Part A
Answer: x = 20--------------------------------
Explanation:
AP = arithmetic progression, which is another way of saying arithmetic sequence.
Let d = common difference
first term = 10second term = first+d = 10+d = xthird term = second+d = x+d = 30Apply substitution like so
x+d = 30
10+d+d = 30 ... replaced x with 10+d
10+2d = 30
2d = 30-10
2d = 20
d = 20/2
d = 10 is the common difference
Therefore,
x = 10+d = 10+10 = 20
The AP {10,x,30} updates to {10,20,30}. We see the gap between terms is 10 units. All AP's have the same gap width between adjacent terms.
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Part B
Answers: x = 10 and y = 14--------------------------------
Explanation:
We use the same ideas mentioned back in part A.
d = common difference = unknown for now
first term = 6second term = first+d = 6+d = xthird term = second+d = x+d = (6+d)+d = 6+2d = yfourth term = third+d = y+d = (6+2d)+d = 6+3d = 18Hopefully you can see how each term builds up to form the next one. We'll solve that last equation like so
6+3d = 18
3d = 18-6
3d = 12
d = 12/3
d = 4
So we then can say:
x = 6+d = 6+4 = 10y = 6+2d = 6+2(4) = 6+8 = 14The arithmetic sequence {6,x,y,18} updates to {6,10,14,18}. There's a gap of 4 between each adjacent term.
If the first term of an A.P is equal to one half of the common difference d, find the eight term of the A. P.
Step-by-step explanation:
The formula for Arithmatic Series is
[tex]a_n=a_1+(n-1)d[/tex]
where a_1 and a_n are the first and n-th term of the series respectively,
d is the common difference of the series.
Now,
The eigth term is given by,
[tex]a_8=(\frac{d}2)+(8-1)d=\frac{15}{2}d[/tex]
Which of the following demonstrates the distributive property?
A. (r + s)t = (s+r)t
B. (r + s)t=r + (st)
C. (r + s)t = t(r + s)
D. (r + s)t = rt + st
Answer:
D. (r + s)t = rt + st
Step-by-step explanation:
Distribute means that the term outside gets multiplied to each term on the inside of the parentheses
(r + s)t = rt + st
2. Write each of these expressions in the form (+)!+, where and are constants.
a)6!+12−3
b)−18+3!+4
Step-by-step explanation:
a)6!+12-3
=6!+9
b)-18+3!+4
=3!-14
=3!+(-14)
both are in the form if (+)!+constant.
Note:if you need to know any question about it please let me know.
What is the slope of the line represented by the equation y = -1/2x+ 1/4
Answer:
y = mx+ b
m=slope
-1/2
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slopeb = y-interceptBy comparing the formula to the equation given, it is clear the slope of the line is -1/2.
Find the least common multiple (LCM) of 6 and 10,
O A. 60
O B. 20
O C. 40
O D. 30
[tex]\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}[/tex]
How do you simplify that expression?
Answer:
[tex]\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}[/tex]
rationalise the denomimator:
[tex] = \frac{ {x}^{ \frac{1}{4} } + 2 }{ {x}^{ \frac{1}{4} } - 2} . \frac{( {x}^{ \frac{1}{4} } + 2)}{ ({x}^{ \frac{1}{4} } + 2)} \\ \\ = \frac{ {x}^{ \frac{1}{2} } + 4 {x}^{ \frac{1}{4} } + 4 }{ {x}^{ \frac{1}{2} } - 4} [/tex]
The temperature at 12:00 p.m. was 8°C. At 7:00 p.m., the temperature was -6°C. What was the change in temperature (in degrees Celsius)?
�� 6-degree increase
�� 14-degree increase
�� 6-degree decrease
�� 14-degree decrease
Answer: 14 degree decrease
Step-by-step explanation:
8-14= -6
Solve the inequality.
-4 < 2x - 6 < 12
[?]
Hi ;-)
-4 ≤ 2x - 6 ≤ 12
2x - 6 ≥ -4 / + 6
2x ≥ 2 / : 2
x ≥ 1
2x - 6 ≤ 12 / + 6
2x ≤ 18 / : 2
x ≤ 9
1 ≤ x ≤ 9If V(r)=4/3pir³, find V(3/4)
Answer:
Step-by-step explanation:
r = 3/4
[tex]V(r) =\dfrac{4}{3}\pir^{3}\\\\V(\dfrac{3}{4})=\dfrac{4}{3}*\pi \dfrac{3}{4}*\dfrac{3}{4}*\dfrac{3}{4}\\\\=\dfrac{3*3}{4*4}\pi \\\\=\dfrac{9}{16}*3.14\\\\=1.77[/tex]
If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.
Therefore, if [tex](x-4)[/tex] and [tex](y+3)[/tex] vary inversely, their product will be the same for all values of [tex]x-4[/tex] and [tex]y+3[/tex].
Let [tex]x=8[/tex] and [tex]y=2[/tex] as given in the problem. Substitute values:
[tex](8-4)(2+3)=(4)(5)=20[/tex]
Hence, the maintained product is [tex]20[/tex].
Thus, we have the following equation:
[tex](x-4)(y+3)=20[/tex]
Substitute [tex]y=-1[/tex] to find the value of [tex]x[/tex] when [tex]y=-1[/tex]:
[tex](x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}[/tex]
Write the equation of the line that passes through the points (-3,6) and (4,1). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y = -5/7x + 27/7
Step-by-step explanation:
y2 - y1 / x2 - x1
1 - 6 / 4 - (-3)
-5 / 7
= -5/7
y = -5/7x + b
1 = -5/7(4) + b
1 = -20/7 + b
27/7 = b
50 POINTS HELP WILL MARK BRAINLIEST
find the value of x.
(picture attached)
Which best describes the meaning of the statement "If A and B ? i dont understand this
A. If A is false then B must be false
B. If A is true then B must be true
C. If A is false , then B must be false
D. if A is true then B might be true
Can someone explain me this please :)
Answer:
39) a) [tex]2^{1}[/tex]= 2
b) [tex]2^{3}[/tex]= 2×2×2=8
c)[tex]2^{t}[/tex]
40) no
Step-by-step explanation:
40) both point A and B is below the point C. therefore it cannot pass through point c
The perimeter of the rectangle below is 16 Solve for X
Answer:
x = 5
Step-by-step explanation:
The opposite sides of a rectangle are equal , then perimeter
2(- 2x - 6) + 2(4x + 4) = 16 ← distribute parenthesis and simplify left side
- 4x - 12 + 8x + 8 = 16
4x - 4 = 16 ( add 4 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5
x=1/4
Step-by-step explanation:
perimeter of a rectangle
2(L+w)
-2x-6(4x+4)
open the bracket
-2x(4x+4)-6(4x+4)
-8x^2-8x-24x-24
-8x^2-32x-24
2(-8x^2-32x-24)
-16x^2-64x-48
coefficient of x is 64
16=64x
x=1/4
Create a real-world situational problem to represent the given equation or inequality.
Answer:
wheres the rest of it
Step-by-step explanation:
Identify the terms in the expression. (Enter your answers as a comma-separated list.)
5y3 + y + 3
5y3+y+3
5y4+3
I'm not sure but I think it will help you out
Using the numbers 2,7,13,11,5 can you get the total of 23? (No negatives, No repetitive Numbers and only)
Answer:
7, 11, 5
Step-by-step explanation:
7 + 11 = 18
18 + 5 = 23
Example 5: Writing and Solving an Equation
The circles are identical. What is the area of each circle?
x + 2
4X
Please help…
Step-by-step explanation:
radius =x+2
diameter=4x
Diameter=2(radius)
4x=2(x+2)
4x=2x+4
4x-2x=4
2x=4
x=4/2
x=2
Subtitute x=2 in radius:
r=2+2=4
Area=πr²
Area=3.14×4²
Area=3.14×16
Area=50.24
Both the circles are identical so area is same.
Note:if you need to ask any question please let me know.
Mary Lindey wants to purchase pumpkins. She finds different markets advertising pumpkins for sale. What market has the lowest price per pumpkin . 3 for 10.59 , 3.75 per pumpkin , 2 for 7.20
*7th grade*
HELP I'M REWARDING 50 POINTS (YA IKR 50 WOW) IF YALL GET THIS RIGHT..
Answer:
232
Step-by-step explanation:
Since the polygon is regular, each side of the polygon is equal
[tex]x + 7 = \frac{4}{3} x - \frac{1}{3} [/tex]
[tex]7 = \frac{1}{3} x - \frac{1}{3} [/tex]
[tex] \frac{22}{3} = \frac{1}{3} x[/tex]
[tex]x = 22[/tex]
This means each side is worth
[tex]22 + 7 = 29[/tex]
or
[tex] \frac{4}{3} x - \frac{1}{3} = \frac{87}{9} = 29[/tex]
There is 8 sides so the perimeter is
[tex]29 \times 8 = 232[/tex]
2x² - 5x+1 has roots alpha and beta. Find alpha²+beta².
Please answer fast. I will mark the best answer as brainliest.
Answer:
[tex]\dfrac{21}{4}[/tex]
Hello,
Step-by-step explanation:
[tex]2x^2-5x+1=2(x^2-\frac{5}{2}+\frac{1}{2} )\\\\\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\frac{1}{2} \\\\(\alpha+\beta)^2=\alpha^2+\beta^2+2\alpha*\beta\\\\\alpha^2+\beta^2\\\\=(\alpha+\beta)^2-2\alpha*\beta\\\\\\=(\dfrac{5}{2} )^2-1\\\\=\dfrac{21}{4} \\[/tex]
Which is the graph of the equation y- 1= 5(x-3)?
Answer:
linked below
Step-by-step explanation:
If you use desmos, it show this which is the correct graph :)
Geometry question. “Find the value of x that will make A||B.” Brainliest to whoever is correct
Answer:
Step-by-step explanation:
The two angles are interior angles on the same side of the transversal. They are supplementary.
2x + 50 + 5x - 80 = 180 Combine like terms
7x - 30 = 180 Add 30 to both sides
7x = 210 Divide by 7 on both sides
x = 210/7
x = 30
Enter an inequality that represents the graph in the box.
Answer:
It will be -8≤×≤8
help help help help help help
Answer:
the answer is no c because the translation is done in clockwise taking y intercept in 6 units
helppppppppppppppppppp
Answer:
x = -4
Step-by-step explanation:
-x+7 = -6x-13
Add 6x to each side
-x+7+6x = -6x-13+6x
5x+7 = -13
Subtract 7 from each side
5x+7-7=-13-7
5x = -20
Divide by 5
5x/5 = -20/5
x = -4
If the function is f(x)=−3x+7, what is f(1/3)=
Answer:
6 is the answer. Hope this helps you! Stay blessed .
Jacob conducted a music survey among his friends. He reported that 0.42 prefer pop, 22% prefer rock, and 2/5 prefer hip hop, Explain what's wrong with Jacob's results. ASAP PLS
Answer:
Step-by-step explanation:
Based on ur graph, in a class of 90 students (20 rock, 40 hip hop, and 30 country...added = 90) , 30 chose country....30/90 reduces to 1/3.....so 1/3 chose country.
In a class of 450 students......1/3 * 450 = 450/3 = 150 chose country
Answer:
The total percentages do not equal 100%, they equal 102%. If all friends answered, his total should equal 100%
Step-by-step explanation:
0.42 is 42%, 22% is 22%, and 2/5 is 0.4 which is 40%. Together that is 102%. If all friends answered, his total should equal 100%
Evaluate :
A. [tex]x^{x^3}=3[/tex]
B. [tex]4^x +6^x =9^x[/tex]
Answer:
A. [tex]x^{x^3} = 3[/tex]log [tex]x^{x^3}[/tex] = log 3x³ log x = log 33x³ log x = 3 log 3x³ log x³ = log 3³[tex]x^3^{x^3}[/tex] = 3³x³ = 3x = [tex]3^{1/3}[/tex]B.4ˣ + 6ˣ = 9ˣ2²ˣ + 2ˣ3ˣ = 3²ˣDivide both sides by 2²ˣ
1 + (3/2)ˣ = (3/2)²ˣSubstitute (3/2)ˣ = t
t² - t - 1 = 0Solve for t:
t = (1 ± √5)/2Positive root is considered as (3/2)ˣ can't be negative.
(3/2)ˣ = (1 + √5)/2x = log [(1 + √5)/2] / log (3/2)x = 1.18681439028