Answer:
[tex]x= 1 +5\sqrt 2,~~ x=1-5\sqrt 2[/tex]
Step-by-step explanation:
[tex]~~~~~~(x-1)^2 = 50\\\\\implies x -1 = \pm\sqrt{50}\\\\\implies x = \pm\sqrt{25 \times 2} +1\\\\\implies x= 1 \pm 5\sqrt 2[/tex]
Explain the difference between 2(7x-4) and (7x-4)^2
Answer:
2(7x-4) = 7x(2)-4(2) = 14x-8
but
(7x-4)^2 = (7x-4) (7x-4)
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
Note: Each horizontal or vertical division represents one unit.
X=
Y=
Answer:
X=1 and Y=4
By counting eacht vetmrtical divided units
PLS HELP QUICKLY
Which pair of functions are inverses of each other?
5
O A. f(x) = -2 and g(x) = +2
B. f(x) = 7x-2 and g(x) = 2
C. f(x) =x/5+ 6 and g(x) = 5x - y
D. f(x) = 3+ 6 and g(x) = 6x³
Answer: B
[tex]f(x) = 7x-2[/tex] and [tex]g(x) = \frac{x+2}{7}[/tex]
How to solve:
check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)
f[g(x)] = x
g[f(x)] = x
Step-by-step explanation:
Checking A.
[tex]f(x) = \frac{5}{x} -2[/tex]
[tex]g(x) = \frac{x+2}{5}[/tex]
[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]
This does not equal x, so we know these are not inverses
Checking B.
[tex]f(x) = 7x-2[/tex]
[tex]g(x) = \frac{x+2}{7}[/tex]
[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]
[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]
since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.
Point D is the midpoint of AB and point E is the midpoint of BC. Select all of the statements to the right that must be true.
Answer + Step-by-step explanation:
» ABC ≅ DBE
» DE // AC
(properties of the mid-segment of a triangle)
» Length of DE = 1/2 length of AC
(properties of the mid-segment of a triangle)
» ∠BDE = ∠DAC
(Corresponding angles)
What are the x-intercepts of the following graph?
1
2 3 4
+
3
G
3
&
a. (0, 2) and (0, -2)
b. (0,4)
c. (2,0) and (-2, 0)
d. (1, 0) and (3, 0)
Answer:
c (2,0) and (-2,0) I hope ot helps
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth.
Answer: 6.64
Step-by-step explanation:
[tex]A=\frac{1}{2}(4.7)(3.2)(\sin 62^{\circ}) \approx \boxed{6.64}[/tex]
A sector of a circle has central angle 120 degrees and arc length 10π
centimeters. What is the radius of the circle
Answer:
the radius = 15 cmStep-by-step explanation:
let r be the radius of the circle.
→ We know that in circle , the length of an arc
and the corresponding central angle are proportional.
180 corresponds to πr
120 corresponds to 10π
Then
[tex]\frac{\uppi r}{180} =\frac{10\uppi }{120}[/tex]
[tex]\Longrightarrow r=\frac{180\times 10\pi }{120\pi } =\frac{180}{12} =15[/tex]
Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0)
The x-intercept is (1, 0) and (-0.5, 0).
The correct option is (a)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function is:
f(x)= [tex]-2x^{2}+x+1[/tex]
So, The graph of this equation is attaches below.
The x- intercepts of this graph
[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]
or
X intercepts: (1, 0) and (-0.5, 0)
Hence, the x-intercept is (1, 0) and (-0.5, 0).
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Sherri solved the equatjon 1/5(x-20)=45. For each step, write the name of the property sherri used
Answer: The awnser is linear.
I hope this helped.
Step-by-step explanation:
Slope of (-9,-2) and (-9,-6)
Answer:
Slope is undefined.
Step-by-step explanation:
What is the equation of a line that passes through (-6,2) and has a slope of -(1)/(2)?
Answer:
y= -1/2x+5
Step-by-step explanation:
Omar paid $8.64 for 5.4 pounds of grapes. what was the cost of 1 pound of grapes?
Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary
The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.
What is Sine (Sinθ)?The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,
Sin(74°) = (Height on the wall)/(Length of the wall)
Sin(74°) = (Height on the wall)/22 ft
(Height on the wall) = 21.148 ft
Hence, the Height on the wall till which the ladder reaches is 21.148 ft.
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Answer:
21.15
Step-by-step explanation:
find the angle of elevation of the sun if a building 325 feet tall casts a shadow 296 feet long
Answer:
Step-by-step explanation:
SOH CAH TOA
we have the (opposite) --> 325
we have the (adjacent) --> 296
so do the inverse tan of opposite over adjacent...
[tex]tan^{-1} (\frac{325}{296} ) = 47.67[/tex] degrees
hat is the slope of the linear relationship shown in this table of values?
x y
-4 11
2 -1
5 -7
By using any two of the points in the table, we will see that the slope is -2.
How to get the slope for the linear relationship?
A general linear relationship is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use the first two points on the table:
(-4, 11) and (2, -1), so the slope is:
[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]
Then the slope of the line is -2.
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What is the slope of the line graphed below?
(-2,2)
(3, 1)
Answer:
-1/5
Step-by-step explanation:
To find the slope, the formula is y2-y1/x2-x1
1-2/3-(-2) = -1/5
Answer:
‐1/5Step-by-step explanation:
hope this helps!!!!
The regular price of a tennis racquet is $79.99 and the sale price is $64.99. Find the percent of discount to the nearest whole percent.
Step-by-step explanation:
$79.99 - $64.99 = $15
(79.99 - 64.99)/|79.99| =15
15/79.99 =
15 ÷ 79.99 =
15 ÷ 79.99 × 100/100 =
(15 × 100 ÷ 79.99)/100 =
(1,500 ÷ 79.99)/100
≈18.752344043005/100 =
18.752344043005% ≈18.75%;
Solve- x/x+1 - 1/2 = -1/x+1
Answer:
Step-by-step explanation:
Remark
x/(x+1) - 1/2 = -1 /(x + 1) is the equation to be solved. Add 1/(x + 1 to both sides
x/(x+1) + 1/(x+1) - 1/2 = -1/(x + 1) + 1/(x + 1) Combine
x/(x+1) + 1/(x + 1) - 1/2 = 0 Combine x/(x+1) + 1/(x+1)
(x + 1)/(x + 1) - 1/2 = 0 Cancel (x+1)/(x+1) = 1
1 - 1/2 = 0 No solution
Answer: No solution
Perform the indicated operation
Answer:
Step-by-step explanation:
Part E
Use the table showing Manuel's and Gretchen's data to determine the mean, median, standard deviation, and
interquartile range for each data set. Use this information to complete the second table. Use the graphing tool to
determine the value of standard deviation.
The mean, median, standard deviation, and interquartile range for each data set is given below.
What is the definition of Interquartile Range (IQR)?When arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
What are the measures of central tendency for Manuels Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 3.13961Mean = 8Median = 8IQR = Q3-Q1 = 10 - 6 = 4What are the measures of central tendency for Grethcen's Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.See the respective Histograms attached.
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Laura worked 8 hours today. She spent
the time in meetings, on the phone,
and the rest of the time on the computer.
Make a circle graph to show how Laura
spent her work day.
For his phone service, Chris pays a monthly fee of $25, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $86.74.
What are the possible numbers of minutes he has used his phone in a month?
Use M for the number of minutes, and solve your inequality for M.
Answer:
1029 minutes or 17.15 hours
Step-by-step explanation:
25+0.06M=86.74
0.06M=61.74
M=61.74/0.06=1029
Help please i need this
Answer:
i can't see the question i would love to help though
Step-by-step explanation:
A mother and daughter decided to add their ages together. The sum of their ages is 76. Six years ago, the mother was 3 times the age of her daughter. How old is the daughter now?
Answer: The answer will be 19
Answer: 23 years old
Step-by-step explanation:
Explain how the expression 32 relates to the diver's depth
Answer:
See below
Step-by-step explanation:
Each 32 feet of depth is 1 more atmosphere of pressure on the diver
A farmer creates a rectangular pen using part of the wall of a barn for one side of the pen and a total of 130 feet of fencing for the remaining 3 sides, as shown in the diagram. Write and equation which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn
The equation that describes the which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn is A = 130x - x²
How to find area of a rectangle?The pen is rectangular. Therefore,
area of a rectangle = lw
where
l = lengthw = widthTherefore,
perimeter = 2w + l
perimeter = 2w + x
130 = 2w + x
130 - x = 2w
w = 65 - 1/ 2 x
A = xw
A = x(65 - 1/ 2 x)
A = 65x - 1 / 2 x²
Therefore, the function that represents A, the area of the pen is as follows:
A = 130x - x²
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On the first day of a song release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day
Answer:
35.4 million
Step-by-step explanation:
We assume the description "increases by 10% per day" means the base of the percentage is the previous day's number of streams. Then the sequence of streams on consecutive days is a geometric sequence with a first term of 20 million and a common ratio of (1 +10%) = 1.10.
__
streams on day nThe n-th term of a geometric sequence is ...
an = a1×r^(n-1) . . . . . where a1 is the first term, and r is the common ratio
The sequence of streams on consecutive days is then ...
an = 20×1.10^(n-1) . . . . millions of streams on day n
seventh dayFor n = 7, the number of streams is ...
a7 = 20×1.10^(7 -1) ≈ 35.4 . . . . million streams
There will be about 35.4 million streams on the seventh day.
State fundamental theorems
Answer:
Step-by-step explanation:
Given: ΔABC (to the right)
AB=15
BD=9
AD⊥BC
m∠C=30°
Find Perimeter of ABC
Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of its 3 sides.
Given the following:
AB = 15 BD = 9m∠C=30°Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:
AD = √(15² - 9²)
AD = 12 units
Use the trigonometric ratios to find DC and AC:
sin 30 = AD/AC
sin 30 = 12/AC
AC = 12/sin 30
AC = 24 units
tan 30 = AD/DC
tan 30 = 12/DC
DC = 12/tan 30
DC ≈ 20.8 units
BC = BD + DC = 9 + 20.8
BC = 29.8 units.
Perimeter of triangle ABC = BC + AB + AC
Perimeter of triangle ABC = 29.8 + 15 + 24
Perimeter of triangle ABC = 68.8 units.
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PLEASE HELP ME ASAP
Does the series converge or diverge? If it converges, what is the sum? Show your work
The series is a convergence series and the sum of the series is -8/3
The type of the seriesThe series is given as:
[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]
The above series has the following properties:
First term; a = -4Common ratio, r = -1/2Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
The sum of the seriesThis is calculated using:
[tex]S_{\infty} = \frac{a}{1 -r}[/tex]
So, we have:
[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]
Evaluate the sum
[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]
Evaluate the quotient
[tex]S_{\infty} = \frac{-8}{3}[/tex]
Hence, the sum of the series is -8/3
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