Answer:
The complete length is 115 cm.
Step-by-step explanation:
Given:
If 20%of a length is 23 cm.
Now, to find the complete length.
Let, the complete length be [tex]x[/tex].
So, according to question:
20% of [tex]x[/tex] = 23 cm
[tex]\frac{20}{100} \times x=23[/tex]
[tex]0.20\times x=23[/tex]
[tex]0.20x=23[/tex]
Dividing both sides by 0.20 we get :
[tex]x=115[/tex]
Therefore, the complete length is 115 cm.
To find the complete length when 20% is 23 cm, divide 23 cm by 0.20 to get 115 cm as the total length.
If 20% of a length is 23 cm, we want to find out what the complete length is. To do so, we recognize that 20% is the same as saying 20 per 100 or 0.20 in decimal form. If 0.20 of the length is 23 cm, it means that 23 cm represents 0.20 of the total length. We can set up the equation like this:
0.20 * Total Length = 23 cm
To find the Total Length, we divide both sides of the equation by 0.20:
Total Length = 23 cm / 0.20
Total Length = 115 cm
Therefore, the complete length is 115 cm.
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:
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).
**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?
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)
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]
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:
rewrite 1/2(x+3)(x+5) in standard form
ANSWER:
1/2 (x+3)(x+5)
= 1/2(x^2+8x+15)_This is the right answer
= x^2/2 + 8x/2 + 15/2
= x^2/2 + 4x + 15/2
Mark me as brainst answer
And
Press on Thank You
multiples of 4 starting from 40
Answer:
40,44,48,52,56,60,64,68...
Step-by-step explanation:
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
What is the equation of a line with a slope of −4 and a point (−2, 5) on the line? Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Answer:
y = - 4x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + b ← is the partial equation
To find b substitute (- 2, 5) into the partial equation
5 = 8 + b ⇒ b = 5 - 8 = - 3
y = - 4x - 3 ← equation of line
Answer:
y= -4x-3
Step-by-step explanation:
to find this, the first step is easy. We know the slope is -4 so we have y= -4x+b. Then we to find the y intersept, so we take the point that we have (-2,5) and make x (the first number) equal to 0. to do this we add two, which means to subtract 8 from give because the slope is -4. This gives the point (0,-3). So the equation is y= -4x-3.
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.
A store advertises that customers can take 25% off original price and then take an extra 10% off is this the same as 35% off discount explain
Answer:
Yes
Step-by-step explanation:
the total discount allowed will be 25% of the original price and futher 10% of the original price which will amount to 10%+25% and this equal 35%
(5,3) and (-2,-3) slope intercept form
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-6}{-7}\implies \cfrac{6}{7}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{6}{7}}(x-\stackrel{x_1}{5}) \implies y-3=\cfrac{6}{7}x-\cfrac{30}{7} \\\\\\ y=\cfrac{6}{7}x-\cfrac{30}{7}+3\implies y = \cfrac{6}{7}x+\cfrac{-30+21}{7}\implies y=\cfrac{6}{7}x-\cfrac{9}{7}[/tex]
Answer:
-6/7? I think I'm right but make sure to comment me to let me know!
Step-by-step explanation:
Okay so the equation for slope intercept form is y2-y1/x2-x1. So we can substitute -3-3=-6 and -2-5=-7 So I think you get -6/7
-viridiancat4, an 8th grader
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
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.
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.
S
A national park in Florida is approximately x 108 square meters in area. A New York State Park
is approximately 2 x 10?square meters in area. Based on these areas, how many times larger is the
national park than the state par?
Answer:
4. 35 times larger
Step-by-step explanation:
Doing Question #4 Only
4.
Before we see this problem's solution. Lets get a background.
Suppose something has an area of "A" sq. meters.
and
Suppose another land has an area of "B" sq. meters.
and suppose A > B
If we want to know how many times A is larger than B, we simply have to divide the larger one (A) by the smaller one (B).
Now, onto our question:
We want to know how many times larger the national is than state park. So we divide the area of national by the area of state. That would be:
[tex]\frac{7*10^8}{2*10^7}[/tex]
Since the numbers are in scientific notation, we look at the rule below on how to divide scientific notation numbers:
[tex]\frac{a*10^b}{c*10^d}=(\frac{a}{c})*10^{b-d}[/tex]
Now, we apply the rule:
[tex]\frac{7*10^8}{2*10^7}\\=\frac{7}{2}*10^{8-7}\\=3.5*10^1\\=3.5*10\\=35[/tex]
So, the national park is 35 times larger than the state park.
A bag contains green marbles and red marbles, 42 in total. The number of green
marbles is 6 more than 5 times the number of red marbles. How many green marbles
are there?
Answer:
The number of green marbles are 36.
Step-by-step explanation:
Given:
Total number of marble bag contains is 42.
The number of green marbles is 6 more than 5 times the number of red marbles.
Let the number of red marbles be [tex]x[/tex].
So, the number of green marbles = [tex]6+5x[/tex]
Now, to get the number of green marbles.
According to question:
[tex]x+(6+5x)=42[/tex]
[tex]6x+6=42[/tex]
Subtracting 6 in both sides :
[tex]6x+6-6=42-6[/tex]
[tex]6x=36[/tex]
Now, by dividing 6 on both sides:
[tex]6x\div 6=36\div 6[/tex]
[tex]x=6[/tex]
The number of red marbles are 6.
And, the number of green marbles are [tex]6+5x[/tex]
= [tex]6+5\times 6[/tex]
=[tex]6+30[/tex]
= [tex]36[/tex]
Therefore, the number of green marbles are 36.
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.
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.
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.
Some facts about powers of ten are shown.
Use what you know about powers of ten to enter numbers that make the equation true.
help please!! :(
Answer:
4.23 * 10³ = 4.23 * 1000 = 4,230
Step-by-step explanation:
We should know that;
10³ = 10 * 10 * 10 = 1000
∴ 4.23 * 10³ = 4.23 * 1000 = [tex]\frac{423}{100}*1000[/tex] = 4,230
Answer:
4.23 * 10³ = 4.23 * 1000 = 4,230
Step-by-step explanation:
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]
The price of a video game was reduced from $60 to $45. by what percentage was the price of the video game reduced what is the answer show the steps
Answer:
Hey.
By what percentage was the price of the video games reduced ?
By 25%.
Step-by-step explanation:
$60 is the 100% price.
Now we have to find what percentage belongs to the reduced price, $45.
45×100/60 = 75.
75% is the percentage of the reduced price.
We can find the difference between them by doing a substraction.
100%-75% = 25%.
Hope I helped you !
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.
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 :)
An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t squared plus 120 t describes the height of the debris above the ground, h, in feet, t seconds after the explosion. When will the debris be 56 feet above the ground?
Answer:
The debris will be at a height of 56 ft when time is 0.5 s and 7 s.
Step-by-step explanation:
Given:
Initial speed of debris is, [tex]s=120\ ft/s[/tex]
The height 'h' of the debris above the ground is given as:
[tex]h(t)=-16t^2+120t[/tex]
As per question, [tex]h(t)=56\ ft[/tex]. Therefore,
[tex]56=-16t^2+120t[/tex]
Rewriting the above equation into a standard quadratic equation and solving for 't', we get:
[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]
Using quadratic formula to solve for 't', we get:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]
Therefore, the debris will reach a height of 56 ft twice.
When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.
Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.
Final answer:
To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.
Explanation:
To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:
h = -16t² + 120t
Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:
56 = -16t² + 120t
This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:
-16t² + 120t - 56 = 0
16t² - 120t + 56 = 0
Dividing by 4
4t² - 30t + 14 = 0
Again reducing by dividing by 2
2t² - 15t + 7 = 0
Now, we need two numbers which add to give 15 and multiply to give 14.
The two numbers are 1 and 14.
2t²- 14t - t + 7 = 0
2t (t - 7) - 1(t - 7) = 0
(t - 7)(2t - 1) = 0
t = 7 or 1/2
Since 1/2 second cannot be an answer, the required answer is 7 seconds
a solid consists of a hemisphere and a cone which shares the common base. the cone has a base radius of 21 cm.l, a height of 28cm and a slant height of 35cm. find the volume and the total surface area of the solid.
Answer:(i) 84 cm.
(ii) 5635π cm^2
Step-by-step explanation:
(i)
The volume of the cone = 1/3 π r^2 h
= 1/3 π 35^2 h.
The volume of the hemisphere = 2/3 π 35^3.
As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:
1/3 π 35^2 h = 2/3 π 35^3 * 6/5
h = 2/3 π 35^3 * 6/5 / 1/3 π 35^2
h = 84 cm (answer).
(ii) Surface area of the hemisphere = 2 π * 35^2 = 2450π cm^2.
Surface area of the cone = π r l where l = slant height.
l = √(35^2 + 84^2) = 91 cm.
So the surface area of the cone = 35*91 π = 3185π.
So the total surface area of the solid is 3185π + 2450π
= 5635π cm^2.
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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