Answer:
[tex]x=\frac{5}{2}[/tex] or x= -4
Step-by-step explanation:
To solve the quadratic equation, start by factorizing it.
[tex]2x^{2} +3x-20=0[/tex]
(2x -5)(x +4)= 0
Since the equation equals to zero, either one of its factor, i.e. (2x -5) or (x +4), can be equal to zero.
2x -5= 0 or x +4= 0
Solve for x:
2x= 5 or x= -4
[tex]\bf{x=\frac{5}{2}}[/tex]
_______
Alternatively, the quadratic formula can be used to solve the equation.
[tex]\boxed{x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]
This is especially useful when the quadratic equation cannot be factorized. To use the formula, ensure that the equation is in the form of [tex]ax^{2} +bx +c=0[/tex].
Additional:
For an example on solving quadratic equations using the quadratic formula, do check out the following!
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Answer:
3/2 or 1.5
Step-by-step explanation:
Finding the gradient
gradient (m) = y₂ - y₁ / x₂ - x₁m = 5 + 1 / 4 - 0m = 6/4m = 3/2 or 1.5Answer:
gradient = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
calculate the gradient (slope) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1 ) and (x₂, y₂ ) = (4, 5 )
m = [tex]\frac{5-(-1)}{4-0}[/tex] = [tex]\frac{5+1}{4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
The richter scale measures the magnitude, m, of an earthquake as a function of its intensity, i, and the intensity of a reference earthquake, . which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? a. b. c. d.
The magnitude of an earthquake with an intensity 10,000 times is [㏒10000]
What is magnitude?magnitude can be regarded as the size or the weight of destruction that is been experienced as a result of the earthquake.
The magnitude as regards Richter scale is
[㏒(I/I₀]
But we were given l as 10000I₀.
Then if we substitute we have, [㏒(10000I₀./I₀)]
If we simplify we have:
[㏒10000]
Therefore, magnitude of an earthquake with an intensity 10,000 times is [㏒10000]
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someone help me find r please!
Answer:
4
Step-by-step explanation:
A particular baseball diamond is actually a square with 76-foot sides. what is the distance from home plate to second base? express the answer in simplified radical form. then find a decimal approximation.
We conclude that the distance between the home plate and the second base is 107.48 feet.
How to get the distance between the home plate and the second base?
We know that the distance will be equal to the diagonal of the square. Remember that for a square of side length S, the diagonal is:
D = S*√2
In this case, the side length is S = 76ft, then the diagonal is:
D = 76ft*√2 = 107.48ft
From this, we conclude that the distance between the home plate and the second base is 107.48 feet.
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Which conditional probabilities are correct? check all that apply. p(d | f) = startfraction 6 over 34 endfraction p(e | d) = startfraction 7 over 25 endfraction p(d | e) = startfraction 7 over 25 endfraction p(f | e) = startfraction 8 over 18 endfraction p(e | f) = startfraction 13 over 21 endfraction
The conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
How to determine the true conditional probabilities ?The formula to compute the conditional probability P(A|B) is:
P(A | B) = P(A and B)/P(B)
The above means that the probability of event A such that the event B has already occurred
When the above formula is applied to the give data in the complete, we have:
P(D | F) = 6/34
P(E | D) = 7/25
P(D | E) = 7/18
P(F | E) = 8/18
P(E | F) = 8/34
Hence, the conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
See attachment for complete question
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Answer: a,b,d
Step-by-step explanation:
trust
Dalia has a jar with 6 red pencils and 4 green pencils. She will randomly pick two pencils without replacement. What is the probability that Dalia will pick two red pencils?
6/25
1/3
9/25
2/5
The probability that Dalia will pick two red pencils without replacement is 1/3.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of picking two red pencils = 6/10 x 5/9 = 1/3
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Jdncjdcnndnsjddnsjdnejd ejdnjendjddnjedn
Answer:okay I don’t know what is this but what do you need help with exactly?
Step-by-step explanation:
What is the longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide, and 11cm tall?
The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.
What is a right rectangular prism?A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.
it is also called the cuboid.
Analysis:
The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.
Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](13)^{2}[/tex]
= 196 + 169 = 365
[tex](diagonal)^{2}[/tex] = 365
diagonal = [tex]\sqrt{365}[/tex] = 19.1cm
In conclusion, the length of the longest diameter is 19.1cm
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An agricultural researcher wishes to see if kelp extract helps prevent frost damage on tomato plants. 100 tomato plants in individual containers are randomly assigned to 2 different groups. plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with kelp extract, while the plants in group 2 are not. after the first frost in the autumn, 12 of the 50 plants in group 1 exhibited damage. 18 of the 50 plants in group 2 showed damage. test the claim to see if there is evidence of a decrease in the proportion of tomatoes suffering frost damage for tomatoes sprayed with kelp extract.
a) state the hypotheses.
b) identify the p-value to the nearest thousandth.
c) state the conclusion in the context of the problem.
The p-value to the nearest thousandth. p value > 0.05
What is null and alternative hypothesis ?A null hypothesis is a statement, in which there is no relationship between two variables. An alternative hypothesis is statement in which there is some statistical significance between two measured phenomenon.
Group 1 n₁ = 50 , x₁ = 12
Group 2 n₂ = 50 , x₂ = 18
p₁ = x₁/n₁ = 12/50 = 0.24
p₂= x₂/n₂ = 18/50 = 0.36
Testing the null and alternative hypothesis
H₀ = p₁ - p₂= 0
Hₓ = p₁ - p₂ < 0
Level of Significance α =0.05
Test Statistic
[tex]\rm z = \dfrac{p_1-p_2}{\sqrt{\dfrac{p_1(1-p_1)}{n_2} +\dfrac{p_2(1-p_2)}{n_2}}}[/tex]
On substituting the values
z = -0.12/0.9086
z = -1.32
p value = p(z > -1.32)
p value = 0.0934
Therefore p value > 0.05
Hence we fail to reject H₀ at 5 % level of significance .
There is no significant evidence that the decrease in proportion of tomatoes suffering frost damage for tomatoes sprayed with the kelp extract.
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Adam is an opera singer. Below are the number of times that his voice cracked during each of six concerts
1,0,3,0,2,1
Using this data, create a dot plot where each dot represents a concert
In this picture dots are clearly shown the frequency of the concert.
What is Frequency?Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.Here, in given data about the six concerts
Concerts Frequency
0 2
1 2
2 1
3 1
Thus, on number line we mark 2 dots on zero, 2 dots on one, 1 dot on two and 1 dot on 3.
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I need help with this question
Answer:A
Step-by-step explanation: because there is an association with the child’s hight and age so the answer is A ( plus I have did this before and got it wrong and the actual Answer was A when I picked B
Answer: A
Step-by-step explanation:
What is 6 3/4 % of $7,600.00
A. 513
B. 520
C. 456
D. 479.25
E. 550
Answer:
A 513
Step-by-step explanation: is your answer
Hope this helps :)
Let x = 0.147 and let y = 0.147.
Answer:
X is a rational number, y is not a rational number, and y is larger.
Step-by-step explanation:
The line above the 0.147 means that the number goes on forever and never stops. This is a characteristic of an irrational number. Rational numbers, however, do stop, so x is rational. Because y goes on forever, it has more values after the 0.147, making it larger.
Write the verbal sentence as an algebraic equation.
The product of a three and a number plus five is 20.
Step-by-step explanation:
product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20
3×x +5=20
3x+5=20
Subtract 5 from both sides
3x+5-5=20-5
3x=15
3x/3=15/3
x=5
Find the first four terms of the sequence given a = 31 and an+1 = an - 3.
A. 31, 26, 23, 20
B. 31, 28, 25, 22
C.31, 25, 22, 19
D. 31, 27, 26, 25
please help me answer this question
Answer:
The answer is21
The midpoint of overline AB is M(-4, 0)M If the coordinates of A are (-6, 6) what are the coordinates of B?
Answer:
(-2, -6)
Step-by-step explanation:
Equating A and B to the Midpoint (M) :
(-4, 0) = (-6 + x / 2, 6 + y / 2)Equations formed :
-6 + x / 2 = -4-6 + x = -8x = -22. 6 + y / 2 = 0
6 + y = 0y = -6Midpoint : (x , y)
(-2, -6)GIVING BRAINLIEST!!!!!
Answer:
(4,1)
Step-by-step explanation:
After being reflected over the x=-3 line it will be (1,4)
then you reflect over the y=x line which makes it (4,1)
The expression above can also be written in the form a=, b=,c=. 3 6/5
The expression above can also be written in the form .
For this expression, a =
, b =
, and c =
.
The value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
[tex]\rm = 3^{\dfrac{6}{5}}[/tex]
We can write it as:
[tex]\rm = \sqrt[5]{3^6}[/tex]
The value of a = 3,
The value of b = 6, and
The value of c = 5
Thus, the value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
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Round this number to the nearest one.
87.6
ANWER:
rounded o the nearesr tens is 88.6
Answer:
88
Step-by-step explanation:
Because 6 is greater than 5 it will rounded off and 87.6 = 88
mr.ellis has started a vegetable garden.he bought 15 bags of soil and 3 bags of fertilizer for 282.72.he realized he didnt have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.what was the cost of each bag of soil and fertilizer?let the cost of each bag of soil =x and the cost of bag of fertilizer = y.
The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Mr. Ellis has started a vegetable garden.
He bought 15 bags of soil and 3 bags of fertilizer for 282.72.
He realized he did not have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.
Let the cost of each bag of soil be x and the cost of a bag of fertilizer be y.
Then we have the linear equations,
15x + 3y = 282.72
5x + 2y = 107.23
On solving the equations 1 and 2, we have
x = 16.25 and y = 12.99
The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.
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I need help! Asap please.
Answer:
3 1/2 square units
Step-by-step explanation:
For this small triangle whose vertices are on grid points, the use of Pick's theorem will give the area with the least work.
__
theoremPick's theorem says that the area is ...
A = i +b/2 -1
where i is the number of grid points inside the boundary, and b is the number of grid points on the boundary.
applicationHere, only the given coordinates are boundary points that are on grid points. (b = 3)
The figure shows us three grid intersections inside the boundary of the triangle. (i = 3)
That means the area is ...
A = 3 +3/2 -1 = 3 1/2 . . . . square units
_____
Alternate solution
The triangle is bounded by a square 3 units on a side. From that, we can subtract a 2×3 triangle at upper left, a 1×2 triangle at upper right, and a 3×1 triangle at the bottom. That leave a figure area of ...
A = 3² -1/2(2×3) -1/2(1×2) -1/2(3×1) = 9 -3 -1 -3/2 = 3 1/2 . . . . square units
(The area of a triangle is 1/2bh, where b and h are the base and height of the triangle.)
__
Another alternate solution can be had by using a formula with the vertex coordinates:
A = 1/2|(x1)(y2 -y3) +(x2)(y3 -y1) +(x3)(y1 -y2)|
= 1/2|(-8)(3 -5) +(-5)(5 -2) +(-6)(2 -3)| = 1/2|16 -15 +6| = 3 1/2 . . . square units
A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If two marbles are
drawn out of the bag, what is the exact probability that both marbles drawn will be
red?
Answer:
28/171
Step-by-step explanation:
The probability initially of drawing a red would be 8/19 since there were 19 marbles in the bag in the beginning. However, without replacement, the probability of drawing another red would be 7/18 as there would be one less red and one less marble in the bag so to find the combined probability of getting 2 red marbles, multiply 8/19 by 7/18 to get: 56/342 = 28/171
HELP ASAP GIVING BRAINLIEST PLEASE HELP FAST
Answer:
Step-by-step explanation:
We find a like term and that is 33 so we mutiply 2/3 by 11 and we get 8 22/33 and do the same to 1 10/11 and we get 1 30/33
8 22/33- 1 30/33 since we can do that we give 22 an extra 33
so 7 55/33 - 1 30/33 (just like subtracting we borrow.)
=6 25/33
Basically i converted 1 of the 8 into a fraction which was 33 and added it to 22 which got me 55 from their it was just a basic subtraction problem. think of what i did like this 43-
34
that wont work so you borrow a 1
PLEASE ANSWER NUMBER 30 PLEASE!!
Answer:
d) x ≤ 3
Step-by-step explanation:
9. Use the Desmos graphing calculator to find slope and y-intercept for the least-squares
regression line for the dataset in the table:
xy
31
45
8 11
10 21
m= 2.55, b= 6.435
m=1.477, b=1.477
m= 1.698, b-0
m=2.55, 6-6.435
Answer:
D) m=2.55, b=-6.435
Step-by-step explanation:
See attached file ("a" represents the slope and "b" represents the y-intercept).
ladder reaches a window 18 ft high,
and makes a 64 angle with the
ground. How long is the ladder?
Round your ancun
Using trigonometric ratio, the length of the ladder that reached the window is 20.03 feet
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let l represent the length of the ladder, using trigonometric ratio:
sin(64) = 18/l
l = 20.03 feet
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Gold can undergo transmutation. superscript 185 subscript 79 baseline upper a u right arrow superscript 181 subscript 77 baseline upper i r superscript 4 subscript 2 baseline upper h e this type of nuclear decay is called .
The type of Nuclear decay that is described where Gold undergoes transmutation is given as 185/79 Au → 181/77 Ir + 4/2 He, it is called Alpha Decay.
What are the characteristics of Alpha Decay?An Alpha Decay can be described as a form of radioactive or Nuclear decay where the atomic nucleus releases an alpha particle (also known as Helium Nucleus).
It then converts into a nucleus that is atomic with an atomic number of two and a mass number of four.
Alpha Decay is usually trigged for two key reasons:
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Which of the following expressions is true?
2^4•2^4>2^7
3^2•3^6=3^7
4^3•4^5<4^8
5^2•5^3=5^6
Answer:
2^4•2^4>2^7
Step-by-step explanation:
Hope it helps you in your learning process.
can you guys help me with this fast
Answer:
1/2¹⁵ or 2⁻¹⁵
Step-by-step explanation:
2³ / (2⁶)³
2³ / 2¹⁸ (The exponents multiply in such cases)
1 / 2⁽¹⁸⁻³⁾
1/2¹⁵ or 2⁻¹⁵
