What is the answer for #7?

Answer:

B. 2x – 1 = 13 and x = 7

Step-by-step explanation:

We are given 4 equations and a solution for each. We have to tell which of the given solution satisfies the given equation.

Option A.

2x -1 = 13 and x = 6

Using this value in the equation, we get:

2(6) -1 = 13

12 - 1 = 13

11 = 13, which is not true. Hence this option is not valid

Option B.

2x - 1 = 13 and x = 7

Using the value in the equation, we get:

2(7) - 1 =13

14 - 1 =13

13 = 13, which is true. Hence this option is valid.

Option C.

2x + 1 =13 and x = 7

Using the value in the equation, we get:

2(7) + 1 = 13

15 = 13, which is not true. So this option is not valid

Option D.

2x - 1 = 13 and x = 11

Using this value in the equation, we get:

2(11) - 1 = 13

21 = 13, which is not true. Hence this option is not valid.

Answer:

  B)  maximum at 15

Step-by-step explanation:

Factor the leading coefficient from the first two terms.

  -(x^2 +6x) +6

Add the square of half the x-coefficient inside parentheses and subtract the same quantity outside.

  -(x^2 +6x +9) +6 -(-9)

  -(x +3)^2 +15

Compared to the form

  a(x -h)^2 +k

we find a=-1, h=-3, k=15. The negative vertical scale factor (a=-1) means the parabola opens downward. The vertex is located at (h, k) = (-3, 15).

The maximum value is 15.

Answer:

yesterday 9 today 10

Step-by-step explanation:

46/5= 9.2

52/5= 10.4

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:

Let "a" and "b" represent Alan and Brian's rates in meters per minute, respectively. The rate at which Alan is lapping Brian is the difference in their rates:

a - b = (450 m)/(9 min) = 50 m/min

This lets us write Brian's rate in terms of Alan's as ...

a -50 = b

The time to complete one oval differs by 3/4 minute (45 seconds), so we have ...

time = distance/speed

450/b - 450/a = 3/4

Multiplying by 4ab/3 gives ...

600(a -b) = ab

Substituting from above, we can rewrite this as ...

600·50 = a(a -50)

a^2 -50a -30000 = 0 . . . . . quadratic rearranged to standard form

(a -200)(a +150) = 0 . . . . . . .factored

a = 200 or -150 . . . . only the positive solution is useful here

Alan's rate is 200 m/min; Brian's rate is 150 m/min.

_____

Check

It takes Alan 450/200 min = 2.25 min to complete one oval. It takes Brian 450/150 = 3 min to complete one oval. That is 3-2.25 = 0.75 min = 45 seconds longer than Alan.

After 9 minutes, Alan will have gone (200 m/min)·(9 min) = 1800 m = 4 laps, while Brian will have gone (150 m/min)·(9 min) = 1350 m = 3 laps. Hence Alan will overtake Brian at the 9-minute mark.

1) 29

2) -15

//Hope this helps.

Answer:

1).   (3² - 4²) = 29

2).  5a - 7b + b² = -15

Step-by-step explanation:

Points to remember

1) (a² - b²) = (a + b) (a - b)

Solve 22 - (3² - 4²)

To find (3² - 4²)

(3² - 4²) can be written as,

(3² - 4²) = (3 + 4 ) (3 - 4) = 7 * -1 = -7

22 - (3² - 4²)  = 22 - (-7) = 22 + 7 = 29

22 - (3² - 4²) = 29

To solve 5a - 7b + b²for a = -1 and b= 5

Substitute the value of a and b in given expression we get,

5a - 7b + b² = (5 * -1) - (7 * 5) + 5²

= -5 - 35  + 25 = -15

Therefore 5a - 7b + b² = -15

Answer:

[tex]10\sqrt{2}[/tex]

Step-by-step explanation:

Pythagorean Theorem

QS^2+SR^2=QR^2

10^2+10^2=QR^2

100+100=QR^2

200=QR^2

[tex]\sqrt{200}=QR[/tex]

[tex]10\sqrt{2}[/tex]

Answer:

In right Δ QRS, right angled at , S.

By Pythagorean theorem

→(Hypotenuse)²=(Altitude)^2 +(Base)²

→ Q S² + SR² = QR²

→10² +10²= QR²

→ QR²=100+100

→ QR²=200

[tex]QR=\sqrt{200}\\\\ QR=\sqrt{10 \times 10 \times 2}\\\\ QR=10\sqrt{2}[/tex]

Option D

Hypotenuse[tex]=10\sqrt{2}[/tex] units

Answer:

  63.7%

Step-by-step explanation:

If a point is chosen from the circle at random, the probability it came from the shaded region is the ratio of the area of the shaded region (square) to the area of the circle.

  area of square = (1/2)(diagonal)^2 = (1/2)·(2 in)^2 = 2 in^2

  area of circle = πr^2 = π·(1 in)^2 = π in^2

Fraction of circle that is shaded = (square area)/(circle area) = 2/π ≈ 63.7%

63.7% good luck hope it’s right

See the attached picture for the complete answers to both questions:

Question A asked how much more water was required to fill the tank, so you need to calculate the full volume, then subtract 3/4 of the volume.

Question B, volume is cubed, so you need to cube the scale factor of 3. 3^3 = 27, so the larger tank is 27 times more.

Question C) Area is squared so you need to square the scale factor. Surface area would be 9 times more. 3^2 = 9

For the 2nd question, calculate the volume of each box and divide to find the number of boxes.

Then see the picture for total surface area for part B.

Answer:

3-,3,0,3

Step-by-step explanation:

For this case we must evaluate the following quadratic equation, [tex]y = -x ^ 2 + 3,[/tex] for [tex]x = -3[/tex], [tex]x = 0[/tex]and [tex]x = 3[/tex]

For [tex]x = -3[/tex]:

[tex]y = - (- 3) ^ 2 + 3\\y = -9 + 3 =\\y = -6[/tex]

For [tex]x = 0[/tex]:

[tex]y = - (0) ^ 2 + 3\\y = 0 + 3\\y = 3[/tex]

For [tex]x = 3[/tex]:

[tex]y = - (3) ^ 2 + 3\\y = -9 + 3\\y = -6[/tex]

Answer:

[tex](-3, -6)\\(0,3)\\(3, -6)[/tex]

So just say the piece of land is in the shape of a rectangle and a triangle put together. To find the length (perimeter) add each sides up and subtract the line where the two shapes meet. To find the acreage (area) find the area of the rectangle (length*width) and add the area of the triangle (1/2*base*height)

Answer:

C:12

Step-by-step explanation:

should be 13.5

The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set.

so the middle number of 10,11,12,15,17,19 is 13.5   since 12+15=27/2=13.5

the closest answer choice is C! Hope this helped!

Answer:

The correct option is C.

Step-by-step explanation:

The given data set is

10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38

Divide the data in two equal parts.

(10, 11, 12, 15, 17), 19, (22, 24, 29, 33, 38)

Divide each parenthesis in two equal parts.

(10, 11), 12, (15, 17), 19, (22, 24), 29, (33, 38)

The first quartile is 12, second quartile or median is 19 and third quartile is 29.

Since the first quartile of the data set is 12 Therefore, the correct option is C.

Answer:

[tex]x=12[/tex] (12 nickels))

[tex]y=5[/tex] (5 dimes)

Step-by-step explanation:

Based on the information given in the problem, you can set up the following system of linear equations, where:

x: number of nickels.

y: number of dimes.

Then

FIRST EQUATION: [tex]x+y=17[/tex]

SECOND EQUATION: [tex]5x+10y=110[/tex]  (in cents)

You can apply the Substitution method:

- Solve for x from the first equation.

- Substitute into the second equation and solve for y.

 Then:

[tex]x=17-y[/tex]

[tex]5(17-y)+10y=110\\85-5y+10y=110\\5y=25\\y=5[/tex]

- Find x:

[tex]x=17-5\\x=12[/tex]

Answer:

s + 10

Step-by-step explanation:

Ruben has s number of shoes. Then, 10 more shoes that Ruben has is

s + 10

Final answer:

To write an expression for 'ten more shoes than Ruben,' define a variable for Ruben's shoes, for example, R, and then add 10. The expression is R + 10.

Explanation:

If you want to write an expression for "ten more shoes than Ruben," you need to start by defining a variable for the number of shoes that Ruben has. Let's say that R represents the number of shoes Ruben has. Then, to express "ten more shoes than Ruben," you simply add 10 to that variable. Therefore, the expression would be R + 10. This straightforward notation clarifies the relationship between Ruben's shoe count and the additional ten pairs. By employing variables and simple arithmetic operations, such as addition, this expression succinctly conveys the concept of having ten more shoes than Ruben, facilitating mathematical communication and problem-solving.

Given a markup of 80% and a selling price of $100.80, the cost price is approximately $56. Subtracting this from the selling price yields a cost to store of $44.80.

To find the cost to store, we need to first calculate the cost price using the selling price and the markup percentage.

Given:

- Markup percentage: 80%

- Selling price: $100.80

Step 1: Calculate the cost price using the formula:

[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Markup Percentage}}{100}} \][/tex]

Substitute the given values:

[tex]\[ \text{Cost Price} = \frac{100.80}{1 + \frac{80}{100}} \][/tex]

[tex]\[ \text{Cost Price} = \frac{100.80}{1 + 0.80} \][/tex]

[tex]\[ \text{Cost Price} = \frac{100.80}{1.80} \][/tex]

[tex]\[ \text{Cost Price} ≈ 56 \][/tex]

Step 2: Calculate the cost to store by subtracting the cost price from the selling price:

[tex]\[ \text{Cost to store} = \text{Selling Price} - \text{Cost Price} \][/tex]

[tex]\[ \text{Cost to store} = 100.80 - 56 \][/tex]

[tex]\[ \text{Cost to store} = 44.80 \][/tex]

So, the cost to store is $44.80.

Answer:

Part 1) The base is [tex]25\ in[/tex]  and the height is [tex]10\ in[/tex]

Part 2) The base is [tex]7.5\ in[/tex]  and the height is [tex]18.75\ in[/tex]

Step-by-step explanation:

case 1) Right isosceles triangle of the left

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

[tex]y+x+y=45[/tex]

[tex]2y+x=45[/tex] ----> equation A

[tex]\frac{x}{y} =\frac{5}{2}[/tex]

[tex]x=2.5y[/tex] -----> equation B

substitute equation B in the equation A

[tex]2y+2.5y=45[/tex]

[tex]4.5y=45[/tex]

[tex]y=10\ in[/tex]

Find the value of x

[tex]x=2.5(10)=25\ in[/tex]

case 2) Right isosceles triangle of the right

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

[tex]y+x+y=45[/tex]

[tex]2y+x=45[/tex] ----> equation A

[tex]\frac{y}{x} =\frac{5}{2}[/tex]

[tex]y=2.5x[/tex] -----> equation B

substitute equation B in the equation A

[tex]2(2.5x)+x=45[/tex]

[tex]6x=45[/tex]

[tex]x=7.5\ in[/tex]

Find the value of y

[tex]y=2.5(7.5)=18.75\ in[/tex]

In Case 1, the sides of the rectangle are 5x, 45, 45, and 2x. In Case 2, the sides of the rectangle are 5x, 45/sqrt(2), 45/sqrt(2), and 2x.

Let's denote the length of one side of the rectangle as 5x and the length of the other side as 2x. Since the triangle is right isosceles, the two legs are of equal length. Let's denote the length of each leg as a. Using the Pythagorean theorem, we can write an equation: a^2 + a^2 = 45^2. Solving for a, we find that a = 45/sqrt(2).

Case 1: Since two vertices of the rectangle lie on the hypotenuse, the length of the rectangle's side that is parallel to the hypotenuse will be equal to the length of that hypotenuse, which is 45. Therefore, the sides of the rectangle will be 5x, 45, 45, and 2x.

Case 2: Since the two vertices of the rectangle lie on the legs of the triangle, the length of the rectangle's side that is parallel to the hypotenuse will be equal to the lengths of the legs, which is 45/sqrt(2). Therefore, the sides of the rectangle will be 5x, 45/sqrt(2), 45/sqrt(2), and 2x.

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Answer:

C. increases rapidly.

Step-by-step explanation:

tan(θ) =  sin(θ)/cos(θ)

Now, when sin 90 = 1

and cos 90 = 0

so, tan(90) = 1/0 = not defined.

(1/0 is infinity and its value is not defined)

So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.

Answer:

  1/3

Step-by-step explanation:

1/2 of 2/3 = 1/2·2/3 = (1·2)/(2·3) = 1/3

Answer:

$43.00

Step-by-step explanation:

final price = marked price + tax

= marked price + (tax rate) · (marked price)

= (marked pric) · (1 + tax rate)

= $40.00 · 1.075

= $43.00

Answer:

[tex]A=163.9in^2[/tex]

Step-by-step explanation:

Let's use the regular polygon area formula when given the radius.

[tex]A=\frac{(r^{2})(n)sin(\frac{360}{n})}{2}[/tex]

r is radius

n is the number of sides

Let's plug in the proper values into this equation and simplify:

[tex]A=\frac{(7.74^{2})(7)sin(\frac{360}{7})}{2}[/tex]

[tex]A=\frac{(59.9076)(7)(0.78183148)}{2}[/tex]

[tex]A=\frac{327.86353299}{2}[/tex]

[tex]A=163.93176649[/tex]

Answer:

Step-by-step explanation:

The problem can be solved by putting the equation into vertex form.

  s - 6 = -16(t^2 -15/4t)

  s -6 -16(15/8)^2 = -16(t^2 -15/4t +(15/8)^2) . . . . add the square of half the x-coefficient inside parentheses and equivalent amount on the other side of the equation

  s -62.25 = -16(t -15/8)^2 . . . . write as a square, simplify the constant

  s = -16(t -1.875)^2 +62.25 . . . . put in vertex form

The vertex of the downward-opening parabola is at (t, s) = (1.875, 62.25).

1. It took 1.875 seconds for the ball to reach its maximum height.

2. The ball went up to 62.25 feet.

Answer:

  9x² -6xy +y²

Step-by-step explanation:

The square of the binomial can be written directly using the relationship ...

  (a +b)² = a² +2ab +b²

where you have a=3x and b=-y.

  area = (3x -y)² = (3x)² + 2(3x)(-y) + (-y)²

  area = 9x² -6xy +y²

Dividing the total batter of 12 cups by the amount needed per muffin, which is 2/3 cup, reveals that the baker made 18 muffins. The answer is option C.

To find out how many muffins the baker made, we need to use the information given about the amount of batter used and how much batter is required for one muffin. According to the problem, the baker used 12 cups of batter in total and each muffin requires 2/3 cup of batter.

We start by setting up a simple division to find the answer:

(Total amount of batter) \/ (Amount of batter per muffin) = Number of muffins

12 cups \/ 2/3 cups per muffin = 18 muffins

This calculation reveals that the baker made 18 muffins. Therefore, the correct answer is (C) 18 muffins.

[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

Step-by-step explanation:

Given :

[tex]\rm \bigtriangleup HLI \sim \bigtriangleup JLK[/tex]  by the SSS similarity theorem.

[tex]\rm \dfrac {HL}{JL} = \dfrac{IL}{KL}[/tex]

Solution :

According to SSS postulate,

KL = IL ----- (1)

HL = JL ----- (2)

HI = JK ------ (3)

From equation (1), (2) and (3) we get,

[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

For more information, refer the link given below

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Triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate. Therefore,

[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

Given :

[tex]\rm \Delta HLI \sim \Delta JLK[/tex] by the SSS similarity.

According to SSS (Side Side Side) postulate:

If all three sides of a triangle are congruent to corresponding three sides of other triangle then the two triangles are congruent.

If triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate.

Therefore, from triangle HLI and triangle JLK we get,

KL = IL  ----- (1)

HL = JL ----- (2)

HI = JK ------ (3)

From equation (1) , (2) and (3) we get,

[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

For more information, refer the link given below

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Answer:

x=2y^2 -24y + 69

Step-by-step explanation: Move the expression to the right side and change its sign.

Here is your answer

D. [tex]\frac{8788}{3}[/tex]π [tex]{units}^{3}[/tex]

REASON:

Formula for volume of sphere

= 4/3×π× r^3

Here, r= 13

So,

volume=4/3×π× 13^3

= 4/3×π× 2197

= 8788/3 ×π

HOPE IT IS USEFUL

The volume of the sphere is [tex]\bold{\frac{8788}{3} \pi ~~unit^3}[/tex]

The correct answer is option (D).

V = (4/3) × π × r³, where 'r' is the radius of the sphere

For given example,

radius of the sphere (R) = 13

Using the formula o the volume of the sphere,

V = (4/3) × π × R³

V = (4/3) × π × 13³

V = 8788/3 π cubic units.

Therefore, the volume of the sphere is [tex]\frac{8788}{3} \pi[/tex] cubic units.

The correct answer is option (D) [tex]\frac{8788}{3} \pi ~~unit^3[/tex]

Learn more about the volume of the sphere here:

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Answer:

B) 5000x^2

Step-by-step explanation:

The exponent of x starts at 5 in the first term and decreases by 1 as the term numbers increase by 1. Hence, the 4th term will have 2 as the exponent of x. (It will have 5-2=3 as the exponent of 5.)

Pascal's triangle tells you the coefficients of the 6 terms in the expansion will be 1, 5, 10, 10, 5, 1, so the 4th term has a coefficient of 10.

The 4th term will be ...

10(2x)^2(5)^3 = 10·4·125·x^2 = 5000x^2

Try suggested solution, note the answers are marked with green colour.

Answer:

7. (4x +10)/(x^3 +3x^2 -16x -48)

9. -320/93

Step-by-step explanation:

7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.

6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))

= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator

= (6x +18 -2x -8)/((x -4)(x +3)(x +4))

= (4x +10)/((x^2 -16)(x +3))

= (4x +10)/(x^3 +3x^2 -16x -48)

_____

9. First you simplify the denominator:

2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400

Then you perform the division. This can be done by multiplying by the inverse of the denominator.

(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93

Total number of people: 65 + 85 +38 +12 = 200

Total male =  65 +38 = 103

Total women: = 200-103 = 97

Total Type A = 65+85 = 150

Total Type B = 38+12 = 50

P(male or type b ) = 103/200 + 50/200 - 38/200 = 0.515 + 0.25 - 0.19 = 0.765 - 0.19 = 0.575

P(male | type b )  = 38/50 = 0.76

The answer is P(male or type b ) < P(male | type b )

Explanation:

The denominator of "miles per hour" is 1 hour, a single unit. When the denominator of a rate is 1 unit, it is called a unit rate.