Answers
[tex]\bf 5x-\cfrac{1}{2}(3x+8)=-4-\cfrac{7}{2}x\impliedby \times \stackrel{LCD}{2} \\\\\\ \boxed{2}\cdot 5x-\boxed{2}\cdot \cfrac{1}{2}(3x+8)=-\boxed{2}\cdot 4-\boxed{2}\cdot \cfrac{7}{2}x \\\\\\ 10x-(3x+8)=-8-7x\implies 10x-3x-8=-8-7x \\\\\\ 7x-8=-8-7x\implies 14x=-8+8\implies 14x=0 \\\\\\ x=\cfrac{0}{14}\implies x=0[/tex]
Related Questions
decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals
Answers
3.0, 3.2, 3.4, 3.6, 3.8
Hope I helped :)
Answer:
Decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:
3.2,3.4 and 3.6
Step-by-step explanation:
We have to find decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals
3.0
3.0+0.2= 3.2
3.2+0.2= 3.4
3.4+0.2= 3.6
3.6+0.2= 3.8
Hence, decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:
3.2,3.4 and 3.6
Given: ∆ABC, AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
m∠ABC = 48°
Find: m∠PCD
Answers
Answer: The measure of angle PCD is 42 degree.
Explanation:
It is given that in ∆ABC,
AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
∠ABC = 48°
Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.
According to the angle sum property the the sum of interior angles of a triangle is 180.
[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]
[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]
[tex]\angle BAC=66^{\circ}[/tex]
The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.
[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]
Since PB=PC , so triangle BPC is an isosceles triangle.
[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]
From the figure it is noticed that,
[tex]\angle PCD+\angle PCB=\angle BCA[/tex]
[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]
[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]
[tex]\angle PCD=42^{\circ}[/tex]
Therefore, the measure of angle PCD is 42 degree.
For a right triangle with an altitude of 12 and a base of 16, find the length of the hypotenuse.
Answers
A=12. B=16. C=?
11^2+16^2=C^2
121+256=C^2
377=c^2
The square root of 377 is bout 19 rounded or it's 19.41 but didn't think you wanted decimals
Hope this helps and is what u r looking for have a nice day
What would be an appropriate measure to describe the amount of water in a puddle?
milliliters
feet
tons
miles
Answers
Answer:
milliliters
Step-by-step explanation:
Factor 9y 2 - 12y + 4.
Answers
The answer is (3y-2)(3y-2) or [tex] (3y-2)^{2} [/tex]
Answer:
Factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
Step-by-step explanation:
As the expression is given in the question be .
= 9y² - 12y + 4
Simplify the above
= 9y² -6y -6y + 4
= 3y (3y -2) -2 (3y - 2)
= (3y-2)(3y-2)
Therefore factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
Introduction to addition or subtraction of fractions with different denominator 3/4-1/8
Answers
so when you multiply, you multiply both on the top and on the bottom, so this would be:
3 x 2 / 4 x 2 = 6 / 8
Now you can add or subtract: 6/8 - 1/8 = 5/8
Hannah bought a jacket on sale for 20% off. The jacket originally costs $48. How much money did Hannah save by buying the jacket on sale?
$9.60
$2.00
$4.40
$10.30
Answers
answer
saved $9.60
If y = 15 when X=12 find Y when X=32
Answers
By acknowledging the linear relationship between X and Y, we set up a proportion based on the given values and solve for Y when X = 32, finding Y approximately equals 40.
Explanation:This problem relates to the concept of
linear relationships
in mathematics. By understanding the relationship between two variables x and y, you can find the value of one by knowing the value of the other. Here, if y = 15 when X = 12, we can say that the ratio of y to x is constant. Therefore to find the value of Y when X = 32, we will maintain the same ratio. Now, set up a proportion 15/12 = Y/32 and solve for Y. Cross-multiplication gives us: Y = 15 * 32 / 12. After calculating this, Y equals approximately 40. Therefore, the value of Y when X is 32 will be around 40, keeping the relationship linear.
Learn more about Linear Relationships here:https://brainly.com/question/31693063
#SPJ2
What percent of 67.5 is 7.02 ? Answer in proportions
Answers
percent formula : is / of = % / 100
of = 67.5
is = 7.02
% = x
set it up
7.02 / 67.5 = x / 100
cross multiply
(67.5)(x) = (7.02)(100)
67.5x = 702
x = 702 / 67.5
x = 10.4
so ur answer is 10.4%
The percent of 67.5 is equal to 7.02 is for the number 10.4.
To find what percent of 67.5 is 7.02, we can use proportions.
Let's represent the unknown percentage as 'x'. The proportion can be set up as follows:
(7.02 / 67.5) = (x / 100)
Now, solve for 'x':
7.02 × 100 = 67.5 × x
702 = 67.5x
x = 702 / 67.5
x ≈ 10.4
Therefore, 7.02 is approximately 10.4 percent of 67.5.
learn more about percent here
brainly.com/question/31323953
#SPJ6
5x+4x2(2x+7)-6x2-9x+(x+3)(x-8)
Write this expression as a polynomial in standard form
Answers
5x + 8x^3 + 21x^2 - 6x^2 - 9x + x^2 - 5x - 24
8x^3 + 16x^2- 9x - 24
5x+8x^3+28x^2-6x^2-9x+x^2-8x+3x-24
Next group like terms ( the x's with the x's, the x^2 with the x^2, and so on)
8x^3+23x^2-9x-24 is your answer
Suppose f(x) = x2 and g(x) = 4x2. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) vertically compressed by a factor of 4.
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
C. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) shifted 4 units left.
Answers
f(x) = x²
g(x) = 4x²
Therefore
g(x) = 4f(x)
This means that the value of g(x) is 4 times the value of f(x). So the graph og (x) is the graph of f(x) vertically stretched by a factor of 4.
The graph shown below confirms the conclusion.
Answer: C.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answers
Answer:Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.
Step-by-step explanation:
At the annual dogs show chantel noticed that there were three more Scottie’s than schnauzers. She also realized that the number of wire haired terriers was five less than twice the number of schnauzers if there were 78 dogs in all how many schnauzers were their?
Answers
The volumes of the two solids are equal, and the cross sections shown are taken at the same height above the bases. Find the missing length of the cross section of the rectangular pyramid. Round your answer to the nearest hundredth.
A. 1.59m
B. 1.62m
C. 1.67m
D. 1.76m
Answers
[tex]area(tri) = (1 \div 2)(base)(height) \\ a(t) = bh \div 2 \\ area(rect) = (length)(width) \\ a(r) = lw[/tex]
Since the triangle is right, and has sides of 4 & 5, then it is a 3-4-5 special right triangle. Now the height can be the side that's 3, and the base 4, since by definition the height us 90° from the base.
[tex]a(t) = bh \div 2 = 3m \times 4m \div 2 \\ = 12 {m}^{2} \div 2 = 6 {m}^{2} [/tex]
Now we know that the a(r) also = 6, because of the congruency of the two shapes, with equal volumes, at the same height. So now let's find our length (l):
[tex]a(r) = lw \: > > 6 {m}^{2} = l(3.6m) \\ l = 6 {m}^{2} \div 3.6m = 1.666m \\ = 1.67m[/tex]
Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
(−6, 0)
(−1, −2)
(−5, −1)
(−16, 2)
(0, −3)
Answers
(-1,-2)
(-5,-1)
Answer:
(−6, 0) , (−1, −2) and (−5, −1)
Step-by-step explanation:
The given inequality is x+3y ≥ −8
Substitute all the given points in this inequality and check which points satisfy.
For (−6, 0)
-6+3(0) ≥ −8
- 6 + 0 ≥ −8
- 6 ≥ −8 => True.
Hence, (−6, 0) is a solution.
For (−1, −2)
-1 + 3(-2) ≥ −8
-1 - 6 ≥ −8
- 7 ≥ −8 => True.
Hence, (−1, −2) is a solution.
For (−5, −1)
-5 + 3 (-1) ≥ −8
- 5 -3 ≥ −8
-8 ≥ −8=> True.
Hence, (−5, −1) is a solution.
For (−16, 2)
-16 +3 (2) ≥ −8
-16 + 6 ≥ −8
-10≥ −8 => False.
Hence,(−16, 2) is not a solution.
For (0, -3)
0 + 3(-3) ≥ −8
-9 ≥ −8=> False.
Hence, (0, -3) is not a solution.
Therefore, below ordered pairs are solutions of the given inequality
(−6, 0) , (−1, −2) and (−5, −1)
HELP!
Solve for x.
−1/3x≤−6
Enter the solution to the inequality in the box.
Answers
Note that multiplying such an inequality requires reversing the direction of the inequality symbol.
I subst. 18 for x in −1/3x≤−6 as a check, and found that the resulting inequality is true.
Answer:
x [tex]\geq[/tex] 18
Step-by-step explanation:
If you travel 156 miles on 4 gallons of gasoline how far can you travel on 12 gallons how many miles on 6 gallons
Answers
You can travel a distance of 468 miles on 12 gallons of gasoline and a distance of 234 miles on 6 gallons of gasoline.
What is Proportion?Proportion is the setting of two or more ratios to be equal.
That is, if there is a ratio between a and b and another ratio between c and d, then we can say that,
a : b = c : d ⇒ a/b = c/d ⇒ a d = b c
We have,
Distance travelled is 156 miles on 4 gallons of gasoline.
We have to find the distance travelled on 12 gallons and 6 gallons of gasoline.
Let x be the distance travelled on 12 gallons of gasoline and y be the distance travelled on 6 gallons of gasoline.
We have a proportional relation here,
156 : 4 = x : 12 = y : 6
First taking the relation,
156 : 4 = x : 12
⇒ 156/4 = x/12
⇒ 39 = x/12
⇒ x = 39 × 12
⇒ x = 468
Taking the second relation,
156 : 4 = y : 6
⇒ 156/4 = y/6
⇒ 39 = y/6
⇒ y = 39 × 6
⇒ y = 234
Hence you can travel 468 miles on 12 gallons and 234 miles on 6 gallons.
To learn more about Proportions, click :
https://brainly.com/question/29774220
#SPJ5
n is the set of real number that are factors of 36
Answers
An equilateral triangle has a perimeter of 3x+9. what is the length of each side of the triangle
Answers
___________________________________
Explanation:
___________________________________
[tex] \frac{3x+9}{3} [/tex] ;
= [tex] \frac{3x}{3}[/tex] + [tex] \frac{9}{3}[/tex] ;
= x + 3 .
___________________________________
Note: An equilateral triangle has 3 SIDES THAT ARE EQUAL IN LENGTH.
___________________________________
The perimeter is the sum of the total length of all three (3) sides. So, to find the length of each side {Note: Each side has an equal length}; we divide the given perimeter, by "3"}.
___________________
The answer is: " x + 3 " .
______________________
To check our answer:
3(x+3) =? 3x + 9 ??
Using the distributive property of multiplication:
_____________________________________
(3*x) + (3*3) =? 3x + 9?
3x + 9 =? 3x + 9 ? Yes!
_____________________________________
In a company, it takes 4 employees 4 days to complete a task. It would take 2 employees 8 days to complete the same task. Which function can be used to represent e, the number of employees working on the task, and d, the number of days it takes them to complete that task?
Answers
The function representing the relationship between the number of employees and the number of days it takes to complete the task is[tex]\[ e \times d = 16 \][/tex].
To represent the relationship between the number of employees (e) and the number of days (d) it takes to complete a task, we can use the formula:
[tex]\[ e \times d = k \][/tex]
where k is a constant representing the amount of work to be done.
Given the information that 4 employees complete the task in 4 days, and 2 employees complete it in 8 days, we can set up two equations using the formula:
[tex]\[ 4 \times 4 = k \][/tex]
[tex]\[ 2 \times 8 = k \][/tex]
Now, solve each equation for ( k):
[tex]\[ 4 \times 4 = 16 \][/tex]
[tex]\[ 2 \times 8 = 16 \][/tex]
Since both equations give us the same constant ( k ), we can conclude that:
[tex]\[ e \times d = 16 \][/tex]
Therefore, the function representing the relationship between the number of employees and the number of days it takes to complete the task is:
[tex]\[ e \times d = 16 \][/tex]
Use the Pythagorean Theorem to find the missing measure when a = 24 and b = 7.
Answers
To start, we know the a and b values which are 24 and 7. As according to the formula, we square them which gives us 576+49=c^2
Then we simplify: 625=c^2
And solve for c= 25 (c represents the missing length)
Tori computers the value of 8 • 95 in her head by thinking 8(100 - 5)= 8•100 - 8•5 which number property is she using ?
Answers
2. Consider the function . a.) Find the inverse of f(x) and name it g(x). Show and explain your work. b.) Use composition to show that f(x) and g(x) are inverses of each other. c.) Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.
First correct answer will get 25 pts and brainliest!!!! So please help! :D
Answers
Given that [tex]f(x)= \frac{1}{3} x+2[/tex], we find the inverse g(x) as follows:
First, we rewrite the function as: [tex]y=\frac{1}{3} x+2[/tex]
Next, we switch x and y and then solve for y as follows:
[tex]x=\frac{1}{3} y+2 \\ \\ \frac{1}{3} y=x-2 \\ \\ y=3(x-2) \\ \\ y=3x-6[/tex]
We then rewrite the equation using function notation to get:
[tex]g(x)=3x-6[/tex]
Part B:
For two function that are inverse of each other, the composition of the two functions gives x.
Thus,
[tex]f \circ g=f(g(x))=f(3x-6)= \frac{1}{3} (3x-6)+2=x-2+2=x \\ \\ g\circ f=g(f(x))=g( \frac{1}{3} x+2)=3( \frac{1}{3} x+2)-6=x+6-6=x \\ \\ \therefore f\circ g=g\circ f=x[/tex]
Since, f o g = g o f = x, hence g(x) is the inverse of f(x).
Part C:
The graphs of f(x) and g(x) are attached.
From the graph it can be seen that the prperties of both graphs are similar, the properties of one graph in the x-axis correspond to the properties of the other graph in the y-axis and vice-versa. Also, the two lines intersect at a point were x = y.
Which number is not in scientific notation?
a. 1.1 x 10^213
b. 7.8 x 10^8
c. 3.02 x 10^-10
d. 35 x 10^4
Answers
d. 35 x 10^4 is not in scientific notation
Denis and Dasha solve this problem in two different ways. The perimeter of a rectangle is 54 centimeters. Its length is 6 centimeters. What is its width? Use the drop-down menus to complete the sentences below.
Answers
Final answer:
To find the width of a rectangle with a perimeter of 54 cm and a length of 6 cm, use the formula P = 2l + 2w. After plugging in the given values and simplifying, the width is calculated to be 21 cm.
Explanation:
Finding the Width of a Rectangle
To solve this problem, we remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 54 centimeters and the length is 6 centimeters, we can set up the equation as follows: 54 = 2(6) + 2w. Simplifying this, we get 54 = 12 + 2w, and then subtracting 12 from both sides gives us 42 = 2w. Dividing both sides by 2, we find the width w to be 21 centimeters.
Step-by-Step Calculation
Start with the formula for the perimeter of a rectangle: P = 2l + 2w.Substitute the given values into the formula: 54 = 2(6) + 2w.Simplify the equation: 54 = 12 + 2w.Isolate the width term: 42 = 2w.Divide both sides by 2 to solve for the width: w = 21.Therefore, the width of the rectangle is 21 centimeters.
Factor this polynomial expression. x2 – 18x + 81
Answers
is your answer
hope this helps
Factorizing the polynomial expression x² - 18x + 81 = (x - 9)²
What is factorization?Factorization is the simplification of an expression into a smaller expression using its factors.
To factor this polynomial expression. x² - 18x + 81, we proceed as follows
Since we have the polynomial expression x² - 18x + 81, we multiply x² by 81 to get x² × 81 = 81x².
Now, we look for the factors of 81x² such that the sum of those factors equal - 18x
So, we have that 81x² = -9x × (-9x)
So, -18x = -9x - 9x
So, replacing this with -18x, we have that
x² - 18x + 81 = x² - 9x - 9x + 81
Now, factorizing, we have that
x² - 9x - 9x + 81 = x(x - 9) - 9(x - 9)
= (x - 9)(x - 9)
= (x - 9)²
So, factorizing x² - 18x + 81 = (x - 9)².
Learn more about factorization of polynomial here:
https://brainly.com/question/30806486
#SPJ6
A clothing store owner tracks the amount of money the last 10 customers spend in her store. The owner concludes that the typical amount spent by any customer is $28.80. The owner's conclusion
A) is valid. The last 10 customers only bought sale items.
B) is correct. This is the average amount spent by any customer.
C) is invalid. This is not a good representation of all customers.
D) is unfair. The last ten people in the store may have been tired.
Answers
Which of the following would eliminate the variable on the left side of the given equation?
36 - 19w = -6w + 41
A.) add -19w
B.) add 6w
C.) add 19w
D.) add -36
Answers
Hope this helps!
the first side of a triangle is 3 m shorter than the second side. the third side is 4 times as long as the first side . the perimeter is 27 m. find the length of each side
Answers
Which statement describes similar figures?
two figures that are the same size
two figures that are the same size but a different shape
two figures that are the same shape but different sizes
none of the above