1)if the equations 2x +y=7 and x-y= 2 are solved simultaneously, then y =
(a)1 (b)-2 (c)-1 (d)+2 (e)3

2)Find the H.C.F of 12, 15 and 18.
(a) 2 (b)6 (c) 4 (d)5 (e)3

3)Express 100011two as a decimal number.
(a) 32 (b) 33 (c) 34 (d) 35 (e) 36​

Answer:

122 degrees-

Step-by-step explanation:

\(m\angle {GOC}=m\angle{GOA}+m\angle{AOC}\\=32^\circ + 90^\circ\\=122^\circ\)

Angle GOA is a vertical angle with angle DOE, so it has the same measure (vertical angles are congruent).

Angle AOC is a right angle because angle COE is a right angle.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

18 hours playing video games

6 hours on tv

Step-by-step explanation:

math

The gradient of the line K that is perpendicular to the line H that has a gradient of 7 is -1/7

Perpendicular lines are lines that form a right angle (90 degrees angle) at the point of their intersection, in which the slope of one of lines is the negative reciprocal of the slope of the other line.

The gradient of the line H = 7

The relationship between the lines K and line H is; Line K is perpendicular to the line H

The slope of a line a, which is perpendicular to another line b with slope m is; -1/m

Therefore, the slope of the line K is -1/7

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Answer:

(2, -5)

Step-by-step explanation:

If you rotate the image in your head or on paper, it'll land in a quadrant on the grapg that can only be (x, -y) so if we use that and calculate about which numbers it is, or we use the options given to find an answer that fits the criteria, we get our answer.

Answer:

B

Step-by-step explanation:

trust

Answer:c) 4/5

Step-by-step explanation:

y= mx+c, here, m is the slope.

In this case, m= 4/5, c= -3

Answer:

different from players, yes

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1 (#3)

The formula for a regular octagon inscribed in a circle of radius \(r\) is \(A=2\sqrt{2}r^2\). Hence, \(A=2\sqrt{2}(4)^2=16*2\sqrt{2}=32\sqrt{2}\approx45.255m^2\).

Thus, C is the correct answer

Problem 2 (#4)

Using the co-function identity \(\displaystyle \sin\biggr(x+\frac{\pi}{2}\biggr)=\cos(x)\), the equation can be rewritten as \(cos(x)=\frac{\sqrt{3}}{2}\). Using a unit circle, it's easy to see that the answer is \(\displaystyle\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}\).

Thus, C is the correct answer

Problem 3

\(f(x)=g(x)\\\\2\sin^2 x-1=-\cos(x)\\\\2(1-\cos^2 x)-1=-\cos(x)\\\\2-2\cos^2 x-1=-\cos(x)\\\\1-2\cos^2 x=-\cos(x)\\\\2\cos^2x-\cos(x)-1=0\)

Let \(u=\cos(x)\), hence:

\(2u^2-u-1=0\\\\(2u+1)(u-1)=0\)

\(\displaystyle2u+1=0\\\\2u=-1\\\\u=-\frac{1}{2}\\ \\\cos(x)=-\frac{1}{2}\\ \\x=\biggr\{\frac{2\pi}{3},\frac{4\pi}{3}\biggr\}\)

\(u-1=0\\\\u=1\\\\\cos(x)=1\\\\x=\{0\}\)

So, the solution set is \(\displaystyle\biggr\{0,\frac{2\pi}{3},\frac{4\pi}3}\biggr\}\)

Thus, B is the correct answer

Problem 4 (#8)

If we construct a right triangle in Quadrant I with an opposite leg length of 1 unit and an adjacent leg length of 1 unit, this shows that \(\displaystyle\tan\theta=\frac{opposite}{adjacent}=\frac{1}{1}=1\). Since \(\displaystyle \csc\theta=\frac{1}{\sin\theta}\) and \(\displaystyle\sin\theta=\frac{opposite}{hypotenuse}\), we must solve for the hypotenuse with the Pythagorean Theorem:

\((opposite)^2+(adjacent)^2=(hypotenuse)^2\\1^2+1^2=(hypotenuse)^2\\1+1=(hypotenuse)^2\\2=(hypotenuse)^2\\\sqrt{2}=hypotenuse\)

Therefore, since \(\displaystyle \sin\theta=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\), then \(\displaystyle \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2\sqrt{2}}{2}=\sqrt{2}\).

Thus, B is the correct answer

Problem 5 (#9)

As no angles are given and only side lengths, we are forced to use the Law of Cosines to solve for the angles:

Angle A:

\(a^2=b^2+c^2-2bc\cos(A)\\400^2=500^2+600^2-2(500)(600)\cos(A)\\160000=250000+360000-600000\cos(A)\\160000=610000-600000\cos(A)\\-450000=-600000\cos(A)\\\frac{3}{4}=\cos(A)\\ A\approx41.410^\circ\)

Angle B:

\(b^2=a^2+c^2-2ac\cos(B)\\500^2=400^2+600^2-2(400)(600)\cos(B)\\250000=160000+360000-480000\cos(B)\\250000=520000-480000\cos(B)\\-270000=-480000\cos(B)\\\frac{9}{16}=\cos(B)\\B\approx55.771^\circ\)

Angle C:

By the Triangle Angle-Sum Theorem, \(C\approx82.819^\circ\)

Hence, we can conclude that angle A is the smallest angle the swimmers must turn between the buoys.

Thus, C) 41.410° is the correct answer

Problem 6 (#unknown)

As we are given two angles and a side length, we can use the Law of Sines to find side length "b". Firstly, we need angle C so we can set up the proportion to find "b". By the Triangle Angle-Sum Theorem, \(m\angle C=60^\circ\).

\(\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(64^\circ)}{b}=\frac{\sin(60^\circ)}{8}\\\\8\sin(64^\circ)=b\sin(60^\circ)\\\\b=\frac{8\sin(64^\circ)}{\sin(60^\circ)}\\ \\b\approx8.303\)

Thus, B is the correct answer (how ironic lol)

Problem 7 (#13)

\(\displaystyle\sqrt{2}\cos2x=\sin^2x+\cos^2x\\\\\sqrt{2}\cos2x=1\\\\\cos2x=\frac{1}{\sqrt{2}}\\\\\cos2x=\frac{\sqrt{2}}{2}\\ \\2x=\frac{\pi}{4},\frac{7\pi}{4}\\ \\x=\frac{\pi}{8},\frac{7\pi}{8}\)

Hence, B is the correct answer

Problem 8 (#14)

\(\displaystyle \sec\theta=2\\\\\frac{1}{\cos\theta}=2\\ \\\cos\theta=\frac{1}{2}\\ \\\theta=\frac{\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n\)

Thus, D is the correct answer

Problem 9 (#19)

The bottom graph looks correct as the period of the tangent function is \(\frac{\pi}{|b|}=\frac{\pi}{2}\).

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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Answer:

0

Step-by-step explanation:

The ace of clubs is black.

There is no red ace of clubs.

p(red ace of clubs) = 0

Answer:

Step-by-step explanation:

There is no Red ace of club. All the clubs are black in colour. So the probability is 0

Answer:

-1/5

Step-by-step explanation:

You are going to multiply across so (2 times -1=-2) and (5 times 2=10) -2/10 simplified is -1/5.

Hope this helped!

Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

Answer:

if we multiply 11/4 to 4/11 it gives product as 1

Therefore , the solution of the given problem of area comes out to be  Area of circle  85π cm2.

Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.

Here,

Given:

Points :P(-7; -2), Q(-1; 9) and R(5; -3).

The area of the circumscribed circle of the triangle.

is:

=> PQ = √(-7 - (-1))² + (-2 - (-9))²

=> PQ = √85

The radius is √85

=> Area of circle = π(√85)²

=>  Area of circle = 85π cm2

Therefore , the solution of the given problem of area comes out to be  Area of circle : 85π cm2.

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The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).

The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.

The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.

In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.

The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.

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Answer:

Katie got to school at 4:30

Step-by-step explanation:

Answer:

4:30 pm

Step-by-step explanation:

She left at 4:00. In the question it says that it took 30 minutes to get there, and 30minutes after 4:00 pm is 4:30pm.

Answer:

mary broke

Step-by-step explanation:

it simple she will need to pay 2338 apples

Step-by-step explanation:

Mary has 28 Apple she gave her mother 2355 how many apples does he have​

there are multiple answers to this

1st is  28-2355= -2327

2nd is there is no answer because it is asking for how many apples he has and there is no mention of how many apples he gives to mary's mother

Answer: A (-7,-4)

Step-by-step explanation:

Took the same test

Answer:

y=\frac{3}{5}x\ +4.4

Step-by-step explanation:

Rise over run which would be 6/10 simplify that and you would get 3/5

Then you are looking for the intercept of y which would be 4.4.

Answer:

Step-by-step explanation:

Answer: a × ba × c = a (bc) = 0

a × ba × c = 2019-2019 = 0

Step-by-step explanation:

Answer: $305

Step-by-step explanation:

1) 12.50 multiplied by 10= 125

2) 12% of 1500 is 180

3) 125+180=305

Answer:

It would be impossible for any of the other angles to be 10 degrees.

Step-by-step explanation:

It is impossible because a scalene triangle means that all the angles have different measurements. If the triangle was isosceles, it means that 2 angles are the same. If it was that, then 10 degrees would be possible, but it is not that for this case. I hope you learn from this answer, and please give me brainliest if you like my answer.

Answer:

Step-by-step explanation:

hm 2x2=4

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

The volume of the trash can is approximately 3,618.2 cubic inches.

Step-by-step explanation:

The volume V of a cylinder is given by the formula:

V = πr^2h

where r is the radius of the base and h is the height of the cylinder.

In this case, the height is 12 inches and the base radius is 6 inches, so we have:

V = π(6)^2(12)

= 1,152π

≈ 3,618.2 cubic inches (rounded to the nearest tenth of a cubic inch)

Therefore, the volume of the trash can is approximately 3,618.2 cubic inches.

Answer:

Step-by-step explanation:

The Meyer family uses a kitchen trash can shaped like a cylinder. It has a height of 12 inches and a base radius of 6 inches.

Height of trash can = 12 inches

Height of trash can = 12 inchesRadius of trash base = 6 inches.

Volume of cylinder = πr²h

= 22/7 × 6² × 12

= 22/7 × 36 × 12

= 9504/7

= 1375.7 inch³

Hence, Volume of the trash can is 1375.7 cubic inch.