If the measures of two angles of a triangle are 96° and 29°, what is the measure of the third angle?

A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The solutions are:

P' = (-4,-7)

Q ' = (-8,-7) (-8,-7)

R ' = (-3,3) (-3,3)

All you have to do is flip the provided points P, Q, and R's x and y coordinates.

The common principle is (x,y) —-> (y,x)

Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.

How do you locate a triangle's vertices?

Finding the triangle's vertices on the line y = x as an image

The steps below are used to locate a triangle's vertices using its midpoints:

Identify the midpoints' x and y values;

Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.

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In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.

h: hypotenuse

c1: shorter leg

c2: longer leg

Longer leg c2 is 3 inches longer than c1:

c2 = c1 + 3

hypotenuse h is 6 inches longer than c1:

h = c1 + 6

The formula for the calculation of the hypotenuse is:

h² = c1² + c2²

you replace for h and c2 in terms of c1:

(c1 + 6)² = c1² + (c1 + 3)²

You solve the previous equation for c1:

c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9

c1² - 6c1 - 27 = 0

the roots of the previous equation are:

(c1 - 9 )(c1 + 3) = 0

c1 = 9

c1 = -3

You take the positive number because there is no length of sides with negative values.

Then, c2 and h are:

c2 = c1 + 3 = 9 + 3 = 12

h = c1 + 6 = 9 + 6 = 15

Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches

The ratio of r-32 to r-125 is 3:2

A ratio in math displays how many times one number is contained in another. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). When both sides of a ratio are whole numbers and cannot be divided by a whole number, the ratio is in its simplest form.

Given,

Refrigerant r-32 and r-125 are the two main constituents of refrigerant r-410.

60 pounds of r-32 and 40 pounds of  r-125 make up to 100 pounds of r-410.

The ratio of r-32 to r-125 = 60/40 =3/2.

Hence, the required ratio of r-32 to r-125 is 3:2

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Answer: 50 degrees

Step-by-step explanation: 23+107+x=180

130+x=180

x=50

the answer is 5896. . . . . . ... . . . . . ......................

Hello!

When multiplying 67 x 88, the correct answer would be 5896.

Hope this helped!

The minimum that could be earned is $150. The required inequalities are solved below:

What is an inequality?

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.

(a) The minimum that could be earned is $150.

(b) The required inequality is given as 150+20x≥630

or, 20x≥630-150

or, x≥480/20

or, x≥24

(c) The required inequality is given as 150+20x≥750

or, 20x≥750-150

or, x≥600/20

or, x≥30

(d) The required inequality is given as 150+20x≤950

or, 20x≤950-150

or, x≤800/20

or, x≤40

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The variable h, as the subject of the given formula is h = 3 / (G.V + 1)

From the question, we are to make h the subject in the given formula

The given equation is

(3 - h) / V = G . h

Multiply both sides of the equation by V

V × (3 - h) / V = G . h × V

3 - h = G . h . V

Add h to both sides

3 - h + h = GhV + h

3 = GhV + h

Factorize h

3 = h(G.V + 1)

Now,

Divide both sides of the equation by (G.V + 1)

That is,

3 / (G.V + 1) = h

∴ h = 3 / (G.V + 1)

Hence, the value of h is 3 / (G.V + 1)

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Answer:

Step-by-step explanation:

Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.

A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.

Synthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...

  p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment

And dividing the cubic by (x -1) gives ...

  p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment

The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.

The rewrite of p(x) is ...

  p(x) = (x +4)(x +3)(x -1)(x -2)

The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.

We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2

The y-intercept is +24, the constant in the polynomial.

With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.

A graph is seen in the first attachment.

Answer:

-20

Step-by-step explanation:

1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4

2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number

3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too

4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously

The value of the travel trailer after 5 years is $8306  .

in the question ,

it is given that

the price of the travel trailer(a)  = $35000

rate of decrease(r) = 0.25

time (x) = 5 years

The exponential expression for the decrease in price after x years is given by the formula

price = a(1-r)ˣ

where, a is the initial amount ,

r is the decay rate ,

x is the time period .

Substituting the values from above in the formula ,

we get

price = 35000(1-0.25)⁵

= 35000(0.75)⁵

= 8305.664

≈8306

Therefore , the value of the travel trailer after 5 years is $8306  .

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The expression that we can replace in the second equation is 4 - y, doing that, we will get the solutions:

x = -8 and y = 12

Here we have the system of equations:

x=4−y

3x+2y=15

Notice that x is already isolated on the first equation, so we can substitute that in the second equation. Then we will get:

3x+2y=15

3*(4 - y) + 2y = 0

So the expression that could be substituted for x in the second equation is 4 - y.

And now we get:

12 - 3y + 2y = 0

12  = y

And the value of x is:

x = 4 - y = 4 - 12 = -8

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Answer:

x = 3 and y = 5

Step-by-step explanation:

1st: The sum of the same side interior angles equal 180°. Use this to solve for x.

45x - 5 + 16x + 2 = 180

61x - 3 = 180

61x - 3 + 3 = 180 + 3

61x/61 = 183/61

x = 3

2nd: find the measure of angle 16x + 2

16x + 2

16(3) + 2

48 + 2

50°

3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.

50 + 26y = 180

50 - 50 + 26y = 180 - 50

26y = 130

26y/26 =130/26

y = 5

We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:

Francs = 100×4.3450 = 434.50

Then, the answer is 434.5 french francs

Answer:

Find the total number of oranges.

Total oranges = 90 × 5

= 450

Since 1/5 were rotten oranges,

Fraction of oranges that were not rotten

= Fraction of total oranges - Fraction of rotten oranges

= 5/5 - 1/5

= 4/5

Number of oranges not rotten = 4/5 × 450

= 360

Answer:

They are congruent by SAS:

Side: AB = CB

Angle: ∠ABD = ∠CBD

Side: BD = BD

Explanation:

Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.

If two of the angles are equal, we can say that all the interior angles are equal.

So, based on the given information we get:

1. AC ⊥ BD means that AC is perpendicular to BD, therefore,

∠ADB = ∠CDB = 90°

2. It is given that ∠A = ∠C

3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:

∠ABD = ∠CBD

4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB

5. BD = BD because it is the same segment.

6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD

Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.

The fraction of the poster does Dwayne use for his friends from school is 5/12.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number that is above the line and the denominator is the number below the line. An example of a fraction is 5/12.

In this question, the numerator is the number of parts he gives his friends from school. The denominator is the total number of parts he divides the poster.

Fraction = parts he gave his friend from school / total number of parts

5 / 12.

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Answer: 50%

Step-by-step explanation:

The error percent of the fish tank is 50%

Error percent:

Error percent means the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. It is also known as the percent error is the relative error multiplied by 100.

The formula to calculate the error percent is

δ = |vA - vE|/vA x 100

δ  = percent error

vA = actual value observed

vE = expected value

Given,

Raul estimated that a fish tank contained 20 gallons of water. He later  found that the fish tank had a 40-gallon capacity.

Here we need to calculate the error percent.

According to the error percent formula,

In this question

The estimated value = 20 gallons

Actual value = 40 gallons.

Now, we have to apply the values on the formula, then we get,

P% = (40 - 20)/40 x 100

P% = 20/40  x 100

P% = 1/2 x 100

P% = 0.5 x 100

P% = 50.

Therefore, the error percent is 50%.

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1.2(3x+5)=3.6x+6

We move all terms to the left:

1.2(3x+5)-(3.6x+6)=0

We multiply parentheses

3.6x-(3.6x+6)+6=0

We get rid of parentheses

3.6x-3.6x-6+6=0

We add all the numbers together, and all the variables

=0

x=0/1

Hence, x = 0

The value of XZ is 32.

What is the value of XZ?

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

From the figure, XY = 15 and YZ = 17

XZ is the sum of XY and YZ:

XZ = XY + YZ

XZ = 15 + 17 = 32

Therefore, XZ is 32.

This shows the concept of trigonometry.

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The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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In this problem the diagonal of the Tv is 19 and the hight is 11 so we can use the pythagorical theorem to find the width (w) so:

and we solve for w so

Answer:

Its A

Step-by-step explanation:

that's literally what a segment is

Answer:

2

Step-by-step explanation:

because average of 1 and 2 is 1.5 rounded is 2

The standard deviation of your revenues in a day is 14.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Let x be the revenue from hats.

And let y be the revenue from sunglasses.

And z be the total revenue.

Then according to the question:

z = 10x + 5y

You know the expected number of hats sold in a day is 10 with standard deviation 1.

σₓ = 1

σy = 2

Taking squares of both of the equation.

σₓ² = 1² = 1

σy² = 2² = 4

To find the standard deviation of your revenues in a day:

V(z) = (10)²σₓ² + 5²σy²

V(z) = (100)(1) + (25)(4)

V(z) = 200

Standard deviation,

σz² = √(200)

σz² = 10√(2)

σz² = 14.14

σz² ≈ 14

Therefore, the required standard deviation is 14.

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4x² - 18x - 5 cannot be factored by grouping.

Factoring a polynomial involves writing it as a product of two or more polynomials.

In other words, it is a process of finding the factor.

Therefore, let's factor the quadratic equation as follows:

4x² - 18x - 5

Factorization by grouping means that we need to group the terms with common factors before factoring.

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

Hence,

4x² - 18x - 5 cannot be factorise by grouping because it has no common factor.

in other word, we cannot, however, use the grouping method to factor 4x² - 18x - 5 because factoring out the GCF from both groupings does not yield a common factor.

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The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).

So, 2q/5 + 4 < 2q/ - 9:

Now, solve for the solution set as follows:

Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).

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Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number

Here you notice that the average is 7, so the coach's statement is true.

Your answer is , No;the mean of her strikeouts is 7

The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Equation of the ellipses:

The Equation of the ellipse with center at (h, k)

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]

where,

a = length of semi-major axis

b = length of semi-minor axis

Given,

Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.

Here we need to find the equation of the ellipse.

According to the formula we we have the following values are given,

We know the value of center of ellipses is written as,

(h, k) = (1, -3)

And the values of

a = 7 and b = 5

Therefore, when we apply the values on the formula then we get,

[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]

When we simplify the term then we get,

[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].

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Answer:

21

Step-by-step explanation:

120*7/10= 84  french
15 are chinese
84+15=99
120-99=21

Answer:

21

Step-by-step explanation:

[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]

The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.

Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.

To solve this, we will first factorise the expression of the denominator as follows;

x² - 9x + 8 = x² - 8x - x + 8

x² - 9x + 8 = x(x - 8) -1(x - 8)

x² - 9x + 8 = (x - 1)(x - 8)

Hence, we can rewrite the rational expression as:

(4x + 2)/[(x - 1)(x - 8)]

we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;

(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]

Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.

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