The Greasy Spoon Restaurant offers 6 appetizers and 14
main courses. In how many ways can a person order a
two-course meal?
84
112
20
196

Answer:

$5 (5) - ($7+$9)=m

$25 - $16 =m

Step-by-step explanation:

$5 (5) - (7+9)=m

$25 - 16 =m

The equation to represent how much money Grace has left is:

m = $25 - $7 - $9

m = $25 − $16

m = $9

Grace earns $5 for each dog walk.

She walks the dog 5 times in one week, so she earns 5 walks * $5/per walk = $25.

She spends $7 on a book and $9 on a building set, so she spends a total of $7 + $9 = $16.

To find out how much money Grace has left, m, we subtract her total spending from her earnings.

So, the equation to represent how much money Grace has left is:

m = $25 − $16

m = $9

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Answer:

none

Step-by-step explanation:

Answer:

The coordinates of the base of the antenna is (-6. 1)

Step-by-step explanation:

Here  we are required to find the center of a circle given points on the circumference

The equation of  a circle is

(x - h)² + (y - k)² = r²

Where:

x and y are points on the circumference

h and k are coordinates of the center of the circle and

r = The radius of the circle

Since we have the values for the points on the circumference, we are left with three unknowns, which we can find with three equations as follows;

By plugging in the values for x and y at the respective points we get,

At (9, -19) → (9 - h)² + (-19 - k)² = r²...............(1)

At (-21, -19) → (-21 - h)² + (-19 - k)² = r².....,...(2)

At (14, 16 ) → (14 - h)² + (16 - k)² = r² ............(3)

Solving, we get  from (1)  (-19 - k)² = r² - (9 - h)²

Plugging in the value of (-19 - k)² in equation (2) we get

(-21 - h)² + r² - (9 - h)² = r²

So that (-21 - h)²  - (9 - h)² = r² -  r² = 0

and   (-21 - h)²  - (9 - h)² = 0 gives

60·h +360 = 0 or h = -6

Plugging in the value of h = -6 in equation (3) we get

(14 - (-6))² + (16 - k)² = r²

20² + (16 - k)² = r² .................(4)

similarly from equation (1) we get

(9 - (-6))² + (-19 - k)² = r²

15² + (-19 - k)² = r²  ................(5)

Subtracting equation (5) from (4) gives

20² - 15² +  (16 - k)² - (-19 - k)² = 0

Which gives

-70·k + 70 = 0

or k = 1

Therefore the coordinates of the base of the antenna = (-6. 1).

Answer:

Length of pipe to Chesterville is 8.376 miles and

Length of pipe to Denton is 5.46 miles

Step-by-step explanation:

Here we have

The distance of Chesterville from the river is 3 miles, while the distance of Denton from the river is 5 miles

The bank of the river is 10 miles long

Therefore, we have

If x is the distance from the point directly opposite to Chesterville to the location of the water works, the equation is;

Cost to Chesterville = [tex]3000\times \sqrt{x^2 + 3^2}[/tex]

Cost to Denton = [tex]7000\times \sqrt{(10-x)^2 + 5^2}[/tex]

Total cost is then;

[tex]7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2}[/tex]

We differentiate the above equation and equate it to zero to get the minimum cost as

[tex]\frac{\mathrm{d} (7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2})}{\mathrm{d} x}[/tex] = 0

[tex]7000\frac{2x-20}{2\sqrt{x^2-20x+125} } +3000\frac{2x}{2\sqrt{x^2+9} } = 0[/tex]

[tex]3500\frac{2x-20}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{\sqrt{x^2+9} }[/tex]

[tex]3500\frac{\sqrt{x^2+9}}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{2x-20 }[/tex]

[tex]x^4-20x^3+10.54x^2-22.05x+110.25 =0[/tex]

Solving the quartic equation we get

x = 7.82 miles

Therefore the length of is given as

Length of pipe to Chesterville  [tex]\sqrt{7.82^{2} +3^2 } = 8.376 \, miles[/tex]

Length of pipe to Denton = [tex]\sqrt{(10-7.82)^2 + 5^2} = 5.46 \, miles[/tex].

Step-by-step explanation:

As it is a quadrilateral so sum of all angles of quadrilateral is equal to 360°

14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°

37x+ 27° = 360°

37x = 360° - 27°

37x = 333°

x = 333° / 37

Therefore x = 9°

Now

<B = 8 * 9° + 7° = 79°

Hope it will help you.

Answer: The answer is 79.0°

Step-by-step explanation:

A quadrilateral will always have 360° and four sides. Keep that in mind, that's a universal rule of geometry.

Here, the sum of all sides is equal to 360°. Therefore, we make an equation:

[tex](14x-11) + (8x+7) + (5x+18) + (10x + 13) = 360[/tex]

Simplify by adding and subtracting like terms.

[tex]37x +27=360[/tex]

Isolate x by first passing the 27 to the other side.

[tex]37x = 333[/tex]

Divide by 37 to isolate x.

[tex]x = 9[/tex]

To find m∠B, we plug in x to [tex](8x+7)[/tex]

which gives you: [tex](8*9+7) = 79[/tex]

The answer is 79.0°

Curious if it is correct? Let's double check.

Plug in the x=9 to all the x values and add them up. You should get 360, which makes the answer correct.

Answer:

Step-by-step explanation3:45

Answer:

3:20 p.m

Step-by-step explanation:

Answer:

it is

Step-by-step explanation:

Any number, all by itself, is a monomial, like 5 or 2700.

Answer:

Yes it is a monomial

Step-by-step explanation:

There's only one number, there's no operations to do so its a monomial :)

Answer:

Yellow Bin

Step-by-step explanation:

Yellow Bin

Length = 11.4 inches,

Width = 4.2 inches,

Height =  [tex]\frac{8}{3}[/tex]

Volume of the yellow bin=LWH[tex]=11.4 X 4.2 X \frac{8}{3}=127.68 \:cubic \:inches[/tex]

Red Bin

Length = 9 inches,

Width = 5.45 inches,

Height =  [tex]\frac{11}{5}[/tex]

Volume of the red bin=LWH[tex]=9X 5.45 X \frac{11}{5}=107.91 \:cubic \:inches[/tex]

The yellow bin has a greater volume since 127.68 is greater than 107.91.

Final answer:

Without more context, the measure of angle 6 cannot be determined from the given information that angle 5 is 120 degrees.

Explanation:

To determine the measure of angle 6, we need additional information about the context in which angle 5 and angle 6 are related. Since the question does not provide sufficient details, such as whether the angles are supplementary, complementary, or part of a geometric figure like a triangle or polygon, it's not possible to provide the measure of angle 6 based solely on the given information that angle 5 is 120 degrees. In geometry, the relationships between angles often depend on the shapes they are part of or the lines intersecting with them. If angle 5 and angle 6 are supplementary angles (angles that add up to 180 degrees), for instance, we could subtract the measure of angle 5 from 180 degrees to get angle 6. However, without more details, we cannot accurately provide the measure of angle 6.

Answer:

  3/8

Step-by-step explanation:

1/4 + 1/8 = 2/8 + 1/8 = 3/8

After you give the fractions a common denominator, you can add their numerators to find the numerator of the result.

Mr. Hawkins's combined bonus payments are 3/8 of his salary.

Given:

The area of the given sphere = 36π in²

To find the volume of the given sphere.

We need to find the radius first.

Formula

where, r be the radius of the sphere.

Now,

According to the problem,

[tex]4\pi r^{2} = 36\pi[/tex]

or,[tex]4r^{2} = 36\\[/tex] [ Eliminating π from both the side]

or, [tex]r^{2} = \frac{36}{4}[/tex]

or, [tex]r = \sqrt{9}[/tex]

or, [tex]r = 3[/tex]

So,

The radius of the sphere is 3 inches

Therefore,

The volume of the sphere is

[tex]V = \frac{4}{3} \pi (3)^{3}[/tex]

or, [tex]V = 36\pi[/tex]

Hence,

The volume of the sphere is 36π cube inches.

Answer:

-4

Step-by-step explanation:

Answer:

The answer to your question is x = -2, y = 5 and z = 7

Step-by-step explanation:

Data

first number = x

second number = y

third number = z

Process

1.- Write equations to solve this problem

                 x + y + z = 10           Equation l

                 2y - x = 12                Equation ll

                  x - y + 2z = 7           Equation lll

2.- Solve equation ll for x

                x = 2y - 12

3.- Substitute the previous equation in equation l and lll

               (2y - 12) + y + z = 10                     (2y - 12) - y + 2z = 7

                2y - 12 + y + z = 10                       2y - 12 - y + 2z = 7

                3y + z = 10 + 12                             y + 2z = 19

                3y + z = 22

4.- Solve for y and z

                     -2(3y + z = 22)

                          y + 2z = 19

                    -6y - 2z = -44

                       y + 2z = 19

                   -5y   + 0 = -25

                      y = -25/-5

                      y = 5

-Find z

                       5 + 2z = 19

                             2z = 19 - 5

                             2z = 14

                               z = 14/2

                               z = 7

5.- Find x

                  x + 5 + 7 = 10

                  x = 10 - 5 - 7

                 x = -2

Listed in order from smallest to largest: -2, 5, 7.

Let's denote the three numbers as follows:

- First number: x

- Second number: y

- Third number: z

We have three equations based on the given information:

1. x + y + z = 10

2. 2y - x = 12

3. x - y + 2z = 7

We can solve this system of equations to find the values of x, y, and z.

From equation 2, we can isolate x:

x = 2y - 12

Now substitute the value of x in equations 1 and 3:

1. (2y - 12) + y + z = 10

3y + z = 22

3. (2y - 12) - y + 2z = 7

y + 2z = 19

Now we have a system of two equations with two variables (y and z):

1. 3y + z = 22

2. y + 2z = 19

Let's solve for one of the variables in terms of the other. From equation 2, we can isolate y:

y = 19 - 2z

Now substitute this value of y into equation 1:

3(19 - 2z) + z = 22

57 - 6z + z = 22

-5z = -35

z = 7

Substitute the value of z back into the equation for y:

y = 19 - 2(7)

y = 5

Now that we have values for y and z, we can substitute them back into the equation for x:

x = 2y - 12

x = 2(5) - 12

x = 10 - 12

x = -2

So, the numbers are:

First number: -2

Second number: 5

Third number: 7

Listed in order from smallest to largest: -2, 5, 7.

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Answer:

x=4± 5sqrt(2)

Step-by-step explanation:

x^2 – 8x – 34 = 0

To complete the square Add 34 to each side

x^2 -8x -34+34=0+ 34

Take the coefficient of x, and divide by 2

-8/2 =-4

Then square it and add it to each side

(-4)^2 =16

x^2 – 8x +16 = 34+16

x^2 – 8x +16 = 50

We replace the left side with (x + the coefficient of x/2)^2

(x -4)^2=50

Take the square root of each side

sqrt((x -4)^2)=±sqrt(50)

x-4 = ±sqrt(25*2)

x-4 = ±sqrt(25)*sqrt(2)

x-4 = ±5sqrt(2)

Add 4 to each side

x=4± 5sqrt(2)

Answer:

4 + 5sqrt(2), 4 - 5sqrt(2)

Step-by-step explanation:

x² - 8x - 34 = 0

x = [-(-8) +/- sqrt((-8)² - 4(1)(-34))]/2

x = (8 +/- sqrt200)/2

x = 4 +/- 5sqrt(2)

Answer:

1.  The mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

2. There is more hemoglobin in the average man than in the woman

Step-by-step explanation:

The confidence interval is from

-1.76 g/dl < μ₁ - μ₂ < -1.62 g/dl

Here we note that the range in the confidence interval for the difference between the two means lie in the negative part of the number line which is indicative of that μ₁ - μ₂ ≠ 0  or μ₁ ≠ μ₂

That is the statistic of the confidence interval implies that the mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

That there is more hemoglobin in the average man than in the woman.

Answer:

The last option

Step-by-step explanation:

To find a percentage of something you need

[tex]\frac{expected}{total}*100[/tex]

The expected is correct marks, the total is the total amount - then you multiply by 100 to turn the decimal into a percentage.

Answer:

the answer is D

Step-by-step explanation:

Answer:

A student solved 3/x−4=x/7 in six steps, as shown:

Step 1:  3=x(x−4)/7  

Step 2: 21=x(x−4)

Step 3: 21=x^2−4(x)

Step 4: 0=x^2−4(x)−21

Step 5: 0=(x−7)(x+3)

Step 6: x=−3, x=7

Which statement is an accurate interpretation of the student's work?

A.The student solved the equation correctly.

B.The student made an error in step 2.

C.The student made an error in step 5.

D.Only x=7 is a solution to the original equation.

Option A is the right choice.

Step-by-step explanation:

Given:

An equation and its step-wise work.

We have to check whether the steps are correct or not.

The equation is:

⇒ [tex]\frac{3}{x-4} = \frac{x}{7}[/tex]

Solution:

⇒ [tex]21=x(x-4)[/tex]              ...cross multiplying terms.

⇒ [tex]21=x^2-4x[/tex]    

⇒ [tex]x^2-4x-21=0[/tex]

⇒ [tex]x^2-7x+3x-21=0[/tex] ...using middle term splitting

⇒ [tex]x(x-7)+3(x-7)=0[/tex]

⇒ [tex](x+3)(x-7)[/tex]

⇒ [tex]x=-3\ and\ x=7[/tex]

The student have solved the question correctly.

Answer:

Step-by-step explanation:

It s 55555555

Answer:

18x^2-45x

Step-by-step explanation:

-9x (5-2x)

=-9x X 5-(-9x) X 2x

=-9 X 5x+9 X 2xx

=18x^2-45x

I hope this helps!

Answer:

Initial value is at t = 0

Y-intercept is the initial value

Answer:

59.1 °

Step-by-step explanation:

-Given that Tan B=1.6732

-Angle B is equivalent to the tan inverse of the tan B value:

[tex]\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree[/tex]

Hence, angle B is 59.1 °

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732.

The measure of angle B is approximately 59.7 degrees.

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732. First, convert the tangent value to radians by using the formula tan(B) = opposite/adjacent. Then, take the arctan of B to find the measure in radians. Finally, convert the radians to degrees by multiplying by 180/pi.

Step-by-step:

Plugging in the given value, B ≈ 59.7 degrees to the nearest tenth of a degree.

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Answer:

4 i did the quizzzzzzzzzzzzzzzzzzzzzzzzz

Step-by-step explanation:

Answer:

30% not likely

Step-by-step explanation:

We have 10 marbles

The probability must equal 100%

10% red

60% yellow

----------------

70 %

That leaves 30% for orange

Orange is 30%

This is less than 50% so it is not likely to occur

Answer:

30%

not likely

Step-by-step explanation:

P(orange) = 100 - 10 - 60

= 30%

Less likely or not likely

Answer:

Step-by-step explanation:

Amount loaned = $10,000

Interest rate = 3%

Duration = 6 years

10,000 / 100 x 3/1 × 6

= 300 × 6

= 1800 + 10,000

Total Amount to pay

= $11,800

To find the lateral surface area of a cylinder with a radius of 30.8 cm and a height of 20.5 cm, use the formula 2πrh. The calculation gives a result of approximately 3981.86 square centimeters.

The question asks for the closest measurement to the lateral surface area of a cylinder with a radius of 30.8 centimeters and a height of 20.5 centimeters. To find the lateral surface area of the cylinder, we use the formula: Lateral Surface Area = 2πrh, where 'r' is the radius, and 'h' is the height of the cylinder. Substituting the given values,

we get Lateral Surface Area = 2 × 3.14 × 30.8 cm × 20.5 cm.

Calculating this, we find:

Lateral Surface Area = 3981.864 square centimeters. Therefore, the closest measurement to the lateral surface area of the cylinder is 3981.86 square centimeters.

Answer:

The answer to your question is Vertex = (5 , -5)

Step-by-step explanation:

Data

Equation                y = - x² + 10x - 30

Process

1.- Add 30 units in both sides

                             y + 30 = -x² + 10x - 30 + 30

2.- Simplify

                             y + 30 = -x² + 10x

3.- Factor -1 in the right side

                             y + 30 = -(x² - 10x      )

4.- Complete the perfect square trinomial

                             y + 30 - 5²= -(x² - 10x + 5²)

5.- Simplify

                             y + 30 - 25 = -(x² - 10x + 25)

                             y + 5 = -(x - 5)²

6.- Find the vertex

                            Vertex = (5 , -5)

Answer:

help with what tho

Step-by-step explanation:

Answer:

with what I can't see it

Step-by-step explanation:

Answer:

If there are eleven apples to be shared between 3 boys and two bananas to be shared between 3 girls, find the difference between them.

Step-by-step explanation:

So there are 11 apples to be shared between 3 boys, which is represented mathematically as 11/3

And 2 bananas to be shared between 3 girls, which can be represented mathematically as 2/3, find the difference.

The difference between them would be 11/3 - 2/3

Solving this problem, they both have the same denominator, so we subtract the numerators directly.

11/3 - 2/3 = 9/3

Which is equals to 3.

So the difference between both of them is 3.

Answer:

60 ft, 120 ft, 182 ft

Step-by-step explanation:

Hi there,

To find the perimiter of a polygon, you need to add of all of the sides.

So, let's do that:

x + 2x + 3x+2

Since we are given the perimeter, we make what we just did above, equal to the perimeter

x + 2x + 3x +2 = 362

Combine lke terms...

6x + 2 = 362

Subtract 2 from both sides to start to isolate the variable...

6x = 360

Divide both sides by 6 to isolate x...

x = 60

But we're not done yet...

The length of the first side is 60 ft, the length of the second side is 2*60 which is 120 ft, and the length of the third side is 3*60 + 2 which is 182 ft.

Let's check...

Does 60 + 120 + 182 = 362?

362 = 362

Our answers are right

Hope this helps! Stay safe!

- Emily