, we get (√3 * √3 * √2) / (3 * 2 * 2) = (√3 * √2) / 12.

Taking the negative sign into account, the final value is -√3/2, which is approximately -0.866.

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Answer:

12/9-6+(4)(6)

=12/3+(4)(6)

=4+(4)(6)

=4+24

=28

The given statement "A and B are n x n matrices. The determinant of A is the product of the diagonal entries in A" is False because the product of the diagonal entries in A for n x n matrix will not be equal to determinant of A.

The determinant of a matrix is a scalar value that can be calculated using a specific formula. The formula for finding the determinant of an n x n matrix involves finding the sum of products of the elements in certain combinations of rows and columns.

The product of the diagonal entries is only one element in the calculation of the determinant of a matrix, and it is not equal to the determinant unless the matrix has all zeros except on the diagonal.

For example, consider the following 2x2 matrices:

A = [2 3; 4 5]

B = [1 0; 0 1]

The determinant of A is (25) - (34) = -2

The product of the diagonal entries in A is 2*5 = 10, which is not equal to the determinant.

The determinant of B is (11) - (00) = 1

The product of the diagonal entries in B is 1*1 = 1, which is equal to the determinant.

Therefore, the statement "The determinant of A is the product of the diagonal entries in A" is false in general, and the determinant of a matrix is typically calculated using a more involved formula that takes into account all the elements in the matrix.

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No, because it fails vertical line test.

What is vertical line test?

Vertical line test is defined as a method used to find if the given equation or graph represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function (equation) at only one point, for it to represent a function.

Hence, in the given graph, the function intercepts the y- axis at two points, therefore, it fails vertical line test.

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Answer:

17

Step-by-step explanation:

20 divided by 5 + 19 - 6

20 divided by 5 = 4

4 + 19 = 23

23 - 6 = 17

Answer:

\(\frac{3}{4}\)

Step-by-step explanation:

\(\frac{1}{4} +\frac{1}{6} +\frac{1}{3}\)

4 = 2 × 2 × 1

6 = 2 × 3 × 1

3 = 3 × 1

GCF = 1

4 × 6 × 3 = 72

\(\frac{18}{72} +\frac{12}{72} +\frac{24}{72}\)

\(\frac{18+12+24}{72}\)

\(\frac{54}{72}\)

54 = 2 × 3 × 3 × 3

72 = 2 × 2 × 2 × 3 × 3

GCF = 2 × 3 × 3

GCF = 18

\(\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}\)

\(\huge\textsf{Hey there!}\)

\(\large\textsf{Looking for your LCD (Least Common Denominator) of each fraction}\downarrow\\\\\\\mathsf{\dfrac{1}{4}=\dfrac{3}{12}}\\\\\\\mathsf{\dfrac{1}{6}=\dfrac{2}{12}}\\\\\\\mathsf{\dfrac{1}{3}=\dfrac{4}{12}}\\\\\\\\\\\large\textsf{The LCD is \underline{12}}\)

\(\mathsf{\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{3}}\)

\(\mathsf{= \ \dfrac{1\times3}{4\times3}+\dfrac{1\times2}{6\times2}+\dfrac{1\times4}{3\times4}}\)

\(\large\textsf{Solving for the numerators (TOP numbers)}\downarrow\\\\\mathsf{1\times3=\boxed{\bf 3}}\\\\\mathsf{1\times2=\boxed{\bf 2}}\\\\\mathsf{1\times4=\boxed{\bf 4}}\)

\(\large\textsf{Solving for the denominators (BOTTOM numbers)}\downarrow\\\\\mathsf{4\times3=\boxed{\bf 12}}\\\\\mathsf{6\times2=\boxed{\bf 12}}\\\\\mathsf{3\times4=\boxed{\bf 12}}\)

\(\mathsf{=\ \dfrac{3+2+4}{12}}\)

\(\large\textsf{Solving for your numerator (TOP number) }\downarrow\\\\\\\mathsf{3+2+4}\\\\\mathsf{= 5+4}\\\\\mathsf{= \boxed{\large\textsf{\bf 9}}}\)

\(\mathsf{=\ \dfrac{9}{12}}\)

\(\mathsf{\dfrac{9\div3}{12\div3}}\\\\\\\\\mathsf{9\div3= \boxed{\large\textsf{\bf 3}}}\\\\\mathsf{12\div3=\boxed{\large\textsf{\bf 4}}}\)

\(\mathsf{= \dfrac{3}{4}}\)

\(\boxed{\boxed{\large\textsf{Answer: }\boxed{\mathsf{\bold{ \dfrac{9}{12}\ or\ \dfrac{3}{4}}\ either\ of\ those\ fractions\ should\ work\ because}}}}\\\boxed{\boxed{\large\textsf{they are equal to each other!}}}\huge\checkmark\)

\(\large\textsf{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

The amswer is "2,4,9....."

Step-by-step explanation:

\(x=\frac{1}{7}\\\\x_d=0.\overline{142857}\\\\x_h=0.\overline{249}\\\\\)

by leave you to work out the other 7 digits:

\(\to \frac{1}{7}\approx \frac{a}{16}\\\\a= \text{first hex digit}\\\\a=floor(\frac{16}{7})=2\\\\\)  

\(\to \frac{1}{7}- \frac{a}{16}\approx \frac{b}{16^2}\\\\b= \text{second hex digit}\\\\b=floor(\frac{16^2}{7} -16a)=4\\\\\)  

\(\to \frac{1}{7}- \frac{a}{16}-\frac{b}{16^2} \approx \frac{c}{16^3}\\\\c= \text{third hex digit}\\\\c=floor(\frac{16^3}{7} -16^2a-16b)=9\\\\\)  

Given

Answer

Which is triangle 2

Answer:

The answer is D

Step-by-step explanation:

The answer is D

Answer:

hi

Step-by-step explanation:

3(x+4)=-18

3 × X + 3× 4=-18

3x+12=-18

3x=-18-12

3x= -30

x= -30/3

x= -10

hope it helps

have a nice day

A. The linear equation is: y = 60x + 45

B. The graphed equation is shown in the attachment below.

A linear equation is defined as, y = mx + b, where the initial value = b; unit rate = m; x and y are the variables.

A. In this situation given, we have:

Substituting the values into y = mx + b, we would have the equation as:

y = 60x + 45

B. The graph of the equation is shown in the image attached below.

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Given:

Total number of students = 10

To find:

How many was can you award first, second, and third place?

Solution:

Total number of students is 10. So, the total possible ways for the first award is 10.

We know that one student can hold only one place. So, after giving the first award, the number of remaining students is 9 and the total possible ways for the second award is 9.

Similarly, the total possible ways for the third award is 8.

Now, the total number of ways to award first, second, and third place is:

\(10\times 9\times 8=720\)

Therefore, the total number of ways to award first, second, and third place is 720.

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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Hey there! I'm happy to help!

to find the volume of a sphere, you cube the radius, multiply it by 4/3, and then multiply it by π.

First, we have to find the radius. To find the surface area you square the radius and multiply it by 4 and then π.

Let's do that formula backwards on our surface area to find the radius.

We divide by π

100÷π=100

We divide by 4.

100÷4=25

We find the square root.

√25=5

Now, we use our radius in the volume formula.

5³=125

125×4/3=500/3

We multiply by π.

500/3π

Therefore, the volume of a sphere if its surface area is 100π ft² is 500/3π ft³.

Have a wonderful day! :D

Answer:

V=166.66\(\pi\) ft³

Step-by-step explanation:

The surface area of a sphere is 4\(\pi\)r²

100\(\pi\)=4

100\(\pi\)/4

25=r²

r=5

Now that we know the radius is 5, we can find the volume.

v=4/3\(\pi\)(5)³

v=(5*5*5*4)/3*\(\pi\)

V=166.66\(\pi\)

Hi there!

Let the equation be

\(y = kx + b\)

When x = 0, y = 2

And

when x = 3, y = 1.25

So, b = 2

3k + b = 1.25

=> k = -0.25

b = 2

Therefore, y = -0.25x + 2 (Substituting the two points)

Hope this helps !

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

X-61=100

X=100-61

X=39%

Step-by-step explanation:

The vectors AB and AC are (-2, -1, 5) and (-5, 1, 5) respectively. The parametric equation of the line passing through A and B is given, and the equation of the plane containing points A, B, and C is y = 0. The area of triangle ABC is calculated to be 7.5 square units.

(a) To find the vectors AB and AC, we subtract the coordinates of point A from the coordinates of points B and C, respectively:

Vector AB = B - A = (2 - 4, 0 - 1, 3 - (-2)) = (-2, -1, 5)

Vector AC = C - A = (-1 - 4, 2 - 1, 3 - (-2)) = (-5, 1, 5)

(b) The parametric equation of the line passing through points A and B can be expressed as:

x = 4 - 2t

y = 1 - t

z = -2 + 5t

The equation of the plane containing points A, B, and C can be determined using the cross product of vectors AB and AC. The normal vector of the plane is given by:

n = AB x AC = (-2, -1, 5) x (-5, 1, 5)

Using the cross product formula, we calculate the cross product:

n = ((-1)(5) - (1)(-5), (5)(-5) - (5)(-2), (-2)(1) - (-1)(-2))

= (-5 - (-5), -25 - (-10), -2 - 2)

= (0, -15, 0)

The equation of the plane can be written as:

0x - 15y + 0z + d = 0

Simplifying, we get:

-15y = 0

y = 0

Therefore, the equation of the plane is -15y = 0, or simply y = 0.

(c) To find the area of triangle ABC, we can use the formula:

Area = (1/2) * |AB x AC|

We already have the vectors AB and AC:

AB = (-2, -1, 5)

AC = (-5, 1, 5)

Calculating the cross product:

AB x AC = ((-1)(5) - (1)(-5), (5)(-5) - (5)(-2), (-2)(1) - (-1)(-2))

= (-5 - (-5), -25 - (-10), -2 - 2)

= (0, -15, 0)

Now we can find the magnitude of the cross product:

|AB x AC| = sqrt(0^2 + (-15)^2 + 0^2) = sqrt(225) = 15

Finally, we calculate the area:

Area = (1/2) * |AB x AC| = (1/2) * 15 = 7.5

Therefore, the area of triangle ABC is 7.5 square units.

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Answer:

4

Step-by-step explanation:

One way to do it: The y-axis is the vertical axis. The point is at 4 on the y-axis.

Another way to do: Coordinates of the point = (2,4)

The y-coordinate is the second number.

We can write the {y} - coordinate of the given point as 4 because the general form of the coordinate in 2 - D plane is (x, y).

Given is to find the value of the {y} coordinate of the plotted point

The given point is (2, 4). We can write the {y} - coordinate of the given point as 4. This is because we know that the general form of the coordinate in 2 - D plane is (x, y).

Therefore, we can write the {y} - coordinate of the given point as 4 because the general form of the coordinate in 2 - D plane is (x, y).

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The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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Answer:

Hi,

6

Step-by-step explanation:

the number divided by 5 has a remainder of 1 , its last digit is 1 or 6.

the number is divisible by 2, its last digit is 0 or 2,or 4, or 6 or 8.

Both conditions give : the last digit must be 6.

The correct statement in the equation is that Natalie will have $34 left if she buys 4 headbands.

Natalie earned some money pet sitting a neighbour's cat.  She's going to use part of the money to buy some of her favourite headbands.

Therefore, the amount of pet-sitting money Natalie will have left after buying headbands is m(n)  = 50 - 4n dollars,

where

Therefore, the true statement of the equation are as follows:

m(n)  = 50 - 4n

m(n) = 50 - 4(4)

m(n) = 50 - 16

m(n) = 34 dollars.

Therefore, Natalie will have $34 left if she buys 4 headbands.

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Answer:

-3 + 9i

Step-by-step explanation:

The conjugate of -3i is - 3 - i.

(- 3 i) × (- 3 - i)

Multiply both terms.

-3 + 9i

The multiplication of the complex number -3i and it’s conjugate 3i is 9.

A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.

For the given situation,

The complex number is -3i.

The conjugate of a complex number a+bi is a-bi.

So, the conjugate of a complex number \(-3i\) is \(3i\)

Now multiply -3i and 3i, we get

⇒ \((-3i)(3i)\)

⇒ \(-9(i^{2} )\)

⇒ \(-9(-1)\)               [∵ \(i^{2}=-1\)]

⇒ \(9\)

Hence we can conclude that the multiplication of the complex number -3i and it’s conjugate 3i is 9.

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As we see, p-value is less than the significance level, so null hypothesis rejected and there is no evidence to support the claim that population mean is 22 degree C.

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values. We have various temperature measurements are recorded at different times for a particular city.

Sample Mean, \(\bar X \) = 20°C

Standard deviations,\(\sigma \)= 1.5° C

Level of significance, = 0.05

We have to test that population mean is 22 degree C. Consider the hypothesis testing, the null and alternative hypothesis are \(H_0 : \mu = 22 \).

\(H_a : \mu ≠ 22 \).

Consider the test statistic, z test for mean formula, \(z = \frac{\bar x - \mu }{\frac{\sigma}{\sqrt{n}}}\).

=> \(z = \frac{20 - 22}{\frac {1.5}{\sqrt{60}}}\).

= - 10.32

Now, using distribution table, the p-value for z = - 10.32 is less than to 0.001. So,

p-value < 0.05, so null hypothesis is rejected.

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Unless specified, all doors are 3′−0′′×7′−0∗; all windows are 3′−0′′×5′−0′′. To calculate the amount of materials required, we must first find the area of each wall and subtract the area of the openings to obtain the total wall area to be covered. Then we can multiply the total area to be covered by the amount of materials required per square foot. The amount of materials required depends on the type of material used (paint, wallpaper, etc.) and the desired coverage per unit.

The table below provides the total area to be covered for each room, assuming that all walls have the same height of 8 feet. Room dimensions (ft) Doors Windows A12′×12′2 35A210′×10′2 30A310′×12′2 35A48′×10′1 25 Total 320 As per the given data, Unless specified, all doors are 3′−0′′×7′−0∗; all windows are 3′−0′′×5′−0′′. The area of the door is 3′−0′′×7′−0′′= 21 sq ftThe area of the window is 3′−0′′×5′−0′′=15 sq ftThe amount of wall area covered by one door = 3′-0′′ × 7′-0′′ = 21 sq ftThe amount of wall area covered by one window = 3′-0′′ × 5′-0′′ = 15 sq ftTotal wall area to be covered for Room A1 = 2 (12×8) - (2x21) - (3x15) = 140 sq ft. Total wall area to be covered for Room A2 = 2 (10×8) - (2x21) - (2x15) = 116 sq ft.Total wall area to be covered for Room A3= 2 (12×8) - (2x21) - (3x15) = 140 sq ft.Total wall area to be covered for Room A4 = 2 (8×8) - (1x21) - (2x15) = 90 sq ft.Total wall area to be covered for all four rooms = 320 sq ft.

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\(\text{Arc length,}\\\\s = r \theta \\\\~~=12\cdot \left(30 \times \dfrac{\pi}{180} \right)\\\\~~=12\cdot \dfrac{\pi}6\\\\~~=2\pi\)

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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