choose the equation below that represents the line passing through the point (1, −4) with a slope of 1/2. a.) y − 4 = 1/2(x − 1) b.) y 4 = 2(x − 1) c.) y 4 = 1/2(x − 1) d.) y − 4 = 2(x 1)

Answers

Answer 1

Answer: Point (1, -4)
Slope=1/2
y=mx+c
y=1/2x +c
-4=1/2(1)+c
-4=1/2+c
c=-4-1/2
c=-4 1/2
y= $(1)/(2) x- (9)/(2)$

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Elsa knows that for every bushel of apples she sells she earns $9 and for every basket of pears she earns $11. She uses the expression 9a + 11p to keep track of her earnings. Part A: Identify the coefficients and variables in the expression. (3 points)Part B: How many terms are in the expression, what are they, and how do you know? (4 points)Part C: Which term in the expression shows the total earned from selling baskets of pears? (3 points)I only need help with b and c ?

A box is sitting on the floor. The box was then pulled with a force, Ft. The box did not move. The free-body diagram of the box is shown.A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline = negative 20 N. The second vector is pointing right, labeled F Subscript t Baseline = 10 N. The third vector is pointing upward, labeled F Subscript N Baseline = 20 N. The fourth vector is pointing left, labeled F Subscript f Baseline = negative 10 N. The up and down vectors are the same length. The right and left vectors are the same length.

Which describes the motion of the box based on the resulting free-body diagram?

It is moving up with a net force of 20 N.
It is moving to the right with a net force of 10 N.
It is in dynamic equilibrium with a net force of 0 N.
It is in static equilibrium with a net force of 0 N.
Mark this and return

Answers

Answer:

It is in static equilibrium with a net force of 0 N.

Step-by-step explanation:

EDGE21

I'm not sure if it is dynamic or static equilibrium but if I had to choose I'd say dynamic

This question was on the most recent SAT Mathematics Level 2 test. If two spheres with unequal diameters intersect, what could be the intersection?a. a point
b. a circle
c. a sphere
d. a point or a sphere
e. a circle or a sphere

99 points. Please provide a detailed and explanative answer.

Answers

It could be a point or a circle.

If the two spheres are tangent, then the intersection is by definition a point.

Since the two spheres are of unequal diameter, their intersection can't be a sphere (that can only happen if the spheres are of the same diameter and at the same point, then they overlap everywhere).

Now what happens if the two spheres are drawn close to each other a random way ? Well, they will intersect along a circle [see the image attached].

If you want more explanations/..., feel free to ask.

A Circle or point is your answer

See attached pictures

The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Answers

Answer-

The line equation is,

$\boxed{\boxed{6x+15y-10=0}}$

Solution-

The line $y =3x-5$ meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

$\Rightarrow 0 =3x-5$

$\Rightarrow 3x=5$

$\Rightarrow x=(5)/(3)$

So, coordinate of M is $((5)/(3),\ 0)$

The line $3y+2x=2$ meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

$\Rightarrow 3y+2(0)=2$

$\Rightarrow 3y=2$

$\Rightarrow y=(2)/(3)$

So, coordinate of N is $(0,\ (2)/(3))$

The line joining M and N can be found out by applying two point formula of straight line,

$\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$

$\Rightarrow (y-0)/((2)/(3)-0)=(x-(5)/(3))/(0-(5)/(3))$

$\Rightarrow (y)/((2)/(3))=(x-(5)/(3))/(-(5)/(3))$

$\Rightarrow -(5)/(3)y=(2)/(3)(x-(5)/(3))$

$\Rightarrow -5y=2(x-(5)/(3))$

$\Rightarrow -5y=2x-(10)/(3)$

$\Rightarrow 2x+5y-(10)/(3)=0$

As it is given that all the coefficients are integers, so multiplying with 3

$\Rightarrow 6x+15y-10=0$

Solution: As given line y =3x-5 meet x-axis at the point M.

On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given by

→ $(y-b)/(x-a) =(q-b)/(p-a)$

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is → $(x)/(a) + (y)/(b) =1$ , where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→ $(x)/((5)/(3)) + (y)/((2)/(3))=1$

→ $(3x)/(5) + (3y)/(2) =1$

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Miles and Nick each separately apply for and receive loans worth $5,000 apiece. Miles has a very good credit score, so his loan has an APR of 7.75%, compounded monthly. Nick’s credit score is rather low, so his loan has an APR of 13.10% interest, compounded monthly. If both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will Nick have paid than Miles? (Round all dollar values to the nearest cent.) a.$619.68 b.$267.50 c.$1,609.57 d.$1,070.00

Answers

Answer:

Ans. Nick paid $619.68 more than Miles (exactly $619.54). So the answer is A)

Step-by-step explanation:

Hi, first we need to find the equal monthly payments for both, Miles and Nick, for that, we need to find the effective monthly rate (because the payments are going to be made monthly), also, we need to convert that 4 year period into months. After doing all that, we need to use the following equation and solve for "A".

$Present Value=(A((1+r)^(n) -1))/(r(1+r)^(n) )$

Where:

A= monthly payments

r= rate of interest (for Miles is 0.075/12=0.006458 and Nick 0.131/12=0.010916)

n= number of periodic payments (both are 4*12=48 months)

First, let´s find out how much money Miles has to pay every month.

$5,000=(A((1+0.00645833)^(48) -1))/(0.00645833(1+0.00645833)^(48) )$

$5,000=A(41.1594758)$

$A=121.48$

So, Miles has to pay $121.48 every month, for 48 months, that is a total of $5,830.98 (121.48*48=5,830.98)

Now, let´s do Nick

$5,000=(A((1+0.01091667)^(48) -1))/(0.01091667(1+0.01091667)^(48) )$

$5,000=A(37.2063189)$

$A=134.39$

So, Nick has to pay $134.39 every month, for 48 months, that is a total of $6,450.52 (134.39*48=6,450.52)

The difference is 6,450.52- 5,830.98=619.54

Means that Nick has to pay $619.54 more than Miles. To your answers, the closest is A) $619.68.

Best of luck

Miles:7.75% (0.0775) x 5,000 = $387.5 x 4 = $1550 (over four year period)Nick:13.10% (0.131) x 5,000 = $655 x 4 = $2620$2620 - $1550 = $1,070 (rounded to nearest cent)So the answer is D.

Sarah scored 68 out of 80 in a test.Write her score as a simplified fraction

Answers

$(68)/(80) \n \n ((4)17)/((4)20) \n \n \boxed{ (17)/(20)}$

If f(x) is the total cost, in dollars, of x candies, which of the following statements best describes the meaning of f(2) = 6? A. The total cost of 2 candies is $6.00./ B. The total cost of 6 candies is $2.00. / C. The total cost of 2 candies is $3.00. / D.The total cost of 3 candies is $2.00.

Answers

Since the cost is a function of the total number of candies (x), therefore the equation relates the total cost per amount of candies.

Since we have 2 candies therefore the correct statement should be that the total cost of 2 candies is $6.00

this statement is letter A of the given choices.

Answer:

The total cost of 6 candies is $2.00.

Step-by-step explanation:

Given : f(x) is the total cost, in dollars, of x candies,

To Find: Which of the following statements best describes the meaning of f(2) = 6?

Solution:

We are given $f(2)=6$