Rectangle PQRS is shown with diagonals, PR and QS. What type of triangle is triangle STR?

Answer:

Step-by-step explanation:

Known fact: all roots of quadratic equation [tex]ax^2 + bx + c = 0[/tex] are real if and only if

discriminant [tex]D = b^2 - 4ac \geq 0.[/tex]

We know that all roots of [tex]x^2 + px + q = 0[/tex] are real. We can derive from this condition that

[tex]p^2 - 4q \geq 0[/tex]. (<----------- HERE)

Let's do some simplification of second equation:

[tex]x^2 + px +q + (x + a)(2x + p) = 3x^2 + x(2p + 2a) + ap + q.[/tex]

So we want according to Known fact prove that discriminant of equation

[tex]3x^2 + x(2p + 2a) + ap + q = 0[/tex] is greater or equal zero.

[tex]D = (2p + 2a)^2 - 4\cdot 3 (ap + q) = 4(p^2 + a^2 + 2ap - 3ap - 3q) = 4(a^2 - ap + p^2 - 3q)[/tex].

To prove that [tex]D \geq 0[/tex], we can view D as polynomial of a:

[tex]D(a) = 4a^2 - a(4p) + 4(p^2 - 3q)[/tex].

Known fact #2: if quadratic polynomial have positive greatest coefficient and it's discriminant [tex]\leq 0[/tex] then polynomial always positive.

So remains to prove that

[tex](4p)^2 - 4\cdot 4\cdot 4(p^2 - 3q) \leq 0[/tex]  

lets divide both side by [tex]4^2[/tex]:

[tex]p^2 - 4(p^2 - 3q) \leq 0[/tex]

[tex]-3p^2 + 12q \leq 0[/tex]

divide by 3

[tex]-p^2 + 4q \leq 0[/tex]

transfer terms to the other side:

[tex]0 \leq p^2 - 4q[/tex]

But we know that from "(<----------- HERE)"!!!

So Q.E.D.

Answer:

900

Step-by-step explanation:

A=S^2

50265=SxS

S=√50265

S=225

P=Sx4

P=225x4

P=900

Answer:

D.

Step-by-step explanation:

The solution to your systems of equations are when the 2 lines intersect.

Answer:

c ,3,1

Step-by-step explanation:

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the motion of an object to the various points without altering its size or shape when its translation takes place in geometry, and all other container throughput shift their vertices or alter their shape.

The scale of the figure doesn't alter the transitions, and  Its statistics remain consistent if the scale and shape of its figure are not modified. In this figure, each point is shifted 2/3 away from the y-axis.

Answer:

The 2nd one. (A translation of 4 units up...)

Step-by-step explanation:

I had a better answer last time in answered this, but a rude user named katie deleted it. (She always does that)

Answer:

D 5

Step-by-step explanation:

Answer:

B. 1/2?

Step-by-step explanation:

Answer:

-4w² - 8w

Step-by-step explanation:

All you need to do is distribute -4w. That means to multiply -4w to w and 2 separately. When you multiply -4w to w, you will get -4w² and when you multiply -4w to 2, you will get -8w.

Answer:

Brainliest!

Step-by-step explanation:

0.0396 x 10^9

10^9 = 1,000,000,000

0.0396 x 1,000,000,000 = 39,600,000

Answer:

39600000

Step-by-step explanation:

1) 10^9 = 1000000000

2) 0.0396*1000000000 = 39600000

Answer:

Equation given in graph B → y = -3x² + 4

Step-by-step explanation:

Equation of the graph A,

y = 3x² - 3

We have to find the equation of the graph (parabola) given in graph (B).

Parabola given in graph B is the inverted form of graph A with vertex at (0, 4)

Therefore, equation of the parabola given in graph B will be,

y = -a(x - h)² + k

where negative notation of the coefficient a shows the inverted form of the parabola given in graph A and (h, k) will be the vertex.

y = -3(x - 0)² + 4

y = -3x² + 4

Answer:

[tex]y = -3x^2 + 4[/tex]

Step-by-step explanation:

Hello!

The equation of a parabola is written as [tex]y = ax^2 + bx + c[/tex].

The [tex]c[/tex] value of the equation determines the y-intercept, or where the graph hits the y-axis (x = 0).

In Graph A we can see that the graph hits the y-axis at -3, showing the y-intercept is also -3. We can use the same logic to determine the y-intercept of Graph B. We can see that it hits the y-axis at 4, so the y-intercept is 4.

The [tex]a[/tex] value determines the direction and width of the graph. If it is positive, it opens up. If it's negative, it opens down.

Since Graph B opens down, we can simply add a negative sign to indicate that it is a negative graph.

We can plug in the values that we solved for [tex]a[/tex] and [tex]c[/tex].

Equation: [tex]y = -3x^2 + 4[/tex]

Answer:

0.4

Step-by-step explanation:

100(0.4)=40

Answer:

He added $25 to the contents of his wallet.

Step-by-step explanation:

Here's what's happening, symbolically:

$6 + m = $31, or m = $25.  Jake added $25 (represented by m) to the contents of his wallet.

Answer:

Step-by-step explanation:

The slope is 3 and the y-intercept is 2 or (0, 2)

Answer:

The y-intercept of the equation is -2.

Step-by-step explanation:

This equation is in slope-intercept form (y = mx + b). b represents the y-intercept, and m represents the slope.

Step-by-step explanation:

y=4/3x+4

y int =4

x int = -1

the graph is an increasing graph line that touch 4 in y and -1 in x

m=4/3

Answer: d) 576

Step-by-step explanation:

Datos:  

El perímetro de un rectángulo es igual a la suma de todos sus lados:  

Perímetro = 2h+2b  

Reemplazando b=4h

120 =2h+ 2(4h)  

Despejando h:

120 = 2h+8h  

120 =10h  

120/10=h  

12 cm=h  

Base = 4h =4(12) =48 cm  

Área de un rectángulo (A)= base x altura  

A = 48 x 12 = 576 cm2  

Answer:

18 quarts, 3 x 6 is 18.

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

=> [tex]4^3[/tex]

=> 4 × 4 × 4

=> 64

Answer:

4 times 4 times 4 = 64

Step-by-step explanation:

When a number is cubed, it is multiplied by itself 3 times.

For example, [tex]x^3=x*x*x[/tex].

In our case, it is [tex]4^3=4*4*4[/tex] which would equal [tex]16*4=64[/tex]

Your answer is "4 times 4 times 4 = 64"

Answer:

cosA = 40/41

tanA = 9/40

Step-by-step explanation:

Step 1: Find the other leg value

a² + b² = c²

9² + b² = 41²

b² = 41² - 9²

b = √1600

b = 40

Step 2: Draw out your triangle.

When you do so, you should see the cosA (adjacent over hypotenuse) is 40/41 and tanA (opposite over adjacent) is 9/40.

Triangle CBA

Length of AC = 40 (Leg)

Length of BC = 9 (Leg)

Length of AD = 41 (Hypotenuse)

cosA = AC/AB = 40/41

tanA = CB/AC = 9/40

Answer:

Cos A = 40/41

Tan A = 9/40

Step-by-step explanation:

Sin A = [tex]\frac{perpendicular}{hypotenuse}[/tex] = [tex]\frac{9}{41}[/tex]

So,

Perpendicular = 9 , Hypotenuse = 41

So, Finding base by Pythagorean Theorem

=> [tex]c^2=a^2+b^2[/tex]

=> [tex]a^2 = c^2-b^2\\[/tex]

=> [tex]a^2 = 41^2-9^2[/tex]

=> [tex]a^2 = 1681 - 81\\a^2 = 1600[/tex]

Taking sqrt

=> base = 40

Now,

Cos A = [tex]\frac{base}{hypotenuse} = \frac{40}{41}[/tex]

Tan A = [tex]\frac{perpendicular}{base} = \frac{9}{40}[/tex]

Answer: C

Step-by-step explanation:

IT is dividing by 6

The value of x in the given diagram of two similar triangle is  9 units.

Let us consider the name of two triangles be ABC and PQR.

Such that,

In triangle ABC,

AB = 12 , BC = 54 , m∠BAC = 90° and marked angle  is ∠ABC .

In triangle PQR,

PQ = 2 , QR = x, m∠QPR = 90° and marked angle  is ∠PQR .

In triangle ABC and PQR we have,

m∠BAC = 90° = m∠QPR

m∠ABC = m∠PQR  (given )

By AA corollary,

Triangle ABC is similar to triangle PQR with correspondence ABC ↔ PQR.

Corresponding sides of the similar triangle are in proportion.

AB / PQ = BC / QR

⇒ 12 / 2 = 54 / x

⇒ 12x  = 54 × 2

⇒ x = ( 54 × 2 ) / 12

⇒ x = 9

Therefore, the value of x in the given triangle is equal to 9 units.

learn more about value here

brainly.com/question/29014670

#SPJ2

Answer: Participants were lead to respond in a specific way.

Step-by-step explanation: Bias is an inherent misjudgment about something. Often, this can mean that the wording of the question leads the participants to respond in a specific way.

The statement "a statistical study is biased" means (D) Participants were led to respond in a specific way.

An event is said to be biased or not fair if the object or source of data is tampered with consciously to control the result or probability of different events. For example, if we make a coin in a way that if we flipped that coin we always get head to make the probability to get tail 0, then the coin is a biased coin and a stud,y using that is a biased study. So in given choices,

(A) Errors in data are mistakes made in the unconscious mind. It cannot be the meaning or cause of the biased event.

(B) If participants were only given three choices then they can make different choices using those three so it is partially biased not fully biased.

(C) Not enough people were surveyed cannot be meaning or reason for biased data as the number of experimental data is mentioned in the experiment. So experiment can be done with any size of the sample depending on which the result will be different but not biased.

(D) If participants lead to respond in a specific way then it is a conscious try to control the statistical data. So it is the meaning of the biased statistical study. Hence the correct option is (D).

Learn more about biased data here -https://brainly.com/question/24491228

#SPJ2

Answer:

  2

Step-by-step explanation:

The given angle is opposite the shortest of the given sides, and sin(A) < 5/6, so there are two possible solutions.

The law of sines tells you that angle C will satisfy ...

  sin(C)/ab = sin(A)/bc

  sin(C) = ab/bc·sin(A) = 6/5·1/2 = 3/5

The given angle is 30°, so the sum of remaining angles must be less than 150°. There are two possible angles less than 150° that have a sine of 3/5:

  C₁ = arcsin(3/5) = 36.87°

  C₂ = 180° -arcsin(3/5) = 143.13°

You can construct two triangles with the given measurements.

__

See the attachments for drawings of them.

Answer:

n = 2

Step-by-step explanation:

Expand the brackets.

1/2n - 2 - 3 = 3 - 2n - 3

Add or subtract terms.

1/2n - 5 = -2n

Add 5 and 2n on both sides.

1/2n + 2n = 5

5/2n = 5

Multiply both sides by 2/5.

n = 5 × 2/5

n = 10/5

n = 2

Answer:

In fractions, each number has a 1/6 chance of occuring. In decimals, that is around 16.6 repeating percent.

Answer:

1/7

The correct answer is 1/7

Answer:

y = 3x - 10

Step-by-step explanation:

Step 1: Rewrite 1st equation

2y = 6x + 4

y = 3x + 4

Step 2: Find 2nd equation

y = 3x + b

-4 = 3(2) + b

-4 = 6 + b

b = -10

Step 3: Rewrite 2nd equation

y = 3x - 10

And we have your parallel equation!

Answer:

We can just multiply 11/6 by 180 which is 330°.

Answer:

112°

Step-by-step explanation:

∠OLM= 2x, ∠PON= x

∠LOK= x

∠OKL= 180-124= 56

∠OLM= ∠OKL+∠LOK

x+56°= 2x

x= 56°

2x= 112°

Answer:

x - 80

Step-by-step explanation:

Ravi had x dollars in all.

x - 80

Answer:

0.35

Step-by-step explanation:

This probability distribution is shown below:

Pitch                   1            2        3          4         5

Frequency         15         20      40        15        10

Probability         0.15     0.2      0.4      0.15      0.1

The probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)

X  is the number of pitches thrown. Therefore:

P(X < 3) = P(X = 1) or P(X = 2)

The additive rule pf probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 3) = P(X = 1) or P(X = 2) = P(X = 1) + P(X = 2) = 0.15 + 0.2 = 0.35

The probability that the pitcher will throw fewer than 3 pitches to a batter = 0.35

Answer:

.35

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

The root will touch the axis and bounce off when the exponent is even. In that case, that means (x + 2)² is the binomial that will bounce. Therefore, the root which bounces and touches the x-axis is x = -2.

Answer:

Options A and C are correct answers.

Similar triangles may or may not be congruent.

The true statements are: [tex]\mathbf{A.\ \triangle ABC \sim \triangle ADB,\ C.\ \triangle ABC \sim \triangle BDC,\ D.\ \triangle ABD \sim \triangle BCD }[/tex]

From the figure, we have the following highlights

This means that:

Hence, the true statements are: (a), (c) and (d)

Read more about similar triangles at:

https://brainly.com/question/14926756

Answer:

The diameter of the semicircle is 10 feet.

Step-by-step explanation:

This is because d=r2 or diameter=radius*2

Answer:

Step-by-step explanation:

[tex]Diameter= 2* Radius\\D = 2* 5\\D= 10[/tex]

Answer:

I'm not 100% sure but I'm pretty sure its 'D'

Answer:

the answer is b

Step-by-step explanation: