According to the information given, the absolute value inequality that can be used to assess which pens are tolerable is:
[tex]|w - 10| \leq 2[/tex]
The absolute value function measures the distance of a point to the origin, and is defined by:
[tex]|x| = x, x \geq 0[/tex][tex]|x| = -x, x < 0[/tex]The weight must be of 10g, with a tolerance of 2g, which means that the absolute value of the difference between the weight w and 10g must be of at most 2g, hence the inequality is:
[tex]|w - 10| \leq 2[/tex]
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I need help on this assignment
[tex]\text{Apply Pythagorean theorem,}~ \text{Hypotenuse side}^2 = \text{Opposite}^2 + \text{Adjacent side}^2[/tex]
[tex]12^2 =y^2 +8^2\\\\\implies y^2 = 12^2 -8^2 \\\\\implies y^2 = 80\\\\\implies y =\sqrt{80} = \sqrt{16\times 5}= 4\sqrt 5~~ \text{Units}[/tex]
Find the Product of (s^2+5s)(s^3+4s^2).
The result of the product [tex](s^2+5s)(s^3+4s^2)[/tex] is [tex]s^5+9s^4+20s^3[/tex]
The product is given as:
[tex](s^2+5s)(s^3+4s^2)[/tex]
Rewrite as:
[tex](s^2+5s)(s^3+4s^2) = (s^2+5s) \times (s^3+4s^2)[/tex]
Expand the expression on the right-hand side
[tex](s^2+5s)(s^3+4s^2) = s^2\times (s^3+4s^2)+5s \times (s^3+4s^2)[/tex]
Distribute the expressions
[tex](s^2+5s)(s^3+4s^2) = s^5+4s^4+5s^4+20s^3[/tex]
Evaluate like terms
[tex](s^2+5s)(s^3+4s^2) = s^5+9s^4+20s^3[/tex]
Hence, the result of the product [tex](s^2+5s)(s^3+4s^2)[/tex] is [tex]s^5+9s^4+20s^3[/tex]
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If f(x) = 9(x - 7)^2 – 8
Find f( – 4)
Answer:
1,081
[tex]f( - 4) = 9( - 4 - 7) {}^{2} - 8 \\ f( - 4) = 9( - 11 {)}^{2} - 8 \\ f( - 4) = 1081[/tex]
what's the Answer ?
[tex] \tiny\sf{6 + 6 \div 3}[/tex]
Answer: 8
Step-by-step explanation:
PEMDAS
division first
6 + 2
8
Answer:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Step-by-step explanation:
6/3 = 2
6+2 = 8
HAVE A NICE DAY
Betty earned $159 by selling 75 Each bracelet was the same price about how much did each bracelet cost estimate the cost of each bracelet what compatible numbers did you use
Answer:
2$ compatible numbers are 200 and 100
Step-by-step explanation:
Cooper Toy Company has designed a new toy that uses a spring that follows a
sinusoidal curve after you wind it up and start it. At t = 5 seconds, the end of
the spring is at its highest point, 18 cm above the ground. Four seconds later,
the spring is at its lowest point, which is 6 cm above the ground. Find an
equation that will determine the height of the spring at any time t.
a) Find the height of the spring after 26 seconds.
b) Find the first time the height of the spring reaches 16 cm above the ground.
Answer:
Step-by-step explanation:
b] find the first time the height of the spring reaches 16 cm above the ground.
Define a variable for the number of cars, and define a variable for the number of vans or trucks. You will need to choose x for one and y for the other.
Answer:
See below!
Step-by-step explanation:
I don't think you included the entire question, but maybe you were just stuck on this part, so I'm happy to help!
You include variables in a math equation to give meaning to a word, phrase, or situation in a shortened way.
For example, if I say, "I run 2 miles every day. How many miles will I run in x days?", your equation should look like this:
miles=2x
Notice that the 2 is a number, because that is the one thing that we know for sure. We know, no matter what, I run 2 miles a day. However, we don't know for how many days. So, for this, we need to put something as a sort of placeholder until we are told how many days.
Variables can be any letter, from A-Z! It is reccomended to stay with letters that avoid s, and i(among others) to make sure that you are using letters that can't be mistaken as letter on accident. For example, s could look like 5. In some cases, i could look like 1.
For your question, you could use:
#of cars=x
#of trucks/vans=y
a diver jumps a platform 16 feet above the water to a depth of 6 feet below the surface of the water. what is the distance he dives
i need help with this question, thx to anyone who helps! :)
Answer:
Golf balls
Step-by-step explanation:
There is a much higher chance of her picking an even number in the golf ball tank because there are way more golf balls with even numbers. (2, 4, 6, 8, etc.)
pls help i really need help STOP SENDING ME LINK
Answer:
0
Step-by-step explanation:
because your making it all to the zero power which equals zero
Answer:
0
Step-by-step explanation:
We will use the rule of order of operations
15 + 4 = 19
20 + 5 = 25
19 squared = 361
3 x 361 = 1083
25 squared = 625
625 x 2 = 1250
New equation =
1083 + 1250
=
2333
But you multiply by 0 so it equals 0
Subtract: -10 - (-21)
About how many times larger is 12 x 10(4) compared with 3 x 10(5)?
0.3
0.4
0.9
1.2
*the ones in parentheses are exponents
We need a minimum of 30 book sales by today. If 10 books were sold yesterday, what are the possible numbers for sales today
A.b> 20
B. b> 10
C.b> 30
D.b> 20
I mean it would be A and D because I don't know why they are both the same answer. If 10 books were sold yesterday, at LEAST 20 are needed to make the goal.
62 out of 100 children prefer strawberries. What percentage of children prefer strawberries
Answer:
it is 62
Step-by-step explanation:
62 out of 100 is equal to 62/100 or 62%
Plz I need help with this I am struggling failing math
Answer:
CB = 5, [tex]m\angle{BDA} = 23^\circ[/tex]
Step-by-step explanation:
Assuming that the marks next to angle D mean that [tex]\angle{BDA} \cong \angle{BDC}[/tex], then there is enough information to conclude that the two right triangles are congruent (HA theorem--hypotenuse/angle).
Then all the corresponding parts of the two triangles are congruent, including segments BA and BC, making them the same length.
4x + 1 = 9x - 4
Solving for x,
1 = 5x - 4
5 = 5x
1 = x
Pluggint x = 1 into the two expressions reveals that the length of segment CB is 5.
The two small angles at D are congruent, so [tex]m\angle{BDA}=23^\circ[/tex].
3927283+8093
Help pls
Answer: 3935376
Step-by-step explanation: 3927283+8093
3935376
The world’s two highest dams are both in Tajikistan. The Rogun dam is 35 meters taller than the Nurek dam. Together they are 635 meters tall. Find the height of the Nurek dam
Answer: Rogun dam is 335m tall and Nurek dam is 300m tall
Step-by-step explanation:
I will use [tex]r[/tex] to represent the height of the Rogun dam and [tex]n[/tex] to represent the height of the Nurek dam.
The system of equations is as follows:
[tex]r+n=635[/tex]
[tex]r-n=35[/tex]
From the second equation, we can rearange it to be:
[tex]r=35+n[/tex]
Then take this new value of [tex]r[/tex] and plug it into our first equation to find [tex]n[/tex]
[tex](35+n)+n=635[/tex]
[tex]35+2n=635[/tex]
[tex]2n=600[/tex]
[tex]n=300[/tex]
This means that the Nurek dam is 300m tall, and the Rogun dam is 335m tall, found by pluggin the value into our first equation:
[tex]r+300=635[/tex]
[tex]r=335[/tex]
Choose the inequality that could be used to solve the following problem.
Three times a number is at most negative six.
(A) 3x ≤ -6
(B) 3x < -6
(C) 3x ≥ -6
(D) 3x > -6
Answer:
I believe the answer is A
Step-by-step explanation:
three times x can be equal to, but never greater than -6
Answer:
A. 3x ≤ -6
Step-by-step explanation:
the sentence ‘3x is at most -6
means that the most 3x is allowed to be is -6
it can be -6 or any number less than -6
So, the phrase 3x is at most -6
’ means ‘
3x ≤ -6
What is the slope of the line with the equation: y+6=24-2x
pleeaseeee
Answer:
The slope is -2
Step-by-step explanation:
y+6=24-2x
y=18-2x
y=-2x+18
Answer:
Slope = -2
Step-by-step explanation:
Changing this problem (y+6=24-2x) to Slope Intercept form turns it into y=-2x+18.
the formula is written as y=mx+b m=slope b=y-intercept and x & y being a certain number that is unknown . Therefore, the slope of the equation y=-2x+18 will be
m=-2/1 rise/run
Expand and simplify (√10-√2)² Give your answer in the formn b-c√5 where b and c are integers
Answer:
12-4√5
Step-by-step explanation:
(√10-√2)²
(√10-√2)(√10-√2)
Foil/distribute
10-√20-√20+2
12-2√20
12-2√4*√5
12-2*2√5
12-4√5
On expansion of the algebraic identity of [tex](a-b)^2[/tex], the expansion of [tex](\sqrt{10}-\sqrt{2})^2[/tex] is [tex]12-4\sqrt{5}[/tex]. Thus making b = 12 and c = 4.
Algebraic identities are expansion of powers of algebraic expressions.
One such algebraic identity is the expansion of [tex](a-b)^2[/tex]. It is given by:
[tex](a-b)^2 = a^2+b^2-2ab[/tex]
Given the question,
[tex](a-b)^2 = a^2+b^2-2ab[/tex]
[tex](\sqrt{10}-\sqrt{2})^2 = ( \sqrt{10})^2+(\sqrt{2})^2 -2 ( \sqrt{10})(\sqrt{2})\\\\=10 + 2 - 2\sqrt{20}\\\\ =12 - 2\sqrt{2*2*5} \\\\= 12 -2*2\sqrt{5} \\\\=12-4\sqrt{5}[/tex]
Given the form, [tex]b - c\sqrt{5}[/tex],
On comparison,
b = 12
c = 4
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Use the graph to find the cost of 8 shirts.
Cost of Shirts
y
200
8 8 8 8 8 8 8 8 8
Cost ($)
120
0
7 8 9 10 11
Number of shirts
O A. The cost of 8 shirts is $120.
OB. The cost of 8 shirts is $150.
Ο Ο Ο Ο
C. The cost of 8 shirts is $8.
O D. The cost of 8 shirts is $15.
Suppose $22,825 is deposited into a savings account with a simple interest rate of 4.03%. Find the account balance after 5 years and 3 months.
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Based on the information that's given, the account balance after the years given will be $27654.20.
The formula for simple interest is calculated as:
= PRT / 100
where,
Principal = $22825
Rate = 4.03%
Time = 5 years, 3 months = 5.25 years
Therefore, the simple interest will be:
= ($22825 × 4.03 × 5.25) / 100
= $4829.20
Therefore, the amount will be:
= $22825 + $4829.20
= $27654.20
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Answer:
The amount will be $27654.20
Step-by-step explanation:
PLS help me 20 points in total
Answer:
-3.5 is the answer
I mean, I think this is referring to positive and negatives which if it is, it would be -3.5 .
pPLEASE HELP ME, I NEED HELP I CANT UNDERSTAND I COULD JUST GUESS BUT ITS IMPORTANT PLS
Answer: where’s the question??
teheheh help please :)
Answer:
Solid line
Step-by-step explanation:
This means that it is equal. The line under the less than sign means it would be a solid line.
can i please have help with this question branliest for the correct answer
Answer:
y = -4x+2
Step-by-step explanation:
To find a perpendicular line, the slope would be -4.
y=-4x
Since the point it has to go through is (0,2), the y-intersept is already given.
y = -4x+2
A line has slope 56 and y–intercept −3.
Which answer is the equation of the line?
y=56x+3
y=−3x+56
y=56x−3
y=3x+56
Answer:
c
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
m=56
b=-3
y=56x-3
Factor out the GCF
4g^3-6g+20g^2
Answer:
[tex]\sf 2g(2g ^2-3+10g)[/tex]Step-by-step explanation:
[tex]\sf 4g^3-6g+20g^2[/tex]
GFC: 2g
We'll Write the GCF first, then, divide each term by the GCF.
[tex]\sf 2g(\frac{4g^3}{2g}-\frac{6g}{2g} +\frac{20^2}{2g} )[/tex]
[tex]\sf 2g(2g ^2-3+10g)[/tex]
PLZ HELP
How would you graph the solution set of x - 2 > 5?
Open circle on 7 and shaded to the right.
Closed circle on 7 and shaded to the right.
Open circle on 7 and shaded to the left.
Closed circle on 7 and shaded to the left.
Answer:
look up demos, it works like a charm everytime!
Step-by-step explanation:
hope this helps :)
To train for an upcoming marathon, Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following weeks.
There are many ways to approach this problem.
Week Miles
1 2
2 2.5
3 3
4 3.5
5 4
6 4.5
Write an equation to represent the nth term of the sequence.
Answer:
f(x)= .5x + 2
Step-by-step explanation:
Now this is not to complicated
first the constant is 2
after each day she gains .5 miles
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation to represent the nth term of the sequence is y=0.5x+2.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Let the distance travelled by Susie in any week,x be represented by y.
Given that Susie will run 2 miles in the initial or in the first week. Therefore, the distance for the initial work week will be,
Initial distance = y-intercept = c = 2
Further, if the daily distance is increased by half a mile each of the following weeks. Therefore, the slope of the equation is the change in the distance, therefore, we can write,
Slope, m = Change in the distance = 0.5
Now, if the equation represents the nth term of the sequence, then we can write,
y = mx + c
y = 0.5x + 2
Hence, the equation to represent the nth term of the sequence is y=0.5x+2.
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