6-3 practice elimination using addition and subtraction

The given sides 5.25, 7 , 8.25 doesn't not constitute a right angled triangle.

The foundation of trigonometry is a right-angled triangle, one of the most significant geometric shapes. The "base," "hypotenuse," and "height" of a right-angled triangle are three-sided triangles with a 90° angle between the base and the height. A right triangle's area is the portion of the triangle that is contained within the triangle's edge.

An angle that is the same as another is known as a right angle (90 degrees). Simply referred to as a right triangle. A right-angled triangle has three sides, the hypotenuse, the leg, and the right angle, which is known as the leg. The two legs are described by the terms "base" and "height," which are interchangeable.

Applying the Pythagoras theorem we can find id the given sides make a right angled triangle or not.

Pythagoras theorem is

c² =  a² + b²

c, the hypotenuses and the longest side

a and b rest of the two legs

Given sides, 5.25, 7 , 8.25

8.25² =  5.25² + 7²

68.0625 ≠76.5625

Thus, The given sides 5.25, 7 , 8.25 doesn't not constitute a right angled triangle.

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y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.

To see the graph of y = 1

Now, According to the question:

What is called graph?

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Hence, y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.

Now, To see the representation of graph  y = 1

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The angle be 5x - 12 and 3x - 8 then the value of x  = 25.

The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner."

A protractor is a precision tool for measuring angles. Angles are measured in degrees, therefore the term "degree measure." Because one full revolution is equivalent to 360 degrees, it is divided into 360 segments.

Let the two angle be 5x - 12 and 3x - 8

5x + 3x - 12 - 8 = 180

Add similar elements: 5x + 3x = 8x

8x - 12 - 8 = 180

Subtract the numbers: -12 - 8 = -20

8x - 20 = 180

Move 20 to the right side

8x = 200

Divide both sides by 8

= 8x / 8 = 200 / 8

x  = 25

Therefore, the value of x  = 25.

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So, the sum of the exterior angles of a polygon with 15 sides is 2340 degrees.

The sum of the exterior angles of a polygon can be found using the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon.

In the case of a polygon with 15 sides, the number of sides (n) is 15. Therefore, the sum of the exterior angles can be found by plugging in 15 for n and solving the equation:

(15-2) * 180 = (13) * 180 = 2340 degrees

Therefore, the sum of the exterior angles of a polygon with 15 sides is 2340 degrees.

It's worth noting that the sum of all exterior angles of a polygon is always 360 degrees less than the sum of the interior angles of a polygon.

The sum of the interior angles of a polygon with n sides is (n-2)*180.

So for a 15 sided polygon the sum of the interior angles is (15-2)*180 = 2340 degrees.

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The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).

The given expression is 9x² - 12x + 4

By splitting the middle term, let us factor this polynomial.

To identify the factors we have to consider factors of 36 as (9 × 4)

9x²- 6x - 6x + 4

=3x(3x - 2) - 2(3x - 2)

=(3x - 2)(3x - 2)

Another example of a quadratic polynomial can be taken to demonstrate similar factorization:

x² + 9x + 20

= x² + 5x + 4x + 20

= x × (x + 5) + 4 × (x + 5)

= (x + 5)(x + 4)

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Area a + b + c = Area of Semi-circle on BC (radius 5). = Area c + d ... Shaded area = Sum of semi-circles on AC and AB – Semi-circle on BC + Triangle Area.

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To solve a 30-60-90 triangle problem, you can use the ratios of the sides of a 30-60-90 triangle. The ratios are:

The hypotenuse is opposite the 60 degree angle, and it is always twice the length of the shorter leg.

The longer leg is opposite the 90 degree angle, and it is always √3 times longer than the shorter leg.

The shorter leg is opposite the 30 degree angle, and it is always equal to x where x is the value of the shorter leg.

So, you can use these ratios to find the missing side length(s) of a 30-60-90 triangle, given the length(s) of the other side(s). For example, if you know the length of the hypotenuse, you can find the lengths of the other two sides by dividing the hypotenuse by 2 and √3, respectively.

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The cable company that has the best rate per channel is given as follows:

Tel-EVision.

The rate per channel is obtained applying the proportions in the context of this problem, dividing the total price by the number of channels.

Hence the rates for each company are given as follows:

The best rate is the lower rate, which is the justification for the answer given at the beginning of the problem.

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the pairs of ratios that form a true proportion: a and b

An equation proving the equality of two ratios is a genuine proportion. Knowing one ratio in a percentage can be used to determine values in the other equal ratio.

Where x is the number of successes and n is the sample size, p′ = x / n. The variable p′ represents the proportion of the sample and acts as a point estimate for the proportion of the genuine population.

Now, given that -

a. 3:6 and 5:10

= 1:2 and 1:2

Thus, it is a true proportion.

b. 4/12 and 6/18

= 4:12 and 6:18

= 1:3 and 1:3

Thus, it is a true proportion.

c. 20/5 and 10/3

= 20:5 and 10:3

= 4:1 and 10:3

Thus, it is not a true proportion.

d. 24:36 and 8:9

= 2:3 and 8:9

Thus, it is not a true proportion.

So, correct pairs of ratios that form a true proportion is: a and b.

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The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expressions are given below.

1/10 of 3 and 1/10 of 0.3

Then the multiplication of the expression is given by putting a cross sign between them. Then we have

⇒ [(1/10) x 3] x [(1/10) x 0.3]

⇒ 0.3 x 0.03

⇒ 0.009

The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.

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The required evaluation of the given fraction 4/5 of 3/4 is 3/5.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by the addition, subtract, dividing, and multiplying built-in functions.

We have to determine the evaluation of 4/5 of 3/4

As per the question, we have

⇒ 4/5 of 3/4

This can be also rewritten as:

⇒ (4/5) × (3/4)

Apply the multiplication operation,

⇒ 12/20

Reduce the above fraction into the simplest form,

⇒ 3/5

Thus, the required evaluation is 3/5.

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The required equation in the given format is given as y = 5(x - 1)² + 90.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,

Given equation,
y=5x² -30x+95

Take 5 commons from terms 5x²  and 30 and put it in parenthesis, in the parenthesis add and subtract 1

y = 5[x² - 2x + 1 - 1]+ 95

y = 5 (x - 1)² - 5 + 95
y = 5(x - 1)² + 90

Thus, the required equation in the given format is given as y = 5(x - 1)² + 90.

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Answer: -0.0555555.....

Step-by-step explanation:

Divide: -1 ÷18

= -0.05555555.....

Answer:

1/18 as a decimal is 0.0555555555555555555555555555555555555555555555555555555555555555...

Step-by-step explanation:

Answer: Jacinta

Step-by-step explanation: But the fraction still can be simplified to 1/7

Answer: j is correct

Step-by-step explanation:

The value of x is 3/7 because the angles of the two intersecting lines at point c, a c e and e c b, have specific values that can be used to solve for x.

Step 1: Calculate the angle of intersection between lines de and ab at point c.

Step 2: Calculate the angle of intersection between lines de and ab at point c.

Step 3: Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b.

Step 4: Divide the difference in angles by 7 to get the value of x.

To calculate the value of x, first calculate the angle of intersection between lines de and ab at point c. This angle is (2x +2) degrees. Then calculate the angle of intersection between lines d e and a b at point c, which is (5x +3) degrees. Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b, which is

(5x + 3) - (2x + 2) = 3x + 1

Divide the difference in angles by 7 to get the value of x, which is

x = (3x + 1)/7 = 3/7.

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The error in the measurement is 3.5%.

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. Mathematically, we can write -

[tex]$\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%[/tex]

Given is that James tries to cut a wooden board 20 inches long. The wooden board ends up being 20.7 inches long.

We can write the percentage error as -

p% = |20.7 - 20|/20 x 100

p% = 0.7 x 5

p% = 3.5%

Therefore, the error in the measurement is 3.5%.

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The method of simultaneous equations is a mathematical technique used to solve systems of equations with two or more unknowns. It involves solving a set of equations simultaneously, that is, finding values for all the unknowns in the equations at the same time.

The method of simultaneous equations is a mathematical technique used to solve systems of equations with two or more unknowns. It involves solving a set of equations simultaneously, that is, finding values for all the unknowns in the equations at the same time. This method is also known as elimination, substitution, or the linear system technique. The method of simultaneous equations involves manipulating the equations to express one of the variables in terms of the others. This can be done by either adding or subtracting the equations from each other, or by multiplying or dividing them by a common factor. Once one of the variables is expressed in terms of the others, the remaining equations can be solved, and the solutions can be substituted into the original equation to find the value of the other variables. The method of simultaneous equations is particularly useful for solving linear systems, which involve equations with linear coefficients, as the equations can be manipulated relatively easily. It is also useful for solving systems of non-linear equations, although it is more difficult to manipulate the equations in this case.

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The probability that the horse will not win the race is 0.5. The result is obtained by subtracting the probability of winning from 1.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

While, the probability for the opposite event is

P(not A) = 1 - P(A)

If the probability that a horse will win the race is 2/4, find the probability that the horse won't win the race!

The probability that the horse will win the race is

P = 2/4 = 0.5

The probability that the horse will lose is

P = 1 - P(A) = 1 - 0.5 = 0.5

Hence, the horse will lose with the probability of 0.5.

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The area, in square meters is 121π m²

The formula for calculating the area of a circle is expressed as;

A = πr²

Where;

Also, the circumference of the circle is expressed as;

Circumference = 2πr

Now, substitute the value of the circumference, we have;

22π = 2πr

Make 'r' the subject of formula, we get;

r = 11

Now, subsitiute into the formula for area;

Area = π(11)²

Find the square

Area = 121π m²

Hence, the value is 121π m²

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The area of the circle in terms of π is 121π metres square.

The circumference of the circle is 22π metres. The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of the circle = 22π metres

22π = 2πr

r = 22π / 2π

r = 11 metres

Let's find the area of the circle.

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = 11² × π

area of the circle = 121π metres²

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Answer:

0.42

Step-by-step explanation:

- 2.4 = - 12/5

The opposite of the reciprocal of – 2.4 is

+ 5/12 ≈ 0.42

Answer: 5/12

Step-by-step explanation:

if -2.4 in fractions is 12/5 the opposite reciprocal is the fraction and sign fliped which is 5/12

The measure of angle 2 from the given figure is 27°.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

Given that, m∠2 = (y+10)° and m∠4 = (3y-24)°.

Here, m∠2=m∠4 (∵ Opposite vertical angles are equal)

(y+10)°=(3y-24)°

3y-y=10+24

2y=34

y=17

So, m∠2 = (y+10)°=27°

Therefore, the measure of angle 2 from the given figure is 27°.

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Applying the definition of a midpoint, the length of SA is: C. 4 m.

The midpoint of a line segment or a side of a triangle is the point where the segment or side is divided into two equal segments.

Based on the information given, we can say that triangles QRS and ASB are similar triangles, therefore, their corresponding sides are proportional to each other.

Thus, let SA = x. We will have the following:

SA/SQ = BA/RQ

x/(x + 4) = 3/6

Cross multiply:

6x = 3(x + 4)

6x = 3x + 12

6x - 3x = 12

3x = 12

3x/3 = 12/3

x = 4

Length of SA is: C. 4 m.

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Answer:

you are right bro keep up

The scale factor of the dilation transformation of the pre-image triangle ΔDEF to the image ΔD'E'F', with the origin as the center of dilation is 3.

A dilation transformation is one in which the lengths of the sides of the pre-image are scaled up by a common factor to get the lengths of the sides of the image.

The coordinates of the vertices of the triangle ΔDEF are;

D(1, 5), E(1, 2), F(3, 2)

The length of the sides of triangle ΔDEF, making use of the difference between the non equal coordinate points, are;

DE = 5 - 2 = 3

EF = 3 - 1 = 2

The length of the side DF can be found using the formula for the distance between two points on the coordinate plane (a form of the Pythagorean Theorem), which is presented as follows;

DF = √((3 - 1)² + (2 - 5)²) = √(2² + (-3)²) = √(13)

The coordinates of the vertices of triangle ΔD'E'F' are; D'(3, 15), E'(3, 6), F'(9, 6)

Therefore; D'E' = 15 - 6 = 9

E'F' = 9 - 3 = 6

D'F' = √((9 - 3)² + (6 - 15)²) = √(6² + (-9)²) = √(9 × 13) = 3·√(13)

The scale factor, s.f. = The ratio of the corresponding sides of the triangles which is found as follows;

D'E'/DE = 9/3 = 3

E'F'/EF = 6/2 = 3

D'F'/DF = 3·√(13)/√(13) = 3

s.f. = D'E'/DE = E'F'/EF = D'F'/DF = 3

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Answer:

17.a)  See below.

17.b)  x = 34.3 cm, y = 34.3 cm

18.a)  See below.

18.b)  r = 8 m

Step-by-step explanation:

Given information (see attachment 1):

According to the Similar Triangles Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.  Therefore, triangles ABC and ADE are similar (refer to attachment 1).

As corresponding sides of similar triangles are always in the same ratio, the ratio of the base to height of the smallest triangle is equal to the ratio of the base to height  of the largest triangle:

[tex]\implies \sf DE:AD=BC:AB[/tex]

[tex]\implies y:80-x=60:80[/tex]

[tex]\implies \dfrac{y}{80-x}=\dfrac{60}{80}[/tex]

[tex]\implies 80y=60(80-x)[/tex]

[tex]\implies y=\dfrac{60(80-x)}{80}[/tex]

[tex]\implies y=\dfrac{3(80-x)}{4}[/tex]

The maximum area of a rectangle is when the length and height are equal:

[tex]\implies x=y[/tex]

Therefore, to find the value of x when the area of the rectangle is at its maximum, substitute x = y into the equation from part (a) and solve for x:

[tex]\implies x=\dfrac{3(80-x)}{4}[/tex]

[tex]\implies 4x=3(80-x)[/tex]

[tex]\implies 4x=240-3x[/tex]

[tex]\implies 7x=240[/tex]

[tex]\implies x=\dfrac{240}{7}[/tex]

[tex]\implies x=34.3\; \sf cm\;\;(nearest\;tenth)[/tex]

Therefore, the dimensions of the rectangle of maximum area to the nearest tenth are:

--------------------------------------------------------------------------------------------

Given information:

The formula for the volume of a cone is:

[tex]V=\dfrac{\pi r^2 h}{3}[/tex]

If the sum of the base radius r and the height h is 12 metres then:

[tex]\implies r + h = 12[/tex]

[tex]\implies h=12-r[/tex]

Substitute the expression for h into the volume of a cone formula to create an equation for V in terms of r:

[tex]\implies V=\dfrac{\pi r^2 (12-r)}{3}[/tex]

[tex]\implies V=\dfrac{12\pi r^2-\pi r^3}{3}[/tex]

[tex]\implies V=\dfrac{12\pi r^2}{3}-\dfrac{\pi r^3}{3}[/tex]

[tex]\implies V=4\pi r^2-\dfrac{1}{3}\pi r^3[/tex]

To find the radius of the cone that yields the maximum volume, differentiate V with respect to x:

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=2 \cdot 4\pi r^{2-1}-3 \cdot \dfrac{1}{3}\pi r^{3-1}[/tex]

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=8\pi r-\pi r^2[/tex]

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=\pi r(8-r)[/tex]

Set the differentiated equation equal to zero and solve for x:

[tex]\implies \pi r(8-r)=0[/tex]

[tex]\implies 8-r=0[/tex]

[tex]\implies r=8[/tex]

(Note: r is also equal to zero, but we can discard that solution since the radius has to be more than zero).

Therefore, the radius of the cone that yields the maximum volume is 8 m.

Answer:

22° and 33°

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

the ratio of the other 2 angles = 2 : 3 = 2x : 5x ( x is a multiplier )

sum the 4 angles and equate to 360

2x + 3x + 74 + 231 = 360

5x + 305 = 360 ( subtract 305 from both sides )

5x = 55 ( divide both sides by 5 )

x = 11

then

2x = 2 × 11 = 22°

3x = 3 × 11 = 33°

the other 2 angles have a measure of 22° and 33°

Answer:

I'm pretty sure the answer to the 1st question is 2.46 and the answer to the 2nd question is just 15. (I'm sorry if I'm wrong!)

Answer:

She would've traveled 4cm on the map

Step-by-step explanation:

If 1cm=18km in the map and Rashmi drove 72km, we just have to divide 72 by 18 to get the distance she traveled on the map.

72÷18=4

The animal shelter has a number of 35 dogs.

According to the statement, the animal shelter has a total of 65 abandoned cats and dogs and cats to dogs ratio is 6 : 7. We are asked to find the number of abandoned dogs in the shelter:

D = [d / (c + d)] · N

Where:

If we know that d = 7, c = 6 and N = 65, then the number of abandoned dogs is:

D = (7 / 13) · 65

D = 35

There are 35 dogs in the animal shelter.

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