Please could you explain this step by step I’m really stuck.
Answer:
x = -2.5
x = 2
Step-by-step explanation:
Hello!
We can remove the denominators by multiplying everything by it.
Solve:
[tex]\frac{5}{x + 3} + \frac4{x + 2} = 2[/tex][tex]5 + \frac{4(x + 3)}{x + 2} = 2(x + 3)[/tex][tex]5 + \frac{4x + 12}{x + 2} = 2x + 6[/tex][tex]5(x + 2) +4x + 12 = (2x + 6)(x + 2)[/tex][tex]5x + 10 + 4x + 12 = 2x^2 + 6x + 4x + 12[/tex][tex]9x + 22 = 2x^2 + 10x + 12[/tex]Let's make one side equal to 0.
[tex]0 = 2x^2 + x - 10[/tex]Solve by factoring, and then the zero product property.
[tex]0 = 2x^2 + x - 10\\[/tex]Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".
[tex]0 = 2x^2 - 4x + 5x - 10[/tex][tex]0 = 2x(x - 2) + 5(x - 2)[/tex][tex]0 = (2x + 5)(x - 2)[/tex]Using the zero product property, set each factor to 0 and solve for x.
2x + 5 = 0The two answers are x = -2.5, and x = 2.
Answer:
x = -5/2, 2
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]
With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.
First, multiply both sides by (x+3)(x+2) to get rid of the denominator.
[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]
Simplify/Expand in:
[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]
Arrange the terms or expression in quadratic equation:
[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]
Factor the expression:
[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]
Solve like linear equation as we get:
[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]
Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2
Pls answer this for. I need it now ASAP, thanks
create a feature writing article on the topic "Parallel lines: Nature's beauty". Including an explanation/proof why the lines are parallel and insights
The angle between two parallel lines is zero, we can prove it by putting the value of tanθ as 0.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
As we know, parallel lines in geometry are co-planar straight lines that do not cross at any point. Parallel planes are planes that never meet in the same three-dimensional space. Curves that do not touch or contact each other and maintain a constant minimum distance are known as parallel curves.
We know that the angle between two parallel lines is zero degrees.
[tex]\rm tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]
tanθ = 0
m1 = m2
Thus, the angle between two parallel lines is zero we can prove it by putting the value of tanθ as 0.
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Evaluate the following expression.
(-3)-² =
Answer:
The answer to this is 9.
Step-by-step explanation:
First of all, you wrote the expression wrong, but that's okay. It's supposed to be written as (-3)².
Second of all, since multiplying two negatives makes a positive and squaring is just multiplying the integer to itself, then -3×-3=9. I hope this helps! :)
I need help on this urgently please thank you
Answer:
g(x) = -√(x+6)
Step-by-step explanation:
The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).
__
solve for yx = f(y)
x = y^2 -6
x +6 = y^2 . . . . . . add 6
-√(x +6) = y . . . . . negative square root
The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).
The inverse of f is g(x) = -√(x +6).
_____
Additional comment
The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.
Tomás bought a new car for $41,000. If the value of the car depreciates by 17% each year, determine the value
of his car in 9 years.
This is a means of reducing the cost of a goods or an asset over time. The value of the car after 9 years is approximately $888
DepreciationThis is a means of reducing the cost of a goods or an asset over time.
Mathematically, the cost of goods after a particular year is expressed as:
P(t) = P0e^-rt
Given
P0 = $41000rate r = 17% = 0.17time t = 9 yearsSubstitute
P(17) = 41000r^0.17(9)
P(17) = 4100(0.21653)
P(17) = 887.79
Hence the value of the car after 9 years is approximately $888
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Choose the triangle that seems to be congruent to △AEC.
△BFC
△ABD
△EFD
Use the Pythagorean Theorem to find the m
14.1
X
X=
14.7
Answer:
x = 4.2
Step-by-step explanation:
14.1² + x² = 14.7²
198.81 + x² = 216.09
216.09 - 198.81 = 17.28
√17.28 = 4.15
x = 4.15
Round to nearest tenth
x = 4.2
12.A circle has a radius of 3.8 feet. Which measurement is closest to the circumference of
the circle in feet?
A. 23.8 ft
B. 45.3 ft
C. 47.7 ft
D. 11.9 ft
Circumference = 2 x radius x PI
Circumference = 2 x 3.8 x 3.14
Circumference = 23.86
answer: the closest one is A. 23.8 FT.
Please Help I Don't Understand!
Answer:18
Step-by-step explanation:
Answer:
C. 16
Explanation:
[tex]\rightarrow \sf \dfrac{9}{4} = \dfrac{x+2}{8}[/tex]
cross multiply
[tex]\rightarrow \sf \dfrac{9(8)}{4} = x + 2[/tex]
simplify integers
[tex]\rightarrow \sf 18 = x + 2[/tex]
exchange sides
[tex]\rightarrow \sf x =18-2[/tex]
subtract integers
[tex]\rightarrow \sf x =16[/tex]
Find the equation of the line with Slope = −7 and passing through (7,−54 . Write your equation in the form y=mx+b
.
The equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5
Equation of a lineThe equation of a line in pint slope form is expressed as:
y - y1 = m(x-x1)
where
m is the slope = -7
(x1, y1) = (7, -54 ) is the point on the line
Substitute
y + 54 = -7(x -7)
Write in slope intercept form
y + 54 = -7(x -7)
y + 54 = -7x + 49
y = -7x - 5
Hence the equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5
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There is 2.50m of rope and 11.5 inch pieces are cut. How many centimeters of rope will be left over?
Answer:
1.42 cm
Step-by-step explanation:
2.5 m = 98.4251 inches
98.4251 in / 11.5 in =8.5587
.5587 inches left over =1.42 cm
There will be 18.87 centimeters of rope left over.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
Let's convert the length of the rope to inches.
1 meter = 39.37 inches
2.50m = 98.43 inches
Now,
The number of 1.5-inch pieces.
= 98.43 / 11.5
= 8.55 pieces
Now,
11.5 inches pieces are cut.
This means,
= 98.43 - (8x11.5)
= 7.43 inches
Now,
1 inch = 2.54 cm
7.43 inch = 18.87 cm
Thus,
There will be 18.87 centimeters of rope left over.
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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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You have 6 different colored balloons. In how many distinct ways can the balloons be ordered?
Select one:
a.
720
b.
365
c.
5040
d.
120
Answer: a. 720
Step-by-step explanation:
You have 6 different sticks to choose from for the first stick. Then there are 5 for the second (6 - 1 = 5), then 4 for the third (5 - 1 = 4), etc all the way to the last stick.
Mathematically, this can be shown with 6!. In other words, 6 factorial.
6 * 5 * 4 * 3 * 2 * 1 = 720
The answer to our question is:
a. 720
Helpppppp asappppp pls
Show your work
I’ll give brainliest!!!!!!
Answer: 3360 ft squared
Step-by-step explanation:
Short side : 30 x 14 = 420
Long side 30 x 3 x 14 = 1260
420 + 420 + 1260 + 1260 = 3360
pls give brainliest
have a nice day
What does s(8) = 6.0 mean in terms of this problem?
A.A tree that is 6 years old is 8 meters tall.
B.A tree that is 8 years old is 6 meters tall.
C.8 different trees are 6 meters tall.
D.6 different trees are 8 meters tall.
Answer: C i think.
Step-by-step explanation:
8 different trees multipled by s equal to 6 meters tall in total.
the diagram shows a right angled triangle .
Answer:
the image should help.
Step-by-step explanation:
image explains everything.
Write an equation that represents the line.
Step-by-step explanation:
a general line equation is
y = ax + b
"a" being the slope is the line, "b" being the y-intercept (the y value when x = 0).
we see from the 2 marked points (by we could choose any points on the line) that
y changes by 2 units, when x changes by 3 units.
so the slope is 2/3.
we use one point (1, 2) to solve for b
2 = 2/3 × 1 + b = 2/3 + b
6/3 = 2/3 + b
4/3 = b
and the full equation is
y = 2/3 x + 4/3
The table shows information about the population of a town. emily takes a random sample of 90 people from the town. 40 of these people have not been to their doctor in the last year. work out an estimate for the number of people in the town who have not been to their doctor in the last year (2 marks)]
The estimate for the number of people in the town who have not been to their doctor in the last year is 7062.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Total population = 1819 + 6150 + 2003 + 5918 = 15890
Emily takes a random sample of 90 people from the town.
40 of these people have not been to their doctor in the last year.
The estimate for the number of people in the town who have not been to their doctor in the last year:
= (40/90)×15890
= 7062.22 ≈ 7062
Thus, the estimate for the number of people in the town who have not been to their doctor in the last year is 7062.
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Please help me solve this composite shape step by step
Answer:
73 cm²
Step-by-step explanation:
Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.
__
setupThis shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)
The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:
4 cm + 5 cm + 3 cm = 12 cm
The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.
The area of each rectangle is the product of its width and height.
A = WH
__
solutiontop rectangle area = WH = (12 cm)(4 cm) = 48 cm²
bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²
Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)
Area = 73 cm²
The area of this composite shape is 73 cm².
_____
Additional comment
The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...
figure area = bounding rectangle area - removed areas
= (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²
= 73 cm²
The following table shows the total number of quizzes taken in high school. how many quizzes are taken per week?
What is the rotation that translates AWXY to AW'X'Y'? Be sure to give the degre
measure AND direction of rotation.
Please help !!!
The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.
What is a rotation in math?Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.
Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.
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Find the value of x. Round to the nearest tenth. B 18 19 A 22° C x = [? ]° X X Law of Sines: sin A a sin B b = sin C C
Answer:
23.292°
Step-by-step explanation:
see the attachment photo.
The value of x to the nearest tenth is 23.3°.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given is a triangle ABC.
Using the law of sines,
AB / Sin C = BC / Sin A
We have to find the angle A.
Substituting,
18 / sin 22 = 19 / sin x
18 × sin(x) = 19 × sin (22°)
sin(x) = (19 × sin (22°)) / 18
sin x = 0.3954
x = 23.29° ≈ 23.3°
Hence the value of x is 23.3°.
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If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients bloodstream after 6 hours if the drug decays at a rate of 20 percent per hour
After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have:
If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.
We know the exponential decay can be given as:
D = a(1 - r)ⁿ
a is the starting value and n is the number of hours.
D = 75(1 - 0.20)⁶
D = 19.66 milligrams
Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
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Which polygon has 11 sides
Answer:
Hendecagon
Step-by-step explanation:
a hendecagon has 11 sides
Answer:
Hendecagon
Step-by-step explanation:
It has 11 sides, 11 corners, and 11 angles inside the shape that equal to 1620 degrees
a
ОЈ
6(3+2d) = 54
I need that answer
Answer:
d = 3
Step-by-step explanation:
6*3=18
2d*6=12d
54-18 = 12d
36/12 = 12d/12
d = 3
Answer:
d = 3
Step-by-step explanation:
6 ( 3 + 2d ) = 54
First, solve the brackets.
18 + 12d = 54
Take 18 to the right side.
12d = 54 - 18
12d = 36
Divide both sides by 12.
d = 3
Help please thanksssssssssss
Answer:
what is your from my from is province philippines
which expression is not equivalent to -1.5(-6m+8n).
Answer:
D
Step-by-step explanation:
-1.5(-6m+8n) = 9m-12n
3(3m -4n) = 9m - 12n
9m -12n = 9m -12n
-6(-1.5m +2n) = 9m - 12n
-2(-4.5m+ 4n) = 9m - 8n
Answer: D. -2(-4.5m + 4n)
Step-by-step explanation:
First, let us simplify -1.5(-6m+8n).
Given:
-1.5(-6m + 8n)
Distribute:
9m - 12n
[A] ✗
9 /3 = 3 and 12 / 3 = 4
This means that 3(3m - 4n) = 9m - 12n = -1.5(-6m+8n)
Option A is not our answer.
[B] ✗
Using this simplified version we did above, option B is not our answer as 9m - 12n = 9m - 12n and 9m - 12n = -1.5(-6m+8n).
[C] ✗
We will distribute option C to see if we reach the same expression. Seeing below, we do, so option C is not our answer.
-6(-1.5m + 2n)
9m - 12n
[D] ✓
Since none of the other options are correct, the answer to your question D because it is not equivalent.
Answer:
D. -2(-4.5m + 4n)
Please Help! The value of m is:
Answer:
The value of m in the figure is 28.
Step-by-step explanation:
When we look at the figure, we see that 6 and 21, are connected with parallel lines to 8 and m. We can also see that 21 is dilated from 6. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)
To get m, we can do the same that we did to get 21, from 6.
To get 21 from 6, you must divide 21 by 6. So when we do the same thing to 8, we should get m.
21 / 6 = 3.5
Now that we have the dilation of 3.5, we simply multiply that by 8.
3.5 * 8 = 28
The value of x in the figure is 28.
[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{21}{6}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{7}{2}[/tex]
[tex]\\ \rm\dashrightarrow 2m=56[/tex]
[tex]\\ \rm\dashrightarrow m=28[/tex]
3x² - 12x +9=0 using quadratic formula
Answer:
The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:
x₁ = 1 and x₂ = 3
Step-by-step explanation:
✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]
either
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]
where
[tex]\bf{\Delta=b^{2}-4ac }[/tex]
Identify the coefficients
a = 3, b = -12 and c = 9
Calculate the discriminant value
Δ = b² - 4ac
Δ = (-12)² - 4.3.9 = 144 - 12.9
Δ = 144 - 108 = 36
Enter the values of a, b and the discriminant value in the quadratic formula
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]
[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]
[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]
As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.
[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]
To find x₁, just choose the positive sign before the square root. Later,
[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]
The midterm score of 45 is the decide
The midterm score of 45 is the 3rd decile, meaning that 42% of the Senior High School students scored below this test.
What is a decile?Deciles are a type of percentile that divides data into groups of 10%. That is, each decile comprises 10% of the dataset.
To determine the decile, sort the data from lowest to highest. Now, divide the result by ten. This number reflects the no. of observed values within each decile.
Sorting the data from lowest to highest, we have:
37, 43, 45, 61, 63, 74, 75, 76, 82, 87, 89, 98, 99, 100= 14/10
= 1.4
Thus, each decile contains only a 1.4 score.
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