Answer:
See Below.
Step-by-step explanation:
The first three terms of an A.P is equivalent to the first three terms of a G.P.
We want to show that this is only possible if r = 1 and d = 0.
If a is the initial term and d is the common difference, the A.P. will be:
[tex]a, a+d, \text{ and } a+2d[/tex]
Likewise, for the G.P., if a is the initial term (and it does not equal 0) and r is the common ratio, then our sequence is:
[tex]a, ar,\text{ and } ar^2[/tex]
The second and third terms must be equivalent. Thus:
[tex]a+d=ar\text{ and } a+2d=ar^2[/tex]
We can cancel the d. Multiply the first equation by -2:
[tex]-2a-2d=-2ar[/tex]
We can now add this to the second equation:
[tex](a+2d)+(-2a-2d)=(ar^2)+(-2ar)[/tex]
Simplify:
[tex]-a=ar^2-2ar[/tex]
Now, we can divide both sides by a (we can do this since a is not 0):
[tex]-1=r^2-2r[/tex]
So:
[tex]r^2-2r+1=0[/tex]
Factor:
[tex](r-1)^2=0[/tex]
Thus:
[tex]r=1[/tex]
The first equation tells us that:
[tex]a+d=ar[/tex]
Therefore:
[tex]a+d=a(1)\Rightarrow a+d=a[/tex]
Hence:
[tex]d=0[/tex]
Q.E.D.
“twice the sum of a number and 6 is more than 84”
i need to write this as an inequality.
Someone please help
Step-by-step explanation:
2x + 6 > 84
2x > 78
x > 39
is the answer
4. Which of these is equal to sin(70°)?
a. cos(1109)
c. cos(20°)
b. cos(160)
d. cos(709)
TRIANGLE SIMILARITY & CONGRUENCE. PICTURE INCLUDED! asa,aas,sss, or sas
Answer:
AA they give you two angles
Find the area of the composite shape below.
Answer: 1106.13 (2 decimal places)
Step-by-step explanation:
To work out the area of this composite shape you would have to put the two semi circles together to form a circle and work out the area of the circle (they have provided the radius which is 11in), then work out the area of the rectangle separately.
The formula for the area of a circle is πr^2 (pi x radius squared).
So when you put the numbers in the formula the area is πx11^2=380.1327111
Then to work out the area of the rectangle you would do base x height.
The height of the rectangle is the same as the diameter of the circle (the diameter is double the radius of a circle) which is 22in.
To find the area of the rectangle you do 22x33=726
So then to find the area of the whole shape you would have to add the area of the circle and the rectangle together.
726+380.1327111=1106.13 (2 decimal places).
Fred drew 2/3 on a number line. Sara broke her number line into 6 equal pieces but found the same fraction on the number line as Fred. What fraction did Sara make?
Answer:
4 / 6
Step-by-step explanation:
Fred fraction = 2/3
Sarah formed a fraction by dividing her number line into 6 equal pieces. This is given as;
x / 6
Since her fraction is equal to that of fred, we have;
x / 6 = 2 / 3
x = 6 * 2 / 3 = 4
Sarah Fraction = 4 / 6
write the recurring decimal 0.25656565656 as a fraction in its simplest form
Answer:
127/495
Step-by-step explanation:
Turning repeating decimals into fractions is a little like surgery: you need to make sure to "cut out" just the right part to let you simplify. In this case, it'd be very nice if we could deal with that repeating 0...565656... part. Let's start by giving our decimal a name:
[tex]x=0.25656...[/tex]
We're gonna split this into two parts: a number we can operate on, and "knife" to make the incision. For both, we'd like the only part to the right of the decimal to be the repeating part. To make our "knife," we'll multiply both sides of the equation by 10:
[tex]10x=2.5656...[/tex]
To make the number we'll be cutting from, we can shift the decimal point by any multiple of two more to the right. I'll keep things simple and stick with 2. This corresponds to multiplying the "knife" equation by 100 on both sides:
[tex]1000x=256.5656...[/tex]
Surgery time! To cut out the repeating bit, we can now just subtract the "knife" equation from the one above:
[tex]1000x-10x=256.5656...-2.5656...\\990x=254[/tex]
And just like that, it's gone! All that's left to do now is divide both sides by 990 and simplify:
[tex]x=254/990=127/495[/tex]
a watch is sold for $130 at a loss of $30. what was the original cost of the watch
Answer:
Step-by-step explanation:
130.00 + 30.00 =$160.00
It was at a loss, so it was reduced by 30.00
THIS IS WORTH 24 FREAKING POINTS SO GIVE ME NO WRONG ANSWER NOW, read the question carefully and answer it correctly and carefully
Answer:
I am not the best at math but I know that u can't change the bottom half of the fraction so it would just be four and then multiply the five and the three which would be fifteen. The answer would be 15/4ths. So you want to color in 15 boxes. Hopefully I could be of some kind of help to you!
Answer:
color in 15 boxes
15/32
Step-by-step explanation:
first off, the points are split so I'm only getting 12, just so that you know.
so 1/8x1/4 is 1/32, so each box is 1/32.
5/8x3/4=15/32 (multiply the top of the first with the top of the second and the bottom of the first with the bottom of the second)
so color in 15 boxes and the answer to the multiplication is 15/32
Hope I could help!
Ted's company has received an order to print 10^6 pages. Ted's company has 100 machines., each of which can print 10^4 pages a day. Ted's coompany can print the 10^6 pages in 1/10 day, 1 day, 10 days, or 100 days?
Answer:
1 day because he has 100 machines not just one
Step-by-step explanation:
Which of the following is a difference of cubes? x^6 + 27y^9 3x^9 - 64y^3 27x^{15} - 9y^3 125x^{21} - 64y^3
Answer:
D) 125x²¹- 64y³Step-by-step explanation:
A) x⁶ + 27y⁹ = (x²)³ + (3y³)³ - sum of cubesB) 3x⁹ - 64y³ - the first term is not a cubeC) 27x¹⁵ - 9y³ - the second term is not a cubeD) 125x²¹- 64y³ = (5x⁷)³ - (4y)³ - difference of cubesCorrect option is the last one
Answer:
D) 125x²¹- 64y³
Step-by-step explanation:
A) x⁶ + 27y⁹ = (x²)³ + (3y³)³ - sum of cubes
B) 3x⁹ - 64y³ - the first term is not a cube
C) 27x¹⁵ - 9y³ - the second term is not a cube
D) 125x²¹- 64y³ = (5x⁷)³ - (4y)³ - difference of cubes
Correct option is the last one
2
Find the Surface area of the prism.
(2 Points)
5 in
3 in
8 in
4 in
Answer:
The surface area of the prism is 108 square in.
1. Both of the equations shown have the same solution when solved for x. What is
the value of k? Show or explain all your work. *
5x + 34 = -2 (1 – 7x) and – 3 (4x + 3) + 4 (6x + 1) = k
Your answer
PLS HELPPPP
Answer:
Step-by-step explanation:
Tom made fruit punch for a party. He mixed 2 gallons of orange juice, 4 quats of pinnapple juice, 3 pints of cranberry juice. How many quarts did he make in all?
Answer:
13.5
Step-by-step explanation:
Tom made fruit punch for a party
He used the following amount of fruits
2 gallons of orange juice
= if 1 gallon is 4 quart then 2 gallon is 4×2= 8 quarts
3 pints of cranberry juice
= if 1 pint is 0.5 quart then 3 pints is 0.5×3 = 1.5 quarts
The amount of quartz he made can be calculated as follows
= 1.5 + 8 + 4
= 13.5
Hence he made 13.5 quarts of fruit punch
I NEED HELP WITH MATH CAN ANYONE HELP!!!
Answer:
ummmmmmmmmm I can try c:
Answer:
YES MAM , WHAT SEEMS TO BE THE PROBLEM < BECAUSE I DONT SEE ONE
Step-by-step explanation:
Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. Check all that apply.
9514 1404 393
Answer:
(a) isosceles
(b), (c) scalene
Step-by-step explanation:
The lengths of the sides can be found from the distance formula:
d = √((x2 -x1)^2 +(y2 -y1)^2)
Here, there are 9 lengths to be computed, so it is useful to let a spreadsheet or graphing calculator do it.
We find triangle (a) has two sides the same length, so it is isosceles.
The other two triangles have three different side lengths, so they are scalene.
_____
Additional comment
It is impossible to specify an equilateral triangle using rational coordinates.
write down the factors of 57 which lie between 1 and 57
Answer:
The factors of 57 which lie between 1 and 57 are as follows:
{1,3,19,57}
5+ 2 1/2 + 7 1/2 + 2 1/2+ 7 1/2 +5=
Answer:
its 30.
Step-by-step explanation:
that's all I know.
(0,2), (3,3), (8,7), (2,2), (3,9)
Domain :
Range:
Answer:
Domain: ( 0, 3, 8, 2 )
Range : (2, 3, 7, 9)
Step-by-step explanation:
Blank plus 1/5 equals 1/2
Answer:
2/10 + ___ = 1/2
Step-by-step explanation:
2/10 + 3/10 = 1/2
What is the image point of (-8, -1) after a translation left 3 units
and up 4 units?
Tucker worked 5.5 hours on Saturday. He earns $7.20 per hour.
How much did he earn on Saturday?
Answer:
$39.6
Step-by-step explanation:
5.5 times 7.20 = $39.6
What is the coefficient in the term 7x-8
Answer:About "Identify the terms and coefficients" Identify the terms and coefficients : A single variable or a constant or a combination of these as a product or quotient forms a term.
Step-by-step explanation:
Answer:
I think you forgot to put the picture
Step-by-step explanation:
but try this:
A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Variables with no number have a coefficient of 1.
There are 320 students in a school. The ratio of the number of boys to the number of girls is 3:2. When some new boys and girls are admitted, the number of boys increases by 8 and the ratio of number of boys and girls changes to 4:3. Find how many new girls are admitted.
28.In the year 2006, the number of malaria patients admitted in the hospital of a state was 4375. Every year this number decreases by 8%. Find the number of patients in the year 2008?
Answer:number of patients in the year 2008 =3,703 Patients.
Step-by-step explanation:
Number of malaria patients admitted in the hospital of a state in 2006= 4375.
Number of malaria patients admitted in the hospital of a state in 2007 if there was Decrease by 8% in 2007
= 8% x 4375 =350
4375-350=4,025 patients
Number of malaria patients admitted in the hospital of a state in 2008 since there was Decrease by 8% in 2008
8% x 4,025.= 322
4,025-322=3,703 Patients.
Please help sbdbdbdbdbdbdndbndbbdbdbdbdb
Answer:
x ≤ [tex]\frac{7}{17}[/tex]
Step-by-step explanation:
multipy both sides by twelve
move the variable to the left side and change the sign
collect like terms
divide both sides by -17 and flip the inequality sign
Raju bought an old car for Rs.125000 and spent Rs.25000 on its repair . He sold the car for Rs.200000 . Find his gain or loss percent .
Answer: [tex]33.33\%[/tex]
Step-by-step explanation:
Given
Raju buy an old car for [tex]Rs\ 1,25,000[/tex]
He spent [tex]Rs\ 25000[/tex] on its repair
The selling price of the car [tex]Rs\ 2,00,000[/tex]
So, the cost price is
[tex]\Rightarrow C.P.=1,25,000+25,000=Rs\ 1,50,000[/tex]
Here, [tex]S.P.> C.P.\quad \text{i.e. gain}[/tex]
Gain percent is
[tex]\Rightarrow \text{Gain percent}=\dfrac{2,00,000-1,50,000}{1,50,000}\times 100=\dfrac{50,000}{1,50,000}\times 100\\\Rightarrow \text{Gain percent}=33.33\ \%[/tex]
A jar contains 660 beans. Of them, 440 are kidney beans and the rest are cranberry
beans. What is the ratio of kidney beans to all beans?
Answer:
Step-by-step explanation:
kidney beans : all beans
440:660 (simplify by dividing each by gcf which is 2^2(5)11=220)
2:3
Answer:
440:660 OR Simplified 2:3
Step-by-step explanation:
You already had the two numbers for the ratio, they added the cranberry beans in the sentence like that to confuse you and draw you away from the real answer. All you needed to do was arrange the numbers into a ratio, and simplify.
These problems are meant to to be confusing, so to stay away from the confusing parts, just reread them and you'll get it correct 24/7!
Hope you get this right.
what is the value of x.
Answer:
x=47
Step-by-step explanation:
180-121=59
180-(59+74)=47
Answer:
x = 47
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
121° is an exterior angle of the triangle, then
x + 74 = 121 ( subtract 74 from both sides )
x = 47
Using the line ab name two line segments
Brainliest
Answer:
A. AC, CB
Step-by-step explanation:
The answer you have selected is correct because a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. Thus the answer A is correct!
Hope this helps
All the love, Ya boi Fraser :)
Answer:
Give him brainliest!
Step-by-step explanation:
What is the length of segment TR?
Answer:
8 units
Step-by-step explanation: