At a farm the ratio of cows to horses was 9:2. If there were 72 cows at the farm, how many horses were there?
A rectangle has a width that is 3 more than twice the length. Its perimeter is 96 inches. What is width of the rectangle, in inches?
The width of the given rectangle is 33 inches.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of the rectangle is W while the length is L.
Given that,
A rectangle has a width that is 3 more than twice the length.
So,
W = 2L + 3
And,
Perimeter = 2(L + W) = 96
L + W = 48
By substitution,
L + 2L + 3 = 48
3L = 45
L = 15
So,
W = 2(15) + 3 = 33
Hence "The width of the given rectangle is 33 inches".
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You have diving lessons every fifth day and swimming lessons every third day. Today have both lessons in how many days will you have both lessons on the same day again.
The diving and swimming lessons will occur on the same day after 15 days because 15 is the smallest common multiple of 3 and 5.
Explanation:The question pertains to finding a common multiple of the numbers 3 and 5. These numbers represent the intervals at which you have swimming and diving lessons respectively. The first common multiple of 3 and 5, other than 1, is 15. Therefore, you will have both lessons on the same day again after 15 days.
This comes from the idea that a number's multiples are the set of numbers formed by multiplying that number by any of the whole numbers. So, the multiples of 3 are 3, 6, 9, 12, 15, 18, etc., while the multiples of 5 are 5, 10, 15, 20, etc. The number 15 is a multiple of both 3 and 5, therefore, it is a common multiple of 3 and 5.
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The French Club is sponsoring a bake sale if their goal is to raise at least $140 how many pastries must they sell at $3.50 each in order to meet the goal write and solve inequality
Answer:
3.50p>(or equal to) 140; p>(or equal to)40
Step-by-step explanation:
It takes an older pump 4 times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 4 hours to drain the pool. How long will it take the older pump to drain the pool working alone?
Let us say that:
x = the time it take for the new pump to drain the pool alone
4x = the time it take for the older pump
And we are given that together they drain the pool in 4 hours, therefore:
1/x + 1/4x = ¼
Multiply everything by x:
1 + ¼ = ¼ x
1.25 = 0.25 x
x = 5 hours
So, 4x = 20 hours
Hence it take the older pump 20 hours draining alone.
Final answer:
The older pump would take 3.2 hours, or 3 hours and 12 minutes, to drain the pool on its own, since it takes 4 times as long as the newer pump which takes 48 minutes alone.
Explanation:
If an older pump takes 4 times as long to drain a pool as a newer pump, and together they take 4 hours to drain the pool, we can find out how long it would take for the older pump to drain the pool on its own by setting up an equation based on their rates of work.
Let's denote the time it takes for the newer pump to drain the pool alone as t hours. This means that the older pump would take 4t hours to do the job on its own.
Working together for one hour, they would collectively drain 1/t + 1/4t of the pool. Since they can drain the entire pool in 4 hours working together, we can write the equation:
1/t + 1/4t = 1/4
Now, solving for t:
4 + 1 = t
4t + t = 4t
5t = 4t
5t = 4
t = 4/5
So, the newer pump takes 4/5 of an hour (which is 48 minutes) to drain the pool alone. Then the older pump, taking 4 times as long, would take 4 * 4/5, which is 16/5 or 3.2 hours (which is 3 hours and 12 minutes) to drain the pool on its own.
Which statements are true about the fully simplified product of (b – 2c)(–3b + c)? Check all that apply. The simplified product has 2 terms. The simplified product has 4 terms. The simplified product has a degree of 2. The simplified product has a degree of 3. The simplified product has a degree of 4. The simplified product, in standard form, has exactly 2 negative terms.
Answer:
The simplified product has a degree of 2.
The simplified product, in standard form has exactly 2 negative terms.
Step-by-step explanation:
[tex](b - 2c)(-3b + c)[/tex]
LEts multiply it using FOIL method
[tex]b* -3b= -3b^2[/tex]
[tex]b*c= bc[/tex]
[tex](-2c) * (-3b)= 6bc[/tex]
[tex](-2c) * c= -2c^2[/tex]
The product is [tex]-3b^2 +bc+6bc-2c^2[/tex]
[tex]-3b^2+7bc-2c^2[/tex]
The simplified product has a degree of 2.
It has two negative terms
Answer: The correct options are,
The simplified product has a degree of 2,
The simplified product, in standard form, has exactly 2 negative terms.
Step-by-step explanation:
Here, the given expression,
[tex](b-2c)(-3b+c)[/tex]
By distributive property,
[tex]=(b-2c)(-3b)+(b-2c)(c)[/tex]
Again by distributive property,
[tex]=b(-3b)-2c(-3b)+bc-2c(c)[/tex]
[tex]=-3b^2+6bc+bc-2c^2[/tex]
[tex]=-3b^2+7bc-2c^2[/tex]
Which is the simplified form of the given expression,
That having three terms in which two terms are negative and the degree ( The highest sum of the exponents of the variables) is 2,
Hence, the correct options are,
The simplified product has a degree of 2,
The simplified product, in standard form, has exactly 2 negative terms.
What is the square root of 98 rounded to the nearest thousandth
If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g x h)(5)
(5 – 7)^2
(5)^2 – 7
(5)^2(5 – 7)
(5 – 7)x^2
Final answer:
To find (g x h)(5), calculate h(5) first, then substitute the result into g(x) and calculate. The equivalent expression is (5)^2 - 7.
Explanation:
To solve (g x h)(5), we need to find g(h(5)). Given h(x) = x - 7 and g(x) = x^2, we first find h(5) = 5 - 7 = -2. Then, we evaluate g(-2) = (-2)^2 = 4. So, (g x h)(5) = g(h(5)) = g(-2) = 4, which corresponds to the option (5)^2 - 7.
for a store contest 4 out of every 65 people who visit the store witll get a free dvd if 455 people went how many dvd's were given away?
how do I solve for X? 37/24=7/8-5x/6
Maria and her family drove 885 miles on their summer vacation . the first 8 on the left in this number has blank of 800
Maria and her family drove 885 miles, and the first '8' in this number represents the hundreds place, meaning it has a value of 800 miles.
The student's question is related to place value in numbers. Maria and her family drove 885 miles on their summer vacation, and the query specifically asks about the value represented by the first digit '8' on the left side of this three-digit number. In this case, the digit '8' is in the hundreds place, which means it represents the hundreds component of the overall number. Therefore, the first '8' has a value of 800. This is because in the number 885, the first '8' represents 8 hundreds, the second '8' represents 8 tens (or eighty), and the '5' represents 5 ones.
How do I start This?
What is the inverse of the logarithmic function
f(x) = log2x?
Answer:
Inverse function, [tex]f^{-1}=2^x[/tex]
Step-by-step explanation:
We are given a function [tex]f(x)=\log_2x[/tex]
We need to find the inverse of f(x)
Step 1: Set f(x)=y
[tex]y=\log_2x[/tex]
Step 2: Switch x and y
[tex]x=\log_2y[/tex]
Step 3: Solve for y (isolate y)
[tex]y=2^x[/tex] [tex]\because \log_ab=x\Rightarrow b=a^x[/tex]
Inverse of function [tex]f(x)\rightarrow f^{-1}(x)=2^x[/tex]
The inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]
The logarithmic expression is given as:
[tex]f(x) = \log_2(x)[/tex]
Replace f(x) with y
[tex]y = \log_2(x)[/tex]
Swap the positions of x and y
[tex]x = \log_2(y)[/tex]
Apply the change of base rule of logarithm
[tex]2^x = y[/tex]
Rewrite as:
[tex]y = 2^x[/tex]
Express y as an inverse function
[tex]f^{-1}(x) = 2^x[/tex]
Hence, the inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]
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The circle below represents a whole, or 1.use subtraction to determine the unknown part of the circle.
What is the sum of the numbers in the series? 15 + 11 + 7 + . . . + (–129)
A. -2,124
B. -2,109
C. -2,052
D. -1,995
Graph the line by locating any two ordered pairs that satisfy the equation y = 1/4x+1
find the center and radius for the circles with the following equation x^2+y^2-4x+6y+11=0
Ted weighs partly used spools to estimate the length of cable that remains. He knows that 1 metre of lighting cable weighs 85 grams, and that an empty spool weighs 260 grams. Ted weighs the partly used spool shown. It has a total weight 1540 grams. Which of these calculations will give Ted an estimate of the number of metres of cable left on the spool?
To find the length of cable remaining on the spool, subtract the weight of the empty spool from the total weight, and then divide the result by the weight of cable per metre.
Explanation:The question involves the process of subtracting, conversion and division. First, we need to subtract the weight of the empty spool from the total weight of the partly-used spool and the remaining cable to find the weight of the remaining cable alone. This means 1540 grams - 260 grams = 1280 grams. Then, we convert the weight of the remaining cable (which is in grams) to metres by dividing it by the weight of one metre of cable (which is 85 grams). So, 1280 grams ÷ 85 grams/metre = approximately 15 metres. Therefore, this is the quantity of cable that Ted has left on the spool.
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The legs of a scalene triangle are represented by (x + 4), (x + 8), and ( 2x − 3). Which polynomial expression BEST represents the perimeter of the triangle?
Answer:
[tex](4x+9)[/tex]
Step-by-step explanation:
we know that
The perimeter of triangle is equal to the sum of the three length sides
therefore
[tex]P=(x+4)+(x+8)+(2x-3)\\ \\P=(x+x+2x)+(4+8-3)\\ \\P=(4x+9)\ units[/tex]
A linear cost function is c(x) = 4x + 300.what is the cost of producing one more item if 50 are currently being produced?
The cost of producing one more item is 4 if 50 are currently being produced.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c.
We have been given that linear cost function is C(x) = 4x + 300.
Here, the slope (4) is the cost per unit,
We have to determine the cost of producing one more item
Since 50 are currently being produced, so substitute the value of x = 51,
So the cost of producing one more item as
⇒ C(51) - C(50) = 4(51) +300 - (4(50) + 300) = 504 - 500 = 4
Therefore, the cost of producing one more item is 4 if 50 are currently being produced.
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Two experiments are to be performed the first can result in any one of m possible outcomes. if the first experiment results in outcome i, then the second experiment can result in any of n possible outcomes ,i=1,2,..,m. what is the number of possible outcomes of the two experiments?
Find the points on the curve y = 2x3 + 3x2 − 12x + 8 where the tangent line is horizontal.
Final answer:
To find where the tangent line is horizontal on the curve y = 2x^3 + 3x^2 - 12x + 8, set its derivative to zero and solve for x, resulting in points (-2, 8) and (1, 1) where the tangent lines are horizontal.
Explanation:
To find the points on the curve y = 2x^3 + 3x^2 − 12x + 8 where the tangent line is horizontal, we look for where the derivative of the curve equals zero because horizontal tangent lines have a slope of zero. The derivative of the given function is y' = 6x^2 + 6x - 12. This derivative represents the slope of the tangent at any point on the curve.
Setting the derivative equal to zero gives us the quadratic equation 6x^2 + 6x - 12 = 0, which can be simplified to x^2 + x - 2 = 0. Factoring this quadratic equation, we get (x + 2)(x - 1) = 0, leading to two solutions for x: x = -2 and x = 1. Substituting these x-values back into the original equation gives us the y-coordinates and therefore the points on the curve where the tangent line is horizontal: (-2, 8) and (1, 1).
why is 5 + (-7) equal to (-2)?
A scuba divers dove 950 feet below the surface in 19 minutes what integer represents the average rate of change for this dive?
will give BRAINEST
For several weeks, the function f(x) = 3(4)x represented the number of birds infected with an illness x weeks after the first birds became sick. How did the number of sick birds change each week?
What Times 4 equals 108
Henry wants to see how many different colored crayons are in the crayons box. If there are 4 rows of 19 crayons , how many different colored crayons are there, assuming no duplicate colors?
The number of different coloured crayons is 76.
Given that, Henry wants to see how many different coloured crayons are in the crayons box. There are 4 rows of 19 crayons.
We need to find how many different coloured crayons are there, assuming no duplicate colours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of different coloured crayons be x.
Now, x=4×19
⇒x=76
Therefore, the number of different coloured crayons is 76.
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A closet contains 10 pairs of shoes. if 8 shoes are randomly selected, what is the probability that there will be
r+15=4r-6
Please show all work!!!!
The value of the solution of expression is, r = 7
We have to give that,
An expression to simplify,
r + 15 = 4r - 6
Now, Simplify the expression by combining like terms as,
r + 15 = 4r - 6
Subtract r on both sides,
r + 15 - r = 4r - r - 6
15 = 3r - 6
Add 6 into both sides,
15 + 6 = 3r
21 = 3r
Divide 3 on both sides,
r = 21/3
r = 7
Therefore, the solution is, r = 7
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weather station records the morning low temperature as −6.1°F and the afternoon high temperature as 10.5°F . Which expression represents the total temperature change, in degrees Fahrenheit, from the morning low to the afternoon high? |10.5+(−6.1)| −6.1+10.5 |10.5−(−6.1)| 10.5+(−6.1)
I am sure the answer is |10.5−(−6.1)| hope this helps and if correct give me the brainliest please
the correct answer is
|10.5-(6.1)|
I took the test