Find the equation of the line passing
through the points (4, 2) and (6,10).
y = [ ? ]x + [ ]

Answer:

9

Step-by-step explanation:

12÷1 [tex]\frac{1}{3}[/tex]=9

Answer:

Step-by-step explanation:

Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25).

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5)

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given function f(x)=40-1.25x,

where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25) then;

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5) then;

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

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Answer:

-2

Step-by-step explanation:

    [tex]\frac{(-2)^3+3 (4)}{-8+6}[/tex]

 [tex]= \frac{-8 + 12}{-2}[/tex]

 [tex]= \frac{4}{-2}[/tex]    

 [tex]= -2[/tex]

Answer:

2.3

Step-by-step explanation:

First we must get rid of the exponent, which is that little 3 at the top.

To do this, we will do:

(-2) × (-2) × (-2) = -8

Now we have -8 + 3.4, which equals -4.6

Next we will combine the numbers in the denominator, to get -2.

Now, all together, we have -4.6/-2.

Last but not least, we will divide -4.6 by -2, to get 2.3

And that's your answer, hope this helps you :)

Sorry if it doesn't, though.

Hey there!

n * 25 = 5 * 60

25n = 5 * 60

25n = 300

DIVIDE 25 to BOTH SIDES

25n/25 = 300/25

CANCEL out: 25/25 because it gives you 1

KEEP: 300/25 because it helps solve for the n-value

NEW EQUATION: n = 300/25

SIMPLIFY IT!

n = 12

Therefore, your answer is: n = 12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The cart slows that at the rate of 20cm/s between 5 and 15secs

Given the rate function expressed as:

r(t) = 2t + 60

If the time is t = 5

r(5) = 2(5) + 60

r(5) = 70cm/s

If the time is t = 15

r(15) = 2(15) + 60

r(15) = 90cm/s

Taking the difference in rate;

Difference = 90cm.s - 70cm/s

Difference = 20cm/s

Hence the cart slows that at the rate of 20cm/s between 5 and 15secs

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Answer:

Step-by-step explanation:

A = 8(14) - 5(14 - 5 - 2) = 77 m²

Answer:

77m (squared)

Step-by-step explanation:

Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²

Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)

Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²

Finally we get this expression : (x-3)²(x+3)²(x-1)

This expression is a polynomial of degree 5 but what is the y intercept of it ?

Basically, we need to replace x by zero and the value of the expression will be the y intercept :

let x = 0

then ,

(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162

We need an y intercept of value = -162

Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)

satisfies all the required condition

Good Luck

Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then

∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt

… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt

… = 7 ∫ √(1 - sin²(t)) cos(t) dt

… = 7 ∫ √(cos²(t)) cos(t) dt

We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so

√(cos²(t)) = |cos(t)| = cos(t)

and the integral reduces to

… = 7 ∫ cos²(t) dt

Recall the half-angle identity for cosine:

cos²(t) = (1 + cos(2t))/2

Then the integral is

… = 7/2 ∫ (1 + cos(2t)) dt

… = 7/2 (t + 1/2 sin(2t)) + C

… = 7t/2 + 7/4 sin(2t) + C

Get the antiderivative back in terms of x. Recall the double angle identity for sine:

sin(2t) = 2 sin(t) cos(t)

We have t = arcsin(x/√7), which gives

sin(t) = sin(arcsin(x/√7)) = x/√7

cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7

Then

∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C

… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C

Answer:

n= 2.9

1:2.9

Step-by-step explanation:

Divide by 15 on both sides

15 divided by 15 is 1

43 divided by 15 is 2.8666666666=>

It states "Give any decimals in your answer to 1 d.p.

Mean we round it to one decimal place

so it is 2.9

Thus the answer for n is 2.9

Hope this helps!

Answer:

x = 15

Explanation:

First, add both equations on one side, and set it equal to 180° because it's supplementary:

2x + 8 + 8x + 22 = 180

combine like terms:

10x + 30 = 180

subtract 30 on both sides of the equation and you end up with:

10x = 150

divide both sides by 10 and you get:

x = 15

Answer:

x=5

Step-by-step explanation:

Answer:

x = 3π/4, 5π/4

Step-by-step explanation:

cos(x+2π) = -√2/2, [0,2π]

cos(x)cos(2π)-sin(x)sin(2π) = -√2/2

cos(x) = -√2/2

x = 3π/4, 5π/4

Remember that the cosine function is periodic, so cos(θ+2π)=cos(θ).

Answer:

5.67

Step-by-step explanation:

The scale factor of the height of the image is 7.89.

The scale factor is defined as the proportion of the new image's size to that of the previous image.  The scale factor is the ratio of the actual size to the scaled size of the object.

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life.

The scale factor will be calculated as,

Scale factor = ( 30 / 3.8)

Scale factor = 7.89

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Answer:

x= 4/5 or x = -2

Step-by-step explanation:

Step 1: Subtract -6x from both sides.

5x^2 -8 - -6x = -6x -6x

5x^2 + 6x - 8 = 0

Step 2: Factor left side of equation.

(5x - 4) (x + 2) = 0

Step 3: Set factors equal to 0.

5x - 4 = 0 or x + 2 = 0

Hense the Answer is x= 4/5 or x = -2

Answer:

16/5=7

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

as it goes further right, it goes further down, so it is a negative slope

Answer:

[tex]\boxed{\boxed{\sf x=-3}}[/tex]

Step-by-step explanation:

[tex]\sf y = -3x - 2[/tex]

[tex]\sf y=7[/tex]

We'll substitute y into the equation:

[tex]\sf 7 = -3x - 2[/tex]

Switch sides:

[tex]\sf -3x-2=7[/tex]

Add 2 to both sides

[tex]\sf -3x-2+2=7+2[/tex]

[tex]\sf -3x=9[/tex]

Divide both sides by -3:

[tex]\sf \cfrac{-3x}{-3}=\cfrac{9}{-3}[/tex]

[tex]\sf x=-3[/tex]

Therefore, the value of x/solution is -3

________________________________________

Answer:

The value of x is  

✔ –3

The solution to this system of equations is  

✔ (–3, 7)

Step-by-step explanation:

Answer: 40 mg

Unitary method:

For 3kg --> 8mg

For 1kg --> 8/3 mg

For 15kg--> (8/3) * 15

              --> 40 mg

The number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.

Given that, for every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, for 1 kg of child's weight pediatricians prescribe [tex]\frac{8}{3}[/tex] mg of fever reducer.

If Nidhi weighs 15 kg, then the fever reducer = [tex]\frac{8}{3}\times15[/tex]

[tex]=8\times5[/tex]

[tex]=40[/tex] mg

Therefore, the number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.

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Answer:

Step-by-step explanation:

Given equation:

Solve for x, divide both sides by 3yz:

Correct choice is C

Answer:

5 po its my volt

Step-by-step explanation:

yan hooo

Answer:

$17.12

Step-by-step explanation:

2.14 · 8 = 17.12

Answer:

22m+4

Step-by-step explanation:

Let's break it down:

13m+-1(-9m-4)

13m+(9m+4)

22m+4

Answer:

22m+4

Step-by-step explanation:

Answer:

a. 587

b. 543

Step-by-step explanation:

a. Mean = sum / number of numbers

To find the sum, we can add the numbers up.

432 + 543 + 348 + 788 + 823 = 2934

There are 5 numbers. Our mean is thus

2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5

b. To find the median, we first must order the numbers. The numbers ordered are this:

348 ,  432 , 543 , 788 , 823

To find the median, we can cross off one number on each side until we are left with one or two numbers.

348 ,  432 , 543 , 788 , 823

cross out one number from each endpoint

432 , 543 , 788

cross out one number from each endpoint

543

Answer:t=10.05s

Step-by-step explanation:

Answer:

what's your question?  

Answer:

x < -15

Step-by-step explanation:

Divide both sides by -2.

Next you will reverse the sign because you are dividing by a negative number.

105/2^9

Step-by-step explanation:

The probability of getting a head in a single toss

p=12

The probability of not getting a head in a single toss

q=1−12=12

Now, using Binomial theorem of probability,

The probability of getting exactly r=4 heads in total n=10 tosses

=10C4(1/2)4(1/2)10−4

=10×9×8×7/4! 1/2^4 1/2^6

=2^44⋅9⋅35/24(2^10)

=105/2^9

Answer:

P = 0.205  (20.5%)

Step-by-step explanation:

[tex]f(x)=(10nCr4)(.5)^{4} (.5)^{6} =(210)(0.0625)(0.015625)=0.205[/tex]

Hope this helps