Step-by-step explanation:
the error:
it is stated that
[tex]\frac{5x}{x+7} +\frac{7}{x} = \frac{5x}{x+7} +\frac{7(7)}{x+7}[/tex]
subtract (5x)/(x+7) from both sides
[tex]\frac{7}{x} = \frac{7(7)}{x+7}[/tex]
multiply both sides by x + 7
7(x+7) = 49x
7x + 49 = 49x
subtract 7x from both sides to isolate x and its coefficient
49 = 42x
thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong
the solution:
we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x by 1.
anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.
(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get
[tex]\frac{7}{x} = \frac{7(x+7)/x}{x+7}[/tex]
substitute this for 7/x in our original problem
[tex]\frac{5x}{x+7} +\frac{7(x+7)/x}{x+7} = \frac{5x}{x+7} +\frac{(7x+49)/x}{x+7} = \frac{5x}{x+7} +\frac{7+49/x}{x+7} = \frac{5x+7+49/x}{x+7}[/tex]
what is the area of the regular polygon shown below?
I can not figure out the length of xy
Answer:
The segment bisector is MN
Step-by-step explanation:
MN divides XY into two equal lengths
sally picks seashells by the seashore.she lost 17 of them on her way home.with the remaining seashells,she planned to fill 5 jars with the same number of seashells in each.how many seashells did she originally pick?
Answer:
5
Step-by-step explanation:
“the product of 6 and
9 decreased by 8"
Answer:
46
Step-by-step explanation:
“the product of 6 and 9 decreased by 8"
“the product of 6 and 9" = 6 * 9
"decreased by 8" = - 8 (subtract 8 from whatever, in this case 6 * 9)
“the product of 6 and 9 decreased by 8" = 6 * 9 - 8 = 46
40 points!!! Please help me solve
Answer:
34.6
Step-by-step explanation:
In this triangle we have an angle which is 38° and the side opposite to it which is 27 and we have to find the adjacent side
There is only one formula which have these two sides
tan
tan∅ = opposite ÷ adjacent
tan 38° = 27 ÷ x
x = 27 ÷ (tan 38°)
x = 34.56
x≈ 34.6
Drag each tile to the correct box. Graph the functions as transformations of f(x)=x^2. Arrange the parabolas with respect to the position of their vertices from left to right. 1: y=f(x)
2: y=f(x-4)
3: y=f(x+3)
4: y=f(x-7)
5: y=f(x+2)
6:y=f(x-1/2)
If a constant is added to a variable then the graph gets shifted toward left and vice-versa. Then the graphs are shown below.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The parabola is given below.
f(x) = x²
Then the parabolas with respect to the position of their vertices from left to right will be
1: y = f(x) = x²
2: y = f(x - 4) = (x - 4)²
3: y = f(x + 3) = (x + 3)²
4: y = f(x - 7) = (x - 7)²
5: y = f(x + 2) = (x + 2)²
6: y = f(x - 1/2) = (x - 1/2)²
The graph of the parabola is given below.
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ1
What is the measure of angle θ in the graph?
angle drawn in standard position on the unit circle, extending counterclockwise in the second quadrant
Group of answer choices
−135°
45°
135°
225°
The measure of the angle θ in the graph as described in the task content is; 135⁰.
What is the measure of angle θ in the graph?From the task content, it follows that we are required to determine the measure of angle θ in the graph as described.
Since, angle θ transverses the first quarter in the counterclockwise direction, it follows that the measure of angle θ by convention is; 90+45 = 135⁰.
Read more on angles;
https://brainly.com/question/25716982
#SPJ1
Average Allowance Amount $20, $15, $10, $5 with frequency ll, 5, 10, 3. What is the range of the allowance amounts?
Answer:
$15
Step-by-step explanation:
Range = Highest number- Lowest number
Range=20-5
=$15
3√6/√15
Solve it using radicals please!!!
Answer:
3√10/5
Step-by-step explanation:
[tex]\frac{3\sqrt{6} }{\sqrt{15} }[/tex]
Rationalize √15
[tex]\hookrightarrow \frac{3\sqrt{6} }{\sqrt{15}}\times\frac{\sqrt{15} }{\sqrt{15} } \\\\\hookrightarrow \frac{3\sqrt{6} \times\sqrt{15} }{15} \\\\\hookrightarrow \frac{3\sqrt{90}}{15} \\\\\hookrightarrow \frac{3\sqrt{10} }{5} \\\\[/tex]
A tractor tire has a radius of 28 inches. If the tire is rotating at 80 degrees per second (i.e. it takes 9/2 seconds to make one revolution), how fast is the tractor traveling in miles per hour? Round your answer to the nearest 0.01 mph. Do not include units in your answer.
The speed of the tractor's tire by means of the information given is; 547.06.
How fast is the tractor moving?According to the task content;
It follows that the radius of the tire is; 28 inches and the period taken for one revolution is; 4.5s.On this note, the speed of the tractor is;
Speed = (πr²) ÷ 4.5
Speed = (3.14×28²)/4.5
Speed = 547.06
Read more on speed;
https://brainly.com/question/6504879
#SPJ1
If the sales per day of a start-up company can be modeled using the function s(d) = d 3 + 10, what is the maximum number of sales per day on the interval 0 < d ≤ 3?
The maximum number of sales will be equal to 37.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given function is:-
s(d) = d³ + 10maximum number of sales per day on the interval 0 < d ≤ 3The maximum value of d = 3
s(d) = d³ + 10
s(d) = (3)³ + 10
s(d) = 27 + 10
s(d) = 37
Therefore the maximum number of sales will be equal to 37.
To know more about function follow
https://brainly.com/question/2833285
#SPJ1
Multiply
[(x-1)/(x^2-2x-3)].[(3x-9)/(x+2)]
Answer:
3(x -1) / (x + 1)(x + 2).
Step-by-step explanation:
(x-1)/(x^2-2x-3)].[(3x-9)/(x+2)
Factoring the denominator and 3x - 9:
= (x - 1) / (x + 1)(x - 3) * 3(x - 3) / (x + 2)
The (x - 3)'s cancel out, so we have:
(x - 1)/(x + 1) * 3 / (x + 2)
= 3(x -1) / (x + 1)(x + 2).
What is the value of x?
A. 10.4
B. 52
C. 61.6
D. 92
Answer:
A. 10.4
Step-by-step explanation:
180-128=52÷5=10.4
Question 1-3
Which gives the exact value of the equation 15x=3?
Answer:
The value of x in 15x=3, is 1/5 or 0.2
The length of a rectangular field is 31 meters and the breadth is 14 meters, outside it a 2 meter wide path is made all around, what will be the cost of laying sand on this path at the rate of 7 per square meter
Cost of laying sand on this path = Rs. 1372 at the rate of Rs. 7 per sq. m
Step-by-step explanation:
[ refer to attachment ]
Area of field + path = L × B
=> 35 × 18
=> 630 m² -------------(1)
Area of field = L× B
=> 31 × 14
=> 434 m² --------------- (2)
Area of path = area 1 - area 2
=> 630 - 434
=> 196 m²
Given Rate = Rs. 7/ m²
If cost of 1m² = Rs. 7
Cost of 196m² = 7×196
=> Rs. 1372
Find the size of the angle marked a
Answer:
57°
Step-by-step explanation:
Given line is straight line
then whole angle is 180°
then 180 - 123 = a = 57
Answer:
57°.Step-by-step explanation:
What we know is:
One angle is 123°.We don't know:
angle a°.So, we add both angles up to 180°:
123 + a = 180.Lets solve 180 - 123:
180 - 123= 57a° = 57°.Angle a° is 57°.What’s 2 x 2^18 divided 329 + 512789
Answer:
1.021769
Step-by-step explanation:
(2 x 2^18 )/(329 + 512789)
=(2 x 262.144)/(513118)
=(524.288)/(513118)
=1.021769
can you please help?
( 9 × 10^ − 7 )^ 2
standard form at the end please
Answer:
Step-by-step explanation:
Answer: 6889.
( 9 × 10^ − 7 )^ 2
standard form 6889.
Solve the following simultaneous equations in ELIMINATION way
Answer:
Here is the solution...hope it helps:)
What is the approximate value of the correlation coefficient for the given graph?
Price of the Car ($1,000)
40
35•
30. •
25. •
20. •
15. •
10. •
5. •
0 1 2 3 4 5 6 7
Number of Years
A. 1
B. 5
C. 3
D. -1
Answer:
the answer is a bc the 1 in this makes sense
Step-by-step explanation:
thats is the best answer i think
The approximate value of the correlation coefficient for the given graph is 5.
To calculate the correlation coefficient, we first need to determine the equation of the line that passes through the points (0, 35) and (6, 5).
The formula for the equation of a straight line is y = mx + b, where "m" is the slope and "b" is the y-intercept.
Given two points (x₁, y₁) = (0, 35) and (x₂, y₂) = (6, 5), we can find the slope "m" as follows:
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - 35) / (6 - 0)
m = -30 / 6
m = -5
Now that we have the slope "m" as -5, we can find the y-intercept "b" by using one of the given points, say (0, 35):
y = mx + b
35 = -5(0) + b
35 = b
So, the equation of the line is y = -5x + 35.
Now, we can use this line to calculate the correlation coefficient "r" for the given graph.
The correlation coefficient "r" is given by the formula:
r = ∑((xᵢ - x')(yᵢ - y')) / √(∑(xᵢ - x')² ∑(yᵢ - y')²)
where (xᵢ, yᵢ) are the data points, x' is the mean of the x-values, ȳ is the mean of the y-values, and ∑ represents the sum.
Without actual data points, we can still deduce the correlation coefficient from the slope "m" of the line. The correlation coefficient for a linear relationship is equal to the square root of the coefficient of determination (R-squared), which is the square of the slope "m" in this case.
So, the correlation coefficient (R) is:
R = √((-5)²) = √25 ≈ 5
Therefore, the approximate value of the correlation coefficient for the given graph is 5.
The correct option is: B. 5
To know more about correlation coefficient, refer here:
https://brainly.com/question/29978658
#SPJ2
Complete Question:
What is the approximate value of the correlation coefficient for the given graph?
A. 1
B. 5
C. 3
D. -1
Help with a exit ticket
Answer:
4. 132°
5. 41°
Step-by-step explanation:
Q4
The arc length is twice the measure of the inscribed angle∡RP = 68° × 2 = 132°Q5
2∠ABC = ∡AC2(5x + 11) = 16x - 2610x + 22 = 16x - 2616x - 10x = 22 + 266x = 48x = 6∠ABC = 5(6) + 11∠ABC = 41°mRP
The angle will be twice the m<Q
So
it's
2(68)136°#2
2(5x+11)=16x-2610x+22=16x-2648=6xx=8m<ABC
5(8)+1140+1151a bag of suger costs $2.12 & contains 145 tablespoons of suger. what is the cost per tablespoon?
Answer:
0.01462069 cost per tablespoon
Step-by-step explanation:
a bag of sugar costs $2.12
145 tablespoons of sugar
145:2.12 is the ratio
1:x where x represents per tablespoon cost
2.12 / 145 = 0.01462069 which rounds up to 0.02
Check if it correct:
145 x 0.01462069 = 2.12
A large rectangular prism has a length of 2 and 1/2 inches, a width of 4 inches, and a height of 1 and 1/2 inches. A smaller cube has a length, width, and height of 1/2 of an inch. How many of the smaller cubes will fit into the larger rectangular prism?
Answer:
120 cubes
Step-by-step explanation:
Volume of prism and cube:We can find the number of smaller cubes that will fit into larger rectangular prism by dividing the volume of prism by the volume of cube.
Rectangular prism:
[tex]\sf l = 2\dfrac{1}{2} =\dfrac{5}{2} \ inches\\\\w = 4 \ inches\\\\h =1\dfrac{1}{2}=\dfrac{3}{2} \ inches\\[/tex]
[tex]\sf \boxed{\text{\bf Volume of rectangular prism= l * w * h}}[/tex]
[tex]\sf =\dfrac{5}{2}*4*\dfrac{3}{2}\\\\= 5*1*3\\\\= 15 \ in^3[/tex]
Cube:
[tex]\sf side = \dfrac{1}{2} \ inches\\[/tex]
[tex]\sf \boxed{\text{ \bf Volume of cube = side * side *side}}[/tex]
[tex]\sf =\dfrac{1}{2}*\dfrac{1}{2}*\dfrac{1}{2}\\\\ =\dfrac{1}{8} \ in^3[/tex]
Number of cubes = Volume of prism ÷ volume of a cube
[tex]\sf = 15 \div \ \dfrac{1}{8}\\\\=15 *\dfrac{8}{1}\\\\= 120[/tex]
120 cubes will fit
It was a busy evening at the restaurant. Ron waited on 48 tables for 3 hours. Joe served 45 customers in 5 hours. Sue waited on 34 tables for 2 hours. Who had the busiest day serving the most number of customers per hour?
Answer:
Sue
Step-by-step explanation:
34/2= 17 which is the highest out of them all.
HELP! I'll give brainliest.
2x+6 ≤x+3<3x+11
Solve the inequality, and please show your work. Thanks in advance!
Answer:
-4 < x ≤ -3
Step-by-step explanation:
The compound inequality needs to be separated into its two parts in order to obtain a solution.
__
We can do a little preliminary work to make the solutions easier.
2x +6 ≤ x +3 < 3x +11 . . . . . given
x +3 ≤ 0 < 2x +8 . . . . . . . . subtract x+3
left sidex +3 ≤ 0
x ≤ -3 . . . . . . . subtract 3
right side0 < 2x +8
0 < x +4 . . . . divide by 2
-4 < x . . . . . . subtract 4
solutionNow, we can rearrange these back into a compound inequality.
-4 < x ≤ -3
_____
The graphing calculator shows the same solution.
What is the solution of x = 2 + StartRoot x minus 2 EndRoot?
Answer:
x = 2 and x = 3
Step by step explanation:
[tex]~~~~~~x = 2 +\sqrt{x-2}\\\\\implies x -2 =\sqrt{x-2}\\\\\implies (x-2)^2 = x-2 ~~~~~~~~~~~~~~~;[\text{Square both sides}]\\\\\implies x^2 -4x+4-x +2 = 0\\\\\implies x^2-5x+6 = 0\\\\\implies x^2-3x-2x+6=0\\\\\implies x(x-3)-2(x-3) = 0\\\\\implies (x-2)(x-3) = 0\\\\\implies x =2,~~x = 3\\\\\textbf{Verifying solutions:}\\\\\text{For x =2,}\\\\2= 2+\sqrt{2-2} \implies 2 = 2~ \\\\ \text{So, x = 2 is a solution.}\\\\\text{For x =3,}\\\\3 = 2+\sqrt{3-2}\implies 3=2+1 \implies 3=3\\ \\[/tex]
[tex]\text{So, x = 3 is a solution.}[/tex]
need help.. again PLEASE HURRY 100 POINTS
Answer:
I think it might be 156 square milimeters. I could be totally wrong though.
Step-by-step explanation:
I need help
Bob scuba dives in the ocean.
He is 150 feet below the surface of the water.
• He swims up toward the surface of the water at a rate of 15 feet for every 30 seconds.
After 2 minutes of ascending, he stops to take a break. How far away is Bob, in feet, from the surface of the water?
Using proportions, it is found that Bob will be 90 feet from the surface of the water after 2 minutes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, every half-minute, he ascends 15 feet. Hence in 2 minutes = 4 half-minutes, he will have ascended 15 x 4 = 60 feet.
He is 150 feet below the surface of the water, hence after 2 minutes he will be 150 - 60 = 90 feet from the surface of the water.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
If sample bias exists, then we can easily trust using the sample as representative of the
whole population. True or False
Explanation:
If the sample is biased, then it does not represent the population. A biased sample favors one or more groups over others.
For example, if the sample consisted of only men, then the sample is biased toward men and leaves out women from the group. Hence, this sample does not represent everyone.