A quadratic equation is in the form of ax²+bx+c. It took 3seconds for the golf ball to reach the green.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
A.) The time that the ball takes to reach the green can be found by equation the equation against zero. As the ball will have 0 height when it will be on the green,
t²+4t-21=0
t²+7t-3t-21=0
t(t+7)-3(t+7)=0
(t+7)(t-3)=0
t = -7, 3
Hence, it took 3seconds for the golf ball to reach the green.
B.) Since the time can not be negative the second value is wrong.
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Which choice belongs in space 5!!!
3. Eden has completed 7⅝ laps of a 10 lap race How many more laps does she still need to run?
eden must run 2 3/8 laps to complete the race.
How to calculate the laps that Eden is missing?To calculate the laps that Eden is missing, we must perform the following operation:
We must take into account that he has already completed 7 laps and a segment of the eighth lap that is equivalent to 5/8, that is to say that he has 3/8 to complete the eighth lap.
On the other hand, once he completes the eighth lap, he will have 2 full laps left to finish the race. Due to the above, it can be stated that it is missing 2 3/8 laps.
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liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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Question 7(Multiple Choice Worth 1 points)
(02.05 LC)
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5.
−4
−5
4
5
The value of k based on the information given will be k = 2.
How to calculate the value?It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).
The slope of x will be:
= (4 - 0)/(0 + 4)
= 4/4
= 1
By using slope point form, y = kx + 4.
Substitute x = 2.
g(-2) = -2k + 4 = 0
2k = 4
k = 4/2 = 2
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True or false? The graph represents a function
Answer:
true
Step-by-step explanation:
The statement is true because every graph associated a unique x-value for each y - value
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
By using the given dimensions and volume of water, we will see that the height of the tank is 36.6cm
How to find the height of the tank?We know that 27,238 cm³ is the volume of water on the tank, and this is equal to 2/3 of the volume of the tank.
So we can write:
27,238 cm³ = (2/3)*V
Then the volume of the tank is:
V = (3/2)*27,238 cm³ = 40,992 cm³
The base of the tank measures 40cm by 28cm, then:
B = 40cm*28cm = 1,120 cm²
Then the height H is such that:
H*1,120 cm² = 40,992 cm³
Solving for H:
H = (40,992 cm³)/(1,120 cm²) = 36.6cm
The height of the tank is 36.6 centimeters.
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Solve number 8 please
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3
this is shown in graph b
What does the word progressive mean in the sentence below
What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me
(Refer to the attached image)
[tex]\sf Sine \ Rue : \ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Given following:
A = 56°B = 77°a = 38 mb = ? mSolve for b (distance between school and mall):
[tex]\dashrightarrow \sf \dfrac{\sin 56}{38} = \dfrac{\sin 77}{b}[/tex]
[tex]\dashrightarrow \sf b= \dfrac{38\sin 77}{\sin 56}[/tex]
[tex]\dashrightarrow \sf b= 44.6615 \quad \approx \quad 45[/tex]
If f(x)=2(3x-5) when f(x) =74,what is the value of x??
Answer:
x = 14
Step-by-step explanation:
given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives
2(3x - 5) = 74 ( divide both sides by 2 )
3x - 5 = 37 ( add 5 to both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Look at the following sequence.
54, 36, 24, 16, . . .
If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.”
Answer:
[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]
Step-by-step explanation:
Calculate the ratio of the progression by dividing a term of it by the immediately preceding one.[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]
We simplify the fractions:[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]
Since the ratio is the same, that is the common ratio.
MissSpanishIs y=2x-3 a funtion?
Answer:
yes
Step-by-step explanation:
Yes.
The graph of y = 2x - 2 is a straight line sloping up to the right.
It passes the vertical line test, so it is a function.
Find A and B if Cos(A - B) = (sqrt(3))/2 ; Sin(A + B) = 1
a number, n is multiplied by -5/8 the product is -0.4 how would you set this up to solve
The value of n in the mathematical statement is 0.64
How to solve the equation?The statement is given as:
n multiplied by -5/8 equals -0.4
Rewrite properly as:
n * -5/8 = -0.4
Multiply both sides by -1
n * 5/8 = 0.4
Multiply both sides by 8/5
n = 0.64
Hence, the value of n in the mathematical statement is 0.64
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What is the probability you spin something larger than 10
The probability you spin something larger than 10 will be 1 / 2.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The given data is:-
There are 8 numbers in the spinner.We need to find the probability of a number greater than 10.The probability will be calculated as:-
Total numbers = 8
Numbers greater then 10 are = 13 , 16 , 22 , 42 = 4
Probability = 4 / 8 = 1 / 2
Therefore the probability you spin something larger than 10 will be 1 / 2.
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tìm số hữu tỉ
(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
Quadrilateral abcd has vertices a(1,0) b(5,0) c (7,2) d(3,2). use slope to prove that abcd is a parallelogram.
[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]
[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]
As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.
If cos θ= 12 /13 and θ is located in the Quadrant I, find sin (2 θ ), cos(2 θ ), tan(2 θ )
Answers: sin(2∅) = 120/169, cos(2∅) = 119/169, tan(2∅) = 120/119
What are trigonometric functions?Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.
Analysis:
If cos∅ = adjacent/hypotenuse = 12/13,
Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5
sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12
sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169
cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169
tan(2∅) = sin(2∅) / cos(2∅) = 120/169 ÷ 119/169 = 120/119
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I need help, please. I don’t understand
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
For a science project, billy observed a chipmunk and a squirrel stashing acorns in trees. the chipmunk hid 3 acorns in each tree. the squirrel hid 4 acorns in each tree. they each hid the same number of acorns, although the squirrel needed 2 fewer trees. you are going to investigate the number of acorns that each animal hid.
The number of acorns that each animal hid is 48
What is an Equation ?An equation is formed when two algebraic expressions are equated by an equal sign.
It is asked to calculate the number of acorns that each animal hid.
Total number of acorns hid = number of acorns hid per tree * number of trees
Let T be the number of trees chipmunk used
For chipmunk: = 3*T
For squirrel: = 4*(T-4)
As both the animals hid same number of acorns.
3T = 4(T-4)
3T = 4T - 16
16 = T
Therefore the chipmunk hid 16 * 3 = 48 acorns
and the squirrel hid 4(16-4) = 48 acorns.
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Which three side lengths best describe the triangle in the diagram?
A. 6 cm, 8 cm, and 10 cm
B. 3 cm, 4 cm, and 5 cm
C. 5 cm, 8 cm, and 10 cm
D. 6 cm, 8 cm, and 9 cm
Please help me
The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.
What is a Triangle?A triangle is a shape that has three sides. The sides can be measured using a ruler.
The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.
Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.
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What is the value of the underline digit?
119.65
For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10
Answer:
a) 13
b) 1/3
c) -2
d) 1
Step-by-step explanation:
This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:
For example:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
________
f(-3) = 3x + 7
f(-3) = 3(-3) + 7
f(-3) = -9 + 7
f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.
f(-3) = -2
The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:
For example:
f(x) = 8
f(x) = 3x + 7
8 = 3x + 7
8 - 7 = 3x
1 = 3x
x = 1/3
f(x)= 10
f(x) = 3x + 7
10 = 3x + 7
10 - 7 = 3x
3 = 3x
3/3 = x
1 = x
I hope this helps!
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
How large the size of a sample needs to be if we want to a 90% confidence level with a margin of error no more than 1.5%
Answer:
A 90 percent level can be obtained with a smaller sample, which usually translates into a less expensive survey. To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000.