Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{1-\sqrt{5} }{1+\sqrt{5} }[/tex]
Multiply the numerator and denominator by the conjugate of the denominator
The conjugate of 1 + [tex]\sqrt{5}[/tex] is 1 - [tex]\sqrt{5}[/tex], hence
[tex]\frac{(1-\sqrt{5})(1-\sqrt{5}) }{(1+\sqrt{5})(1-\sqrt{5}) }[/tex]
Expand numerator/ denominator
= [tex]\frac{1-2\sqrt{5}+5 }{1-5}[/tex]
= [tex]\frac{6-2\sqrt{5} }{-4}[/tex]
= [tex]\frac{6}{-4}[/tex] + [tex]\frac{-2\sqrt{5} }{-4}[/tex]
= - [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] [tex]\sqrt{5}[/tex]
Answer:
-3/2 + (1/2)*sqrt(5)
Note: a=-3/2 , b=1/2 , c=5
Step-by-step explanation:
I think this is meant to be written as (1-sqrt(5))/(1+sqrt(5)).
First step: Multiply top and bottom by the conjugate of the bottom which is 1-sqrt(5).
When you multiply conjugates, you do have to do the whole foil thing... just do first and last because the others will cancel.
So what I'm saying is when multiply (1+sqrt(5))(1-sqrt(5)) you will get 1-5=-4.
Second step: Multiply top out... you have to do the whole foil here because you aren't multiplying conjugates. So (1-sqrt(5))(1-sqrt(5))=1-sqrt(5)-sqrt(5)+5=
1-2sqrt(5)+5=6-2sqrt(5).
Third step: Second step/first step =(6-2sqrt(5))/-4
Fourth step: Separate fraction 6/-4 - 2sqrt(5)/-4
Fifth step: Simplify each fraction: -3/2 + (1/2)*sqrt(5)
Sixth step: If you compare the form you want it in to the form I wrote my answer in, then you should see that a=-3/2 , b=1/2 , c=5
what is the measure or angle C?
•25 degrees
•30 degrees
•60 degrees
•75 degrees
Answer:
25
Step-by-step explanation:
look B=C
so,
A+B+C=180 Sum of all <s of Tri
x+5+3x+3x=180
7x=175
x=175÷7
x=25
Answer: A or 25
Step-by-step explanation:
did the exam on edge 2020
Which term describes lines that intersect at 90 degrees angles
Answer:
They would be perpendicular because the lines intersect at a ninety degree angle. Hope this helps! Please mark brainliest!
Step-by-step explanation:
Follow below steps:
The term that describes lines that intersect at 90-degree angles is perpendicular. Lines that are perpendicular to each other form four angles at the point of intersection. Each of these angles is a right angle, which measures 90 degrees. This is a fundamental concept in geometry, which is a branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.
For example, in the context of a coordinate plane, the x-axis and y-axis are perpendicular to each other. Moreover, theorems in geometry further explain the properties of perpendicular lines, such as the fact that if a line segment is drawn joining the extremities of two equal lines which are perpendicular to a given line, the joining segment is bisected at right angles by a third perpendicular line.
what is the solution set of the quadratic inequality x^2-5< or equal to 0
[tex]x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle[/tex]
For this case we must indicate the solution of the following inequality:
[tex]x ^ 2-5 \leq0[/tex]
Adding 5 to both sides of the inequality:
[tex]x ^ 2\leq5[/tex]
We apply square root on both sides of the inequality to eliminate the exponent:
[tex]x \leq\pm \sqrt {5}[/tex]
So, we have two solutions:
[tex]x\leq \sqrt {5}[/tex]
Since it is an inequality, the sign for the negative portion is changed:
[tex]x\geq- \sqrt {5}[/tex]
Answer:
[tex]x\leq \sqrt {5}\\x\geq-\sqrt {5}[/tex]
PLEASE someone help me with maths
You are on the right tracks.
Since angle ABC is a right angle, that means lines AB and BC are perpendicular.
Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.
You have already worked out the gradient of AB ( 1/2) (note it's easier to leave it as a fraction)
Now lets get the gradient of BC:
[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]
Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:
[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]
So:
[tex]\frac{5-k}{2}=-2[/tex] (Now just solve for k)
[tex]5-k=-4[/tex]
[tex]-k=-9[/tex] (now just multiply both sides by -1)
[tex]k = 9[/tex]
That means the coordinates of C are: (4, 9)
We can now use this to work out the gradient of line AC, and thus the equation:
Gradient of AC:
[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]
Now to get the equation of the line, we use the equation:
y - y₁ = m( x - x₁)
Let's use the coordinates for A (-2, 1), and substitute them for y₁ and x₁ and lets substitute the gradient in for m:
y - y₁ = m( x - x₁)
[tex]y - 1=\frac{4}{3}(x +2)[/tex] (note: x - - 2 = x + 2)
Now lets multiply both sides by 3, to get rid of the fraction:
[tex]3y - 3 = 4(x+2)[/tex] (now expand the brackets)
[tex]3y - 3 = 4x+8)[/tex]
Finally, we just rearrange this to get the format: ay + bx = c
[tex]3y - 3 = 4x+8[/tex]
[tex]3y = 4x+11[/tex]
[tex]3y - 4x = 11[/tex]
And done!:
________________________________
Answer:
The equation of a line that passes through point A and C is:
[tex]3y - 4x = 11[/tex]
Which mapping represent a relation is a function PLEASE HELP ASAP
Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.
Find the 11th term of this sequence -10, 20, -40
Answer:
Step-by-step explanation:
the nth term of the geometric sequence is : An =A1 × r^(n-1)
A1 = -10
r= -40/20=20/-10=-2
n =11
A11 = -10× (-2)^(11-1)
A11 = -10× (-2)^(10)
A11 = - 10240
Answer:
-10,240.
Step-by-step explanation:
This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.
The nth term = a1r^(n-1) where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)
= -10 * 1024
= -10,240.
Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?
f(x) = x + 4
f(x) = x + 6
f(x) = x – 10
f(x) = x – 1
Answer:
[tex]\large\boxed{f(x)=x+4}[/tex]
Step-by-step explanation:
[tex]y-8=(x-4)\\\\y-8=x-4\qquad\text{add 8 to both sides}\\\\y-8+8=x-4+8\\\\y=x+4\to f(x)=x+4[/tex]
Find the value of z.
Answer:
[tex]\large\boxed{\dfrac{50}{3}}[/tex]
Step-by-step explanation:
If the polygons are similar, then the corresponding sides are in proportion:
[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex] cross multiply
[tex]12z=(10)(20)[/tex]
[tex]12z=200[/tex] divide both sides by 12
[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]
The equation below describes a circle. What are the coordinates of the center of the circle? (X-6)^2+(y+5)^2=15^2
Answer:
Step-by-step explanation:
6,-5 ON APEXXXXX
Answer: (6, -5)
Step-by-step explanation:
The general equation of a circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.
Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]
[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]
Comparing to the general equation of circle , we get
[tex](h,k)=(6, -5)[/tex]
Hence, the coordinates of the center of the circle = (6, -5)
Which expression best estimates 6 3/4 divided by 1 1/2?
Answer:
7/2
Step-by-step explanation:
Round 6 3/4 to 7
Round 1 1/2 to 2
7 divided by 2
=7/2
roumd 33 to the nearest 100
Answer:
Step-by-step explanation:
Trick question. Good to know.
0 is the closest 100.
33 will round to 0
Find the value of x in each of the following exercises:
Check the picture below.
let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.
[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]
Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,1). What is the distance from B to B’?
Answer:
The distance from B to B’ is [tex]5\ units[/tex]
Step-by-step explanation:
we know that
In a translation the shape and dimensions of the figure are not going to change.
therefore
AA'=BB'=CC'=DD'
Find the distance AA'
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(1,5)\\A'(-2.1)[/tex]
substitute the values
[tex]AA'=\sqrt{(1-5)^{2}+(-2-1)^{2}}[/tex]
[tex]AA'=\sqrt{(-4)^{2}+(-3)^{2}}[/tex]
[tex]AA'=\sqrt{25}[/tex]
[tex]AA'=5\ units[/tex]
therefore
[tex]BB'=5\ units[/tex]
Rewritten in vertex form please!!! Asap!!!
Answer:
vertex form: [tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]
B correct
Step-by-step explanation:
[tex]y=(x+3)^2+(x+4)^2[/tex]
[tex]y=x^2+9+6x+x^2+16+8x[/tex]
[tex]y=2x^2+14x+25[/tex]
[tex]y=2(x^2+7x)+25[/tex]
[tex]y=2(x^2+7x+\dfrac{49}{4}-\dfrac{49}{4})+25[/tex]
[tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = (x + 3)² + (x + 4)² ← expand and simplify
= x² + 6x + 9 + x² + 8x + 16
= 2x² + 14x + 25
To obtain vertex form use the method of completing the square
The coefficient of the x² term must be 1
Factor out 2 from 2x² + 14x
y = 2(x² + 7x) + 25
add/ subtract ( half the coefficient of the x- term )² to x² + 7x
y = 2(x² + 2([tex]\frac{7}{2}[/tex]) x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] ) + 25
y = 2(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{2}[/tex] + [tex]\frac{50}{2}[/tex]
y = 2(x + [tex]\frac{7}{2}[/tex] )² + [tex]\frac{1}{2}[/tex]
he graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. Which statement about the domain and range of each function is correct? The range of the transformed function and the parent function are both all real numbers greater than or equal to 4. The domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. The range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. The domain of the transformed function and the parent function are both all real numbers.
Answer:
Out of the four, the only statement true about the parent and the transformed function is:
"The domain of the transformed function and the parent function are all real numbers."
Step-by-step explanation:
Parent function:
f(x) = |x|
Applying transformations:
1. Stretched by a factor of 0.3:
f(x) = 3|x|
2. Translated down 4 units:
f(x) = 3|x| - 4
Transformed function:
f(x) = 3|x| - 4
We can see that:
Range of the parent function = All real numbers greater than or equal to 0.
Range of the transformed function = All real numbers greater than or equal to -4.
Domain of the parent and the transformed function is same and equal to all real numbers.
Hence, the first three statements are wrong and the fourth one is true.
Answer:
The domain of the transformed function and the parent function are both all real numbers.
Step-by-step explanation:
Stretching a function by any factor doesn't change either its domain nor its range.
Translating up or down a function changes its range. In this case, the lowest value the parent function can take is 0 when x=0; after translation, for x = 0 then f(x) = -4. Therefore,
f(x) = |x|
domain = all real numbers
range = [0, infinity)
f(x) = 0.3*|x| - 4
domain = all real numbers
range = [-4, infinity)
Which best describes a system of equations that has no solution?
Answer:
i think the answer is undefined
Step-by-step explanation:
Answer: 1. inconsistent, 2. infinite, 3. (4, -1), 4. exactly two solutions.
Step-by-step explanation: HOPE THIS HELPS. ;))))
Which of the following is the ratio between the number of successes and the number of possible outcomes of an event?
A line goes through the points
(−5,−8)
and
(5,2)
. Find its slope.
Answer:
Slope is 1
Step-by-step explanation:
Rise over Run. Delta y over Delta x. -8-2/-5-5 = -10/-10 = 1
Determine which type of transformation is illustrated in the figure. If none of the listed transformations apply, choose "none of these."
Answer:
15 ounces
Step-by-step explanation:
If there is 165 ounces in 11 boxes then divide the ounces by the boxes to get the amount of ounces in one box.
Answer:
15
Step-by-step explanation:
please help!! Thanks!!
Answer:
a = sqrt(33)
Step-by-step explanation:
a^2 + 4^2 = 7^2
a^2 + 16 = 49
a^2 = 33
a = sqrt(33)
There are 19 sticks of gum left in one packet, and 6 sticks of gum in another packet that are going to be split evenly between 2 people. How many sticks of gum does each person get? Choose the correct answer from the choices below.
[tex]19 + 6 = 25 \div 2 = 12.5[/tex]
Answer:
12.5
Step-by-step explanation:
19+6=25 , 25÷2= 12.5
cube root of y equals 4
Answer:
y = 64Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]
Solve the given inequality. If necessary, round to four decimal places.
13^4a < 19
Answer:
The solution of the inequality is a < 0.2870
Step-by-step explanation:
* Lets talk about the exponential function
- the exponential function is f(x) = ab^x , where b is a constant and x
is a variable
- To solve this equation use ㏒ or ㏑
- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)
* Lets solve the problem
∵ 13^4a < 19
- To solve this inequality insert ㏑ in both sides of inequality
∴ ㏑(13^4a) < ㏑(19)
∵ ㏑(a^n) = n ㏑(a)
∴ 4a ㏑(13) < ㏑(19)
- Divide both sides by ㏑(13)
∴ 4a < ㏑(19)/㏑(13)
- To find the value of a divide both sides by 4
∴ a < [㏑(19)/㏑(13)] ÷ 4
∴ a < 0.2870
* The solution of the inequality is a < 0.2870
Answer:
a < 0.2870
Step-by-step explanation:
We are given the following inequality which we are to solve, rounding it to four decimal places:
[tex] 1 3 ^ { 4 a } < 1 9 [/tex]
To solve this, we will apply the following exponent rule:
[tex] a = b ^ { l o g _ b ( a ) } [/tex]
[tex]19=13^{log_{13}(19)}[/tex]
Changing it back to an inequality:
[tex]13^{4a}<13^{log_{13}(19)}[/tex]
If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].
Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].
[tex]4a<log_{13}(19)[/tex]
[tex]a<\frac{log_{13}(19)}{4}[/tex]
a < 0.2870
What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?
ANSWER
The radius is 4
EXPLANATION
The given equation is:
[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]
We complete the square to get the expression in standard form:
[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]
[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]
We factor using perfect squares to get:
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]
This implies that,
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]
Comparing to
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The radius is r=4
Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?
Answer: [tex]945\ pixels[/tex]
Step-by-step explanation:
We know that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore, we can find the scale factor.
Divide the width of the new photo by the width of the original photo. Then the scale factor is:
[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]
The final step is to multiply the height of the original photo by the scale factor calculated.
Therefore the height of the new photo will be:
[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]
Answer:
945 pixels.Step-by-step explanation:
Givens
The original photo dimensions are (800 wide x 600 high )pixelsThe new photo is 1,260 pixels wide.First, we need to find the scale factor by dividing
[tex]s=\frac{1260}{800}=1.575[/tex]
Then, we multiply the height by the scale factor
[tex]600 \times 1.575 = 945[/tex]
Therefore, the new height is 945 pixels.
Factor this polynomial completely.
12x^2+ x-6
Answer:
(3 x - 2) (4 x + 3)
Step-by-step explanation:
Factor the following:
12 x^2 + x - 6
Factor the quadratic 12 x^2 + x - 6.
The coefficient of x^2 is 12 and the constant term is -6.
The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.
So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):
3 (3 x - 2) + 4 x (3 x - 2)
Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):
Answer: (3 x - 2) (4 x + 3)
The answer is (3 x - 2) (4 x + 3).
Polynomials
Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.
Factor the following:
[tex]$$12x^{2}+x-6$$[/tex]
Factor the quadratic
[tex]$12x^{2} +x-6$[/tex]
The coefficient [tex]x^{2}[/tex] is 12 and the constant term is -6.
The product of 12 and -6 is -72.
The factors of -72 which sum to 1 exist at -8 and 9.
So
[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]
[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]
[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]
Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)
Hence, The answer is (3 x - 2) (4 x + 3).
To learn more about Polynomials refer to:
https://brainly.com/question/13769924
#SPJ2
What’s the answer help plz
9 x 5 = 45 -> total $ on Friday
99 - 45 = 54 -> total $ on Saturday
54 ÷ 9 = 6 hours
Answer:
A, B.
Step-by-step explanation:
If Matt charges $9 an hour, and he worked for 5hrs on Friday night, then that means we have to do multiplication.
So, $9x5=$45.
And then it says he babysat again on Saturday, and in TOTAL, he earned $99.
So, if he already made $45, and he has a total of $99, then we need to work backwards to figure out how much he made on Saturday.
$99-$45=$54
So, he made $45 on Friday and $54 on Saturday.
Now, we continue to work backwards and divide how much he made on Saturday ($54), by how much he charges per hour.
$54/9=6
So, Matt worked a total of 6hrs on Saturday.
What are the roots of the polynomial ?
Answer:
B and E
Step-by-step explanation:
By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.
Answer:
B & E
Step-by-step explanation:
see attached
Please explain now thanks
Answer:
24x - 20
Step-by-step explanation:
4(6x-5)
= 4(6x) - 4(5).............. (Distributive property)
= 24x - 20 (Ans)
Hello There!
The answer would be (24x-20)
We use order of operations so first we would multiply 4 by 6 and get 24x
then, we would multiply 4 by -5 and get -20
Your answer would be 24x - 20
Identify the method that will be used in solving for x.
5+x=
distributive property
multiplication property of equality
division property of equality
subtraction property of equality
Answer:
subtraction property of equality
Step-by-step explanation:
The equation in the question is incomplete, the complete equation is:
5 + x = 2
To solve this equation we have to use the subtraction property of equality, that is, if you subtract some number at both sides of the equal sign, the equation doesn't change. So:
5 + x - 5 = 2 - 5 (You must select a number which isolate x)
x = -3
And the answer is gotten.
d
ur welcome its right