After working 10 years as a bus driver, Izabel Antocicco was in an accident and became permanently disabled. She was 63 years old at the time and was planning to retire on her 65th birthday. Her final salary was $55,700 per year. Her rate of benefits was 4.5%. What is her monthly disability benefit?


A. $2,506.50

B. $3,458.90

C. $3,508.11

D. $6,458.22

Answer:

see explanation

Step-by-step explanation:

x³ + y³ ← is a sum of cubes and factors as

(x + y)(x² - xy + y²) ← in factored form

Answer:

B.

Step-by-step explanation:

P(something not happening)+P(something happening)=1 or 100%.

So if we have

P(something not happening)+40%=100%

Then the P(something not happening)=60% since 60%+40%=100%.

Yes I was using the event="something not happening" as the complement of something happening.

In fancy notation, some people might write:

[tex]P(A)+P(A')=1[/tex]

or

[tex]P(A)+P(A^c)=1[/tex]

Answer:

A)

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

now plug in the expressions of f(x) and g(x) :

(f+g)(x) = [tex]x^{2} -7x-1 + 2x-3[/tex]

we combine like terms we get :

(f+g)(x) = [tex]x^{2} -7x+2x -1-3[/tex]

we simplify we get :

(f+g)(x)=[tex]x^{2} -5x-4[/tex]

so the answer is A)

Answer:a

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

I think I'm going to go with the plug in method here.

If you get the same value on both sides, then the point is contained on the line.

A)

4x-y=-6

Test (-1,2):  4(-1)-2=-6

4(-1)-2=-6

-4-2=-6

-6=-6

True; the equation holds for (-1,2).

Test (3,1): 4(3)-1=-6

4(3)-1=-6

12-1=-6

11=-6

False; the equation doesn't hold for (3,1).

A isn't the right choice.

B)

x+4y=7

Test (-1,2): -1+4(2)=7

-1+4(2)=7

-1+8=7

7=7

True, the equation holds for (-1,2).

Test (3,1): 3+4(1)=7

3+4(1)=7

3+4=7

7=7

True, the equation holds for (3,1).

Since the equation held for both (-1,2) and (3,1) then B is the right answer.

-------------------Let's also go ahead and find the equation another way:

(3,1) and (1,-2) are points on your line.

I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.

I will then rearrange into standard form like your choices are in.

m=slope=rise/run.

To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.

Like so:

(-1,2)

-(3,1)

---------

-4    1

The slope is 1/-4 or -1/4.

So the equation so far is y=-1/4 x+b since m=-1/4.

Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).

y=-1/4 x+b

2=-1/4 (-1)+b

2=1/4+b

Subtract 1/4 on both sides:

2-1/4=b

7/4=b

So the equation of the line is y=-1/4 x +7/4.

Now the goal is to write in ax+by=c form where a,b,c are integers.

Multiply both sides of y= -1/4 x +7/4 by 4 giving you:

4y=-1x+7

Add 1x on both sides:

1x+4y=7

or

x+4y=7 since 1x=x

So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.

The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

Option B is true.

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The points on the line are  (-1, 2) and (3, 1).

Since, The equation of line will be;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁)/ (x₂ - x₁) is slope of the line.

And, (x₁, y₁) is the point on the line.

Thus, Slope = (1 - 2) / (3 - (-1))

                  = (-1)/4

                  = -1/4

So, The equation of line with slope -1/4 and point (-1, 2) will be;

y - 2 = -1/4 (x - (-1))

4 (y - 2) = - 1(x + 1)

4y - 8 = -x - 1

x + 4y = 8 - 1

x + 4y = 7

So, The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

Learn more about the equation of line visit:

https://brainly.com/question/25969846

#SPJ2

Answer:

-2 + i

Step-by-step explanation:

The midpoint is the average:

[ (-7 + 4i) + (3 − 2i) ] / 2

Combine like terms:

(-4 + 2i) / 2

Divide:

-2 + i

[tex]1 \frac{3}{4}[/tex]

Fractional division is fractional multiplication with the second fraction the reciprocal of itself. This means the problem can be written as [tex]\frac{7}{9}*\frac{9}{4}[/tex]. Fractional multiplication results in the multiplication of the numerators and denominators---in this case, [tex]\frac{7}{4}=1\frac{3}{4}[/tex]

Answer:

Option B) a = 1, b = 3, c = 4  

Step-by-step explanation:

We are given the following information in the question:

We are given an expression:

[tex]\displaystyle\frac{7}{9} \div \frac{4}{9} = a\frac{b}{c}[/tex]

The solving of the above expression can be done in the following manner:

[tex]\displaystyle\frac{7}{9} \div \frac{4}{9}\\\\\frac{7}{9}\times \frac{9}{4}\\\\\frac{7}{4} =\frac{(4\times 1) + 3}{4}= 1\frac{3}{4}[/tex]

Comparing the right side of the expression, we have,

[tex]a\displaystyle\frac{b}{c} = 1\frac{3}{4}[/tex]

Comparing, we get,

a = 1, b = 3, c = 4

Option B) s the correct option.

Answer:

3

Step-by-step explanation:

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

According to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Knowing this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

For the first exercise, we get:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

For the second exercise, we get:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

[tex]\bf V=(x)(4x+3)(4x)\implies \cfrac{V}{4x}=(x)(4x+3)[/tex]

Answer:

[tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]                        

Step-by-step explanation:

Given : Expression [tex]V = (x)(4x+3)(4x)[/tex]

To find : Suppose you multiplied the cereal box dimensions in a different order ?

Solution :

The given expression is the product of three numbers,

[tex]V = (x)(4x+3)(4x)[/tex]

First we multiply first two terms,

[tex](x)(4x+3)=4x^2+3x[/tex]

Substitute back,

[tex]V = (4x^2+3x)(4x)[/tex]

Then multiply the left terms,

[tex]V =16x^2+12x[/tex]

Therefore, [tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]

Answer:

14 weeks

Step-by-step explanation:

t = 25 + 8.25w

Len  needs 135.75

135.75 =  25 + 8.25w

Subtract 25 from each side

135.75-25 = 25-25 + 8.25w

110.75 = 8.25w

Divide each side by 8.25

110.75/8.25 = 8.25w/8.25

13.42424 = w

Since we need at least 135.75, it will take Len a little more than 13 weeks, so it will take Len 14 weeks to have enough money

Answer:

14 weeks

Step-by-step explanation:

It will take 14 weeks for Len to save enough money to buy a television.

t = 25 + 8.25w

135.75 =  25 + 8.25w

Hope this helps!

Answer:

(-2,-7)

Step-by-step explanation:

Answer:

x= -2

Step-by-step explanation:

-b/2a = x

-(12)/2(2) = x

-12/6 = x

-2 = x

Answer:

b. winter wear, appropriate for around 20-45°F c.

Step-by-step explanation:

Answer:

b. winter wear, appropriate for around 20-45°F

Step-by-step explanation:

When it is 6:00 hours in Honolulu, it is 15:00 hours in London, this means that there are 15 - 6 = 9 hours of difference.

Paul got into London at 12:00 p.m, that is, at 12 - 9 = 3:00 p.m. Friday Honolulu time. Paul’s flight left Honolulu at 2:00 p.m. Thursday, so he spent 25 hours flighting.

When the flight started, the temperature in London was 30 °C, after 25 hours the temperature dropped 25 °C, so it was 30 - 25 = 5 °C.

To convert from °C to °F, we use the following formula:

(x °C × 9/5) + 32 = y °F

Replacing with x = 5

(5 °C × 9/5) + 32 = 41 °F

Answer:

y+4=-2(x-4)

Simplified- y=-2x+4

Step-by-step explanation:

y+4= -2(x-4)

y+4= -2x+8

-4. -4

y=-2x+4

Answer:

10.2 inches

Step-by-step explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

[tex]a=12\ in, b=15\ in[/tex]

Applying the Pythagoras Theorem

Find the length of the hypotenuse

[tex]c^{2}=a^{2} +b^{2}[/tex]

substitute

[tex]c^{2}=12^{2} +15^{2}[/tex]

[tex]c^{2}=369[/tex]

[tex]c=19.2\ in[/tex]

Second case

The given lengths are one leg and the hypotenuse

so

[tex]a=12\ in, c=15\ in[/tex]

Applying the Pythagoras Theorem

Find the length of the other leg

[tex]b^{2}=c^{2} - a^{2}[/tex]

substitute

[tex]b^{2}=15^{2} - 12^{2}[/tex]

[tex]b^{2}=81[/tex]

[tex]b=9\ in[/tex]

Find the difference between the two possible lengths of the third side of the triangle

so

[tex]19.2-9=10.2\ in[/tex]

Answer:

10.2

Step-by-step explanation:

is a pimp ting

Answer:

This is a false statement:

Step-by-step explanation:

According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).

P(x)= (x+/-a) q(x)+r(x)

P(x)=(x+a) q(x)+r(x). Note that for x=-a

P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)

P(-a)=r(-a)

It means that P(-a) is the remainder not P(a)

Thus the given statement is false....

Answer:

[tex]\cos (115\degree)=-0.423[/tex]

Step-by-step explanation:

The parametric equations of a circle is

[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]

The radius of the unit circle is 1 unit.

This implies that any point on the unit circle is represented by:

[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]

where [tex]\theta[/tex] is the angle in standard position,

From the question, the given angle in standard position is [tex]115\degree[/tex].

This angle intersects the unit circle at [tex]x=-0.423[/tex]

But [tex]x=\cos \theta[/tex]

We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]

This implies that: [tex]\cos (115\degree)=-0.423[/tex]

Answer:

The translation is 2 units at left and 7 units up

Step-by-step explanation:

we have that

The rule of the translation is

(x, y) → (x – 2, y + 7)

That means----> The translation is 2 units at left and 7 units up

Answer:

2 units at left and 7 units up

Step-by-step explanation:

If the rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7), 2 units at left and 7 units up describes this translation.

Answer:  The length of the indicated segment is 14.45 units.

Step-by-step explanation:  We are given to find the length of the indicated segment.

From the figure, we note that

A chord is bisected by the radius of the circle that makes a right-angled triangle with hypotenuse measuring 16.1 units and the other two sides measures x units and 7.1 units.

Using Pythagoras theorem, we get

[tex]x^2+7.1^2=16.1^2\\\\\Rightarrow x^2+50.41=259.21\\\\\Rightarrow x^2=259.21-50.41\\\\\Rightarrow x^2=208.8\\\\\Rightarrow x=\pm\sqrt{208.8}\\\\\Rightarrow x=\pm14.45.[/tex]

Since x is the length of side of a triangle, so we get

x = 14.45.

Thus, the length of the indicated segment is 14.45 units.

Answer:

True

Step-by-step explanation:

Let, [tex]P_0[/tex] be the initial population,

Given,

The population is decreasing by 3%  each year,

Thus, the population after t years would be,

[tex]P=P_0 (1-\frac{3}{100})^t[/tex]

[tex]\implies P=P_0(1+\frac{-3}{100})^t[/tex]

Since, if a population is changing by a constant rate then the population after t years is,

[tex]P=P_0(1+\frac{r}{100})^t[/tex]

Where, r is the rate of changing per period.

Hence, in the given situation the population is changing by the constant rate.

Answer:

x=1

Step-by-step explanation:

1/2x-3/4=3/8-5/8

Combine like terms on the right hand side

1/2x-3/4=-2/8

Simplify the fraction

1/2x-3/4=-1/4

Add 3/4 to each side

1/2x-3/4+3/4 = -1/4+3/4

1/2x = 2/4

Multiply each side by 2

1/2x *2 = 2/4*2

x = 4/4

x=1

Answer:

the answer its 1

Step-by-step explanation:

Answer:

x squared plus two times x minus one = zero.

Step-by-step explanation:

(This is a Quadratic equation in the variable x).

Answer:

One less than the sum of square of a number  and twice the number is 0

Step-by-step explanation:

[tex]x^2+ 2x - 1 = 0[/tex]

x represents any number. x^2 represents square of a number

2x represents twice the number

[tex]x^2+2x[/tex] can be written as sum of square of a number  and twice the number

[tex]x^2+2x-1[/tex]

One less than the sum of square of a number  and twice the number

[tex]x^2+2x-1=0[/tex]

One less than the sum of square of a number  and twice the number is 0

Answer:

P(4, - 1 )

Step-by-step explanation:

The ratio 1 : 1 represents the midpoint of segment AB

Using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = (13, 1) and (x₂, y₂ ) = (- 5, - 3), so

P = [0.5(13 - 5), 0.5(1 - 3) ] = [0.5(8), 0.5(- 2) ] = (4, - 1 )

the midpoint P has the coordinates (4, −1).

To find the coordinates of point P that partitions segment AB in a 1:1 ratio, also known as the midpoint, we use the midpoint formula. Given the coordinates A(13,1) and B(−5,−3), the midpoint formula is ((x1 + x2)/2, (y1 + y2)/2).

Applying the values from A and B:

Therefore, the midpoint P has the coordinates (4, −1).

A. obtuse. The angle R is obtuse.

An obtuse angle is an angle greater than 90° and less than 180°. So, in the image attached we can see that the angle R is greater than 90° and less than 180°.

Answer:

- cos 25°

Step-by-step explanation:

Cosine function is one of the trigonometric functions. Cosine function is regarded as an even function, which means that f(-x) = f(x). Also, cosine function is positive in the first quadrant and the last quadrant and negative in the second quadrant and the third quadrant. 155° lies in the second quadrant since 155° is smaller than 180°. Therefore, the basic angle or the reference angle of 155° is 180° - 155° = 25°. We know that cos 155° will be negative because it lies in the second quadrant and cos 25° will be positive because it lies in the first quadrant. Since cos 55° is positive, and cos (-25°) = cos 25° by the even function property, therefore option 2 and option 3 are incorrect since cos 155° is negative. Therefore, option 1 is the correct answer i.e. cos 155° = - cos 25°!!!

Answer:

- [tex]cos25^{o}[/tex]

Step-by-step explanation:

Hope This Helps!!!

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Te formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have two points: (2, -3) and (4, 2). Substitute:

[tex]m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]

[tex]y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)[/tex]

Convert it to the standard form [tex]Ax+By=C[/tex]:

[tex]y+3=\dfrac{5}{2}(x-2)[/tex]           multiply both sides by 2

[tex]2y+6=5(x+2)[/tex]        use the coordinates of the point

[tex]2y+6=5x+10[/tex]          subtract 6 from both sides

[tex]2y=5x+4[/tex]              subtract 5x from both sides

[tex]-5x+2y=4[/tex]        change the signs

[tex]5x-2y=-4[/tex]

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ [tex]A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)[/tex]

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ [tex]B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)[/tex]

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is [tex]m=\frac{c-0}{b-a}=\frac{c}{b-a}[/tex]

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is [tex]m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}[/tex]

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

Answer:

b,c

Step-by-step explanation:

That guy above took so long

To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.

To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.

The initial population of birds is 10 and then it triples every year.

Therefore, the function that describes the number of birds after x years would be:

f(x) = 10 × 3^x

Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.

Final answer:

The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.

Explanation:

The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.

To find the number of birds after x years, we can use the following function:

B(x) = 10 × 3^x

Where:

B(x) is the number of birds after x years

10 is the initial number of birds

3 is the growth factor, as the population is tripling each year

x is the number of years since the birds were first released into the habitat

This equation models exponential growth and gives us the predicted population of the birds for any given year x.

Answer:

b

Step-by-step explanation:

because perimeter of rectangle is 2(l+b)

For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2a + 2b[/tex]

Where:

a: It is the length of the rectangle

b: It is the width of the rectangle

We have as data that:

[tex]P = 230 \ ft\\b = 30 \ ft[/tex]

Then, replacing we have:

[tex]230 = 2a + 2 (30)[/tex]

Answer:

Option B

1 minute  = 60 seconds

240 minute  = 240 × 60 = 14400 seconds