Which graph shows the line y- 1 = 2(x + 2)?

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: 10

Step-by-step explanation:

√10 x √10

When a square root of an expression is multiplied by itself, the result is that expression...

10

Answer:

D

Step-by-step explanation:

(160x243)^1/5=8.27

D also equivalates to 8.27

Answer:

so the answer for that is D.

Step-by-step explanation:

160 X 243= 38880

38880^.2 (or 1/5) = 8.27

D. 5 carrot thing 5= 1.379..x 6= 8.27

Answer:

The new rate would be  3.75%

Step-by-step explanation:

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate=4.5%-0.75%=3.75%

Answer: mine was: 4.125%

Step-by-step explanation:

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:

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:

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: 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:

-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:

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°

The complete question is as follows.

The equation a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex] can be used to determine the area , a, of a trapezoid with height , h, and base lengths, [tex]b_1[/tex] and [tex]b_2[/tex]. Which are equivalent equations?

(a) [tex]\frac{2a}{h} - b_2 = b_1[/tex]

(b) [tex]\frac{a}{2h} - b_2 = b_1[/tex]

(c) [tex]\frac{2a - b_2}{h}[/tex] = [tex]b_1[/tex]

(d) [tex]\frac{2a}{b_1 + b_2} = h[/tex]

(e) [tex]\frac{a}{2(b_1 + b_2)}[/tex] = h

Answer: (a) [tex]\frac{2a}{h} - b_2 = b_1[/tex]; (d) [tex]\frac{2a}{b_1 + b_2} = h[/tex];

Step-by-step explanation: To determine [tex]b_1[/tex]:

a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]

2a = ([tex]b_1 + b_2[/tex])h

[tex]\frac{2a}{h} = b_1 + b_2[/tex]

[tex]\frac{2a}{h} - b_2 = b_1[/tex]

To determine h:

a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]

2a = [tex](b_1 + b_2)h[/tex]

[tex]\frac{2a}{(b_1 + b_2)}[/tex] = h

To determine [tex]b_2[/tex]

a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]

2a = [tex](b_1 + b_2)h[/tex]

[tex]\frac{2a}{h} = (b_1 + b_2)[/tex]

[tex]\frac{2a}{h} - b_1 = b_2[/tex]

Checking the alternatives, you have that [tex]\frac{2a}{h} - b_2 = b_1[/tex] and [tex]\frac{2a}{(b_1 + b_2)}[/tex] = h, so alternatives A and D are correct.

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.

Answer:

x - 80

Step-by-step explanation:

Ravi had x dollars in all.

x - 80

Answer:

6.48

Step-by-step explanation:

you have to use the sin rule

Answer:

6.48

Step-by-step explanation:

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:

900

Step-by-step explanation:

A=S^2

50265=SxS

S=√50265

S=225

P=Sx4

P=225x4

P=900

Answer:

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

Answer:

the answer is b

Step-by-step explanation:

Answer:

3fx

Step-by-step explanation:

f(x)+f(x)+f(x)

remove parenthesis: (a)=a

add similar elements: fx+fx+fx

=3fx

Answer: for edge

3f(x)

3x2

12

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: 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:

-10

Step-by-step explanation:

expand: 3x-12>5x+2

subtract 3x and subtract 2 to both sides

-14>2x

which is just

2x<-14

so x<-7.

the only value is -10. :D

Answer:

-10

Step-by-step explanation:

3(x – 4) > 5x + 2

Distribute

3x -12 > 5x+2

Subtract 3x from each side

3x-12-3x > 5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12 -2 > 2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

X must be less than -7

-10 is less than -7

Answer:

D 5

Step-by-step explanation:

Answer:

B. 1/2?

Step-by-step explanation:

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:

30% percent profit

Step-by-step explanation:

100 pence in a pound.

1000 grams in a kilogram.

She bought 5000g of sweets.

She pays 10×100=1000 pence.

She put them into 5000÷250=20 bags.

She sells the bags for 65 pence each.

She sells them all for 20×65=1300 pence.

She gets a profit of 300 pence or 3 pounds.

She gets a percent profit of 30%.

Answer:

Sale-person's total salary for the year is  $ 82,050

Step-by-step explanation:

Base salary of salesperson = $37,000

commission percentage of salesperson = 17% of sales

sales made in a year = $265,000

commission for salesperson in $ = 17% of sales

commission for salesperson in $ = 17 / 100 *  $265,000 = $45,050

Thus, total commission for the given year salesperson is   $45,050

Total salary for year = Base salary + total commission for the given year

Total salary for year = $37,000  +  $45,050 = $ 82,050 (Answer)

Answer:

12 in^2

Step-by-step explanation:

A = l*w

   = 2in * 6 in

  = 12 in^2

Answer:

Area = 12 in.²

Step-by-step explanation:

Area = length × width

Where w = 2 and L = 6

So,

Area = 2 × 6

Area = 12 in.²

Answer:

Numerical expression to represent this situation : 41 = 20 + P

Martha's profit is $21

Step-by-step explanation:

Total cost price for earrings for Martha = total money invested in material  to make earrings = $20

No. of ear rings made = 10

No. of earrings sold for $5= 7

Total Price for these 7 earrings= $5*7 = $35

No. of earrings sold for $2= 3

Total Price for these 3 earrings= $2*3 = $6

Total price for all of the ten earrings = $35+$6 = $41

We know that

selling price = cost price + profit

Total price for all of the ten earrings = Total cost price for 10 earrings + total profit made on those 10 earrings

let total profit be P

41 = 20 + P

Thus,

P = 41-20 = 21

numerical expression to represent this situation : 41 = 20 + P

Thus, Martha's profit is $21

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:

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:

6

Step-by-step explanation:

Since the two triangles are similar, their ratios of sides must be constant. Therefore:

[tex]\dfrac{9}{3}=\dfrac{x}{2} \\\\x=2\cdot 3=6[/tex]

Hope this helps!