Answer:
width = 5
length = 15
Step-by-step explanation:
width: x
length : 3x
x + 3x + x + 3x = 40
8x = 40
x = 5
width = 5
length = 15
3 When Klorina swims with the current, she swims 10 km
In 2 h. Against the current, she can swim only 8 km in
the same time. How fast can Klorina swim in still water?
What is the rate of the current?
Speed in still water [tex]=[/tex] 9km
Speed of the current [tex]=[/tex] 1 km
Answer:
Step-by-step explanation:
Speed of the current [tex]=[/tex] C
Speed of the still water [tex]=[/tex] S
Speed with the current [tex]=[/tex] [tex]([/tex] speed of the still water ₊ speed of the current [tex])[/tex]
[tex]=[/tex] S ₊ C
Speed with the current [tex]=[/tex] S ₊ C [tex]=[/tex] 10km
Speed against the current [tex]=[/tex] [tex]([/tex] speed of the still water ₋speed of the current [tex])[/tex]
[tex]=[/tex] S ₋ C
Speed against the current [tex]=[/tex] S ₋ C [tex]=[/tex] 8km
Speed in still water [tex]=[/tex] Speed with the current ₊ Speed against the current[tex])[/tex]÷ 2
[tex]= ([/tex] 10 ₊ 8 [tex])[/tex] ÷ 2
[tex]=[/tex] [tex]([/tex] 18 [tex])[/tex] ÷ 2
Speed in still water [tex]=[/tex] 9km
Speed of the current [tex]= ([/tex] Speed with the current ₋ Speed against the current[tex])[/tex] ÷ 2
[tex]= ([/tex] 10 ₋ 8 [tex])[/tex] ÷ 2
[tex]=[/tex] [tex]([/tex] 2 [tex])[/tex] ÷ 2
Speed of the current [tex]=[/tex] 1 km
Factor over the complex numbers, if possible:
x^2+2xyi-y^2
Step-by-step explanation:
x² + 2ixy − y²
x² + 2ixy + i²y²
(x + iy)²
Answer:
(X+yi )(X+yi)
Step-by-step explanation:
2 sin^2 theta + 3 cos theta = 3
Answer:
θ = ±π/3 + 2kπ
θ = 0 + 2kπ
Step-by-step explanation:
2 sin² θ + 3 cos θ = 3
Use Pythagorean identity:
2 (1 − cos² θ) + 3 cos θ = 3
2 − 2 cos² θ + 3 cos θ = 3
0 = 2 cos² θ − 3 cos θ + 1
Factor:
0 = (2 cos θ − 1) (cos θ − 1)
cos θ = 1/2
θ = ±π/3 + 2kπ
cos θ = 1
θ = 0 + 2kπ
prism M and pyramid n have the same base area and the same height. cylinder p and prism Q have the same height and the same base perimeter. cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y the figures_ and _ have the same volume
Answer:
The volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume.
Step-by-step explanation:
The volume of a cylinder having base area 'A' and height 'H' is given by V = AH, and the volume of a cone having the same base area as the cylinder i.e. A and height 3 times the height of the cylinder i.e. 3H is given by [tex]V' = \frac{1}{3} A(3H) = AH[/tex].
So, V = V'
Hence, the volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume. (Answer)
If Jamie wants to maintain the relationship of black
beads to red beads, could she make a bracelet with
5 red beads? Explain your answer.
How would I get an answer??
Answer:for every five red beeds their are 5 black beeds
Step-by-step explanation:
To maintain the relationship of black beads to red beads, we need to know the ratio of black beads to red beads in the existing bracelet or the desired ratio. If the ratio is 1:1, for example, then you would need to use an equal number of black and red beads.
However, based on the information provided, it's not clear what the current or desired ratio is. If Jamie wants to maintain a specific ratio, you need to know that ratio.
For example, if the ratio is 2:1 (2 black beads for every 1 red bead), and you want to use 5 red beads, you would need 5×2=10 black beads to maintain the 2:1 ratio.
Without more information on the desired or existing ratio, it's not possible to determine whether using 5 red beads alone would maintain the relationship of black beads to red beads.
complete step by step
To maintain the relationship of black beads to red beads in a bracelet, we need to understand the existing ratio and then apply it to the new situation.
Let's say the current ratio of black beads to red beads in Jamie's bracelet is 3:2. This means that for every 3 black beads, there are 2 red beads.
Now, Jamie wants to make a bracelet with 5 red beads. To maintain the same ratio, we need to determine the corresponding number of black beads.
The ratio of black beads to red beads is 3:2, which simplifies3x:2x for some positive value of x.
Since Jamie wants 5 red beads, we set up the equation: 2x-5
Now, solve for x:
x- 5/2
Now that we know the value of x, we can find the number of black beads:
Number of black beads - 3x-3 x (5/2) - (15/2) - 7.5
However, since the number of beads must be a whole number, we need to adjust. In this case, Jamie cannot make a bracelet with exactly 5 red beads while maintaining the ratio of 3:2. She would need to choose a different number of red beads that allows for a whole number of black beads according to the established ratio.
In conclusion, to maintain the relationship of black beads to red beads, Jamie cannot make a bracelet with exactly 5 red beads. The number of red beads chosen must allow for a whole number of black beads based on the given ratio.
Michael added 15 fish to his pond over a period of 5 days he added the same number of fish each day what was the change in the number of fish in the pond each day
Answer:
3
Step-by-step explanation:
15 fish / 5 days = 3 fish per day
Answer:
3
Step-by-step explanation:
15 fish / 5 days = 3 fish per day
5. Mike weighs 200 pounds and plans to
lose 1.5 pounds a week. Jeff weighs 180
pounds and plans to lose 0.5 pounds a
week. When will Mike and Jeff weigh the
same?
Answer:
20 weeks
Step-by-step explanation:
200-1.5x=180-.5x
20=1x
X=20
What is 78 divided by 2418
Answer:
0.0322580645
Step-by-step explanation:
i feel like u meant 2418/78 but ok
Final answer:
To calculate 78 divided by 2418, you will get approximately 0.0322 when rounded to four significant figures.
Explanation:
The question asks for the result of the division 78 divided by 2418.
To find the answer, you need to perform the division either manually or by using a calculator. When you do so, you will find that the answer is a decimal. Taking the division to four significant figures, which is a common practice in mathematics to maintain precision without excessive digits, the calculation would look as follows:
78 ÷ 2418 = 0.0322
Thus, when dividing 78 by 2418, the result is approximately 0.0322 to four significant figures.
Which graph represents the function over the interval [−3,3] ?
f(x)=⌈x+1⌉
Answer: The correct graph is the bottom left graph.
Step-by-step explanation:
Given function is f(x)=ceil(x+1)
To plot graph of f(x) in interval of(-3,3) :
ceil(x+1) is ceiling function
The output of ceil(x) is least integer greater than x
for example ceil(5.5)=6
For an interval of (-3,-2):
Take x=(-2.4)
x+1=(-1.4)
y=f(x)=ceil(x+1)=(-1)
Similarly,
For an interval of (-2,-1):
Take x=(-1.4)
x+1=(-0.4)
y=f(x)=ceil(x+1)=(0)
For an interval of (-1,0)
y=f(x)=1
For an interval of (0,1)
y=f(x)=2
For an interval of (1,2)
y=f(x)=3
For an interval of (2,3)
y=f(x)=4
Thus, The correct graph is the bottom left graph.
Answer:
The bottom left graph
Step-by-step explanation:
I took this quiz
A man went into a bank to cash a check. In handing over the money the cashier, by mistake,
gave him dollars for cents and cents for dollars. He pocketed the money without examining it,
and spent a nickel on his way home. He then found that he possessed exactly twice the amount
of the check. He had no money in his pocket before going to the bank. What was the exact
amount of that check?
Final answer:
The exact amount of the check is $5.
Explanation:
To solve this problem, we can set up an equation based on the given information. Let's assume that the amount of the check is x dollars. According to the problem, the man received the amount in cents instead of dollars, so he actually received x dollars and x cents. He then spent a nickel, which means he had x dollars and (x-5) cents left. It's stated that he had exactly twice the amount of the check after spending the nickel, so we can write the equation:
x + (x-5) = 2x
Simplifying the equation, we get:
2x - x = 5
x = 5
Therefore, the exact amount of the check is $5.
Identify the standard form of a circle equation x^2+2x+y^2-2y=2
Answer:
The standard from of the expression is: [tex](x +1)^2 + (y-1)^2 = (2)^2[/tex]
Step-by-step explanation:
Here the given expression is :
[tex]x^2+2x+y^2-2y=2[/tex]
Now, the standard form of a circle is given as :
[tex](x-h)^2 + (y -k)^2 = r^2[/tex]
Here, (h,k) = Coordinates of Center, r = Radius
Also, use the algebraic identity:
[tex](a \pm b)^2 = a^2 + b^2 \pm 2ab\\[/tex]
Now, converting the given expression in the standard form, we get:
[tex]x^2+2x+y^2-2y=2[/tex]
Add 2 on both sides of the equation, we get:
[tex]x^2+2x+y^2-2y +2=2 + 2\\\implies x^2+2x + 1 + y^2-2y + 1 = 4\\\implies (x^2+2x + 1 )+ (y^2-2y + 1) = 4\\\implies (x +1)^2 + (y-1)^2 = (2)^2[/tex]
So, here the standard from of the expression is:
[tex](x +1)^2 + (y-1)^2 = (2)^2[/tex]
Center coordinates here are (h,k) = ( -1 ,1) and Radius = 2 units
y equals 3/8 x+ 12 write the equation in standard form using integers
Answer:
-3x + 8y - 96 = 0
Step-by-step explanation:
Standard form is ax + by + c = 0.
Converting from standard to slope-intercept form:
ax + by + c = 0
by = -ax - c
y = -a/b x - c/b
Compare the conversion formula to y = 3/8 x + 12.
In the equation, the slope is 3/8, which is the result of -a/b.
a= -3 and b=8
In the equation, 12 is a result of -c/b.
If b is 8:
-c/b = 12
-c/8 = 12
-c = 96
c = -96
Test a= -3 and b=8 and c= -96 in standard form converts to y=3/8 x+ 12
ax + by + c = 0
-3x + 8y - 96 = 0
-3x + 8y = 96
8y = 3x + 96
y = 3/8 x + 96/8
y = 3/8 x +12
This is correct. Therefore a= -3, b=8 and c= -96.
The standard form is -3x + 8y - 96 = 0
Which set of ordered pairs is a function?
A. (1,2) (3,4) (5,6) (3,-4)
B. (8,4) (4,3) (2,2) (8,1)
C. (2,5) (3,10) (4,15) (5,20)
D. (2,4) (2,3) (2,1) (2,0)
Answer:
OPTION C
Step-by-step explanation:
An element in the domain should be mapped to exactly one element on the co-domain. Also, every element in the domain should be mapped to an element in the co-domain.
These two conditions are satisfied to call a relation, a function.
Two different elements in the domain can be mapped to the same element in the co-domain. But the same element in the domain cannot be mapped to two different elements in the co-domain.
A) (1,2), (3,4), (5,6), (3,-4)
Here, the element '3' is mapped to 4 and -4. So, this is not a function.
B) (8,4), (4,3), (2,2), (8,1)
'8' is mapped to 4 and 1. So, it is not a function.
C) (2,5), (3,10), (4,15), (5,20)
All the elements in the domain are mapped to an element in the co-domain. Also, every element in the domain has exactly one image in the co-domain. So, this relation is a function.
D) (2,4), (2,3), (2,1), (2,0)
The element '2' has more than one image. Clearly, it contradicts the definition of a function.
So, only OPTION C is the answer.
The sum of two numbers is 138 one number is 20 less than the other find the numbers
Answer:
The answer is 59 & 79
Step-by-step explanation:
59+79=138
79-20=59
59+20=79
Maria says if I multiply the current temperature by 4 and then subtract 40 the results is the same as 3 times the current temperature Richard says the current temperature is 20 degrees is Richard correct
Answer:
No, Richard is incorrect, the current temperature is 40 degrees.
Step-by-step explanation:
4x-40=3x
4x-3x=40
x=40
d=rt when r=35 mi/h and t= 2 h
Answer:
The distance, D for the given expression is 70 miles
Step-by-step explanation:
Given as :
D = r t
r = 35 mi/ h
t = 2 h
Now, According to question
Distance = speed × Time
Where speed = r
Time = t
Distance = D
Now, from question
D = 35 miles per hour × 2 hours
So, D = 70 miles
Hence The distance, D for the given expression is 70 miles . answer
The digits of a two-digit number sum to 8. When the digits are reversed the resulting number is 18 less than the onginal
number. What is the original number?
Answer:
53
Step-by-step explanation:
Given: The sum of two digit number is 8
Reversing the digit will get us number 18 less than the original.
Lets take x as tenth digit of our number and y as unit digit of our number.
As given sum of digit is 8
∴ [tex]x+y= 8[/tex]
∴ [tex]y= 8-x[/tex] - equation 1
We also know that reversing the digit will get us number 18 less than the original.
∴ [tex]10y+x = 10x +y-18[/tex]
Now, lets put the value of y from equation 1
⇒ [tex]10(8-x) + x = 10x+ (8-x)- 18[/tex]
⇒ [tex]80-9x= 9x-10[/tex]
⇒ [tex]90= 18x[/tex]
∴ [tex]x= 5[/tex]
Next, substituting the value of x in equation 1
[tex]y= 8-x[/tex]
⇒ [tex]y= 8-5 = 3[/tex]
∴ [tex]y= 3[/tex]
∴ The original number is 53, sum of the digit is 8 and if we reverse the digit of the number, we get 35, which is 18 less than the original number.
Factor completely x2 - 16y2
Answer:
(x+4y)(x-4y)
Step-by-step explanation:
Since
[tex]\large a^2-b^2=(a+b)(a-b)[/tex]
we can see that
[tex]\large x^2-16y^2=(x+4y)(x-4y)[/tex]
18 36 72 96
What number goes between 36 and 72 to finish the sequence ?
Answer:56
Step-by-step explanation:
difference between 36 and 18 is 18
difference between 96 and 72 is 24
so that means 18, 20, 22, 24
I HOPE THIS HELPS :)
solve the equation x^4-64=0
Answer:
A
Step-by-step explanation:
x^4=64
x^2= +- 8
x = +-sqrt2, x= +- i sqrt2
Answer:
A
Step-by-step explanation:
x^4-64=0
factor
(x^2+8)(x^2-8)=0
zero property
x^2+8=0, x^2-8=0
x^2=0-8-8,
x^2=-8,
x^2=0+8=8,
x^2=8,
----------------
sqrt(8) & sqrt(-8),
gives you 2*sqrt(2) and -2*sqrt(2),
also, the square root of a negative number contains the imaginary number, i. Because sqrt(-1)=i, don't forget this formula.
So sqrt(-8)=2i*sqrt(2) and -2i*sqrt(2).
3. Which of the following statements is true about the triangles below?
ABC ABD by SSS
ABC ABD by ASA
ABC & ABD by SAS
ABC ABD by AAA
Answer:
ASA rule.
Step-by-step explanation:
See the diagram with the problem.
Given that Δ ABC and Δ ABD are congruent i.e. Δ ABC ≅ Δ ABD.
Now, we have to select the rule by which we can say that Δ ABC and Δ ABD are congruent.
Given in the figure that between Δ ABC and Δ ABD,
(i) ∠ CAB = ∠ BAD
(ii) AB is the common side, and
(iii) ∠ ABC = ∠ ABD
Therefore, by Angle-Side-Angle i.e. ASA rule we can say that Δ ABC ≅ Δ ABD.
Hence, option 2 is correct. (Answer)
Answer: B the second choice
Step-by-step explanation:
What is the answer to this equation? (picture attached)
Answer:
x = [tex]\frac{42}{5}[/tex]
Step-by-step explanation:
Given
19 - [tex]\frac{5x+6}{4}[/tex] = 7 ( subtract 19 from both sides )
- [tex]\frac{5x+6}{4}[/tex] = - 12
Multiply both sides by - 4 to clear the fraction and the negative signs
5x + 6 = 48 ( subtract 6 from both sides )
5x = 42 ( divide both sides by 5 )
x = [tex]\frac{42}{5}[/tex]
Can someone help me on 1, 2, 3 and 4 plz I really need help
Answer:
NO
YES
NO
NO
Step-by-step explanation:
For a number to be the solution of the equation, the number should satisfy it.
To check if t satisfies, plug the number and compare LHS and RHS.
1) 3z + 4 = 15
Substituting z = -5, we get 3(-5) + 4 = -15 + 4 = -11 [tex]$ \ne $[/tex] 15.
Therefore, -5 is not the solution of the equation.
2) 8 - [tex]$ \frac{x}{2} $[/tex] = 0
Substituting x = 16, we get 8 - [tex]$ \frac{16}{2} = 8$[/tex]
⇒ 8 - 8 = 0
Therefore, 16 is a solution of the equation.
3) 4(p + 5) = 60
Substitute p = 12. 4(12 + 5) = 4(17) [tex]$ \ne $[/tex] 60.
Not a solution.
4) 8 - k = -48
If k = -40, then 8 - (-40) = 48
On the RHS we have -48. Not equal. So, it is not a solution.
An item is regularly priced at $55. It is now priced at a discount of 25 off the regular price.
Use the ALEKS calculator to find the price now.
Step-by-step explanation:
Do 25% of $55 which is $13.75
You have the right idea but you're supposed to then subtract $13.75 from the original
So:
55 - 13.75 = $41.25
**URGENT:** It will take Mr. Warner 15 1/2 hours to install a fence. Each day, he works 1 1/3 hours on the fence. After he finished working on the fence yesterday, he had 3 1/2 hours left to do. For how many days has Mr. Warner worked on the fence?
A girl cut off 2/5 of a ribbon. The piece she cut off was 5 meters long.How
many meters long was the original ribbon?
Answer:
12.5
Step-by-step explanation:
5/2*5=12.5
Answer:
Your answer is 12.5 meters long
Step-by-step explanation:
so you would want to see how long each 1/5 is so if 2/5 is 5 then 1/5 would be half of that so 2.5 then times that by 5 to get your answer which is 12.5.
Choose the property of addition that justifies the equation.
(6 + x) + 8 = 6 + (x + 8)
(Choose one)
Answer:
Associative
Step-by-step explanation:
Associative property is the one that says that when 3 or more numbers are summed, the grouping of such numbers has no effect on the result of the sum. It is:
(a + b) + c = a + (b + c) for every a, b and c real numbers.
PLEASE HELP DUE TONIGHT!!!!!in the number that should go in the blank. Use a slash (/) to show a fraction.
Abigail bought 3/4 of a pound of hard candy. She has 3/8 of a pound of candy left, so she has eaten Answer
pound of candy.
Abigail has eaten 3/8 of a pound of candy.
This is the answer because 3/4 is equivalent to 6/8, and if Abigail has eaten 3/8 of a pound of that 6/8 pound of candy, then there will be 3/8 remaining (6/8 - 3/8 = 3/8).
To find out how much candy Abigail has eaten, we subtract the amount of candy she has left (3/8 of a pound) from the original amount she bought (3/4 of a pound). The calculation shows that Abigail has eaten 3/8 of a pound of candy.
The student is asking how much candy Abigail has eaten if she originally bought 3/4 of a pound and now has 3/8 of a pound left. To calculate the amount of candy eaten, we subtract the amount left from the original amount. Since we are working with fractions, we ensure the denominators are the same before subtracting.
The steps to solve the problem are as follows:
Original amount of candy: 3/4 pound
Amount left: 3/8 pound
Calculate how much has been eaten: (3/4) - (3/8)
Convert the first fraction to have a denominator of 8: (6/8) - (3/8)
Subtract the second fraction from the first: (6/8) - (3/8) = 3/8
Abigail has eaten 3/8 of a pound of candy.
which value will make the fraction x-3/x+6 undefined?
Step-by-step explanation:
x+6=0
x=(-6)
so if x =(-6) it will be undefined.
Answer:
x = −3
or
x = 6
Any number multiplied by 0 is 0. This means that either x+3 or x−6 can be 0.
(x+3)(x−6) to be 0. if x+3=0, then x=−3 if x−6=0,
then x=6 hence, x can either be −3
or 6.x= −3 or x=6
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets—2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
The total number of tickets sold over these two days is 9,640.
Let's complete the table for Saturday:
For Saturday:
Adult Tickets: [tex]\(2 \times \text{Number of Adult Tickets on Friday}\)[/tex]
Children's Tickets: [tex]\(3 \times \text{Number of Children's Tickets on Friday}\)[/tex]
Using the information from Friday's sales:
Adult Tickets on Saturday: [tex]\(2 \times 976 = 1952\)[/tex]
Children's Tickets on Saturday: [tex]\(3 \times 1678 = 5034\)[/tex]
Now, we can complete the table:
[tex]\begin{array}{ccc}\text { Day } & \text { Adult Tickets } & \text { Children's Tickets } \\\text { Friday } & 976 & 1,678 \\\text { Saturday } & 1,952 & 5,034\end{array}[/tex]
To find the total number of tickets sold over these two days, add the tickets for Friday and Saturday:
Total Tickets Sold = Adult Tickets on Friday + Children's Tickets on Friday + Adult Tickets on Saturday + Children's Tickets on Saturday
[tex]\[ \text{Total Tickets Sold} = 976 + 1,678 + 1,952 + 5,034 \][/tex]
[tex]\[ \text{Total Tickets Sold} = 9,640 \][/tex]