The expressions in which the numbers, or variables, or both, are connected by operational signs (+, - etc.) are called algebraic expressions. For example 5, 4x, a+b, x−y.
Answer:
Sometimes in math we describe an expression with a phrase. For example, the phrase
"2222 more than 5555"
can be written as the expression
2+52 + 52+52, plus, 5.
Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).
For example,
"3333 more than xxxx"
can be written as the algebraic expression
x+3x+ 3x+3x, plus, 3.
But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.
Different words for addition, subtraction, multiplication, and division
Here is a table that summarizes common words for each operation:
Operation Words Example algebraic expression
Addition plus, sum, more than, increased by x+3x + 3x+3x, plus, 3
Subtraction subtracted, minus, difference, less than, decreased by p−6p - 6p−6p, minus, 6
Multiplication times, product 8k8k8k8, k
Division divided, quotient a÷9a \div 9a÷9a, divided by, 9
For example, the word "product" tells us to use multiplication. So, the phrase
"the product of 8888 and kkkk
Let's take a look at a trickier example
Write an expression for "mmmm decreased by 7777".
Notice that the phrase "decreased by" tells us to use subtraction.
So the expression is m−7m - 7m−7m, minus, 7.
Use properties of operations to write two expressions that are equivalent
to 3/4n + (8 + 1/3z).
Answer:
(9z+96nz+4n)/12nz
Step-by-step explanation:
3/4n + 8+ 1/3z. distributive property
The required equivalent expression is [9z + 96nz + 4n] / 12nz and the property used is distributive property.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
= 3/4n + (8 + 1/3z)
Using the distributive property for the association,
= 3/4n + 8 / 1 + 1/3z
= [9z + 96nz + 4n] / 12nz
Thus, the required equivalent expression is [9z + 96nz + 4n] / 12nz, and the property used is the distributive property.
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A plane is descending into an airport. When its altitude is 3 1/2 miles, it is 250 miles from the airport. When its altitude is 1 mile, it is 75 miles from the airport. At 2 1/2 miles, it is 175 miles from the airport. Problem 6 a. If the pilot follows the same pattern, what will the plane's altitude be at 25 miles from the airport? *
Answer: 1/2 miles
Step-by-step explanation:
Given the following:
Altitude (miles) - - - - - - - - - - distance (miles)
3 1/2 - - - - - - - - - - - - - - - - - - - 250
2 1/2 - - - - - - - - - - - - - - - - - - - - 175
Calculate the plane's altitude at 25miles from the airport
7/2 = 250
5/2 = 175
(7/2 - 5/2) miles = (250 - 175)miles
1 mile = 75 miles
From the above, the plane craft 's altitude reduces by 1 mile for every 75 miles moved
Therefore, at a distance of 25 mile from the airport,
Distance moved = (250 - 25)miles = 225miles
225miles / 75 miles = 3
Therefore, the altitude will reduce by 3 miles from the initial altitude at 250 miles
Therefore,
( 3 1/2 - 3) miles = 1/2 miles
Therefore, the plane craft will have an altitude of 1/2
Karina is making accessories for the soccer team. She uses 628.86 inches of fabric on headbands for 45 players and 2 coaches. She also uses 384.30 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answer:
21.92 inches
Step-by-step explanation:
628.86 inches of fabric on headband for 45 players and 2 coaches
Total persons=45 players +2 coaches=47
Each person uses 628.86/47 inches of fabrics
=13.38 inches per person
384.30 inches for wristband for players only
Each player uses 384.30/45 inches of fabrics
=8.54 inches per person
Karina uses 13.38 inches of fabric for headband and 8.54 inches of wristband for each player
13.38+8.54
=21.92 inches of fabric for each player
Help me please I think you have to find the area
Answer:
I got B) ; 54m2
Step-by-step explanation:
the above diagram is a trapezium.
the area is gotten by; 1/2 (a+b)h
a = shortest side.
b = the longer side that is directly opposite to (a).
h = height.
1/2(3 + 9)9
1/2 by 12 by 9
to get 54
4x - 20 = -2(-3x + 22)
Answer: x = 12
Step-by-step explanation:
[tex]4x-20=-2(-3x+22)[/tex]
Begin by distributing -2
[tex]4x-20=6x-44[/tex]
Subtract 6x
[tex]4x-6x-20=-44[/tex]
Add 20
[tex]4x-6x=-44+20[/tex]
Combine like terms;
[tex]-2x=-24[/tex]
Divide by -2
[tex]x=\frac{-24}{-2}\\ x=12[/tex]
I really need help on this, please help out
Answer:
x+y= idk
Step-by-step explanation:
sorry i need the points
Answer:
15
Step-by-step explanation:
so you know that the hypotenuse for the triangle with "x"'s is 5 square root two, and because we know that the triangle is an isoceles triangle we know the other two side are equal and as a result x=5. Now for the next triangle it is 5 square root 2 on both sides and that is also an isoceles triangle and y is the hypotenuse so it 5 square root 2 times square root 2 which just becomes 2 so then it is 5 times 2 which is 10. So Y=10 and X=5 so X+Y=15.
what is t if 5/7t = 15
Answer:
21
Step-by-step explanation:
15/ 5/7 = 21
Find the first four terms in the sequence an=15+6n.
A. 18, 12, 6, 0
B. 20, 26, 32, 38
C. 21, 27, 33, 39
D. 20, 14, 8, 2
The first four terms in the sequence an=15+6n are 21, 27, 33, and 39.
The correct option is C. 21, 27, 33, 39
From the question, the equation to calculate the nth term is given which is
an=15+6n.
Now, let a1, a2, a3 and a4 denote the first, second, third and fourth terms respectively.
For the first term, a1
n = 1,
From the given equation, an=15+6n
∴ a1 = 15 + 6(1)
a1 = 15 + 6
a1 = 21
∴The first term is 21
For the second term, a2
n = 2,
From the given equation, an=15+6n
∴ a2 = 15 + 6(2)
a2 = 15 + 12
a2 = 27
∴The second term is 27
For the third term, a3
n = 3,
From the given equation, an=15+6n
∴ a3 = 15 + 6(3)
a3 = 15 + 18
a3 = 33
∴The third term is 33
For the fourth term, a4
n = 4,
From the given equation, an=15+6n
∴ a4 = 15 + 6(4)
a4 = 15 + 24
a4 = 39
∴The fourth term is 39
Hence, the first four terms in the sequence an=15+6n are 21, 27, 33, and 39.
The correct option is C. 21, 27, 33, 39
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Which transformation of ABC produces the Congruent image DEF?
Please someone answer ASAP
Answer:
Rotate 90° counterclockwise about the origin, then translate 9 units right and 1 unit down.
Step-by-step explanation:
If you use some kind of see through paper like parchment, and trace Triangle ABC and rotate it around the origin 90° counterclockwise, translate 9 units right and 1 down, it should overlap Triangle DEF
The correct sequence of transformations is -
Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.What are triangles?A triangle is a polygon with three edges and three vertices.
Given is a transformation of ΔABC to the Congruent image ΔDEF.
Congruent triangles have both the same shape and the same size.
The statement that correctly matches the transformation is -
Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.Therefore, the correct sequence of transformations is -
Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.To solve more questions on congruent triangles, visit the link below -
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Simplify the slope of AC.
Answer:
1
Step-by-step explanation:
The slope of a line can be found by dividing the rise over the run, or how much the line rises over a certain amount of sideways movement. In this case, the line AC moves from (0,0) to (a,a), meaning that it rises and moves sideways the same amount. Since a/a=1, the slope of this line is 1. Hope this helps!
Answer:
1
Step-by-step explanation:
Point A is (0, 0) and Point C is (a, a).
The "rise" from A to C is a and the "run from A to C" is also 1.
Thus, the slope of line A is m = rise / run = 1 / 1 = 1.
13 POINTS!!!
In ΔABC, c = 4.2 inches, ∠C=24° and ∠A=115°. Find the area of ΔABC, to the nearest 10th of an square inch.
Answer:
12.9 [tex]in^{2}[/tex]
Step-by-step explanation:
So to find the area of this triangle, you will need to use the equation
Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)
Here, we have ∠A, ∠C, and side c
We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.
First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,
∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°
Now that we have all three angles, we can solve for the sides
Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.
Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b
Now we can solve for the remaining side, a, using the same method.
Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a
Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒
Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]
30 points! Fraction Equasion
Answer: -3.3
Step-by-step explanation:
Answer:
-3.3
Step-by-step explanation:
-2.3 - (4.5 - 3 1/2)
Change the fraction to a decimal)
-2.3 - (4.5 - 3.5)
Parentheses first
-2.3 - (1)
Subtract
-3.3
Determine the vertex of the function f(x) = 3x2 – 6x + 13.
1. Identify the values of a and b.
a =
and b =
2. Find the x-coordinate of the vertex.
negative StartFraction b Over 2 a EndFraction =
3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.
The vertex is
.
Answer:
1.)
A=3
B=-6
2.)
1
3.)
(1,10)
Answer:
1. Identify the values of a and b.
a =
✔ 3
and b =
✔ –6
2. Find the x-coordinate of the vertex.
negative StartFraction b Over 2 a EndFraction =
✔ 1
3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.
The vertex is
✔ (1, 10)
What type of number is -4\pi−4πminus, 4, pi?
Choose all answers that apply:
(Choice A)
Whole number
(Choice B)
Integer
(Choice C)
Rational
(Choice D)
Irrational
Answer:
Choice C Rational
Step-by-step explanation:
Answer:
d irrational
Step-by-step explanation:
i did it
PLEASE HELP ASAP 10 POINTS AND ITS MULTIPLE CHOICE
Which equation represents the line that is parallel to the following?
Y=-3x-4
A. Y=3x+4
B. Y=3x+1
C. Y=-1/3x-4/3
D. Y=1/3x-4
Answer:
A. Y=3x+4
Step-by-step explanation:
Plz help! Question on picture :)
Answer:
125 students participated
Step-by-step explanation:
66% + 30% = 96%
100% - 96% = 4%
4% = 5 students
100% ÷ 4% = 25
25 × 5 = 125
125 students participated
Answer:
125 students
Step-by-step explanation:
30+66=96
100-96=4
5 students make up 4%.
100/4=25
25x5=125 students
plzzzzzzzzz help me im dewwwwwww plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz pros
Answer:
C
Step-by-step explanation:
[tex]x^2-2x-80=[/tex]
[tex](x-10)(x+8)[/tex]
You can confirm this by expanding this:
[tex](x-10)(x+8)=[/tex]
[tex]x^2-10x+8x-80=[/tex]
[tex]x^2-2x-80[/tex]
Therefore, the answer is choice C. Hope this helps!
Answer:
C
Step-by-step explanation:
x^2-2x-80
(x^2+8)+(-10x-80)
factor out the -10 for -10x-80
=x(x+8)-10(x+8)
(x+8)(x-10)
pls mark me brainliest
When we plot all the points that satisfy an equation or inequality we __ it.
Hello can someone please help me with this question will give brainliest
Answer:
X and Y have a weak, negative correlation.
Answer:
The answer is x and y have a weak negative correlation
Step-by-step explanation:
The points do not form a very straight line, so that is considered weak.
The points are arranged from higher on the left to lower on the right, indicating a negative slope.
I hope this helps! :)
Carlos bought 80 feet of wire for $17.60. He needs 30 more feet. If the unit price is the same, how much will he pay for the extra 30 feet of wire?
Answer:
Carlos bought 80 feet of wire for $17.60.
Then the price for 1 feet of wire is 17.6/80 = 0.22
=> 30 feet of wire would cost: 30 x 0.22 = 6.6
Hope this helps!
:)
Please help. I’ve been here for hours and no one wants to help. I’ll give brainliest answer :(
1. D
2. J
3. L
4. A
5. B
6. K
7. C
8. I
9. F
10. G
Radius = Center to Perimeter of Circle
Minor Arc = Arc that goes around less than 1/2 of circle
Major Arc = Arc that goes around more than 1/2 of circle
Chord = The straight line segment between 2 points on a circle
Secant = A line that passes through 2 points on a circle
Semicircle = 1/2 Circle
Tangent = Line that touches 1 point on a circle's perimeter
Central Angle = Angle with a vertex at the center of a circle
Inscribed Angle = Angle whose 3 points (vertex & 2 other points) are on the outside of the circle
Right Angle = Angle with 90 degree measure
Describe in your own words what a hyperbola is.
Answer:
A conic section that can be thought of as an inside-out ellipse
Step-by-step explanation:
Hyperbola is a two-branched open curve-conic section.
What is a hyperbola?Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.
For the given situation,
We need to describe about a hyperbola.
A hyperbola is two curves that are like infinite bows. It is a two-branched open curve, a conic section produced by the intersection of a circular cone and a plane that cuts both nappes of the cone.
The standard equation of hyperbola is
[tex][\frac{x^{2} }{a^{2} }-\frac{y^{2} }{b^{2} }]=1[/tex]
where,[tex]b^2 = a^2 (e^2 -1)[/tex]
a,b are the points on the plane and e is the eccentricity.
Hence we can conclude that hyperbola is a two-branched open curve-conic section.
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True or False: Sine is the ratio of opposite side to adjacent side in a right triangle? *
Answer:
The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.
how many days are in a year. ALSO ANSWER MY OTHER MATH QUESTION PLEASE!
Answer:
365 1/4 days
Also I haven't seen your other question
Answer:
365, 366 every 4 years. 366 on 2020, 2024, 2028, 2032, 2036, 2040 and so on
6. David leaves the house to go to school He walks 200 m west and 125 m
north. Calculate how far he is from the sting point.
Answer:
~235.8
Step-by-step explanation:
200^2 +125^2= distance traveled^2
55625= distance traveled^2
235.849528301
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8.50. The auditorium can hold at most 79 people. The drama club must make no less than $460 from ticket sales to cover the show's costs. If 53 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses.
Answer:
79 people can only be in this so we have 53 kids so 53 * 4 = 212
Step-by-step explanation:
However, there is 53 kids to find how many adults you will have to do 79 - 53 which that = 26 so 26 adults were there. so 26 * 8.50 = 221.
To fine how much money they earn you will just have to add them up so
$212 + $ 221 = $433 so they didn't really earn the amount of money they really want which is $ 460.
Thus the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses is 29 tickets.
Given,
The drama club is selling tickets to their play to raise money for the show's
expenses.
Each student ticket sells for $4 and each adult ticket sells for $8.50.
The auditorium can hold at most 79 people.
The drama club must make no less than $460 from ticket sales to cover
the show's costs.
If 53 student tickets were sold, determine the minimum number of adult
tickets that the drama club must sell in order to meet the show's expenses.
How to find the number of items from a total cost where each item cost is the same?We will divide the total cost by the cost of each item.
Example:
Cost of each item = $3
Total cost = $9
Number of items = $9 / $3 = 2
We have,
Student ticket:
Cost of each ticket = $4
Number of tickets sold = 53
Total sell from student tickets sold = 53 x $4 = $212
Adult ticket:
Cost of each ticket = $8.50
Number of adult tickets sold = M
Total sell of adult tickets sold = M x $8.50
Total number of people the auditorium can hold = 79
Minimum amount to make from ticket sales = $460
The remaining amount that needs to sale from adult tickets:
= $460 - $212
= $248
The number of adult tickets sold:
M = $248 / $8.50 = 29
Thus the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses is 29 tickets.
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Some Insight: This is a Unit Rate question. Please Answer soon as possible.
Answer: C
Step-by-step explanation:
Because it only shows a single price and we don’t know what that price is for.
All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.
Complete question:
An airplane takes off, levels off, and lands according to the diagram shown below.
All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.
Answer: 13.3km
Step-by-step explanation:
Kindly see attached picture for detailed explanation.
The question is missing data. The full question is here.
An airplane takes off, levels off and lands according to the diagram shown below. All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.
Answer: d = 13.3 km
Step-by-step explanation: The image show 2 right triangels and 1 square. To determine x and y, use Pythagorean Theorem.
To find x:
hypothenuse² = side² + side²
5² = 3² + x²
x² = 25 - 9
x = [tex]\sqrt{16}[/tex]
x = 4
To find y:
7² = 3² + y²
y² = 49 - 9
y = [tex]\sqrt{40}[/tex]
y = 6.32
Now, to determine the total horizontal distance, sum up all the parts:
d = x+y+3
d = 4 + 6.3245 + 3
d = 13.3
The horizontal distance from start to finish position is 13.3 km
HHELP HELP PLZZ PLZ SHOW WORK PLZZZZZ
Answer:
B. 43.3
Step-by-step explanation:
Find the area of one of the triangles:
[tex]\frac{1}{2} *b*h[/tex]
[tex]\frac{1}{2} *5*4.33=10.825[/tex]
10.825*4=43.3
Answer:
B.) 43.3 square centimetres
Step-by-step explanation:
The height is 4.33 cm and the side length is 5 cm. The surface area of the net would be the sum of the areas of all the triangles, which is 4 triangles. Since they are equilateral triangles, you can multiply. Use the formula for the area of a triangle:
[tex]A=\frac{1}{2} bh[/tex]
Insert the values:
[tex]A=\frac{1}{2} *4.33*5[/tex]
Simplify:
[tex]A=\frac{1*4.33*5}{2} \\\\A=10.825[/tex]
Multiply the area of one triangle by 4:
[tex]10.825*4=43.3[/tex]
The surface area of the pyramid is [tex]43.3[/tex] [tex]cm^2[/tex]
:Done
A given line has the equation 10x+2y=−2 .
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Answer:
Step-by-step explanation:
2y = -10x - 2
y = -5x - 1
y - 12 = -5(x - 0)
y - 12 = -5x + 0
y = -5x + 12