Answer:
(a) x=1.5 or x=-4.5
(b) x=-1
(c) x=10 or [tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
(a) |2x+3|=6
⇒ 2x+3=6 or 2x+3=-6
⇒ 2x=3 or 2x=-9
⇒ x=1.5 or x=-4.5
(b) |x-2|=x+4
⇒ x-2=x+4 or x-2=-(x+4)
x-2=x+4
-2≠4 x∈Ф
or x-2=-(x+4)
x-2=-x-4
2x=-2
x=-1
(c) |2x-7|=|x+3|
⇒ 2x-7=x+3 or 2x-7=-(x+3)
2x-7=x+3
x=10
or 2x-7=-(x+3)
2x-7=-x-3
3x=4
[tex]x=\frac{4}{3}[/tex]
The solutions of modulus equations are shown below:
(a) x=1.5 or x=-4.5
(b) x=-1
(c) x=10 or x=4/3
Step-by-step explanation:
(a) |2x+3|=6
⇒ 2x+3=6 or 2x+3=-6
⇒ 2x=3 or 2x=-9
⇒ x=1.5 or x=-4.5
(b) |x-2|=x+4
⇒ x-2=x+4 or x-2=-(x+4)
⇒x-2=x+4
⇒-2≠4 x∈Ф
or x-2=-(x+4)
⇒x-2=-x-4
⇒2x=-2
⇒x=-1
(c) |2x-7|=|x+3|
⇒ 2x-7=x+3 or 2x-7=-(x+3)
⇒2x-7=x+3
⇒x=10
or 2x-7=-(x+3)
⇒2x-7=-x-3
⇒3x=4
⇒x=4/3
Therefore, the solution of modulus equation are as:
(a) x=1.5 or x=-4.5
(b) x=-1
(c) x=10 or x=4/3
To learn more about "Modulus function" here:
brainly.com/question/13586158
PLEASE HELP I NEED THIS NOW, AND IS POSSIBLE A EXPLICATION
Answer:
you forgot the pic
Step-by-step explanation:
plssssssssssssssssss helpppppppppppppppppppppppppppppppppppppppppppppppppp
At the beginning of the year, Evelyn had $30 in savings and saved an additional $12 each week thereafter. Cooper started the year with $75 and saved $7 every week. Let E E represent the amount of money Evelyn has saved t t weeks after the beginning of the year and let C C represent the amount of money Cooper has saved t t weeks after the beginning of the year. Write an equation for each situation, in terms of t , t, and determine the interval of time when Evelyn has more in savings than Cooper.
Answer:
E=12t+30 C=7t+75
Evelyn has more in savings than Cooper when t > 9 weeks.Step-by-step explanation:
A cone has a height of 7 ft and a radius of 4 ft. Which equation can find the volume of the cone?
ovaj x(798412
OV==(42)(7)
O V = 3x(72)(4)
O V = 3x(42)(7)
Answer:
1/3pi(16)(7)
Step-by-step explanation:
Find the circumference and the area of a circle
with the dimensions listed. Use the value 3.14 for π
,and do not round your answers. Be sure to
include the correct units in your answers.
a) diameter of 3 cm
b) radius of 5 ft
In response to the question, we may say that As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
a) 3 cm diameter: The radius (r) of a circle is half its diameter, hence r = 3 cm/2 = 1.5 cm
The formula C = 2r gives the circumference of a circle, where is approximately equivalent to 3.14.
As a result, C = 2 3.14 1.5 cm = 9.42 cm.
The formula A = r2 calculates the area of a circle.
As a result, A = 3.14 (1.5 cm)2 = 7.065 cm sq.
As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
What is 2x-3y=-1
y=x-1
Answer: (4, 3)
Step-by-step explanation:
Let's use substitution.
So for y in the first equation we will substitute the expression for y in the second.
2x - 3(x-1) = -1
2x -3x + 3 = -1
-1x + 3 = -1
-3 -3
-1x = -4
-1x / -1 = -4 / -1
x = 4
Now plug in x for the second equation
y = 4 - 1
y = 3
Now check it using the first equation:
2(4) - 3(3) = -1
8 - 9 = -1
-1 = -1
It's true so it's correct
Helps me is urgent Match each type of insurance with an example of what it would pay for.
Renter's
insurance
?
Repair on a car involved in
an accident
Auto insurance
2
Replacement of a
computer stolen from an
apartment
Life insurance
2
Funeral expenses
Health insurance
?
A trip to the emergency
room
PREVIOUS
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer: the answer is c
Step-by-step explanation:
Answer:
Angles STQ & RQT
Step-by-step explanation:
They are on opposite sides, but they are also interior.
Hope this helps! Have a good day!
Solve for x. hint:half circle.
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
Given
The attached circle
Required
Find the measure of x
From the attached image:
[tex]11x + 2[/tex] and [tex]-2 + 7x[/tex] form a semi-circle
So:
[tex]11x + 2 -2 + 7x = 180[/tex]
Collect like terms
[tex]11x + 7x = 180+ 2 -2[/tex]
[tex]18x = 180[/tex]
Solve for x
[tex]x = \frac{180}{18}[/tex]
[tex]x = 10[/tex]
find the area of the figure 4m 7m
Answer:
Step-by-step explanation:
where is the picture?!
Answer:
28m squared
Step-by-step explanation:
7*4 is 28
NO LINKS
Please help
Answer:
V≈1287.88
A≈1152.98
Step-by-step explanation:
The radius of a sphere is 6 units. Which expression represents the volume of the sphere, in cubic units?
Answer:
ccc
Step-by-step explanation:
Helpppppppppppppppppppp
Answer:
Step-by-step explanation:
x=100 (vertically opposite angle)
PLEASE HELP ASAPPPP!!
question: write in standard form.
2x^2+x^3-3+4x^5
Answer:
+4X^5+X^3+2X^2-3
Step-by-step explanation:
Hope this helps :*
HELP PLS HURRY! The graph shows the proportional
relationship between the total cost and the
number of pounds of cashews purchased.
What would the total price in dollars be for
11.5 pounds of cashews?
Answer:
57.5$
Step-by-step explanation:
5$ a pound, 11.5 pounds, multiply them and you get 57.5$
Answer:
45
Step-by-step explanation:
find the geometric mean of 9 and 14
Answer:
foće de moçhò de casà là ocoreatane
Turtles and tortoises have long life spans. A tortoise can live as long as 150 years. There are 365 days in one year. About how many days could a tortoise live?
Answer:
54,750 days
you just multiply 150 by 365
The National Assessment of Educational Progress (NAEP) includes a "long-term trend" study that tracks reading and mathematics skills over time, and obtains demographic information. In the 2012 study, a random sample of 9000 17-year-old students was selected.24 The NAEP sample used a multistage design, but the overall effect is quite similar to an SRS of 17-year-olds who are still in school. In the sample, 51% of students had at least one parent who was a college graduate. Estimate, with 99% confidence, the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college.
Answer:
The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 9000, 51% of students had at least one parent who was a college graduate.
This means that [tex]n = 9000, \pi = 0.51[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 - 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.4964[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 + 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.5236[/tex]
The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
9514 1404 393
Answer:
slope: 10 m/srepresents speed in meters per secondStep-by-step explanation:
The slope is the change in the quantity on the vertical scale, divided by the corresponding change in the quantity on the horizontal scale.
Here, the line goes from 0 to 100 meters on the vertical scale, corresponding to a change from 0 to 10 seconds on the horizontal scale. So, the slope is ...
m = (100 m)/(10 s) = 10 m/s . . . . slope of the line
The ratio of distance to time is given the name "speed", so ...
the slope represents the sprinter's speed in meters per second.
help please, i need it asap. tyty
Answer:
Step-by-step explanation:
[tex]\frac{3}{x}[/tex] = [tex]\frac{2}{5}[/tex]
2x = 15
x = 7.5
If ∠X and ∠Z are complementary, and the measure of ∠Z is 45°, what is the measure of ∠X?
Answer:
The measure of ∠X is 45°.
Step-by-step explanation:
Complementary angles are two angles that have a sum of 90°.
I subtracted 45 from 90 (90-45) and got 45°.
What are the growth/decay factors and rates for the following functions?
a. y=1000(1.03)x
b. f(x)=200(0.8)x
Answer:
gududu0hxosjvacsivhxhvsaiojvxsaxisahvhvhxsaixjs
Find the perimeter of the figure.
2) Eileen wants to borrow $40,000 to buy a new car. I She is willing to make monthly payments for 5 years. The Metro Bank offers her a loan of $40,000 for five years; the rate of interest is 6% compounded monthly. If Eileen chooses to borrow the money,
a) how much total interest will she pay?
b) how much simple interest will she pay?
c) how much compound interest will she pay?
Answer:
BLM
Step-by-step explanation:
Find the area of a sector, whose perimeter is 40 cm, and the radius is 8 cm.
Answer:
96 cm²
Step-by-step explanation:
From the question,
s = (2πr∅/360)+2r................. Equation 1
Where s = Perimeter of a sector, r = radius, ∅ = angle subtend by the sector at the center of the circle.
Given: s = 40 cm, r = 8 cm
Constant : π = 3.14.
Substitute into equation 1 and solve for ∅
40 = (2×8×3.14×∅/360)+(2×8)
40 = (50.24∅/360)+16
40-16 = 50.24∅/360
50.24∅/360 = 24
50.24∅ = 24×360
50.24∅ = 8640
∅ = 8640/50.24
∅ = 171.97°
Area of a sector (A') = ∅πr²/360
A' = 171.97×3.14×8²/360
A' = 95.997
A' ≈ 96 cm²
The order is for 500 mL D5 1/2 NaCl to run in 6 hours. Set calibration is 15 gtt/mL calculate the flow rate in mL/hrs
Answer:
16 is correct
Step-by-step explanation:
a line has a slope of 9/5 if one of the points on the line is (-10, -16), which of the following could be another point on the line?
Answer:
(0,2) is the answer - Option C.
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the slope and the point is [tex](x_0,y_0)[/tex]
Slope of 9/5 if one of the points on the line is (-10, -16)
This means that [tex]m = \frac{9}{5}, (x_0,y_0) = (-10,-16)[/tex]. So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - (-16) = \frac{9}{5}(x - (-10))[/tex]
[tex]y + 16 = \frac{9}{5}(x + 10)[/tex]
Which of the following could be another point on the line?
We have to find a point for values of x and y which gives us an identity. So
Option A:
x = -5, y = -6
Lets see
[tex]-6 + 16 = \frac{9}{5}(-5+10)[/tex]
[tex]10 = \frac{9*5}{5}[/tex]
[tex]10 = 9[/tex] -> False
So this is not the answer.
Option B:
x = 4, y = 11
[tex]11 + 16 = \frac{9}{5}(4 + 10)[/tex]
[tex]27 = 9*14/5[/tex]
False
Option C:
x = 0, y = 2
[tex]2 + 16 = \frac{9}{5}(x+10)[/tex]
[tex]\frac{90}{5} = 18[/tex]
[tex]18 = 18[/tex]
True, so (0,2) is the answer - Option C.
GIVING OUT BRAINLIEST TO WHOEVER CAN PROVIDE THE CORRECT ANSWER !! Asap
please help! what is the measure of each central angle?
Answer:
9.3
Step-by-step explanation:
PLEASE HELPP ASAPPP will mark brainlist
Answer:
I think this is the answer for the second question.