Name times when the hands of a clock form
an acute angle, a right angle, and an obtuse
angle.​

Answer: x=7     x=10

Step-by-step explanation:

[tex]x^2+70=17x\\x^2+70-17x=17x-17x\\x^2-17x+70=0\\x^2-7x-10x+70=0\\x(x-7)-10(x-7)=\\(x-7)(x-10)=0\\x-7=0\\x=7\\x-10=0\\x=10[/tex]

Answer:

x = 7, x = 10

Step-by-step explanation:

x² + 70 = 17x ( subtract 17x from both sides )

x² - 17x + 70 = 0 ← in standard form

consider the factors of the constant term (+ 70) which sum to give the coefficient of the x- term (- 17)

the factors are - 10 and - 7 , since

- 10 × - 7 = + 70 and - 10 - 7 = - 17 , then

(x - 10)(x - 7) = 0 ← in factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x - 10 = 0 ⇒ x = 10

Answer: sin(60°)= [tex]\frac{\sqrt{3}} 2[/tex] and cos(60°)=[tex]\frac{1} 2[/tex]

Step-by-step explanation:

sine means opposite/hypothenus (SOH)

opposite=[tex]\frac{\sqrt{3}} 2[/tex] and hypothenus is 1

sin(60°) = [tex]\frac{\sqrt{3}} 2[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex]

cosine means adjacent/hypothenus (CAH)

adjacent= [tex]\frac{1} 2[/tex] and hypothenus is 1

cos(60°) =  [tex]\frac{1} 2\\[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex]

Answer:

819,200

Step-by-step explanation:

First start by raising all the numbers to the power indicated:

5^4 = 625

8^5 = 32768

2^9 = 512

5^2 = 25

Then divide the numerators by the denominators:

625 / 8 = 78.125

32768 / 64 = 512

512 / 25 = 20.48

Finally, multiply all the numbers together

78.125 * 512 * 20.48 = 819200

Answer:

ikj

Step-by-step explanation:

In a triangle:

When labeling angles and sides of triangles, it is convention to label the side opposite an angle with the same letter but in lower case.  

Therefore in ∆JLK:

As 16 < 73 < 91

⇒ m∠I < m∠K < m∠J

As the angles of ∆JLK in order from smallest to largest are IKJ, then the sides of ∆JLK in order from smallest to largest are ikj.

Answer:

Circumference = 75.4

Step-by-step explanation:

Since the circles are identical, that means that the radii must be equal.

4x=3x+3

x=3

That means that radius = 12

The formula for the circumference = 2pi × radius

2pi × 12 = 24pi ≈ 75.4

Answer:

75.4 (nearest tenth)

Step-by-step explanation:

The diameter of a circle is the distance from one side of the circle to the other through the center. The diameter is the widest part of the circle.

The radius of a circle is the distance from the center to the circumference.  The radius is half the diameter of a circle.

We have been given the radius of the circle on the left:  r = 4x.

Therefore, as the diameter is twice the radius, the diameter of the circle on the left is:  d = 2(4x) = 8x

We have been given the diameter of the circle on the right:  d = 6x + 6

Equate the two diameters and solve for x:

⇒ 8x = 6x + 6

⇒ 8x - 6x = 6x + 6 - 6x

⇒ 2x = 6

⇒ 2x ÷ 2 = 6 ÷ 2

⇒ x = 3

Substitute the found value of x into one of the diameter expressions to find the diameter of both circles:

⇒ d = 8x

⇒ d = 8(3)

⇒ d = 24

Circumference of a circle

C = πd

(where d is the diameter)

Substitute the found diameter into the circumference formula:

⇒ C = πd

⇒ C = 24π

⇒ C = 75.39822...

⇒ C = 75.4 (nearest tenth)

Therefore, the circumference of each circle is 75.4 units (nearest tenth).

Answer:

18

Step-by-step explanation:

Answer:

[tex] \frac{ - 5}{4} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6} \div \frac{ - 2}{3} [/tex]

When dividing two fractions, we turn the second fraction upside-down and multiply two expressions instead.

[tex] \frac{5}{6} \times \frac{ - 3}{2} = \frac{ - 15}{12} [/tex]

Now simplify the fraction by dividing it with biggest common divisor which is 3 in this case.

[tex] \frac{ - 5}{4} [/tex]

is the final result.

Answer:

Inequality 1 is incorrect; it should be g ≤ 80.

Step-by-step explanation:

Kyle's grandmother is not more than 80. This means that she is either equal to 80 or less than 80.

This gives us the inequality: g ≤ 80

The required equation for sharing the bills equally is 5x = 62.65 and each will pay $12.53

How many friends went to the restaurant altogether?

The fact that the person went with  4 friends and paid for every means that he made payments for the 5 of them and he is expected to get refund from 4 persons, in other words, in order to share bills equally, the 5 friends would have to contribute equally, which means we would divided total bills by the number of friends, which is 5 not 4 because the first person would also his part of the bills

Let x be the amount paid person, the total amount paid would be x paid person multiplied by the number of friends, 5

total amount paid=5*x

total amount paid =5x

the amount paid in dollars is $62.65

5x=62.65

x=62.65/5

x=$12.53

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Answer: 8.3 hours

Step-by-step explanation: 15.76-15.01 is 0.75

Now just divide 0.75 from 0.09 and you get 8.3

Answer:

Step-by-step explanation:

Stock A= $15.01 increases by $0.13 an hour. $15.14

Stock B =$15.76 decreases by $0.09 an hour $15.65

15.65-15.14= 0.51

Answer:

-28

Step-by-step explanation:

Answer: 208 in^2

Step-by-step explanation:

4 2*8 rectangles

1 8*8 square

4 5*8/2 triangles

4(2*8)+8*8+4(5*8/2)=

4(16)+64+4(5*4)=

64+64+4(20)=

128+80=208 in^2

For the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.

We are given the equations:

7 x - y = 7   … (1)

x + 2 y = 6

x = 6 - 2 y   … (2)

Substitute equation (2) in equation (1), we get that:

7 ( 6 - 2 y ) - y = 7

42 - 14 y - y = 7

15 y = 35

y = 35 / 15

y = 7 / 3

x = 6 - 2 ( 7 / 3)

x = 18 - 14 / 3

x = 4 / 3

Therefore, for the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.

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Answer:

an identity............

Answer:

An identity

Step-by-step explanation:

An identity is an equation, which is true for all values of the variables in the equation.

The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)

People eating hamburger P(h) =0.38

People eating burritos P(b) = 0.31

Number of people eating pizza = 35

    Let's suppose the total number of people is 1

So,

    By adding the total number of people eating hamburgers and burritos                                          

                                                           = 0.38+0.31

                                                            = 0.69

    The ratio of the total number of people eating pizza = 1.00 - 0.69

                                                                                            = 0.31

   So total number of people eating pizza = 0.31 = 35

   By solving :

              1 = 35 / 0.31

                = (35*100)/31

                = 3500/31

                 = 112.9 (we have to write it down in the nearest whole number)

Here we writing the approximate value of 112.9 = 113 (Approximate)

Hence, the total number of people in the food court in the nearest whole number is 113

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Answer: 2

Step-by-step explanation: I just did this lesson

A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.

If the height of the actual airplane is 20m and the in the scale drawing the height is 10m.

The scale factor of the airplane is 200.

A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.

We have

The height of the plane in scale drawing:

= 10 cm

The height of the plane in an actual airplane.

= 20 m

The scale factor of the height of the airplane:

= 20m / 10 cm

[ 1 m = 100 cm ]

= (20 x 100) cm / 10 cm

= 200

Thus,

The scale factor of the airplane is 200.

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Answer:

10 cards

Step-by-step explanation:

In order to find how many packs Joel needs to buy we need Make an equation

Equation = 5c + 15 = 65

where,

5c+15=65

Step 1: Subtract 15 from both sides.

5c+15−15=65−15

5c=50

Step 2: Divide both sides by 5.

5c/5 = 50/5

c=10

Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards

Answer:

See answers below

Step-by-step explanation:

This type o problem is known as a Diamond problem

From the diamonds on the top row, it is clear that the top cell of the diamond is the product of the two side numbers and the bottom is the sum of these numbers.

I will use top for the top cell and bottom for the bottom cell, left for and right respectively for left and right cells

a. Top = 2 x 5 = 10; Bottom = 2 + 5 = 7

b. Top = -2 x -1 = 2; Bottom = -2 - 1 =  -3

c. Top = Left x Right = 8
  Bottom = Left + Right = 6.  The only two numbers that satisfy this equation are Left = 4 and Right = 2 since 4 x 2 = 8 and
4 +2 = 6
Answer to c: Left = 4, Right = 2

d We have Let unknown left be L and unknown bottom be B
We have L x  (1/2) = 4 for the product
[tex]\rm{\frac{L}{2} = 4}\\\\L = 2 x 4 = 8[/tex]

We have Bottom = Left + Right = 8 + 1/2  = [tex]8\frac{1}{2}[/tex] = 17/2
Answer to d. : Left = 8, Bottom = 17/2

e. Similar to c.

Top = Left x Right = 12;
Bottom = Left + Right = -7
12 can be 2 x 6 or 3 x 4 (same as 4 x 3) or 12 x 1. 4 and 3 are the obvious choices and since they add up to - 7 they both have to be negative
So Left = -3, Right = -4

Note: (-3) x (-4) results in +12

Answer:

the number is ..let X

The equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m

The expression is given as

4p^2+5.5m+2.5p^2-m+3m

Rewrite properly as

4p^2 + 5.5m + 2.5p^2 - m + 3m

Collect the like terms in the above equation

4p^2 + 5.5m + 2.5p^2 - m + 3m = 4p^2 + 2.5p^2 + 5.5m - m + 3m

Evaluate the like terms in the above equation

4p^2 + 5.5m + 2.5p^2 - m + 3m = 6.5p^2 + 7.5m

Hence, the equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m

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The required solution of the given expression is 7x-24.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given:

The given expression is

[tex](x-3)(x+8)+(2x-x^{2} )[/tex]

According to given question we have

By the expansion theorem we have

The expression is

[tex](x-3)(x+8)+(2x-x^2)\\\\=x^{2} +8x-3x-24+2x-x^{2} \\\\=7x-24[/tex]

Therefore, the required solution of the given expression is 7x-24.

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The equation of the parabola is (x - 6)² = 6(y + 5.5).

Given that, a focus at (6,-4) and a directrix at y= -7.

We need to find the equation for a parabola.

Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).

The standard form of the equation of the parabola is  (x - h)² = 4p(y - k), where

The vertex of the parabola is (h , k)

The focus is (h, k + p)

The directrix is at y = k - p  

∵ The focus of the parabola is at (6, -4)

The coordinates of the focus are (h, k + p)

∴ h = 6

∴ k + p = -4 ⇒ (1)

∵ The directrix of the parabola is at y = -7

The directrix is at y = k - p

∴ k - p = -7 ⇒ (2)

Solve the system of equations to find k and p

Add equations (1) and (2) to eliminate p

∴ 2k = -11

Divide both sides

∴ k = -5.5

Substitute the value of k in equation (1) to find p

∵ -5.5 + p = -4

Add 5.5. to both sides

∴ p = 1.5

∵ The form of the equation is (x - h)² = 4p(y - k)

Substitute the values of h, k, and p in the form

∴ (x - 6)² = 4(1.5)(y - -5.5)

∴ (x - 6)² = 6(y + 5.5)

Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).

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Your question is incomplete, probably the complete question/missing part is:

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

3x+y=0 and x+2y=7

i)

a= intercept on x axis

b= intercept on y axis

from the question

a=2b

x/2b+ y/b=1

x+2y=2b

since it passes through the point (3,2)

then 3+4=2b

7/2=b

x+2y=7     putting the value of b

ii) given b =3a

then x/a+ y/ 3a =1

3x+y=3a

it passes through ( -1,3) then

-3+3=3a

a=0

3x+y=0

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The equation which has no solution among the answer choices as given in the task content is; b + 2 = b-2.

It follows from the task content that the equation which has no solution is to identified.

On this note, the equation in which case, the variable diminishes and the equality does not hold represents that which has no solution.

Hence, the required equation is; b + 2 = b-2.

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The cube root of 35 would be plotted on a number line A. Between 3 and 4, but closer to 3.

It should be noted that cube root of a number simply means a number that you can multiply three times that will give the original number.

In this case, the cube root of 35 will be 3.2.

This means that it's closer to 3. It's also between 3 andmd 4.

Therefore, the cube root of 35 would be plotted on a number line between 3 and 4, but closer to 3.

In conclusion, the correct option is A.

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Based on the coordinates of XY which are X(7, 2) and Y(2, 0), the domain and range are:

The domain of a line refers to all the points on that line that the value of the x-axis can take.

In line XY, the only two x-axis values are 7 and 2. This means that the domain is therefore (2, 7).

The range of a line on the other hand, are all the points that the value on the y-axis can take.

The range in this case is therefore (0, 2).

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Answer: x = -2

Step-by-step explanation:

4x=0.5(2x−12)

Use the distributive property to multiply 0.5 by 2x−12.

4x=x−6

Subtract x from both sides.

4x−x=−6

Combine 4x and −x to get 3x.

3x=−6

Divide both sides by 3.

x= 3−6

Divide −6 by 3 to get -2.

The interval that represents the inequality 1 < x ≤ 6 is given by:

B. (1,6].

The standard interval notation of an interval of lower bound a and upper bound b is given by:

[a,b].

The inequality notation is:

a ≤ x ≤ b

The set builder notation is:

{x | a ≤ x ≤ b}.

In this problem, we are given the inequality 1 ≤ x ≤ 6, hence a = 1 and b = 6, and open at x = 1 and closed at x = 6, hence the interval is:

B. (1,6].

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So nearest hundred of calories of pizza is 3384.

As it is given that its an pizza of 16 inches .

A Calorie is unit of heat used to indicate the amount of energy foods produce in the human body that is equal to 1000 calories.

Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

So as we all know pizza of 16 inches contains 3384.00 calories

And its been asked to the nearest hundred so divide it by 100And we get 3384 calorie. So a 16 inch pizza contains 3384 calories.

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Answer:

1. STEPS FOR SOLVING LINEAR EQUATION

[tex] \frac{4m}{3} = 8[/tex]

Multiply both sides by 3.

4m=8×3

Multiply 8 and 3 to get 24.

4m=24

Divide both sides by 4.

[tex]m = \frac{24}{4} [/tex]

Divide 24 by 4 to get 6.

m=6

2. 2p+3=7; p=2 pounds