Let x is the days and the y is the height of the plant.
Let the change between x and y is linear.
So, the relation between x and y will take the form ⇒ y = ax + b
where a and b are constants.
At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)
At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)
solve (1) and (2) to find a and b
subtract (1) from (2)
∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60
substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5
So, the equation which represents the plants growth is
∴ y = (11/60) x + 12.5
Answer:
Let x is the days and the y is the height of the plant.
Let the change between x and y is linear.
So, the relation between x and y will take the form ⇒ y = ax + b
where a and b are constants.
At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)
At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)
solve (1) and (2) to find a and b
subtract (1) from (2)
∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60
substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5
So, the equation which represents the plants growth is
∴ y = (11/60) x + 12.5
Step-by-step explanation:
At his birthday party Joey got $100 from each of his 2 grandmothers $40 from his dad and $5 from sister, how much did he get? Draw a picture write and solve the equation. Then at the bottom of the paper there 3 columns one with an h another with a t and the last one an o or a zero not sure
He got $245 for his birthday
3 hours 20 minutes - 1 hour 48 minuets
A. 2.12
B. 2.52
C. 1.32
D. 1.53
an item that was selling for $72.00 is reproduced to $60.00. find the precent decrease in price.
( [72-60] / 72 )*100 = 50 / 3 = 16.7 %
wha is the solution of - 28 = 22 - 5× ?
To solve the equation we have to rearrange the terms i.e. like terms on one side
[tex]-28 = 22 - 5x[/tex]
Subtracting 22 from both sides we get
[tex] -28 -22 = 22-5x - 22[/tex]
[tex] -50 = -5x[/tex]
Divide both sides by -5 we get
[tex]\frac{-50}{-5} = \frac{-5x}{-5}[/tex]
On simplifying we get
[tex] x =10[/tex]
Hence, x= 10 is your answer
Hope this will help
sin10° + tan40° × cos10° = ?
how to solve this??
Final answer:
To find the value of sin10° + tan40° × cos10°, calculate each trigonometric function separately, multiply tan40° by cos10°, then add sin10° to the product. The approximate result is 1.0005, but use a calculator for a precise value.
Explanation:
To solve the expression sin10° + tan40° × cos10°, we first need to calculate the individual trigonometric values. The cosine of 10 degrees (cos(10°)) is approximately 0.9848.
Next, we calculate the tangent of 40 degrees (tan(40°)). According to the provided data, tan(40°) is approximately 0.839.
Using the trigonometric identity for the sine of a sum of angles, we cannot directly simplify the expression because the addition and multiplication involve different angles. Therefore, we perform the multiplication first:
tan40° × cos10° = 0.839 × 0.9848 ≈ 0.8265
Next, we add the value of sine of 10 degrees (sin10°) to this result. Given that sin10° is approximately 0.174:
sin10° + (tan40° × cos10°) = 0.174 + 0.8265 ≈ 1.0005.
However, due to possible rounding in intermediate steps, the actual value might be slightly different when calculated using more precise values or a calculator set to the correct mode.
Y over x-2= m; find an equation to solve for y
Answer:
y = m(x - 2)
Step-by-step explanation:
If y over x-2= m and we want to solve for y, multiply both sides of the equation y over x-2= m by (x - 2) first, to remove fractions:
y = m(x - 2)
2(3 – 4a) + 5(a – 7) what are the steps to solve this? please.
2(3 – 4a) + 5(a – 7)
Distribute 2 and 5 inside the parenthesis
Step 1: 2*3 - 2*4a + 5*a - 5*7
When we multiply it we will get
Step 2: 6 - 8a + 5a -35
Now we combine like terms. The terms that as same variables are like terms
-8a + 5a is -3a
6 - 35 is -29
6 - 8a + 5a -35
Step 3: -3a -29
Final answer is -3a-29
Rachel earned $34 in 4 work hours at her job today. she wants to know how much money she can earn (e) tomorrow if she works for 10 hours at the same rate
Anyone I need some help ?
Which of the following represents “nine less then three times a number is forty?
We are given
nine less than three times a number is forty
we know that
we always start our order of operation from left to right
This sentence represents equality
Let's assume that number as 'x'
Left side is :
3x-9
Right side is :
40
so, we can write as
[tex]3x-9=40[/tex].............Answer
Problem It takes 48 minutes for 7 people to paint 7walls. How many minutes does it take 20 people to paint 20 walls?
Bess practices trumpet 1/2 hr on Monday and 1 3/5 hr on Wednesday. How many hours does Bess practice trumpet? PLEASE ANSWER QUICKK
2 and 1/10 of an hour
In other words, it is 2 hours and 6 minutes
Add 1/2 and 1 and 3/5 together to get 21/10
What is 1/4 - [-3/8] =
1/4 - [-3/8]
[tex]\frac{1}{4}- (-\frac{3}{8})[/tex]
Negative times negative become positive
[tex]\frac{1}{4} + \frac{3}{8}[/tex]
Now to add fractions we make the denominator same
4 and 8 are in the denominator
Least common denominator of 4 and 8 is 8
To make denominators same , we multiply the numerator and denominator of first fraction by 2.
[tex]\frac{1*2}{4*2} + \frac{3}{8}[/tex]
[tex]\frac{2}{8} + \frac{3}{8}[/tex]
The denominators are same so we combine the numerators
[tex]\frac{2+3}{8}[/tex]
[tex]\frac{5}{8}[/tex]
Is x^2 + 20x - 100 a perfect square trinomial? Explain why or why not.
No, x^2 + 20x - 100 is not a perfect square trinomial.
Explanation:No, x^2 + 20x - 100 is not a perfect square trinomial.
In order for a trinomial to be a perfect square, it must be in the form (a + b)^2 or (a - b)^2.
The given trinomial can be factored as (x + 10)(x - 10), which is not in the form of a perfect square.
-2x + 2y + 3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5
Steps:
isolate " x " for -2x + 2y + 3z = 0 ; x = - ( - 3z - 2y ) / 2
Subsititute : x = - ( - 3z - 2y ) / 2
- 2 * ( - ( - 3z - 2y ) / 2 ) - y + z = - 3
2 * ( - ( - 3z - 2y ) / 2 ) + 3y + 3z =5
isolate " z " for : - 2 ( - ( - 3z - 2y ) / 2 ) - y+ z = - 3 ; z = - ( - 3 + 3y / 2 )
subsititute z = - ( - 3 + 3y / 2 ) :
2* ( - ( -3* ( - ( - 3 +3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5
isolate y for 2 ( -( - 3 ) - 3 + 3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5
y = 1
for z = - ( - 3+ 3y ) / 2
subsititute y = 1
z = - ( - 3 + 3 * 1 ) / 2
z = 0
For x = - ( - 3z - 2y ) / 2
subsititute y = 1
subsititute z = 0
x = - ( - 3 *0 - 2 * 1 ) / 2
x = 1
x = 1 , y = 1 , z = 0
Write the 15.97 as a mixed fraction.
15.97 as amixed fraction would be 15 97/100
Hope helps! -Aparri
The decimal number 15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].
To write 15.97 as a mixed fraction, we need to express it as a whole number combined with a fraction.
The whole number part can be obtained by taking the integer part of 15.97, which is 15.
To determine the fraction part, we need to consider the decimal portion. Since 15.97 has two decimal places.
we can express it as a fraction with a denominator of 100 (since there are two decimal places).
The decimal portion, 0.97, can be written as 97/100.
Putting it together, 15.97 can be expressed as the mixed fraction:
15 + 97/100
Therefore, 15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].
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Would the same methods work if both the numbers were positive? What if one of the numbers were positive and the other negative?
use the formula to help you answer the question below. do not include units in your answer.
5x+7 greather than or equal to
2(x-3)+4
5x+7 is greater because 2(x-3)+4 =2x-2
If one store is selling 3/4 of a bushel of apples for $9 and another story selling 2/3 of a bushel of apples for $9 which store has the better deal.
***I know the answer is calculate the $ amount first. 9 divided 3/4 total $12
9 divided 2/3 total $13.50 better deal 3/4 is cheaper...
But my question is how can identify when is division or multiplication??
I was doing multiplication but it did not work,.....why division this time?
For this case we have,
store 1:3/4 of a bushel of apples -----------------------> $ 9
1 bushel of apples -------------------------------> x
From here the value of x is cleared, resulting in:
[tex]x =\frac{(1)(9)}{\frac{3}{4} } \\\\x = 12\\[/tex]
store 2:2/3 of a bushel of apples -----------------------> $ 9
1 bushel of apples -------------------------------> x
From here the value of x is cleared, resulting in:
[tex]x = \frac{(1)(9)}{\frac{2}{3} }\\\\x = 13.50 \\[/tex]
Therefore it is convenient to buy apples in store 1 because it is cheaper.
Answer:
It is convenient to buy apples in store 1 because it is cheaper. A division must be made for each case because you want to find the unit cost of a product having the total cost and the amount in fraction.
Cynthia, Annie, and Suz went to Pepe's Pizza Palace for dinner after band practice. They shared a large pizza and each girl ordered a soda. When the bill came, they talked about how to split it up fairly. "Annie, you had three slices and a medium soda so you should pay one-third of the bill," said Suz. "Well, I'll chip in a dollar more than that," replied Annie. "And since you only had two slices and also ordered a small soda, you should only pay 20% of the bill." "That seems fair," said Cynthia. "I ate three slices and had a large soda, so I should pay the most. I'll pay the remaining $8.80." How much was the total bill for the pizza and the three sodas, and how much did each girl pay?
Final answer:
The total bill at Pepe's Pizza Palace was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid the remaining $8.80.
Explanation:
To determine the total bill and how much each girl paid, we first acknowledge that Cynthia has stated she would pay the remaining $8.80. This gives us a starting point to figure out the portions of the bill that Annie and Suz will pay.
Suz suggests that Annie pays one-third of the bill and offers to pay $1 more than that amount. Suz is to pay 20% of the bill. If Cynthia pays the remaining amount, let's denote the total bill as B.
Using the information given:
Annie pays one-third of the bill plus $1: (1/3)B + $1
Suz pays 20% of the bill: 0.20B
Cynthia pays the remaining $8.80.
Add these up to get the total bill.
(1/3)B + $1 + 0.20B + $8.80 = B
Solving this equation:
0.33B + 0.20B + $8.80 - $1 = B - $1
0.53B + $7.80 = B
B - 0.53B = $7.80
0.47B = $7.80
Dividing both sides by 0.47:
B = 7.80 / 0.47
B = $16.60 (rounding to two decimal places)
Therefore, the total bill amounts to $16.60. Now to find out how much each girl pays:
Annie's portion:
(1/3)*16.60 + $1 = $5.53 + $1 = $6.53
Suz's portion:
0.20*16.60 = $3.32
Cynthia's portion is the amount she agreed to pay:
$8.80
To summarize, the total bill was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid $8.80.
A motorboat traveling a distance of 120 miles in 2 hours while traveling with the current. Against the current, the same trip took 3 hours. Find the rate of the boat in calm water and the rate of the current. Rate of boat in mph and rate of current in mph
1. The rate of the boat in calm water is 50 miles per hour.
2. The rate of the current is 10 miles per hour.
How the rates are determined:
Let:
[tex]r_b[/tex] be the rate of the boat in calm water (in miles per hour).
[tex]r_c[/tex] be the rate of the current (in miles per hour).
Given:
With the current:
Distance: 120 miles
Time: 2 hours
Speed: [tex]r_b + r_c[/tex] (since the current aids the boat)
So, the equation is:
[tex]r_b + r_c = \frac{120}{2}[/tex] = 60 (Equation 1)
Against the current:
Distance: 120 miles
Time: 3 hours
Speed: [tex]r_b - r_c[/tex] (since the current opposes the boat)
So, the equation is:
[tex]r_b - r_c = \frac{120}{3}[/tex] = 40 (Equation 2)
Step 1: Solve the System of Equations
We have the system:
[tex]r_b + r_c = 60[/tex] (Equation 1)
[tex]r_b - r_c = 40[/tex] (Equation 2)
Step 2: Add the Two Equations
Adding Equation 1 and Equation 2:
[tex]r_b + r_c + r_b - r_c[/tex] = 60 +40
[tex]2r_b[/tex] = 100
[tex]r_b = 50[/tex] (Rate of the boat in calm water)
Step 3: Substitute [tex]r_b[/tex] into one of the Equations
Substitute [tex]r_b[/tex] =50 into Equation 1:
50+[tex]r_c[/tex] = 60
[tex]r_c[/tex] = 10 (Rate of the current)
Please help! Polygon ABCDE rotates 45° clockwise about point F to form polygon FGHIJ, shown in the figure. Find the measure of each angle of polygon ABCDE.
Polygon FGHIJ is the result of the rotation of ABCDE.
A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°
The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°
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Answer:
m∠ABC = 117 °
m∠BCD = 90 °
m∠DEA = 90°
m∠CDE = 127°
Step-by-step explanation:
Since this is a series of rigind transformations, the angles of the figure do not change, so:
A=F= 117°
B=G=117°
C=H=90°
D=I=127
E=J=90°
Write the equation in standard form: 3x-1=2y?
A.3x+2y=1
B.3x-2y=1
C. 3x+2y=-1
D. 3x-2y=-1
Standard form: Ax + By = C
So 3x - 1 = 2y
3x - 2y = 1
Answer
B. 3x - 2y = 1
The standard form of the equation is 3x-2y=1, the correct option is B.
What is the standard form of the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line.
The standard form of linear equation is;
[tex]\rm ax+by=c[/tex]
Given
The linear equation is;
3x - 1 = 2y
The equation can be expressed in the standard form
[tex]\rm 3x - 1 = 2y\\\\ 3x -1 -2y=0\\\\3x-2y=0+1\\\\3x-2y=1[/tex]
Hence, the standard form of the equation is 3x-2y=1.
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Find the measure of ∠FEG.
1. 25°
2. 65°
3. 80°
4. 90°
The correct answer is 65 degrees.
HELP ME PLEASE ASAP!!
Which is the solution to the equation -3x-4=5(x+4)
Step 1. Expand
-3x - 4 = 5x + 20
Step 2. Add 3x to both sides
-4 = 5x + 20 + 3x
Step 3. Simplify 5x + 20 + 3x to 8x + 20
-4 = 8x + 20
Step 4. Subtract 20 from both sides
-4 - 20 = 8x
Step 5. Simplify -4 - 20 to -24
-24 = 8x
Step 6. Divide both sides by 8
-24/8 = x
Step 7. Simplify 24/8 to 3
-3 = x
Step 8. Switch sides
x = -3
If two large single-topping pizzas cost $25.00, how much will 9 pizzas cost?
Answer:
$112.50
Step-by-step explanation:
You take 25 + 25 +25 +25 = 100
that equals 8 pizzas
half of 25 is 12.5
so for one pizza it is $12.50
100 + 12.5 = 112.50
What is 20/7 as a mixed number in simplest form?
Answer:
2 6/7
Sorry if I'm wrong.
Graded Assignment
Unit 2 End of Unit 2 Assignment: Adding and Subtracting Rational Numbers
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 4 points)
1. Use both methods to find the distance between the points on the number line.
Method A: Count the number of units between the points.
Method B: Take the absolute value of the difference of the two numbers.
When taking the absolute value, show the larger number first, then show the lesser number first when finding the difference.
Answer:
A.
B.
(Score for Question 2: ___ of 5 points)
2. The table shows several animals that live in or below a tree. The table also shows the elevation of their dwellings, relative to ground level.
Dwellings Elevation (m)
Groundhog burrow -1.2
Red squirrel den 0.3
Robin’s nest 3.6
(a) Plot and label the elevation of each dwelling on a vertical number line.
(b) Calculate the vertical distance between each pair of dwellings. Organize your results in a table.
Answer:
a) Plot and label the elevation of each dwelling on a vertical number line. (2 pts)
b) Calculate the vertical distance between each pair of dwellings. (3 pts)
Groundhog burrow to Red squirrel den
Red squirrel den to Robin’s nest
Groundhog burrow to Robin’s nest
(Score for Question 3: ___ of 6 points)
3. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar.
(a) How many total cups of ingredients are there? Find a common denominator and then show your work using a number line.
(b) Which of the following mixing bowls should you use to make the recipe: 2-cup, 3-cup, or 4-cup? Explain why you choose this mixing bowl.
Answer:
a) How many total cups of ingredients are there? Find a common denominator and then show your work using a number line. (4 pts)
b) Which of the following mixing bowls should you use to make the recipe: 2-cup, 3-cup, or 4-cup? Explain why you choose this mixing bowl. (2 pts)
Answer:
Okay Im going off of my work because we did some in class and then the rest by ourselves but i turned mine in yesterday but didnt recieve a grade yet but i hope these help you...
The number number line it is seven units apart.
The absolute value larger number smaller number would be 2 - (-5). So what you do with that is keep the 2 change the subtraction sign to plus sign and change the negative 5 to positive 5. So your answer would be 7.
And smaller number to larger number would be -5 - 2. And then you do the same steps as the last one. Keep the negative five, change the subtraction sign to addition sign and make the two negative. And that answer would be -7
2. For the number two problem you would plot the robins nest just below the top of the verticle line. the red squirrel den would be right next to the zero but a tad up. And the groundhog burrow would be below the zero mark and a little before the end of the verticle line.
Next, for groundhog burrow to red squirrel den you put the number 0.3-(-1.2)=1.5 Red squirrel den to Robin’s nest 3.6 – 0.3 = 3.3. And for the last one Groundhog burrow to Robin’s nest 3.6 – (-1.2) = 4.8.
3. you have to turn the 1 1/2 and 3/4 into 8ths. 1/2= 3*4 = 12 and for the denominator 2*4 = 8. So 12/8.
The next one is 3*2 which is 6 and 4*2=8
so now you have 12/8, 6/8, and 1/8
you have to add the points on the chart (i cant really help you on this part because i do not know how to upload picture) but you would make 24 and then you find where 12/8 would go and draw the hops but on mine the hop looks like how you would draw a rainbow but just one for the 12. Then do the same for the 6 and add 1 for the last one to make 19.
On mine I add the 12 + 6 + 1 = 19 so that is how i got mine. (sry if this a bad explination)
it should kinda look like this on the chart.
| | | | | | | | | | | | | | | | | | | | | | | | they should be spaced apart like this.
and for the last one i put cup 3 because it bigger than the amount of ingrident in the recipe. (im not sure if that one was the answer this is the only part we didnt get help on in class)