The cruise control function on Georgina's car should keep the speed of the car within 3 miles per hour of the set speed. The set speed is 55 miles per hour. Write a compound inequality to show the leaves that are within each range. Then graph the solutions.
Answers
Answer:
Given,
Set speed of car = 55,
∵ The speed of the car within 3 miles per hour of the set speed.
So, the maximum speed of car = 55 + 3,
And, the minimum speed of car = 55 - 3
Let x shows the current speed of car,
x ≤ 55 + 3 or x ≥ 55 - 3
x - 55 ≤ 3 or x - 55 ≥ - 3
x - 55 ≤ 3 or -(x-55) ≤ 3
⇒ | x-55 | ≤ 3
Which is the required compound inequality,
Now, 55 - 3 ≤ x ≤ 55 + 3
52 ≤ x ≤ 58
⇒ [52, 58]
Which is the solution of the above compound inequality.
Also, the graph is shown below.
Related Questions
In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?
A) AB ≅ CD
B) AC ≅ BD
C) AB ⊥ BD
D) CD ⊥ BD
Answers
The additional piece of information is needed to determine that ABDC is a parallelogram is,
⇒ AB ≅ CD
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In quadrilateral ABDC,
⇒ AB ∥ CD.
Now,
We know that;
When opposite side of a quadrilateral are parallel and equal to each other, then the quadrilateral are called a parallelogram.
Here, In quadrilateral ABDC,
⇒ AB ∥ CD.
Hence, The additional piece of information is needed to determine that ABDC is a parallelogram is,
⇒ AB ≅ CD
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what is the simplified form of 3abc/abc, when abc does not equal 0? explain using the properties of real numbers
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3abc/abc = 3 .....when abc does not equal 0
the properties is : (ac/bc = a/b ... c ≠ 0 )
Which graph represents the solution to the inequality?
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-2x > = -17 - 3
-2x > = - 20...change the inequality sign when dividing by a negative
x < = -20/-2
x < = 10.........graph D
how to describe and compare a box plot.
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if p - 4 = 2, find the value of 5p - 20
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p-4=2
+4 +4
then p=6
5p-20
5(6)-20
30-20
the answer is 10
Solve for p: 3p-2(p-4) =7p+6
Plz help asap
Thanks
Answers
3p-2p+8=7p+6
then we will separate the variable and solve for it:
3p-2p-7p=6-8
-6p = -2
6p = 2
p = 2/6 = 1/3
Eliana's calculator displays a number as 5.378 E9.
What is this number in standard form?
Enter your answer in the box.
Answers
Most calculators are configured so that when the number is too big, it automatically shows it on scientific notation. The E represents exponent. The calculator is trying to say [tex]5.378 * 10^9[/tex]. It means we should move the decimal point 9 spaces to the right.
The number in standard form would be: 5,378,000,000
You can feel free to let me know if you have any questions regarding this!
Thanks!
- TetraFish
Answer:
5,378,000,000
Step-by-step explanation:
5.378E9
5.378 x 10^(9)
5,378,000,000
12 25 10 38 12 19 8 12 17 41 7 22 10 19 12 16 5 14 find the mean, median, and mode of these weights
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Write a two-column proof given 2x + 6 96 prove: x = 46
Answers
Analyze the statements below and complete the instructions that follow. p: A point has a y-coordinate of zero. q: A point lies on the x-axis. Determine the truth values of the statements
Answers
The height of a triangle is 3cm less than the length of its base and is area is 27m,find the height
Answers
27= x(x-3)/2
27= (x^2-3x)/2
54= x^2-3x
x^2-3x-54=0
(x-9)(x+6)=0
x=9, x=-6.
In this case, x must equal 9 since the base cannot be a negative number.
Final answer: Height=6 m
Find the value of k so that the equation has the solution set {-3}
3(2x-1) = x(2-k)
Answers
The perimeter of a triangle is 465 cm. The length of the sides are consecutive integers. Find the length of the smallest side.
Answers
x=180/3
x=60 cm. for the shortest side.
60+2=62 cm. for the middle side.
60+4=64 cm. for the longest side.
side B= 155cm
side C= 154cm
Twice a number is 24 less than 4 times the number find the number
Answers
2n + 24 = 4n
24 = 4n - 2n
24 = 2n
n = 24/2
n = 12
The question asks for a number which when multiplied by 2 gives a result that is 24 less than the result of the number when multiplied by 4. The solution to this problem is the number 12.
Explanation:The student's question asks about algebraic expression and solving for a value. This could be written as an equation:
2x = 4x - 24
First, let's simplify this equation by subtracting 2x from both sides, this gives you:
2x = 24
Then, solve the equation by dividing both sides by 2, and we find that the number is:
x = 12
So, the number that the student is searching for is 12. Twice this number is 24, which is indeed 24 less than 4 times the number (48).
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Find the value of x for which p is parallel to q, if m∠1 = (4x) and m∠3 = 100. The diagram is not to scale.
a. 96
b. 25
c. 104
d. 100
Answers
4x = 100
x = 100 / 4
x = 25
answer
b. 25
A student writes the difference between 15 and the product of 5 and y to describe the expression 5y - 15. Explain the error
Answers
Write an equation of the line that has a slope of 6 and contains (1,1) in point-slope form.
Answers
m= 6 (given), then y = 6x+b. Calculate b:
y = 6x + b
1 = 6(1) + b
b = -5
y = 6x - 5
Step 2) y - y1 = 6(x - x1)
Step 3) y - y1 = 6(x - 1)
Step 4) y - 1 = 6(x - 1)
-----------------------------------------------------------------------
Explanation of each step:
Step 1) General Formula for Point Slope Form
Step 2) I replaced the slope m with 6 .
Step 3) I replaced the x1 with 1 as this is the x coordinate of the point the line goes through.
Step 4) I replaced y1 with 1 as this is the y coordinate of the point the line goes through.
-----------------------------------------------------------------------
Final Answer: y - 1 = 6(x - 1)
Change 56/7 to a whole or mixed number
Answers
Determine the value of y in the equation: -5y-9=-(y-1) (show all work)
Answers
The value of y in the equation is -2.5.
Explanation:To determine the value of y in the equation -5y-9=-(y-1), we can start by distributing the negative sign to both terms within the parentheses. This gives us -5y-9=-y+1. Next, we can combine like terms by adding y to both sides of the equation. This simplifies the equation to -4y-9=1. To isolate y, we can subtract 9 from both sides of the equation, resulting in -4y=10. Finally, we divide both sides of the equation by -4 to find the value of y, which is -2.5.
please help !!!!!!!!!
Answers
Change=600-576=24
24/600=0.04= 4%
Final answer: 4%
Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006, approximately what was the total employment in 2006? a. 214,000 b. 188,000 c. 195,000 d. 189,000
Answers
1+(6.3/100) = 1.063
Then divide the final number by the original multiplier:
201,000 / 1.063 = 189087
So the answer is d
Hope this helps! :)
Answer:
189,000
Step-by-step explanation:
The are of a rectangle is 117 square centimeters. The width of the rectangle is 9 centimeters. What is the length of the rectangle?
Answers
What is the remainder when 14,952 is divided by 41
Answers
Answer:
the answer is 28 A
Step-by-step explanation:
What common angle do CDG AND FCE share?
FBG is congruent to DBE
CEF is congruent to CGD
CDG is congruent to CFE
GCE is congruent to ECG
Answers
This means angle GCE equals to angle ECG
Answer: GCE is congruent to ECG
Answer:
The correct option is 4.
Step-by-step explanation:
From the given figure it is noticed that the triangle CDG and triangle FCE have a common vertex C. So both triangle are sharing same angle at vertex C.
In triangle CDG and triangle FCE
[tex]\angle GCD\cong \angle FCE[/tex]
If the length of two adjacent sides increases, then the inclined angle remains the same.
If the side CD increased to E and side CF increased to G, then
[tex]\angle GCE\cong \angle ECG[/tex]
Therefore option 4 is correct.
A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that ∠ADC is a right angle and that m∠BDC is 32° greater than m∠ADB. Write and solve an equation to find m∠BDC and m∠ADB
Answers
Let x be m ∠ADB.
Because m ∠BDC is 32° greater than m ∠ADB, thereforem ∠BDC = x + 32°
Each angle of a rectangle is 90°, therefore:
x + (x + 32) = 90
2x + 32 = 90
2x = 58
x = 29°
x + 32 = 61°
Answer:
m ∠BDC = 61°
m ∠ADB = 29°
Number 8. Solve the equation for variable d. Correct answer will get brainliest.
Answers
The first step is to multiply both sides by 3
c = (2d+1)/3
3c = 3*(2d+1)/3
3c = 2d+1
Then you subtract 1 from both sides to get
3c-1 = 2d+1-1
3c-1 = 2d
2d = 3c-1
Finally divide both sides by 2 to fully isolate d
2d = 3c-1
2d/2 = (3c-1)/2
d = (3c-1)/2
which is what choice B is showing
Can anyone solve this problem???
One person can complete a typing project in 6 hours, and another can complete the same project in 8 hours. How long will it take the two people working together to complete the project???
Answers
3/24x + 4/24x = 1
7/24x = 1
x = 24/7 hours
Time taken to complete the project if two people worked together is required.
It would taken around 3.4 hours to complete the project if both the people worked together
Time taken to complete the work by first person is 6 hours
Time taken to complete the work by second person is 8 hours
The work equation will be be
[tex]\dfrac{1}{6}+\dfrac{1}{8}=\dfrac{1}{x}\\\Rightarrow \dfrac{4+3}{24}=\dfrac{1}{x}\\\Rightarrow x=\dfrac{24}{7}\approx 3.4\ \text{hours}[/tex]
So, it would taken around 3.4 hours to complete the project if both the people worked together.
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what is
7x-4=-2x+1+9x-5
Answers
remember, you can do anything to an equation as long as you do it to both sides
7x-4=-2x+1+9x-5
group like terms
7x-4=-2x+9x+1-5
add like terms
7x-4=7x-4
add 4 to both sides
7x=7x
divide both sides by 7
x=x
true
x=all real numbers
since it sipmlifies to x=x (it could somiplify to 0=0 as well), it is an identity and all real numbers work for x
The equation 7x-4=-2x+1+9x-5 has infinitely many solutions
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 7x-4=-2x+1+9x-5
We have to take the variable terms on one side and constant on other side
In the given equation x is the variable and plus comma minus are all operators.
We need to solve for x.
7x+2x-9x=1-5+4
9x-9x=0
0=0
So the equation has infinitely many solutions
Hence, the equation 7x-4=-2x+1+9x-5 has infinitely many solutions
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A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find:
Answers
[tex]s=60-12t [/tex]
Now you can answer questions such as "how far was the bicyclist from the station after 3 hours?" Substitute 3 for t. s = 60 - 12(3) = 60 - 36 = 24 km.
Answer:
s=18
Step-by-step explanation:
First of all, the formula is s=60-12t. thanks to the person who answered this question first (teehee)
S=distance and t=duration.
We also know that the distance is 60 km, the bicyclists's speed is 12 km/h, and the duration for this example is 3.5 hours.
So, using the formula, we substitute all the variables and s=18.
Thanks!
Also, for how the formula is what it is, look at the previous answer cuz yea.
Maybe this helped?
hehe- EG
what are the roots to this quadratic equation?
Answers
x^2=9/18
x=sqrt(9/16)
x=3/4,-3/4
so the root of the quadratic equation are 3/4 and -3/4
Answer:
[tex]\frac34[/tex] and [tex]-\frac34[/tex]
Step-by-step explanation:
Hello!
We have to solve for x to find the roots of the quadratic.
Solve for x[tex]16x^2 = 9[/tex][tex]x^2 = \frac{9}{16}[/tex][tex]\sqrt{x^2} = \sqrt{\frac{9}{16}}[/tex][tex]x = \pm\frac{\sqrt9}{\sqrt{16}}[/tex][tex]x = \pm\frac34[/tex]The roots of the quadratic are [tex]\frac34[/tex] and [tex]-\frac34[/tex].
The roots of the quadratic is when the value of y is 0, or when the graph intersects the x-axis.