equation for perpendicular to the line -7x + 3y = -10j contains the point (-2,-4)

9514 1404 393

Answer:

  (b) 7x + 2y = 1

Step-by-step explanation:

You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)

  7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does

The equation is ...

  7x +2y = 1

__

Additional comment

The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.

Answer:

b

Step-by-step explanation:

Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).

Use the concept of the rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given that,

Rectangle dimensions: 2 feet by 8 feet

And here are the options provided:

A) 4 feet by 16 feet

B) 6 feet by 12 feet

C) 12 feet by 32 feet

D) 22 feet by 28 feet

To determine if two rectangles are similar,

Compare their corresponding side lengths.

In this case,

A rectangle with dimensions 2 feet by 8 feet.

After simplifying it we can write 1:4

Let's check each option to see if it matches the similarity:

A) 4 feet by 16 feet:

The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,

Which simplifies to 1:4 as well.

So, option A is similar to the given rectangle.

B) 6 feet by 12 feet:

The given rectangle has side lengths of 6:12,

Which simplifies to 1:2.

So, option B is not similar to the given rectangle.

C) 12 feet by 32 feet:

The given rectangle has side lengths of 12:32,

Which simplifies to 3:8.

So, option C is not similar to the given rectangle.

D) 22 feet by 28 feet:

The given rectangle has side lengths of 22:28,

Which simplifies to 11:14.

So, option D is not similar to the given rectangle.

To learn more about rectangle visit:

https://brainly.com/question/15019502

#SPJ3

Answer:

The number of flowers on the plant

Step-by-step explanation:

Answer:

C: Number of flowers on the plant

Step-by-step explanation:

i got it right on my test

Option 4

3-1/2"

Must click thanks and mark brainliest

Answer:

3 1/2

Step-by-step explanation:

That’s the distance from 0 to the green rectangle

Answer:

Step-by-step explanation:

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:

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.

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:

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:

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

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.

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:

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: 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

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

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

Step-by-step explanation:

| - 5 | + | - 4 |

5 + 4

= 9

| - 6| - 4

6 - 4

2

I hope this answers your question.

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:

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:

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:

Step-by-step explanation:

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:

-1/3x+3 = x-1

Step-by-step explanation:

The solution is (3,-2)

Check and see if the point solves the equation

-1/3x+3 = x-1

-1/3(3) +3 = 3-1

-1+3 = 3-1

2=2 yes

Answer:

C

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is D.

Answer:

5/9

Step-by-step explanation:

In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:

Negative -> Positive

Positive -> Positive

Since we are working with a negative value, it will turn positive.

Best of Luck!

Answer:

2500 mg

Step-by-step explanation:

Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.

Since r(t) =  50 (e^-01t - e^-0.20t)

m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)

= 50∫₀⁰⁰(e^-01t - e^-0.20t)

= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]

= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)

= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})

= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})

= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})

= 50(1/-0.01[- 1] - {1/-0.02[- 1]})

= 50(1/0.01 - 1/0.02)

= 50(100 - 50)

= 50(50)

= 2500 mg

From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.

In first place, you must know that the roots or solutions of a quadratic function are those values ​​of x for which the expression is 0. This is the values ​​of x such that y = 0. That is, f (x) = 0.

Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c

The solutions of a quadratic equation can be calculated with the quadratic formula:

[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]

The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c

The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.

If the discriminant:

In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:

discriminant= 10² -4*(-40)*(-1)

Solving:

discriminant= 100 - 160

discriminant= -60

The discriminant is negative, so the quadratic function has no real solutions.