Find the range of values of x for which 2x-3<7 and 2x+1>-3x-4.
Given:
The inequalities are:
[tex]2x-3<7[/tex]
[tex]2x+1>-3x-4[/tex]
To find:
The range of values of [tex]x[/tex] for the given inequalities.
Solution:
We have,
[tex]2x-3<7[/tex]
Adding 3 on both sides, we get
[tex]2x-3+3<7+3[/tex]
[tex]2x<10[/tex]
Divide both sides by 2.
[tex]\dfrac{2x}{2}<\dfrac{10}{2}[/tex]
[tex]x<5[/tex] ...(i)
The second inequality is:
[tex]2x+1>-3x-4[/tex]
Subtracting 1 from both sides, we get
[tex]2x+1-1>-3x-4-1[/tex]
[tex]2x>-3x-5[/tex]
Adding [tex]3x[/tex] on both sides, we get
[tex]2x+3x>-3x-5+3x[/tex]
[tex]5x>-5[/tex]
Divide both sides by 5.
[tex]\dfrac{5x}{5}>\dfrac{-5}{5}[/tex]
[tex]x>-1[/tex] ...(ii)
Using (i) and (ii), we get
[tex]-1<x<5[/tex]
Therefore, the required range is [tex]-1<x<5[/tex].
Si el velocimetro de un auto marca un 25% mas que la verdadera velocidad y en este momento marca 100km/h entonces la velocidad verdadera es?
Answer:
True speed of the car is 87 km/h.
Step-by-step explanation:
Speed = 100 km/h
hike in speed = 25 %
Let the true speed is v.
[tex]v + 15% of v = 100 \\\\v + 0.15 v = 100 \\\\1.5 v = 100\\\\ v = 87 km/h[/tex]
Given m||n, find the value of x and y
Answer:
x=20,y=34
Step-by-step explanation:
x+14=2x-6 (vertically opposite angles)
x-2x = -6-14
-x = -20
x=20
x+14=y (corresponding angles)
20+14=y
y=34
Answer:
x = 20, y = 34
Step-by-step explanation:
(2x - 6) and (x + 14) are vertical angles and are congruent, then
2x - 6 = x + 14 ( subtract x from both sides )
x - 6 = 14 ( add 6 to both sides )
x = 20
Then
2x - 6 = 2(20) - 6 = 40 - 6 = 34
y and (2x - 6) are alternate angles and are congruent , so
y = 34
Her result was x =-4.
A- What is the correct value of x? B- What was Samira’s error? Explain.
Question 9 of 10
If you apply the changes below to the absolute value parent function, f(x) = |xl,
what is the equation of the new function?
• Shift 4 units left.
• Shift 2 units up.
Answer:
[tex]g(x) = |x+4|+2[/tex]
What is the slope of the line whose equation is y-4=5/2(x-2)?
Answer:
5/2
Step-by-step explanation:
We know,
Equation of the slope is, y = mx + c. Where m is the slope.
y - 4 = 5/2*(x-2)
y = 5/2*(x-2) + 4
y = (5/2)x - 5 + 4
y = (5/2)x - 1
y = (5/2)x + (-1) [y = mx + c form]
Slope, m = 5/2
Hope this will help. Please mark me brainliest.
Simplify 52⋅(x−2)52⋅(x-2). Apply the distributive property. y−4=5/2x+5/2⋅−2 Combine 5252 and x
y−4=5x2+5/2⋅−2 Cancel the common factor of 2.Factor 2 out of −2
y−4=5x2+52⋅(2(−1))y-4=5x2+52⋅(2(-1))
Cancel the common factor.
y−4=5x2+52⋅(2⋅−1)y-4=5x2+52⋅(2⋅-1)
Rewrite the expression.
y−4=5x2+5⋅−1y-4=5x2+5⋅-1
Multiply 55 by −1-1.
y−4=5x2−5
Add 44 to both sides of the equation.
y=5x2−5+4y=5x2-5+4
Add −5-5 and 44.
y=5x2−1
Reorder terms.
y=52x−1
THE ANSWER IS M = 5/2
Joel purchased an engagement ring with his credit card. His card has an APR of
13.99% and he must pay at least 3% of the balance at the end of each month. If
his carry-over balance for this month is $9,026.74 and he has made no
additional purchases, what would Joel's finance charge be at the end of the
month?
Round your answer to the nearest cent.
Answer:
What is your definition of finance charge?
the interest is $105.24
3% of what he owes (the minimum) is $273.96
Step-by-step explanation:
$9,026.74
+9,026.74 * (.1399/12) = $105.2367438
($9,026.74 + $105.24)*(.03) = $273.96
Answer:
33.19
Step-by-step explanation:
$2846.89
$2846.89 * (.1399/12) = 33.189992583333333333333333333333
Finance Charge is $33.19
The graph below shows the solution to which system of inequalities?
Answer:
A
Step-by-step explanation:
Which of the sequences is an arithmetic sequence?
O A. 1, 8, 16, 24, 32, ...
B. -3, -10,-17, -24, -31, ...
C. 3, 6, 9, 15, 24,...
O D. 1,-2, 3, -4, 5, ...
Answer:
Answer B as the difference between the values is the same
Need help please anwer all its one page question i put in two bc it didnt fit
Answer:
sorry only doing the ones i know how to do
b) for the histogram, just write all the numbers on the table on the bottom, theres 13 lines but 2 repeats so it should be even. on the side write a range of minutes
c) mean = 7.8 ; standard deviation = 3.13
d)
min = 2
max = 13
range = 11
q1 = 5.5
q3 = 10.75
iqr = 5.25
median = 8
what does iqr represent? it represents the middle 50% of all the values
e) write the numbers from the table without repeats and mark them how many times theyre written
Change to vertex form
1) f(x) = x² - 4x + 4
2) f(x) = -x ² + 8x-16
3) f(x) = 2x ²-x+3
4)f(x)=2x ²-3x-1
Answer:
- y = 7 is a line which is-(A) Parallel to y-axis (B) Parallel to x-axis (C) Passing through (7, 7) (D) Passing through origin
What the hcf of 24 and 180
Answer:
12
Step-by-step explanation:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance
around the track is 400 meters. Determine the radius of the semicircular ends of the track in terms of y.
Answer:
r = (200 - y)/π
Step-by-step explanation:
The question details includes;
The shape of the indoor track = Two semi-circular ends and a mid rectangular region
The distance around the indoor track = 400 meters
The radius, r, of the semicircular ends in terms of y = Required
Let y represent the length of the rectangular middle area of the track, we have;
The perimeter of the indoor track = The distance around the track = 400 m
The perimeter of the indoor track = 2 × π·r + 2 × y = 400
2 × (π·r + y) = 400
∴ π·r + y = 400/2 = 200
r = (200 - y)/π
For homework, Anya had to find the width of a bedroom after the scale changed from 1 inch : 4 feet to 1 inch : 7 feet. Her work is shown below.
1 inch = 4 feet. 1 inches = 7 feet. A rectangle with length of 4 inches and width of 2 inches. StartFraction 1 over 7 EndFraction = StartFraction x over 2 EndFraction. 7 x = 2. x = StartFraction 2 over 7 EndFraction feet.
1
7
= x
2
7x = 2x = 2
7
feet
What error did Anya make?
Answer:
she set up the proportion incorrectly; the second ratio should be 2/x
Step-by-step explanation:
To obtain the width :
Scale drawing :
Initial = 1 inch = 4 feet
New = 1 inch = 7 feet
Width of rectangle = 2 inches
New width should be in the form :
new scale = width of rectangle / width of drawing
If width of drawing = x
1 / 7 = 2 / x
Cross multiply
x = 7*2
x = 14
Answer:
its A
Step-by-step explanation:
Which of these expressions is equivalent to log (9.4)?
O A. log (9) + log (4)
O B. log (9) - log (4)
O c. 9. log (4)
O D. log (9) • log (4)
Answer:
log (9) + log(4)
Step-by-step explanation:
log (9.4)
Log (ab) = log (a) + log (b)
log (9) + log(4)
Answer:
A. log ( 9 ) + log ( 4)
Step-by-step explanation:
log( 9.4)
use log (a*b) = log (a) + log (b) to expand expression
log (9) + log (4)
Solve the problem correctly and show ur work
1 . 3/5 ( 15x + 30 )
Answer:
9(x + 2)
Step-by-step explanation:
3/5(x+30)
multiply fractions
3(15x + 30)/5
factor 3(15x + 30) = 45(x + 2)
divide the numbers
45(x + 2)/5
45/5=9
= 9(x + 2)
Answer:
9x + 18
Step-by-step explanation:
[tex]\frac{3}{5} ( 15x + 30 )[/tex]
9x + 18
Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?
x = –24, x = 16
x = –16, x = 24
x = –1, x = 9
x = 1, x = –9
Answer:
x = - 16, x = 24
Step-by-step explanation:
Given f(x) = 7 then equate f(x) to 7
0.5 | x - 4 | - 3 = 7 ( add 3 to both sides )
0.5 | x - 4 | = 10 ( divide both sides by 0.5 )
| x - 4 | = 20
The expression inside the absolute value bars can be positive or negative, so
x - 4 = 20 ( add 4 to both sides )
x = 24
OR
- (x - 4) = 20
- x + 4 = 20 ( subtract 4 from both sides )
- x = 16 ( multiply both sides by - 1 )
x = - 16
Answer:
The Answer is B
Step-by-step explanation:
Your Welcome
The cuboid and the triangular prism have the same volume. Find the value of x.
Answer:
x = 25
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular face and l is its length )
A = [tex]\frac{1}{2}[/tex] bh = 0.5 × 5 × 8 = 20 cm² , then
V = 20 × 20 = 400 cm³
The volume of the cuboid is calculated as
V = lbh = 3.2 × 5 × x = 16x
Given V = 400 cm³ , then
16x = 400 ( divide both sides by 16 )
x = 25
The solution of the equation3^×=2 is
Answer:
x = log 2 / log 3
x=0.63092
Step-by-step explanation:
3^×=2
Take the log of each side
log 3^×= log2
We know that log a^b = b log a
x log 3 = log 2
Divide each side by log 3
x = log 2 / log 3
x=0.63092
Answer:
x ≈ 0.63093
Step-by-step explanation:
[tex] \small \sf \: 3 {}^{x} = 2[/tex]
Take the log of both side
[tex] \small \sf \: log 3 {}^{x} = log 2[/tex]
Use log a( a ^ x ) = x to simplify the equation
x log 3 = log 2
Divide each side by log 3
x = log 2 / log 3
x ≈ 0.63093
20% of a number is 30. What is 60% of the number?
Answer:
90
Step-by-step explanation:
30 / 0.2 = 150
150 x 0.60 = 90
Step-by-step explanation:
Well, if 20% = 30, then 40% = 60, and 60% = 90
In ΔXYZ, x = 71 cm, y = 91 cm and z=71 cm. Find the area of ΔXYZ to the nearest square centimeter.
Answer:
2479.95
Step-by-step explanation:
i worked out that guys problem who wouldnt work it out for you.
An electric blender has a price of $240 after import duty is added to the cost price.What is the cost price of the blender if import duty is 20%?
Answer:
$200
Step-by-step explanation:
Given :
Cost of blender + import duty = $240
Import duty = 20% of cost price
Let :
Cost of blender = x
Import duty = 20% of x = 0.2x
Therefore,
x + 0.2x = $240
1.2x = 240
x = 240 / 1.2
x = $200
Cost of blender = $200
A line is parallel to y = 3x + 5 and intersects the point (-2 , 6). What is the equation of this parallel line?
Answer:
y = 3x + 12
Step-by-step explanation:
Slope of y = 3x + 5 is 3
Line parallel will have same slope 3
Line intersects point at (-2, 6)
Replace into y = mx + b to find
6 = 3(-2) + b
6 = -6 + b
12 = b
Equation of line:
y = 3x + 12
Answer:
y = 3x + 12
Step-by-step explanation:
Lines parallel to each other will have the same slope but different y-intercepts. This means that the equation of this parallel line has a slope of 3.
y = 3x + b
Now we need to find the y-intercept by plugging in the point (-2, 6) into the equation. (Replace x with -2 and y with 6.) Then we solve it.
y = 3x + b
6 = 3(-2) + b
6 = -6 + b
+6 +6
12 = b
The y- intercept is 12. So the equation of the parallel line is y = 3x + 12
write the time on the digital watch in words 21:02
It is two minutes past nine
Anyone know the answer?
Answer:
565.6854249 without rounds
Answer:
Step-by-step explanation:
Well, the area is 400m^2 so we know each side is 20 feet long. Then with that we can make a 40deg 40deg 90deg triangle with the side lengths 20, 20, and x. So, the proportion would be 20/1=x/rad2. This gives us x=28.28, so the fence is 28.28m long. Hope this helps :))
I need to draw also no files just type it in and tell me what to draw
Answer:
Draw 8 boxes with 8 cupcakes in each one of them.
Step-by-step explanation:
34+30=64, and 64/8 also equals 64.
identify the center and radius of the circle with equation.
( please help me )
Answer:
Center = (4, -5)
radius = 6
======================================================
Explanation:
The general template of any circle is
(x-h)^2 + (y-k)^2 = r^2
Rewrite the given equation into this form
(x-4)^2 + (y- (-5))^2 = 6^2
We can see that (h,k) = (4,-5) is the center and r = 6 is the radius.
Sally plots (−4,π)on the polar plane.
How does she proceed?
Drag a phrase to each box to correctly complete the statements.
Solution :
As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.
My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.
If k is a non-zero constant, determine the vertex of the function y = x2 - 2kx + 3 in terms of k.
Answer:
Set y = 0, evaluate the quadratic at h=−b2a and solve for k.
k=9 I think..... I'm not completely sure but I think that's how it is
Answer:
[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]
Step-by-step explanation:
We are given the quadratic equation:
[tex]y=x^2-2kx+3[/tex]
Where k is a non-zero constant.
And we want to determine the vertex of the parabola in terms of k.
The vertex of a parabola is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -2k, and c = 3.
Find the x-coorinate of the vertex:
[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]
To find the y-coordinate, we substitute the value we acquired back into the equation. So:
[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]
Therefore, our vertex in terms of k is:
[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]
In order for the parallelogram to be a rhombus x = ?
The value of the x is 27.
We have given that the diagram of a rhombus
We have to determine the value of the x
What is the angle of the rhombus?The angle is sitting on a right angle because rhombuses have 4 right angles
90 = 4x-18
108 = 4x
x = 27
Therefore the value of the x is 27.
To learn more about the rhombus visit:
https://brainly.com/question/20627264
#SPJ1
Answer: It's 14, not 27.
Step-by-step explanation:
