Based on the true statement above, is the following argument valid as part of a proof?

Two lines are perpendicular; therefore, they intersect to form right angles.

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

Answer:

13.68

Step-by-step explanation:

if you do 4.56*4 you get 18.24 and 18.24 minus 25 percents is 13.68

Answer:

She should spend $57.5 each day

Answer: $57.5

Step-by-step explanation:

Answer:

85.2

Step-by-step explanation:

17,892 ÷ 210

85.2

Best of Luck!

Answer:

h(x) = 4x^2 - 3

Step-by-step explanation:

(a) The expected number of questions answered correctly by both A and B is 28.

(b) The variance of the number of questions answered correctly by either A or B is 4.5.

Let's define the following variables:

X = Number of questions answered correctly by A

Y = Number of questions answered correctly by B

(a) Expected number of questions answered correctly by both A and B:

We can use the formula for the expected value of the product of two independent random variables:

E(X × Y) = E(X) × E(Y)

The probability of A answering a question correctly is 0.7, and the probability of B answering a question correctly is 0.4.

Since the questions are independent, we can calculate the expected values for X and Y:

E(X) = 10 (number of questions) × 0.7 (probability of A answering correctly) = 7

E(Y) = 10 (number of questions) × 0.4 (probability of B answering correctly) = 4

Now, the expected number of questions answered correctly by both A and B is:

E(X× Y) = E(X) × E(Y)

= 7×4

= 28

(b) Variance of the number of questions answered correctly by either A or B:

Variance is calculated differently for independent events. Since A and B's performances are independent, we can use the following formula:

Var(X + Y) = Var(X) + Var(Y)

The variance of a binomial distribution with n trials and probability p of success is given by np(1-p).

For A and B:

Var(X) = 10× 0.7 × (1 - 0.7)

= 2.1

Var(Y) = 10 × 0.4× (1 - 0.4)

= 2.4

Now, the variance of the number of questions answered correctly by either A or B is:

Var(X + Y) = Var(X) + Var(Y)

= 2.1 + 2.4

= 4.5

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Answer: 3

Step-by-step explanation: If he takes one YOU have 2 but in TOTAL you still have 3

Answer:

h=16

Step-by-step explanation:

        1

Simplify   —

           2

Equation at the end of step

1

:

         1

 72 -  ((— • h) • 9)  = 0

         2

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          72     72 • 2

    72 =  ——  =  ——————

          1        2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

72 • 2 - (9h)     144 - 9h

—————————————  =  ————————

      2              2    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  144 - 9h  =   -9 • (h - 16)

Equation at the end of step

3

:

 -9 • (h - 16)

 —————————————  = 0

       2      

STEP

4

:

When a fraction equals zero

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 -9•(h-16)

 ————————— • 2 = 0 • 2

     2    

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -9  •  (h-16)  = 0

Equations which are never true:

4.2      Solve :    -9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    h-16 = 0

Add  16  to both sides of the equation :

                     h = 16

Answer:

51

Step-by-step explanation:

2x - 2/3x = 68

4/3x = 68

4x = 204

x = 51

Answer: Negative 3

Step-by-step explanation: 2n(5)=9n-3. 10n=9n-3. Subtract 9n from both sides. n= -3

Answer:

Step-by-step explanation:

Slope of the line:

[tex]m = \frac{y-y1}{x-x1} \\[/tex]

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

[tex]m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0[/tex]

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

Answer:

See attached

Step-by-step explanation:

The first one

The second one

Answer:

r < 3/2 or r < 1.5

Step-by-step explanation:

-8r - 9 > 21

-8r > -21 +9

-8r > -12

divide both sides by -8

= r < 3/2 or 1.5

Answer:

1.92449%

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

Step 1: Define variables

Principle amount P = 11000

Total amount A = 11000 + 1100 = 12100

Years n = 5

Step 2: Substitute and Evaluate for r

12100 = 11000(1 + r)⁵

11/10 = (1 + r)⁵

1.01924 = 1 + r

r = 0.019245

Step 3: Convert to percentage

0.019245 × 100 = 1.92449%

9514 1400 393

Answer:

  (-0.25, ±√4.6875)

Step-by-step explanation:

The square of the distance from a point on the ellipse to the point (1, 0) is ...

  d^2 = (x -1)^2 +y^2

Using the equation of the ellipse to write an expression for y^2, we have ...

  d^2 = (x -1)^2 +5 -5x^2

  d^2 = -4x^2 -2x +6

The expression on the right is that of a downward-opening parabola with ...

  a = -4, b = -2, c = 6

The maximum is located at ...

  x = -b/(2a) = -(-2)/(2(-4)) = -1/4

The value of y there is ...

  y^2 = 5 -5(-1/4)^2 = 4 11/16

  y = √4.6875

The points on the ellipse farthest from (1, 0) are (-0.25, ±√4.6875).

Answer:

The answer is A.

Step-by-step explanation:

Answer:

it is 240

Step-by-step explanation:

put in equation and solve

2/3t+10=170

t=240

Answer:

it would cost him $3

Step-by-step explanation:

$9 divided by the 15 pencils is 0.6 cents

0.6 times 5 equals $3

Answer:

12

Step-by-step explanation: divide 26.9 by six and you get 4.48 which is the price for one then you divide 53.8 by 4.48 and you get 12.0 which is just 12

Answer:

21 and -3

Step-by-step explanation:

Hope this helps!!! :)

A circle is defined geometrically as the set of all points (x, y) in a two-dimensional plane that are equidistant from a fixed point called the center of the circle.

In other words, for any point (x, y) on the circle, the distance between that point and the center is constant.

To elaborate, let's consider a circle with center (h, k) and radius r. Any point (x, y) lying on the circle satisfies the equation of distance as follows:

√((x - h)² + (y - k)²) = r

This equation represents the Pythagorean theorem applied to the right triangle formed by the distance between the point (x, y) and the center (h, k), with the hypotenuse being the radius r. Since all points on the circle have the same distance from the center, this equation holds true for any point on the circle.

The constant distance, or radius, is the key characteristic of a circle. It determines the size of the circle and is defined as the distance from the center to any point on the circumference. The radius is typically denoted by the lowercase letter "r" and can be used to calculate various properties of the circle, such as its area and circumference.

In summary, a circle is the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is constant, and this distance is defined as the radius of the circle. The geometric definition provides a clear understanding of the fundamental properties and characteristics of a circle.

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Answer:

B 7.5

Step-by-step explanation:

Answer:

B 7.5 because it's a dilation of -5, meaning you divide 15/2 to get the answer.

Step-by-step explanation:

Answer:

the answer to the question is 4

Step-by-step explanation:

Answer:

11x+6

Step-by-step explanation:

Using FOIL

(x+1)-(-2x-5)-original

F-first=(x+2x)=3x

O-outside=(x+5)=5x

I-inside=(1+2x)=3x

L-last=(1+5)=6

11x+6

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Mean distance of earth from the sun = 93 million miles

Let mean distance of earth from the sun = d

The variation on the distance is as much as 1. 6 million miles

Possible distances of the earth from the sun can be modeled using :

|d - 93| = ± 1.6

Where d = distance from earth to the sun

d = - 1.6 million + 93 million

d = 91.4 million

d = 1.6 million + 93 million

d = 94.6 million

Hence, possible distance from earth to the sun :

91.4 < d < 94.6