Determine the slope of a line that is perpendicular to the line y = -2x + 7
Select one:
O A. Slope = -1/2
O B. Slope = 2
O C. Slope = 1/2
O D. Slope = -7​

Answer:

The length of the blue rope is 80.25 meters.

Step-by-step explanation:

B = Blue Rope

G = Green Rope

R = Red Rope

B=3R (Blue is 3 x as long as Red)

G=5B (Green is 5 x as long as Blue)

B+G+R = 508.25 (The three ropes together are 508.25 meters)

Since B=3R, I will rewrite the equation above

3R + G + R = 508.25

Now, I will write G in terms of R:

G=5B

B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.

Rewrite the equation again in terms of R:

3R + 15R + R = 508.25

19R = 508.25 (combine like terms)

R = 26.75 (divide both sides by 19 to solve for R)

Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):

B=3R

B=3(26.75)

B=80.25 meters

Answer:

The greatest possible value for b is 26.

Step-by-step explanation:

Given that the line passes through the Origin O(0, 0); A(-2, b - 14) &

B(14 - b, 72).

Let us assume the points are in the order: AOB.

Since the line passes through all these points the slope of the line segment AO = The slope of the line segment AB.

Slope of a line with two points: [tex]$ \frac{y_2 - y_1}{x_2 - x_1} $[/tex]   where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the points given.

[tex]$ (x_1, y_1) = (0,0) $[/tex]

[tex]$ (x_2, y_2) = (-2, b - 14) $[/tex]

Therefore, the slope of the line segment AO = [tex]$ \frac{b - 14}{-2} $[/tex]

Similarly, for the slope of the line segment OB.

The two points are [tex]$ (x_1, y_1) = (0, 0) $[/tex] and [tex]$ (x_2, y_2) = (14 - b, 72) $[/tex].

The slope is:  [tex]$ \frac{72}{14 - b } $[/tex]

Since, the slopes are equal we can equate:

[tex]$ \frac{b - 14}{-2} = \frac{72}{14 - b} $[/tex]

[tex]$ \implies \frac{b - 14}{-2} = \frac{72}{-(b - 14)} $[/tex]

[tex]$ \implies (b - 14)^2 = 72 \times 2 = 144 $[/tex]

[tex]$ \implies (b - 14)^2 = 12^2 $[/tex]

Taking square root on both sides we get:

[tex]$ \implies (b - 14) = \pm 12 $[/tex]

[tex]$ \implies b = 2 \hspace{2mm} or \hspace{2mm} 26 $[/tex]

Therefore, the maximum value of b = 26.

Hence, the answer.

Answer:

3x^2 - 10x - 1 = 0 $OPTION D ON EDGE$

Step-by-step explanation:

Answer:

3x2 – 10x + 6 = 0

Step-by-step explanation:

Givena general quadratic equation

ax²+bx+c = 0

The general formula for finding x is;

x = -b±√b²-4ac/2a

Where a,b and c are the coefficient of x², x and x° respectively

Given the solution in question to be;

x = 5±2√7/3

The quadratic equation that has thw above general solution will be;

3x²-10x+6 = 0

From the equation, a = 3, b= -10 and c = 6

Substituting this value in the general formula to get x we have;

x = -(-10)±√(-10)²-4(3)(6)/2(3)

x = 10±√100-72/6

x = 10±√28/6

x = 10±√7×4/6

x = 10±2√7/6

Dividing through by 2 gave;

x = 2(5±2√7)/6

x = 5±2√7/3 (which gives the solution in question)

Answer:

b and d

Step-by-step explanation:

The following D Tether ball pole shadow: 0.6\,\text{m}0.6m0, point, 6, start text, m, end text Flagpole shadow: 1.36\,\text{m}1.36m1, point, 36, start text, m, end text and E Tether ball pole shadow: 2\,\text{m}2m2, start text, m, end text Flagpole shadow: 4.8\,\text{m}4.8m could be the lengths of the shadows. Correct Option is 4 and 5.

Let's assume "x" is the length of the tether ball pole shadow, and "y" is the length of the flagpole shadow.

According to the information given, the proportional relationship can be expressed as:

Tether ball pole height / Tether ball pole shadow length = Flagpole height / Flagpole shadow length

The height of the tether ball pole is 333 meters, and the height of the flagpole is 6.8 meters.

So, we have the following equation:

333 meters / x = 6.8 meters / y

Now, let's solve for "y" in each choice and check which choices satisfy the proportional relationship:

Choice A:

333 / 1.35 = 6.8 / 3.4

246.67 ≈ 2

Choice B:

333 / 1.8 = 6.8 / 4.08

185 ≈ 1.67

Choice C:

333 / 3.75 = 6.8 / 8.35

88.8 ≈ 0.81

Choice D:

333 / 0.6 = 6.8 / 1.36

555 ≈ 5

Choice E:

333 / 2 = 6.8 / 4.8

166.5 ≈ 1.42

The two choices that satisfy the proportional relationship are:

(Choice D) Tether ball pole shadow: 0.6 m, Flagpole shadow: 1.36 m

(Choice E) Tether ball pole shadow: 2 m, Flagpole shadow: 4.8 m

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Answer:

1/12

Step-by-step explanation:

Answer:

7.41%

Step-by-step explanation:

16/216 =

16 ÷ 216 =

0.074074074074074 =

0.074074074074074 × 100/100 =

0.074074074074074 × 100% =

(0.074074074074074 × 100)% ≈

7.407407407407% ≈

7.41%;

If I remember correctly, the x-coordinate 3 goes 4 left and the new ordered pair is (-1,-8). Don't take my word for it unless I'm actually right.

Answer:

1/2

Step-by-step explanation:

2(x+1.25)=3.5

2x+2.5=3.5

2x=3.5-2.5

2x=1

x=1/2

Answer:

Step-by-step explanation:

Is you simplify, you get 16x-12

6x+2(5x-6)

6x+10x-12

16x-12

Answer:

Assuming you just want it simplified, the answer would be 16x - 12

Step-by-step explanation:

6x + 2(5x - 6)

6x + 10x - 12

16x - 12

Answer:

1. 3 is a constant term of the expression.

2. 9 is constant term of the expression.

3.7 is a constant term of the expression.

Step-by-step explanation:

1. 3+c+e

Here 3 is a constant term of the expression.

c and e are the variables.

The coefficient of c is 1.

The coefficient of e is 1.

It is a trinomial expression.

2.

5m +9

9 is constant term of the expression.

m is a variable of the expression.

The coefficient of m is 5.

It is a binomial expression.

3.

3p²+7

7 is a constant term of the expression.

p is the variable.

The coefficient of p² is 3.

It is a binomial expression.

Answer:

-2

Step-by-step explanation:

The solution of the expression x + 4 = 2 is shown in image.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

Expression is,

⇒ x + 4 = 2

Now, We can simplify as;

⇒ x + 4 = 2

Subtract 4 both side,

⇒ x + 4 - 4 = 2 - 4

⇒ x = - 2

Thus, The solution of the expression is,

\⇒ x = - 2

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Answer: 20m³

Step-by-step explanation:

From the statement

V <> 1/p --------------------- 1

V = k/p --------------------- 2

K. = VP ---------------------- 3

V = 60 , p = 1

To find k which is a constant, we put those values in equation 3

K = 60 x 1

= 60.

Now from the second statement

V = k/p where p is 3

Therefore,

V = 60/3

= 20m³

Answer:

6<8

Step-by-step explanation:

This is actually simple since the 6 is less than 8 the thing will face away from the 6 and towards the 8.

Answer: x = 15

Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.

We can now establish the ratio of the similar sides.

Line AB = Line ED

Line AC = Line EC

AB/ED = AC/EC

24/40 = 2x/3x + 5

3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}

Next we cross multiply and that gives us

3(3x + 5) = 5(2x)

9x + 15 = 10x

Subtract 9x from both sides of the equation

15 = 10x - 9x

15 = x

Answer:

[tex]AC = 25\ miles[/tex]

Step-by-step explanation:

Given:

Distance for north side = 7 miles.

Distance for east side = 24 miles.

We need to find the displacement.

Solution:

Figure shows Point A is starting point and AB = 7 miles is North side distance and BC = 24 miles is east side distance and AC is shown as displacement.

Using Pythagoras theorem to find displacement (AC).

[tex](AC)^{2}=(AB)^{2}+(BC)^{2}[/tex]

Substitute AB = 7 and BC = 24 in above equation.

[tex](AC)^{2}=(7)^{2}+(24)^{2}[/tex]

[tex](AC)^{2}=49+576[/tex]

[tex](AC)^{2}=625[/tex]

[tex]AC = \sqrt{625}[/tex]

[tex]AC = 25\ miles[/tex]

Therefore, displacement of the car [tex]AC = 25\ miles[/tex]

Answer:

15%

Step-by-step explanation:

we call the original price 100% and to find the discount amount :

Multiply 100 by $476 then divide by $560

100 × $476 ÷ $560 = 85

$476 is 85% of the original price therefore the amount of discount as in percentage is 100 - 85 = 15%

To add 471 and 582, line up the numbers by place value and add each column, carrying over as needed. The sum is 1053. You check by reversing the order of the numbers and adding again; the sum should remain the same.

To add the following numbers and use the checking method (add down and then add up), perform the following steps:

If you obtain the same result by both adding down and adding up, your answer is verified as correct.

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You will need 119 cups to sell all of the lemonade.

Step-by-step explanation:

Given,

Diameter of cups = 9 cm

Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]

Height of cups = 12 cm

We will find volume of cup.

[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]

Putting all the values

[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]

Therefore;

Each cup can hold 254.34 cubed centimeter of lemonade.

Number of gallons = 8

1 gallon = 3785 cm³

8 gallons = 3785*8 = 30280 cm³

Let,

x = Number of cups

Volume of lemonade in one cup * Number of cups = Volume of 8 gallons

254.34x=30280

Dividing both sides by 254.34

[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]

Rounding off to nearest whole number

x = 119

You will need 119 cups to sell all of the lemonade.

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Answer:

1 - 32.5

Step-by-step explanation:

If the perimider is less then 172, that the limit is 171. 171 - (53)2 = 65. divide that by the two sides that are the width it equals 32.5

Perimeter is the sum of the length of the sides used to make the given figure. The range of the width of the rectangle is (0,33).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that the perimeter of a rectangle must be less than 172 feet. Also, given that the length of the rectangle is 53 feet. Therefore, we can write inequality of the width of the rectangle as,

2(Length) + 2(Width) < Perimeter

2(53 feet) + 2(Width) < 172 feet

106 feet + 2(Width) < 172 feet

2(Width) < 172 feet - 106 feet

2(Width) < 66 feet

Width < 66feet / 2

Width < 33 feet

Hence, the range of the width of the rectangle is (0,33).

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Answer:

35

Step-by-step explanation:

Total number of students in class is 40

87.5% of the class = 87.5/100 *40 =35

The students in Ms. Carr's class that live less than 10 miles from school are 35 students.

To find out how many students in Ms. Carr's class live less than 10 miles from school, we can use the percentage provided in the question.

1. Identify the total number of students in the class:

  Ms. Carr has a total of 40 students in her class.  

2. Determine the percentage of students living less than 10 miles from school:

  We know that 87.5% of these students live less than 10 miles from school.  

3. Convert the percentage to a decimal for calculation:

To convert 87.5% to a decimal, we divide by 100:  

[tex]\[ 87.5\% = \frac{87.5}{100} = 0.875 \][/tex]

4. Calculate the number of students:  

Now, multiply the total number of students by the decimal:  

Number of students = 0.875 × 40 = 35

5. Conclusion:

Therefore, 35 students in Ms. Carr's class live less than 10 miles from school.

Answer:sin =perpendicular/hypotenuse

Step-by-step explanation:

Sin angle is given use tan theta or cos theta to find the RS

Answer:

C 147in2

Step-by-step explanation:

Formula: [tex]\frac{bh}{2}[/tex]

b=base

h=height

21*14=294

294/2=147

Step-by-step explanation:

Let x be the smaller than 4 ×[tex]10^{-2}[/tex].

To find, the number of times smaller is 2 × [tex]10^{-3}[/tex] than 4 × [tex]10^{-2}[/tex] = ?

∴ x = [tex]\dfrac{4\times 10^{-2}}{2\times 10^{-3}}[/tex]

= 2 × [tex]10^{-2}[/tex] × [tex]10^{3}[/tex]

Using the identity,

[tex]a^{m}=\dfrac{1}{a^{-m}}[/tex]

= 2 × [tex]10^{-2+3}[/tex]

Using the identity,

[tex]a^{m} \timesa^{n}=a^{m+n}[/tex]

= 2 × [tex]10^{1}[/tex]

= 2 × 10

= 20

Thus, the required "option A) 20" is correct.

Answer:

  15°

Step-by-step explanation:

The exterior angle at vertex S is 360°/12 = 30°. That angle has a measure that is equal to the sum of the congruent angles at R and T of ΔRST. In other words, ...

  ∠T = 30°/2 = 15°

The size of angle STR is 15°.

The sides of a regular polygon are congruent.

The size of STR is 15 degrees

The polygon is 12-sided.

This means that:

[tex]\mathbf{n =12}[/tex]

The sum of angles in a regular hexagon is 360.

So, the angle at vertex S is:

[tex]\mathbf{\theta = \frac{360}{n}}[/tex]

This gives

[tex]\mathbf{\theta = \frac{360}{12}}[/tex]

[tex]\mathbf{\theta = 30^o}[/tex]

The external angle of a triangle equals the sum of the opposite internal angles.

This means that:

[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]

Where:

[tex]\mathbf{ \angle STR = \angle SRT}[/tex]

So, we have:

[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]

[tex]\mathbf{\theta = 2\angle STR}[/tex]

Substitute [tex]\mathbf{\theta = 30^o}[/tex]

[tex]\mathbf{30^o = 2\angle STR}[/tex]

Divide both sides by 2

[tex]\mathbf{15^o = \angle STR}[/tex]

Rewrite as:

[tex]\mathbf{\angle STR = 15^o }[/tex]

Hence, the size of STR is 15 degrees

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Answer:

Circumference of circle= 37.68 units

Circumference of sector= 6.28 units

Step-by-step explanation:

The given figure is a circle with given radius OB= 6 units.

The circumference of a circle is the total length of its boundary.

For the complete circle its circumference can be calculated by;

           Circumference= [tex]2\pi r[/tex]

                                 [tex]=2*3.14*6\\=37.68[/tex] units

For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:

                              [tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units

So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.

Question:

A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting

a. write an expression for the combined area of the painting and frame.

b. use the expression to find the combined area when the height of the painting is 12 in.

c. use the expression to find the combined area when the height of the the painting is 15 in.

Answer:

a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame

b) The combined area when h = 12 is 544 square inches

c) The combined area when h = 15 is 760 square inches

Solution:

Given that,

A frame that is 2.5 inches wide goes around the painting

The frame will go around all 4 sides of the painting.

That means that the length of each side of the painting will increase by 2.5 inches

Therefore,

The height of painting and frame is:

h = h + 2.5 + 2.5

h = h + 5

(2.5  inches on the top and the bottom)

Also given that,

Width of a rectangular painting is 3 inches more than twice the height

w = 3 + 2h

Now the width of painting and frame is:

w = 3 + 2h + 2.5 + 2.5

(Again, 2.5 inches on the top and the bottom)

w = 2h + 8

Thus the combined area of the painting and frame is:

[tex]Combined\ area = (h+5)(2h+8)[/tex]

B) Substitute h = 12 inches

[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]

Thus the combined area when h = 12 is 544 square inches

C) Substitute h = 15 inches

[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]

Thus combined area when h = 15 is 760 square inches