subtracting linear expressions 30 points this is 3 more
The linear expressions are subtracted to:
-2x + 17. Option A
-4x - 2. Option B
2x + 6. Option B
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, coefficients, and constants.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc.
Given the expression:
A. (4x + 8) - (6x - 9)
expand the bracket
4x + 8 - 6x + 9
collect like terms
-2x + 17
B. (3x - 4) - (7x - 2)
expand the bracket
3x - 4 - 7x + 2
collect like terms
-4x - 2
C. (10x + 2) - (8x - 4)
expand the bracket
10x + 2 - 8x + 4
collect like terms
2x + 6
Thus, the linear expressions are subtracted to -2x + 17, -4x - 2, 2x + 6
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Reynard and his friends visited an orchard on Sunday. They picked 12.34 pounds of apples and
9.56 pounds of bluberries. How much did the fruits weigh in all?
What affect does an outlier have on a box plot?
Answer:
The outliers affect the mean, median, and other percentiles
Step-by-step explanation:
Because extreme points are highlighted in a box plot, it is simple to identify data points for further investigation. You may discover that the outliers are errors in your data or that they are unusual for another reason.
What kind of angles are 1 and 5 in the picture below?
A. vertical
B. corresponding
C. exterior
D. alternate interior
Based on the angles given of 1 and 5, the type of angles that they are is B. Corresponding angles.
What are corresponding angles?Corresponding angles are angles that form as a result of a parallel line, or parallel lines being intersected by transverse lines. As a result, the same angles are created in certain instances.
When the angles given appear in the same position on the different transverse and parallel lines, then they are corresponding.
This means that angles 1 and 5 are corresponding angles because they appear in the same position.
In conclusion, the angles are corresponding.
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dogs to cats is 2:7 there are 90 animals how many are cats
Answer: 70 cats
Step-by-step explanation:
add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.
Mercury is 5.8 x 10^7 km from the sun. Neptune is 4.5 x 10^10 km from the sun. How much further is Neptune from the sun than Mercury?
a
Multiply the distances: (5.8 x 10^7) x (4.5 x 10^10) = (5.8 x 4.5) x (10^17) = 26.1 x 10^17 = 2.61 x 10^16
b
Divide the distances: (4.5 x 10^10) / (5.8 x 10^7) = .76 x 10^3 = 7.6 x 10^2
c
Add the distances together: (5.8 x 10^7) + (4.5 x 10^10) = 10.3 x 10^17 = 1.03 x 10^18 km
d
Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7) = (4.5 x 10^10) - (.0058 x 10^10) = 44.99 x 10^10 km
Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B
What is ratio?A ratio can be defined as the comparison of two or more number indicating their sizes in relation to each other.
It also explains how any times a number contains another.
From the information given, we have;
Mercury is 5.8 x 10^7 km from the sun.Neptune is 4.5 x 10^10 km from the sunTo determine the distance Neptune is from the sum than Mercury, we divide the distance for Neptune by that of Mercury
= 4.5 x 10^10/ 5.8 x 10^7
= 776. 86
Turn into scientific notation
= 7. 76 × 10^2
Thus, Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B
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The equation F = ma states that the force F on an object is equal to the mass m of the object times the acceleration a of the object. The force is measured in a unit called "newtons*.
A single grain of medium grain rice has a mass of 2.4 x10-5 kg. If this grain of rice is dropped, the acceleration it will have due to gravity is 9.8 m/s?. Use the above equation to calculate the amount of force on the grain of rice.
Choose the answer that represents this value in scientific notation.
The amount of force on the grain of rice is 23.52 × 10⁻⁵ newtons.
The right format for scientific notation is a × 10ᵇ, where an is an integer or decimal number with an absolute value more than or equal to one and less than ten, or 1 < |a| < 10. For the scientific notation to be mathematically equivalent to the original value, b must be a power of 10.
The Force of a particle is given as:
F = ma, where m is the mass and a is the acceleration.
Now, the mass of a grain of rice is 2.4 × 10⁻⁵ kg.
The acceleration due to gravity is 9.8 m/s².
Therefore, the force on the grain of rice is :
F = ma
F = 2.4 × 10⁻⁵ kg × 9.8 m/s²
F = 23.52 × 10⁻⁵ newtons
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Simplify to a single power of 3:
Answer:
5
Step-by-step explanation:
[tex]\frac{3^8}{3^3}=3^{8-3}=3^{\boxed{5}}[/tex]
Answer:
3⁸
3³
(since they have the same numbers , you subtract → divide means subtract → law of indices)
Answer = 3⁸ - 3³
= 3⁵
You roll a dice twice. What is the probability the first roll is a 2 and the second roll is
an odd number?
The probability the first roll is a 2 and the second roll is an odd number is 1/12
When we are unsure of the outcomes or simply want to know how probable something is to happen, we talk about probabilities. A random event is mathematically represented by probability. The collection of all potential outcomes is the sample space S for a probability model.
When we roll a dice there are 6 possible outcomes S={1, 2, 3, 4, 5, 6}.
The probability of showing a 5 is
Probability of showing 2 = 1/6
And the probability of showing an odd number is
Probability of showing an odd number = 3/6
Rolls are independent of one another, so there is a chance that the first roll will show a 5 and the second roll will reveal an even number.
( Probability of showing 2) ( Probability of showing an odd number) = 1/6 × 3/6 = 1/12.
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3x^2-(4y)^2
When x=5 y=1
Answer: 59
Step-by-step explanation:
What is the solution of |X - 15 =-6
Answer:
x = 9
Step-by-step explanation:
Add 15 on both sides
[tex]x - 15 + 15 = -6 + 15[/tex]
Simplify it
[tex]-6 + 15 = 15 - 6 = 9\\x = 9[/tex]
please help me in my maths question
annie is sitting in a park her weight is 50kg she went home on cycle calculate the distance between park and her house
Answer:
1.2 miles.
Step-by-step explanation:
because her weight is similar to that of a teenaged girl, she wouldn't be able to pedal very hard, or for long periods of time- she doesn't have the stamina for a cross-country ride. Therefore, using various statistics on house location in relation to park location, we can assume that the distance is about 1.2 miles.
I know that I would use dv/dt but I’m confused on what to do #39 and 41
Starting with the volume of a cube with side length [tex]x[/tex],
[tex]V(x) = x^3[/tex]
differentiate both sides with respect to time [tex]t[/tex]. By the chain rule,
[tex]\dfrac{dV}{dt} = 3x^2 \dfrac{dx}{dt}[/tex]
We're given that [tex]\frac{dx}{dt} = 2\frac{\rm in}{\rm min}[/tex].
39. At the moment [tex]x=8\,\rm in[/tex], solve for [tex]\frac{dV}{dt}[/tex].
[tex]\dfrac{dV}{dt} = 3 (8\,\mathrm{in})^2 \left(2\dfrac{\rm in}{\rm min}\right) = 384 \dfrac{\rm in^3}{\rm min}[/tex]
41. Find [tex]x[/tex] when [tex]V = 55\,\rm in^3[/tex].
[tex]55\,\mathrm{in}^3 = x^3 \implies x = 55^{1/3} \,\rm in[/tex]
Solve for [tex]\frac{dV}{dt}[/tex].
[tex]\dfrac{dV}{dt} = 3 \left(55^{1/3} \,\mathrm{in}\right)^2 \left(2\dfrac{\rm in}{\rm min}\right) = 6\cdot55^{2/3}\dfrac{\rm in^3}{\rm min}[/tex]
NO LINKS!! Which of the following formulas defines an arithmetic sequence?
18+7(n-3)
=======================================================
Explanation:
We can rewrite the right hand side of choice C like so
18+7(n-3)
18+7(n-1-2)
18+7(n-1)+7(-2)
18+7(n-1)-14
4+7(n-1)
Which is now in the form a+d(n-1)
a = 4 = first termd = 7 = common differenceThis confirms choice C to be arithmetic. The other choices cannot be written in the format of a+d(n-1). Choices A and B are quadratic sequences while choice D is exponential.
The first few terms of choice C are: 4, 11, 18, 25, 32, ...
To get new terms, add 7 to the previous one.
-------------
Notice how if n = 5 for instance, then,
[tex]a_n = 4+7(n-1)\\\\a_5 = 4+7(5-1)\\\\a_5 = 32\\\\[/tex]
and
[tex]b_n = 18+7(n-3)\\\\b_5 = 18+7(5-3)\\\\b_5 = 32\\\\[/tex]
This confirms that [tex]a_n = b_n[/tex] when n = 5. I'll let you check other positive integer values for n.
Answer:
[tex]\textsf{c)} \quad s_n=18+7(n-3)[/tex]
Step-by-step explanation:
An arithmetic sequence has a constant difference between each term.
General formula of an arithmetic sequence
[tex]\boxed{s_n=a+(n-1)d}[/tex]
where:
sₙ is the nth term.a is the first term.d is the common difference between terms.n is the position of the term.When expanded, the formulas for answer options a and b will both contain an n² term, so we can immediately discount them since an arithmetic sequence is linear.
Similarly, we can also discount option d since this formula includes an exponential term and is therefore not linear.
Therefore, the only valid answer is option c.
To confirm, rewrite the formula for c in the general form for an arithmetic sequence:
[tex]\begin{aligned}\implies s_n&=18+7(n-3)\\s_n&=18+7n-21\\s_n&=7n-3\\s_n&=7n-7+4\\s_n&=7(n-1)+4\\s_n&=4+(n-1)7\end{aligned}[/tex]
Therefore, formula that defines an arithmetic sequence is:
[tex]\boxed{s_n=18+7(n-3)}[/tex]
5. How many ways can you make change for 55¢ using only nickels, dimes, and quarters?
(Type a whole number.)
Answer: 11
Step-by-step explanation:
If you use 0 dimes, you can use 11 nickels.
If you use 1 dime, you can use 9 nickels.
A chart develops:
0 11
1 9
2 7
3 5
4 3
5 1
So there are 6 ways to make 55 cents with nickels and dimes alone.
Now for the situation with 1 quarter:
We can have 0 dimes and 6 nickels.
We can have 1 dime and 4 nickels.
A chart follows:
0 6
1 4
2 2
3 0
So there are 4 ways to make change with nickels and dimes and 1 quarter.
Finally, if we use 2 quarters, we have 5 cents left over which must be a nickel adding 1 more way.
So there are 6 + 4 + 1 ways = 11 total ways to make 55 cents with nickels dimes and quarters.
Answer:1 quarter 1 dime 4 nickels=55¢
Step-by-step explanation:
a quarter is 25¢ a dime is 10¢ and a nickel is 5¢ so i have 25¢+10¢ thats 35¢ so i added 4 more 5¢ and i got 55
on Practice Describe each of the following events as impossible, unlikely, as likely as not, likely, or certain.
a. Gavin rolls an even number on a number cube.
Using probability we can say that the event that Gavin rolls an even number on a number cube is as likely as not.
Probability is the study of chance. The likely chance that an event can occur in a random experiment written as a fraction is called probability.
Probability of a event is calculated as the ratio of the favorable outcomes of an event to all the possible outcomes of the event.
Given as experiment: A number cube is rolled by Gavin.
Event : An even number comes up on the face of the cube.
Favorable outcomes : {2,4,6} = 3 outcomes
Total outcomes or sample space: {1,2,3,4,5,6} = 6 outcomes
Probability that an even number comes up:3/6=1/2
Probability that an even number does not come up=1-1/2=1/2
From the above probabilities we see that :
P(even)=P(not even)=1/2
Hence the Gavin rolls an even number is as likely as not likely.
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What is the difference? 19,832,216 – 9,089,689
Answer:
10742527
Step-by-step explanation:
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
1
3
4
12
Answer:
if there is lettuce, carrots, and broccoli... those are three ingredients.
Step-by-step explanation:
3, because of the amount of ingredients
Neee help fast taking a test right after
Answer:
A
Step-by-step explanation:
The rays that form the angles can extend for infinite length.
A classmate writes
(1.3 × 10³) + (3.4 x 10^5) = 4.7 x 108 on the
board. Is their equation true? Explain.
Answer:
no bc the answer to the problem would be 341300
2. The lengths of the sides of a triangle are (2a + 1) cm, (3a + 2) cm and (4a - 1) cm. (a) Find the perimeter of the triangle in terms of a. (b) If the perimeter of the triangle is 47 cm, find the value of a. 3a + 2 4a-1 2a + 1
Answer:
(a) 9a + 2
(b) a = 5
Step-by-step explanation:
Perimeter of a triangle = sum of sides
=
2a + 1 +
3a + 2 +
4a - 1
----------
9a + 2 Answer (a)
If perimeter = 47 , then 9a + 2 =47
Subtract 2 from both sides
==> 9a = 47 -2
9a = 45
a = 45/9
a = 5
A cylinder aquarium is 8 ft across. When filled, it weighs 15680 lbs. The water weighs 62.42 lb/ft3. What is the height of the aquarium
the height of the aquarium is 2.5ft
What is the height of the aquarium?The aquarium is filled with water that weights 15,680 pounds in total, and we know that the density of water is 62.42 lb/ft^3, then the volume of water is:
V = 15,680/62.42 = 251.20 ft^3
Now, this is the volume of the cylinder will be 251.20 ft^3, and if the diameter is 8ft (the radius is 4ft) then the height H will be such that the volume:
V = 2*3.14*R^2*H
Is:
251.20 ft^3 = 2*3.14*(4ft)^2*H
251.20ft = 100.48ft^2*H
251.20ft/100.48ft^2 = H = 2.5ft
So the height of the aquarium is 2.5ft
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The number on ribens ticket has a value between the values 739214 and 74000”
The statement as an inequality expression is 739214 < x < 740000
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to represent the statement as an Inequality expression?The statement is given as
"The number on Riben's ticket has a value between the values 739214 and 740000”
Let the value on the ticket be x
So, the statement can be represented as
"x has a value between the values 739214 and 740000”
"Between" means the values are exclusive
So, the statement can be represented as
739214 < x < 740000
Hence, the statement as an inequality expression is 739214 < x < 740000
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Possible question
Represent the following statement as an inequality
"The number on Riben's ticket has a value between the values 739214 and 740000”
Tree loaves of bread cost $2.43.how much do two loaves cost
Answer:
$1.62
Step-by-step explanation:
If you divide $2.43 by 3 it's 0.81 and that's the cost of one loaf of bread so multiply that by 2 and you get the cost of two loaves of bread which is $1.62
pls help i gtg in 3 mins
28
Step-by-step explanation:
Given,
No. of cameras that Gretta has : 103
No. of Cameras she misplaced : 75
1 full box contains 1 camera each
No. of full boxes that she can ship:
= No. of Cameras she has - no. of cameras she misplaced.
= 103-75
= 28
Therefore, the no. of full boxes that Gretta can ship is 28.
Use the given equation to complete the table. Use the table to list of the ordered pairs that satisfy the equation. y=5x
Answer:
x = -1
y = -5
(x,y) = (-1,-5)
x = 0
y = 0
(x,y) = (0,0)
x = 1
y = 5
(x,y) = (1,5)
Step-by-step explanation:
y = 5(-1)
y = 5*-1
y = -5
y = 5(0)
y = 5*0
y = 0
y = 5(1)
y = 5*1
y = 5
A car is traveling down the street at a constant speed described by the equation d=35t How many miles does the car travel in one hour
Answer:
im assuming D equals miles so id have to say 35
Step-by-step explanation:
V = 1/3πr²h; solve for h
Answer:
[tex]\displaystyle{h = \dfrac{3V}{\pi r^2}}[/tex]
Step-by-step explanation:
Given the equation of:
[tex]\displaystyle{V=\dfrac{1}{3}\pi r^2 h}[/tex]
The equation is also reference to volume of a cone. To solve an equation for h-term, we’ll multiply both sides by 3 first to clear all denominator:
[tex]\displaystyle{V \cdot 3 = \dfrac{1}{3}\pi r^2 h \cdot 3}\\\\\displaystyle{3V = \pi r^2 h}[/tex]
Then divide both sides by [tex]\displaystyle{\pi r^2}[/tex]:
[tex]\displaystyle{\dfrac{3V}{\pi r^2}=\dfrac{\pi r^2 h}{\pi r^2}}\\\\\displaystyle{h = \dfrac{3V}{\pi r^2}}[/tex]
Prove that the quadratic Sequence 44:52:64; 80: will always have even terms
The sequence is will always have even numbers, is hence proved.
Given, the quadratic sequence is: 44:52:64:80
Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.
The formula is: Tₙ = 2n² ₊ 2n ₊ 40
take 2 common
Tₙ = 2(n² ₊ n ₊ 20)
in other words n² ₊ n ₊ 20 = y
therefore , Tₙ = 2y
which by definition makes Tₙ an even number at all times.
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Find the exact value of tan sin
5
13
The trigonometric functions is y = 5/12.
The trigonometric functions sine, cosine, tangent, cosecant, secant, and cotangent really execute the opposite operation, which is what the inverse trigonometric functions do. We are aware that the right angle triangle is particularly amenable to trig functions. When two sides of a right triangle's measure are known, these six crucial functions are employed to determine the angle's measurement.
The convention symbol uses arc-prefixes such as arcsin(x), arccos(x), arctan(x), arccsc(x), arcsec(x), and arccot to denote the inverse trigonometric function (x).
arc sin(x) = arc tan (x/√1-x^2), x ∈ (0,1)
let,
y = tan (arc sin(5/13)) _____(1)
y = tan (arc tan ( 5/13/√1-(5/13)^2))
y = tan ( arc tan ( 5/ √13^2 - 5^2))
y = tan (arc tan (5/12))
y = 5/12
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