Please help me it’s getting late and it’s due tomorrow
For what value(s) of b does the equation
x +3 - x = (bx - 5) have
exactly one solution?
Answers
Answer:
[tex]b = \dfrac{11}{x} + 1[/tex]
Step-by-step explanation:
The equation is given as follows;
[tex]x + 3 - \dfrac{1}{2} \cdot x = \dfrac{1}{2} \cdot (b \cdot x - 5)[/tex]
By expanding and collecting terms in x we get;
[tex]3 + \dfrac{x}{2} = \dfrac{b \cdot x}{2} - 2.5[/tex]
[tex]\therefore 3 + 2.5 + \dfrac{x}{2} = 5.5 + \dfrac{x}{2} = \dfrac{b \cdot x}{2}[/tex]
b = (11 + x)/x = 11/x + 1
The equation has exactly one solution when b = 11/x + 1
Related Questions
m∠RST =______because they are __________ (Fill in the blanks)
Answers
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
−6⋅20.1x=−100
Which of the following is the solution of the equation?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
x
=
2
(
50
)
2
(
3
)
x=
log
2
(3)
log
2
(50)
x, equals, start fraction, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction
(Choice B)
B
x
=
10
2
(
50
3
)
x=10log
2
(
3
50
)x, equals, 10, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis
(Choice C)
C
x
=
10
2
(
50
)
2
(
3
)
x=
log
2
(3)
10log
2
(50)
x, equals, start fraction, 10, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction
(Choice D)
D
x
=
2
(
50
3
)
x=log
2
(
3
50
)x, equals, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis
Answers
Answer:
The answer (D)
x=log2(50/3)
Thus, [tex]x=10log_{2}\frac{50}{3}[/tex] so option (B) is the correct answer.
What is a logarithm?"A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse (opposite) of exponentiation. Just as an exponential function has three parts, a logarithm has three parts as well: a base, an argument, and an answer (also called power)".
For the given situation,
The equation is
[tex]-6(2)^{0.1x} = -100[/tex]
The equation can be expressed in logarithm as
[tex]a^{x}=b\\[/tex]
⇒ [tex]x=log_{a}b[/tex]
So, [tex]-6(2)^{0.1x} = -100[/tex]
⇒ [tex]2^{0.1x}=\frac{-100}{-6} \\[/tex]
⇒ [tex]0.1x=log_{2}\frac{50}{3}[/tex]
⇒[tex]\frac{1}{10}x=log_{2} \frac{50}{3}[/tex]
⇒[tex]x=10log_{2}\frac{50}{3}[/tex]
Hence we can conclude that [tex]x=10log_{2}\frac{50}{3}[/tex] option (B) is the correct answer.
Learn more about logarithm here
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Need help with this question
Answers
Answer:
B.
Step-by-step explanation:
you know that (a+b+c)/d is the same as a/d + b/d + c/d.
and (a×b)/(c×d) is the same as (a/c)×(b/d).
and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.
14a⁸y³ / 7a⁴y
14/7 = 2
a⁸/a⁴ = a⁴
y³/y = y²
=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.
but let's practice and look at the second part :
-7a⁴y⁵ / 7a⁴y
-7/7 = -1
a⁴/a⁴ = 1
y⁵/y = y⁴
=> -y⁴ is the second part. B is still confirmed.
the third part :
28a¹²y² / 7a⁴y
28/7 = 4
a¹²/a⁴ = a⁸
y²/y = y
=> + 4a⁸y is the third part. B confirmed.
Area of base=
A)8 square units
B)6 square units
C)12 square units
Answers
Answer:
its 8
Step-by-step explanation:
4 times 2 is 8 and you cant get 6 or 12
Answer:
A
Step-by-step explanation:
Area of base = length x width = 4 * 2 = 8 square units
7.80/hour=________ cents/minute?
Answers
Answer: 0.13 cents per minute.
Step-by-step explanation:
7.80 divided by 60(min per hour.)= .13 cents.
$7.80/hour = (7.8*100) cents / (1*60)minutes
= 780 cents/60 minutes
= 13 cents/minute
Write this number in scientific rotation. 1,490,000.
Answer and explain.
Answers
Answer:
4.9 x 10^5
Step-by-step explanation:
the answer is 4.9 x 10^5
1 490 000 = 1.49 x 1 000 000 = 1.49 x 10^6
Which function has zeros at x = -2 and x = 5?
Answers
Answer:
f(x) = x² - 3x - 10
Step-by-step explanation:
Given zeros x = - 2 and x = 5, then the corresponding factors are
(x + 2) and (x - 5) , so
f(x) = (x + 2)(x - 5) ← expand using FOIL
= X² - 3X - 10
Answer:
f(x) = x² - 3x - 10
(option D)
Step-by-step explanation:
Sum one helpppp meeeee
Answers
Answer:
Step-by-step explanation:
total cost of the meal = $120
tip = 20%
tip amount = ?
total cost of the meal with tip = ?
tip amount = tip% 0f total cost of the meal
=20/100 * $120
=$2400/100
=$24
total cost of the meal with tip = total cost of the meal without tip + tip amount
=$120 + $24
=$144
Which of the equations below represents a line perpendicular to the yaxis?
A. y= -6
B. x= 6
C. y=6x
D. y=x
Answers
Answer:
A. y=-6
Step-by-step explanation:
Using the answer, it would make a horizontal line which would be perpendicular to the y axis.
The radius of the circle is 7 cm. What is the area of the shaded part? Use π = 227
Answers
Answer:
227 * 7^2
Put into calculator
Step-by-step explanation:
Area of a circle is pi * r^2 (pi times radius squared)
Just put the numbers in
227 * 7^2
Put into calculator and there you go
7.2 cm
6 cm
15 cm
8 cm
Answers
Answer:
i need to know the answer or the question plz
Which steps can be done to both sides of the equation to determine the value of x ?
3.2.2 - 9.6 = 38.4
A. subtract 9.6, then multiply by 3.2.
B. Add 9.6, then multiply by 3.2.
C. Add 9.6, then divide by 3.2.
D. Subtract 9.6, then divide by 3.2.
Answers
Answer:
C. Add 9.6, then divide by 3.2.
Step-by-step explanation:
[tex]3.2x−9.6=38.4[/tex]
[tex]3.2x=38.4+9.6[/tex]
[tex]3.2x=48[/tex]
[tex]x = \frac{48}{3.2} [/tex][tex]x = 15[/tex]
Hope it is helpful...At the start of 2014, Mike's car is worth 12000. the car depreciates by 30 percent every year. how much is his car worth in 2017
Answers
Answer:
$4,116
Step-by-step explanation:
Worth of Mike's car at the start of 2014 = $12,000
If the car is said to depreciates every year by 30% = 30/100 = 0.3
The worth of the car at the start of 2017 is what we are to determine.
This means that the car depreciated by 30% (0.3) for 3 years since 2014 (2017 - 2014 = 3 yrs)
The worth at the start of 2017 would be calculated as follows:
12,000 × (1 - 0.3)³
= 12,000 × (0.7)³
= 12,000 × 0.343
= 4,116
Worth of the car at the start of 2017 would be $4,116
Estimate the perimeter and area of the figure to the nearest whole number. Please help!!
Answers
Answer:
29 ; 37
Step-by-step explanation:
The figure is composed by a square, a rectangle, and a right triangle
The perimeter of the square is 6 units
The perimeter of the rectangle is 10 units
The triangle is composed by a side of 6 units and a side of 5 units
The third side can be find with the Pythagorean theorem
[tex]\sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}[/tex] = 7,81025
The total perimeter is
6 + 10 + 5 + 7,81025 = 28,81025 = 29
Area of the square = 2^2 = 4 square units
Area of the rectangle = 6 x 3 = 18 square units
Area of the triangle = (5 x 6)/2 = 15 square units
Total area = 4 + 18 + 15 = 37 square units
Brian spends 3 5 of his wages on rent and 1 3 on food. If he makes £735 per week, how much money does he have left?
Answers
Answer :
Brian has $49 left.
Step by step explanation :
Step 1 : Find how much money Brian spends on rent and food.
First question we should be asking is what is 3/5 of 735?
Let's find that.
[tex]\frac{3}{5}[/tex] * [tex]\frac{735}{1}[/tex]
= [tex]\frac{(3)(735)}{(5)(1)}[/tex]
= [tex]\frac{2205}{5}[/tex]
= 441
We know Brian spends $441 on rent. Now we find how much he spends on food.
[tex]\frac{1}{3} * \frac{735}{1}[/tex]
= [tex]\frac{(1)(735)}{(3)(1)}[/tex]
= [tex]\frac{735}{3}[/tex]
= 245
Brian spends $245 on food.
Step 2 : Add what he spends on rent and food together.
$441 + $245 = $686
Step 3 : To find out how much money Brian has left, we subtract $686 from $735.
$735 - $686 = $49
Conclusion : Brian has $49 left.
Hope this helps, please mark brainliest if possible. Have a nice day.
If a,b, and c are three different numbers, which of the following equations has no solutions?
A. ax= bx+c
B. ax+b=ax+c
C. ax+b=ax+b
Answers
Answer:
C
Step-by-step explanation:
if you divide both sides by ax+b you get 1=1 which is not a solution for x.
I really need help with this question as fast as possible
Answers
Answer:
-1625
Step-by-step explanation:
→ (-125) × 5 + (-125) × 8
Taking (-125) as in common,
→ (-125) × (8 + 5)
→ (-125) × 13
→ -1625
Find the area of triangle.
Answers
Answer:
16cm2
Step-by-step explanation:
(1/2) × 8 ×4=16cm2
the answer is 16 cm squared
Answer:
The area is 16 cm^2
Why? Below I explain.
Step-by-step explanation:
In that triangle, there are 2 sides, so you need to use this formula:
B * H / 2
Using those values:
4 * 8 / 2 is equal to 16.
Aere are two squares. A and B.
A
B
The length of each side of square B is 4 cm greater than the length of each side of square A.
The area of square B is 70 cm² greater than the area of square A.
Find the area of square B.
Give your answer correct to 3 significant figures.
You must show all your working.
Answers
Answer:
116 cm²
Step-by-step explanation:
a = side length of A
b = side length of B
b = a + 4
b² = a² + 70
(a+4)² = a² + 70
a² + 8a + 16 = a² + 70
8a + 16 = 70
8a = 54
a = 54/8 = 27/4 = 6.75
b² = a² + 70 = 6.75² + 70 = 45.5625 + 70 =
= 115.5625 ≈ 116 cm²
our does your teacher mean 3 significant figures after the decimal point ? then it would be
115.563 cm²
Which row in the table is the closest to the actual solution?
Answers
Answer:
0.8
Step-by-step explanation: 6 22 6 06
I plotted both sides of the equation using DEMOS graphing calculator and located the intersection at (0.779, 2.135) I found that easier than finding the delta difference of both sides of the equation for the table or solving for x.
The points A, B, C and D lie on a circle centre O.
Angle AOB = 90° angle COD= 50° and angle BCD= 1239
The line DT is a tangent to the circle at D.
Find
(a) angle OCD
Answers
The measure of angle OCD from the given figure is 58°.
Given that, the points A, B, C and D lie on a circle Centre O.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, OC and OB are radius of a circle, then BOC is isosceles triangle
Now, ∠BOC+∠OBC+∠OCB=180°
50°+∠OBC+∠OBC=180°
⇒ 2∠OBC=130°
⇒ ∠OBC=65°
Here, ∠OCD=∠BCD-65°
⇒ x=123-65=58°
Hence, the measure of angle OCD from the given figure is 58°.
To learn more about the circle visit:
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part A: Which expression can be used to find the value of x in the triangle shown?
part B: write the value of x to the nearest tenth.
Answers
Answer:
D and x=11.55
Step-by-step explanation:
Find the zeros of the function f(x) = (x + 2)(x - 3)(x + 12)
Answers
Step-by-step explanation:
f(x) = (x + 2)(x - 3)(x + 12) = 0
(x + 2)(x - 3)(x + 12) = 0
so, the zeros of the function :
=> x1 = -2
=> x2= 3
=> x3 = -12
The expression
3(x+6)-x
can be simplified to the form
2x + a)
What is the value of a?
Answers
Answer:
a = 18
Step-by-step explanation:
3(x+6)-x = 2x + a
Distribute
3x +18 -x = 2x+a
2x +18 = 2x+a
Subtract 2x from each side
18 = a
Please help me !!!
What is the image of (-8,-1) after a reflection over the line y = -x?
Answers
Answer:
Step-by-step explanation:
Reflection of (-8 , -1) over y = -x is (-1 , 8)
Image of (x , y) over the line y = -x is (y, -x)
Answer:
reflection on the y axis (x,y)=(-x,y)
(-8,-1)=(8,-1)
Step-by-step explanation:
hope this is helpful
Manipulate the radius of the sphere, setting it to different values. In the table below, record each radius you chose and the exact volume of the sphere (in terms of π). Also calculate the decimal value of each volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answers
Answer:
641654654
Step-by-step explanation:
Answer:
1) r=9 v=972
2) r=6 v=288
3) r=12 v=2,304
Step-by-step explanation:
Sample Answer on edmentum
If a +b+c=9 and a square +b square +square =1 then ab+bc+ca
Answers
Answer:
ab + bc + ca = 40
Step-by-step explanation:
Using the expansion identity
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) , that is
9² = 1 + 2(ab + bc + ca)
81 = 1 + 2(ab + bc + ca) ← subtract 1 from both sides
80 = 2(ab + bc + ca) ← divide both sides by 2
40 = ab + bc + ca
can someone help please
Answers
Answer:
3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic
(ii). Sequence [tex]W_{n}[/tex] is in Geometric
3b. 2520 Sum of First 20 Arithmetic Sequence
3c. 98292 Sum of First 13 Geometric Sequence
Step-by-step explanation:
According to the Question,
3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....
it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12
(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....
A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2
3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]
(Where, a=first term of sequence , n= number of term & d=common difference)
[tex]S_{n}[/tex]=10[2×12 + 19×12]
[tex]S_{n}[/tex] =10×252 ⇔ 2520
3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]
(Where, a=first term of sequence , n= number of term & r= common ratio)
[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1
[tex]S_{n}[/tex]=12×8191 ⇔ 98292
Amber works as a waitress at a restaurant. She earns an hourly wage and also earns tips. One night, she worked 6 hours and earned a total of $69.20, which included tips of $15.50. Explain how the equation 6w + 15.5 = 69.2 represents this situation. Then, calculate Amber’s hourly wage.
Answers
Answer:
Hey there!
The given equation helps us understand the relationship between Amber's tips earned and the money she earned through her hourly wage. This information will add up to equal a grand total of $69.20.
We know that Amber earns $15.50 in tips during her 6 hour shift. Therefore, this is not considered part of her wage. This would be one of the constants of our equation.
We also know that Amber earns a fixed hourly wage, but we don't know what this wage is. We need to find w.
[tex]6w+15.5=\$69.20[/tex]
Subtract 15.5 from both sides of the equation (and get rid of the currency symbol).
[tex]6w=69.20-15.5\\6w=53.7[/tex]
Divide both sides of the equation by 6.
[tex]\displaystyle \frac{6w}{6}=\frac{53.7}{6}\\\\w=8.95[/tex]
Therefore, Amber's hourly wage is $8.95.
A line has the equation 3x–4y–12=0 what is the slope of this line
Answers
Answer:
The slope of this line is 3/4.
Step-by-step explanation:
Solving this equation 3x–4y–12=0 for y puts the equation into the form
y = mx + b, where m is the slope of the line.
One way of solving for 4y here is to add 4y to both sides, obtaining:
3x - 12 = 4y
Dividing all three terms by 4 yields
y = (3/4)x - 3
The slope of this line is 3/4.