![2(2x+1)-9.2x+4=0[tex] 2^2x + 1 - 9.2 ^x + 4 = 0 [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/DtwY3xMNmz4l8PLEtPeOmcWmw5BTLVfC.jpeg)
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[tex]\displaystyle\2^{2x+1}-9\cdot 2^x+4=0 \quad ; \qquad \boxed{ 2^x=t \; ; \; 2^{2x}=t^2} \\\\2t^2-9t+4=0 \\\\D=81-32 =49 \\\\ t_1=\frac{9+7}{4} =4 \\\\ t_2=\frac{9-7}{4} =\frac{1}{2} \\\\1) \ 2^x=4 \Longrightarrow x_1=2 \qquad 2) \ 2^x=2^{-1}\Longrightarrow x_2=-1 \\\\Answer: \boxed{x_1=2 \quad ; \quad x_2=-1}[/tex]
Related Questions
I you borrow 500 for 4 years at an annual interest rate of 6% HOW MUCH WILL YOU PAY altogether
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Answer:
620
amount= p+i , to find interest .I=500*4*6/100 =120 amount=500+120=620
someone help me please with this algebra homework
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Solve for xx. Round to the nearest tenth, if necessary.
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Answer:
x ≈ 7.1
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{x}[/tex] ( multiply both sides by x )
x × cos27° = 6.3 ( divide both sides by cos27° )
x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )
Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?
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Given:
Reese read twice as many pages Saturday than she read Sunday.
She read a total of 78 pages over the weekend.
To find:
The number of pages she read on Sunday.
Solution:
Let x be the number of pages she read on Sunday.
Reese read twice as many pages Saturday than she read Sunday. So, the number of pager she read on Saturday is 2x.
Total number of page she read over the weekend is:
[tex]Total=x+2x[/tex]
[tex]Total=3x[/tex]
She read a total of 78 pages over the weekend.
[tex]3x=78[/tex]
[tex]x=\dfrac{78}{3}[/tex]
[tex]x=26[/tex]
Therefore, Reese read 26 pages on Sunday.
Circle W has a radius of 20 in and right central angle, ZVWX. Find the length of vx. Leave your answer in terms of pi.
5
10
15
20
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Answer:
The length of the arc is 10 pi
Step-by-step explanation:
Mathematically, the length of an arc is calculated as;
theta/360 * 2 * pi * r
theta represents the central angle subtended by the arc which is a right angle according to the question (a right angle is 90 degrees)
r is the circle radius which is 20 inches
so we have the length of the arc as;
90/360 * 2 * pi * 20 = 40 pi/4 = 10 pi
if you want to make some money and do my acellus academy math and science subject in 1 day ill pay $25 dollars
Answers
Answer:
no tHank you hope someone can help
Step-by-step explanation:
Find the length of line segment XY, assuming that M is the midpoint of XY
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Answer:
Step-by-step explanation:
M is the midpoint. SO length of XM equals length of MY
MY = XM
9x + 12 = 5x + 8
Subtract 12 from both sides
9x = 5x +8 - 12
9x = 5x - 4
Subtract 5x from both sides
9x - 5x = -4
4x = -4
Divide both sides by 4
x = -4/4
x = -1
XY = 5x + 8
= 5*(-1) + 8
= -5 + 8
XY = 3
MY = 9x + 12
= 9*(-1)1 + 12
= -9 + 12
MY = 3
X Y = 3+3
XY = 6
Select the correct answer. Help
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Helppppp and explain !!!!
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Answer:
dat I don't know the answer sorry I could not answer u
what is the equation of the parabola?
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If < A and < B form a linear pair, and < A = x - 13 degrees, and < B = x + 7 degrees, then find x.
Select one:
a. 124
b. 101
c. 46
d. 93
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Answer:
d
Step-by-step explanation:
A linear pair sum to 180° , then
x - 13 + x + 7 = 180
2x - 6 = 180 ( add 6 to both sides )
2x = 186 ( divide both sides by 2 )
x = 93 → d
1. Slope and the properties of perpendicular and parallel can be used to confirm that a polygon is a specific type of
quadrilateral.
What types of quadrilaterals can you determine by using these properties? List at least two types of quadrilaterals.
2. Choose one type of quadrilateral from your answer to Question 1. Explain in complete sentences how you can use
properties of perpendicular and parallel lines, together with slope, to confirm that a given polygon is the type of
quadrilateral you chose. Be sure to clearly state the properties that you need to use.
Please number your responses to the questions as they are shown (1 and 2).
NOTE from Ms. Kliban:
I found this answer on the Internet. *If it were an original answer, below is how I would grade it and why
1. The two would be rectangle and trapezium
2. You can determine with the properties that are given, that it's a polygon because with the slope already known that gives
a in to see which lines are perpendicular to which lines and which aren't. Also, with the properties you can tell if everything
Is parallel lines with the slope formula. Some slopes might be different but doesn't mean the polygon Isn't perpendicular
because two sides can have the same slope and the other two won't
GRADE: First off, in the United States, we don't use the word "trapezlum."
For part 2, it says, you can determine with the properties that are given." What properties? There are no properties given.
There are shapes. The next thing said in part 2 is that the slope is already known. No, it's not. You have to find the slope.
PLEASE HELP!!!!! 70 points !!!!
The grammar is bumpy. In other words, I stumbled over it when I tried to read it.
In order to do well on this assignment, part one only needs to have two quadrilaterals stated. You don't even have to have it
In a sentence.
For part 2. you do need to use complete sentences. You need to explain how to find slope and why you need to find the
slope. Then also explain how parallel and perpendicular lines help you to make sure you have the shape you stated in part
sat
Answers
Answer: Rectangle and Trapezium
Step-by-step explanation:
If you have the slopes, then you can tell when two lines are parallel.
A rectangle has two pairs of parallel sides
A trapezium has exactly one pair of parallel sides
We can determine whether a quadrilateral is a rectangle or a trapezium using the slope and the properties of parallel and perpendicular lines.
2. How are the slopes of perpendicular sides related?Product of the slopes of perpendicular lines = -1.
M₁ * M₂ = -1 .
How are the slopes of parallel sides related?Slopes of parallel lines are equal.
M₁ = M₂.
How do we determine a rectangle?Suppose we have a quadrilateral ABCD.
AB and CD are one pair of opposite sides.
BC and DA are another pair of opposite sides.
AB is adjacent to BC. BC is adjacent to CD. CD is adjacent to DA. DA is adjacent to AB.
Slope AB = M₁
Slope BC = M₂
Slope CD = M₃
Slope DA = M₄
For ABCD to be a rectangle, by properties opposite sides need to be parallel and adjacent sides need to be perpendicular.
∴ If M₁ = M₃, M₂ = M₄ (for opposite sides to be parallel)
and if M₁.M₂ = -1, M₂.M₃ = -1, M₃.M₄ = -1, and M₄.M₁ = -1 (for adjacent sides to be perpendicular) then the given quadrilateral ABCD is a rectangle.
Learn more about quadrilaterals, the slope of parallel lines, and the slope of perpendicular lines at
https://brainly.com/question/23935806
https://brainly.com/question/26172639
https://brainly.com/question/1362601
#SPJ2
Which table represents a linear function?
Answers
Answer:
C
Step-by-step explanation:
The slope of C is 3/2 and it stays consistent unlike the other ones.
A) { -3 , -1 , 1, 3 , 6 }
B) { 3, -1 , 2, 0, -2}
C) all real numbers
D) {3,-2,-1,0,1,2,3,4,5,6,7,8}
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Domain is always the X input or left side of a relation. Range is Y/ f(x) input or right side of a relation
Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is
Look at image for reference
Answers
Answer:
(3)11
Step-by-step explanation:
We are given that
[tex](x^2-12x+35)(x^2+10x+24)=504[/tex]
We have to find the sum of positive roots of the equation.
[tex]x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504[/tex]
[tex]x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504[/tex]
[tex]x^4-2x^3-61x^2+62x+840-504=0[/tex]
[tex]x^4-2x^3-61x^2+62x+336=0[/tex]
Factor of 336
2,3,4,6,8,7,
Let x=2
[tex]2^4-2^4-61(2^2)+62(2)+336\neq0[/tex]
x=2 is not the root of equation
x=-2
[tex](-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0[/tex]
Hence x=-2 is the root of equation.
x+2 is a factor of equation.
x=3
[tex]3^4-2(3^3)-61(3^2)+62(3)+336=0[/tex]
Therefore, x=3 is the root of equation.
[tex](x+2)(x-3)(x^2-x-56)=0[/tex]
[tex](x+2)(x-3)(x^2-8x+7x-56)=0[/tex]
[tex](x+2)(x-3)(x(x-8)+7(x-8))=0[/tex]
[tex](x+2)(x-3)(x-8)(x+7)=0[/tex]
[tex]x-8=0\implies x=8[/tex]
[tex]x+7=0\implies x=-7[/tex]
Positive roots are 3 and 8
Sum of positive roots=3+8=11
Option (3) is true.
which values are soloutions to the inequality -3x - 4 < 2 ? check all of the boxes that apply
Answers
Given:
The inequality is:
[tex]-3x-4<2[/tex]
To find:
The values that are solutions to the given inequality.
Solution:
We have,
[tex]-3x-4<2[/tex]
Adding 4 on both sides, we get
[tex]-3x-4+4<2+4[/tex]
[tex]-3x<6[/tex]
Divide both sides by -3 and change the inequality sign because -3 is a negative value.
[tex]\dfrac{-3x}{-3}>\dfrac{6}{-3}[/tex]
[tex]x>-2[/tex]
Therefore, all the real values greater than -2 are the solutions to the given inequality.
The equation of line r is y = 1/2 * x + 1 line runs parallel to line r and passes through (2, 5) what would be the equation of line 8 ?help please
Answers
Answer:
x - 2y + 8 = 0
Step-by-step explanation:
that is the procedure above
solve the system of equations using the substitution method pls show work
4x+y=7
3x+2y=9
Answers
Answer:
x = 1 ; y = 3Step-by-step explanation:
[tex]4x + y = 7 \\ y = 7 - 4x[/tex]
Now we know the value of y is 7 - 4x we plug this value to the second equation with y, So,
[tex]3x + 2(7 - 4x) = 9 \\ 3x + (14 - 8x) = 9 \\ - 5x = 9 - 14 \\ - 5x = - 5 \\ x = \frac{ - 5}{ - 5} \\ x = 1[/tex]
Now to find the value of y we use the first equation
[tex]y = 7 - 4x \\ y = 7 - 4(1) \\ y = 7 - 4 \\ y = 3[/tex]
Hope this helps you :)
Answer:
x = 6/5 or 1.2 y = 11/5 or 2.2
Step-by-step explanation:
4x + y = 7
y = -4x + 7
y = 7 - 4x
3x + 2y = 9
3x + 2(7 - 4x) = 9
3x + 14 - 8x = 9
-5× + 15 = 9
-5x = 9 - 15
-5x = -6
x = -6/-5
x = 6/5
4x + y = 7
4(6/5) + y = 7
24/5 + y = 7
y = 7 - 24/5
y = 35/5 - 24/5
y = 11/5
A company borrows $100,000 for 5 years at a simple interest rate of 10.5%. Find the interest paid on the loan
The interest paid on the loan is ?
The total amount paid is ?
Answers
Answer:
$52,500
$152,500
Step-by-step explanation:
$100,000 * .105 = $10500
Si 4/9 de los adolencentes que confirmaron su asitencia fueron varones y 4/5 de las mujeres a pesar que confirmaron su asistencia no participaron y 24 que confirmaron su asistencia si participaron ¿cuantos adolecentes en total confirmaron su asitencia?¿Cuantos adolencentes varones confirmaron su asistencia?
Answers
Answer:
216 adolescentes confirmaron su asistencia, de los cuales 120 fueron mujeres y 96 varones.
Step-by-step explanation:
Dado que 4/9 de los adolescentes que confirmaron su asistencia fueron varones, y 4/5 de las mujeres a pesar que confirmaron su asistencia no participaron, y 24 que confirmaron su asistencia si participaron, para determinar cuántos adolescentes en total confirmaron su asistencia y cuántos adolescentes varones confirmaron su asistencia se deben realizar los siguientes cálculos:
5/9 x 1/5 = 24
5/45 = 24
1/45 = 4.8
4.8 x 45 = 216
216 / 9 x 5 = 120
216 / 9 x 4 = 96
Por lo tanto, en total 216 adolescentes confirmaron su asistencia, de los cuales 120 fueron mujeres y 96 varones.
given the polynomial : (3x+4)^5. find the coefficient of x³ !
Answers
Answer:
[tex] \displaystyle 4320 {x }^{3} [/tex]
Step-by-step explanation:
to solve binomials like this there's a way called binomial theorem given by
[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
but for this question we need the following part
[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]
from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute
[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]
simplify which yields:
[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]
and we are done!
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle.
Are the two triangles similar. If so, State how
Answers
Answer:
SAS
Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)
Please tell me the ans fast
Answers
Answer:
B
Step-by-step explanation:
mgh=PE
(5)(9.8)(2.5)=pe
122.5j=pe
is the answer to your question
Missy’s rotation maps point K(17, –12) to K’(12, 17). Which describes the rotation?
270 degrees counterclockwise rotation
90 degrees counterclockwise rotation
90 degrees clockwise rotation
180 degrees rotation
Answers
it's a 90 degree counterclockwise rotation around the origin (0,0).
see the screenshot for illustration
Answer:
B.
Step-by-step explanation:
Christopher's car can drive 230 miles on a full tank of gas. He plans to drive with a full tank from Austin to Dallas, which is 195 miles. How many miles will be left once he arrives in Dallas?
Answers
Answer:
35 miles
Step-by-step explanation:
Total Miles driven at full tank = 230 miles
Miles drive at full tank from Austin to Dallas = 195 miles
How many miles will be left once he arrives in Dallas?
Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas
= 230 miles - 195 miles
= 35 miles
PLEASE ANSWER CORRECTLY FOR BRAINLIEST:
25.
26.
27.
29.
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Step-by-step explanation:
25.
[tex] \frac{t}{5} = b[/tex]
where b is the no. if 5 dollar bills.
26.
[tex]x +( x + 2) +( x + 4) = x + (x + 2)[/tex]
[tex]3x + 6 + 9 = 2x + 2[/tex]
[tex]3x + 15 = 2x + 2[/tex]
[tex]x + 15 = 2[/tex]
[tex]x = - 13[/tex]
Since x=-13 the intergers are
[tex] - 13[/tex]
[tex] - 11[/tex]
[tex] - 9[/tex]
27.
Represent the function as
[tex]x + x + 6 = 44[/tex]
[tex]2x + 6 = 44[/tex]
[tex]2x = 38[/tex]
[tex]x = 19[/tex]
The shorter piece should be 19 inches.
28.
Solve for h.
[tex]s = 2\pi \times rh + 2\pi {r}^{2} [/tex]
[tex]s - 2\pi {r}^{2} = 2\pi \times rh[/tex]
[tex] \frac{s - 2\pi {r}^{2} }{2\pi \times r} = h[/tex]
29.
[tex] \frac{16 + x}{2} \times 6 = 108[/tex]
[tex] \frac{16 + x}{2} = 18[/tex]
[tex]16 + x = 36[/tex]
[tex]x = 20[/tex]
sketch the graph of y² = -2x + 5
Answers
Answer:
[tex] {y}^{2} = - 2x + 5[/tex]
Step-by-step explanation:
vertex = [tex]( \frac{5}{2} \: ,0)[/tex]
Hope it is helpful....Is the number of hits to a website in a day a discrete random variable, a continuous random variable, or not a random variable?
Answers
Answer:
The random variable is discrete. :)
Step-by-step explanation:
Which point on the number line represents a drop in temperature of 3 degrees from 0 degrees?
Answers
Answer:
Point A
Step-by-step explanation:
The question is asking for a drop in 3 degrees. That means whatever point we start on, we subtract 3 from it. We start on 0, so 0-3=-3. That is point A.
Answer:
A
Step-by-step explanation: