Consider the system of quadratic equations
y = 3x^2 - 5x,
y = 2x^2 - x - c,
where c is a real number.
(a) For what value(s) of c will the system have exactly one solution (x,y)?
(b) For what value(s) of c will the system have more than one real solution?
(c) For what value(s) of c will the system have no real solutions?
Solutions to the quadratics are (x,y) pairs. Your answers will be in terms of c, but make sure you address both x and y for each part.
9514 1404 393
Answer:
(a) c = 4
(b) c < 4
(c) c > 4
Step-by-step explanation:
(a) The solutions to the system of equations can be found by substituting one expression for y into the other equation:
3x^2 -5x = 2x^2 -x -c
x^2 -4x +c = 0 . . . . . . . subtract the right side expression
The discriminant is
d = b^2-4ac = (4)^2 -4(1)(c) = 16-4c.
The system will have exactly one solution when d = 0.
16 -4c = 0
4 -c = 0
__
(b) There will be more than one real solution when d > 0
4 -c > 0
c < 4 . . . . two real solutions
__
(c) There will be no real solutions when d < 0.
4 -c < 0
c > 4 . . . . no real solutions
_____
Additional comment
The question posed here simply asks for a value of c. It does not ask for the solutions (x, y). We can count them without knowing exactly what they are.
The graph of a 4th-degree polynomial is shown. How many real zeros does this function have?
A. 1
B. 2.
C. 3
D. 4
Answer:
C: 3
Step-by-step explanation:
The graph touches or crosses the x-axis in 3 places; thus, there are 3 real zeros.
Please help me thank you
Answer:
19/24 option d is correct
What is the volume of this solid figure made with cubes?
Answer:
15 cubic units
Step-by-step explanation:
Use multiplication (V = l x w x h) to find the volume of a solid figure.
3*5=15
I don’t know what 2⁄3 × 1⁄8 × 5⁄9 =
Answer:
5/108
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
5/108
Step-by-step explanation:
2/3 * 1/8 is 2/24
^2/24 can be simplified to 1/12
^ 5/9 * 1/12 is 5/108.
Therefore,
Your answer is 5/108 , if I understood the question correctly.
The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?
••no links just answers••
I know it's not linear but I dont know why.
Answer:
Not a linear relationship
Step-by-step explanation:
Given
The attached table
Required
Linear or not
To do this, we simply calculate the slope of the table at different intervals.
Slope (m) is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (0.5,7.2)[/tex]
So, the slope is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{7.2 - 0}{0.5-0}[/tex]
[tex]m = \frac{7.2}{0.5}[/tex]
[tex]m = 14.4[/tex]
Let:
Let:
[tex](x_1,y_1) = (1,10.7)[/tex]
[tex](x_2,y_2) = (2,12.2)[/tex]
So, the slope is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{12.2 - 10.7}{2 - 1}[/tex]
[tex]m = \frac{1.5}{1}[/tex]
[tex]m = 1.5\\[/tex]
See that the calculated slopes are not equal.
Hence, it is not linear
The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Use the regression equation to predict the life span, y, for a gestation period of 6 months, x. Assume the variables x and y have a significant correlation. Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span, y 30 12 6 3 25 12 10 40
Answer:
For a gestation period of 6 months, the life span is 15.
Step-by-step explanation:
Gestation(months) x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Life span (years) y 30 12 6 3 25 12 10 40
y =? x= 6 months
Assuming the variables x and y have a significant correlation
Graphing the data on a spreadsheet
Using the linear equation obtained
y = 1.5229*x + 6.3425
x=6
y = 1.5229*6 + 6.3425
y = 15. 5
PLEASEEEEE HELPP
Karen is having a party. She’ll have 2 tables fir every 6 guest
Answer:
i hate these questions lol her name do be karen sorry um you do multiplicaton for this question i hate aleks expesially thqat question i feel you bro
Step-by-step explanation:
Answer: it’s all in the explanation!
Step-by-step explanation:
So, in the question, it states that she’s gunna have two tables for every six guests. You’re gonna need to find out how much people are going to be at ONE table, so two divided by six! And as you know, that equals three. For the first space, since it’s a odd number, you need to use the three instead of six since there’s gunna be one table by itself. So three times 5. The first space is gunna be 15 :). The second space is somewhat the same process. What times three equals 21? Seven! So for the second space, you’re gunna pit seven. For the third one, you do 8 times three, which equals 24. And for the last space, it’s 10, for three times ten :), hoped this helped!
Of 300 students in the cafeteria, 180 had lunch. Write the simplified ratio of the students in the cafeteria to the students that had lunch.
Answer:
300 : 180 = 5 : 3
The values and 14 are plotted on the number line.
&
What is the approximate clifference in tenths between the two values?
1.1
Answer: 12.9
Step-by-step explanation:
A line of infinite extent whose points correspond to the real numbers according to their distance in a positive or negative direction from a point arbitrarily taken as zero. I hope this explain the answer better!
NO LINKS-DOCS ETC
PLZ SOLVE ASAP
LOTS OF POINTS
WILL MARK BRAINLYEST
Answer: Betsy is incorrect.
Step-by-step explanation:
The area of a trapezoid is a+b/2 multiplied by h.
First, we should do 5+8/2= 6.5
Next, we multiply 6.5 with 4 because 4 is the height of the trapezoid.
6.5 times 4= 26
Betsy thought the answer was 52, but it is 26 so she is incorrect.\
I hope this helps, may god bless you! :)
Harold can solve 25 math problems in 40 minutes. At that rate, how many minutes will it take Harold to solve 60 math problems?
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
(b) Rewrite the percentage in the sentence below as a decimal.
The photographer filled 40% of her memory card with animal pictures.
david invest $10,000 in a CD that pays 8% compounded quarterly. how long will it take his investment to double
Answer:
Step-by-step explanation:
1. Write a equation
[tex]10,000(1+\frac{0.08}{4})^4^x[/tex]
2. plug in 20,000 to y
[tex]20,000=10,000(1+\frac{0.08}{4})^4^x[/tex]
3. Solve
In the diagram below of triangle HJKHJK, LL is a midpoint of \overline{HJ}HJ and MM is a midpoint of \overline{JK}JK. If LM=71-9xLM=71−9x, and HK=23-xHK=23−x, what is the measure of LMLM?
Answer:
Step-by-step explanation:
Since J is the midpoint of HK, then HJ=JK and 3x+5=9x-3 solve for x
6x=8 x=8/6=4/3 so HJ=3x+5=3(4/3)+5=9 = JK HK=2(9)=18
the full segment HK is 18, each half of it is 9 =HJ=JK
HELP PLEASE ONCE MORE
Answer:
40 cubic units
Step-by-step explanation:
16x 3 = 48
48- 8 is 40
What are the missing numbers in the data set? Assume the numbers are in order.
24, 28, 32, 39, ___ Range = 18
Group of answer choices
41
42
43
44
Answer:
42
Step-by-step explanation:
To find the range, first put all the numbers in order. Then subtract the lowest number from the highest.
Hope this helps!If you have any questions revolving around this topic,feel free to ask me and I will be happy to help,Good luck!
Find the surface area of the following triangular pyrarnid using the net.
Each triangle is congruent, with a base of 7 ftand a height of 6ft.
Answer:
B 84 is our answer
Step-by-step explanation:
triangle formula for surface area is base x height divided by 2 so 7 x 6 = 42 42 ÷ 2 = 21 All the other triangles are going to be the same so 21 x 4 = 84 so 84 is our surface area
A trapezoid with a height of 19 meters has a base of 26 meters and another base of 46 meters. What is the area of the trapezoid?
the area of the trapezoid is
A 342m2 B 598m2 C 684 m2D 1,368m2
Answer:684
Step-by-step explanation:
A= 1/2 h (b1+b2)
A= 1/2 19 (46+26)
A= 9.5 (72)
A=684
14. Classify the figure below. Identify how many faces, vertices, and edges.
Answer:
5 faces
8 edges
5 vertices
Find the measure of minor arc KL.
(x - 1)
G
H (5x + 7)04
Answer:
m(minor arc KL) = 153°
Step-by-step explanation:
"Measure of intercepted arcs between two diameters are equal in measure"
By this property,
m(JK) = m(HL)
(7x - 1)° = (5x + 7)°
7x - 5x = 7 + 1
2x = 8
x = 4
Therefore, m(arc HL) = (5x + 7)
= 5(4) + 7
= 27°
Now measure of minor arc KL = m(arc KH) - m(arc HL)
= 180° - 27°
= 153°
Therefore, measure of minor arc KL is 153°
Plz show work,... need help fast please
Step-by-step explanation:
For 18:
[tex] {10}^{2} + {y}^{2} = {26}^{2} \\ 100 + {y}^{2} = 676 \\ {y}^{2} = 676 - 100 \\ {y}^{2} = 576 \\ y = \sqrt{576} \\ y = 24 \: in[/tex]
For 19
[tex] {10}^{2} + {( \frac{15}{2}) }^{2} = {c}^{2} \\ 100 + \frac{225}{4} = {c}^{2} \\ \frac{625}{4} = {c}^{2} \\ c = \sqrt{ \frac{625}{4} } \\ c = \frac{25}{2} \\ c = 12.5 \: m[/tex]
What are all the values of x that make the quadratic A
equation below true?
x² – 16=0
Suppose you buy a $10,000 bond at face value. The bond pays $450 annual interest. What is the yield on this bond? (Calculate to one decimal place)
HELP ASAP
Answer:
Yield on this bond = 4.5%
Step-by-step explanation:
Given:
Face value of bond = $10,000
Annual interest receives from bond = $450
Find:
Yield on this bond
Computation:
Yield on bond = [Annual interest / Face value]100
Yield on this bond = [Annual interest receives from bond / Face value of bond]100
Yield on this bond = [450 / 10,000]100
Yield on this bond = [0.045]100
Yield on this bond = 4.5%
(4x-1)2=11
whats the solution
Answer:
x = 13/8
Step-by-step explanation:
(4x−1)(2)=11
Simplify both sides of the equation.
(4x−1)(2)=11
(4x)(2)+(−1)(2)=11 (Distribute)
8x+−2=118x+−2=11
8x−2=11
Add 2 to both sides.
8x−2+2=11+2
8x=13
Divide both sides by 8.
8x/8 = 13/8
which brings you to the answer of
x = 13/8
(Note:If this was a little confusing,feel free to ask me any questions revolving around this topic)
Factorial – is the product of natural numbers, for example:
5! = (5)(4)(3)(2)(1) = 120
Simplify the following expression:
1) 11! 2) 15! 3) 20!
8!(7-3)! 10!(9-5)! 13!
Answer:
Step-by-step explanation:
11! = 11*10*9*8*7*6*5*4*3*2*1 = 3991600
15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1=1.307674368 * [tex]10^{12}[/tex]
also looks like this 1,307,674,368,000
20! = 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2 = 2.432902008 * [tex]10^{18}[/tex]
also looks like this 2,432,902,008,000,000,000
8!(7-3)! = 8!4! = (8*7*6*5*4*3*2)(4*3*2) = 967,680
10!(9-5)!13! = 10!4!13! =3,628,800*24*6,227,020,800 = 5.423187139*[tex]10^{17}[/tex]
What value of x and y will make the polygon below a parallelogram?
Answer:
[tex]x = 4[/tex]
[tex]y =1[/tex]
Step-by-step explanation:
Given
The attached figure
Required
x and y
If the attached is a parallelogram, then:
Either segment of a diagonal are equal; So, we have:
[tex]3x = 12[/tex]
[tex]x + y = 5y[/tex]
In [tex]3x = 12[/tex]
Divide both sides by 3
[tex]x = \frac{12}{3}[/tex]
[tex]x = 4[/tex]
Substitute [tex]x = 4[/tex] in [tex]x + y = 5y[/tex]
[tex]4 + y = 5y[/tex]
Collect like terms
[tex]5y - y =4[/tex]
[tex]4y = 4[/tex]
Divide both sides by 4
[tex]y = \frac{4}{4}[/tex]
[tex]y =1[/tex]
Helppppppp mmemeeeeme plzzzz
Hope this helps you solve your math problem.
One coin is flipped six times. What is the probability of flipping two heads and four tails?
Answer:
1/6 x 1/6 = 1/36
1/36 is our probability of getting two heads and four tails.