Answer:
I solved 26 problems correctly.
What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm
The area of wafer required to make the ice cream cone 68.75 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
Given:
r= 2cm, l=9 cm
Surface area,
=πr(l +r)
=3.14*2(9 + 2)
= 6.25*11
=68.75 cm²
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35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903
Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warrior's helmet. Which of the following are pairs of congruent segments? Check all that apply. A. PO and ON B. FR and NR C. NO and NM D. RC and RO E. DV and EW
Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
What is congruence in geometry?The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.
We have:
The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.
Unfolded paper can be seen in the provided figure. The sheet is square.
The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.
FR ≅ NR
AO ≅ ON
RC ≅ RO
NO ≅ NM
DV ≅ HV
Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
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A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
A cooler contains five colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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What is the surface area of the image below?
Answer:
Step-by-step explanation:
Comment
I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.
There are 2 semicircular ends which add up to 1 whole circle.
There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.
Solution
2 semi circles
r = d / 2
r = 20/2
r = 10
Area = pi r^2 This area is for 2 semicircles which = 1 circle.
Area = 3.14 * 10^2
Area = 3.14 * 100
Area = 314
Trough
r = d / 2
d= 20
r = 20/2
r= 10
w = 2*pi*r / 2
w = 2*3.14 *10/2
w = 31.4 cm
L = 15 cm
Area = 15 * 31.4
Area = 471
Total Area = 785
Warm Shelters.org received a donation of $32,000 to buy beds and dressers for its new dormitories. Each bed will cost $320.00 and each dresser will be $75.00 each. A total of 132 pieces of beds and dressers are needed. What is the percentage of dressers with respect to the number of beds?
Please HELP
Answer:
you can buy 98 beds and buy dresses by rest of the money
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
If function f was translated down 4 units, the _
values would be _
A point in the table for the transformed function would be _
Using translation concepts, the correct statement is given by:
If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:
x 1 2 3 4 5
f(x) 9 15 33 87 249
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Answer:
The CORRECT answer is:
1. f(x)
2. decreased by 4
3. (4, 87)
Step-by-step explanation:
Took the test
Mr.Baker is making a box using all of a 48-inch strip of oak. the box will be 14 inches wide. how long will the box be?
The length of the box made by Mr. Baker is 10-inch
Mr. Baker has strip of 48- inch long oak, by this strip he is making the rectangle box of width 14-inch.
The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.
As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.
The width of the box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches
Thus the Mr. Baker made the box which is 10 inches long.
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Terick ran 2 3of a mile in 8 minutes. It took Chad 40 minutes to run 3 1 4miles. a. If Terick runs at that speed, how long will it take him to run one mile?
The time taken for Terick to run one complete mile is determined as 12 minutes
Speed of Chad
The speed of chad is calculated as follows;
s = distance/time
s = (3.25 miles)/(40)
s = 0.08125 miles/min
Total distance ran by Terick2/3 of a mile = 8 mins
1/3 of a mile = ?
1/3 of a mile = 4mins
1 mile = 8 mins + 4 mins = 12 mins
Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.
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The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)
Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:
[tex]6\sigma = 800 - 200[/tex]
[tex]\sigma = 100[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
To ensure a margin of error of 20, we solve for n when M = 20, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.96 \times 100[/tex]
[tex]\sqrt{n} = 1.96 \times 5[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]
n = 96.04.
Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.
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If the line segment AB is on a number line, and point A is at 6 and Point B is at 13, then the length of AB is ____.
Answer:
7
Step-by-step explanation:
The length of AB is the distance between A and B which is B-A -> 13-6= 7
Solve the formula d = rt for t
What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)
You must make 3 shots in a row to win the fairs basketball game. The hoop is uneven and the backboard curved. Only 5 players out of 100 win the game. What percentage of players do not win.
Answer:
95%
Step-by-step explanation:
5 player won, meaning 95 player didn't.
This means that 95% of the players didn't win.
9x+9y=9. Solve for Y
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9 ( divide through by 9 )
x + y = 1 ( subtract x from both sides )
y = 1 - x
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9
First, take 9x to the right side.
9y = 9 - 9x
9y = 9 ( 1 - x )
Divide both sides by 9.
y = 1 - x
has a slope of 2 and contains what point? y-3=2(x+4)
We know immediately that the line must pass through (-4, 3).
please help me with this problem ! would appreciate it!!!
[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]
Answer: correct radical forms are:
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
Step-by-step explanation:
Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.
therefore,
radical form of given values are :
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
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*30pts*What is the value of x in the triangle?
Answer:
A.4
Step-by-step explanation:
Using the sine rule
sin(α)/A equals sin(β)/B
From the question & inserting values,
sin(90°)/8 equals sin(30°)/x
∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8
∴x equals 4
You can learn more on the sine rule in case you get confused.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 8 ( divide both sides by 2 )
x = 4
3. Multiply the polynomials (a² + 3a-7) and (2a²-a + 4). Simplify the answer. Show your work.
Answer:
Answer:
[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]
Step-by-step explanation:
Which of the following points lies on the graph of the function y = 2*3^x? a. (1, 0) c. (3, 6) b. (2, 9) d. (0, 2) Please select the best answer from the choices provided A B C D
The point which lies on the graph of the given function is; Choice D; (0, 2).
Which of the following points lies on the graph of the function y = 2*3^x?The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.
Hence, y = 2*3^0;
y = 2 ×1 = 2.
Hence, the point is; (0,2).
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Please help whilst I try to solve as well.
Answer:
Step-by-step explanation:
Answer:
420 cm³Step-by-step explanation:
we find the volume as if it were a parallelepiped and we remove the volume of the missing part.
8 * 6 * 10 = 480 cm³
480 - 2 * 3 * 10 = 420cm³
simplify 3 + [5n - (2-n)]
Answer:
6n+1
Step-by-step explanation:
Eliminate the parenthesis by changing the symbol of each term inside
3+[5n-2+n]
Eliminate the bracket and group similar terms
5n+n+3-2
Simplify terms
6n+1
Paulo is flying a kite as shown
in the right. Find the length of the kite string.
The length of the kite string is 50 ft
How to determine the length of the kite string?The string and the kite form a right triangle.
So, the length can be calculated using Pythagoras theorem as follows:
c^2 = 30^2 + 40^2
This gives
c^2 = 2500
Take the square roots
c = 50
Hence, the length of the kite string is 50 ft
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Drainpipe comes in lengths of 2.5 metres. A man wants to buy drainpipe to fit down
one side of his house from the ground to the gutter.
Estimate how many lengths he will need.
lengths
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:
Number of drainpipe needed = 15 m / 2.5 m = 6
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
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The required quantity of drainpipe is mathematically given as six.
L=6
What is the lengths he will need?Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:
In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.
L=15/2.5
L=6
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Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answer:
operant conditioning and schedules of reinforcement
what is the fraction 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's
solve for x -
[tex]\bold{x {}^{2} + 5x + 6 = 0}\\\\[/tex]
ty! ~
The solution of the given quadratic equation is x=-2 or x=-3.
The given quadratic equation is x²+5x+6=0.
What are different methods to solve a quadratic equation?The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.
By using the splitting middle term method we can solve x²+5x+6=0.
That is, x²+2x+3x+6=0
⇒x(x+2)+3(x+2)=0
⇒(x+2)(x+3)=0
⇒(x+2)=0, (x+3)=0
⇒x=-2 or x=-3.
Therefore, the solution of the given quadratic equation is x=-2 or x=-3.
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which is the correct graph for the inequality
