We have to evaluate the expressions.
We have to solve each operation in the correct order: first the operations within the parenthesis, and within them, first the powers, then the multiplication/quotients and lastly the adds/subtractions. Then, we apply the same sequence for the terms outside the parenthesis.
a)
[tex]\begin{gathered} 9^2\cdot2-4^2 \\ 81\cdot2-16 \\ 162-16 \\ 146 \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{2\cdot(10-2)}{2^2} \\ \frac{2\cdot8}{2^2} \\ \frac{2\cdot8}{4} \\ \frac{16}{4} \\ \\ 4 \end{gathered}[/tex]c)
[tex]\begin{gathered} 30-(3^2-8) \\ 30-(9-8) \\ 30-1 \\ 29 \end{gathered}[/tex]Answer: a) 146, b) 4 c) 29
what is the length of the course from point A to point W?
The length of the course is 480 m.
Length is used to measure distance. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the meter.
Nevertheless, depending on the item's position, this is not always the case. A fixed object's length is commonly understood to be its greatest extended dimension.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.From the given figure we can infer that W is the mid-point of AB. Therefore we know that AW = WB
Now the distance is given by
5x -110 = 2x +100
or, 5x - 2x = 100 + 110
or, 3x = 210
or, x = 70
Therefore total length = 5x -110 + 2x +100 = 7x - 10 = 490 - 10 = 480 m
Therefore the length is 480 m.
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There are 15 year 12 pupils in a football club, out of a total of 46 pupils. write this proportion as a percentage. give your answer correct to 1 decimal place when appropriate.
In the football club, the percentage of 15-year 12 pupils out of 46 pupils is equal to 30%.
The proportion can be found by dividing the number of 15-year pupils by the total number of pupils. Therefore;
number of 15-year pupils / total number of pupils = 12 / 46 = 0.260
Rounding it to one decimal;
0.260 = 0.3
Percentage in mathematics can be defined as a number or a rate in each hundred. A decimal value can be converted into a percentage by multiplying the decimal value by 100.
0.3 × 100 = 30%
Therefore, the proportion of the 15-year pupils in the football club is 12/46 and this proportion can be written in percentage as 30%.
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Find the distance between the two points in simplest radical form.
The distance between the two points is 13 unit.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Given that,
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 unit
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
Therefore, distance between the two points is 13 unit.
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how would i write The product of 2 and the cube of a number. if a number is x
the Algebraic representation of the expression "product of 2 and the cube of a number" is 2x³
How to write Algebraic expression?Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
The product of 2 and the cube of a number
The unknown number = xProduct means MultiplicationSo,
product of 2 and the cube of a number
= 2 × x³
= 2x³
For instance, if x = 2
2x³
= 2×(2)³
= 2 × (2 × 2 × 2)
= 2 × 8
= 16
Therefore, the expression "product of 2 and the cube of a number" can be written as 2x³
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f(t) = -3t+4
f( )=19
Answer:
-5
Step-by-step explanation:
[tex]-3t+4=19 \\ \\ -3t=15 \\ \\ t=-5[/tex]
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.25 per slice of pizza. Justin purchased a membership to this pizza shop. How much would Justin have to pay the pizza shop if he bought 12 slices of pizza this month? What would be the monthly cost for x slices of pizza?
PLEASE HURRY!
The amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza this month is $15.
The monthly cost for x slices of pizza is $25 + $1.5x
What is the total cost?In order to determine the amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza can be determined by multiplying the cost per pizza by the number of pizzas sold.
Multiplication is the operation used in mathematics that is used to calculate the product of two or more numbers. The sign that is used to represent multiplication is x.
Cost of 12 slices of pizza = discounted price x number of slices bought
$1.25 x 12 = $15
The monthly cost is the sum of the membership fee and the total cost of the pizzas bought
Monthly cost = monthly membership fee + cost of the slices
Monthly cost = monthly membership fee + (discounted price x number of slices bought)
$25 + (1.25 x x)
$25 + $1.25x
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What is the equation of the line that passes through (7,4) and (4, -2)?
Oy=2x-10
Oy=-2x-10
Oy=2x+18
Oy=-2x+18
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -3 }\implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{7}) \\\\\\ y-4=2x-14\implies {\Large \begin{array}{llll} y=2x-10 \end{array}}[/tex]
A group of friends decided to buy bulk chocolate from a candy store. If some friends
each want 1/7 of a kilogram of chocolate of the 10 kilograms of chocolate
purchased, then how many people can get a share of chocolate?
Answer:
Your answer is [tex]70[/tex].
Step-by-step explanation:
[tex]10[/tex] ÷ [tex]\frac{1}{7}[/tex] [tex]= 70[/tex]
Solve for x in the equation below 3(x-5)=5x-(3-x)
Answer:
x = -4
Step-by-step explanation:
3(x-5) becomes 3x-15
5x-(3-x) becomes 6x-3
3x - 15 = 6x - 3
+ 15 + 15
3x = 6x + 12
-6x -6x
-3x = 12
divide -3 on both sides
X = - 4
Answer:
x = -4.
Step-by-step explanation:
3(x-5) = 5x-(3-x)
3x - 15 = 5x - 3 + x
3x - 5x - x = -3 + 15
-3x = 12
x = -4.
in a recent year, 389 of the 281,421,906 people in the united states were struck by lightning. estimate the probability that a randomly selected person in the united states will be struck by lightning this year.
Answer:
0.000001382 if you divide
steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 8 am, and walks steadily at 2 miles per hour. elsie sleeps in, and starts walking west at 2.5 miles per hour starting at 11 am.
After 2.57 hours, the distance between Steve and Elsie will be 25 miles.
What exactly is the distance?Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending point. Use the formula d = st, or distance equals speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable.So, let t (hours) represent the amount of time Elsie needs to travel before they are 25 miles apart.
Steve takes longer because he is 2 hours earlier, so his time is t + 2.
Steve travels x[tex]s_s=2(t+2)[/tex] miles to the north.Elsie travels a distance [tex]s_c=2.5 t[/tex] to the west.So, according to the formula the distance between Steve and Elsie will be:
[tex]\sqrt{s_s^2+s_c^2}=\sqrt{(2(t+2))^2+(2.5 t)^2}=25[/tex]Solve for t as follows:
[tex]\begin{aligned}&(2(t+2))^2+(2.5 t)^2=25^2=625 \\&4(t+2)^2+6.25 t^2=625 \\&4\left(t^2+4 t+4\right)+6.25 t^2=625 \\&10.25 t^2+16 t-609=0 \\&t=\frac{-b \pm \sqrt{t^2-4 a x}}{2 a} \\&t=\frac{-16 \pm \sqrt{(16)^2-4 *(10.25) *(-109)}}{2 *(10.25)} \\&t=\frac{-16 \pm 68.74}{20.5}\end{aligned}[/tex]
So, t = 2.57 or t = -4.13.
As we know that time can only be positive so it t = 2.57.Therefore, after 2.57 hours, the distance between Steve and Elsie will be 25 miles.
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The correct question is given below:
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 8 AM, and walks steadily at 2 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 10 AM. When will the distance between them be 25 miles?
If a segment has one endpoint at (0,0) and a midpoint at (4,-6) where is the other endpoint?
The coordinates of the second end point of the line is (8, -12).
What is defined as the mid point of coordinate?For the points on the coordinate axes, the midpoint formula is defined. Let the endpoints of the a line segment be (x)1, (y)1, and (x)2, (y)2. The midpoint is equal to one-half of the sum of the two points' x-coordinates and half of a sum of the two points' y-coordinates.For the given question;
The end point of the line segment is (0,0).
The mid-point of the line segment is at (4,-6).
Thus,
(x₁, y₁) = (0,0)
(x₂, y₂) = ?
(xₐ, yₐ) = (4,-6)
Thus, the formula for finding the mid point is;
xₐ = (x₁ + x₂)/2
Put the values;
4 = (0 + x₂)/2
On simplification;
x₂ = 8.
For y coordinate;
Thus, the formula for finding the mid point is;
yₐ = (y₁ + y₂)/2
Put the values;
-6 = (0 + y₂)/2
On simplification;
x₂ = -12
Thus, the coordinates of the second end point of the line is (8, -12).
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The sizes of four cell phone displays are 5.625 inches, 5 1/2 inches, 6 1/4 inches, and 5.125 inches. How much longer is the longest display than the shortest display? a) 3/4 in, b) 1 in, c) 1.125 in, d) 1 1/4 in
Longest display is 1.125 inches longer than the shortest display.
What is fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Given Data
Size of cell phones
5.625 inches
5[tex]\frac{1}{2}[/tex] inches = [tex]\frac{11}{2}[/tex] inches
5.5 inches
6[tex]\frac{1}{4}[/tex] inches = [tex]\frac{25}{4}[/tex] inches
6.25 inches
5.125 inches
Longest display = 6.25 inches
Shortest display = 5.125 inches
Difference = longest display - shortest display
Difference = 6.25 - 5.125
Difference = 1.125
Longest display is 1.125 inches longer than the shortest display.
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there are 6 quarters in a jar. jill adds 2 quarters to the jar every day. which linear equation represents the total amount of quarters in the jar after x days? responses 6y
Divide negative 2 and 3 over 4 ÷ negative 5 and 1 over 7.
negative 77 over 144
negative 221 over 28
221 over 28
77 over 144
The fractions are divided to give 77/144. Option A
What is a fraction?A fraction can simply be defined as the part of a whole set or element.
The types of fractions includes;
Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractionsExamples of simple fractions are: 1/2 , 1/4
Examples of proper fractions are; 2/3, 5/6
Examples of improper fractions are; 5/3, 9/7
Examples of mixed fractions are; 2 1/2, 3 1/4
Given the expression as;
2 3/4 ÷ 5 1/7
Turn into improper fractions
11/4 ÷ 36/7
Take the inverse of the divisor
11/4 × 7/36
Multiply the numerators and denominators
77/144
Thus, the value is 77/144
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Answer: #1 / A
Step-by-step explanation:
Select the correct answer.
The sine of the angle based on the information about the cosine is D. ✓91 / 10.
How to illustrate the information?It should be noted that cos is calculated as:
= adjacent / hypothenuse.
This was given as 3/10.
It should be noted that sine = Opposite / Hypothenuse
The opposite will be:
Opp² + Adj² = Hyp²
Opp² + 3² = 10²
Opp² + 9 = 100
Opp² = 100 - 9
Opp² = 91
Opp = ✓91
Therefore, the sine of the angle will be ✓91 / 10
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PLS HELP WILL GIVE 20 POINTS AND BRAINLIEST!! ASAP!!!!
Answer:
7/49
Step-by-step explanation:
there is a sequence so you just need to follow it
so 11, 10, 9, 8 then the next one will be 7
HELP ME PLEASE I GOT A 67 IN MATH
Answer:
0.5
Step-by-step explanation:
(-6,-5) ( 6,1) The slope is the change in y over the change in x.
([tex]x_{1}[/tex],[tex]y_{1}[/tex]) ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) Will will use this for the points above and then put in the numbers
[tex]\frac{y_{2 - y_{1} } }{x_{2 - x_{1} } }[/tex]
[tex]\frac{1 - -5}{6 - -6}[/tex]
[tex]\frac{1+ 5}{6+6}[/tex]
[tex]\frac{6}{12}[/tex]
[tex]\frac{1}{2}[/tex] = 0.5 as a decimal
If you start at any point on the line and go up one unit and 2 units of the right, you will end up on the line again. This pattern repeats over and over and over.
A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3).
What is the area of rectangle ABCD?
Answer: 80un^2
Step-by-step explanation:
The length of AB is 10
The length of BC is 8
The length of CD is 10
The length of DA is 8
10 x 8 = 80 and there are two pairs of 8 and ten which makes it 80un^2
What is 183 divided by 13
Answer:
14.077 appr. 14.1
Step-by-step explanation:
183/13=
18÷13=1 remainder 5
53÷13=4 remainder 1
therefore the answer is 14.1
PLEASE MARK BRAINLEST
A group of friends wants to go to the amusement park. They have no more than $710
to spend on parking and admission. Parking is $9, and tickets cost $10.75 per person,
including tax. Which inequality can be used to determine p, the maximum number of
people who can go to the amusement park?
The inequality for maximum number of people is 710 ≥ 9 + 10.75p
The correct option is (d)
Given,
Total money spend on amusement park is $710
Parking charge is $9.
and, tickets cost $10.75 per person
To find the inequality for maximum number of people (p) who can go to the amusement park?
Now, According to the question:
Costs of people tickets = 10.75 p
Total Cost will be = 9 + 10.75p
The inequality will be
9 + 10.75p ≤ 710
=> 710 ≥ 9 + 10.75p
Hence, The inequality for maximum number of people is 710 ≥ 9 + 10.75p .The correct option is (d).
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write a new function that is a horizontal stretch of f(x)=(x+2)^3+5
New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]
What is horizontal stretch ?The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).
F(x)=[tex](x+2)^{3} + 5[/tex]
F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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Julian is making potato salad for his family picnic. At the market, he spends $5.58 on red potatoes and $4.68 on yellow potatoes. If each type of potato cost $0.90 per pound, how many total pounds of potatoes does he buy
Answer:
11.4 pounds
Step-by-step explanation:
I need help. Answer first and get brainest.
Answer:
1,312.5
Step-by-step explanation:
6.25x10=62.5
3500x62.5%=2,187.5
3500-2,187.5=1,312.5
I hope this is correct :-|
we have
3500 = Pe^(0.0625) x(10)
3500= Pe^(0.625)
P = 3500 / e^(0.625) = 1873
thus 1873 Macaws remaining in 10 years
If an airplane rises at a rate of 42 meters per second, how high will it be flying after 3 minutes?
Answer:
7560 meters
Step-by-step explanation:
42 meters a second -> 2520 meters a minute -> 7560 meters for 3 minutes
Answer:
The airplane will be 7560 meters after three minutes of flying.
Step-by-step explanation:
one minute= sixty seconds
42*1800=7560
3*60=1800
Not sure if I did the math right but I'm positive I got the right answer.
– 0.3+ – 0.8×0.5–0.1 using PEMDAS
Answer:
-0.8
Step-by-step explanation:
=0.3-0.8*0.5-0.1
= -0.3-0.4-0.1
= -0.7-0.1
= -0.8
What value of b will cause the system to have an infinite number of solutions?
y = 6x – b
–3x + StartFraction one-half EndFractiony = –3
b =
2
4
6
8
The value of b that will cause the system to have an infinite number of solutions is 6.
System of equationGiven the following system of equation expressed as:
y = 6x – b
-3x + 1/2 y = -3
Rewrite equation 2:
1/2 y = 3x - 3
y = 6x - 6
Equate the right hand side of both equations
6x - b = 6x - 6
For the equation to have infinite number of solutions, the expression on both sides must be the same.
Comparing both sides;
-b = -6
b = 6
This gives the required value of b
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Simplify.
3c + 6d + 3d
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3c + 6d + 3d}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (3c) + (6d + 3d)}\\\mathsf{= 3c + 6d + 3d}\\\mathsf{= 3c + 9d}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{3c + 9d}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Help fast. I need help with this one as fast as you can. I mark brainliest
The true statement about the values x = - 2 and y = -0.5 is that: D. they are the only values that make both equations true.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.
This ultimately implies that, a point of intersection simply represents the ordered pairs (values) that make a system of equations true.
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Complete Question:
Lan graphs these equations and finds that the lines intersect at a single point,
(-2,-0.5).
Equation A: 4y - 3x = 4
Equation B: -2x + 8y = 8
Which statement is true about the values x = -2 and y = -0.5?
A. They satisfy equation A but not equation B.
B. They satisfy equation B but not equation A.
C. They show that the equations represent the same line.
D. They are the only values that make both equations true.
Find the slope of the line that passes through (1, 9) and (8, 1).
Answer:
Slope = -1
Step-by-step explanation:
m = second y - first y / second x - first x
second y = 1
first y = 9
second x = 9
first x = 1
1 - 9 = -8
9 - 8 = 8
-8/8 = -1
Find the slope of a line.
We mark the points: (x₁ = 1, y₁=9) and (x₂ = 8, y₂ = 1)
X₁ = 1X₂ = 8Y₁ = 9Y₂ = 1We have that the formula is:
[tex]\boldsymbol{\sf{m=\dfrac{Y_{2}-Y_{1} }{X_{2}-X_{1}} }}[/tex]
Now we apply the formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{1-9}{8-1} =\dfrac{-8}{7} }}[/tex]
[tex]\boldsymbol{\sf{m=\dfrac{-8}{7} }}[/tex]
The slope of the line through (1, 9) and (8, 1) is -8/7.