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yawa3891 [41]
3 years ago
14

Trina planted plants in her garden last week. She planted twice as many cucumbers as zucchini and eight more tomatoes than cucum

bers. Write and solve an equation to find the number of each kind of plant in her garden. If you need to, use the 5-D Process to help you organize your thinking. Be sure to define your variable.
Mathematics
1 answer:
maxonik [38]3 years ago
3 0

Answer:

7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

Step-by-step explanation:

  • Let the number of tomatoes=t
  • Let the number of cucumber planted=c
  • Let the number of zucchini planted=z
  • Total Number of Plants=43

She planted twice as many cucumbers as zucchini, this is written as:

  • c=2z

She also planted eight more tomatoes than cucumbers, this is written as:

  • t=c+8=2z+8

In total, she planted 43 plants

Therefore:

z+(2z)+(2z+8)=43

5z+8=43

5z=43-8

5z=35

Divide both sides by 5

z=7

Number of Cucumbers, c=2z=2 X 7 =14

Number of Tomatoes, t=c+8=14+8=22

Therefore, she planted 7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

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Which of the following are solutions to this equation 3n+4=24-n a) n=1 b) n=3 c) n=5 d) n=7​
g100num [7]

Answer:

The correct option is c) n=5.

Therefore the solution to

3n+4=24-n

is

n=5

Step-by-step explanation:

Given:

3n+4=24-n

To Find;

n = ?

Solution:

3n+4=24-n      ........Given

Add + n to both the side

3n+4+ n=24-n+n\\4n+4=24

Now Subtract 4 on both the side

4n+4-4=24-4\\4n=20

Dividing by 4 on both side

\dfrac{4n}{4}=\dfrac{20}{4}\\\\n=5

Therefore the solution to

3n+4=24-n

is

n=5

4 0
2 years ago
What is the mathematical phrase of the ratio v to seven​
kicyunya [14]

Answer:

v:7

Step-by-step explanation:

uh i think its v:7

6 0
2 years ago
Lolita deposited 500 in her savings account that earns 5% intrest compounded anually. She forgot about it until now, 15 years la
Sonja [21]

Answer:

P = 1039.5

Step-by-step explanation:

Given:-

- The initial amount deposited, Po = 500

- The interest rate applied, I = 5% compounded annually

Find:-

- The amount on her bank statement after 15 years?

Solution:-

- We see that the principal amount increases every year and no transactions have been made in the course of 15 years.

The total amount left in her savings account would be given by the following formula:

                         P = Po * ( 1 + I/100 )^n

- Where, n = number of years passed since deposit. (15 years)

                        P = 500 * ( 1 + 5/100 )^15

                        P = 500 * (1.05)^15

                        P = 1039.5  

6 0
3 years ago
Relative density was determined for one sample of second-growth Douglas fir 2 x 3 4s with a low percentage of juvenile wood and
Citrus2011 [14]

Answer:

0.03865

Step-by-step explanation:

Since the true density for the two types of trees are given, we would evaluate the average for both of them

Low percentage of juvenile wood density = 0.523 and 0.0543

Average density = 0.523 + 0.0543/2

Average density = 0.55015

Moderate percentage of juvenile wood density = 0.489 and 0.0450

Average density = 0.489 + 0.0450/2

Average density = 0.5115

Therefore, difference in true average density for the two woods are = 0.55015 - 0.51150

= 0.03865

5 0
3 years ago
If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta​
Ivahew [28]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

  • PQ = Opposite side
  • QR = Adjacent side
  • RP = Hypotenuse
  • ∠Q = 90°
  • ∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}

Since, we know that,

  • cosθ = 5/13
  • QR (Adjacent side) = 5
  • RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}

\rule{200}{3}

\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}

Where,

  • Opposite side = 12
  • Hypotenuse = 13

Therefore,

\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}

  • By substituting the values, we get,

\rule{200}{3}

\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the required answer is 17/7.

6 0
2 years ago
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