Which of these equations are true? Select TWO correct answers. Answer A −8×3=24 B −4+3=1 C 15−(−2)=−13 D −5 ×7=−35 E −10 + −10 = −20

The distance across the lake is 552.98 ft

Define Cosine Rule.

According to the Cosine Rule, the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them. Law of cosines and Cosine Formula are other names for the cosine rule.

We have,

a = 217 ft

b = 347 ft

y = 53°

We have cosine formula,

c² = a² + b² – 2ab cos ∠z

Here, ∠z =  53°

let, c = distance across the lake

Now, plug in the values like that

c² = (217)² + (347)²  - 2 * 217 * 347 cos 53

   = (217)² + (347)²  - 2 * 217 * 347 * (-0.91828278621)

   = (217)² + (347)² - (-138291.551037654)

   = 47,089 + 120409 + 138291.551037654

   = 167498 + 138291.551037654

c² = 305789.551037654

c = 552.982414763 or 552.98 ft

Therefore, the distance across the lake is  552.98 ft

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Answer:

difference = 1

Step-by-step explanation:

the absolute value function always gives a positive value , that is

| - a | = | a | = a

then

| - 10 | = | 10 | = 10

| 9 | = 9

difference is the 10 - 9 = 1

Answer:

1

Step-by-step explanation:

1) substitute z with 4 in the equation

(m^3)^4

2) multiply the index

m^3*4

=m^12

3) m^12≠ m^7

therefore, 1 is a lie

The statements above which is a lie is number 1

Statement 1 :

(m^3)^z = m^7

m^3z = m^7

3z = 7

z = 7/3 (False)

Statement 3 :

(4^5)^z = 4^20

4^5z = 4^20

5z = 20

z = 4 (True)

Statement 2 :

(12^3)^2 = 12^6

(12^y)^x = 12^6

12^6 = 12^6

(True)

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The equation is x = 4f - 148 and value of f is 62 degree Fahrenheit.

Given,

In the question:

The number of snowy tree cricket chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.

The equation x= 4f - 148 relates the number of chirps per minute x and the outside temperature in degrees Fahrenheit f.

Now, According to the question:

Let x = number of Chirps.

f = temperature in Fahrenheit

Equation Connecting the two is

x = 4f -148

When, x = 100

100 = 4f - 148

100 + 148 = 4f

248 = 4f

f = 248/4

f = 62

Hence, The equation is x = 4f - 148 and value of f is 62 degree Fahrenheit.

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Answer:

Don't be a secret agent. You never know what's going to happen.

Step-by-step explanation:

Until he slipped on a puddle of goose poop. His hat flew off, revealing a shiny, bald head, which he immediately grabbed his scarf to cover. In his rush, he failed to notice a goose prodding at the secret package in his pocket. With a flurry of wingbeats, the goose flew off with the secret package in its beak. The secret agent suddenly realized that the goose was a spy in disguise from a rival organization.

Answer: 23 rounded to the nearest whole number .

Step-by-step explanation:

5/6 = 1.2

1 serving = 1.2

multiply 1.2 by 19 servings you'll get 22.8 after round it then you'll get 23.

The surface area of a square pyramid is 192 cm²

What is the surface area of a square pyramid?

The term "surface" refers to the "outer or exterior part of an object or body." As a result, the total surface area of a square pyramid is the sum of its lateral face and base areas.

To find the surface area of the square pyramid, we'll use the mathematical formula.  

Mathematically, the formula for calculating the surface area A  of a square pyramid is :

S.A. = s² + sl

where,

s is the pyramid height,

l is the base length.

S.A. = (8)² + 8 * 16

S.A. = 64 + 128

S.A. = 192 cm²

Hence, the surface area of a square pyramid is 192 cm².

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The equation of the line q that is perpendicular to line p is  y = - 3 / 5 x - 9.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, p has an equation of y = 5 / 3 x - 4 Line q includes the point (-10,-3) and is perpendicular to line p.  The equation of line q can be found as follows:

The product of the slope of perpendicular lines is equals to negative one.

Therefore, let's find the slope of line q.

m₁m₂ = -1

5 / 3m₂ = - 1

m₂ = - 3 / 5

Hence, the equation of line q is y = - 3 / 5x + b.

Let's find the y-intercept using (-10, -3)

-3 = - 3 / 5(-10) + b

-3 = 6 + b

-3  - 6 = b

b = -9

Therefore, the equation of line q is y = - 3 / 5 x - 9

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The probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 6724,

The mean life of a battery, m = 645,

The total number of samples, n = 152

Calculate the probability of a mean battery life of lower than 636.4 minutes by the following formula,

z = m - x / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 645 - 636.4  / (82 / √ 152)         [σ = √ variance = √6724 = 82]

z = 1.29

Consult the cumulative standard normal table

P (z < 636.4) = 0.9032,

But we know that

P (z > 636.4) = 1 - P (z < 636.4)

P (z > 636.4) = 1 - 0.9032 = 0.0968

Therefore, the probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.

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Answer: The second earthworm is 15 inches long

Step-by-step explanation: 5 X 3 = 15

Answer:

15 inches long

Step-by-step explanation:

the first one is 5 inches long

let it be x

the second one is 3 times as long

that is: 3×x

the value of x is 5

3×5=15 inches long

The confidence is 66%. We are 66% confident that the mean score for the students is in the given interval

Given: standard deviation(s) = 16, number of sample(n) = 110, margin of error(E) = 1.471

E = z x s /√n where z is z-score

1.47 = (z x 16)/√110

z = (1.471x√110)/16 = 0.96

Use the z-score to check the value of p in the table for Area under normal curve (image attached) to determine:

p(-0.96 < z< -0.96)

The value shows that about 66.3% of area under the curve is between -0.96 and 0.96

Therefore, confidence level is 66%. So we are 66% confident that the mean score for all students taking the exam is in the interval

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Answer:

[tex]\huge\boxed{\sf 1 \frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle =\frac{2}{3} + \frac{4}{6} \\\\Equalize \ the \ denominator \\\\= \frac{2 \times 2}{3 \times 2} + \frac{4}{6} \\\\= \frac{4}{6} + \frac{4}{6} \\\\Add \\\\=\frac{4+4}{6} \\\\= \frac{8}{6} \\\\Simplify\\\\= \frac{4}{3} \\\\Convert \ into \ mixed \ fraction\\\\= 1 \frac{1}{3} \\\\\rule[225]{225}{2}[/tex]

The sum of interior angles of a tray that is of pentagon shape is 540°

Given,

There is a tray which is of pentagon shape.

We have to find the sum of interior angles of the tray.

We have to find the sum of interior angles of pentagon.

That is,

Sum of interior angle of polygon formula = (n - 2) × 180°

Where, n is the number of sides in a polygon.

Here,

Pentagon has 5 sides.

Then,

Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°

That is,

The sum of interior angles of a tray that is of pentagon shape is 540°

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The question is incomplete. Completed question is given below;

Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be

The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of the cuboid = length × height × width.

As per the given cylinder,

The radius of the base of the cylinder = 3

Height = 7

Base area = π(radius)²

Base area = π(3)²

Base area = 9π

The volume of the cylinder = Base area × Height

Volume = 9π × 7 = 198.

Hence "The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198".

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The Area of the parallelogram is 27.57 cm² .

If the length of the parallelogram with sides a and b , and the angle between the sides a and b is θ , then

Area of Parallelogram = a × b × Sin(θ)

In the question ,

it is given that

the length of the parallelogram is 4cm and 7 cm , and the angle between is 100° .

By substituting the values in the formula for Area of parallelogram

we get ,

Area = 4 × 7 × Sin(100°)

= 4 × 7 × 0.9848              ....because Sin(100°) = 0.9848  

= 27.57 cm²

Therefore , The Area of the parallelogram is 27.57 cm² .

The given question is incomplete , the complete question is

If the length of the sides of parallelogram is 4 cm and 7 cm and the angle between them is 100° , Work out the Area of the parallelogram ? Give your answer to 2 significant figures. ​

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Answer:

2

Step-by-step explanation:

5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

Let x be the number of pints of the first fruit juice (i.e., 30%) and y be the number of pints of the second fruit juice (i.e., 80%).

Since the total number of pints to make the 75% pure fruit juice is 50, it can be represented using the equation:

x + y = 50 -----(1)

Also, x pints of the first juice = 0.30x, y pints of the second juice = 0.80y and 50 pints of the mixture to be produced = 50(0.75)= 37.5. Therefore:

This is represented as ;

30% × x + 80% × y = 50 of 75%

Make x in the subject x + y = 50

Substitute:

x = 50 - y in 30% × x + 80% × y = 50 of 75%

0.30 (50 - y) + 0.8 × y = 50 of 0.75

15 - 0.3y + 0.8y = 37.5

Collect like terms :

-0.3y + 0.8y = 37.5 - 15

0.5y = 22.5

y = 45

Recall that :

x = 50 - y

x = 50 - 45

x = 5

Hence, 5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

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To prove both triangle similar ratio of their sides must be equal

AC/GI = BC/HI

Therefore last option is correct .

The difference between congruence and similarity can be examined mathematically. These two words are defined by  shape, proportion, and angle.

Congruent shapes have the same dimensions and overlap when stacked. Two congruent objects have the same size and shape, but different orientations and placements in  space. This doesn't change the fact that they are the same as they have the same physical properties, angles and dimensions.

Similarity means similar but not identical. A shape can be mathematically equivalent in its base form as follows: B. Circles, but different sizes.

to prove both triangle similar ratio of their sides must be equal

AC/GI = BC/HI

Therefore last option is correct .

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Answer:

Step-by-step explanation:

a) Translation rule has been used in first image.

b) Reflection rule has been used in second image.

Transformations can be divided into four categories: translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognise which ones have already been done. A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given,

Transformations used:

a) Translation rule has been used in first image.

b) Reflection rule has been used in second image.

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The perimeter of the right triangle would be 66.6 cm.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a right triangle with side 19 centimeters and side 20 centimeters.

Using the Pythagoras theorem, we get -

h² = (19 x 19) + (20 x 20)

h² =  761

h = 27.6 cm

The perimeter will be -

P = [h] + [p] + [b]

P = 27.6 + 19 + 20

P = 66.6 centimeters

Therefore, the perimeter of the right triangle would be 66.6 cm.

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The volume of the sphere can be calculated using the formula V = 4/3πr³

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface

We have a sphere.

Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -

V = 4/3πr³

Where -

[r] is the radius of sphere

Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

now, to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}} \implies \cfrac{-4}{-3 +6} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{4 }{ 3 }}(x-\stackrel{x_1}{(-6)}) \implies y -6 = - \cfrac{4 }{ 3 } ( x +6) \\\\\\ \stackrel{\textit{multiplying both sides by}\stackrel{LCD}{3}}{3(y-6)=3\left( - \cfrac{4 }{ 3 } ( x +6) \right)} \implies 3y-18=-4(x+6) \\\\\\ 3y-18=-4x-24\implies 3y=-4x-6\implies {\Large \begin{array}{llll} 4x+3y=-6 \end{array}}[/tex]

Since the area of this kite is 5 times the shorter diagonal, the length of the longer diagonal is 10 cm and the area is equal to 30 cm².

In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:

A = ½ × d₁ × d₂

Where:

For the longer diagonal, we have:

d₁ = d₂ + 4

For the area of kite, we have:

Area = 5d₂ = 5(6) = 30 cm²

Substituting the given parameters into the formula, we have;

30 = ½ × d₁ × 6

60 = 6d₁

d₁ = 60/6

d₁ = 10 cm.

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Answer:

Yes and it would equal 96

Step-by-step explanation:

I don’t think I need to explain further you seem to understand but let me know if you do

hopes this helps please mark brainliest

Correct, the area of a parallelogram is always the width of the base by the perpendicular height. You can find the height by using the Pythagorean Theorem after separating one of the right triangles.

6.25 more students received a B than that received a grade of A.

Total students = 30

No. of students received grade B = 1/3 of 30

                                                        = (1/3)*30

                                                        = 10

No. of students received grade C = 1/4 of 30

                                                        = (1/4)*30

                                                        = 7.5

No. of students received grade D = 1/6 of 30

                                                        = (1/6)*30

                                                        = 5

No. of students who failed = 1/8 of 30

                                            = (1/8)*30

                                            = 3.75

Total students with grade B,C,D or fail = 10 + 7.5 + 5 + 3.75

                                                                = 26.25

No. of students received grade A = 30 - 26.25

                                                        = 3.75

Difference between grade B and grade A = 10 - 3.75

                                                                      = 6.25

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i) Angle 5 and 7 - Adjacent angles are supplementary

ii) Angle 3 and 5 - Same side interior angles are supplementary

iii) Angle 1 and 7 - Same side exterior angles are supplementary

Adjacent Supplementary Angles

Same side interior angles are supplementary

Same side exterior angles are supplementary

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