Find the equation of the line with slope m = 3/2 that contains the points (2,1).

Answer:

  C.  -7x- 5y = -48

Step-by-step explanation:

The vector AB is ...

  AB = B -A = (4, 4) -(-3, -1) = (4+3, 4+1) = (7, 5)

The dot-product of this vector and the one in the direction of the line through B will be 0:

  (7, 5)·(x -4, y -4) = 0

  7(x -4) +5(y -4) = 0

  7x +5y -48 = 0

Multiplying by -1 gives the form we see in answer choice C:

  -7x -5y = -48

Answer:

150

Step-by-step explanation:

We know that Scott's ratio of making the basket is 9/12. All we need to do is find out how many baskets he'll make if he attempts 200 shots.

So, 9/12 needs to become x/200. We don't know what x is yet, but there's a shortcut.

9/12 can be simplified by dividing 3 on the top and bottom.

9/12 ÷ 3/3 = 3/4

We can then see how many times 4 can go into 200.

200/4 = 50

So, we multiply 3/4 by 50 on both the top and bottom.

3/4 × 50/50 = 150/200.

So, if he attempts 200 shots then he'll make 150 of them.

Scott can expect to make approximately 150 baskets if he attempts 200 shots with his success rate being 9 out of 12, which equates to a 75% success rate.

The question asks how many baskets Scott can expect to make if he tries 200 shots given that his average success rate is 9 out of 12. To find the answer, we can set up a proportion because Scott's shooting is a matter of probability and ratios. First, we determine Scott's success rate as a fraction: 9/12 which simplifies to 3/4 or a success rate of 75%.

Then, we apply this success rate to the new number of attempts (200) to find the expected number of successful baskets:

Therefore, if Scott attempts 200 shots, he can expect to make approximately 150 baskets.

Answer:

Step-by-step explanation: solution.. 8/10 of candy bar left over to be split into 1/3 pieces...

(8/10)÷1/3=12/5=2.4pieces

Answer:

11

3Step-by-step explanation:

Given

3(x - 1)² + 2x - 7 ← substitute x = 3 into the expression

= 3(3 - 1)² + 2(3) - 7

= 3(2)² + 6 - 7

= 3(4) - 1

= 12 - 1

= 11

The first step in evaluating the expression is to substitute 3 for x.

The first step in evaluating the expression 3(x-1)^2 + 2x - 7 for x=3 is to substitute 3 for x. This is because before you can simplify or combine like terms, you need to know the value of the variables involved. Once substitution is done, you can proceed with further simplification such as distributing and combining like terms.

Answer:

Therefore,

Slopes are Equal, Hence the Lines are not Perpendicular.

Step-by-step explanation:

Given:

[tex]y-4=2(x-2)=2x=-4\\\\y=2x[/tex] .......Equation ( 1 )

[tex]4x-2y=5\\2y=4x-5\\\\y=2x-\dfrac{5}{2}[/tex]  .......Equation ( 2 )

Comparing with,  

[tex]y=mx+c[/tex] ......General Slope point form  

Where m =slope  

We get  

[tex]Slope = m1 = 2[/tex]   For Equation ( 1 )

[tex]Slope = m2 = 2[/tex]   For Equation ( 2 )

Hence,

[tex]m1=m2[=2[/tex]

Therefore, Slopes are Equal Hence the Lines are Parallel not Perpendicular.

For Perpendicular we require

[tex]m1\times m2=-1[/tex]

Therefore,

Slopes are Equal, Hence the Lines are not Perpendicular.

Answer:

The correct answer is Area = Pir2, The area formula can be found by breaking apart the circle and forming a parallelogram, and The area formula can be found by breaking apart the circle and forming a parallelogram. B,D,and E.

Step-by-step explanation:

Answer:

B, D, E

Step-by-step explanation:

Thats the correct answer bye

To solve this ratio problem, we need to determine the relationship between the given numbers and apply it to find the answer.

The given expression is:

9:3 :: 49 :

To solve this, we need to determine the relationship between 9 and 3, and then apply the same relationship to 49.

The symbol '::' represents the ratio or proportion between the numbers before and after it.

9 divided by 3 is equal to 3, so the relationship here is that the first number is three times the second number.

Now, let's apply the same relationship to 49:

49 divided by 3 is equal to 16.33, so we can say that the answer is 16.33.

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The final answer is 9 : 3 :: 49 : 16.33.

Here's a step-by-step solution:

The answer to the question is therefore 49 : 16.33.

Answer:

no

Step-by-step explanation:

24 x 5 = 120

40 x 4= 160

Answer:

3

(-5x - 3)(-5x + 3)

Step-by-step explanation:

Difference of squares is a special type of factoring when you are subtracting two numbers that are perfect squares. Perfect squares are numbers that, when you find its square root, it is a whole number.

Difference of squares follows this rule:

a² - b² = (√a² - √b²)(√a² + √b²) = (a - b)(a + b)

Notice in the factored form, you take the same number in both brackets. In one set of brackets you add the numbers. In the other brackets, you subtract the numbers.

In (-5x - 3)(-5x + __), the blank in the second bracket will use the same number as the second number in the first brackets.

(-5x - 3)(-5x + 3)

Option D: Two irrational solutions

Explanation:

The equation is [tex]17+3 x^{2}=6 x[/tex]

Subtracting 6x from both sides, we have,

[tex]3x^{2} -6x+17=0[/tex]

Solving the equation using quadratic formula,

[tex]x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}[/tex]

Simplifying the expression, we get,

[tex]\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}[/tex]

Taking out the common terms and simplifying, we have,

[tex]\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}[/tex]

Dividing by 3, we get,

[tex]x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}[/tex]

Hence, the equation has two irrational solutions.

Answer:

Check the attachment, then plug in values as needed

Step-by-step explanation:

angle list: k,l,j:

sides are:  LJ, KJ, KL

To find the sides of triangle JLK in order from smallest to largest, we need to compare the measures of the angles. The side opposite the largest angle is the longest side, so we can determine the order of the sides based on the angle measures.

The triangle JLK has angles J, L, and K with measures 82, 57, and 41 degrees, respectively. To determine the sides of JLK in order from smallest to largest, we can use the fact that the side opposite the largest angle is the longest side. So, we need to identify the largest angle and its corresponding side.

Comparing the measures of the angles, we can see that M∠J is the largest angle. Therefore, the side opposite angle J, which is side JL, is the longest side. Next, we compare the measures of the remaining angles. M∠L is the next largest angle, so the side opposite angle L, which is side LK, is the second longest side. Finally, M∠K is the smallest angle, so the side opposite angle K, which is side JK, is the shortest side.

Therefore, the sides of triangle JLK in order from smallest to largest are JK, LK, JL.

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Hey there!

When we say (f + g)(2), we are adding both functions together and plugging in 2 for x.

Since f(x) is equal to 2x + 210 and g(x) is equal to 2x + 125, (f + g)(x) is equal to (2x + 210) + (2x + 125).

That can be simplified to 4x + 335.

So, (f + g)(x) = 4x + 335.

Let's plug 2 in for x and solve.

(f + g)(2) = 4(2) + 335

Multiply.

(f + g)(2) = 8 + 335

Add.

(f + g)(2) = 343

The x value is consistent for the values of both equations, in both x is defined as the number of hours spent exercising.

So, (f + g)(2), which is 343, is the amount of calories burned and the calorie deficit on a diet when 2 hours are spent exercising.

Hope this helps!

Answer:

Its D

Step-by-step explanation:

Answer: The nth term of a geometric progression is Tn = ar^(n-1)

A. 12

B. 3.6

C. -3/4

D. 0.6

Step-by-step explanation:

The nth term of a geometric progression is Tn = ar^(n-1)

Where Tn= nth term

a = first term

r = common ratio

n = number

A. a6 = (2*6) = 12

B. a6 = (0.6*6) = 3.6

C. a6 = (-1/8*6) = -3/4

D. a6 = (0.1*6) = 0.6

Option C:

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]

Solution:

Given expression:

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]

Summation means sum of the numbers.

Put n = 1  to 5 and sum all the numbers.

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]

           [tex]=3(0.2)^{1-1}+3(0.2)^{2-1}+3(0.2)^{3-1}+3(0.2)^{4-1}+3(0.2)^{5-1}[/tex]

           [tex]=3(0.2)^{0}+3(0.2)^{1}+3(0.2)^{2}+3(0.2)^{3}+3(0.2)^{4}[/tex]

Using exponential rule: [tex]a^0=1[/tex], so that [tex]0.2^0=1[/tex]

           [tex]=3(1)+0.6+0.12+0.024+0.0048[/tex]

           [tex]=3.7488[/tex]

           = 3.75

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]

Option C is the correct answer.

Hence approximate value of [tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex] is 3.75.

Answer:

C

Step-by-step explanation:

edge

The expression (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6 after distributing the negative sign and combining like terms.

To solve the expression (1.3x + 2.4) - (6.1x - 3.2), we'll distribute the negative sign inside the second parentheses and then combine like terms:

(1.3x + 2.4) - (6.1x - 3.2)

Distribute the negative sign:

1.3x + 2.4 - 6.1x + 3.2

Combine like terms:

(1.3x - 6.1x) + (2.4 + 3.2)

Combine the x terms:

-4.8x + 5.6

So, (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6.

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The probable question may be:

Simplify (1.3x + 2.4) - (6.1x - 3.2)

Question:

Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?

Answer:

The expression could represent how many dishes crispy clovers new menu has is:

[tex]D + \frac{1}{5}D \text{ or } 1.2D[/tex]

Solution:

Given that,

The new menu had 20% more dishes than the previous menu

The previous menu had D dishes

Therefore,

Previous menu = D dishes

New menu = 20 % more dishes than previous menu

Which means,

New menu = 20 % of previous menu + previous menu

Therefore,

New menu = 20 % of D + D

Solve the above equation

[tex]New\ menu = 20 \% \times D + D\\\\New\ menu = \frac{20}{100} \times D + D\\\\New\ menu = 0.2 \times D + D\\\\New\ menu = 0.2D + D = \frac{D}{5} + D = 1.2D[/tex]

Therefore, new menu has 1.2D dishes

Final answer:

The total surface area of a square prism with a base edge of 6 km and height of 5 km is 192 km².

Explanation:

The question is about finding the surface area of a square prism (also known as a rectangular prism where the base is a square). A square prism has six faces: two square bases and four rectangular sides. To find the total surface area, we calculate the area of each face and sum them up.

The formula for the area of a square is side × side. Since the base of the prism is a square with each side measuring 6 km, the area of one square base is:

Since there are two square bases:

The formula for the area of a rectangle is length × width. The four rectangular sides each have one dimension that is the height of the prism (5 km), and the other dimension is the length of a side of the base (6 km), so:

There are four such sides:

Adding the areas of the bases and the sides:

Answer:

An acute Angle

Step-by-step explanation:

Any Angle that is from 1 to 89 degrees is considered an acute Angle.

Answer:

Step-by-step explanation:87

87

Total distance walked by Layla is 300 yards

Solution:

Given that,

Layla is walking in a rectangular park

She walks one side that is 50 yards and then the other  side that is 120 yards

Length = 120 yards

Width = 50 yards

Layla develops a cramp in her leg and walks diagonally through the park  to head back home

Let us find the length of diagonal of rectangle

[tex]d=\sqrt{w^2+l^2}[/tex]

[tex]d = \sqrt{50^2+120^2}\\\\d = \sqrt{2500+14400}\\\\d = \sqrt{16900}\\\\d = 130[/tex]

Thus length of diagonal is 130 yards

What is the total distance that layla walked?

Given that Final answer is  perimeter of the triangle park

The diagonal and length and width forms a right angle triangle

Perimeter of triangle = diagonal length + width + length

Perimeter of triangle = 130 + 50 + 120 = 300

Thus total distance walked by Layla is 300 yards

The total distance Layla walked, including the two sides of the park and the diagonal path, is calculated using the Pythagorean theorem to be 300 yards.

The question asks us to find the total distance Layla walked while going through the rectangular park diagonally. Layla first walks one side of the park which is 50 yards long and then the adjoining side which is 120 yards long. To do this, we will first find the length of the diagonal using the Pythagorean theorem and then add it to the sum of the two sides she walked to get the total distance. The Pythagorean theorem states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c2 = a2 + b2.

Applying the Pythagorean theorem to find the diagonal (hypotenuse):

Now, we can find the total distance Layla walked:

Therefore, the total distance Layla walked is 300 yards.

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The answer is 591 to the problem.

z(5 , 3) = 10

Step-by-step explanation:

x = 5

y = 3

z(x,y) = x/ y(x-y)

z (5, 3) = 5/ 3(5-3)

            = 4x5/ 2

            = 20/2

z (5- 3) = 10

Answer:

- 6r³.

Step-by-step explanation:

Here, we have to find the product of r², - 3 and 2r.

Now, the product is, P = (r²)(- 3)(2r)

⇒ [tex]P = (- 3) \times (2) \times r^{2}\times r[/tex]

{Seperating each terms as the terms are in product form}

⇒  [tex]P = - 6 \times r^{2 + 1}[/tex]

{Using the property of exponent that [tex]x^{a}\times x^{b} = x^{a + b}[/tex]}

⇒ P = - 6r³ (Answer)

Answer:

41

Step-by-step explanation:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.  40 prints must she sell next month if she wants to earn at least $2000

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Melissa sells her art online for $49.50 per print.

We need to find how many prints she has to sell to earn atleast $2000.

Let us consider x be the number of prints.

Let us form proportional equation

Forty nine point five zero by one equal tp two thousand by x.

49.50/1=2000/x

Apply cross multiplication

49.50x=2000

Forty nine point five zero times of x equal to two thousand.

Divide both sides by 49.50

x=40.40

Hence 40 prints must she sell next month if she wants to earn at least $2000

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Answer:

the answer is 97, I'll explain in the comments in a bit

^^

guy above me its right

Answer:$11200

Step-by-step explanation:

I = prt

I = 40,000( .07)(4)

I = $11200