A triangle has sides with lengths of 30 millimeters, 40 millimeters, and 48 millimeters. Is it a
right triangle?
yes
no

Step-by-step explanation:

Hello all beautiful your day

Answer:

Form: (x+5)^2 = 2

Solution: -6.41, -3.59

Answer:

Candy is 21 years old

Step-by-step explanation:

If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.

If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).

16+8+21=45

45÷3=15

Hope this helps!

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.

Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,

x = 2y                                    ...(1)

x - 5 = z                                 ...(2)

(x + y + z) / 3 = 15                  ...(3)

From equations (1), (2), and (3), then

x + x / 2 + x - 5 = 45

(5/2) x = 50

x = 20

Then the age Candy is calculated as,

z = 20 - 5

z = 15

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

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Answer:

B) y = x - 50

Step-by-step explanation:

It is B because the graph's y-intercept lies on the point (0, -50), hence the equation, y = x - 50. In addition, you can verify that B is the correct answer because the slope of the graph is positive, and so the x-value also must be positive.

Answer:

3k

Step-by-step explanation:

8k and 5k are "like terms" because they have the same variable to the same degree. So because the are like terms they can be subtracted. Similarly to how 8-5 is 3,

8k - 5k is 3k

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Answer:

x-intercepts:  x = 1 and x = -3

vertex:  (-1, -36)

Step-by-step explanation:

x-intercepts are when y = 0

⇒  9(x + 3)(x - 1) = 0

Divide both sides by 9:

⇒  (x + 3)(x - 1) = 0

Therefore:

⇒  (x + 3) = 0 ⇒ x = -3

⇒  (x - 1) = 0 ⇒ x = 1

Therefore the x-intercepts are x = 1 and x = -3

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

Completing the square

[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]

Therefore:

[tex]y=9(x+3)(x-1)[/tex]

[tex]\implies y=9x^2+18x-27[/tex]

Completing the square to rewrite the equation in vertex form:

[tex]\begin{aligned}y & =9x^2+18x-27\\& =9\left(x^2+\dfrac{18}{9}x\right)-27\\\\& =a\left(x^2+\dfrac{18}{9}x+\left(\dfrac{18}{2(9)}\right)^2\right)-27-9\left(\dfrac{18}{2(9)}\right)^2\\\\& =9\left(x-\left(-\dfrac{18}{2(9)}\right)\right)^2-27-\dfrac{18^2}{4(9)}\\\\& =9(x+1)^2-36\end{aligned}[/tex]

Therefore, the vertex is (-1, -36)

Answer:

A)Reduction

B)0.5

Step-by-step explanation:

A)It gets smaller

B)A-D=12

A'-d'=6

6/12=0.5

Answer:

temperature > -15

Answer:

42 meters

Step-by-step explanation:

if his math teacher is 6 meters ahead of him and his science teacher is 7 meters to the right of him than you multiply to get the area of distance from each other.

6 x 7 = 42

the teachers are 42 area meters away from each other

Answer

the range is the spread of your data from the lowest to the highest value in the distribution

Answer:

9

Step-by-step explanation:

To find the range, subtract the biggest number (here it's 9) and the smallest number (here it's 0).

9 - 0 = 9

The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft

The equation is given as:

(6 + x) * (9 + x) = 88

Express 88 as a product of two factors

(6 + x) * (9 + x) = 8 * 11

Express 8 and 11 as a sum

(6 + x) * (9 + x) = (6 + 2) * (9 + 2)

By comparison, we have:

6 + x = 6 + 2

9 + x = 9 + 2

This means that

x = 2

So, we have:

The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft

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Answer: D) two possible amounts by which the dimensions were changed

Step-by-step explanation:

Edg 2022

Answer:

x=45, y=45, z= 131

Step-by-step explanation:

x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.

Now that there are 2 right angles, that makes up 180. 180+49=229

A full rotation is 360, so you subtract that. 360-229=131
z=131.

Answer:

Step-by-step explanation:

The relevant relations are ...

__

The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.

  y = 49°

The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.

  x + y = 90°

  x + 49° = 90°

  x = 41° . . . . . . . . . subtract 49°

The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")

  49° +z = 180°

  z = 131° . . . . . . . subtract 49°

The measures of the marked angles are ...

  x = 41°

  y = 49°

  z = 131°

Answer:

See below

Step-by-step explanation:

You don't give any options, but here's the information you can get from just the equation itself:

Look for these characteristics and find the appropriate graph.

Question 1 True or False: A sector of a circle with a measure of 72 and radius of 12 cm has an arc length of about 15cm. True O False

Step-by-step explanation:

its false

The given statement about the sector of the circle is true.

A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre. A circle is also the set of all points that are equidistant from the centre.

Given that we need to check whether a sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm, or not,

Arc length = central angle / 360° × 2π × radius

= 72/ 360° × 2(3.14) × 12

= 0.2 × 6.28 × 12

= 15.072

≈ 15

Therefore, yes the sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.

Hence, the given statement about the sector of the circle is true.

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Answer:

  p(x) = x⁴ -7x³ +59x² -343x +490

Step-by-step explanation:

Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.

__

The given roots mean the polynomial can be written in factored form as ...

  p(x) = (x -2)(x -5)(x -7i)(x -(-7i))

We can combine multiply these factors together to simplify the polynomial.

  p(x) = (x² -7x +10)(x² +49)

  p(x) = x⁴ -7x³ +59x² -343x +490

_____

Additional comment

Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.

  a² -b² = (a -b)(a +b)

  (x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)

Answer:

6.28 meters

Step-by-step explanation:

Circumference is D[tex]\pi[/tex]

D=2 meters

2*3.14 = 6.28

The value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

Trigonometric ratios are the ratio of sides of a right angled triangle. There are 6 types of trigonometric ratios: sin, cos, tan, cosec, sec, and cot.

Sine trigonometric ratio is the ratio of perpendicular (side opposite to the angle) to the hypotenuse.

In the given figure, the side opposite to the angle [tex]\beta[/tex] is AC = 4 and the hypotenuse is AB = 5.

So, the sine ratio will be equal to,

[tex]\sin \beta=\dfrac{4}{5}[/tex]

Therefore, the value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

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Using the normal distribution, it is found that the desired measures are given by:

a. Z = -0.67.

b. X = 2.2.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In item a, we have that [tex]X = 36, \mu = 40, \sigma = 6[/tex], and want to find Z, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 40}{6}[/tex]

Z = -0.67.

In item b, we have that [tex]\mu = 1.3, \sigma = 0.6, Z = 1.5[/tex], and want to find X, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.5 = \frac{X - 1.3}{0.6}[/tex]

X - 1.3 = 0.6 x 1.5

X = 2.2.

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Answer:

(- 2, 0 )

Step-by-step explanation:

5x - 4y = - 10 → (1)

- 4x + 5y = 8 → (2)

multiplying (1) by 4 and (2) by 5 and adding result will eliminate x

20x - 16y = - 40 → (3)

- 20x + 25y = 40 → (4)

add (3) and (4) term by term to eliminate x

9y = 0 , thus

y = 0

substitute y = 0 into either of the 2 equations and solve for x

substituting into (1)

5x - 4(0) = - 10

5x - 0 = - 10

5x = - 10 ( divide both sides by 5 )

x = - 2

solution is (- 2, 0 )

Answer:

  10∠126.87°

  r = 10; θ = 126.87°

Step-by-step explanation:

The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...

  r = √(x² +y²)

  θ = arctan(y/x) . . . . paying attention to quadrant

__

For the given complex number, we have ...

  r = √((-6)² +8²) = √(36 +64) = √100 = 10

  θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant

  θ ≈ -53.13° +180° = 126.87°

The equivalence is ...

  -6 +8i  ⇔  10∠126.87° . . . . . in the form r∠θ

_____

Additional comment

Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.

Answer: 18x + 15

Step-by-step explanation:

(qor)(x)

q(r(x))

q(6x+5)

3(6x+5)

⇒18x + 15   This is your answer I believe

if we were solving for x then..

⇒x = [tex]-\frac{15}{18}[/tex]

=========================================================

Explanation:

We have a triangle with these side lengths

The order of 'a' and b doesn't matter, but we must have c as the largest value. Usually a,b,c are in ascending order.

Plug those values into the formula for the pythagorean theorem. If we get the same thing on both sides, then we have a right triangle.

[tex]a^2 + b^2 = c^2\\\\31^2 + 72^2 = 78^2\\\\961+5184 = 6084\\\\6145 = 6084\\\\[/tex]

We have a false statement at the end, which means the original equation is false for those a,b,c values.

Therefore, we do not have a right triangle.

Instead, this triangle is acute since the [tex]a^2+b^2[/tex] side is larger than the [tex]c^2[/tex] side

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

Rules to have in your notebook or on a reference sheet:

[tex]\text{If }a^2 + b^2 = c^2 \text{ then it is a right triangle}\\\\\text{If }a^2 + b^2 > c^2 \text{ then the triangle is acute}\\\\\text{If }a^2 + b^2 < c^2 \text{ then the triangle is obtuse}\\\\[/tex]

For more information, check out the converse of the pythagorean theorem.

Answer:

a) 1

b) 0

c) hundreths

d) .8

Step-by-step explanation:

The order, for this problem, is:

hundreds, tens, ones,

then after the decimal

tenths, hundredths, thousandths, ten thousandths, etc.

as for step d, imagine .08 as 8/100, and 8/10. Would you rather have 8 slices of pizza out of 100 slices, or 8 out of 10 slices of the whole?

I hope I helped!

Answer: 3 square inches

Step-by-step explanation:

   See attached for how I broke the shape up. Since each square is equal to 1 square inch, and the shape is about 3 squares, the answer should be;

O 3 square inches

Please note that different people may estimate differently.

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Answer:C

Step-by-step explanation:First multiply 5*5=25 then divide 125/5 = 5