The Side-Side-Side (SSS) similarity theorem states that triangles are similar if the corresponding sides of the triangles are congruent.

True

False

Answer:

-8 and 4

Step-by-step explanation:

4x = 32 -x^2

Subtract 4x from both sides and rearrange the equation:

-x^2 -4x +32 = 0

Use the quadratic equation x = -b +\ - sqrt(b^2-4ac)/ 2a

From the rewritten equation: a=-1, b = -4 and c = 32

Solving for x you get x = -8 and x = 4

The solutions are -8 and 4

Answer: First answer is a^2 b^3. Second one is 3m^2n^5. Thrid is 15x^7y^3

Step-by-step explanation:

1.  there is no numbers to multiply together, so just add the a's and b's

2.3 stands alone. add the m's and n's together. getting m^2 and n^5

3. Do 5*3 getting 15, add the x's together, same with the y's getting the answer of 15x^7y^3

Lmk if it helps. :)

Answer:

0,-11

Step-by-step explanation:

-p^2 − 11p = 0

Factor out -p

-p( p+11) =0

Using the zero product property

-p =0    p+11 =0

p =0      p = -11

Answer:

C

Step-by-step explanation:

Constant means unchanging. You can see that there is a portion in the graph where the line is just flat. That means that the graph is constant in that interval. Find where the constant line starts and ends. Since the coordinates are increasing by 2, and the constant line starts between 0 and the first tick (2), the constant line starts at 1. Do the same thing to find where it ends(the last point where the line is flat). This should be 6.

That means the line is unchanging(constant) from 1 to 6, which can be represented by C.

Answer:

D

Step-by-step explanation:

f(x)=(3/5)x-10

f(5)=(3/5)(5)-10=

3-10=

-7

Hope this helps!

Question: What is the Question?

Answer:

  A

Step-by-step explanation:

Rotating ABC 90° will make segment AB parallel to segment DE, facilitating comparison of sides and angles. The triangles are marked with two angles and the side between them, so the appropriate theorem to use is the ASA theorem. (That theorem refers to a side (S) between two angles (A..A).)

She can use what she knows about rotations and triangle congruence to prove that triangle congruence as per option A.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given figure, we have triangles in which two angles and one side are equal.

∠A = ∠E = 65° (angle)

BA = ED (side)

∠A = ∠E = 30° (angle)

By rotating ABC 90°, section AB becomes parallel to segment DE, allowing for easier comparison of sides and angles. Because the triangles are defined by two angles and the side between them, the ASA theorem is relevant. (This theorem is about a side (S) between two angles (AA).)

Thus, the correct answer is option A.

Learn more about congruent triangles here:

brainly.com/question/4364353

#SPJ7

Answer:

1) a²-9a+20

2)a²-12a+20

3)a²+a-20

4)a²-8a-20

Step-by-step explanation:

use (foil)

front

outside

inside

last

Answer:

C

Step-by-step explanation:

5×2=10

10-15x-20

-10-15x

5(-2-3x), or -5(x+4)(x-1) solve it and find your answer

The complete question is:

A certain element has a half life of 4.5 billion years.

You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock?

Answer:

Age of rock = 7.82 billion years

Step-by-step explanation:

For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.

We are given that;

fraction remaining = 30% = 0.3

Thus;

0.3 = 0.5n

To find n, we have to use the log function;

log 0.3 = n log 0.5

-0.5229 = -0.301 n

n = -0.5229/-0.301

n = 1.737

We are given that;

Half life = 4.5 billion years

So, 1.737 half lives would give;

1.737 × 4.5 = 7.82 billion years

So, age of rock = 7.82 billion years

Answer:

Step-by-step explanation:

Translation: You move the shape by moving the points on the shape by the number, it changes the location of the shape.

Reflection: There is a line of reflection and the shape will be reflected by that, like a mirror, so it will be the same shape, same size.

Rotation: There is a point of rotation and the shape will just move around that point and will change the positioning if the shape. Always has coordinates

Answer:

I'm glad you asked!

Step-by-step explanation:

So let's simplify the number which is all you can do .

[tex]x^{4} -8x^{2} -33-14y-y^{2}[/tex]

= [tex]x^{4} +-8x^{2} +-33+-14y+-y^{2}[/tex]

Answer:

=[tex]x^{4} -8x^{2} -y^{2} -14y+-y^{2}[/tex]

Answer:3/4

Step-by-step explanation:

1x3=3

Answer:

I used an online calculator and I got 0.75

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

9x^2 - 16

Comparing this with the standard form

ax^2 + bx + c

ac = 9*-16 = -144

b = 0

-12 and 12 multiply to get ac and add to get b.

Factored form is

(3x - 4)(3x + 4).

The value of ac is,

⇒ - 144

The value of b is,

⇒ b = 0

And, The factored form is,

⇒ (3x - 4) (3x + 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic equation is,

⇒ 9x² - 16

Now, We know that;

General form of quadratic equation is,

⇒ ax² + bx + c

Here, The quadratic equation is,

⇒ 9x² - 16

Hence, By comparing,

⇒ a = 9

⇒ b = 0

⇒ c = - 16

Thus, The value of ac is,

⇒ ac = 9 × - 16

        = - 144

And, The factored form is,

⇒ 9x² - 16

⇒ (3x)² - 4²

⇒ (3x - 4) (3x + 4)

Thus, The value of ac is,

⇒ - 144

The value of b is,

⇒ b = 0

And, The factored form is,

⇒ (3x - 4) (3x + 4)

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ3

Step-by-step explanation:

Isosceles means that two sides are equal.

if the base is 1½s the other two sides will be ½s and½s

thus perimeter=1½+½+½ =2½s

smaller triangle:

perimeter=½(1½s+½s+½s)

=½(2½s)

=1¼s convert to decimal

=1.75s

The simplified expression of the given situation is 1.75s.

The correct option is C.

A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.

Given:

The base of an isosceles triangle is one and a half times the length of the other two sides.

Let s represents the side of the triangle.

The base = ([tex]1\frac{1}{2}[/tex])s = 3s/2

So, the other two sides are s and s.

So, the perimeter,

= 3s/2 + s/+ s

= 7s/2

A smaller triangle has a perimeter that is half the perimeter of the first.

That means,

the perimeter of the smaller triangle,

= 1/2(7s/2)

= 7s/4

= (1.75)s

Therefore, (1.75)s is the required expression.

To learn more about the isosceles triangle;

https://brainly.com/question/2456591.

#SPJ3

Answer:

340 songs, 17000/50 = 340 lol

Answer:

340

Step-by-step explanation:

17000÷50=340.

hope this helps

I assume you meant h(t) = 160t - 16t^2, as h(t) = 160t - 16t2 has no maximum.

There's two ways of solving this:

(i) By completing the square and finding the maximum turning point.

(ii) By using Calculus methods to find derivative and equating it to 0 in order to find maximum turning point.

(i) h(t) = 160t - 16t^2

h(t) = -16t^2 +160t

h(t) = -16(t^2-10t) (by taking out a common factor of -16)

h(t) = -16[(t-5)^2 - 25] (by completing the square)

h(t) = -16(t-5)^2 + 400 (on multiplying out by -16)

From this we see that the turning point is at (5;400), therefore the maximum height is 400 feet and is reached after 5 seconds.

Or...

(ii) h(t) = 160t - 16t^2

h`(t) = 160 - 32t (where h`(t) = derivative of h(t))

Now to find maximum of h(t), we set h`(t) = 0 and solve for t:

0 = 160 - 32t (on substituting h`(t) = 0)

32t = 160 (on solving for t)

t = 160/32 (on dividing both sides by 5)

t= 5

Now we have found that at 5 seconds, we will reach our maximum height. So to find this maximum height, we'll have to substitute t=5 into h(t) = 160t - 16t^2.

h(5) = 160(5) -16(5)^2

h(5) = 800 - 400

h(5) = 400 feet

So, once again we have shown that maximum height is 400 feet and is reached after 5 seconds.

Answer:

Millionths

Step-by-step explanation:

It is the fartherst decimal place that thier is.

Answer:  [tex]\bold{\cot\theta=-\dfrac{5}{12}\qquad \sec\theta = \dfrac{13}{5}\qquad \cos\theta = \dfrac{5}{13}}[/tex]

Step-by-step explanation:

90° ≤ θ ≤ 180° means that it is in Quadrant II →   x is + ,  y is -

[tex]\cos \theta = \dfrac{5}{13}\quad \rightarrow\quad x = 5, \ r = 13\\\\\\\text{Use Pythagorean Theorem to find y}:\\x^2+y^2=r^2\quad \rightarrow \quad 5^2+y^2=13^2\quad \rightarrow \quad y = -12\\\\\\\cot\theta=\dfrac{x}{y}\quad =\dfrac{5}{-12}\quad =\large\boxed{-\dfrac{5}{12}}\\\\\\\sec\theta=\dfrac{r}{x}\quad = \dfrac{13}{5}\quad = \large\boxed{\dfrac{13}{5}}\\\\\\\cos\theta =\dfrac{5}{13}\quad \text{(Given)}\\[/tex]

Answer:

[tex] \boxed{\sf (f-g)(x) = -{x}^{2} + 3x + 7} [/tex]

Given:

[tex] \sf f(x) = 3x + 1 \\ \sf g(x) = {x}^{2} - 6 [/tex]

To find:

[tex] \sf (f - g)(x) = f(x) - g(x)[/tex]

Step-by-step explanation:

[tex] \sf \implies(f - g)x = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) - ( {x}^{2} - 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) + (- {x}^{2} + 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3x + 1 - {x}^{2} + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - {x}^{2} + 3x + 1 + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = -{x}^{2} + 3x + 7 [/tex]

Answer:

Rise: 200.25

Descent 300.2

Minutes

Step-by-step explanation:

A)        We are using the Pythagorean theorem for the climb and descent. (a^2 + b^2 = c^2)

For climb a = 200, b = 10 c = ?

200^2 + 10^2 = c^2 = 40000 + 100 = c^2 = 40100 = c^2

c = about 200.25

For the descent: a = 300, b = 10

300²+10² = c²

90000 + 100 = c²

90100 = c²

c = about 300.2

B) If a plane is going 600 km/h and it goes about 10 km that means the plane is only going for 10/600 of an hour.

10/600 is 1/60, so only a couple minutes difference.

Answer:

7.809 g/cm^3

Step-by-step explanation:

Density is mass over volume so we need to find the mass and volume of the steel.

First we find the volume of the wood:

Vw = 9*6*6 = 324 cm^3

now we can find the mass of the wood, as mass = density * volume

mw = .68*324 = 220.32g

subtracting the mass of wood from total mass, we get the mass of steel

970-220.32 = 749.68g

now we can find the volume of the pyramid

Vs = 1/3 *6*6* (17-9) = 96 cm^3

Now we divide mass by volume to get density

749.68/96 = 7.809 g/cm^3

Confirming this with known data, density of steel is roughly between 7.75 and 8.05 g/cm^3 so we know we're correct.

Answer:

9x^2 +12x

Step-by-step explanation:

To find the area of a rectangle you need to multiply the length by the width. So,

3 by 3x^2 = 9x^2

3 by 4x = 12x

So the area of the entire rectangle is: 9x^2 + 12x

Answer:

three angles of a polygon are each 105.5,the sum of the angles in the polygon is 2520. find each of the other angles if they are equal to each other. For a polygon with n sides and n angles, the sum of the measures of all the interior angles equals (n-2)180 degrees. 16-3=13

Answer:

144cm²

Step-by-step explanation:

Answer:

-7/4

Step-by-step explanation:

((5 + 1)^2- (11 +32))/ 4=(36-43)/4= -7/4

Answer:

31

Step-by-step explanation:

Answer:

The roots are real and unequal (3, -3)

Step-by-step explanation:

x²-9=0

ax²+bx+c=0

Comparing we get,

a= 1

b= 0

c = -9

Determinant: b²-4ac

= 0² - 4(1)(-9)

= 36>0

D > 0

Therefore, the equation has real and unequal roots.

Algebraic identity:

x² - a² = (x-a)(x+a)

Using this identity

x²-9 = (x+3)(x-3)

Roots are 3 and -3 which are real and not equal to each other

Hope this answer helps you ..

Answer:

2 real solutions

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

This is the distance formula. To find the distance, solve as shown:

[tex]d=\sqrt{(6-9)^{2}+(3-(-2))^{2} } \\d=\sqrt{(6-9)^{2}+(3+2)^{2} } \\d=\sqrt{(-3)^{2}+(5)^{2} } \\d=\sqrt{9 +25 } \\d=\sqrt{34 }[/tex]

Answer: 384 miles

Step-by-step explanation:

From the question, Mrs. Schroeder, a school principal, drove her own car for a class trip, by taking a different route and we are told that the principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip.

Since it used 1 gallon of gas for 32 miles, 12 gallons will be for:

= 32miles × 12

= 384 miles

The principal drove for 384 miles.