Numerical expressions contain numbers, while algebraic expressions contain variables and numbers.
Numerical Expression
"Difference" indicates that we'll be subtracting 13 from 48.
48 - 13 = 35
Algebraic Expression
Variables represent the unknown number, in this case the difference between 48 and 13. Let d represent the difference between the two.
48 - 13 = d
35 = d
Each side of a rhombus is 30 units long. One diagonal makes a 25 degree angle with a side. What is the length of each diagonal to the nearest tenth of a unit?
Answer:
25.4 units
54.4 units
Step-by-step explanation:
Given that,
length of each side of rhombus = 30 units
interior angle = 25 x 2
= 50°
other interior angle = (360-(50x2)) / 2 = 130°
Formula to use
c² = a² + b² - ab cosC
First diagonal
√(30² + 30² - 2*30*30*cos 50)
= 25.35 u
Second diagonal
√(30² +30² - (2*30*30*(cos 130)))
= √(1800-1800cos130)
= 54.37 units
PLEASE HELP
A plane intersects a cylinder parallel to the cylinder’s bases. What’s the area of the resulting cross section? Use 3.14 for π. Round your answer to the nearest tenth
Answer:
The area of the resulting cross section is [tex]78.5\ m^{2}[/tex]
Step-by-step explanation:
we know that
The resulting cross section is a circle congruent with the circle of the base of cylinder
therefore
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]\pi=3.14[/tex]
[tex]r=10/2=5\ m[/tex] -----> the radius is half the diameter
substitute the values
[tex]A=(3.14)(5)^{2}=78.5\ m^{2}[/tex]
In the solution of the equation 5-3x=2x+9,3x is added to the equation first. Which of the following should be done next?
Answer:
the correct answer is -9
Step-by-step explanation:
There are 150 more passenger cars than trucks on Highway. For every 9 passenger cars, there are 7 trucks. How many vehicles (trucks and passenger cars) are on the highway?
Answer:
The number of passenger cars is [tex]675[/tex]
The number of trucks is [tex]525[/tex]
Step-by-step explanation:
Let
x-----> the number of passenger cars
y-----> the number of trucks
we know that
[tex]x=y+150[/tex] ----> equation A
[tex]\frac{x}{y}=\frac{9}{7}[/tex]
[tex]x=\frac{9}{7}y[/tex] -----> equation B
equate equation A and equation B
[tex]\frac{9}{7}y=y+150[/tex]
[tex]\frac{9}{7}y-y=150[/tex]
[tex]\frac{2}{7}y=150[/tex]
[tex]y=525[/tex]
Find the value of x
[tex]x=525+150=675[/tex]
Find the measure of an angle with measure between 0 degrees and 360 degrees that is coterminal with an angle measuring -865 degrees.
Answer:
[tex]\large\boxed{215^o}[/tex]
Step-by-step explanation:
[tex]\text{Coterminal angle with}\ \alpha:\\\\\alpha+360^o\ and\ \alpha-360^o.\\\\\text{Firs\ step}\\\\-865^o:360^o=2\ and\ rest\ -145^o\\\\-865^o=-145^o\\\\\-145^o+360^o=215^o[/tex]
Answer:
its 280
Step-by-step explanation:
:D
(30___5) ÷ 2= 3
complete the number sentence to make it true.
You would have to divide because 30/5= 6 and 6/2= 3
Answer:
The answer is 6.
Step-by-step explanation:
Start with the parentheses. Think of what operations can work for this. Since the answer (3) is small, division makes sense.
(30 / 5) = 6
Then, divide 6 by 2. The answer is 3.
I hope this helped! :-)
Nina made 14 curtains of the same length out of 30 1 3 yards of fabric. What is the length of each curtain?
The length of each curtain is [tex]2\frac{1}{6} [/tex] yards of fabric.
Given that,
14 curtains required [tex]30\frac{1}{3} [/tex] yards of fabric.
1 curtain required is,
[tex]=30\frac{1}{3} \div14\\ \\ =\frac{91}{3}*\frac{1}{14}\\ \\ =\frac{91}{42}=\frac{13}{6}=2\frac{1}{6} [/tex]
Hence, The length of each curtain is [tex]2\frac{1}{6} [/tex] yards of fabric.
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Number 36 please for geometry
Answer:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:
3 - 1
x = -----------
2
and
-1
y = ----------
2
The center is at x = 1 and y = -1/2: (1, -1/2).
b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):
diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,
radius = (1/2)√65.
square of the radius = r² = 65/4
The general equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r². In this case, the equation is:
(x - 1)² + (y + 1/2)² = 65/4
An astronaut who weighs 126 lb on earth weighs 21 lb on the moon. How much would a person who weighs 234 lbs on the moon weigh on earth
Answer:
[tex]1,404\ lb[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{126}{21}\frac{earth}{moon} =\frac{x}{234}\frac{earth}{moon}\\ \\x=126*234/21\\ \\x=1,404\ lb[/tex]
Answer: 1,404 lb
Step-by-step explanation:
1. You have the following information given in the problem:
- The weight of the astronaut on eart is 126 lb.
- The weight of the astronaut on the moon is 21 lb.
2. Therefore, you can calculate the weight of a person on earth, knowing that that person weighs 234 lb of the moon, as following:
[tex]weight_{earth}=\frac{(234lb)(126lb)}{21lb}\\\\weight_{earth}=1,404lb[/tex]
Then, the person would weighs 1,404 lb on earth.
Classwork backside T
Answer:
17) Length of arc QPT = 20.9 inches
18) Length of arc QR = 12.6 feet
19) Length of arc PQR = 39.3 meters
20) x = 161°
21) x = 123°
22) x = 24 units
23) EB = 4 units
24) EB = 14 units
Step-by-step explanation:
∵ The length of any arc = Ф/360 × 2πr
where Ф is the central angle subtended by this arc
17) ∵ m∠RZQ = 60° ⇒ central angle
∵ m∠QZP = 90° ⇒ centeral angle
∵ m∠RZT = 180° ⇒ Z ∈ TR
∴ m∠TZP = 180 - 90 - 60 = 30°
∴ m∠QZT = 90 + 30 = 120° ⇒ central angle
∵ ∠QZT subtended by arc QPT
∵ m∠QZT = 120 , r = 10 inches
∴ Length arc QPT = 120/360 × 2π × 10 = 20.9 inches
18) ∵ m∠QZR = 60° ⇒ central angle subtended by arc QR
∵ r = 12 feet
∴ The length of arc QR = 60/360 × 2π × 12 = 12.6 feet
19) ∵ m∠PZR = 60° + 90° = 150°⇒ central angle subtended
by arc PQR
∵ r = 15 meters
∴ The length of arc PQR = 150/360 × 2π × 15 = 39.3 meters
20) ∵ SU = ST
∴ Measure of arc SU = measure of arc ST
∵ The measure of the circle is 360°
∵ Measure of arc UT = 38°
∴ x = (360 - 38) ÷ 2 = 161°
21) ∵ AB = AC
∴ Measure of arc AB = measure of arc AC
∵ The measure of the circle is 360°
∵ Measure of arc BC = 114°
∴ x = (360 - 114) ÷ 2 = 123°
22) ∵ The two arcs are equal
∴ Their chords are equal in length
∴ 2x - 12 = 36 ⇒ 2x = 36 + 12 ⇒ 2x = 48
∴ x = 24
23) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 20 , CD = 24
∴ CE = 24/2 = 12
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 20 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(20² - 12²) = 16
∵ AB = 20 ⇒ radius
∴ EB = 20 - 16 = 4
24) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 35 , CD = 56
∴ CE = 56/2 = 28
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 35 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(35² - 28²) = 21
∵ AB = 35 ⇒ radius
∴ EB = 35 - 21 = 14
What is the answer to this
Answer:
The answer I would choose is C
Hope this helped :)
Answer:
B
Step-by-step explanation:
Multiplying f(x) by g(x)
= (2x² + x - 3)(x + 2)
Each term in the first factor is multiplied by each term in the second factor, that is
x(2x² + x - 3) + 2(2x² + x - 3) ← distribute both parenthesis
= 2x³ + x² - 3x + 4x² + 2x - 6 ← collect like terms
= 2x³ + 5x² - x - 6 → B
what are the outputs of -1 and 1 in g(x)
Answer:
g(-1) = -0.571
g(1) = -7
Step-by-step explanation:
To easily solve this problem, we can use a graphing tool to plot both f(x) and g(x) and
f(x) = 2*(3.5)^x
g(x) = -2*(3.5)^x
g(-1) = -2*(3.5)^(-1) = -0.571
g(1) = -2*(3.5)^(1) = -7
Jellybeans cost $0.80 per pound. Howard buys 412 pounds of jellybeans for himself and 1 pound for his friend. What is the total cost of the jellybeans Howard buys?
(A.) $4.00
(B.) $4.40
(C.) $4.50
(D.) $4.60
412 pounds for him + 1 pound for his friend = 413 total pounds x $0.80 per pound = $330.40
Sorry, I don’t see this as an answer choice.
Answer:
I am assuming you meant to say '4' instead of '412'. In which case the answer is A.
Step-by-step explanation:
4 + 1 x .80 is 4.00 even. Good luck in your endeavors!
Dwight deposits $150 into his new savings account. The account earns 5% interest compounded annually.
Write a function to model the amount in his account, A, over t years, assuming he makes no other deposits or withdrawals. Write your function in the form A=P(1 +r)^t
2Points
Use the math editor to write your function.
Answer the question in complete sentences.
Hint:
P is the initial amount in the account.
Change the interest rate from a percent to a decimal by moving the decimal 2 places to the left and substitute this number in for r.
Answer:
[tex]A=\$150(1.05)^{t}[/tex]
Step-by-step explanation:
we know that
The compound interest formula for this problem is equal to
[tex]A=P(1+r)^{t}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods in years
in this problem we have
[tex]P=\$150\\ r=5\%=0.05[/tex]
substitute in the formula above
[tex]A=\$150(1+0.05)^{t}[/tex]
[tex]A=\$150(1.05)^{t}[/tex]
90 centimeters greater than 9 millimeters
Answer:
909 mm
Step-by-step explanation:
There are 10 mm in a cm
90 x 10 = 900
900 + 9 = 909 mm
(Unless you're asking if this is true/false; if so, it is true)
Who's good at Algebra? I have a few Questions about somethings on my home work.....
Answer:
I will try my best to answer
Answer: who trynna hlp me take a bath nooo kap
Step-by-step explanation:
what is the value of 5 1/2 + 7 3/4 - (-4)
your answer is 17 1/4 or 17.25 I think
Can you list all the prime numbers (in base 7) up to 100?
Hint: There are only 21 of them.
2,3,5,11,13,23,25,31,35,41,43,53,55,61,65,71,73,83,85,91,95
Answer:
Step-by-step explanation:
Prime numbers are neat.
Here they are:
2,3,5,11,13,23,25,31,35,41,43,53,55,61,65,71,73,83,85,91,95
Best,
jrodt
Help Plz Will mark brainliest
Answer:
Step-by-step explanation:
Expression: [tex]x^3-xy+y^2-9[/tex]
7. How could y^2 be rewritten?
y^2 can be rewritten as y*y
8. What does the term xy mean?
The term xy mean that the value of x is multiplied with the value of y or we can sy that we are taking product of x and y.
9. Can you combine all the Xs and Ys in this expression?
No, because the term xy has one x term and one y term and due to this we cannot combine all the Xs and Ys in this expression. We can only combine like terms that have same variables.
Which algebraic property is used to rewite (3 + m) + y as 3 + (m + y)?
Distributive property
Commutative property
Associative property of multiplication
Associative property of addition
(._.)✌ please help me my dudes
Answer:
Associative property of addition
ur welcome "my dude" :o)
Answer:
The associative property of addition.
Step-by-step explanation:
The associative property basically says that it doesn't matter if you add y to 3 + m or you add m + y to 3; you'll come out with the same answer in both cases. Put another way, it tells us we can group terms however we want, and it won't effect the outcome. For another example, (3 + 5) + 4 = 3 + (5 + 4) -- it doesn't matter whether we start with 3 + 5 or 5 + 4. The associative property is why we're allowed to write addition without parenthesis.
Please help ASAP!!!!!
Answer:
The Bottom Right Corner
Step-by-step explanation:
The number line represents 1 whole mile and is split in to 6 sections. So if Ms. P drives 2/6s she would drive 2 sections in that line
7. T or F Congruent means having the same measure
Answer:
True
Step-by-step explanation:
Congruent means that two (or more) side lengths for line segments have "the same measurements.
~
help please asap!!!!!!!!!!!!!!
Answer:
2w-4
Step-by-step explanation:
That is your answer. The word twice means 2 and decreased means minus. So your answer is 2w-4.
I need help!!! Brainliest for anyone who answers correctly on both!!!
Answer:
The first answer: 390m The second answer: x = 7; m<1 = 17; m<2 = 73
Step-by-step explanation:
First problem:
It's asking for the distance he walks by walking around a rectangular box which is the perimeter.
Two of the sides will have length 115m and two will have length 80m. So this perimeter is 115 + 115 + 80 + 80 = 390m.
Second problem:
Complementary angles add to 90 degrees. So m<1 and m<2 added together will equal 90
-4x +45 + 7x + 24 = 90
3x + 69 = 90
3x = 21
x= 7.
Plug back x into both m<1 and m<2 to find the measure of the angles.
m<1 = -4(7) + 45 = 45-28 = 17
m<2 = 7(7) + 24 = 49 + 24 = 73
This pair of figures is similar. Find the missing
Answer: x = 63
Step-by-step explanation:
since they are proportional to each other,
36/4 = 9
90/10 = 9
126/14 = 9
7*9 = 63
Answer:
x = 63
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{90}{10}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )
10x = 630 ( divide both sides by 10 )
x = 63
the two-way table shows the number of students in a school who like painting and/or dance.
Like Painting
Do Not Like Painting
Total
Like Dance
28
?
51
Do Not Like Dance
17
18
35
Total
45
41
86
What is the missing number in the table?
16
23
33
79
The total for liking and not liking painting is 51.
28 like painting, so to find the missing number subtract 28 from 51.
The missing number is 23
The missing number in the table is 23, option B is correct.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given table is below
Like Dance 28 ? 51
Do Not Like Dance 17 18 35
Total 45 41 86
We have to find the number of people who like dance when 18 donot like dance and total is 41.
We calculate this by removing 18 from 41 which gives the missing number x
x=41-18
=23
Hence, the missing number in the table is 23, option B is correct.
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Name the following in the figure shown below the base or bases, the part labeled PQ and the figure itself
A circle, radius, sphere
B circle, diameter, cylinder
C none, radius, cylinder
D none, diameter, sphere
Answer: The answer is B because
The Circumference of a circle or a sphere is equal to 6.2832 times the Radius. The Circumference of a circle or a sphere is equal to 3.1416 times the diameter.
a poster is 8in by 6in what are the dimensions if the poster is enlarged by a factor of 7/2
Answer:
[tex]21\ in[/tex] by [tex]63\ in[/tex]
Step-by-step explanation:
we know that
To find the dimensions of the enlarged poster, multiply the original dimensions of the poster by the scale factor
so
[tex]18(\frac{7}{2})=63\ in[/tex]
[tex]6(\frac{7}{2})=21\ in[/tex]
therefore
The dimensions of the enlarged poster are [tex]21\ in[/tex] by [tex]63\ in[/tex]
A fruit punch contains 20% fruit juice is combined with 100% fruit juice how many ounces of each should be used to make 40oz of a mixture that is 60% fruit juice
Final answer:
To make a 40-ounce mixture that is 60% fruit juice, equal amounts (20 ounces each) of 20% fruit juice and 100% fruit juice should be used.
Explanation:
Calculating the Fruit Juice Mixture
To solve this problem, we'll use a system of equations. Let's assume that the amount of 20% fruit juice used is x ounces, and the amount of 100% fruit juice used is y ounces. We are trying to make 40 ounces of a mixture that is 60% fruit juice.
First, the total amount of the mixture should be 40 ounces:
x + y = 40
Second, the total percentage of fruit juice in the mixture should be 60%:
0.20x + 1.00y = 0.60 * 40
Now, let's solve these equations step-by-step:
From the first equation, we can say y = 40 - x.
Substitute y in the second equation: 0.20x + 1.00(40 - x) = 24.
Simplify: 0.20x + 40 - x = 24.
Combine like terms: 40 - 0.80x = 24.
Subtract 40 from both sides: -0.80x = -16.
Divide both sides by -0.80 to find x: x = 20.
Substitute x back into y = 40 - x to find y: y = 20.
Therefore, to achieve a 60% fruit juice mixture, 20 ounces of the 20% fruit juice and 20 ounces of the 100% fruit juice should be combined.
Which are simplified forms of the expression cot^2θcos2θ. Select two of the following there must be two selections!
Answer:
Second Option and Fourth Option
Step-by-step explanation:
[tex]cot ^ 2(\theta) cos(2\theta)[/tex]
We know that:
[tex]cot(\theta) = \frac{1}{tan(\theta)}[/tex]
Then:
[tex]cot^2(\theta)cos(2\theta) = cos(2\theta)\frac{1}{tan^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =\frac{cos(2\theta)}{tan^2(\theta)}[/tex]
Also:
For the sum of angles identity:
[tex]cos(2\theta) = cos(\theta + \theta)\\\\cos(\theta + \theta) = cos(\theta)cos(\theta) - sin(\theta)sin(\theta)\\\\cos(2\theta) = cos^2(\theta) - sin^2(\theta)\\\\cos(2\theta) = (1-sin^2(\theta)) - sin^2(\theta)\\\\cos(2\theta) = 1-2sin^2(\theta)[/tex]
Then:
[tex]cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)}{sin^2(\theta)}[1-2sin^2(\theta)]\\\\cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)[1-2sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2\frac{cos^2(\theta)[sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2cos^2(\theta)[/tex]