Step-by-step explanation:
the degree of a polynomial determines 1:1 the number of solutions.
a quadratic equation (degree 2) has 2 solutions.
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -4
b = -4
c = -1
so,
x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)
when we look at the square root
16 - 16
we see that it is 0.
the square root of 0 is 0, and there is no difference between -0 and +0.
so, we get only one (real) solution : 4/-8 = -1/2
but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.
so, I am not sure what your teacher wants to see in this case as answer.
my answer would be 2 real identical solutions.
Santiago's Snow Globes designs custom snow globes. To ship a recent large order, Santiago's Snow Globes first packed individual snow globes in cube-shaped boxes with edges 6 inches long. The boxes were packed into a larger shipping container until it was completely full. The shipping container is shaped like a rectangular prism that is 24 inches long, 24 inches wide, and 30 inches tall
The number of boxes packed to fill the rectangular prism shaped container is: 80 boxes.
What is the Volume of a Rectangular Prism?Volume = length × width × height.
Find the volume of one cube-shaped box:
Volume = 6 × 6 × 6 = 216 in³
Find the volume of one rectangular prism:
Volume = length × width × height = 24 × 24 × 30 = 17,280 in³.
Number of boxes packed to fill the rectangular prism shaped container = 17,280/216 = 80 boxes.
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A system of linear equations is given by these equations 3y-2x=-9 y=-2x+5 The solution to this system is
Answer:
(3, -1) or x=3, y=-1
Step-by-step explanation:
using substitution for y, the first equation becomes 3(-2x + 5) - 2x = -9
distribution of the 3 gets your equation to be -6x + 15 - 2x = -9
from here you combine like terms to get -8x + 15 = -9
from here it's just a two step equation
subtract 15 from both side to get -8x = -24
divide and get x = 3
substitute x in the equation for y to get y = -2(3) + 5
distribution gets you y = -6 + 5, which makes y = -1
to check your work you can just plug in the variables equivalents in the first equation, which upon doing you can see that the answer is indeed 3, -1
Answer:
(3,-1)
Step-by-step explanation:
Plato
The coordinates of the three vertices of a square are shown in the figure. What are the coordinates of the fourth vertex?
Answer:
(-2, 1)
Step-by-step explanation:
The 4th point must be vertically above (-2, -4) and horizontally to the left of (3, 1).
Its coordinates are (-2, 1).
In the equation x + y = 6, find the value of x if y = 2
A. 2
B. 4
C. 6
D. 12
Answer: B
Step-by-step explanation:
ANSWER AS SOON AS POSSIBLE
Marty bought Dr. Pepper in 2000 that was $4 for a case and now it is $7 a case. What is the percent increase of the Dr. Pepper?
Answer:
75%
Step-by-step explanation:
Change in price =7-4 (new-original)
Percent is (change/orginal) 3/4
.75x100=75%
Answer:75% increase
Step-by-step explanation:
What is the slope of the line that contains these points?
The slope can be found with two sets of points
The points can be any points, but in this case I choose the point (-1,10) and (1,2)
Slope = [tex]\frac{y2-y1}{x2-x1} =\frac{10-2}{-1-1} =\frac{8}{-2} =-4[/tex]
The slope of the line that contains these points is -4.
Hope that helps!
a. 36 ft
b. 6 ft
c. 12 ft
d. 3 ft
***ASAP PLEASE***
A brand new smartphone costs $1200. It decreases in value by 13. 3% every year
after its purchase. Which function models the value of the phone x years after its
puchase?
A. F(x) = 1200(0. 867)^x
B. F(x) = 1200(1. 133)^x
C. F(x) = 1. 133(1200)^x
D. F(x) = 0. 867(1200)^x
The function of the brand new smartphone is an exponential function
The function that models the value of the phone x years after its puchase is f(x) = 1200(0.867)^x
How to model the function?The given parameters are:
Initial value (a) = $1200
Rate (r) = 13.3%
An exponential function that represents a decrement in value is illustrated using:
[tex]f(x) = a(1 - r)^x[/tex]
Substitute known values
[tex]f(x) = 1200(1 - 13.3\%)^x[/tex]
Evaluate the difference
[tex]f(x) = 1200(0.867)^x[/tex]
Hence, the function that models the value of the phone x years after its puchase is f(x) = 1200(0.867)^x
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Find the supplementary and complementary angle for 49°
Elena and her mom are on a road trip outside the United States. Elena sees this road sign (Maximum 80). Elena's mom is driving 75 miles per hour when she gets pulled over for speeding. The police officer explains that 8 kilometers is approximately 5 miles. If the speed limit is 80 kilometers per hour, and Elena's mom was driving 75 miles per hour, was she speeding? How many kilometers per hour was she OVER THE SPEED limit of 80kph?
Given :
Maximum speed limit, s = 80 km/hr
Elena's mom is driving at u = 75 mph.
The police officer explains that 8 kilometres is approximately 5 miles.
To Find :
Was she speeding and by how many km/hr.
Solution :
It is given that 8 km = 5 miles
So,
[tex]1\ miles=\dfrac{8}{5}\ km\\\\1\ miles = 1.6\ km[/tex]
Now, Speed of Elena's mom in km/hr is :
[tex]Speed =\dfrac{75\ miles\times\dfrac{1.6\ km}{1\ miles} }{1 \ hour}\\\\Speed = \dfrac{120\ km}{1 \ hour}\\\\Speed = 120\ km/hour[/tex]
Yes, she is over speeding and by ( 120 - 80 ) = 40 km/hr.
Hence, this is the required solution.
Elena's mom was driving at 120 km per hour, with which she was effectively speeding, exceeding the allowed speed by 40 km per hour.
To determine if Elena's mom was speeding and to determine how many kilometers per hour was she over the speed limit of 80kph the following calculation should be performed:
5 = 8 75 = X 75 x 8/5 = X 120 = X
Therefore, Elena's mom was driving at 120 km per hour, with which she was effectively speeding, exceeding the allowed speed by 40 km per hour.
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Express
2x^2 + 8x + 3
in the form 2(x + p)^2+q
You want to build a sandbox for your little brother. You know you need to buy wood to frame the outside of the box. If the dimensions of the box will be 6ft by 8ft, how many feet of lumber will you have to buy?
Answer:
48ft²
Step-by-step explanation:
I am not sure, but thinking it as a rectangle,
area of rectangle= l×b=6×8=48ft²
Question 3 (1 point)
Gerrit cole's salary pitching for the Yankees in 2020 is $36,000,000. Cole averages about 2,000 pitches each year. About how much money does
Gerrit cole make per pitch?
Answer:
18,000$ per pitch
Step-by-step explanation:
You divide 36,000,000 by 2,000 and there's your answer.
Need help on this question
Answer:
Step-by-step explanation:
Write an equation for the line in slope-intercept form.
Answer:
y=2x+2
Step-by-step explanation:
the equation for slope intercept form is y=mx+b where b is the y intercept and m is the slope. From the graph we can see that where x is 0 y is 2 which makes 2 be the y intercept, and when x is 1 y is 4 which then you replace y for 4 and x for 1 which would be 4=m(1)+2,now u subtract 2 from both sides which leaves you with 2=m(1) and m times 1 is m so now your left with 2=m which means the slop is 2
Hey guys wnna talk for a bit?
Answer:
what do u want to talk about
Step-by-step explanation:
The perimeter of a rectangle is 40 units. The length of the rectangle, L, is 7 units.
Answer:
L=7
W=13
Perimeter=40
Area=91
Step-by-step explanation:
Perimeter = 2L+2W
40=2(7)+2W
40=14+2W
-14 -14
26=2W
Divide both sides by 2
13=W
Area=L x W
7 x 13 = 91
Answer:
length = 7 units
width = 13 units
area = 91 square units
perimeter = 40 units
Step-by-step explanation:
What is the area of a rectangle?
❖ The area of a rectangle can be found by multiplying the length and
width of the rectangle.
What is the perimeter of a rectangle?
❖ The perimeter of a rectangle is the sum of all sides- length and
width. In this case, we're given the perimeter as 40 units and the
length as 7 units, but the width is unknown. Formula to find
perimeter of rectangle is 2(l + w) = P.
Solving for Width
[tex]40=2(7+w)[/tex] [tex]40=14+2w[/tex] [tex]26=2w[/tex] [tex]w=13[/tex]Solving for Area
[tex]7*13[/tex] 91 square unitsHow much is 4 dollars 5 quarters 4 nickels and 1 pennies
Answer:
$5.55
Step-by-step explanation:
Given the following question:
We are given 4 dollars, 5 quarters, 4 nickels, and 1 penny.
[tex]1d=1d[/tex]
[tex]4=4[/tex]
[tex]1q=0.25[/tex]
[tex]0.25\times5=1.25[/tex]
[tex]5q=1.25[/tex]
[tex]1n=0.5[/tex]
[tex]0.5\times4n=0.20[/tex]
[tex]4n=0.20[/tex]
[tex]1p=0.1[/tex]
[tex]4+1.25+0.20+0.1=5.55[/tex]
[tex]=5.55[/tex]
The money together in total is worth "$5.55."
Hope this helps.
plz help asap
Construct an equation from the values given in the table
Answer:
y = 3x + 1
Step-by-step explanation:
SOMEONE HELP A GIRL OUT PLSSALOT OF POINTS
GiRL i got u period go subscribe to my utube and follow my ing at iiam.sneek
Answer:
I think it is the second option
Step-by-step explanation:
Solve for b in the literal equation a b = c.
Answer:
b = [tex]\frac{c}{a}\\[/tex]
Step-by-step explanation:
divide both sides by a
OR
bring the a over to the other side and put it under the c as the opposite of times is divide
Cindy wants to paint a border around her circular picture frame. The
distance around the frame was 18 inches. What is the approximate
diameter of the picture frame?
O 12 in
5 in
6 in
13 in
Answer
6 inches
Step-by-step explanation:
A student adds 10 grams of four different powdered solids into four different beakers. The student then adds 100 mL of water to each beaker, stirs the mixtures, and allows them to sit for half an hour before recording observations. Which question is the student most likely trying to answer with this investigation?
Answer:
Which substance dissolves in water?
Step-by-step explanation:
The student adds the same amount of substance of different types i.e., 10 grams to each beaker and the same amount of water i.e., 100 mL to each beaker. All of them are stirred and observations are taken down at the end of thirty minutes.
That is all that is mentioned in the question. The student is most likely measuring which substance dissolves in water. As all the other variables are kept constant.
So, the student here is most likely trying to answer the question "Which substance dissolves in water?"
the angle measures of a triangle in the diagram.
choose
15
45
12
30
Answer:
Step-by-step explanation:
( 3x )° + ( 2x - 15 )° + 45° = 180°
5x + 30 = 180
5x = 150
x = 30
45° , 90° , 45°
Paul has a 3/4 inch long bolt. he buys a bolt that is longer 1/8 and a bolt that is inch shorter 3/4 - inch than the bolt. what are the lengths of the two bolts he buys?
Answer:
Step-by-step explanation:
The first bolt he buys has length 3/4 in plus 1/8 in, which comes out to
6/8 + 1/8 inch, or 7/8 inch.
The second bolt length cannot be determined using the information given: "3/4 - inch shorter." Ensure that you have copied down this probjem completely and accurately.
En el grupo
de prmero A hay28 alumnos, 17 de ellos levantaron la mano¿Qué porcentaje del 2 puntos
grupo
votó?
*
60%
h
0 36%
65%
69%
Don’t need an explanation just an answer pls <3
The y-intercept is (0,2)
you can find the y-intercept by finding the value of y when x = 0The slope is -5/2.
you can find the slope by using the equation below and any two points on the line, such as (0,2) and (2,-3)[tex]\frac{y2-y1}{x2-x1}=\frac{-3-2}{2-0}=\frac{-5}{2} =-\frac{5}{2}[/tex]
Hope that helps!
Answer:
y- intercept is (0, 2)
Slope is -5/2
Rewrite using the distributive property
Answer:
7m + 7n or 7(m + n)
What is the standard form of the following equation? 4x2 + 9y2 + 24x – 36y + 36 = 0
Answer:
[tex]\frac{ (x+3)^2}{9} + \frac{ (y-2)^2}{4} =1[/tex]
-step explanation:
The standard form of the given equation was reduced, representing an ellipse.
The given equation is:
[tex]4x^{2} +9y^{2} +24x-36y+36=0[/tex]
What is an equation?An equation is a statement that equates to two expressions.
We know the above equation represents an ellipse.
Rearranging the given equation
[tex]4x^{2} +24x+9y^{2} -36y+36=0[/tex]
[tex]4(x^2+6x)+9(y^{2} -4y)+36=0[/tex]
[tex]4(x^2+6x+9)+9(y^{2} -4y+4)=36[/tex]
[tex]4(x+3)^2+9(y-2)^2=36[/tex]
[tex]\frac{4(x+3)^2}{36}+\frac{9(y-2)^2}{36} =1[/tex]
[tex]\frac{(x+3)^2}{9}+\frac{(y-2)^2}{4} =1[/tex], which is the standard form of the given equation.
Hence, the standard form of the given equation was reduced.
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HELP ME PLEASE:(:(:(
Answer:
Step-by-step explanation:
42. -5 -2 -2 3 8