Answer:
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
Step-by-step explanation:
The diagonal of a rectangle is represented by [tex]\sqrt{length^2+width^2}[/tex].Area of rectangle is = length×widthPerimeter of a rectangle = 2(length+width).Assume x be the width of the rectangle.
The length of the rectangle is to be 6 cm more than twice the width.
The length of the rectangle is= (2x+6) cm
Then the diagonal of the rectangle is [tex]\sqrt{length^2+width^2}[/tex]
[tex]=\sqrt{(2x+6)^2+x^2}[/tex]
[tex]=\sqrt{4x^2+24x+36+x^2}[/tex]
[tex]=\sqrt{5x^2+24x+36}[/tex] cm
According to the problem,
[tex]\sqrt{5x^2+24x+36}=15[/tex]
Squaring both sides
[tex]\Rightarrow{5x^2+24x+36}=15^2[/tex]
[tex]\Rightarrow{5x^2+24x+36}=225[/tex]
[tex]\Rightarrow{5x^2+24x+36-225=0[/tex]
[tex]\Rightarrow{5x^2+24x-189=0[/tex]
⇒5x²+45x-21x-189=0
⇒5x(x+9)-21(x+9)=0
⇒(x+9)(5x-21)=0
⇒x+9=0 or, 5x-21=0
[tex]\Rightarrow x=-9, \frac{21}5[/tex]
⇒x= -9, 4.2
Since the width of a rectangle can not negative.
So, x=4.2 cm
The width of rectangle is = 4.2 cm
The length of the rectangle is =(2×4.2+6)
=14.4 cm
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
To find the dimensions of a rectangle with a given diagonal length and a relationship between its length and width, we can set up a system of equations and use the Pythagorean theorem.
Explanation:To solve this problem, we can set up a system of equations using the given information. Let's assume the width of the rectangle is x. The length of the rectangle is then 2x + 6. We can use the Pythagorean theorem to set up an equation using the diagonal and the sides of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem, we have:
x^2 + (2x + 6)^2 = 15^2
Simplifying and solving this equation will give us the value of x, which is the width of the rectangle. We can then calculate the length of the rectangle by substituting the value of x into the expression 2x + 6.
Let's solve the equation:
x^2 + (2x + 6)^2 = 15^2
Expanding the equation and simplifying:
x^2 + 4x^2 + 24x + 36 = 225
Combining like terms:
5x^2 + 24x + 36 = 225
Moving 225 to the other side of the equation:
5x^2 + 24x + 36 - 225 = 0
Simplifying further:
5x^2 + 24x - 189 = 0
Now we can solve this quadratic equation for x. We can factor it or use the quadratic formula.
By factoring, we find that x = -9 or x = 7.8. Since we are dealing with dimensions, we can ignore the negative value and take x = 7.8 centimeters as the width of the rectangle.
The length would then be 2(7.8) + 6 = 22.6 centimeters. So, the dimensions of the rectangle should be a width of 7.8 centimeters and a length of 22.6 centimeters.
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Pip was thinking of a number. Pip halves the number and gets an answer of 87.2. Form an
equation with x from the information.
Answer:
x/2=87.2
Step-by-step explanation:
Pip was thinking of a number - Let's call this number x
Pip halve the number - So half of x = x/2 (or 1/2 x)
And gets an answer of 87.2 - x/2=87.2
So your equation would be x/2=87.2
I hope this helps :)
Final answer:
Pip's mystery number is found by taking the equation x / 2 = 87.2, where x is the original number. By solving it, we find that x = 174.4.
Explanation:
Pip is thinking of a number. When Pip halves this number, the result is 87.2. To formulate an equation with x based on this information, we consider that halving a number is equivalent to multiplying that number by 0.5 or dividing it by 2.
Therefore, we can represent the situation with the equation x / 2 = 87.2. This equation states that half of Pip's unknown number (x) equals 87.2.
To solve for x, we multiply both sides of the equation by 2:
x = 87.2 × 2
Which simplifies to:
x = 174.4
This means that Pip was thinking of the number 174.4.
helpppppp pleaseeee!!!
Answer:
C (I'm not 100% sure that this is correct)
Step-by-step explanation:
I don't think that an act of genocide in the regions of Africa occurred recently.
Answer:
I think you might get a better answer if you put this question under the social studies category instead of math.
A storekeeper wants to mix two types of flour to get 300 pounds, so he can sell it by 2.50$ per pound. If he uses flour worth $2.40 a pound with another flour worth $3.00 a pound, how many pounds of each does he use?
Answer:
90 pounds, 210 pounds
Step-by-step explanation:
Given:
A storekeeper wants to mix two types of flour to get 300 pounds, so he can sell it by 2.50$ per pound.
He uses flour worth $2.40 a pound with another flour worth $3.00 a pound.
Question:
How many pounds of each does he use?
Solution:
Let pounds of one type of flour mixed = [tex]x[/tex]
Then pounds of another type of flour mixed = [tex]300-x[/tex]
Cost of 1 pound of one type of flour = $2.40
Cost of [tex]x[/tex] pounds of one type of flour = [tex]2.4x[/tex]
Similarly,
Cost of 1 pound of another type of flour = $3
Cost of [tex]300-x[/tex] pounds of another type of flour = [tex]3(300-x)=900-3x[/tex]
Cost of mixed flour per pound = $2.5
Total cost of mixed flour per pound = $2.5 [tex]\times[/tex] 300 = $750
Cost of [tex]x[/tex] pounds of one type + Cost of [tex]300-x[/tex] pounds of another type = $750
[tex]2.4x+900-3x=750\\\\ -0.6x+900=750\\ \\ Subtracting\ both\ sides\ by\ 900\\ \\ -0.6x+900-900=750-900\\ \\ -0.6x=-150\\ \\ Minus\ canceled\ by\by\ minus\\ \\ 0.6x=150\\ \\ Dividing\ both\ sides\ by\ 0.6\\ \\ x=90[/tex]
Pounds of one type of flour mixed = [tex]x[/tex] = 90 pounds
Pounds of another type of flour mixed = [tex]300-x[/tex] = 300 - 90 = 210 pounds
Thus, 90 pounds of one and 210 pound of another type of flour mixed.
Answer:
50lb of 3.00
250lb of 2.40
Step-by-step explanation:
As the SAT is used for college admissions the GRE is used for graduate school admissions. A sample of verbal and
quantitative scores from the GRE are both normally distributed, with the values of H and a are given below.
Verbal Quantitative
670 550
1121 148
Kevin scored 610 on the verbal section and 700 on the quantitative section. Use the standard deviation as a unit of
measurement to comnare Kevin's verhal and quantitative scores on the GRE
Answer:
Step-by-step explanation:
Kevin’s verbal score is 610 is 140 points above the mean,which is 470. the standard deviation is 121 so his verbal score is 140/121≈1.16 standard deviations above the mean. Kevins quantitative score of 700 is 150 points above the mean, which is 500. The standard deviation is 148, so his quantitative score is 150/148 ≈ 1.01 standard deviation above the mean.Thus, Kevins verbal score is better than his quantitative score.
Which is the equation of a trend line that passes through the points (7, 450) and (14, 401)?
y = negative 7 x + 499
y = negative StartFraction 1 Over 7 EndFraction x + 451
y = StartFraction 1 Over 7 EndFraction x + 449
y = 7 x + 401
Answer: a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i got it correct on edg
have a good day :D
Kaci bought a birthday cake like the one shown below. If a=5inches,b=5inches,c=10 inches, and d=3inches what is the volume of the cake
Answer:
75+150=225 in^2
Step-by-step explanation:
Separate each layer.
Area1+Area2= Total area
A1= a*b*d
A2=a*c*d
A1=5*5*3=75 in^2
A2=5*10*3=150 in^2
75+150=225 in^2
Answer:
210
Step-by-step explanation:
Which statement is the clearest translation of 4 j - 9 = 1?
A number, times four minus nine, is one.
A number times, four minus, nine is one.
A number times four, minus nine, is one.
A number times four minus nine is one.
Answer:
i think:
A number times four minus nine is one
how many solutions does this eq
Answer:
There's one solution to this equation and that is 2
Step-by-step explanation:
5 (2x-3) = 5 multiply inside the parenthesis by 5
10x - 15 = 5 add 15 to both sides
10x - 15 + 15 = 15 + 5
10x = 20 divide both sides by 10
x = 2
Find the quotient.
214
27
A) 22
B) 27
C) 221
D) 298
What is the circumference of a circle
with a diameter of 4?
Type in your response.
Answer:
12.57
Step-by-step explanation:
hope this helps
Answer:
3.14 x 4 = 12.57
Step-by-step explanation:
The scale of the drawing was 1 millimeters,2 meters in the drawing, the lawn in the backyard is 28 millimeters long, what is the length of the actual lawn
Answer:
The length of the actual lawn is 56 meters.
Step-by-step explanation:
Given:
The scale of the drawing was 1 millimeters : 2 meters, in the drawing the lawn in the backyard is 28 millimeters long,
Now, to find the length of the actual lawn.
Let the length of the actual lawn be [tex]x.[/tex]
The length of the lawn in the drawing = 28 millimeters.
The scale of the drawing was 1 millimeters : 2 meters.
So, 1 millimeters is equivalent to 2 meters.
Thus, 28 millimeters is equivalent to [tex]x.[/tex]
Now, to get the length of the actual lawn by using cross multiplication method:
[tex]\frac{1}{2} =\frac{28}{x}[/tex]
By cross multiplying we get:
[tex]x=56\ meters.[/tex]
Therefore, the length of the actual lawn is 56 meters.
what is the answer to this question
Answer:
[tex]b^6z^612a^5[/tex]
Step-by-step explanation:
The first step is to combine like terms, and multiply them together first. Since multiplication is commutative, it doesn't matter in what order you do it. Therefore, this can be rewritten as [tex](2a^2\cdot 6a^3)\cdot(b^4\cdot b^2)\cdot(z\cdot z^5)=(12a^5)\cdot(b^6)\cdot(z^6)=b^6z^612a^5[/tex]. Hope this helps!
Answer:
Step-by-step explanation:
(2a²b⁴z)(6a³b²z⁵ = 2*6*a²⁺³ b⁴⁺² z¹⁺⁵
= 12a⁵b⁶z⁶
Tyler kicks a football into the air from a height of 3 feet with an initial vertical velocity of 48 feet per second. Use the vertical motion model, h= -16t^2 + vt + s, where v is the initial velocity in feet per second and s is the height of the football. Round your answer to the nearest tenth if necessary. Maximum height: Feet?
Answer:
39 feet
Step-by-step explanation:
In this problem, the height of the football at time t is modelled by the equation:
[tex]h(t)=-16t^2+vt+s[/tex]
where:
s = 3 ft is the initial height of the ball
v = 48 ft/s is the initial vertical velocity of the ball
[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)
Substituting these values, we can rewrite the expression as
[tex]h(t)=-16t^2+48t+3[/tex]
Here we want to find the maximum height reached by the ball.
This is equivalent to find the maximum of the function h(t): the maximum of a function can be found requiring that the first derivative of the function is zero, so
[tex]h'(t)=0[/tex]
Calculating the derivative of h(t), we find:
[tex]h'(t)=-32 t+48[/tex]
And imposing it equal to zero, we find the time t at which this occurs:
[tex]0=-32t+48\\t=-\frac{48}{-32}=1.5 s[/tex]
And substituting back into h(t), we can find the maximum height of the ball:
[tex]h(1.5)=-16\cdot (1.5)^2 + 48\cdot 1.5 +3=39 ft[/tex]
Using the vertical motion model, the time when the football reaches maximum height is calculated to be 1.5 seconds. Substituting this into the model, the maximum height of the football is found to be 39 feet.
Explanation:To find the maximum height, we consider the vertical motion model h = -16t^2 + vt + s, where v is initial velocity in feet per second and s is the initial height of the football. The information provided include: initial velocity v = 48 feet/sec and initial height s = 3 feet.
The maximum height reached by the football is achieved when the velocity becomes zero (time at which the ball reaches its highest point). This time can be calculated using the formula t = v / (2 * g), with g being half the coefficient of t^2 (g = 16 feet/sec^2 in this case). Substituting v and g gives us approximately t = 1.5 seconds.
We then substitute this time into our initial equation to find the maximum height. This gives: h = -16*(1.5)^2 + 48*1.5 + 3 = 39 feet. Therefore, the maximum height reached by the football is 39 feet.
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Six pounds of grapefruit costs $3.00 5 pounds of apple costs $2.65.
What is the cost per pound for each fruit.
Huan deposited $850 into a college savings account earning 4.8% interest compounded annually. He also deposited $850 into a second account earning 4.8% simple interest. He made no additional deposits. How much interest does the first account earn in 10 years?
Answer:
$508.41
Step-by-step explanation:
Compound interest is calculated with the formula:
[tex]CI = P(1 + R)^T - P[/tex]
where P = Principal/ Initial amount = $850
R = Rate = 4.8% = 0.048
T = Time elapsed = 10 years
Hence, the compound interest is:
[tex]CI = 850(1 +0.048)^{10} - 850\\\\\\CI = 850(1.048)^{10} - 850\\\\\\CI = (850 * 1.598) - 850\\\\\\CI = 1358.41 - 850\\\\\\[/tex]
CI = $508.41
The interest after the first 10 years is $508.41
The first account with an initial deposit of $850 at a 4.8% interest rate compounded annually will earn approximately $510.87 in interest over 10 years.
The student asked how much interest the first account, which is a college savings account with an initial deposit of $850 at a 4.8% interest rate compounded annually, will earn in 10 years. To calculate this, we can use the formula for compound interest:
A = P(1 + r/n)^nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case, P = $850, r = 4.8/100 = 0.048, n = 1 (since the interest is compounded annually), and t = 10 years. So, the calculation is:
A = 850(1 + 0.048/1)1*10
A = 850(1 + 0.048)10
A = 850(1.048)10
A ≈ 850(1.60103)
The total amount in the account after 10 years will be approximately $1,360.87.
To find the interest earned, we subtract the original principal from the total amount:
Interest Earned = Total Amount - Original Principal
Interest Earned ≈ $1,360.87 - $850
Interest Earned ≈ $510.87
Therefore, the interest earned in the first account after 10 years is approximately $510.87.
The
The point (2,6) is on the line given by which equation below?
Answer:
A y = 3x
Step-by-step explanation:
We can check each line to see if the point is on it
A y = 3x 6 = 2*3 6=6 this is true so the point is one the line
B y = 4-x 6 = 2-4 6 = -2 false
C y = -3x 6 = -3(2) 6=-6 false
D y =-x+4 6 = -2+4 6 = 2 false
I NEED HELP ASAP PLSSS
Answer:
y = x^2 - 4x - 5
y = (x + 1)(x - 5)
Answer:
[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\
Factored\: from:\:y = (x + 1) (x - 5)[/tex]
Step-by-step explanation:
[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]
Please respond quickly thanks
Answer:
cookies
Step-by-step explanation:
Please help question in picture
Answer:
I think the answer is B
Step-by-step explanation:
180 - 104 - 36 = 40
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) what is the probability that a randomly selected bag contains between 11001100 and 14001400 chocolate chips? (b) what is the probability that a randomly selected bag contains fewer than 10001000 chocolate chips? (c) what proportion of bags contains more than 12001200 chocolate chips? (d) what is the percentile rank of a bag that contains 10501050 chocolate chips?
Answer:
a) P ( 1100 < X < 1400 ) = 0.755
b) P ( X < 1000 ) = 0.755
c) proportion ( X > 1200 ) = 65.66%
d) 5.87% percentile
Step-by-step explanation:
Solution:-
- Denote a random variable X: The number of chocolate chip in an 18-ounce bag of chocolate chip cookies.
- The RV is normally distributed with the parameters mean ( u ) and standard deviation ( s ) given:
u = 1252
s = 129
- The RV ( X ) follows normal distribution:
X ~ Norm ( 1252 , 129^2 )
a) what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips?
- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:
P ( x1 < X < x2 ) = P ( [ x1 - u ] / s < Z < [ x2 - u ] / s )
- Taking the limits x1 = 1100 and x2 = 1400. The standard normal values are:
P ( 1100 < X < 1400 ) = P ( [ 1100 - 1252 ] / 129 < Z < [ 1400 - 1252 ] / 129 )
= P ( - 1.1783 < Z < 1.14728 )
- Use the standard normal tables to determine the required probability defined by the standard values:
P ( -1.1783 < Z < 1.14728 ) = 0.755
Hence,
P ( 1100 < X < 1400 ) = 0.755 ... Answer
b) what is the probability that a randomly selected bag contains fewer than 1000 chocolate chips?
- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:
P ( X < x2 ) = P ( Z < [ x2 - u ] / s )
- Taking the limit x2 = 1000. The standard normal values are:
P ( X < 1000 ) = P ( Z < [ 1000 - 1252 ] / 129 )
= P ( Z < -1.9535 )
- Use the standard normal tables to determine the required probability defined by the standard values:
P ( Z < -1.9535 ) = 0.0254
Hence,
P ( X < 1000 ) = 0.755 ... Answer
(c) what proportion of bags contains more than 1200 chocolate chips?
- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:
P ( X > x1 ) = P ( Z > [ x1 - u ] / s )
- Taking the limit x1 = 1200. The standard normal values are:
P ( X > 1200 ) = P ( Z > [ 1200 - 1252 ] / 129 )
= P ( Z > 0.4031 )
- Use the standard normal tables to determine the required probability defined by the standard values:
P ( Z > 0.4031 ) = 0.6566
Hence,
proportion of X > 1200 = P ( X > 1200 )*100 = 65.66% ... Answer
d) what is the percentile rank of a bag that contains 1050 chocolate chips?
- The percentile rank is defined by the proportion of chocolate less than the desired value.
- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:
P ( X < x2 ) = P ( Z < [ x2 - u ] / s )
- Taking the limit x2 = 1050. The standard normal values are:
P ( X < 1050 ) = P ( Z < [ 1050 - 1252 ] / 129 )
= P ( Z < 1.5659 )
- Use the standard normal tables to determine the required probability defined by the standard values:
P ( Z < 1.5659 ) = 0.0587
Hence,
Rank = proportion of X < 1050 = P ( X < 1050 )*100
= 0.0587*100 %
= 5.87 % ... Answer
Sue and Kathy have $20 left for a cab fare home. The cab fare is $3 per mile plus a $2 flat rate fee. What is the maximum number of miles they will be able to travel in the cab
Answer:
The answer should be 6 miles..
3(6)x2=20
Step-by-step explanation:
30 POINTZ
What is the determinant of the coefficient matrix of this system?
Answer:
Determinant of matrix = 12
Step-by-step explanation:
rewrite this system with matrices
[{4 , -3]
[8, -3]]
determinant = 4*(-3) - (-3)*8 = -12 + 24 = 12
are you finding the inverse too?
the system should look like A* v = C
where matrix A is
[{4 , -3]
[8, -3]]
and V = [x , y] vector
C = [-8, 12] vector
Answer:
Explanation: When the determinant of the coefficient matrix of a system of linear equations equals zero it means that at least one equation in the system is a scalar multiple of another equation. Hence it is not possible to find the inverse matrix and so the system cannot be solved.
Step-by-step explanation:
The ratio of boys to girls in the class is 4:5. How many boys are there if there are 27 students?
Answer:
12 boys
Step-by-step explanation:
boys : girls
4 : 5
Add a total column
boys : girls: total
4 : 5 : 4+5 =9
To get to a total of 27 we multiply each term by 3
boys : girls: total
4*3 : 5*3 : 9*3
12 :15 :27
There are 12 boys
Final answer:
There are 12 boys in the class of 27 students.
Explanation:
The ratio of boys to girls in the class is 4:5, which means for every 4 boys, there are 5 girls. To find out how many boys there are, if there are 27 students in total, we need to work with this ratio.
Step-by-step Solution:
Determine the total number of parts in the ratio by adding the parts for boys and girls together: 4 parts for boys + 5 parts for girls = 9 parts in total.Divide the total number of students by the total number of parts to find out how many students make up 1 part: 27 students ÷ 9 parts = 3 students per part.Multiply the number of parts for boys by the number of students per part to find the total number of boys: 4 parts × 3 students per part = 12 boys.Therefore, there are 12 boys in the class of 27 students.
What is the value of x?
10 + 2х
Answer:
x = -5
Step-by-step explanation:
Get 2x by itself, so subtract to the other side. 2x = -10. Then get x alone, so divide by 2. Then your answer is -5
PLEASE MARK BRAINLIEST!
Answer:
I think you meant a "=" instead of a "+"
Step-by-step explanation:
10 = 2x
10 = 2x
2 2
5 = x
Your answer is 5I hope this helps!
- sincerelynini
A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference. If \orange{\angle ADC}?ADCstart color orange, angle, A, D, C, end color orange measures 35^\circ35 ? 35, degree, what does \blue{\angle ABC}?ABCstart color blue, angle, A, B, C, end color blue measure?
Answer:
∠ABC=[tex]70^0[/tex]
Step-by-step explanation:
In the attached diagram,
If Angle ADC =[tex]35^0[/tex]
Since the center of the circle is at B
∠ABC is the angle subtended at the center by arc AC.
∠ADC is the angle subtended at the circumference by arc AC.
Theorem
The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle's circumference.
Therefore by the theorem above
∠ABC = 2 X ∠ADC
=2 X 35
∠ABC=[tex]70^0[/tex]
If cos 0 = 0.3846 where 3pi/2 is less than 0 is less than 2pi, what is the approximate value of sin 0?
Answer:
-0.9231
Step-by-step explanation:
Given cos theta = 0.3846 within the range 3π/2<theta<2π
Costheta = 0.3846
Theta = arccos(0.3846)
Theta = 67.38°
Since 67.38° didn't fall within the range of theta, we will locate our theta using the quadrant.
Since cos is positive in the 4th quadrant,
Theta = 360-67.38°
Theta = 292.62°
Sin(theta) = sin(292.62°)
= -0.9231
I need help with this
Answer:
Which ones
Step-by-step explanation:
11.a
Range: 16
To find the range, you subtract the biggest number(52) from the smallest number(36)
52-36=16
11.b
Mean: 43.75
To find the mean, you have to add all the numbers, then divide by the total amount of numbers
(36+45+52+40+38+41+50+48)/2 = 43.75
Median: 43
To find the median, the numbers must be put in either ascending or descending order and the middle must be found. In this case, there were 2 numbers(41 and 45) so you add the two and divide by 2.
36,38,40,41,45,48,50,52 (41+45)/2=43
Mode: N/A
The mode is the number that occurs the most and in this case each number is only seen once , so there is no mode
I am going to put the answers for the rest since I've explained the process
12a.
Range: 3655
12b.
Mean: 1014.166667 = 1014.17
Median: 608.5
Mode: N/A
13a.
Mean: You: 4 Friend: 8
Median: You: 17 Friend: 17
Mode: You: N/A Friend: 20
13b.
Your Friend
I need some help with Parent Functions
Expand each expression. ln (2x)4 4 ln 2 + 4 ln x 4 ln 2 + ln x 8 ln x
Equivalent expression are expressions that have equal values, when expanded. The equivalent expression of ln(2x)^4 is 4ln(2) + 4ln(x))
How to determine the expanded expressionThe expression is given as:
[tex]\ln(2x)^4[/tex]
Apply the following logarithmic rule to the above equation
[tex]\ln(a)^b = b\ln(a)[/tex]
So, we have:
ln(2x)^4 = 4ln(2x)
Next, apply the following product rule of logarithm to the above equation
ln(ab) = ln(a) + ln(b)
So, we have:
ln(2x)^4 = 4 * [ln(2) + ln(x)]
Expand the bracket
ln(2x)^4 = 4ln(2) + 4ln(x))
Hence, the equivalent expression of ln(2x)^4 is 4ln(2) + 4ln(x))
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Answer:
ln (2x)4
✅ 4 ln 2 + 4 ln x
❎ 4 ln 2 + ln x
❎ 8 ln x
ln
4y5
x2
❎ ln 4 - 2 ln x - 5 ln y
✅ ln 4 - 2 ln x + 5 ln y
❎ -8 ln x + 5 ln y
A planter in the shape of a
square pyramid is being filled
with soil. Soil cost $0.78 per
cubit cubic foot What is the
cost of filling the planter with
soil?
a $24.00
b $8.00
c. $6 24
d. $18.72
The cost of filling the planter with soil is $6.24. option C
What is the cost of filling the planter with soil?
Length = 2 ft
Width = 2 ft
Height = 6 ft
Volume of the square based pyramid = ⅓ × length × Width × height
= ⅓ × 2 × 2 × 6
= ⅓ × 24
= 8 cubic feet
Cost of soil per cubic foot = $0.78
Therefore,
Cost of filling the planter with soil = Volume of the square based pyramid × Cost of soil per cubic foot
= 8 × $0.78
= $6.24
Complete question:
A planter in the shape of a square pyramid with dimensions 2 ft by 2 ft by 6 ft is being filled with soil. Soil cost $0.78 per cubit cubic foot What is the cost of filling the planter with soil?
a $24.00
b $8.00
c. $6 24
d. $18.72