The solution to the given equation in the real number system is x = 2 or x = -4 or x = -3/2
What is a real number system?A real number system comprises rational numbers, irrational numbers, integers, and whole numbers. When solving a polynomial in a real number system, we need to first factor the polynomial by grouping;
i.e.
= 2x³ + 7x ² - 10x - 24
= 2x³ + 11x² + 12x - 4x² - 22x - 24
= x(2x² + 11x + 12) - 2(2x² + 11x + 12)
= (x - 2) (2x² + 11x + 12)
= (x - 2) (2x² + 8x + 3x + 12)
= (x - 2) (2 (x² + 4x) + 3(x + 4))
= (x - 2) (2x (x + 4) + 3(x + 4) )
= (x - 2) (x + 4) (2x + 3)
In a real number system;
x = 2 or x = -4 or x = -3/2
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A researcher wishes her patients to try a new medicine for depression. how many different ways can she select 5 patients from 50 patients?
There are 2118760 ways to select 5 patients from 50 patients.
What is Combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Here, Total patients= 50
Number of selection is to made = 5
So, total ways of selection = ⁵⁰C₅
= (50X49X48X47X46) / (5X4X3X2X1)
= 2118760 ways
Thus, There are 2118760 ways to select 5 patients from 50 patients.
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Answer:
2118760
Step-by-step explanation:
She can select 5 patients from 50 patients in :
[tex]50c_{5}[/tex]
= [tex]\frac{50!}{5! (50-5)!}[/tex]
= [tex]\frac{50!}{5! 45!}[/tex]
= 50 x 49 x48 x47 x46 x45!
= 2118760
(Refer to the attached image)
===========================================
Work Shown:
side a = 8side b = 5angle C = 88 degreesApplying the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 8^2 + 5^2 - 2*8*5*cos(88)
c^2 = 64 + 25 - 80*cos(88)
c^2 = 86.2080403
c = sqrt(86.2080403)
c = 9.2848285
c = 9
Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.
What are the domain and range of the function f(x)=-log(5-x)+9?
Answer:
Domain: x < 5
Range: all numbers, -∞, ∞
This is because the problem will be able to be solved with multiple solutions as long as there are no specific values assigned to x. The problem will have a solution from a range of negative infinity to infinity, meaning every number or solution you can think of.
i like cheese burger do u liek cheese burgers 2+2+12-21+492
The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2). determine the lengths of the outside edges of the garden. write your answer in
simplest form.
The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
What is the scale factor?In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.
Given that:-
The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2)The length and width of the outside edge will be:-
The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-
Length = 3 ( 2x+4 ) = 6x + 12
Width = 3 ( 3x+2 ) = 9x + 6
Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
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Multiplying 10 by what number will produce an irrational number?
O √4
O 3π
O 10
O 10.5
Answer:
Multiplying 10 by pi will produce an irrational number.
Step-by-step explanation:
10 and 10 are both rational, 10 and 10.5 are both rational, 10 and √4 are both rational (I researched to double check), leaving 10 rational and 3π irrational, meaning that the answer is B 3π.
It cost Makayla $2.80 to send 28 text messages. How much would it cost to send 163 text messages?
Answer:
$16.30
Step-by-step explanation:
Hope this helps! Have a great day!!
The cost of 163 text messages is $16.3
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.Given:
price for 28 text messages = 2.80
So, price for 1 text messages = 2.80/ 28
= $ 0.1
Now, the price for 163 messages = 163 * 0.1
= $16.3
Hence, the price for 163 text messages be $16.30.
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4 x2-5x-6=0 quadratic form
Step-by-step explanation:
[tex]4 {x}^{2} -5x-6=0 [/tex]
Solve using quadratic formula
Solution:
We know that
[tex] \rm \: Quadratic \: Formula = \cfrac{ - b± \sqrt{ {b}^{2} - 4(ac) } }{2a} [/tex]
ATQ,here,
a = 4b = -5c = -6Substitute the values into the quadratic formula.
[Let Quadratic Formula = x][tex]\rm\implies x = \cfrac{5 ± \sqrt{( - 5) {}^{2} - 4 \times (4 \times - 6) } }{2 \times 4} [/tex]
[tex]\rm\implies{x} = \cfrac{5 ± \sqrt{25 - 4 \times (24) } }{2 \times 4} [/tex]
[tex] \implies \rm \: x = \cfrac{5 ± \sqrt{25 - 96} }{8} [/tex]
[tex] \implies \rm \: x = \cfrac{5± \sqrt{121} }{8} [/tex]
[tex] \implies \rm \: x = \cfrac{5± \sqrt{11 \times 11} }{8} [/tex]
[tex] \implies \rm \: \: x = \cfrac{5±11}{8} [/tex]
The answer will be the combination of both solutions[tex]\boxed{x = 2}[/tex]
OR
[tex]x = \boxed{- \cfrac{3}{4}} [/tex]
Which if the following r-values represents the strongest correlation?
A. 0.35
B. 0.45
C. 0.25
D. 0.55
Answer:
0.55 hope it will help you
A die has six sides, with the numbers 1, 2, 3, 4, 5, and 6. What is the probability of rolling a number greater than 2?
Answer:
1/2
Step-by-step explanation:
There are 3 numbers greater than 2: 3, 4, 5, and 6. There are 6 numbers, so it is 3/6=1/2.
(04.01 MC)
The tables show some input and output values:
Table A
Table B
Input Output
Input Output
1
7
6
1
2
9
7
3
3
7
2
4
5
8
5
Which tables represent functions?
O Only A
O Only B
O Both A and B
ONeither A nor B
Answer:
table a represents functions table b does not
Solve for the value of s.
(s+1)°
(2S-1)°
Answer
90*
Step-by-step explanation:
Answer:
s = 30
Step-by-step explanation:
The three angles lie on a line.
The sum of angles on a line are supplementary, meaning they add up to 180 degrees.
s + 1 + 90 + 2s - 1 = 1803s = 90s = 30Use for #3 and #4. The 8th grade had a cooler of water for the pass the cup competition. It had 15 gallons of water. Each cup of water held 8 oz. of water. (There are 128 oz of water in 1 gallon.) 4. Solve for x. (awnsers) 240 270 200 210
Answer:
I believe the answer is 240
Does the table below represent a function? Why or Why Not?
Answer:
A.
Step-by-step explanation:
For the x value (6) there are two different output values(y) 5 and 6.
If it's a function then there must be one output value for every input.
If you wanted to make the graph of y=3x+1 steeper which equation could you use
Answer:
Increase the slope
Step-by-step explanation:
The slope of this line is '3' ......a steeper line has a higher number than '3' in front of the 'x' like y = 4x+3 or y = 7x + 12
Don’t know how to solve
Answer:
Θ ≈11.31°
Step-by-step explanation:
the model is a right triangle with side opposite being the height and side adjacent the horizontal length , in relation to angle Θ , then
using the tangent ration
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4}{20}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{20}[/tex] ) ≈ 11.31° ( to 2 dec. places )
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Slope question
What is Y?
Y=2x+8
A triangle cannot have one obutse angle and one right angle. True or flase?
Answer:
No
Step-by-step explanation:
Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.
Answer:
false
Step-by-step explanation:
Rachel rides her bike due east at 9 miles per hour. Amos rides his bicycle due north at 12 miles per hour. If they left from the same point at the same time, how far apart will they be in 1 hour? Geometry and measurement :))) help please.
They will be 15 miles apart after one hour if they left the same point at the same time.
How do we measure and calculate the distance in Geometry?The distance between two points in geometry can be calculated by using the Pythagoras theorem.
Mathematically, the Pythagoras theorem can be expressed as:
[tex]\mathbf{d = \sqrt{x^2 +y^2}}[/tex]
where;
x and y are opposite and adjacent sides respectively.[tex]\mathbf{d = \sqrt{(9)^2 +(12)^2}}[/tex]
[tex]\mathbf{d = \sqrt{81+144}}[/tex]
[tex]\mathbf{d = \sqrt{225}}[/tex]
d = 15 miles
Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.
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In a city, the distance between the library and the police station is 3 miles less than twice the distance between the
police station and the fire station. The distance between the library and the police station is 5 miles. How far apart
are the police station and the fire station?
O 1 mile
O 3 miles
O4 miles
O6 miles
Answer:
C. 4 milesStep-by-step explanation:
Let the distance between police station and the fire station be x.
According to question we have:
the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station,the distance between the library and the police station is 5 miles.It can be expressed as:
5 = 2x - 3Solve the equation for x:
2x = 5 + 32x = 8x = 4Correct choice is C
In the diagram below, GH is parallel to DE . If GH is 3 more than EH FH=10, and DE=12 find the length of EH. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answer: 5
Step-by-step explanation:
Since [tex]\overline{GH} \parallel \overline{DE}[/tex], by the corresponding angles theorem, [tex]\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED[/tex]. This means [tex]\triangle FGH \sim \triangle FDE[/tex] by AA.
As corresponding sides of similar triangles are proportional,
[tex]\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5[/tex]
However, as distance must be positive, we consider the positive solution, x=5.
Therefore, the answer is 5
A baseball is thrown into the air from a height of 5 feet. the ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. which equation models the height of the baseball? assume that acceleration due to gravity is –16 ft/s2. h(t) = 16t2 49.64t 5 h(t) = -16t2 5t 49.64 h(t) = -16t2 49.64t 5 h(t) = 16t2 5t 49.64
The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².
Maximum height reached by the base ball
The maximum height reached by the baseball is calculated as follows;
H = y₀ + v₀yt + ¹/₂gt²
Assuming negative direction for upward motion
H = y₀ + v₀yt - ¹/₂gt²
0 = y₀ + vt -16(t)²
0 = 5 + 3.2v - 16(3.2)²
0 = 5 + 3.2v - 163.84
3.2v = 158.84
v = 158.84/3.2
v = 49.64
Required equation modelH(t) = 5 + 49.64t -16(t)²
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Answer:C?
Step-by-step explanation:
edge
A school had a lot of problems with
student absences and wanted to try a
intervention program to see if it
encouraged students to come to school
more often. As a trial, 20 students were
split into two equal size groups. Group 1
would get the new intervention and
Group 2 got no intervention. The mean-
number of absences was calculated after
one month for each group, as shown in
the table below. What inference can be
made about the results?
The inference is that the results of the study are statistically significant.
How to make the inference about the results?For group 1, we have:
Mean = 1.7
For group 2, we have:
Mean = 3.3
The mean of group 2 is greater than group 1, and the mean difference is:
Difference = 3.3 - 1.7
Evaluate
Difference = 1.6
Based on the sample values, the mean difference of 1.6 is significant.
Hence, the inference is that the results of the study are statistically significant.
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a hypotenuse = 24?
√2, √2, 24
24√2, 24√2, 12
24, 24, 24√2
12√2, 12√2, 24
The sides of the triangle are (d) 12√2, 12√2, 24
How to determine the side lengths?The given parameters are:
Hypotenuse = 24Angle = 45-45-90 degree anglesIn a 45-45-90 degree angle triangle, we have:
Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2
This means that:
Opposite =Adjacent
So, we have:
24 = Adjacent√2
Divide both sides by √2
Adjacent = 24/√2
Evaluate
Adjacent = 12√2
This means that:
Opposite = 12√2
Hence, the sides of the triangle are (d) 12√2, 12√2, 24
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Which points are 19 units apart?
(-14, 12) and (5, 12)
(-5, 19) and (-12, 19)
l(-20, 5) and (1, 5)
(14, 12) and (5, 12)
ous Activity
#1
√(-14-5)²+(12-12)²√19²√36119Yes
#2
√(-5+12)²√7²7No
#3
√(-20-1)²√21²21No
#4
√(14-5)²√9²9No
Answer:
(-14, 12) and (5, 12)
Step-by-step explanation:
From inspection of the points given, we can see that all pairs of points share the same y-values.
Therefore, each pair of points are on the same horizontal line.
To find the distance between the points, simply find the difference between the x-values.
Given points: (-14, 12) and (5, 12)
⇒ Difference between x-values = 5 - (-14) = 19 units
Given points: (-5, 19) and (12, 19)
⇒ Difference between x-values = 12 - (-5) = 17 units
Given points: (-20, 5) and (1, 5)
⇒ Difference between x-values = -20 - 1 = -21 = 21 units
Given points: (14, 12) and (5, 12)
⇒ Difference between x-values = 14 - 5 = 9 units
What are two possible measures of the angle below?
What is the equation in point slope form of the line that is parallel to the given line and passes through the point (4,1)?
A Y-1=-2(x-4)
B y-1=-1/2(x-4)
C y-1=1/2(x-4)
D y-1=2(x-4)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y-1=\stackrel{\stackrel{m}{\downarrow }}{2}(x-4)\qquad \impliedby \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}[/tex]
so we're really looking for the equation of a line with a slope of 2 and that it passes through (4 , 1)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \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}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{4})[/tex]
kinda twins.
the prom committee is made up of 8 boys and girls. If there are 12 boys and 15 girls in the group to pick the committee from, how many ways can the committee be organized?
1). 1860 ways
2). 3185325 ways
3). 2220075 ways
4). 675675 ways
Thanks guys!!
The number of ways can the committee be organized will be 2220075. Then the correct option is 3.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
The prom committee is made up of 8 boys and girls.
If there are 12 boys and 15 girls in the group to pick the committee from.
Then the number of ways can the committee be organized will be
Then the number of ways is given by the combination formula. Then we have
Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀
Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495
Number of ways = 2220075
Thus, the correct option is 3.
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2+7x1232 = what pls help its matth
Answer:
8626
Step-by-step explanation:
use a calculator in instead of here this was a EZ question but thanks for the points and if you have a harder question i'll be waiting
Answer: 8,626
Step-by-step explanation:
PEMDAS
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes first:
2+ (7x1232)
Next, addition:
2+8624
8626
Hope this helps :)) Brainliest would be appreciated :D
How many combinations of 3 playing cards (from a 52-card deck) exist?
25,000
1,649
523
its not 22,100 btw....
Answer:
Step-by-step explanation:
To determine the number of combinations of 3 playing cards from a standard 52-card deck, we can use the formula for combinations, which is given by:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
C(52, 3) = 52! / (3!(52-3)!)
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
3! = 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
C(52, 3) = 52 x 51 x 50 / (3 x 2 x 1)
Cancelling out the common factors:
C(52, 3) = (52 x 17 x 25) / (3 x 2 x 1)
C(52, 3) = 22,100
Therefore, there are 22,100 combinations of 3 playing cards that can be chosen from a 52-card deck.