Answer:
[tex] \sqrt{4} = 2[/tex]
Step by step explaination:
[tex] \sqrt{4} \\ = \sqrt{ {2}^{2} } \\ = 2[/tex]
[tex]\sf\therefore \sqrt{4}=? [/tex]
[tex]\sf\implies \sqrt{ 2 \times2} [/tex]
[tex]\sf\implies \sqrt{2^2} [/tex]
[tex]\sf\implies 2[/tex]
[tex]\large{\boxed{\bf{ \implies \:2\:}}}[/tex]
______________Ralph Chase plans to sell a piece of property for $170000. He wants the money to be paid off in two waysa short-term note at 12% interest and a long-term note at 9% interest. Find the amount of each note if the total annual interest paid is $18000.
Answer: $90,000 at 12%
and $80,000 at 9%
Step-by-step explanation:
given data:
cost of property = $170,000.
short term = 12%.
long term = 9%.
total interest paid = $18,000.
Step 1
= 0.12x + 0.09 (170,000-x) = 18,000
collect like terms
= 0.12x + 15300 – 0.09x = 18,000
divide both Sides by 0.03
0.03x = 2700
x = $90,000 at 12%
and $80,000 at 9%
2) Subtract –3x2 + 5x – 9 from 2x2 + 3(x2 – 6).
8x2 – 5x - 9
Eliminate
A)
ling
2x2 + 5x -9
B)
C) 5x2 + 5x – 27
D) 6x2 + 5x – 27
Answer:
[tex]2x^{2}[/tex]+5x+9
Step-by-step explanation:
The difference of the given expression is 8x²-5x-9.
The given expressions are -3x²+5x-9 and 2x²+3(x²-6).
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Now, subtract -3x²+5x-9 from 2x²+3(x²-6)
2x²+3(x²-6)-(-3x²+5x-9)
= 2x²+3x²-18+3x²-5x+9
= 8x²-5x-9
Hence, the difference of the given expression is 8x²-5x-9.
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A batch of cookies calls for 1/4 cup of flour. You want to make 2/3 of a batch. How much flour will dimitra need to make 2 1/4. Batches of cookies
Answer: 1/4
Step-by-step explanation: You will need 1/4 of cup flour to make 1/2 of a bath of cookies.
please help, thank you!!
Answer:
D (4)
Step-by-step explanation:
So we have the function:
[tex]f(t)=3t^2+5t+6[/tex]
And we want to find f(-3).
To do so, substitute -3 for x. Thus:
[tex]f(-3)=3(-3)^2+5(-3)+6[/tex]
Square:
[tex]f(-3)=3(9)+5(-3)+6[/tex]
Multiply:
[tex]f(-3)=27-15+6[/tex]
Add:
[tex]f(-3)=18[/tex]
So, our answer is D (4)
5 Adoncia makes a scale drawing of the front of
the Lincoln Memorial. She uses a scale of 15 ft
in the monument to 1 in. in the drawing. The
front of the monument is about 80 ft high and
200 ft long. Will Adoncia's drawing fit on an
sin.-by-11 in. sheet of paper? Explain.
8
Answer:
Since the length of the drawing is 200 ft. and equivalent to 13.33 in. with a scale of 15 ft to 1 in. and the length of the paper is 11 in., Adoncia's drawing will not fit on the sheet of paper
Step-by-step explanation:
The given parameters are;
The scale of the drawing is 15 ft = 1 in.
The actual dimensions of the monument;
Height = 80 ft.
Length = 200 ft.
Therefore, we have;
The required dimension of the paper height = 80/15 = 16/3 = 5.33 in.
The required dimension of the paper length = 200/15 = 40/3 = 13.33 in.
The given paper dimension by 11 in. which is of a dimension of that of a standard letter paper size of 8.5 in. by 11 in.
Drawing length, 13.33 in. > Paper length > 11 in.
Adoncia's drawing will not fit on the sheet of paper.
You watch a football game. The team you cheer for loses 8 yards on four plays in a row. Which expression shows the total loss in yards?
Answer:
Lose 8 yards on four plays in a row
Answer:
-8x4
Step-by-step explanation:
solve the equation 9=8(n+4)-7
Answer:
n= -2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
10 to the third power divided by 10 to the third power
For a parade, attendance was rounded as 10,000 to the nearest hundred. What was the
greatest and least number of people that could have attended the parade? Explain your
answer.
Answer: (9,950 to 10,049)
Step-by-step explanation:
The nearest hundred is the third digit (counting from the right).
When we round up/down, we must look at the previous digit (the second in this case).
If the digit is larger than 5, we round up
if the digit is 5 or less, we round down.
Then if the rounded number is 10,000.
The rounded down version will be:
10,049
(49 < 50, then we should round down to 10,000)
The rounded up version will be:
9,950.
this number would be the smallest number that can be rounded up to 10,000.
Then the possible range is:
(9,950 to 10,049)
please help me to prove this..
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
[tex]\sin x+\sin y=2\sin\bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=-2\sin\bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin \theta-\sin 3\theta+\sin 5\theta -\sin 7\theta}{\cos \theta -\cos 3\theta -\cos 5\theta +\cos 7\theta}[/tex]
[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{(\sin 5\theta+\sin \theta)-(\sin 7\theta +\sin 3\theta)}{-(\cos 5\theta -\cos \theta) +(\cos 7\theta -\cos 3\theta)}[/tex]
[tex]\text{Sum to Product:}\quad \dfrac{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\cos \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\cos \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\sin \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\sin \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 3\theta \cos 2\theta-2\sin 5\theta \cos 2\theta}{2\sin 3\theta \sin 2\theta-2\sin 5\theta \cos 2\theta}[/tex]
[tex]\text{Factor:}\qquad \qquad \dfrac{\cos 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}{\sin 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 2\theta}{\sin 2\theta}\\\\.\qquad \qquad \qquad =\cot 2\theta[/tex]
LHS = RHS: cot 2Ф = cot 2Ф [tex]\checkmark[/tex]
a solid pyramid with a square base with side 12 cm and height 25 cm is made of metal. The metal is melted to form spherical ball bearings of radius 7 mm. How many pyramids are needed to form 2490 ball bearings?
Answer:
3 pyramids.
Step-by-step explanation:
The volume of one pyramid is 1/3 * b^2 * h
= 1/3 * 12^2 * 25
= 1200 cm^3.
The volume of one ball bearing = 4/3 * π * 0.7^3
= 1.43676 cm^3.
Therefore the volume of 2490 ball bearings = 2490 * 1 .43676
= 3577.53 cm^3.
So we need 3577.53 / 1200 = 2.98 = 3 pyramids.
HELP !! it’s due soon
Answer:
108
Step-by-step explanation:
they are supplemntary meaning the sum of the equals 180
180 - 72 = 108
Answer:
<7= 108
Step-by-step explanation:
Angle 6 and angle 7 form a straight line. A straight line always equals to 180, so you subtract 180 from 72. 180-72=108
ghrhrtjtjtjttjtjjrryjutkkyjktrjjetjrkjrjrjdjrkrjjrjrjrjrrrtjr
Answer:
s.jnufdhgvsgvru
Step-by-step explanation:
Calculus is the relationship between change (in forms of rates, slopes, differentials) and content (measure by examples: volume, area, distance) It's a field that connects how big something is to how much it grows when small changes are made or, conversely, how knowing the rate that something is changing can tell you how much "stuff" you've accumulated.
a. True
b. False
Answer:
a. True
Step-by-step explanation:
Calculus is the mathematical study of continuous change. Calculus is usually developed by working with very small quantities. Calculus has two major branches, which are, differential calculus and integral calculus. Differential calculus involves instantaneous rates of change, and the slopes of curves, while integral calculus deals with the accumulation of quantities, and areas under or between curves.
Consider the variable race. What frequency of observations are Black and what frequency are Latino? A. 7 are black and 5 are Latino B.7 are Black and 4 are Latino C. 4 are black and 8 are latino D.8 are black and 4 are Latino E. 1 is black and 1 is Latino
Answer:
The answer is 8 are Black and 4 are Latino
help fast i am lazy
Answer:
Step-by-step explanation:
yes
Which of the following is rational?
1) 3xPi
2) 2/3+9.26
3) \/45+\/26
4) 14.3+5.7876239...
BTW this ( \/ ) means the squared sybol. i did it like that because iididn't know how to do the squared symobl on a keyboard.
_
And the 3 in 14.3 is a repeating 3
what is 0.86 x 0.24 help me with this.
Answer:
0.86 x 0.24 = 0.2064
Step-by-step explanation:
An Axiom in Euclidean geometry states that in space, there are at least three points that do
Answer:
...not lie on the same plane.
Step-by-step explanation:
Before each rainstorm, Ozzie put out rain gauges to measure how many inches of rain fell during the storms that month?
there isn't enough information
you need to put the image or the amount of inches of rain to get an answer
Sebastien hand-crafts circular braided rugs. The graph shows the prices of various sizes of his rugs. A customer ordered 3 identical rugs for a total of $1,350. Use the graph to determine the radius of each rug in the order. (Enter numerical answer only).
Please help.
Answer:
The radius of each rug on the order is 6 ft
Step-by-step explanation:
The graph shows the relationship between the price of a rug and the radius of the rug
The number of rugs ordered by the customer = 3 rugs
The total cost of the rugs ordered by the customer = $1,350
Therefore, the cost of each rug = $1,350/3 = $450
The radius of the rugs as determined from the chart
At $450, the radius of the rug = 6 ft
Therefore;
Given that all the rugs are identical, the radius of each rug on the order = 6 ft.
Ariana borrowed some money from her friend in order to help buy a new video game
system. Ariana originally borrowed $150 and agreed to pay back her friend $15 per
week. Write an equation for L, in terms of t, representing the amount Ariana owes
her friend after t weeks.
Answer:
L = 150 - 15t
Step-by-step explanation:
Money borrowed by Ariana = $150
Money she returns each week = $15
Amount of borrowed money will decrease by $15 each week.
In 1 week she will return $15
in 2 week she will return $15*2 = $30
in 3 week she will return $15*3 = $45
...........................
similarly after t week
money she will return = Money she returns in 1 week* no of weeks
money she will return in t weeks = 15*t = 15t
where 15t unit is dollar
So, Amount of borrowed money will decrease by $15t in t week.
Amount of money she woes after t week = Money borrowed by Ariana - money returned in t weeks
Amount of money she woes after t week = 150 - 15t
Since L represents the amount Ariana owes ,her friend after t weeks
L = 150 - 15t is the correct answer
An airplane flew across the Pacific Ocean. The table shows the amount of time and the distance traveled when the airplane was traveling at a constant speed. What is the distance traveled for 2 hours? *
Answer:
Step-by-step explanation:
time(hours) | distance traveled(miles)
_____________|_______________________
2 | 1100
_____________|_______________________
3 | 1650
_____________|_______________________
6 | 3300
The distance covered by the airplane after 2 hours given a constant speed is 1100 miles
Since, the speed of the plane is said to be constant ;The speed of the plane can be calculated from the information in the table thus : Speed = distance ÷ time Distance traveled = 1650 miles ; time = 3 hours Speed = 1650 / 3 = 550 miles per hour Hence, the speed of the airplane = 550 miles per hour Distance covered in 2 hours will be : (Speed × time) Distance covered in 2 hours = (550 × 2) = 1100 milesThe distance covered by the plane in 2 hours is 1100 miles
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Quadrilateral WXYZ is a rhombus. What is the measure of < XWZ?
A) 64
B) 26
C) 52
D) 32
Answer:
C. 52°Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below.
Since all the sides and angles of a rhombus are the same, hence, all the right angled triangle in each quadrant are also the same.
From the diagram, < XWZ = < XWV + < VWZ and < XWV = < VWZ
Therefore < XWZ = < VWZ + < VWZ
< XWZ = 2<VWZ
let us calculate the angle <VWZ first.
From ΔVWZ, <WVZ +<WZV + <VWZ = 180°... 1
From the diagram <WVZ = 90°, <WZV = <VZY = 64°
On substituting into 1
90°+64°+ <VWZ = 180°
154°+ <VWZ = 180°
<VWZ = 180°-154°
<VWZ = 26°
Since < XWZ = 2<VWZ
< XWZ = 2(26°)
< XWZ = 52°
Hence the measure of < XWZ is 52°
Which equation represents the graphed function?
A)-3x + 2 = y
B) -2/3x+2=y
C)3/2x-3=y
D)2x-3=y
Answer:
(C) 3/2x-3=yStep-by-step explanation:
The point on the x-axis is 2
The point on the y - axis is -3
A woman bought a new color television with
a $40 down payment and 16 monthly pay-
ments of $20 each. What was the total cost
of the television?
18-A $450
18-B $360
18-C $320
18-D
$280
Answer:
B
Step-by-step explanation:
The total cost of the television is $360 if a woman bought a new color television with a $40 down payment and 16 monthly payments of $20 each.
It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We know the formula for the monthly payment:
[tex]\rm Monthly \ Payment \:=\:\dfrac{\left A\left(i\right)\left(1+i\right)^{n}\right}{\left(1+i\right)^{n}-1}[/tex]
It is given that:
A woman bought a new color television with a $40 down payment and 16 monthly payments of $20 each.
Down payment = $40
Number of months = 16
Per month payment = $20
The total cost of the television = 40 + 16(20)
The total cost of the television = 40 + 320
The total cost of the television = $360
Thus, the total cost of the television is $360 if a woman bought a new color television with a $40 down payment and 16 monthly payments of $20 each.
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1) 3x²y3 . 3y4
A) 4x®y4
C) 9x?y?
B) -2x®ys
D) 2x®y4
calculate the area of a rectangle with length of 8m and a width of 4m
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{32 \: {m}^{2} }}}}}[/tex]
Step-by-step explanation:
Given,
Length of a rectangle( l ) = 8 m
Width of a rectangle ( w ) = 4m
Area of a rectangle ( A ) = ?
Finding the area of a rectangle having a length of 8m and a width of 4m
[tex] \boxed{ \bold{ \sf{area \: of \: a \: rectangle = length \times width}}}[/tex]
plug the values
⇒[tex] \sf{ area \: of \: a \: rectangle = 8m \times 4m}[/tex]
Multiply the numbers : 8 and 4
⇒[tex] \sf{area \: of \: a \: rectangle = 32 \: {m}^{2} }[/tex]
Hope I helped!
Best regards!!
If James can read two pages in three minutes how long will it take him to read a 250 page novel? 750 minutes 500 minutes 375 minutes 167 minutes
Answer:
750 minutes
Step-by-step explanation:
james read 2 pages in 3 minutes so to read 250 pages it will be 250 x 3=750
If the first term of AP is 4 and the sum of first five term is equal to one-fourth of the sum of the next five term, then find the 15th term?
Answer:
15th term = 116
Step-by-step explanation:
a= 4
Sum of an A.P = n/2 {2a + (n-1)d}
sum of first five term is equal to one-fourth of the sum of the next five term
5/2{ 2*4 + (5-1)d} = 1/4 × 10/2{2*4 + (10-1)d
5/2 {8 + 4d} = 1/4 × 5{ 8 + 9d}
40/2 + 20/2d = 1/4{ 40 + 45d)
20 + 10d= 40/4 + 45/4d
20 + 10d = 10 + 45/4d
20 - 10 = 45/4d - 10d
10 =45d - 40d /4
10 = 5/4d
Divide both sides by 5/4
10 ÷5/4 = d
10×4/5 = d
40/5 = d
8 = d
d= 8
Find the 15th term
15th term = a + (n-1)d
= 4 + (15-1)8
= 4 + (14)8
= 4 + 112
= 116
The 15th term is 116