Solution :
We have to find all the possible solutions for the inequality [tex]2x+7<3x-5[/tex].
The given inequality can be solved as,
Subtracting 7 from both side , we get
[tex]2x+7-7 < 3x-5-7\\\\\Rightarrow 2x<3x-12[/tex]
Now, Subtracting 3x from both side, we get
[tex]2x-3x<3x-12-3x\\\Rightarrow -x <-12\\[/tex]
As we here we can see that both sides have similar sign, so we can cancel them out.
[tex]\Rightarrow x < 12[/tex]
Hence, the possible solution of the inequality [tex]2x+7<3x-5[/tex] is [tex]x< 12[/tex]
If f(x)=3(x+5)+4/x what is f ( a+2 )
[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]
Answer:
The value of [tex]f(a+2)[/tex] is [tex]3a+21+\frac{4}{a+2}[/tex].
Step-by-step explanation:
Consider the provided function [tex]f(x)=3(x+5)+\frac{4}{x}[/tex]
In order to find the value of [tex]f(a+2)[/tex]
Substitute x = a + 2 in the provided function.
[tex]f(a+2)=3((a+2)+5)+\frac{4}{a+2}[/tex]
[tex]f(a+2)=3(a+2+5)+\frac{4}{a+2}[/tex]
[tex]f(a+2)=3(a+7)+\frac{4}{a+2}[/tex]
Now, apply the distributive property: [tex]a(b+c)=ab+ac[/tex]
[tex]f(a+2)=3a+21+\frac{4}{a+2}[/tex]
Therefore, the value of [tex]f(a+2)[/tex] is [tex]3a+21+\frac{4}{a+2}[/tex].
what is the missing length of a square
3 because length times width = area right. so 3x3=9.
it is 3452 miles round trip to Craigs aunts house. if he travels to her house 3 times this year how many miles did he travel in all
3452 divide 2 multiply by 3 is 5178
Answer: There are 10,356 miles in all he traveled.
Step-by-step explanation:
Since we have given that
Number of miles round trip to Craigs aunts house = 3452 miles
Number of times he travels to her house this year = 3
So, we need to find the number of miles he travel in all.
So, the number of miles he travel in all is given by
[tex]3\times 3452\\\\=10,356\ miles[/tex]
Hence, there are 10,356 miles in all he traveled.
A basketball player shoots a free throw in a game. The quadratic expression models the height of the ball, in feet, where t is the time, in seconds.
-16t^2 + 25t+7
What does the constant, 7, in the expression represent?
A.
the initial velocity of the ball when the player releases it
B.
the maximum height the ball reaches while in the air
C.
the initial height of ball when the player releases it
D.
the total time the ball spends in the air
Answer:
the initial height of ball when the player releases it
Step-by-step explanation:
A basketball player shoots a free throw in a game. The quadratic expression models the height of the ball, in feet, where t is the time, in seconds.
y= -16t^2 + 25t+7
Given equation is in the form of
y= -16x^2 + V t + h
Where V represents the initial velocity and h represents the initial height of the ball
Now we compare our equation with the general equation
We have 7 in the place of h
So , 7 is the initial height of the ball
Answer is 7 is the initial height of ball when the player releases it
Answer:
A,D,E
Step-by-step explanation:
slope of (4,6) and (-1,2)
We can use the slope formula to find the slope between these two points:
[tex]\frac{y.2 - y.1}{x.2 - x.1} = m[/tex]
2 - 6 / -1 - 4
-4 / -5
Because there are two negatives, they cancel out.
The slope of the line between these two points is 4/5.
[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\(4,\ 6)\to x_1=4,\ y_1=6\\(-1,\ 2)\to x_2=-1,\ y_2=2\\\\\text{substitute}\\\\m=\dfrac{2-6}{-1-4}=\dfrac{-4}{-5}=\dfrac{4}{5}=0.8[/tex]
if f(x)=3/x+2- sqrt x-3 f(7)=?
To get the answer, you need to solve the equation for x = 7.
f(7) = 3/7 + 2 - sqrt(7) - 3.
= 3/7 - 1 - sqrt(7).
If you need to simplify it further:
= -4/7 - sqrt(7).
If you need it in decimal form: = -3.2171798824
Answer:
f(7)=-3.217
Step-by-step explanation:
We are given that [tex]f(x)=\frac{3}{x}-\sqrtx-3[/tex]
We have to find the value of f(7).
Substitute the value of x=7
Then, we get
[tex]f(7)=\frac{3}{7}+2-\sqrt7-3=\frac{3}{7}-1-\sqrt7[/tex]
[tex]f(7)=\frac{3-7}{7}-\sqrt7=-\frac{4}{3}-\sqrt7[/tex]
[tex]f(7)=-\frac{4}{7}-2.646[/tex]
Because [tex]\sqrt7=2.646[/tex]
[tex]f(7)=-\frac{4+18.522}{7}=-\frac{22.522}{7}[/tex]
[tex]f(7)=-3.217[/tex]
Hence, f(7)=-3.217
y=-5x-20x-26
what is the axis of symmetry, the vertex, and sketch
Copy these incomplete number lines. Label the missing numbers on each of them.
a.
20/2 = 10
0, 10, 20, 30, 40, 50
b.
32.4/4 = 8.1
0, 8.1, 16.2, 24.3, 32.4, 40.5
c.
8.8/4 = 2.2
0, 2.2, 4.4, 6.6, 8.8, 11
d.
10/3 = 3.3
0, 3.3, 6.7, 10, 13.3, 16.7
Answer:
(a) 0, 10, 20, 30, 40, 50.
(b) 0, 8.1, 16.2, 24.3, 32.4, 40.5.
(c) 0, 2.2, 4.4, 6.6, 8.8, 11.
(d) 0, 3.33, 6.67, 10, 13.33, 16.67.
Step-by-step explanation:
Part a.
From the given number line it is clear that
2 units = 20
So, length of 1 unit is
[tex]\frac{20}{2}=10[/tex]
Therefore, the numbers on the number line are 0, 10, 20, 30, 40, 50.
Part b.
From the given number line it is clear that
4 units = 32.4
So, length of 1 unit is
[tex]\frac{32.4}{4}=8.1[/tex]
Therefore, the numbers on the number line are 0, 8.1, 16.2, 24.3, 32.4, 40.5
.
Part c.
From the given number line it is clear that
4 units = 8.8
So, length of 1 unit is
[tex]\frac{8.8}{4}=2.2[/tex]
Therefore, the numbers on the number line are 0, 2.2, 4.4, 6.6, 8.8, 11.
Part d.
From the given number line it is clear that
3 units = 10
So, length of 1 unit is
[tex]\frac{10}{3}=3.33[/tex]
Therefore, the numbers on the number line are 0, 3.33, 6.67, 10, 13.33, 16.67.
The Quotient 250 divided by 5/8 tells about how far a sloth may move in one hour How far can a sloth go in 90 minutes?
Given condition is:
A sloth moves in one hour = [tex]\frac{250}{5/8}[/tex]
[tex]\frac{5}{8}=0.625[/tex]
So, a sloth moves in one hour = [tex]\frac{250}{0.625}=400 units[/tex]
Hence, in 60 minutes a sloth moves = 400
In 1 minute sloth will move = [tex]\frac{400}{60}[/tex]
In 90 minutes it will move = [tex]\frac{400}{60}\times90=600[/tex]
The answer is 600 units.
Answer:
A sloth can move 600 units in 90 minutes.
Step-by-step explanation:
The problem says that if you divide 250 in [tex]\frac{5}{8}[/tex] you obtain how far a sloth move in one hour, then:
[tex]250:\frac{5}{8}=\frac{250.8}{5}= \frac{2000}{5}=400[/tex]
A sloth moves 400 units in one hour (60 minutes).
We can use a rule of three,
400 units ⇒ 60 minutes
x ⇒ 90 minutes
[tex]x=\frac{90.400}{60} \\\\x=\frac{36000}{60}\\\\x=600[/tex]
A sloth can move 600 units in 90 minutes.
The temperature decreased at a constant rate for 12 hours. If the temperature dropped a total of 18 degress over thoes 12 hours, what was the hourly change in temperature?
1.5 degrees per hour
There was a decrease of 1.5 degrees per hour.
What is unit rate?A unit rate means a rate for one of something.
Given that, The temperature decreased at a constant rate for 12 hours, the temperature dropped a total of 18 degrees over those 12 hours,
In 12 h = -18 degrees
In 1 h = 18/12 = 1.5 degrees.
Hence, There was a decrease of 1.5 degrees per hour.
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Mr Klinker is 35 and his daughter is 10. In how many years will Mr.Klinker be twice as old as his daughter? Right an algebriac equation and solve.
Final answer:
Mr.Klinker will be twice as old as his daughter in 15 years.
Explanation:
To find the number of years in which Mr. Klinker will be twice as old as his daughter, we can set up an equation:
Let x be the number of years in the future.
Mr. Klinker's age: 35 + x
Daughter's age: 10 + x
According to the problem, Mr. Klinker will be twice as old as his daughter, so we can write the equation:
35 + x = 2(10 + x)
Now, let's solve for x:
35 + x = 20 + 2x
Move the 2x to the left side:
x - 2x = 20 - 35
-x = -15
Divide both sides by -1:
x = 15
Therefore, Mr. Klinker will be twice as old as his daughter in 15 years.
Um what is 20 +10 I want to give points
Im only 4 but I think the answer is 30. JK im 13 :D:D
Him wants to run 1800 miles this year, and he plans to run at least 6 miles per day. If Jim has already run 720 miles so far this year, what is the maximum number of days that it will take him to run the remaining miles?
1800-720=1080
He has 1080 miles left, he'll run 6 days per day so 1080/6=180
He won't need more than 180 days
Answer:
Step-by-step explanation:
Write and solve an inequality for d, the # of days:
720 mi + (6 mi / day)d ≥ 1800 mi. Then:
(6 mi/day)d ≥ 1800 mi - 720 mi, or (6 mi/day)d ≥ 1080 mi.
Solving for d, we get 1080/6 days: 180 days. If he runs 6 miles per day for 180 days, he will have covered 1800 miles. His running more days will, of course, increase the total number of miles covered.
If you subtract twelve from twice a number, the result is six.what is the number?
Final answer:
The number in question is 9. This is found by setting up the equation 2x - 12 = 6 and solving for x.
Explanation:
To find the number when twelve is subtracted from twice the number and the result is six, we set up the equation 2x - 12 = 6. To solve for the number (x), follow these steps:
Add 12 to both sides of the equation: 2x - 12 + 12 = 6 + 12, which simplifies to 2x = 18.Divide both sides by 2 to isolate x: 2x/2 = 18/2, which simplifies to x = 9.Therefore, the number that satisfies the condition is 9.
PLEASE HELP! 25 POINTS
listen the question number then answer
Answer: <
Explantion:
[tex]8*4-2(4)=24[/tex]
[tex]5(10-4)=30[/tex], because you factor the 5 into 10 and 4 so
[tex]50-20=30[/tex]
The second one you want will be integers.
1 . When x = 4
Lhs 8.4-2x = 32- 2(4) =32-8 =24
Rhs 5(10-x) = 5( 10- 4) = 5 (6)= 30 as lhs is less than rhs therefore sign will be <
2.the integers are all the counting numbers
Henri's bill at a restaurant is $19.62. He wants to leave a tip of 20%, or , of the bill. To find the exact amount of the tip, he should multiply the bill by .20. A good estimate for the amount of the tip is ____. A good estimate for the total bill, including the tip, is ____.
Answer:
The tip is $3.92. The total bill is $23.54.
Step-by-step explanation:
I simply used a calculator to find the answer. It's just basic multiplication for the tip and addition for the total bill.
Answer:
1st blank = $4
2nd blank = $24
Step-by-step explanation:
Henri's bill at a restaurant is $19.62. He wants to leave a tip of 20%
Estimated round off of $19.62 is $20.
Estimations are made for easy calculations in mind, this is why we round to nearest 0.
So, 20% of $20 is :
[tex]0.20\times20=4[/tex] dollars
And the total bill, including the tip is estimated to be :
= [tex]20+4=24[/tex] dollars
What do you multiply 3.2 by to get 32?
The answer to this question is 10
write 2.96 as a mixed number or fraction in simplest form show your work
To write 2.96 as a mixed number or fraction in simplest form, we divide the decimal part by 100, convert it to a fraction, and simplify it. The final answer is 2 24/25.
Explanation:To write 2.96 as a mixed number or fraction in simplest form, we first need to understand that 2.96 is a decimal number. The whole number part is 2 and the decimal part is 0.96. To convert the decimal part to a fraction, we take the decimal part as the numerator and 100 as the denominator. So, 0.96 becomes 96/100. Now, we can write the mixed number as 2 96/100. To simplify this fraction, we divide both the numerator and the denominator by their greatest common factor, which is 4. Dividing 96 by 4 gives us 24, and dividing 100 by 4 gives us 25. So, the simplest form of 2 96/100 is 2 24/25.
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Jim and Carla are scuba diving. Jim started out 12 feet below the surface. He descended 17 feet, rose 3 feet, and descended 8 more feet. Then he rested. Carla started out at the surface. She descended 19 feet, rose 3 feet, and descended another 17 feet. Then she rested. Which person rested at a greater depth? Complete the explanation.
Answer:
Jim reached a greater depth by one foot, as he started 12 feet below the surface.
Step-by-step explanation:
Jim
12 feet+17 feet = 29
29-3 feet (rose 3 feet) = 26
26+8= 34 feet
Carla
0 feet (surface)+ 19 feet= 19
19-3 feet= 16
16+17= 33 feet
After performing the depth calculations for both Jim and Carla's scuba diving, it was found that Carla is resting at a greater depth than Jim. Jim ended 24 feet below the surface, and Carla ended 33 feet below the surface.
Explanation:To start with, let's calculate how deep Jim and Carla each ended their dives. We begin with Jim, who started 12 feet below the surface, descended 17 feet, went up 3 feet and then descended another 8 feet. His total depth is therefore 12 - 17 + 3 - 8 = 24 feet below the surface.
Now let's calculate Carla's depth. Carla started at the surface (0 feet below), then descended 19 feet, ascended 3 feet, and descended another 17 feet. Her total depth is therefore 0 - 19 + 3 - 17 = 33 feet below the surface.
Comparing these two figures, Carla is resting at a greater depth than Jim.
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Convert 6.7 hours to hours and minutes. A) 6 hours and 30 minutes B) 6 hours and 36 minutes C) 6 hours and 42 minutes D) 6 hours and 48 minutes E) 6 hours and 54 minutes
The answer would be C because 6.7 hours is converted to 402 minutes. In 6 hours, there are 360 minutes. 402-360=42, therefore 6.7 hours is equal to 6 hours and 42 minutes.
Final answer:
6.7 hours is equal to 6 hours and 42 minutes. The conversion is done by multiplying the decimal part of the hour by 60 to get the minutes.
Explanation:
To convert 6.7 hours to hours and minutes, first, note that the integer part of the number represents the hours. Therefore, we have 6 hours. The decimal part (0.7) represents the fraction of the hour. Since there are 60 minutes in one hour, we convert the fraction of the hour to minutes.
To do this, we multiply 0.7 by 60:
0.7 hours * 60 minutes/hour = 42 minutes
So, 6.7 hours is equal to 6 hours and 42 minutes, which corresponds to the answer C) 6 hours and 42 minutes.
Find the missing number so that the equation has infinitely many solutions. - 4x+15= - 4x+
Answer:
15
Step-by-step explanation:
In order to have infinite solutions, the left and the right side must be the same. In order to make each side identical, you must add 15.
Answer: 7
Step-by-step explanation:
you and four of your friends go to carnival. The cost to get in is $10 per person plus $2 for each ride. The cost per person can be represented by the function f(x)=2x + 10 write a rule for the total cost for you and your friends if you all ride the same number of rides
f(x) = 10x + 50
multiply the cost per person by 5 ( you and 4 friends )
f(x) = 5(2x + 10) = 10x + 50
Please help me!!!! I'm having a lot of trouble with this math
Line BD is intersecting Line AC making it perpendicular.
Triangle ABC is congruent to Triangle ADC because line AC bisects the kite.
Line AB is congruent to line AD because it is just a direct shift of the line
Angle BAC is congruent to angle DAC again because line AC bisects the kite, creating equal angles.
olisa has a garden shop. One customer wants to buy 42 Snapdragon plants. There are six snapdragons in a pack. How many packs should olisa sell to her customer?
the answer for your problem is 7
what is 11 feet and 8 inches plus 2 feet and 9 inches
Answer:
14 feet and 5 inches
Step-by-step explanation:
11 feet + 2 feet= 13 feet
9 inches + 8 inches = 17 inches
17 inches = 1 foot and 5 inches
13 + 1 = 14 feet
5 inches + 0 inches = 5 inches
Emre pays a $20 sign-up fee to join a video streaming service and $12 for each month of his membership. The equation c = 12w + 20 gives the total cost for w weeks. Which statement correctly describes what happens when w increases?
We are given equation: c = 12w + 20, that represents total cost for w number of weeks.
We need to describle, what happen when w that is number of week increases.
w is an independent variable there. But c is a dependent variable.
As the number of weeks w increase the total cost c increases. But that would not effect fix $20 sign-up fee for joining a video streaming service.
Therefore, we could say:
The number of weeks and the total cost increase, but the sign-up fee stays the same.Answer:
The number of weeks and the total cost increase, but the sign-up fee stays the same.
Step-by-step explanation:
A 10 meter ladder rest against a vertical wall so that the distance between the foot of the ladder and the wall is 2 meter. Find the angle the ladder makes with the wall and height above the ground at which the upper end of the ladder touches the wall
Answer:
78.46 degrees
Step-by-step explanation:
We can use inverse cosine of the measurements since we know the measurements and need the angle.
cos-1(2/10)= angle
Do this on a calculator and set the mode to degrees to get the answer
Write a # where the value of the 4 in the thousands place is x1/10 the # 854,093
We are to find the place value of 4 in
854,093
Firstly, we can rewrite it
[tex]854,093=800000+50000+4000+000+90+3[/tex]
we can see that 4000 is added
so, the place value of 4 in 854,093 is
4000........Answer
How do I work this out oof
I am so sorry for giving you the wrong answer at first.
Here's the processs
1x=-0.5555
Move the decimal point in the repeating decimal one space forward
10x=-5.55555
Then subtract
10x=5.5555
x=-0.5555= 9x=-5
Divide both sides by 9
9x=-5
9x/9=-5/9
-5/9 is your final answer!
Hope this helps!
The length of a rectangular field is 6 m less than twice the width. The perimeter is 312 m. Find the length of the field.
Length = 102
hope this helps :)
A) L +6 = 2W OR
A) L +6 -2W = 0
B) 2L + 2W = 312 Adding A and B
3L +6 = 312
3L = 306
Length = 102