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.
=============================================================
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.
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 = 1.18681439028Which 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 :)
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.
Create a real-world situational problem to represent the given equation or inequality.
Answer:
wheres the rest of it
Step-by-step explanation:
50 POINTS HELP WILL MARK BRAINLIEST
find the value of x.
(picture attached)
[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]
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 ≤ 9help help help help help help
Answer:
the answer is no c because the translation is done in clockwise taking y intercept in 6 units
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
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
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%
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
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]
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]
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
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
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.
Enter an inequality that represents the graph in the box.
Answer:
It will be -8≤×≤8
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
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
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*
If 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]
Find the least common multiple (LCM) of 6 and 10,
O A. 60
O B. 20
O C. 40
O D. 30
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
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]
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
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.
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
If the function is f(x)=−3x+7, what is f(1/3)=
Answer:
6 is the answer. Hope this helps you! Stay blessed .