Explain or show that the point (5,−4) is a solution to this system of equations:

3x−2y=23

2x+y=6

Answer:

3 miles

Step-by-step explanation:

5-1+2=3

From the calculation done using the pythagoras theorem, the distance from Sarah's apartment is 12m

This theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Using the pythagoras theorem

BC² = AB² + AC²

The sides of the triangle are x, x - 1 and 5

x² = (x-1)² + 5²

x² = (x-1)(x-1) +25

x² = x²-x-x -1 + 25

collect like terms

2x = 24

divide through the equation by 2

x = 24/2

= 12m

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Step-by-step explanation:

Maple calculator used.........................

Answer:

Step-by-step explanation:

[tex]f(x)={x^2\sqrt{1+x}\over{(1+x^2)^{3\over{2}}}}\\\\f^\prime (x)=\frac{{{(x^2\sqrt{1+x})^\prime (1+x^2)^{\frac{3}{2}}+ (x^2\sqrt{1+x})}((1+x^2)^{\frac{3}{2}}})^\prime}{((1+x^2)^\frac{3}{2})^2}}}[/tex]

[tex](x^2 \sqrt{1+x})^\prime=2x\sqrt{1+x}+ \frac{x^2}{2\sqrt{1+x}}[/tex]

[tex]((1+x^2)^{\frac{3}{2}})^\prime=\frac{3}{2}(1+x^2)^{\frac{1}{2}} (2x)=3x(1+x^2)^{\frac{1}{2}}[/tex]

[tex]f^\prime(x)=\frac{\{(1+x^2)^{\frac{3}{2}}\}(2x\sqrt{1+x}+\frac{x^2}{2\sqrt{1+x}})+(x^2 \sqrt{1+x})(3x\sqrt{1+x^2})}{(1+x^2)^{3}}}[/tex]

[tex]\sqrt{1+x^2}=\sqrt{(1+x)(1-x)}[/tex]

[tex]f^\prime (x)=x\sqrt{1+x}~\frac{(1+x^2)^{\frac{3}{2}}(2+\frac{x^2}{2(1+x)})+3x^2\sqrt{1-x}}{(1+x^2)^3}[/tex]

Answer:

V=πr2h /3

so we just substate and we get

V≈130.9

Answer: 130.83 units cubed

Step-by-step explanation:

The formula for finding the volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]

We will use 3.14 for pi.

[tex]3.14r^2\frac{h}{3}[/tex]

Now let's sub in our variables and solve

[tex]3.14(5^2)(\frac{5}{3})\\3.14(25)(\frac{5}{3})\\78.5(\frac{5}{3})\\130 \frac{5}{6}[/tex]

5/6 is about .83

130.83

Answer:

Step-by-step explanation:

yes

Answer:

(1)

compound amount = 802.5 $

invest earned = 52.5 $

Step-by-step explanation:

total amount = 10000 $

let amount x invested in ventures A and remaining (1000-x) on ventures B

now,

6x/100 +23/400(1000-x ) = 588.75

{24x+23(1000-x)}/400 =588.75

x=235500-230000

x=5500

Amount invested on A = 5500$

Amount invested on B = 4500$

(2)

principle=750$

time= 1 year

effective invest rate = 7%

a) compound amount = p(1+(r/w)^t

=750{1+(7/100)}^1

=802.5$

b) invest earned = 802.5-700 = 52.5$

Answer:

the area is 27

Step-by-step explanation:

Answer:

the base of this shape is 6

lets break it up into a rectangle and a triangle

the rectangle is 6(base) time 3(height)=18

the triangle is 6(base) times 3(height) divided by two = 9

18 plus 9 = 27

Answer:

Step-by-step explanation:

7x + 2x =90 (being perpendicular)

9x =90

x =90/9

x =10

substiute the value of x

7x

=7*10

=70

2x

=2*10

=20

Answer:

x = 10

Step-by-step explanation:

See image. Due to the logic of vertically opposite angles (when one angle is equal to the other that is "vertically opposite" to it), the two angles that I have marked in the diagram are going to equal.

Therefore, if we were to write it out:

2x + 7x = 90

(vertically opposite angles)

       9x = 90

     ∴  x = 10

Answer:

The graph is in the second attached image.

Step-by-step explanation:

In the first attached image, you have three equation graphed, the first is in red color, it's the original equation:

I graphed this to obtain a clear relation between the equation and its derivatives, the second graphed equation is in blue color and it's the first derivative:

And at last, we have in green color the second derivative:

As you can see, you only need the first and the second derivatives in the exercise, by this reason, in the second attached image you have the graph as you need to show in this exercise.

Answer:

Yes, this graph represents a function

Step-by-step explanation:

The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.

Answer:

The graph does represent a function

Step-by-step explanation:

The function is at about 30y = x^3

Answer:

3,964 ft

Step-by-step explanation:

555 / tan 8° = 555/0.14 = 3,964 ft

Answer:

B

Step-by-step explanation:

You always have to use the Big Three trig functions (those that are on your calculator when answering this kind of question involving right angle triangles).

y is the adjacent side of the triangle. It is the side (other than the hypotenuse -- which is the longest side of the right triangle) that makes up the cosine.

Cos(45) = y / 4 sqrt(2)

Cos(45) = sqrt(2)/2

Multiply both sides by 4 sqrt(2)

4*sqrt(2) * cos(45) = y

4*sqrt(2) * sqrt(2)/2 = y

2*2 = y

y = 4

I can't tell you where all the other choices are coming from.

Answer:

4, or B

Step-by-step explanation:

Answer:

16 3/2

Step-by-step explanation:

So lets go thru each one.

16 3/2 is just 17.5

A square root cancels out a square.

A cubed root cancels out a cube.

So, in the next answer:

16 squared, to the square root is just 16, since the squaring and root cancels out.

64 sqaured to the cube root must be 16. Lets break it all down:

2^6=64.  We need to square this, so we can rewrite it as:

64^2 = [tex](2^6)^2[/tex]

Normally we add/subtract exponents, but since the 6 exponent is in parethesese, it is multiplied by the 2 exponent. This makes it 2^12. So we can rewrite [tex]\sqrt[3]{64^2}[/tex] as:

[tex]\sqrt[3]{2^1^2}[/tex]

Now, when we divide a exponent by a exponent, we subtract.

However, when we root a exponent, it is division.

So it is the 2 [tex]\frac{^1^2}{^3}[/tex]

=

[tex]2^4[/tex]

Or

16

Finally we have the cubed root of 8^4.

using the same steps as above, 8^4 = [tex](2^3)^4[/tex]. This equals [tex]2^1^2[/tex]

Then again, we cube root it.

This is division of the 12 exponent by the 3 root, so we get:

[tex]2^4[/tex]

=

16

So in the end:

A - 17.5

B - 16

C - 16

D - 16

So a is the largest number

Hope this helps!

9514 1404 393

Answer:

  (d)  reflection about the x-axis, up 6 units

Step-by-step explanation:

The parent function y=1/x is multiplied by -1, which reflects it over the x-axis. Then 6 is added, which shifts it up 6 units.

The transformations are ...

  reflection about the x-axis, up 6 units

Answer:

See image below for answer:)

Step-by-step explanation:

The inequality b < - 1.4 written as interval notation is b ∈ (- ∞, - 1.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality b < - 1.4.

We know in interval notation if x is greater than a and less than b we write

a < x < b.

Therefore, The inequality b < - 1.4 can be written as,

- ∞ < b < - 1.4 Or b ∈ (- ∞, - 1.4).

learn more about inequalities here :

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Answer:

I think it's simple sentence

Answer:

55

Step-by-step explanation:

It is 55 minutes more because 1 1/2 hrs = 90 minutes and when you add 20 plus quarter of an hour it equal to 35. SO than you subtract 35 from 90 and you get 55 which is the more minutes .

Step-by-step explanation:

Everything has been written ..

Answer:

34

Step-by-step explanation:

The angles of a triangle add to 180

56+ F + 90 = 180   ( the box means 90 degrees)

Combine like terms

146+F = 180

Subtract 146 from each side

F = 180-146

F = 34

Step-by-step explanation:

n(AUB)=n(A)+n(B)-n(AnB)

hope it helps

Answer:

m<1 = 60

m<2 = 30

m<3 = 80

Step-by-step explanation:

1. Solve for angle (1)

The sum of angles in any triangle is (180) degrees. As one can see, there is a (30) degree angle in this triangle, and a (90) degree angle. Bear in mind that the box around an angle indicates that it is a (90) degree angle. One can form an equation and solve for the unknown angle using this given information;

(30) + (m<1) + (90) = 180

Simplify,

120 + m<1 = 180

Inverse operations,

m<1 = 60

2. Solve for angle (2)

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this theorem here by stating the following,

m<2 = 30

Thus one gets their answer, the measure of angle (2) must be (30) degrees by the vertical angles theorem.

3. Solve for angle (3)

As states above, the sum of angles in a triangle is (180) degrees. Since one has found the measure of angle (2), one can form an equation and solve for the measure of angle (3) using the given information, combined with the information found.

(m<2) + (70) + (m<3) = 180

Susbtitute,

30 + 70 + (m<3) = 180

Simplify,

100 + m<3 = 180

Invers eoperations,

m<3 = 80

Answer:

Alternate exterior

Step-by-step explanation:

Angles 2 and 7 are on exterior sides of the transversal and also are opposite to one another. They are classified as alternate exterior.

Answer:

alternate exterior angles

Step-by-step explanation:

2 and 7 are on opposite sides of the transversal so they are called alternate

They are on the outside of the parallel lines so the are called exterior

Answer:

The number is four (4)

Step-by-step explanation:

look at the picture above, it explains everything

Answer:

20x² + 40y²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x(2x + 3x) + 5y(5y + 3y)

Step 2: Simplify

Answer:

20 x ² + 40 y ²

Step-by-step explanation:

4 x ( 2 x + 3 x ) + 5 y ( 5 y + 3 y )

Combine likes term

4 x ( 5 x ) + 5 y ( 8 y )

multiply, we get

20 x ² + 40 y ²

Answer:

81

Step-by-step explanation:

4 quarts = 1 gallon

there are 22 gallons so multiply 4 by 22

that equals 88 quarts then subtract 7

leaving you with 81 quarts

Answer:

[tex]36 - 3m[/tex]

Step-by-step explanation:

[tex]3(12−m)[/tex]

[tex]3 \times 12+3(−m)[/tex]

[tex]36+3(−m)[/tex]

[tex]36−3m[/tex]

Step-by-step explanation:

Objective: Recall the properties.

a) 3+1=4

b) 3+7=7+3

c) 3+(7+4)=7+(3+4)

d). 3(7+4)=(3×7)+(3×4)

Answer:

It's C

Step-by-step explanation:

because there is a 90 degrees sigh behind it and those two angles need to add up to 90

Answer:

31

Step-by-step explanation:

b+59=90

b=90-59

b=31

hope it helps

Answer:

a. {(1,3), (1,4) ,(2,3), (2,4) }

b. {(1,4), (1,5), (2,4), (2,5)}

Answer:

PxR={(1,4)(1,5)(2,4)(2,5)}

PxQ={(1,3)(1,4)(2,3)(2,4)}

Step-by-step explanation:

Each of the members of set P is multiplying by each member of set Q or R,

so, 1 in set P has to multiply by 3 and 4 in set Q or 4 and 5 in set R. (We do the same for 2)

When a member of a set multiplies with another, we put the two members of two sets we are multiplying in parentheses.