Answer:
one Bush costs $19 and one geranium costs $6
Step-by-step explanation:
Let the cost of one Bush be x
Let the cost of one geranium be y
If Heather spent $50 on 2 rose bushes and 3 geraniums, then the equation that represent the statement is:
2x+3y = 50….... 1
If amanda spent $186 on 6 rose bushes and 12 geraniums, then the equation representation will be:
6x+12y = 186…......2
Solve equations 1 and 2 simultaneously
2x+3y = 56..... 1 × 3
6x+12y = 186 ..... 2 × 1
.......…............
6x+9y = 168
6x+12y = 186
Subtract
9y - 12y = 168-186
-3y = -18
y = -18/-3
y = 6
Substitute y = 6 into equation 1:
2x+3y = 56
2x+3(6) = 56
2x+18 = 56
2x = 56-18
2x = 38
x = 38/2
x = 19
Hence one Bush costs $19 and one geranium costs $6
NB: note that the y rose bushes in the question was corrected and 6 rose bushes was used instead in the equation.
A farmer builds a fenced-in, rectangular pen for goats to clear brush from a section of land. The
pen has three sides of fencing because the width of the pen sits against the side of a barn.
If the farmer has 180 feet of fencing, what dimensions maximize the area of the pen?
a. 40 ft by 100 ft
b. 45 ft by 45 ft
c. 45 ft by 90 ft
d. 50 ft by 65ft
The dimension that maximize the are of the pen is 45 ft by 90 ft.
Area of a rectanglearea = lw
where
l = length
w= width
Therefore,
perimeter of a rectangle = 2(l + w)
The barn is occupying one part of the rectangle . Therefore,
perimeter = 2l + w
180 = 2l + w
w = 180 - 2l
area = lw
Therefore,
area = l(180 - 2l)
area = 180l - 2l²
To maximize area
l = -b / 2a
l = - (180) / 2 × -2
l = -180 / -4
l = 45 ft
Therefore,
w = 180 - 2(45)
w = 180 - 90
w = 90 ft
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Katy invests £14 000 in a savings account for 3 years.
The account pays simple interest at a rate of 1.5% per annum.
Calculate the amount in her savings account Katy will get at the end of the 3 years
Simple interest formula:
Total = start x ( 1 + rate x time )
Total = 14,000 x ( 1 + (0.015 x3))
Total = 14,000 x 1.045
Total = 14,630
Answer:
£14,630
Step-by-step explanation:
Simple interest formula: A = P(1 + rt)
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)t = time (in years)Given:
P = £14,000r = 1.5% = 0.015t = 3 years⇒ A = 14000(1 + 0.015 · 3)
⇒ A = 14000(1.045)
⇒ A = £14,630
Prove this equation
I'll give brianliest!!
[tex](\frac{1}{sin\alpha } -sin\alpha )(\frac{1}{cos\alpha } -cos\alpha )=cos\alpha *sin\alpha \\\\\\(\frac{1}{sin\alpha } -\frac{(sin\alpha)^2}{sin\alpha} )(\frac{1}{cos\alpha } -\frac{(cos\alpha)^2}{cos\alpha } )=cos\alpha *sin\alpha \\\\\\(\frac{1-(sin\alpha )^2}{sin\alpha } )(\frac{1-(cos\alpha)^2 }{cos\alpha } ) = cos\alpha *sin\alpha\\\\\\(\frac{(cos\alpha)^2 }{sin\alpha } )(\frac{(sin\alpha )^2}{cos\alpha } )=cos\alpha *sin\alpha\\\\\\cos\alpha *sin\alpha = cos\alpha *sin\alpha[/tex]
Identities used
[tex](sin\alpha )^2+(cos\alpha)^2=1[/tex]the second to last step to the last step was just a matter of simplificationHope it helped!
p.s. If you can give me a brainly, it would help a lot since the formatting of these equations were a lot of work
how many milliliters are equivalent to 7.3 liters
drag each tile to the correct box not all tiles will be used. consider the expression
3x+6 2x
-------- + ----------
x²- x- 6 x²+ x- 12
please help
Answer:
7->6->1->5->3
Step-by-step explanation:
The answer us 7->6->1->5->3.
A gym charges a membership fee of $10 per month plus a $100 application fee. Which equation best models the total cost for a gym membership for x months?
Answer:
10(m)+100
Step-by-step explanation:
$10 is multiplied by m becuase that price depends on how many months you want the memberhsip, plus the $100 for applying.
I hope I helped <33
A population of 75 foxes in a wildlife preserve triples in size every 13 years. the function y equals 75 times 3 superscript x , where x is the number of 13 -year periods, models the population growth. how many foxes will there be after 39 years?
Answer:
675 Foxes
Step-by-step explanation:
y=75*3x
39/13=3
y=75*3*3
y=75*9
y=675
In ΔRST, r = 690 cm, s = 410 cm and ∠T=64°. Find the area of ΔRST, to the nearest square centimeter
The area of the triangle RST is the amount of space on the triangle RST
The area of the triangle RST is 127135 square cm
How to determine the area?The given parameters are:
r = 690 cm, s = 410 cm and ∠T=64°.
Using the sine function, the area of ΔRST is calculated as:
[tex]A = 0.5rs\sin(T)[/tex]
Subsitute known values
A = 0.5 * 690 * 410 * sin(64 degrees)
Evaluate the sine ratio
A = 0.5 * 690 * 410 * 0.8988
Evaluate the product
A = 127135.26
Approximate
A = 127135
Hence, the area of the triangle RST is 127135 square cm
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Talhah drove 45 miles in 1 hour. At this rate, how many miles will he drive in 4 hours?
Answer:
He will drive 180 miles in 4 hours. ( I think)
Step-by-step explanation:
If he keeps going at his rate which is 45 mph then if you multiply that by 4 then your answer should just be 180 miles.
Answer:
180 miles
Step-by-step explanation:
so he goes 45 miles per hour
since you need to find 4 hours just multiply 45 by 4
45 x 4 = 180
there's your answer
Enter a numerical expression that represents the sum of four squared and thirty three
Answer:
33+4^2
Step-by-step explanation:
Expression: Does not require an equal sign.
Sum: addition of
four squared: 4^2
thirty three: 33
The correct numerical expression that represents the sum of four squared and thirty three is,
⇒ 4² + 33
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
''the sum of four squared and thirty three''
Now, We get;
The correct numerical expression that represents the sum of four squared and thirty three is,
⇒ 4² + 33
Thus, The correct numerical expression that represents the sum of four squared and thirty three is,
⇒ 4² + 33
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A year’s subscription of Salmon Snax costs $172.80. California sales tax is 7.25% and Colorado’s is 2.9%. How much less does a customer in Colorado pay than a customer in California?
11 find the measure of the interior angle.
12 and 15 find the measure of the exterior angle.
answer fast for brainliest!!! What key words would tell you it's a two step problem? (SELECT ALL)
Question 2 options:
Total Bill
Amount of Savings
Sale Price
Final Cost
Price with Tax
Discount
Commission
Answer:
Final Cost, Price with tax, and Discount.
Step-by-step explanation:
Explain how to estimate the length of an object.
Answer:
To measure the length of an object, choose the correct tool for measuring it, like a ruler for small, flat items, or a measuring tape for items with curves. Then, line up the zero mark on your measuring tool with one end of the object.
The table shows the average cost of gasoline in the United States in dollars per gallon for the given years.
Year 1995 1996 2000 2001 2005 2006 2010 2011 2013 2014
Price per gallon ($) 1.13 1.14 1.33 1.49 1.88 2.36 2.77 3.15 3.39 3.40
(a) Write the least squares regression equation that models the data. Let x = time in years since 1995 and let y = price per gallon.
(b) Use the equation to estimate the price per gallon in 2030. Show your work.
From the given table, the year values, and prices, we have the following
equation and values;
(a) The least squares regression equation is; y ≈ 0.1316·x - 261.73
(b) The estimate of the price per gallon in 2030 is approximately $5.418
How can the equation and price be obtained from the table?(a) The coefficients of the least squares regression formula are
presented as follows;
[tex]a = \mathbf{\overline y - b \cdot \overline x}[/tex]
[tex]b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]
Entering the given values in MS Excel, we have;
[tex]\overline x[/tex] = 2005.1
[tex]\overline y[/tex] = 2.204
[tex]b = \dfrac{56.456 }{428.9} \approx 0.1316[/tex]
a = 2.204 - 0.1316 × 2005.1 ≈ -261.73
The least squares regression equation is therefore;
[tex]\underline{y =0.1316\cdot x - 261.73}[/tex](b) In the year 2030, we have;
The price, y ≈ 0.1316 × 2030 - 261.73 = 5.418
In the year 2030, the price per gallon will be approximately $5.418
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1/3 of the people in a club are men.The number of men in the club is n.Write down an exprssion,in terms of n, for the number of people in the club.
Answer: The answer is where the n is the number of people in the club
Step-by-step explanation:
A)Write down an expression, in terms of n, for the number of people in the club.
B) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.
What is the measure of Angle WZY?
5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12
The temperature of a hot iron rod drops by 8° every hour. If the temperature of the iron rod is 118°, find the temperature after 4 hours.
118 - 4 x 8 = 118 - 32 = 86°
help me with this please
Which table most likely relates the height, h(t), in meters, over time, t, in seconds, of a ball dropped from above ground level that hits the ground sometime between 4 and 6 seconds after it is dropped? A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 70, 50. 4, negative 8. 4, negative 106. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 100, 80. 4, 21. 6, negative 76. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries negative 150, negative 130. 4, negative 71. 6, 26. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 180, 160. 4, 101. 6, 3. 6.
The table which most likely relates the height h(t), in meters, over time, t, in seconds is: Option D:
t (in seconds) h(t) (in meters) 0 180 2 160.4 4 101.6 6 3.6What are the values the height function can achieve if the object is always above the ground?If the height function is function of time 't', and the object's height is measured from the ground level and object never goes inside ground, then that means height can never be negative. It will always assume non-negative values.
What are equations of motion?There are three equations of motion that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where the symbols have following meanings:
u = initial velocity of the considered objectv = final velocity of the objecta = acceleration of the objects = distance traveled by the object in 't' time.All the tables given except the last table have negative height values. That shows that if those negative valued tables are true, then the ball went inside ground.
Since no such event of ball going inside the ground is specified in the considered situation, thus, only the last table is valid here in terms of sign of height.
The last table is:
t (in seconds) h(t) (in meters)
0 180
2 160.4
4 101.6
6 3.6
Checking the truthfulness of the last table by using law of motion in straight path:
u = initial velocity of ball = 0
a = gravitational acceleration = -g ≈ -9.8 m/s sq.
Now, height of ball at time t = initial height of ball - distance it traveled from starting point in direction of reaching ground.
Thus, h(t) = 180 - |s| (assuming first value is true in the table)
where |s| = non-negative value of s
[tex]s= ut + (1/2)at^2\\s = 0t + (1/2)(-9.8)t^2\\\\|s| = 4.9t^2 \: \rm m/s^2[/tex]
Thus, h(t) = 180 - 5t² m/s sq.
[tex]h(2) = 180 - 4.9(2)^2 = 160.4\\h(4) = 180 - 4.9(4)^2 = 101.6\\h(6) = 180 - 4.9(6)^2 = 3.6\\[/tex]
Thus, the table which most likely relates the height h(t), in meters, over time, t, in seconds is: Option D:
t (in seconds) h(t) (in meters) 0 180 2 160.4 4 101.6 6 3.6Learn more about equations of motion here:
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Complete the following multiplication exercises.
43 × 7 =
12 × 9 =
10 × 6 =
9 × 7 =
7 × 5 =
6 × 3 =
0 × 8 =
30 × 3 =
11 × 8 =
73 × 2 =
83 × 5 =
16 × 8 =
392 × 7 =
29 × 4 =
761 × 9 =
4,829 × 6 =
12 × 7 =
25,500 × 4 =
43 × 7 = 301
12 × 9 = 108
10 × 6 = 50
9 × 7 = 63
7 × 5 =35
6 × 3 = 18
0 × 8 = 0
30 × 3 =9
11 × 8 =88
73 × 2 =146
83 × 5 = 166
16 × 8 = 128
392 × 7 =2,744
29 × 4 = 116
761 × 9 = 6,849
4,829 × 6 = 28974
12 × 7 = 84
25,500 × 4 =102,000
HELP!! Rashida had 18 correct answers and 12 incorrect answers. What was Rashida's score? Each correct answer is worth 2 1/4 points, and each incorrect answer is worth -1/2 point.
Number of incorrect answers Rashida got = 12
Number of correct answers Rashida got = 18
Given :-
Points for each correct answer =
[tex] = 2 \frac{1}{4} [/tex]
Points for each incorrect answer =
[tex] = \frac{ - 1}{ \: \: \: 2} [/tex]
Points Rashida will get for her correct answers :-
[tex] = 2 \frac{1}{4} \times 18[/tex]
[tex] = \frac{(4 \times 2+ 1)}{4} \times 18[/tex]
[tex] = \frac{9}{4} \times 18[/tex]
[tex] = \frac{162}{4} [/tex]
[tex] = 40.5 \: points[/tex]
Points Rashida will get for her incorrect answer :-
[tex] = \frac{ - 1}{ \: \: \:2} \times 12[/tex]
[tex] = \frac{ - 12}{ \: \: \: \: \: 2} [/tex]
[tex] = - 6 \: points[/tex]
So , Rashida gets 40.5 points for her correct answer and -6 points for her incorrect answer .
Rashida's total score :-
[tex] = 40.5 + ( - 6)[/tex]
[tex] = 34.5 \: points[/tex]
Therefore , Rashida gets 34.5 points as her total score .
The overall score of Rashida will be 34.5 for the given exam.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
Number of correct answers = 18
Points of correct answer = 2 1/4 = 9/4
Scores of correct answer = 18 × 9/4 = 40.5
Number of incorrect answers = 18
Scores of incorrect answer = 12 × (-1/2) = -6
Total score = 40.5 - 6 = 34.5
Hence "The overall score of Rashida will be 34.5 for the given exam".
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Which choices contain equivalent statements? Check all that apply.
Answer:
A C and E
Step-by-step explanation:
Edge
The choices that contain equivalent statements are:
a) ln 3x = 6 → 3x = e⁶
c) log 4x = 8 → 4x = 10⁸
e) 5.6554 = 10ˣ → log 5.6554 = x
To determine which choices contain equivalent statements, let's analyze each option one by one:
a) ln 3x = 6 → 3x = e⁶
This statement is true. It represents the inverse relationship between the natural logarithm (ln) and the exponential function with base e. Taking the exponential of both sides of the equation allows us to isolate the variable.
b) log 3x = 9 → 9x = 10³
This statement is not true. It seems to confuse the base of the logarithm. If the logarithm is not specified with a base, it is usually assumed to be base 10 (log base 10). In this case, the correct equivalent statement would be 3x = 10⁹.
c) log 4x = 8 → 4x = 10⁸
This statement is true. Similar to the previous option, assuming a base 10 logarithm (log base 10), the equivalent statement would be 4x = 10⁸.
d) 0.577 = e⁵ˣ → ln 5 = x / 0.577
This statement is not true. The equation given at the beginning, 0.577 = e⁵ˣ, cannot be transformed into the second equation using the properties of logarithms or exponentials. The two statements are unrelated.
e) 5.6554 = 10ˣ → log 5.6554 = x
This statement is true. It correctly represents the relationship between the logarithm and exponential functions. By taking the logarithm (base 10) of both sides of the equation, we can solve for x.
In summary, the choices that contain equivalent statements are:
a) ln 3x = 6 → 3x = e⁶
c) log 4x = 8 → 4x = 10⁸
e) 5.6554 = 10ˣ → log 5.6554 = x
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James won the grand prize on a game show and decided that he would pick the following plan. On day 1 he will
get paid one penny, on day 2 he will get paid 2 pennies and on day 3 he will get paid 4 pennies. Assuming this
trend continues how much will he get paid on the 28th day?
Answer:
$134217728
Step-by-step explanation:
Day 1: $1
Day 2: $2
Day 3: $4
Day 4: $8
Day 5: $16
Day 6: $32
Day 7: $64
Day 8: $128
Day 9: $256
Day 10: $512
Day 11: $1024
Day 12: $2048
Day 13: $4096
Day 14: $8192
Day 15: $16384
Day 16: $32768
Day 17: $65536
Day 18: $131072
Day 19: $262144
Day 20: $524288
Day 21: $1048576
Day 22: $2097152
Day 23: $4194304
Day 24: $8388608
Day 25: $16777216
Day 26: $33554432
Day 27: $67108864
Day 28: $134217728
Jillian was asked to translate the expression 9 n into words. She wrote "a number increased by nine. " Which best describes the accuracy of Jillian’s answer? It is incorrect. The variable would come first in the expression "a number" (n) "increased by" ( ) "nine" (9). It is incorrect. The phrase "increased by" refers to the inequality symbol "greater than" (>), not addition. It is correct. A number increased by nine (n 9) is the same as nine increased by a number (9 n). It is incorrect. A number increased by nine refers to a multiplication expression (n times 9).
A number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.
What is the pharse in mathematics?
A mathematical phrase is a set of words or a combination of words and numbers that can be written as a mathematical expression.
Given
Jillian was asked to translate the expression 9 + n into words.
She wrote "a number increased by nine.
The expresion can be written into the two formate which is;
(n+9) and (9+n)
Hence, a number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.
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draw a graph of f(x) =(x-5)^2 by shifting rule
[tex] \tt \tiny \gray{thanks}[/tex]
A 20% apple juice drink is mixed with a 100% apple juice drink. The function f(x)=(2)(1.0)+x(0.2)2+x models the concentration of apple juice in the drink after x gallons of the 20% drink are added to 2 gallons of pure juice. What will be the concentration of apple juice in the drink if 6 gallons of 20% drink are added? Give the answer as a percent but do not include the percent sign (%).
Answer: 40
Step-by-step explanation:
The concentration of pineapple when 2 gallons of pineapple juice are added to 6 gallons of the other juice is; 8.24
What are Functions?The function is a type of relation, or rule, that maps one input to a specific single output.
Given that the functions that model the concentration of apple juice in the drink after x gallons of the 20% drink are added to 2 gallons of pure juice.
f(x)=(2)(1.0)+x(0.2)²+x
If the concentration of apple when 2 gallons of apple juice are added to 6 gallons of the other juice;
f(6) = (2)(1.0)+ 6(0.2)²+ 6
f(6) = 2.0 + 6.24
f(6) = 8.24
Hence the concentration of pineapple when 2 gallons of pineapple juice are added to 6 gallons of the other juice is; 8.24
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A scale drawing for a backyard is shown below. In the drawing, 3 cm represents 4 m. Assuming the patio is rectangular, find the area of the real patio. 18 cm 9 cm Patio 3 cm Lawn → 3 cm
Answer:
288m^2
Step-by-step explanation:
ratio is 4000/3, though the thousand does not matter because we can just exchange units
18*4/3=24
24 meters
9*4/3=12
12 meters
24*12=288
Find the slope between the two points given. Then, use the slope and the first point to write the equation of the line in Point-Slope form. State the slope. Point One: (−4,5) Point Two: (0,0)
The slope is -5/4 and the equation of the line in point-slope form is y-5 = -5/4(x+4) + c.
What is slope of a line?The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The points are (x1,y1) is (−4,5) and (x2,y2) is (0,0)
The formula of slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
⇒ [tex]m=\frac{0-5}{0-(-4)}[/tex]
⇒ [tex]m=\frac{-5}{4}[/tex]
The equation of the line in point-slope form is
[tex]y-y1=m(x-x1)[/tex]
⇒ [tex]y-5=\frac{-5}{4} (x-(-4))[/tex]
⇒ [tex]y-5=\frac{-5}{4} (x+4)[/tex]
Hence we can conclude that the slope is -5/4 and the equation of the line in point-slope form is y-5 = -5/4 (x+4).
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What is the approximate value of q in the equation below? q log subscript 2 baseline 6 = 2 q 2 –1.613 –1.522 0.585 3.079
The approximate value of q in the logarithmic equation is 0.585.
The given logarithmic equation is [tex]\rm q+log_2(6)=2q+2[/tex]
It is required to find the value of 'q'.
What is Logarithm?
It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b=c\\\rm log_ac=b[/tex]
We have a logarithmic equation:
[tex]\rm q+log_2(6)=2q+2[/tex]
After simplification the above equation we get;
[tex]\rm q+log_2(6)=2q+2\\\rm q-2q=-log_2(6)+2\\\rm -q=-log_2(6)+2\\[/tex].....(1)
From the logarithmic table, we get the value of [tex]\rm log_2(6)[/tex]
[tex]\rm log_2(6)=2.5849[/tex]
Putting this value in equation (1), we get:
[tex]\rm -q=-log_2(6)+2\\\rm -q=-2.5849+2\\\rm -q=-0.5849\\\rm q=0.5849 \approx 0.585\\[/tex]
Thus, the approximate value of q in the logarithmic equation is 0.585.
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