Find the slope m and y-intercept of the equation:
y = (-1/5)x + 7

Answer:

Step-by-step explanation:

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

Answer:

21

Step-by-step explanation:

Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].

Answer:

C

Step-by-step explanation:

The expression is x>55 and 55 isn't included

Answer:

c

Step-by-step explanation:

So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.

22 hours x $8.50 = $187

Subtract that from the cost of the computer:

899-187 = $712

She needs $712 more.

Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75

Divide what she needs by amount per shift:

712 / 46.75 = 15.22 shifts

She needs to work 16 more shifts.

Answer:

m=1/2

y-8=1/2(x-1)

y-8=1/2x-1/2

multiply through by 2

2y-16=x-1

2y-16+1-x=0

2y-15-x=0

2y-x-15=0

Answer:

"D"

if you multiply by Conjugate

the denominator would end up A^2 - b^2

the answer has 25 - 10x

that is D

Step-by-step explanation:

If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.

But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.

That number is 7396 which when square rooted gives 86 soliders on the side.

Subtract 7396 from 7500 and get how many soliders were left out,

[tex]7500-7396=\boxed{104}[/tex]

Hope this helps :)

Answer:

Step-by-step explanation:

P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32

The required perimeter of the playground is 10x-32.

The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.

Perimeter, is the measure of the figure on its circumference.

The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)

= 10x-32

Thus the required perimeter of the playground is 10x-32.

learn more about perimeter here:

brainly.com/question/6465134

#SPJ2

Answer:

Step-by-step explanation:

Let the quadratic function be

y=a(x+4)²-1

∵(-7,8) lies on it.

8=a(-7+4)²-1

8+1=a(-3)²

9a=9

a=9/9=1

so quadratic function  is

f(x)=1(x+4)²-1

or

f(x)=x²+8x+16-1

so quadratic function is

f(x)=x²+8x+15

Answer:

a = 11

b = -5

c = 25

Step-by-step explanation:

a.

6 + 4x = 50

50 - 6 = 44

4x = 44

x = 11

b.

(x+9) * -2 = -8

(x+9) = 4

x = -5

c.

2(37.5) + 2(x) = 125

75 + 2x = 125

125 - 75 = 2x

50 = 2x

x = 25

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. x is treat any other variable as a constant.

dz/dx=0-2x-0

dz/dx=-2x

Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.

Since this result is negative, it mrans as x increases z decreases.

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. y is treat any other variable as a constant.

dz/dx=0-0-2y

dz/dx=-2y

Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.

Since this result is positive it mrans as y increases z decreases.

Answer:

x = 8

Step-by-step explanation:

undefined slope => m = oo

passes (8, -3) => (x1, y1)

the equation is : y-y1 =m(x-x1)

y+3 = oo(x-8)

=> x -8 = (y+3)/oo

x -8 = 0

x = 8

so, the equation is: x = 8

Step 1: Find the area of the rectangle

A = base x height

A = 39 x 20

A = 780

Step 2: Find the area of the semi-circles

---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.

A = pi x r^2

A = pi x 10^2

A = 100pi = 314

Step 3: Find the area of the figure

Area = area of the rectangle - area of the semi-circles

A = 780 - 314

A = 466 cm^2

Hope this helps!

Answer:

466 cm^2

Step-by-step explanation:

This one is done basically the same as the other.

Rectangle = 20 x 39

Circle = (3.14) x 10^2

Rectangle = 780

Circle = 314

rectangle - circle

780 - 314 = 466

Answer: y=29 / (4,29)

Step-by-step explanation:

By graphing [tex]f(x)=8x-3[/tex] and [tex]f(4)=0[/tex] on Desmos. You'll be able to find that when x is 4, y is 29.

Similarly, you can plugin 4 into the original equation ([tex]f(x)=8x-3[/tex]) Which looks like:

[tex]8(4)-3\\32-3=29[/tex]

Additionally, you can change [tex]f(x)=[/tex] to [tex]y=[/tex] as it is the exact same thing. With that in mind, you can do the same with [tex]f(x)=0[/tex] and just change it to x=4. As you're wanting to know what the y-value is when x=4.

Answer:

4x²-3x+c is our original equation

Step-by-step explanation:

we have an independent number I called this number c

put 4 from x and try to find c

f(4)=4*(4²)-3*(4)+c=0

we have to be careful about f(4) is 0

64-12+c=0 and c is -52 so our original equation is 4x²-3x-52

Split up the integral:

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]

For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get

[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]

and

[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]

Then

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]

Answer:

2.46×10

Step-by-step explanation:

24.6

2.46 ×10

.....................

Step-by-step explanation:

| - 5 | + | - 4 |

5 + 4

= 9

| - 6| - 4

6 - 4

2

I hope this answers your question.

Answer:

b=1

Step-by-step explanation:

2a+1 =1

Subtract 1 from each side

2a+1-1 = 1-1

2a=0

a=0

Now find b from the second equation

b-a =1

b-0=1

b=1

Answer:

Equation: 2a+1=1

Subtract 1 from both sides: 2a=0

Divide by 2: a=0

Equation: b-a=1

Substitute: b-0=1

Combine: b=1

So, b=1.

Let me know if this helps.

Answer:

Option D is the correct answer.

Step-by-step explanation:

The equation of the function is in vertex form. Thus, we can analyze the equation to determine the x and y values of the vertex. We know that the template format of a vertex form equation is as follows:

f(x) = a(x – h)2 + k . The only constants we need are h and k, where 'h' is the x-value of our vertex and 'k' is the y-value of our vertex.

The value of 'k' can be found quite simply by looking at the equation: -9.

The value of 'h' is a little trickier, as we must take into account the 'subtract' sign of the template equation, meaning that the '+7' in the given equation actually means that we are subtracting negative seven. Thus, the value of 'h' is -7.

Thus, the vertex of this graph is (-7,-9).

This means that option D is correct.

Answer:

The vertex is at ( -7, -9)

Step-by-step explanation:

y = (x+7)^2 -9

This is written in vertex form

y = a( x-h)^2 +k where ( h,k) is the vertex

y = ( x - -7)^2 + -9

The vertex is at ( -7, -9)

It seems like you want to find the sum of 38 to 115:

[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]

If we notice, this is arithmetic series or the sum of arithmetic sequences.

To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.

[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]

This formula only applies to the sequences that have the common difference = 1.

Given that a1 = first term of sequence/series, n = number of terms and a_n = last term

We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.

To find the n, you can use the following formula.

[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]

Substitute an = 115 and a1 = 38 in the formula of finding n.

[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]

Therefore the number of sequences is 78.

Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.

[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]

Hence, the sum is 5967.

Answer:

Two tailed test

Test statistic = 3.20

Pvalue = 0.001

H1 : p ≠ 0.91

Step-by-step explanation:

Given :

Test of p=0.91 vs p≠0.91

The use if not equal to ≠ sign in the null means we have a tow tailed test, which means a difference exists in the proportion which could be lesser or greater than the stated population proportion.

The test statistic :

This is the Z value from the table given = 3.20

The Pvalue = 0.001

Since Pvalue < α ;Reject H0

Answer:

The guy above me is correct

Step-by-step explanation:

2022

Answer:

number of seeds planted per square foot

Step-by-step explanation:

response is the yield explained by how many seeds are planted

Answer:

x is 18, and y is 9 √ 3

Step-by-step explanation:

Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.

The relationship is listed below:

The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3

So x is 18, and y is 9√3

Answer:

Step-by-step explanation:

Answer:

answers in the explanation cz I'm too lazy to type :(

not entirely sure tho

Step-by-step explanation:

w²+2w-42=0

*quadratic formula*

w= -1+ square root 43 m

or w= -1- square root 43 m

then since the length is 2m more than w

add 2 to both answers

l= 1+ square root 43 m

l=1- square root 43 m

9514 1404 393

Answer:

Step-by-step explanation:

Given:

  a rectangular patio of width w meters, length w+2 meters, and area 42 m²

Find:

  width and length

Solution:

The area is ...

  A = LW

  42 = w(w +2)

  43 = w² +2w +1 . . . . . . add 1 to complete the square

  √43 = w+1

  w = √43 -1 ≈ 5.557 . . . meters

  l = w+2 = √43 +1 ≈ 7.557 . . . meters

The width and length of the patio are 5.557 m and 7.557 m, respectively.