8. Daisies and tulips are planted in a
garden. There are 11 fewer tulips
planted than daisies.
a. Write an expression that represents
the number of tulips in terms of the
number of daisies. Define any
variables used.
b. If 18 daisies are planted, how many
tulips are planted?

Answer:

  1680

Step-by-step explanation:

To find the product of the two numbers, you can work out the values of the numbers, or you can work directly with the sum and difference figures.

__

We note that the square of a sum is ...

  (a +b)² = a² +2ab +b²

and the square of a difference is ...

  (a -b)² = a² -2ab +b²

The difference of these squares is ...

  (a +b)² -(a -b)² = (a² +2ab +b²) -(a² -2ab +b²) = 4ab

__

That is, dividing the difference of the squares of the sum and difference by 4 will give the desired product:

  P = (83² -13²)/4 = (6889 -169)/4 = 6720/4 = 1680

The product of the two numbers is 1680.

_____

Additional comment

If we factor the formula we derived, we find ...

  P = ((a +b)² -(a -b)²)/4 = ((a +b) +(a -b))/2 × ((a +b) -(a -b))/2

This simplifies to ...

  (2a)/2 × (2b)/2 = a × b

In short:

Using this fact, we find a=(83+13)/2 = 48; b=(83-13)/2 = 35, and the product is (48)(35) = 1680, as above.

Answer:

The answer is 5 or D

Hope this helps!

Answer: [tex]z=91.6[/tex]

Step-by-step explanation:

A pentagon has 5 sides and 5 angles and equals up to 540 degrees

So we need to make the equation of

[tex]145+120.1+112.3+71+z=540[/tex]

[tex]448.4+z=540[/tex]

[tex]448.4+z=540\\-448.4 = -448.4[/tex]

[tex]z=91.6[/tex]c

To check work just plug in 91.6 for z in the equation that was created [tex]145+120.1+112.3+71+91.6=540[/tex]

Step-by-step explanation:

Let the angle of triangle be x , so each angle will be 1x , 2x , 3x respectively.

We know that sum of all angles in triangle is 180°

So ,

1x + 2x + 3x = 180°

6x = 180°

x = 30°

Therefore , each angle would be 30° , 60° , 90° respectively.

The answer is  Yes because StartFraction 16 Over 10 EndFraction equals StartFraction 24 Over 15 EndFraction is correct.

From the diagram we have

Corresponding segments in triangles LKM and LJN are proportional, so the triangles are similar and KM ║ JN.

The parallel line does not intersect each other

The other yes choice does not properly show corresponding segments

So, actually makes a false claim.

It is not true that 16/10 = 15/24.

To learn more about the fraction visit:

https://brainly.com/question/78672

Answer: Yes,  16/10 equals 24/15

Step-by-step explanation: bc im cool like that

Answer:

Step-by-step explanation:

$5,400

Answer:

80°

Step-by-step explanation:

2x+20=180°

2x= 180°-20°

x=160/2

x=80°

Answer:

80%

Step-by-step explanation:

using equivalent fractions:

40/50 = 80/100 = 80%

also since 50 is half of 100 (in other words 100%), you can just multiply 40 by 2 to get a number out of 100 which is your percentage

hope this helped :)

The number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

From the data given in the table:

The number of children who disliked the smoothie = 9

The total number of children = 27

To find the conditional relative frequency that a customer disliked the new smoothie(if the person is a child)

It is the ratio of total number of children who disliked the smoothie to total number of children, mathematically:

= 9/27

= 0.3333

= 0.3333×100

= 33.33 ≈ 33%

Thus, the number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

Learn more about the conditional relative frequency here:

https://brainly.com/question/8358304

Answer:

9, 27, 33

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Add all the number of marbles which is 12. 8 of them are not red. 8/12 when simplified equals 2/3.

Answer:

one mile is 5280 feet

40 x 5280 = 211,200 feet per hour

pretty sure im right

Answer:

the area of rectangle should be 1/8 square

Step-by-step explanation:

1/6*3/4

=1/8

Step-by-step explanation:

seems to be multiplication, because the differences between the numbers change.

so, let's find the factor.

2 × f = 5

f = 5/2

5 × f = 5 × 5/2 = 25/2

ok, the factor 5/2 is confirmed.

a1 = 2

a2 = a1 × 5/2 = 2 × 5/2 = 10/2 = 5

a3 = a2 × 5/2 = a1 × 5/2 × 5/2 = 2 × 5/2 × 5/2 = 25/2

an = an-1 × 5/2 = a1 × (5/2)^(n-1) = 2 × (5/2)^(n-1)

a9 = 2 × (5/2)⁸ = 2 × 390,625/256 =

= 390,625/128 = 3,051.7578125

The geometric sequence's 9th term will be 3,051.7578.

A geometric sequence is one in which each term is obtained by multiplying the previous term by the same number throughout the series.

Let a₁ represent the first term and r represent the common ratio. The geometric sequence's nth term is then given as,

aₙ = a₁ x (r)ⁿ⁻¹

The sequence is given below.

2, 5, [tex]\dfrac{25}{2}[/tex],

The first term is 2. And the common difference is given as,

[tex]r = \dfrac{5}{2}[/tex]

r = 2.5

Then the 9th term is given as,

a₉ = 2 x  (2.5)⁹⁻¹

a₉ = 2 x (2.5)⁸

a₉ = 2 x 1525.8789

a₉ = 3,051.7578

The 9th term of the geometric sequence will be 3,051.7578.

Learn more about the geometric sequence here;

brainly.com/question/1509142

#SPJ2

Answer:

∠ N = 42°

Step-by-step explanation:

the measure of a secant- secant angle is half the difference of the measures of the intercepted arcs , that is

∠ N = [tex]\frac{1}{2}[/tex] ( HE - XP ) = [tex]\frac{1}{2}[/tex] ( 122 - 38)° = [tex]\frac{1}{2}[/tex] × 84° = 42°

Answer:

(-3,1)

Step-by-step explanation:

As their are two lines so these are simultaneous linear equations

Hence this is (-3,1)

Note: The solution of a graph is the intersection of 2 lines.

Plotting the solution on the graph:

To plot the solution on the graph,

Identifying a solution on the graph:

To identify the solution, you willl need to determine it's coordinates.

     1. Determine the x and y coordinate by drawing a line going                                 downwards and rightwards. Keep in mind that the                                               intersection of the lines on the x and y axis are the x and y                               coordinates repectively.

    2. The x and y coordinate obtained should be put in (x,y) form.

Determining the solution on the graph:

⇒ Intersection point: (x, y) = (x = -3; y = 1) = (-3, 1)                [Refer to image]

Answer:

  a. 0.41

  b. 0.22

Step-by-step explanation:

The sum of probabilities over all outcomes is 1. This fact can be used to fill the table. The other questions can be answered by reference to the table.

__

The total of all probabilities is 1:

  k +0.23 +0.18 +0.26 +2k = 1

  3k = 0.33 . . . . . . . collect terms, subtract 0.67

  k = 0.11 . . . . . . . divide by 3

  2k = 0.22 . . . . find 2k

Then the table is ...

  [tex]\begin{array}{c|ccccc}n&1&2&3&4&5\\p(n)&0.11&0.23&0.18&0.26&0.22\end{array}[/tex]

Landing on 2 or 3 are mutually exclusive outcomes, so the probability of one or the other is the sum of their individual probabilities:

  p(2 or 3) = 0.23 +0.18

  p(2 or 3) = 0.41

__

The table tells us ...

  p(5) = 0.22

The surface area of the roof is the amount of space on it

The surface area of the roof is 600 square meters,

From the complete question, we have the parameters for the roof:

The surface area of the roof is calculated using:

[tex]A = b^2 + 2b \sqrt{\frac{b^2}4 + h^2}[/tex]

So, we have:

[tex]A = 15^2 + 2 * 15 \sqrt{\frac{15^2}4 + 10^2}[/tex]

Evaluate the exponents

[tex]A = 225 + 30 * \sqrt{\frac{225}4 + 100[/tex]

The equation becomes

[tex]A = 225 + 30 * 12.5[/tex]

Evaluate the sum

[tex]A = 600[/tex]

Hence, the area of the roof is 600 square meters

Read more about surface areas at:

https://brainly.com/question/6613758

Answer:

3,628 sq ft

Step-by-step explanation:

Answer:

The distributive property states that you can "distribute" the contents of one parentheses into the other to find an answer.

Let's first break down the larger number in the second parentheses:

400 + 10 + 5.

Then, let's multiply all those numbers by 3.

400 x 3 = 1200. 10 x 3 = 30. 5 x 3 = 15.

Then add up all the numbers and you get 1245.

Answer:

1245

Step-by-step explanation:

400+10+5

400×3=1200. 10×3=30. 5×3=15

Let's simplify this equation:

    ⇒ first, consider what we can simply typically

By considering the equation given

 ⇒ we can simply simplify the coefficient of the variable with the

  denominator

   [tex]\frac{20v}{5} =\frac{5*4*v}{5} =\frac{5}{5}*4*v =1*4*v=4v[/tex]

Thus the simplified expression is 4v

Answer: 4v

Hope that helps!

Answer:

240 cm²

Explanation:

The shape given above is a parallelogram.

Area of parallelogram = base × perpendicular height

Identify the following:

So here area = b × h = 20 × 12 = 240 cm²

Fractions are rations of two integers. The height of the scale model in inches is 78 inches

Fractions are ratios of two integers and they are also used to represent ratios.

Given that scale model of the Texas Capitol is  2 inches to represents 8 feet, the height of the capitol in inches is the heght in feet is 312 feet is expressed as:

Height  = 312 * 2/8
Height in inches = 312/4
Height in inches = 78 inches

Hence the height of the scale model in inches is 78 inches

Learn more on proportion here: https://brainly.com/question/19994681

The equation represents the line that passes through (–6, 7) and (–3, 6) [tex]\rm y=\dfrac{-1}{3}x+5[/tex].

For all lines in slope y-intercept form, it would be very simple to just find the answer by finding yourself the slope and y-intercept of the line in question.

The slope of the line is;

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m =\dfrac{7-6}{-6-(-3)}\\\\m = \dfrac{1}{-3}[/tex]

The equation represents the line that passes through (–6, 7) and (–3, 6) is;

[tex]\rm y=\dfrac{-1}{3}x+b\\\\6=\dfrac{-1}{3}(-3)+b\\\\6=1+b\\\\b = 6-1\\\\b=5[/tex]

The required line of the equation is;

[tex]\rm y =mx+c\\\\y=\dfrac{-1}{3}x+5[/tex]

Hence, the equation represents the line that passes through (–6, 7) and (–3, 6) [tex]\rm y=\dfrac{-1}{3}x+5[/tex].

To know more about the equation of line click the link given below.

https://brainly.com/question/8955867

Answer:

I'm pretty sure the answer is B sorry if I'm wrong

Step-by-step explanation:

Answer:

GCF and the Distributive Property - YT here is a yt video on how to do it hope it helps i just looked up the answer

Step-by-step explanation:

height of mt.= 4000meters

hope it helps...!!!

[tex]~~~~~\dfrac 12 \left(x-\dfrac 34 \right) = \dfrac 5{12}\\\\\\\implies \dfrac{4x-3}4= \dfrac{5 \times 2}{12}\\\\\\\implies 4x-3 = \dfrac{5 \times 2 \times 4}{12}\\\\\\\implies 4x -3=\dfrac{40}{12}\\\\\\\implies 4x -3 = \dfrac{10}3\\\\\\\implies 4x = \dfrac{10}3 +3\\\\\\\implies 4x = \dfrac{19}3\\\\\\\implies x = \dfrac{19}3 \times \dfrac 1 4\\\\\\\implies x = \dfrac{19}{12}[/tex]

The required factorized form of the given expression is 50(x+2), where 50 is the greatest common factor (GCF).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

We have been given that the expression below as

50x + 100

We have to determine the factor of the expression 50x + 100

First, we have to find the Greatest Common Factor (GCF).

GCF = 50

2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

50(50x/50 + 100/50)

Simplify each term in parentheses.

50(x+2)

Therefore, the required factorized form of the given expression is 50(x+2).

Learn more about the Factorization here:

brainly.com/question/4184435

#SPJ2