Answer:
aₙ= n²-6
Step-by-step explanation:
The sequence:
- 5, -2, 3, 10, 19, ...
The difference between terms:
3, 5, 7, 9
The next term would be: 19+11= 30
Let's work out the formula:
a₁= -5a₂= a₁+3= a₁+4-1= a₁+2²-1a₃= a₁+5= a₁+3+5= a₁+8= a₁+9-1= a₁+3²-1a₄= a₁+7= a₁+8+7= a₁+15= a₁+16-1= a₁+4²-1...sowe can put for nth term:aₙ= a₁+n²-1= -5+ n²-1= n²-6
Let's test this formula for 5th and 6th terms:
a₅= 5²-6= 25-6= 19a₆= 6² -6= 30So the nth term is:
aₙ= n²-6Angle X measures _____ degrees. Angle Y measures _____ degrees. The value of x is ______ degrees. Tha value of y is _____ degrees.
Answer:
Angle x measures 64 degrees and Angle y also measures 64 degrees. X is 11. The value of y is also 11.
Step-by-step explanation:
Alright, so this triangle is an isosceles triangle since there are lines on two sides meaning they are congruent to each other. So, if the sides are congruent, then the angles are also congruent. Angle y is congruent to angle x. First, lets find what they measure totally. Since they are congruent, we can write the equation with 2x+angle w which is 52=180 because the sum of all angles in a triangle is 180. Subtract 52 from both sides 2x=132 divide both sides by 2, and you get 64. You found what angle x and y equal. Now you can find what the value of x and y. For finding x, 4x+20=64 and for y, 6y-2=64. Isolate each variable, and you get 11 for both the value of x and y.
I NEED HELP PLEASE, THANKS! :)
Answer: D) reflection over the x-axis, vertical shrink by a factor of 7/8, horizontal shift 3 units to the left, and vertical shift 3 units up.
Step-by-step explanation:
[tex]Consider\ f(x)=Ae^{Bx-C}+D\qquad where[/tex]
A = vertical stretch by a factor of A (|A| < 1 is a vertical shrink)-A = reflection across the x-axisB = horizontal shrink by a factor of 1/BC = horizontal shift C units (positive = right, negative = left)D = vertical shift D units (positive = up,, negative = down)[tex]f(x)=e^x\\\\g(x)=-\dfrac{7}{8}e^{x+3}+3[/tex]
→ A = -(7/8)
The negative sign represents a reflection across the x-axis.
(7/8) < 1 so it is a vertical shrink by a factor of (7/8)
→ C = -3 x +3 = x - (-3)
This is a horizontal shift 3 units to the left.
→ D = +3
This is a vertical shift 3 units up.
enter the correct value so that the expression is a perfect square trinomial x^2 - 10x +
Answer:
25
Step-by-step explanation:
The correct value can be calculated by doing (b/2)²
In this expression, it would be (-10/2)²
Which equals 25
Answer:
x^2 -10x+25
Step-by-step explanation:
Take the coefficient of x
-10
Divide by 2
-10/2 =5
Square it
5^2 =25
Add this to make a perfect square trinomial
x^2 -10x+25
heklp me again please if you dont mind
Step-by-step explanation:
This is the answer of this question.
A line passes through the point(8,-6) and has a slope of-5/4 . Write an equation in point-slope form for this line.
Answer:
y+6 = -5/4(x-8)
Step-by-step explanation:
The point slope form of the equation of a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y --6 = -5/4 ( x - 8)
y+6 = -5/4(x-8)
The standard form of the equation of a circle is (x−4)2+(y−2)2=9. What is the general form of the equation? x2+y2−8x−4y+11=0 x2+y2+8x+4y+11=0 x2+y2−8x−4y−29=0 x2+y2+8x+4y−29=0
The general form of the equation of the circle will be x² + y² − 8x − 4y + 11 = 0.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The standard form of the equation of a circle is (x − 4)² + (y−2)² = 9
Then the general form of the equation of the circle will be
x² + 4² − 8x + y² + 2² − 4y = 9
x² + y² − 8x − 4y + 20 = 9
x² + y² − 8x − 4y + 11 = 0
Then the correct option is A.
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plz help!! marking brainiest!! (btw jus to clarify, i dont have three questions, they're jus graphs)
Answer:
c
Step-by-step explanation:
helppppppp pls I don't get itttt
Answer:
c: 5 x 3/5
Step-by-step explanation:
so the is 15 blocks shaded on the 25 grid
so i would work out each fraction answer and find which one makes 15/25
5 x 5/3 = 25/25
3/5 + 3/5 + 3/5 + 3/5 + 3/5 + 3/5 = 21/5
5 x 3/5 = 15/25
hope this helps :)
if the answer is wrong plz comment and i will fix thanks :)
Answer:
c) 5x3/5
Step-by-step explanation:
Look at one of the bars only. We see that 3 blocks out of 5 are colored in.
So that means the fraction is 3/5. But since there are 5 bars, we must multiply the fraction by 5.
Therefore, the answer is c) 5x3/5
hope this helped:)
P.S. If you like the answer, could you mark as brainliest plz?
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Which expression is equivalent to (150x-80y+ 50-50x-25y+20)?
20x-214+ 14
20x+ 11y + 14
20x-11y+6
20x+21y+6
Answer:
20x+21y+14
Step-by-step explanation:
Combine like terms:
150x-80y+50-50x-25y+20=
100x-80y+50-25y+20=
100x-105y+50+20=
100x-105y+70
100x-105y+70 can be divided by 5 and get 20x+21y+14.
Answer:a
Step-by-step explanation:
Find the value of x. 5x+18+2x=5
Answer: x=-1.9
Step-by-step explanation:
[tex]5x+2x=7x[/tex]
[tex]7x+18=5[/tex]
-18 on both sides
[tex]7x=-13[/tex]
divide 7 on both sides
[tex]x=-1.9[/tex]
Answer
X=-1.9solution
[tex]5x + 18 + 2x = 5 \\ or \: 5x + 2x + 18 = 5 \\ or \: 7x + 18 = 5 \\ or7x = 5 - 18 \\ or \: 7x = - 13 \\ \: x = - \frac{13}{7} [/tex]
X=-1.9
hope this helps..
Good luck on your assignment...
Calculate the area and perimeter of the following ring where
a = 7cm,
b = 14cm
Area of Ring:
Perimeter of Ring:
(its urgent)
Answer:
Area=19
perimeter=21
which of the following is equal to the rational expression when x ≠ -1 or -7
Answer:
A.
Step-by-step explanation:
When you simplify the equation down by getting rid of (x + 1) (and that creates a hole in the graph), you should end up with A as your answer.
A blue sqaure is placed inside a large yellow square The centres of the squares are aligned one over the other one side of the square is (3x + 2)cm and the other side is (8 - x)cm the area of the blue square is 36% the area of the yellow square. Find the dstance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Answer:
the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
Step-by-step explanation:
From the information given;
A blue square is placed inside a large yellow square and the centres of the squares are aligned one over the other
So ; if one side of the square is (3x + 2)cm (i.e the blue side)
the other side is (8 - x)cm (i.e the yellow sides)
since the two shapes given are squares ; we can say that:
(3x+2)= (8 - x)
3x +x = 8 -2
4x = 6
x = 6/4
x = 1.5
Let replace x = 1.5 for the sides of the square and find the actual length of the square sides.
So, for the yellow side; we have:
= (8 - x)cm
= (8 - 1.5 ) cm
= 6.5 cm
We all know that the area of the square = l²
then the area of the yellow side = (6.5 cm )²
the area of the yellow side = 42.25 cm²
Let y be the distance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Since the blue region is inside the yellow region; to calculate for the side of the blue region ; we have:
(6.5y -y+y) cm
(6.5 - 2y )cm
The area of the blue side =( (6.5 - 2y )cm)²
The area of the blue side = (6.5 - 2y )² cm²
However; we are also given that :
the area of the blue square is 36% the area of the yellow square.
Thus;
(6.5 - 2y )² = 36/100 × 42.25
(6.5 - 2y )² = 0.36 × 42.25
(6.5 - 2y )² = 15.21
(6.5 - 2y ) = [tex]\sqrt{15.21}[/tex]
(6.5 - 2y ) = 3.9
6.5 - 2y = 3.9
6.5 - 3.9 = 2y
2.6 = 2y
y = 2.6/2
y = 1.3 cm
Therefore , the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
terrace buys a new car for 20,000 the value of the car depreciates by 15% each year if f(x) represents the value of the car after x years which function represents the care value
Answer:
f(x)= 20,000[tex](0.85)^{x}[/tex]or 20,000 (0.85) to the power of x.
Step-by-step explanation:
Okay, so based on the question, we know that the car is depreciates its value every year. In case you don't know, when something depreciates, it is becoming smaller or less in value. It comes to a point where the item becomes worthless. Recall, that the formula for an exponential function is y= a(b) to the power of x. A is your initial value or your y-intercept. B is the multiplicative rate of change. Lets put 20,000 for a because that is value of the car that terrace purchased before any depreciation happened. Since it says that it is decaying every year, we don't want to graph how much it is decaying, we want to graph what the value is of the car. So, do 100 percent minus 15 which is 85 percent. You need to change it into decimal, so it is 0.85. Therefore, there is your function.
Hope this helps!
If 3x-5=6x-2 is -1. Then how do I do a check step? :(
Answer:
ok,just substitute the x for -1
3x-5=6x-2
3(-1)-5=6(-1)-2
-3-5 = -6-2
-8 = -8
TRUE
So,the solution is correct.-1 is the correct solution
I hope this help,Please give me the brainliest
Step-by-step explanation:
What is the value of x? [PART 2] A.285˚ B.105˚ C.75˚ D.15˚
Answer:
x = 17
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
5x-18 + 4x+45 = 180
Combine like terms
9x +27 = 180
Subtract 27 from each side
9x+27-27 =180-27
9x =153
Divide by 9
9x/9 = 153/9
x =17
What are the intercepts of the function?
The x-intercepts are
Consider the function f(x) = x2 + 12x + 11.
x-intercepts:
0= x2 + 12x + 11
0 = (x + 1)(x+ 11)
The y-intercept is
y-intercept
f(0) = (0)2 + 12(0) + 11
) Intro
Done
Answer:
see explanation
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
x² + 12x + 11 = 0 ← in standard form
(x + 1)(x + 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 11 = 0 ⇒ x = - 11
The x- intercepts are x = - 11 and x = - 1
To find the y- intercept let x = 0, that is
f(0) = 0² + 12(0) + 11 = 0 + 0 + 11 = 11
The y- intercept is 11
Which points are on the perpendicular bisector of the given segment? Check all that apply. (−8, 19) (1, −8) (0, 19) (−5, 10) (2, −7)
Answer:
−8, 19
1, −8
-5, 10
Step-by-step explanation:
The points that are on the perpendicular bisector of the given segment is (-5, 10)
What is the perpendicular bisector?Perpendicular bisector is defined as a line that divide an angle into two equal parts at 90 degrees.
The standard equation of a line in point-slope form is expressed as
y-y₁ = m(x-x₁)
First, we need to get the equation of the line using the coordinates (-20, 0) and (10, 15)
Get the slope of the line
m = 15-0/10-(-20)
m = 15/30
m = 1/2
The slope of the line perpendicular to the line is -2
Using the point (-5, 10) on the line, get the equation in the point-slope form:
y - 10 = -2(x + 5)
y - 10 = -2x - 10
y + 2x = -10 + 10
y + 2x = 0
y = -2x
To check which points are on the perpendicular bisector of the given segment, hence;
For the coordinate (-8, 19)
19 = -2(-8)
19 ≠ 16 (This is not a solution)
For the coordinate (1, -8)
-8 = -2(1)
-8 ≠ -2 (This is not a solution)
For the coordinate (-5, 10)
10 = -2(-5)
10 = 10 (This is a solution)
Hence, the point that is on the perpendicular bisector of the given segment is (-5, 10)
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Which equations are correct? Select each correct answer.
Answers:
Option two, 5[tex]y^{4}[/tex](2[tex]y^{5}[/tex]) = 10[tex]y^{9}[/tex] and option 4, 5[tex]x^{3}[/tex](6[tex]x^{4}[/tex]) = 30[tex]x^{7}[/tex]
Step-by-step explanation:
O1 + O3 = incorrect, the powers have been multiplied together. Laws of indices suggest that if you are multiplying powers together, you must add them, not do 4 x 5 or 2 x 2.
Please remember:
2y squared x 3y cubed = 6y to the power 5
Answer:
Solution(s) : Option # 2 and # 4
Step-by-step explanation:
One quick way to identify which solutions are accurate would be adding the exponents of the terms provided ( b, y, c etc ). As you can see in each example two expressions are being multiplied, and hence the exponents of each term are being added.
Therefore the second and fourth example are correct, as 4 + 5 = 9, the co - efficient of y. And 3 + 4 = 7, the co - efficient of x.
Check :
[tex]5y^4\left(2y^5\right)[/tex] = [tex]5\cdot \:2y^{4+5}[/tex] = [tex]5\cdot \:2y^9[/tex] = [tex]10y^9[/tex]
[tex]5x^3\left(6x^4\right)[/tex] = [tex]5\cdot \:6x^{3+4}[/tex] = [tex]5\cdot \:6x^7[/tex] = [tex]30x^7[/tex]
Brittany uses the rowing machine and the stair machine at the gym for an exercise program. Her trainer wants her on an exercise program that meets these two conditions:
After 5 minutes of stretching, Brittany will exercise for 30 minutes, dividing her time between the two types of machines.
Brittany will spend three times as much time on the stair machine as on the rowing machine.
Write an equation.
Answer:
The equations are: [tex]x+ y = 30[/tex] and [tex]x = 3y[/tex].
Step-by-step explanation:
We are given that Brittany uses the rowing machine and the stair machine at the gym for an exercise program.
Let the time spend by Brittany on the stair machine be represented by the variable [tex]x[/tex].
and the time spend by Brittany on the rowing machine be represented by the variable [tex]y[/tex].
Now, there are two conditions stated by her trainer;
The first condition states that Brittany will exercise for 30 minutes, dividing her time between the two types of machines, that is;[tex]x + y = 30 \text{ minutes}[/tex]
The second condition states that Brittany will spend three times as much time on the stair machine as on the rowing machine, that is;[tex]x = 3y[/tex]
So, the equations are: [tex]x+ y = 30[/tex] and [tex]x = 3y[/tex].
These equations can be solved either using the substitution method or the elimination method.
Which would be appropriate compatible numbers to use to estimate (19 4/5)(4/6)
Answer:
Approximately 10
Step-by-step explanation:
19 / 5 Approximately 4
4 * 4 = 16
16 * 4 / 64
64 / 6 * = Approximately 10 / 10.6 ish
Actual Answer is 10.133
a rectangle has an area of 40 sq units , then length is 6 units greater than the width
Answer:
A=L*W
Let w be width
L=(w+6)
40=(w+6)*w
40= w^{2} +6w
w^{2} +6w-40=0
w^{2}+10w-4w-40=0
w(w+10)-4(w+10)=0
(w-4)(w+10)=0
w=4
Length= 10 units
Width=4 units
Step-by-step explanation:
Find the 98th term of the arithmetic sequence 14, 10, 6, ...
Answer:
-374
Step-by-step explanation:
We know that a₁ = 14 and the common difference = -4 so the explicit rule is aₙ = 14 + (n - 1) * (-4) = -4n + 18. a₉₈ = -4 * 98 + 18 = -374.
Answer:
Brainliest!!!!
Step-by-step explanation:
the equation is this...
y = -4x + 14
97 x -4 = -388
-388 + 14 = -374
you might wonder why I did 97... that is becuase 14 is the first term
rewrite 2^4=16 as a logarithmic equation
Answer:
The 1st option
Step-by-step explanation:
The base of a logarithm is always the base of an exponent. The log of part would always be the final powered form of the exponent. So, 2 would be the base, 16 would be logged, and 4 would be your answer.
Sam bright a Canada saving bond paying 4% interest and a provincial government bond paying 5% interest. He invested a total of $15,000 and earned $690 in interest in the first year. How much did he pay for each bond? PLEASE ANSWER THIS ASAP
Answer:
Money invested in Canada saving bond is $6000.
Money invested in provincial government bond is $9000.
Step-by-step explanation:
First of all, let us have a look at the formula for simple interest:
[tex]SI = \dfrac{P\times R\times T}{100}[/tex]
Where P is the amount invested
R is the rate of interest and
T is the time
We are given here, 2 bonds in which a total of $15000 were invested
Let money invested in Canada saving bond [tex]P_1[/tex], = $x
Rate of interest, [tex]R_1=4\%[/tex]
Time, [tex]T_1 = 1\ year[/tex]
[tex]SI_1 = \dfrac{P_1\times R_1\times T_1}{100}\\\Rightarrow \dfrac{x\times 4\times 1}{100} ..... (1)[/tex]
Let money invested in provincial government bond [tex]P_2[/tex], = $(15000-x)
Rate of interest, [tex]R_2=5\%[/tex]
Time, [tex]T_2 = 1\ year[/tex]
[tex]SI_2 = \dfrac{P_2\times R_2\times T_2}{100}\\\Rightarrow \dfrac{(15000-x)\times 5\times 1}{100} ..... (2)[/tex]
We are given that
[tex]SI_1+SI_2=$690\\\text{Using equations (1) and (2):}\\\\\Rightarrow \dfrac{4x}{100} + \dfrac{(15000-x)\times 5}{100} = 690\\\Rightarrow 4x + (75000-5x) = 69000\\\Rightarrow x = \$6000[/tex]
Money invested in Canada saving bond = $6000
Money invested in provincial government bond = $15000-$6000 = $9000
Rearrange to make x the subject
Answer:
[tex]x = \frac{3t}{b} [/tex]
for the following geometric sequence find the recursive formula. {1, -3, 9, ...}
Answer:
[tex]g_{n}=g_{n-1} *-3[/tex]
Step-by-step explanation:
A recursive formula is [tex]g_{n}=g_{n-1} *r[/tex]. N is the number of terms and r is the rate of change. R here equals -3 because you are multiplying by -3 eachtime. Therefore, the recursive formula is [tex]g_{n}=g_{n-1} *-3[/tex]
11(4x+13)+12x-17 PLZ HELP WILL HAVE MORE QUESTIONS. ANSWER ASAP
Answer:
56x + 126
Step-by-step explanation:
Step 1: Distribute
44x + 143 + 12x - 18
Step 2: Combine like terms
56x + 126
[tex]\text{Simplify the expression}\\\\11(4x+13)+12x-17\\\\\text{Use the distributive property}\\\\44x+143+12x-17\\\\\text{Combine like terms}\\\\\boxed{56x+126}[/tex]
Stephanie saw in an ad in the paper that her favorite kind of perfume was I feel for 25% off if the sale price was $15 what was the original price of the perfume
Answer: $20
Step-by-step explanation:
Here os the correct question:
Stephanie saw in an ad in the paper that her favorite kind of perfume was on sale for 25% off. If the sale price was $15, what was the original price of the perfume?
Let the original price of the perfume be y.
Since we are told that 25% is off, that means that 25% has been deducted from the original price. This can be written as:
y - (25% of y) = $15
y - (25/100 × y) = $15
y - 0.25y = $15
0.75y = $15
Divide both side by 0.75
0.75y/0.75 = $15/0.75
y = $20
The original price of the perfume is $20
How much x% sugar syrup can you make if you have 100 grams of sugar?
Answer:
100/x/100
Step-by-step explanation:
Step-by-step explanation: