solve for x -
[tex]x {}^{2} - 6x + 5= 0[/tex]


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1. Height of the equilateral triangle is: √3 units

2. Area of the equilateral triangle = √3 units²

3. Area = √3/4 x², when each side is x.

A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.

1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:

h = √(2² - 1²)

h = √(4 - 1)

h = √3

2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)

Area of the equilateral triangle = √3 units²

3. If x is the side length of the equilateral triangle, we would have:

height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x

Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²

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Answer:

58°

Step-by-step explanation:

Apply trig inverse properties

W = arccos(0.53)

W = 2[tex]\pi[/tex] - arccos(0.53)

Answer:

There can be alot of equations for this since you didn't say anything specific. But since u didnt say anything specific, this can be one of the equations: 20 + 8, 30 - 2, 4 x 7

Answer:

a) 150

b) 2650

Step-by-step explanation:

6% of 2500 is 150

150 + 2500 = 2650

Answer:

one of them is two trapezoids

Step-by-step explanation:

Answer:

-6x²+xy-6y²

Step-by-step explanation:

3y² - 4x² + xy - 2x² - 9y²

-4x²+ xy - 2x² - 6y²

-6y² + xy - 6y²

Answer:

−6x² + xy − 6y²

Step-by-step explanation:

Simplify 3y²-4x² + xy - 2x² - 9y²​

Step 1

Subtract 9y² from 3y²

−4x² +xy −2x² −6y²

Step 2

Subtract 2x²  from −4x²

−6x²  + xy  − 6y²

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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The answer of the following questions is discussed below

Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.

The radius of each circle

r1= 2.5 inches.

r2= 1 inches

Area of circle large circle,

= πr1²

=3.14*2.5*2.5

=19.625 inch²

Area of small circle,

= πr2²

= 3.14*1*1

=3.14 inch²

Area of large circle minus area of small circle,

= 16.485  inch²

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The weekday hours you purchased is 5 hours.

The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.

2a + 10b = 220 equation 1

a + b = 26 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 260 equation 3

Subtract equation 3 from equation 2

8a = 40

a = 5 hours

(5 x 3) + b = 26

15 + b = 26

b = 26 - 15

b = 11 hours

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education Roman Catholic School one five two weeks

Answer:

Given:

To Find:

Solution:

According to the question:

(1) The product of 7 & x

➝ 7x

(2) The sum of 9 and 3 and 2

➝ 9 + 3 + 2

➝ 14

From (1) and (2) , we get:

➝ 7x = 14

➝ x = 14 ÷ 7

➝ x = 2

Let's check whether our answer is correct or not:

• To check our answerer, let's putting the value of x :

♣ 7(2) = 14

♣ 14 = 14 ✅

Thus, our answer is correct....The value of x is 2.

Answer:

-9,40

Step-by-step explanation:

Midpoint Formula:

[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]

Answer:

Midpoint = (−9,40)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Depending on whether or not the g(x) is x^2 or 2x, I have both ways.

If g(x) is x^2 - 9...

--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11

If g(x) is 2x...

--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11

Hope this helps!

Answer:

[tex]x = 49degrees[/tex]

Step-by-step explanation:

[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]

The required value of x for the given figure is 49°.

A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.

The sum of the angles on a straight line is always 180°.

In the given figure the angles 131° and x° are on the same straight line.

Since, the sum of the angles on a straight line is 180°.

The following equation can be written for the given figure,

x + 131 = 180

=> x = 180 - 131

       = 49

Hence, the value of x for the given figure is 49°.

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Answer:

angles in a triangle add up to 180°

5:12:13 = 30

180 ÷ 30 = 6

6 × 5 = 30°

6 × 12 = 72°

6 × 13 = 78°

angles = 30°, 72°, 78°

Answer:

x = -6.

Step-by-step explanation:

First thing to notice is that this is the third angle in a triangle, and all 3 angles have to equal 180.

Subtract 75 and 40 from 180 to get the missing angles value.

180 - 75 - 40 = 65

So now we know the missing angle has to be 65, or can be written as:

x + 71 = 65.

To solve this, just subtract 71 from both sides.

x = -6.

Let's see

[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]

Use distributive law

[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]

[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]

Answer:

[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Step-by-explanation:

Given expression:

[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]

Use the Distributive Property Law  (b ± c)a = ab ± ac
to remove the parentheses:

[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]

Simplify by multiplying the coefficients of each term:

[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:

[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]

[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Answer:

  x²

Step-by-step explanation:

The area of rectangle ABJH is the product of its dimensions.

__

The dimensions are given as ...

  AB = x

  AH = x

The area of ABJH is ...

  area = length × width = (x) × (x) = x²

The area of ABJH is x².

The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.

The complete answer is given below and the figure is attached with the answer.

Consider the diagram and proof by contradiction.

Given: △ABC with ∠B ≅ ∠C

Prove: AB ≅ AC

It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.

What is the missing reason in the proof?

the converse of the triangle parts relationship theorem

substitution

definition of congruency

the converse of the isosceles triangle theorem

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Isosceles triangle two sides of the triangle are equal and their opposite angles too.

Given

△ABC with ∠B ≅ ∠C

Prove that

AB ≅ AC

How to give a conclusion?

From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.

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Answer:

3

Step-by-step explanation:

blue, white, and red colors

Answer:

positive

Step-by-step explanation:

(-a) (-a) (-a) (-a) = a

(-a)(-a) = a

a (-a) = -a

-a (-a) = a --> positive sign

If you multiply four negative numbers, what is the sign of the product?

You can test this with numbers, the easiest with -1:

(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) =  1

General:

(-a)(-b)(-c)(-d) = abcd

The sign of the product of four negative numbers is positive.

If you multiply five negative numbers, what is the sign of the product?

Testing with -1:

(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1

General:

(-a)(-b)(-c)(-d)(-e) = -abcde

The sign of the product of five negative numbers is negative.

General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

p = 0.7, n = 8.

The probability that fewer than 7 of them show up is given by:

[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]

In which:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]

[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]

Then:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]

[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]

0.7447 = 74.47% probability that fewer than 7 of them show up.

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Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.

A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.

In Mathematics, there are four measures of dispersion for a data set and these include the following:

In this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.

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Answer:

  58.1 cm

Step-by-step explanation:

The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.

__

The theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...

  c² = a² +b²

For the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.

  30² = 7.5 +b²

  b² = 900 -56.25 = 843.75

  b = √843.75 ≈ 29.0473

The length of each support rod is twice this value, so ...

  rod length = 2b = 2(29.0473) = 58.0947

Each support rod is about 58.1 cm long.

71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.

71 + y = 180

y = 109

The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.

109 + 46 + x = 180

x = 25

Answer: x = 25 degrees

Hope this helps!