The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
Given that
A 4 cm bean plant grows at a rate of 1/2cm per week.
A 5.5 cm flower grows at a rate of 1/4cm per week.
If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
According to the question
The solution of the system of equation is;
h = 1/2t + 4
h = 1/4t + 5.5
Substitute the value of h from equation 1 in equation 2
[tex]\rm h = \dfrac{1}{4}+5.5\\\\\dfrac{1}{2}t +4 = \dfrac{1}{4}t +5.5\\\\\dfrac{1}{2}t-\dfrac{1}{4}t = 5.5-4\\\\\dfrac{2t-t}{4} = 1.5\\\\\dfrac{t}{4} = 1.5\\\\t = 4\times 1.5\\\\t = 6[/tex]
Substitute the value of t in equation 1
[tex]\rm h = \dfrac{1}{2}\times 6+4\\\\h = 3+4\\\\h = 7[/tex]
Hence, The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
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2. Alice Hall, who loves to cook, makes an apple cake (serves 6) for her family. The recipe calls for 2 1/2 pounds of apples, 2 1/4 cups of flour, 1/5 cup of margarine, 1 1/4 cups of sugar and 4 eggs. Since guests are coming, she would like to make this cake so it will serve 24. How many pounds of apples should she use?
...?
Answer:
10 pounds
Step-by-step explanation:
We are given that Alice hall makes an apple cake (serves 6) for her family
Apples=[tex]2\frac{1}{2}=\frac{5}{2}[/tex]pounds
Flour=[tex]2\frac{1}{4}=\frac{9}{4}[/tex] cups
Margarine=[tex]\frac{1}{4}[/tex] cups
Sugar=[tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups
Eggs=4
For 6 persons , apples required =[tex]\frac{5}{2}[/tex] pounds
For 24 persons=[tex]\frac{\frac{5}{2}}{6}\times 24[/tex]
For 24 persons=[tex]\frac{5}{12}\times 24=10[/tex] pounds
Hence, she should use 10 pounds of apples.
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.
f(x) = - 3x + 45
f(x) = 3x + 45
f(x) = - 3x + 60
f(x) = 3x + 60
The correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
To find the linear equation representing the amount of trash removed each week, we need to determine the slope and the y-intercept.
Given:
- In week 5, there were 45 dumpster loads.
- In week 10, there were 30 dumpster loads.
Step 1: Calculate the Slope
The slope m of a line is calculated by:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Here,[tex]\((x_1, y_1) = (5, 45)\) and \((x_2, y_2) = (10, 30)\).[/tex]
[tex]\[m = \frac{30 - 45}{10 - 5} = \frac{-15}{5} = -3\][/tex]
Step 2: Write the Equation in Point-Slope Form
Using the point-slope form of the equation [tex]\( y - y_1 = m(x - x_1) \):[/tex]
[tex]\[y - 45 = -3(x - 5)\][/tex]
Step 3: Convert to Slope-Intercept Form [tex]( \( y = mx + b \) )[/tex]
Simplify the equation:
[tex]\[y - 45 = -3(x - 5)\][/tex]
[tex]\[y - 45 = -3x + 15\]\[y = -3x + 15 + 45\]\[y = -3x + 60\][/tex]
Thus, the equation in function form that shows the amount of trash removed each week is:
[tex]\[f(x) = -3x + 60\][/tex]
Therefore, the correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
solve for x. 27^(2x)=9^(x-3) ...?
**PLEASE HELP??? ****STUCK ON THIS!!!!
Suppose that f(w) varies inversely with w and f(w) = 0.75 when w= 8.
What is f(w) when w= 2?
A.) 12
B.) 6
C.) 3
D.) 1.5
My answer choice is C.) 3. I'm not very confident in my answer so..... :/
Answer:
C.3
Step-by-step explanation:
We are given that
f(w) varies inversely with w.
f(w)=0.75 when w=8
We have to find the value of f(w) when w=2
According to question
[tex]f(w)\propto\frac{1}{w}[/tex]
[tex]f(w)=\frac{k}{w}[/tex]
Where k=proportionality constant
Substitute the given values then, we get
[tex]0.75=\frac{k}{8}[/tex]
[tex]k=0.75\times 8[/tex]
[tex]k=6[/tex]
Substitute the value of k then, we get
[tex]f(w)=\frac{6}{w}[/tex]
Substitute the value of w=2
Then, we get
[tex]f(w)=\frac{6}{2}=3[/tex]
[tex]f(w)=3[/tex]
Hence, option C is true.
What is is the answer for g-9=-19?
You purchase a home for $125,000. The value of the property increases by 1.9% every year. After ten years, you decide to sell the home. In the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. How much will you sell the house for, to the nearest hundred dollars?
We can use the formula:
F = P · ( 1 + i )^n
where: P = $125,000, i = 0.019 ( 1.9 %), n = 10
F = $125,000 · ( 1 + 0.019 )^10
F = $125,000 · 1.019^10
F = $125,000 · 1.207096
F = $150,887
And we have to add $48,3000 ( for renovations and improvements )
$150,887 + $48,300 = $199,187 ≈ $199,200
Answer: You will be sell the house for $199,200.
Answer:
$199,200
Step-by-step explanation:
Which of these can be a result of inflation?
Businesses grow cautious about spending
The government has to cut spending
The price of household items increases
Workers benefit from a lower cost of living
The price of household items increases is a result of inflation, option C is correct.
Inflation typically leads to a general rise in prices across the economy.
As the value of money decreases, it takes more money to purchase the same goods and services.
Therefore, the prices of household items, along with other consumer goods, tend to increase during periods of inflation.
However, it's important to note that inflation does not affect all goods and services uniformly.
Some prices may rise more rapidly than others, leading to changes in relative prices.
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How much of the circle is shaded? Write your answer with as a simplified fraction, with an explanation. Thank you.
How do you use the half angle formula for
sin (5π/12)?
To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.
Explanation:The half angle formula for sine is given by:
Sin(x/2) = ±√{(1 - cos x) / 2}
To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.
Step 1: Substitute cos x value (-√3/2) into the formula:
Sin(5π/12) = √{(1 - (-√3/2 )) / 2}
Step 2: Simplify the expression inside the square root:
Sin(5π/12) = √{(1 + √3 / 2) / 2}
Step 3: Calculate the square root:
Sin(5π/12) = ± √{3 + √3 / 4}
Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:
Sin(5π/12) = √{3 + √3 / 4}
So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.
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Choose the words or phrases that best complete the sentences.
A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.
Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK
What is the equation in point slope form of the line that passes through the point (1, –2) and has a slope of 3?
y−2=3(x+1)
y+2=3(x−1)
y+1=3(x−2)
y−1=3(x+2)
which of the following comparisons is false 4 liters< 1 gallon, 1 foot< 1 meter, 25 grams< 1 ounce, 10 kilometer< 9 miles
HELP ASAP!!!
The markup on candy at the discount store is 45%. A bag of candy has a wholesale cost of $1.15. What will be the retail price for the candy?
A. $1.45
B. $1.60
C. $1.67
D. $1.78
Answer:
Option C. $1.67
Step-by-step explanation:
The price of a bag of candy at wholesale = $1.15
The markup on candy at the discount store = 45%
The retail price for the candy = 1.15 +(45% × 1.15)
= 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)
= 1.15 + (0.45 × 1.15)
= 1.15 + 0.5175
= 1.6675 ≈ $1.67
The retail price for the candy would be $1.67.
A bedroom set lists for $12,000 and carries a trade discount of 30 percent. Freight (FOB shipping point) of $150 is not part of list price. Calculate the delivered price of the bedroom set including the freight. Assume a cash discount of 2 percent:
Which of the expressions are not polynomials? Check all that apply.
A. 8x^10 + 2x^5
B. 5x^-1 + 4x^-2
C. x^5 + 2
D. 5x^5
E. x2 +(square root of x) + 4
F. x^2-(square root of x ) -3 ...?
What is the vertex of the parabola defined by the equation(x − 2)^2 = -12(y − 2)?
Witch Decimal is equal to six-tenths?
0.6 0.15 0.2 0.3 0.4
Which is the most accurate name for the polygon shown?
concave pentagon
convex pentagon
concave hexagon
convex hexagon
help with secx/sinx-sinx/cosx
Which of the following has a graph that is a straight line?
Equation 1: y = 2x + 7
Equation 2: y2 = x − 1
Equation 3: y = 2x2 + 4
Equation 4: y = 3x3
Use implicit differentiation to find dy/dx.
ln xy + 5x = 30. Please write out the steps.
Final answer:
To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x. Then apply the chain rule and simplify.
Explanation:
To find dy/dx using implicit differentiation, we first differentiate both sides of the equation with respect to x. Let's go through the steps:
ln(xy) + 5x = 30Differentiate both sides with respect to x:d/dx[ln(xy) + 5x] = d/dx[30]Apply the chain rule to differentiate ln(xy):(1/xy) * (x(dy/dx) + y) + 5 = 0Simplify the equation:x(dy/dx) + y + 5xy(dy/dx) = 0Collect terms with dy/dx:dy/dx = -(y + 5xy)/(x + 5xy)
Find the value of 3x + 2 when 7+ x = 5
Integrate (2 ln x)/x ...?
A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.
They start at x=0 hours with y=30 gal of paint;They end at x=10 hours with y=0 gal of paint (they worked until they used all the paint).The dependence between x and y is linear.Conclusion: the only possible sketch is A.
Answer: correct choice is A.
9/5 times c plus 32 how do solve this
Answer:
9/5×c+32 I.e.
if it is equal to 0 then
c=-32 ×5/9
c = -160/9
Step-by-step explanation:
10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have diameters of 8 inches, 10 inches and 12 inches. Small Medium Large a) What is the circumference of each size of pizza? Small = _________________ Medium = ___________________ b) What is the area of each size of pizza? Small = _________________ Medium = _________________ Large = _______________ Large = _________________ c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of pizza should he order? Why?
Answer:
Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.
The percentage decrease is 0.05%
Step-by-step explanation:
Number of pizzas sold yesterday is 65 pizzas.
The owner offers the employees a bonus if the number of pizzas sold increases by 20%
So 20% of 65 pizzas is, pizzas.
Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.
But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,
Therefore, the percentage decrease
The altitude dropped to the base of an isosceles triangle is a median, an angle-bisector, and a perpendicular bisector?
True
False ...?
To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answer:
True
Step-by-step explanation:
Identify the factors of x2 + 25y2. ...?
Answer:
(x-5y)^2 or (x-5y)(x-5y).
Step-by-step explanation:
hope this helps have a nice day! :D
Final answer:
To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.
Explanation:
The factors of x² + 25y² are (x + 5yi)(x - 5yi).
To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²
By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.