Diane is filling a candle order for a wedding. She needs 6 large arrangements and 13 small arrangements .The large arrangements each contain 25 candles. The small arrangements each contain 12 candles. How many candles does diane need in all?

The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Given a taxi charges $2.50 for the first mile and $0.40 for each mile

We are required to make an expression showing total cost and total cost of a 20 mile ride.

let the miles ride by tax be x.

Total cost of the product or service=Number of units*price of one units.

We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.

So,the expression showing looks like 2.50+0.40x.

Now to find the cost when taxi travels 20 miles, we have to put x=20,

Cost=2.50+0.40*20

=2.50+(40*20)/100

=2.50+800/100

=2.50+8

=$10.50

Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Learn more about expression at https://brainly.com/question/723406

#SPJ4

Answer:

Θ ≈ 37° , x ≈ 13 cm

Step-by-step explanation:

(a)

using the cosine ratio in the right triangle

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ([tex]\frac{8}{10}[/tex] ) ≈ 37° ( to the nearest whole number )

(b)

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{15}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 15[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 7.5[tex]\sqrt{3}[/tex] ≈ 13 cm ( to the nearest whole number )

Answer:

2.25 ft

Step-by-step explanation:

Volume = length x height x width

54= 8 x 3 x ?

Combine: 54= 24 x ?

Find ?: 54/24=2.25

Recheck: 24 x 2.25 = 54

The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.

If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:

a² + b² = c².

In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.

We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.

We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.

The diagram is attached.

Now, we get a right triangle ABC, right-angled at B.

By Pythagoras' Theorem, we know that:

AB² + BC² = AC²,

or, AB² + 6² = 10²,

or, AB² = 10² - 6² sq. inches,

or, AB² = 100 - 36 sq. inches,

or, AB = √64 inches,

or, AB = 8 inches.

Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

Learn more about the Pythagoras Theorem at

https://brainly.com/question/17082309

#SPJ4

The provided question is incomplete. The complete question is:

"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"

Answer:

138

Step-by-step explanation:

There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.

23 * 6 = 138

Using it's concept, the domain of the function shown in the graph is:

B. [tex]-6 \leq x \leq 6[/tex].

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.

From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:

B. [tex]-6 \leq x \leq 6[/tex].

More can be learned about the domain of a function at https://brainly.com/question/10891721

#SPJ1

El número decimal que no es un decimal periódico es dado por:

B. [tex]\frac{11}{400}[/tex].

Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.

La conversión de las fracciones para decimales són:

Puede-se aprender más a cerca de números decimales periódicos en https://brainly.com/question/1192529

#SPJ1

Part A

The two factors are 5 and 4x+6.

Part B

The first factor, 5, has 1 term.

The second factor, 4x+6, has 2 terms.

Part C

The coefficient of the variable term is 4.

The length of the road that connects the service station with Cray is 46.2 mi.

We need to apply the principle of similar triangles to obtain the length of the road that will connect the service station with Cray as shown in the image attached.

Hence;

The distance between Alba and Blare = 130 mi

The distance between Alba and Cray = 120 mi

Road connecting the service station with Cray =x

And;

120/130 = x/50

x =  46.2 mi

Learn more about similar triangles:https://brainly.com/question/12100952

#SPJ1

The length and width of the computer monitor is 23.36 inches

and 13.14 inches.

According to the given statement

we have given that  

The length of diagonal of rectangular monitor = 27 inches

The length to width ratio is 16:9

So , Let the Length of monitor = 16x

and The Width of monitor  = 9x

And we have to find the length and width of the computer monitor.

So, For this purpose,

From Pythagoras theorem

(Diagonal)² = Length² + width²

Put the values in it and then

27² = (16x)² + (9x)²

729 = 256x² + 81x²

After solving we get

337x² = 729

So, x² = 2.16

∴  x =  = 1.46 inches

So, The length = 16x = 23.36 inches

And The width = 9x = 13.14 inches.

Hence, The length and width of the computer monitor is 23.36 inches

and 13.14 inches.

Learn more about Pythagoras theorem here https://brainly.com/question/2437195

#SPJ4

The computation shows that the average monthly amount is 61.64.

The amount that's left will be:

= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075

= 3314.85 + 1853.3 - 3600 - 1075

= 493.15

The average monthly amount will be:

= 493.15/8

= $61.64

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

Answer:

16. C

17. C

Step-by-step explanation:

16.

this is just a multiplication of the 2 functions.

that means we multiply the functional expressions, and the result is the new functional expression of the multiplied functions.

2(3x - 5) × (-2x + 1) = (6x - 10) × (-2x + 1) =

= 6x×-2x + 6x×1 + -10×-2x + -10×1 =

= -12x² + 6x + 20x - 10 = -12x² + 26x - 10

17.

the domain of a function is the interval or set of all valid x values (or input values).

the range is the interval or set of all valid y or functional result values.

so, for the domain we need to see what values x may have for a 4th root.

for this we can imagine that a 4th root is the square root of the square root of x.

this is directly related to x⁴ being the square of the square of x.

the valid input values for a square root are all positive numbers (incl. 0). the result will be again a positive number (incl. 0), which is again a valid input number for the second square root.

therefore, the valid values of x for a 4th root are also the valid values for a square root. and vice versa.

and that is

0 <= x < infinity

FYI : we can never say x = infinity, because infinity is not a number, just a generation concept. so, infinity can never be included in any interval, it can only be listed as an excluded limit concept.

Answer:

Step-by-step explanation:

B is the answer

Answer:

f(2) = 3

Step-by-step explanation:

Plug in 2 for x

You did not provide directions. What do you want us to do with your 8th degree polynomial?

Answer:we smoking fredoooooooooo

Answer:

==================

y = 3x² - 12x + 7 =

     3(x² - 4x) + 7 =                                  Factor out 3

     3(x² - 4x + 4) - 3*4 + 7 =                   Complete the square

     3(x - 2)² - 5                                       Simplify

Answer:

  y = 3(x -2)² -5

Step-by-step explanation:

It looks like you want to write the standard-form quadratic ...

  y = 3x² -12x +7

in vertex form.

The process is similar to that of "completing the square."

Factor out the leading coefficient

Do this for the variable terms only.

  y = 3(x² -4x) +7

Identify the x-term coefficient

The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.

  x coefficient: -4

  binomial constant: -4/2 = -2

  square of this: (-2)² = 4

Add this inside parentheses

To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.

  y = 3(x² -4x +4) +7 -3(4)

Simplify to vertex form

Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.

  y = 3(x -2)² -5

The cost of one gizmo is $18.

The cost of one thingamajigs is $9

3g + 6t = 102 equation 1

5g + 11t = 179  equation 2

Where:

Multiply equation 1 by 5 and equation 2 by 3

15g + 30t = 510 equation 3

15g + 33t = 537 equation 4

Subtract equation 3 from equation 4

3t = 27

t = 27 / 3

t = $9

Substitute for t in equation 1

3g + 6(9) = 102

3g + 54 = 102

3g = 102 - 54

3g = 48

g = 48 / 3

g = $18

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

Answer:

The volume of the cylinder is 2,400pi cubic units

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

y =sin(x)

Step-by-step explanation:

small brain

Answer:

B: k pi for any integer k

Step-by-step explanation:

I took the test

Answer:

1/2

1/3

Step-by-step explanation:

x=1/2

x=-1/3

Answer:

[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]6x^{2} -x-1=0[/tex]

Factoring the equation:

[tex](3x+1)(2x-1)=0[/tex]

Extract the roots:

First factor

[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]

Second factor

[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]

Hope this helps

The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].

Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].

We are required to find the solution of the differential equation when y(0)=1.

dy/dx=[tex]2xy/(x^{2} -1)[/tex]

Taking y to left side and dx to right side.

1/y dy=2x/[tex](x^{2} -1)[/tex] dx

Integrating both sides.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1

log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

Solving right side.

[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

let [tex]x^{2} -1[/tex]=z

differentiating both sides with respect to x.

2x=dz/dx

2x dx=dz

Put 2x dx=dz in 1.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]

log y=log z+log c

Put z=[tex]x^{2} -1[/tex]

log y=log([tex]x^{2} -1[/tex])+log c

log y=log [{[tex]x^{2} -1[/tex])c]

y=([tex]x^{2} -1[/tex])c------------2

Put x=0 and y=1

1=(0-1)c

1=-c

c=-1

Put c=-1 in 2 to get the solution.

y=-1([tex]x^{2} -1[/tex])

y=[tex]-x^{2} +1[/tex]

Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is

y=[tex]-x^{2} +1[/tex].

Learn more about differential equation at https://brainly.com/question/25731911

#SPJ1

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

The probability that the next toss will be heads is 1/8.

The likelihood of an event occurring is described by probability. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.

Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the probability of an event happening can range from 0 to 1.

Probability of getting two tails and next heads in three tosses is,

=1/2*1/2*1/2

=1/8

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

[tex]\sf 1\dfrac{2}{5} \ cm[/tex]

Step-by-step explanation:

    If two sides of the triangle are equal, then the triangle is called isosceles triangle.

Let the two equal sides = x cm

Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm

[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]

      [tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]

             [tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]

[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]

Answer:

7. a) slope = 5

7. b) slope = 1/2

8. slope = 1

Step-by-step explanation:

slope = rise/run

rise is the vertical change, run is the horizontal change

7. a)

Pick any two points on your line. (0,0) and (1,5) are easy to work with.

The vertical change between the two points is 5

The horizontal change between those points is 1

so slope = 5/1 = 5

7. b)

Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.

slope = 4/2 = 1/2

8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...

m = slope = (y2-y1) / (x2-x1)

= (8 - 4) / (5 - 1)

= 4/4

= 1

I hope that helped!

Answer:

23/75

Step-by-step explanation:

8/15 + x = 21/25

x = 21/25 - 8/15

now we need to bring both fractions to the same denominator (bottom part), so that we can do the subtraction.

what is the least common multiple (LCM) of 25 and 15 ? that will be the common denominator.

I usually use the prime factor factorization of the involved numbers.

15 : 3, 5 (15 = 3×5, there are no smaller prime factors)

25 : 5, 5 (25 = 5×5, there are no smaller prime factors)

the LCM is the combination of the longest chains of each prime factor :

3×5×5 = 75

so, we bring both fractions to 75 denominators.

how many 1/75th are 1/25 ? as 25×3 = 75, we have 3/3 × 1/25 = 3/75 (= 1/25).

so,

21/25 = 21×3/75 = 63/75

how many 1/75th are 1/15 ? as 15×5 = 75, we have 5/5 × 1/15 = 5/75 (= 1/15).

so,

8/15 = 8×5/75 = 40/75

remember, we have to multiply the numerator and the denominator by the same value to keep the original value of the fraction unchanged.

and now our equation looks like

x = 63/75 - 40/75 = 23/75

Question 2

1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)