Answer:
Discriminant D = -4 , no real solution
Step-by-step explanation:
Here our equation is
[tex]x^{2}-4x+5=0[/tex]
Discriminant (D)= [tex]b^2-4ac[/tex]
where
a = coefficient of term containing [tex]x^{2}[/tex]
b= coefficient of the term containing [tex]x[/tex]
c is the constant term
hence
a=1 , b =-4 and c=5
Hence
[tex]D=b^2-4ac\\D=(-4)^2-4*1*5\\D=16-20\\D=-4\\[/tex]
Hence D is less than 0 , therefore we do not have any real solution to this quadratic equation.
Answer:
b on edge-The discriminant is −4, so the equation has no real solutions.
Step-by-step explanation:
AB is tangent to \odot ⊙ O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth.
Answer:
r = 15.2
Step-by-step explanation:
Where AB meets the circle creates a right angle. This is a right triangle problem involving missing sides. This means that we will use Pythagorean's theorem to find the length of the radius. Pythagorean's theorem applies this way:
[tex]10^2+r^2=(r+3)^2[/tex]
Foiling the right side gives us the equation:
[tex]100 + r^2=r^2+6r+9[/tex]
When we combine like terms, we find the squared terms cancel each other out, leaving us with
100 = 6r + 9 and
91 = 6r so
r = 15.2
The function f(x) = 7 – 4x + x2 written in vertex form is f(x) = (x – 2)2 + 3. What is the axis of symmetry for the function? X = –3 x = –2 x = 2 x = 3
Answer:
x = 2
Step-by-step explanation:
The vertex form tells you the vertex is (x, y) = (2, 3). The vertical line through the vertex, x=2, is the axis of symmetry.
Answer:
x = 2
Step-by-step explanation:
took the test on edge
Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |x| ≤ 1, |y| ≤ 1}
Looks like [tex]f(x,y)=x^2+y^2-x^2y+7[/tex].
[tex]f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1[/tex]
[tex]f_y=2y-x^2=0\implies2y=x^2[/tex]
If [tex]x=0[/tex], then [tex]y=0[/tex] - critical point at (0, 0).If [tex]y=1[/tex], then [tex]x=\pm\sqrt2[/tex] - two critical points at [tex](-\sqrt2,1)[/tex] and [tex](\sqrt2,1)[/tex]The latter two critical points occur outside of [tex]D[/tex] since [tex]|\pm\sqrt2|>1[/tex] so we ignore those points.
The Hessian matrix for this function is
[tex]H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}[/tex]
The value of its determinant at (0, 0) is [tex]\det H(0,0)=4>0[/tex], which means a minimum occurs at the point, and we have [tex]f(0,0)=7[/tex].
Now consider each boundary:
If [tex]x=1[/tex], then[tex]f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4[/tex]
which has 3 extreme values over the interval [tex]-1\le y\le1[/tex] of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).
If [tex]x=-1[/tex], then[tex]f(-1,y)=8-y+y^2[/tex]
and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).
If [tex]y=1[/tex], then[tex]f(x,1)=8[/tex]
which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).
If [tex]y=-1[/tex], then[tex]f(x,-1)=2x^2+8[/tex]
which has 3 extreme values, but the previous cases already include them.
Hence [tex]f(x,y)[/tex] has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).
The function must first have its partial derivatives set to zero to find its critical points. Also, considering the given domain's boundaries with Lagrange multipliers can establish the function's maximum and minimum points.
Explanation:This function is a multivariable function and to find its extreme values within a specified domain you would use multivariable calculus methods. For the given function f(x, y) = x2 + y2 − x2y + 7, we first find its critical points by setting its partial derivatives equal to zero and then solve for x and y. Additionally, we need to consider the boundaries of the set {|x| ≤ 1, |y| ≤ 1} by using the method of Lagrange multipliers. The extreme values are obtained at the critical points within the domain, including the boundary.
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Philip has 0.5 (half) of a bar of chocolate .He lts Lena eat 0.25 of his chocolate .What fraction of the whole bar of chocolate does Lena eat?
Answer: Lena eats 1/4 of the whole bar
Step-by-step explanation:
Half of the bar is 50. A full bar would be 100%. If Phillip has half, amd Lena eats half of that half, she eats 0.25 out of 0.5. 0.5 is half of the whole bar, so 0.5×0.5 is 1, and if lena ate 0.25 of 1, that is 1/4.
Please answer this recent question CORRECTLY for 30 points and brainliest!!
Answer:
C. population; students
Step-by-step explanation:
Since every member of the population is asked, the survey is not a sample. If opinions are given equal weight, there are more students than staff, so we expect students to have more influence on results.
Answer:
C population, students
Step-by-step explanation:
Since everyone is asked the question, a population is used (sample only uses part). There are more students than staff, so students will have a bigger influence on the results
to describe a sequence of transformations that maps triangle ABC onto triangle a"b"c", a student starts with a reflection over the x-axis.how should the student complete the sequence of transformations to map triangle ABC onto triangle a"b"c"?
plz help
i dont quite get the question but...
i guess this is how it is.
Take the mirror image of∆ABC Through the a line through the point y=3.
The new ∆ABC would have point C=(4,2)
B=(3,-6) A=(1,-3)
Now shifting the ∆ABC one unit (i.e. 2 acc. to the graph as scale is 1 unit =2) towards right ( or adding 2 to the x coordinates of ∆ABC)
We get the Coordinates of triangle ABC as A=(3,-3) B=(5,-6) C=(6,2).
This coordinate is the same coordinates of ∆A"B"C".
Hope it helps...
Regards;
Leukonov/Olegion.
The frequency distribution below shows arrival delays for airplane flights. arrival delay (min) frequency (minus−60)-(minus−31) (minus−30)-(minus−1) 0-29 30-59 60-89 1010 2828 88 11 22 use the frequency distribution to construct a histogram. which part of the histogram depicts flights that arrived early, and which part depicts flights that arrived late?
The answer is in the attachment below!
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I don’t understand. Explain mate
what is the measure of XY?
XV is 1/2 a circle , which is equal to 180 degrees ( a full circle is 360).
ZW = WY, so ZV = VY = 43.
XY = XV-43 = 180 - 43 = 137
The answer is B. 137
Circle 1 is centered at (−4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes
The circles are similar because you can translate Circle 1 using the transformation rule (blank, blank) and then dilate it using a scale factor of blank.
If you translate circle 1 with the vector (6,-4), the center will become
[tex](-4,5)+(6,-4) = (-4+6,5-4)=(2,1)[/tex]
So, circles 1 and 2 are now concentric. The radii are, respectively, 2 and 6. This means that, if we dilate circle 1 with a scale factor of 3, its radius will become 6 as well.
After this two transformations, both circles will have center (2,1) and radius 6.
The transformation rule is (x+6, y-4).
We dilate by a factor of 3.
What is a circle?A circle is a perfectly round shape meaning any point around its curve is the same distance from its central point called the center
How to know what transformations can be applied to Circle 1 to prove that the circles are similar?Basically, we have two circlesFirstly we need to shift the center.
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).Again we need to dilate the circle.
Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.Find more about "Circles" here: https://brainly.com/question/17326298
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Please help me find the area of two similar octagons
Answer:
3:5
Step-by-step explanation:
The areas of two similar octagons are 9m² and 25m²
The scale factor of their areas is [tex]\frac{25}{9}[/tex] or 9:25
The scale factor of their side lengths is [tex]\sqrt{25/9}[/tex] or 3:5
ANSWER
3:5
EXPLANATION
The given similar octagons have areas 9 m² and 25m² .
Let the scale factor of their side lengths be in the ratio:
m:n
[tex] {( \frac{m}{n}) }^{2} = \frac{9}{25} [/tex]
We take square root of both sides to get;
[tex] \frac{m}{n} = \sqrt{ \frac{9}{25} } [/tex]
We simplify the square root to get
[tex] \frac{m}{n} = \frac{3}{5} [/tex]
Therefore the scale factor of their side lengths is 3:5
Need help with this math question PLEASE HELP
Answer:
(- 1, 4)
Step-by-step explanation:
The line x = 1 is a vertical line.
The point P(3, 4) is 2 units to the right of x = 1 ( 3 - 1 = 2 )
Hence the reflection will be 2 units to the left of x = 1, that is (1 - 2)
P'(- 1, 4)
The reflection of point P(3, 4) about the vertical line x = 1 is P'(-2, 4).
Reflection is a transformation that flips a figure over a line or a plane. It is a type of symmetry transformation that maintains the same shape and size of the object but changes its orientation with respect to the line or plane of reflection.
Given: Point P(3, 4).
The line x = 1 is a vertical line.
Now, let's find the reflection of point P(3, 4) about the vertical line x = 1:
To reflect a point about a vertical line, we reverse the sign of the x-coordinate while keeping the y-coordinate the same.
So, the reflection of P(3, 4) will be (-2, 4).
Hence, the reflection of point P(3, 4) is P'(-2, 4).
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NEED HELP WITH A MATH QUESTION TO FIND THE VALUE OF X
Answer:
x=6.5 cm
Step-by-step explanation:
The tangent meets the circle at right angles.
Therefore the triangle formed is a right triangle.
From the Pythagorean Theorem;
[tex]x^{2} +20.2^2=(x+14.7)^2[/tex]
We expand to obtain:
[tex]x^{2} +408.4=x^2+29.4x+216.04[/tex]
We group like terms to get:
[tex]x^{2} -x^2+408.4-216.04=29.4x[/tex]
We simplify now to get:
[tex]192.36=29.4x[/tex]
We divide both sides by 29.4 to get:
x=6.5 to the nearest tenth.
Lauren in making 15 liters of mimosas for a brunch banquet. Orange juice costs her $1.50 per liter and champagne costs her $12 per liter. How many liters of orange juice and how many liters of champagne should she use for the mimosas to cost Lauren $5 per liter?
Answer:
10 liters of orange juice5 liters of champagneStep-by-step explanation:
Let c represent the number of liters of champagne Lauren uses. Then (15-c) will be the number of liters of orange juice. The total cost of the mix will be ...
12c +1.50(15-c) = 5.00(15)
10.5c = 52.50 . . . . . subtract 22.50, simplify
52.50/10.5 = c = 5 . . . . divide by the coefficient of c
Then the amount of orange juice is ...
15 -c = 15 -5 = 10 . . . . liters
Lauren should use 5 liters of champagne and 10 liters of orange juice.
Triangle ABC has coordinates A(1,-1), B(0,2), and C(2,1) and it is reflected over the line y = x to form triangle A'B'C'. What are the coordinates of triangle A'B'C answer the question using complete sentences...please help
Answer:
The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
- ABC is a triangle, where A = (1 , -1) , B = (0 , 2) , C = (2 , 1)
- The Δ ABC reflected over the line y = x to form ΔA'B'C'
∵ The image of the point (x , y) after reflected across the line y = x
is (y , x)
∴ We will switch the coordinates of each point in Δ ABC to find the
coordinates of Δ A'B'C'
# Vertex A
∵ A = (1 , -1) ⇒ x = 1 , y = -1
∴ The x-coordinate of the image is -1
∴ The y-coordinate of the image is 1
∴ A' = (-1 , 1)
# Vertex B
∵ B = (0 , 2) ⇒ x = 0 , y = 2
∴ The x-coordinate of the image is 2
∴ The y-coordinate of the image is 0
∴ B' = (2 , 0)
# vertex C
∵ C = (2 , 1) ⇒ x = 2 , y = 1
∴ The x-coordinate of the image is 1
∴ The y-coordinate of the image is 2
∴ C' = (1 , 2)
* The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)
In 2014 the population of Kenya was estimated to be 45,121,040 with a growth rate of 2.7%. Question 1 Use the exponential growth formula to write an equation that estimates the population y in terms of the time t. Enter your answer in the box.
Answer:
y = 45,121,040×1.027^t
Step-by-step explanation:
An exponential growth equation is generally of the form ...
value at time t = (initial value)(growth factor)^t
where the growth factor is the multiplier for a period equal to one time unit.
Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...
y = 45,121,040×1.027^t . . . . where t = years after 2014
Felicity babysat 2 hours each night for 10 nights.She earned a total of $180 babysitting .Felicity wants to calculate her hourly rate.How much did felicity earn per hour babysitting
Answer:
$9 per hour
Step-by-step explanation:
given that falicity babysat for 2 hours each night for 10 nights
Total hours spent babysitting = 10 nights x 2 hours = 20 hours
hourly rate = total amount earned / total time spent babysitting
= $180 / 20 hrs = $9 per hour
Use the intersect method to solve: x^2+1=-x^2+9
Answer:
x={-2,2}
Step-by-step explanation:
Graph them when intersecting.
Algebraically:
x^2 + 1 = -x^2 + 9
Add x^2 on both sides and subtract 1 on both sides.
2x^2 = 8
Divide 2 on both sides
x^2 = 4
Square root on both sides
|x| = 2
Remove abs value by putting + or - on the other side
x = {-2,2}
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2,2
B in edge
I am taking the test
The surface area of sphere r is 565.2 units squared the surface of sphere s is 22680 units squared how many times larger is the radius of sphere s compared r
Answer:
[tex]\dfrac{r_s}{r_r}\approx 6.3346[/tex]
Step-by-step explanation:
The ratio of the radii is the square root of the ratio of the areas:
[tex]\dfrac{r_s}{r_r}=\sqrt{\dfrac{22680}{565.2}}\approx 6.3346[/tex]
The radius of sphere s is about 6.3346 times as large as the radius of sphere r.
To determine the ratio of the sizes of the radii of the two spheres based on their surface areas, you can use the ratios of the square roots of the surface areas. Using this method, the radius of Sphere S is found to be roughly 8 times larger than Sphere R
Explanation:The subject topic of this question is related to geometry, specifically looking at the relationship between the surface areas of two spheres and their respective radii. Given that the surface area (SA) of a sphere is given by the formula SA=4πr², you can set up a ratio for the radii.
The square roots of the ratios of the surface areas of the spheres will give us the ratio of the radii. In other words, sqrt(SA of sphere S/ SA of sphere R) = ratio of the radii. Substituting the given values, we get sqrt(22680/565.2) which approximately equals to 8.
Therefore, the radius of Sphere S is approximately 8 times larger than Sphere R.
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PLS HELP HOW DO U SLOVE THIS
Explanation:
There is nothing to "solve." This equation is a trig identity.
Often, it works well to express all trig functions in terms of sine and cosine. When you're trying to prove an identity, you usually pick one side to rearrange, and leave the other side alone. Here, we will rearrange the right side.
[tex]\csc\theta=\dfrac{\cot\theta+1}{\cos\theta+\sin\theta}\\\\\csc\theta=\dfrac{\dfrac{\cos\theta}{\sin\theta}+1}{\cos\theta+\sin\theta}=\dfrac{\left(\dfrac{\cos\theta+\sin\theta}{\sin\theta}\right)}{\cos\theta+\sin\theta}=\dfrac{1}{\sin\theta}\\\\\csc\theta=\csc\theta[/tex]
Geometry PEOPLE HELP
Answer: second option.
Step-by-step explanation:
Given the transformation [tex]T:(x,y)[/tex]→[tex](x-5,y+3)[/tex]
You must substitute the x-coordinate of the point A (which is [tex]x=2[/tex]) and the y-coordinate of the point A (which is [tex]y=-1[/tex]) into [tex](x-5,y+3)[/tex] to find the x-coordinate and the y-coordinate of the image of the point A.
Therefore, you get that the image of A(2,-1) is the following:
[tex](x-5,y+3)=(2-5,-1+3)=(-3,2)[/tex]
You can observe that this matches with the second option.
what is the ratio for the surface areas of rectangle prisims shown below given that they are similar and that the ratio of their edge lengths is 7:3
Answer:
B. 49:9
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of edge lengths:
7² : 3² = 49 : 9
The question is stated in the picture. These problems I do not understand at all. I appreciate any help provided, thank you.
Answer:
b. 10
Step-by-step explanation:
For the most part, these are problems in addition. The measures of the different angles add up according to the relationships given in the problem statement.
From the picture, you can tell that ∠JKN is the sum of ∠1 and ∠2, which are said to be equal (congruent). That is, ∠1 has a measure that is half of that of ∠JKN.
Since ∠JKN is a right angle, 90°, and the measure of ∠1 is half that, m∠1 is 45°.
So, to find t, we equate the given expression for m∠1 to 45 and solve.
4t +5 = 45
4t = 40 . . . . . subtract 5
t = 10 . . . . . . . divide by 4 . . . . . matches answer choice B
What is the factorization of 121b4 − 49? (11b − 7)(11b − 7) (11b + 7)(11b − 7) (11b2 − 7)(11b2 − 7) (11b2 + 7)(11b2 − 7)
Answer:
Step-by-step explanation:
121b^4 - 49 is a "difference of squares."
Formula for factoring a "difference of squares:"
a² - b² = (a - b)(a + b)
So: rewrite your 121b4 - 49 as 11²b^4 - 7² = (11b²)² - 7²
= (11b² - 7)(11b² + 7)
This answer matches the last of the four given answer choices.
6. A restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts. How many different lunch specials are possible?
Show your work
Answer:
The answer is 420 lunch specials
Step-by-step explanation:
10×7=70 70×6=420
Answer:
the total different lunches is 420
Step-by-step explanation:
Given that:
Number of appetizers: 7Number of entrees: 10Number of desserts: 6As we know that, a customer can choose 3 of the above items in their lunch and it is a combination problem.
So we have:
P(A)The possible outcome when a customer choose appetizer : 7 P(E)The possible outcome when a customer choose entree: 10P(D)The possible outcome when a customer choose desert: 6So the total different lunches is:
P(A) *P(E)*P(D)
= 7*10*6
= 420
Hope it will find you well.
Perform the indicated operation. 3m-6/4m+12*m^2+5m+6/m^2-4
A) 1/4
B)3/4
C)4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{3m-6}{4m+12} \cdot \frac{m^2+5m+6}{m^2-4}[/tex]
We factor to get:
[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+2)(m+3)}{(m-2)(m+2)}[/tex]
Cancel out the common factors to get:
[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+3)}{(m-2)}[/tex]
We cancel further to get:
[tex]\frac{3(m-2)}{4(m+3)} \cdot\frac{(m+3)}{(m-2)}=\frac{3}{4}[/tex]
The correct chice is B.
Michael is making a deposit with a check and wants cash back. His deposit slip has his name, his account number, the date, the amount of the check, the amount of cash that he wants, his signature, and what else?
a.his date of birth
b.his social security number
*c.the net deposit amount*
d.the balance of money in the account
(edit) ANSWER: *C*
Answer:
The correct answer option is c. the net deposit amount.
Step-by-step explanation:
We know that Michael is making a deposit with a check and wants some cash back.
According to The Federal Reserve System and The Federal Deposit Insurance Corporation, the deposit slip must have the name his name, his account number, date, amount of the check, amount of cash that he want, his signature and the net deposit amount.
Answer:
C
Step-by-step explanation:
The coins in the stores cash register total $12.50. The cash register contains only nickels, dimes, and quarters. There are twice as many dimes and nickels. There are also twice as many quarters as dimes. How many dimes are in the cash register?
Answer:
20 dimes
Step-by-step explanation:
We can group the coins into groups that are ...
4 quarters + 2 dimes + 1 nickel
Then each group satisfies the ratio requirements, and the total value of a group is $1.25.
Since the total value in the register is $12.50, there must be 10 such groups, hence 20 dimes.
Which expression is equivalent to (4x^3*y^5)(3x^5*y)^2 \
A) 24x^13*y^7
B) 36x^13*y^7
C) 36x^28*y^7
D) 144x^16*y^12
Answer:
B) 36x^13*y^7
Step-by-step explanation:
The two rules of exponents that apply are ...
(a^b)^c = a^(b·c)(a^b)(a^c) = a^(b+c)Expanding the second factor gives ...
(4x^3*y^5)(3^2*x^(5*2)*y^2)
= 36*x^(3+10)*y^(5+2)
= 36x^13*y^7 . . . . . . matches selection B
Melissa sees a lighthouse from her sailboat. She knows the height of the lighthouse is 154 feet. She uses a measuring device and determines that the angle to the top of the lighthouse from her boat is 35°. How far is the sailboat from the base of the lighthouse?
Answer:
219.9 feet to the nearest tenth.
Step-by-step explanation:
Use trigonometry:
tan 35 = opposite / adjacent side
= 154/x
x = 154 / tan35
= 219.93
Answer:
219.9 ft
Step-by-step explanation:
After looking at pic, cross multiply to get x tan(35)=154
then divide both sides by tan(35) giving x=154/tan(35)
x is approximately 219.9 ft
Identify the regular tessellation. Please HELP!!
Answer:
see below
Step-by-step explanation:
A regular tessellation is created by repeating a regular polygon. The first and third diagrams show multiple regular polygons of different sizes and shapes. The second diagram has no regular polygons in it.
The last diagram shows a regular tessellation.