Answer:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
Step-by-step explanation:
The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:
[tex]3-x^{2}=x[/tex]
and then solve for x. We move everything to one side of the equation so we get:
[tex]x^{2}+x-3=0[/tex]
and we use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
and we substitute:
[tex]x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}[/tex]
and solve
[tex]x=\frac{-1\pm \sqrt{1+12}}{2}[/tex]
[tex]x=\frac{-1\pm \sqrt{13}}{2}[/tex]
so our two answers are:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
A blue scarf is 7/8 of a yard in a race car is 5/8 of a yard find the difference in length of the two scars write your answer as a simplified fraction
Answer:
Difference in length = 1/4 yards
Step-by-step explanation:
Given:
Blue scarf in yard = 7/8 yard
Another car in yard = 5/8 yard
Find:
Difference in length
Computation:
Difference in length = Blue scarf in yard - Another car in yard
Difference in length = 7/8 - 5/8
Difference in length = 2/8
Difference in length = 1/4 yards
Josh has 212 marbles. Peck has 314 marbles. Round each number to the nearest hundred. Then, type how much marbles more does Peck have.
Round each number to the nearest hundred.
212 = 200.
314 = 300.
How much more marbles does Peck have?
314 - 212 = 102.
That is your answer. Hope this helps!
Answer:
100 more marbles
Step-by-step explanation:
So first let's round the numbers to the nearest hundred. So 212 rounds to 200, and 314 rounds to 300. Then we do 300-200 and get 100. SO the answer is 100.
A piece of carpet is 360 cm long. Mr. Smith cuts it into three pieces in the ratio 2:3:4. Workout the length of the longest piece of carpet.
Answer:
The longest length of carpet is 160 cm.
Step-by-step explanation:
Given that the total ratio(units) of the carpet is 9(2+3+4). So first, you have to find the length of carpet in 1 unit :
[tex]9 \: units = 360 \: cm[/tex]
[tex]1 \: unit = 360cm \div 9[/tex]
[tex]1 \: unit = 40 \: cm[/tex]
Next, you have to find the length of carpet in 4 ratio as the question wants the longest length :
[tex]4 \: units = 40 \: cm \times 4[/tex]
[tex]4 \: units = 160 \: cm[/tex]
Answer:
160cm
Step-by-step explanation:
2+3+4= 9
4/9 x 360= 160cm
Problem 1: Solve the systems of equations by the method of your choice.
2x+y=5
x-y=1
Problem 2: The difference of two complementary angles is 30 degrees. Set up a system of linear equations that would find the angles. Do not solve the system.
Problem 3: A cashier has 30 bills, all of which are $10 or $20 bills. The total value of the money is $460. Set up a system of linear equations that would find how many of each type of bills the cashier has. Do not solve the system.
Problem 4: Give an example of a system of linear equations that has no solutions. Explain how can you decide the number of solutions without solving the system.
Answer:
x=2 and y=1
Step-by-step explanation:
2x+y=5
x-y=1
buy adding both equations we get
3x=6
x=2 ( divide 3 on both sides)
put x=2 in any equation
2-y=1
y=2-1
y =1
p2
Problem#2
Let say two complementary angles are A & B
difference of two complementary angles is 30°
=> A - B = 30
Sum of two complementary angles is 90°
=> A + B = 90
Hence A = 60° , B = 30°
Problem#3
Total bill = 30
$ 10 Bills = A
$ 20 Bills = B
10 * A + 20* B = 460
A + B = 30
A = 14 , B = 16
Problem#4
4x+2=y
2y−8x=10
The first step is to simplify the second equation into
y=mx+b form.
2y−8x=10y
y−4x=5
y=4x+5
Now, the two equations are:
y=4x+2
y=4x+5
What is the polynomial function of least degree whose only zeros are -4,2, and 3?
Answer:
never heard about it
Step-by-step explanation:
Find the midpoint (1,2)(8,-9)
Answer:
(4,5)
Step-by-step explanation:
Which theorem can be used to show that △JKL ~ △MNP?
In this case the answer would be the last option
because it is shrunk by 2/3 on just the x side
D is the only one who has that first transformation
By a theorem of similarity, it can be shown that △JKL ~ △MNP.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
Another example is all circles are similar circles.
The ratio of corresponding sides of similar objects is always the same.
Any two triangles will be similar if the ratio of their corresponding side is same.
If △JKL ~ △MNP then their corresponding side ratio will definitely same.
If corresponding side is same order in JKL and MNP then,
JK/KL = MN/NP
Hence "By a theorem of similarity, it can be shown that △JKL ~ △MNP".
To learn more about similarity,
https://brainly.com/question/23620710
#SPJ5
Find the common ratio of each geometric sequence.
a) 2, 4, 8, ... r = 2
b) -2, 6, -18, L =
c) -3, -12, -48, ... r =
1 1 1
d)
3 927
9
..
e) 0.3, 0.6, 1.2, ... r =
f)
1.
re
.
42
Answer:
d
Step-by-step explanation:
If 20% of X =y, then y% of 20 is the same as:
Answer:
4% of x
Step-by-step explanation:
20% of x
20% of x = 0.2x20% of x = y ⇒ 0.2x = yy% of 20
y% of 20 = 20*y/100 = 0.2y0.2y = 0.2*0.2x = 0.04xy% of 20 = 4% of xHope it is what you are looking for
The expanded form for 300684 can be written with only 4 add ends. Explain how this is possible for a number with 6 digits
Answer:
This can be because our number, 300,684, has only four digits different than zero.
Then we can write this number as:
300,684 = 300,000 + 600 + 80 + 4.
So we add only 4 terms.
So when we write a number in this form, we will have the same numbers of terms in the addition that the number of digits different than zero in our original number.
Give an expression that generates all angles coterminal with each angle. Let n represent any interger?
1. 60°
2. 120°
Answer:
The expression to this question can be defined as follows:
Step-by-step explanation:
Given angle:
1. 60°
2. 120°
Formula:
[tex]\to \bold{\ angle + 360 \ n}[/tex]
The Expression for point 1:
[tex]\to 60^{\circ} + 360 \ n\\[/tex]
The Expression for point 2:
[tex]\to 120^{\circ} + 360 \ n\\[/tex]
what are the domain and range of the function f(x)=5x-3+1?
Answer:
Domain : (-∞,∞)
Range : (1 , ∞)
If you earned 892.50 after depositing 1400 at 4.25% simple interest, how long was it invested ? Using the simple interest formula, solve for t. Formula I=Prt
Answer:
Time t = 15 years
Step-by-step explanation:
Interest = 892.50
Principal = 1400
Rate = 4.25%
Time = unknown
But
interest I = Principal p * rate r * time t
Time t = interest I/(principal P * rate r)
Time t=( 892.50*100)/(1400*4.25)
Time t=89250/5950
Time t = 15 years
16.9 is what percent of 22.9? Round to the nearest percent.
Answer:
74%
Step-by-step explanation:
16.9/22.9。。。。。。。
Answer:
74%
Step-by-step explanation:
22.9=100%
16.9= ?
16.9×100÷22.9=73.8
Round to the nearest % =73.8=74
Answer =74%
The distance between the point (2,1,1) and the plane x-2y=5 is
The given plane has normal vector
[tex]x-2y=5\implies\mathbf n=\langle1,-2,0\rangle[/tex]
Scaling n by a real number t gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation
[tex]\mathbf r(t)=\langle1,-2,0\rangle t+\langle2,1,1\rangle=\langle 2+t, 1-2t, 1\rangle[/tex]
This line passes through (2, 1, 1) when t = 0, and the line intersects with the plane when
[tex]x-2y=5\implies(2+t)-2(1-2t)=5\implies5t=5\implies t=1[/tex]
which corresponds the point (3, -1, 1) (simply plug t = 1 into the coordinates of [tex]\mathbf r(t)[/tex]).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
[tex]\sqrt{(2-3)^2+(1-(-1))^2+(1-1)^2}=\boxed{\sqrt5}[/tex]
Write the following number in standard form.
one hundred four billion, twenty-seven thousand, five hundred seventy-one
140,027,000,571
140,270,571,000
104,000,027,571
104,000,270,571
Answer:
The third one, 104,000,027,571
Step-by-step explanation:
The first and second ones are not the answers because the problem does not say one hundred forty billion.
The last one is not the answer because the problem doesn't say two hundred seventy thousand.
Thus leaving the third one, which fits the description of the number.
The table shown classifies the 35 students in a
college statistics course by year (1st, 2nd, 3rd, 4th)
and type of major (Humanities, Sciences, Other). A
student from this course will be selected at random.
What is the probability that the student's major is
Humanities?
The correct answer is 0.45 or 45%
Explanation:
In this case, the probability of selecting a student whose major is Humanities can be calculated by finding the number of Humanities students, which is considered as the desired outcome, and dividing this by the total of outcomes or students. The process to find the probability is shown below:
[tex]P = \frac{Desired outcomes}{Total outcomes}[/tex]
[tex]P= \frac{Students from Humanities}{Total students}[/tex]
[tex]Students of Humanities = 5 + 5 + 3 + 3 = 16 students[/tex] (Add the students of each year that are part of Humanities)
[tex]Total of students = 35[/tex] (This number is provided in the question but can also be found by adding all numbers in the table)
[tex]P = \frac{16}{35}[/tex]
[tex]P = 0.45[/tex]
Multiply the probability by 100 to know its equivalent in percentages 0.45 x 100 = 45. This means the probability that a student of humanities is selected is 0.45 or 45%.
Check each equation whose graph is the line that
contains the points (4, -7) and (1,5).
y=-4x + 9
y=-4x – 23
y-1 =-4(X-5)
y + 7 = -4(x – 4)
4x + y = 9
DONE
Answer:
Points P ( 4 , - 7 ) and Q ( 1 , 5 ) belong to the equations:
1 ; 4 ; and 5
Step-by-step explanation:
Equations 1 ; 4 and 5 are the same equation
Equation 1 y = - 4*x + 9
Equation 4
y + 7 = - 4 * ( x - 4 ) ⇒ y + 7 = - 4*x + 16 ⇒ y = - 4*x - 7 + 16
y = -4*x + 9
Equation 5
4*x + y = 9 ⇒ y = - 4*x + 9
Now for the equation y = - 4*x + 9
P ( 4 , -7)
For x = 4 y = - 4*(4) + 9 ⇒ y = - 16 + 9 ⇒ y = - 7
Then point P is in the line y = - 4*x + 9
Point Q (1 , 5 )
For x = 1 y = - 4 * ( 1) + 9 ⇒ y = - 4 + 9 ⇒ y = 5
Point Q is in the line y = - 4*x + 9
Equation 2
y = - 4*x - 23
Point P ( 4 , - 7 )
For x = 4 y = 16 - 23 y = - 7
Point P is in the line
Point Q
For x = 1 y = - 4 *(1) - 23 ⇒ y = - 27
Then poin Q is not in the line
Equation 3
y - 1 = - 4 * ( x - 4 )
y - 1 = -4*x + 16 ⇒ y = - 4*x + 17
Point P ( 4 , - 7 )
For x = 4
y = - 16 + 17 ⇒ y = 1
Point P is not in the line
And Point Q ( 1 , 5 )
For x = 1
y = - 4* ( 1 ) + 17 ⇒ y = 13 Q is not in the line
Answer:
1 4 5
Step-by-step explanation:
jus took the test
Solve: x/3+1/4 =1/3 . Explain your work.
Steps to solve:
x/3 + 1/4 = 1/3
~Subtract 1/4 to both sides
x/3 = 1/12
~Multiply 3 to both sides
x = 1/4
Best of Luck!
What is the surface area of a cube with side length 3/2 units?
Answer:
Surface area = 13.5 unit square.
Step-by-step explanation:
We have given the side length of cube = 3/2 units
Now we have to find the surface area of the cube by using the given information. Therefore we must use the below formula to find the surface area. the formula is as follows:
Surface area = 6 (side)^2
Now plug the given information in the formula.
Surface area = 6 (3/2)^2
Surface area = 13.5 unit square.
What is 2 cents as a fraction
7 out of 10 doctors If there are 4200 doctors that prefer Cough-Up brand syrup, how many total doctors are there? * A)6000 B)2940 C)14000 D)1260
NEED HELP ASAP!!! Please explain your answer. Solve 0 = (3x - 4) / 5
Answer:
x= 1.333333333333 or 1 1/3
Step-by-step explanation:
solve for x, 0 times 5= 0 plus 4 is 4 div by 3 is 1 and 1/3
PLEASE HELP ASAP! Far away on the horizon, we saw the tiny figures of a lonely traveler and his mule ______ into the sunset. A. Receed B. Famished
Answer:
Recede
Step-by-step explanation:
Famished means extremely hungry
Recede means go or move back or further away from a previous position
Answer:
Recede
Step-by-step explanation:
So let's look at the meanings of these two words.
Recede: To go or move back backward; become more distant.
Famished: Severely suffering from hunger.
So now you can see that recede is the word that makes more sense in the blank.
Far away on the horizon, we saw the tiny figures of a lonely traveler and his mule Recede into the sunset.
Hope this Helps!
please answer thank you!
Answer:
X= -2
Step-by-step explanation:
Given: 16 = -4(x - 1) + 4
Solution:
Subtract 4 from both sides
12 = -4(x -1)
Divide -4 on both sides
-3 = x - 1
Add -1 on both sides
x = -2
Need help ASAP!!!!!!!!!!!!
Answer:
[tex]-\frac{7}{2} x+12[/tex]
Step-by-step explanation:
if you need step by step explanation i will upload.
Use the slider to rotate AABC about point P through different angles of rotation (a). As you move the slider, you'll see the image, AA'B'C'.
move on the screen. At what angles of rotation does AA'B'C' coincide with each of the other triangle images?
Answer:
Step-by-step explanation:
Answer:
The angles of rotation coincide as follows:
DEF is 45°
GHI is 115°
JKL is 210°
Step-by-step explanation:
NEED HELP ASAP (30Points!!) Which answers are examples of the Law of Syllogism? Select each correct answer. A) If there is a children’s movie playing at the cinema, Maria’s mother will take her to see it. When Maria’s mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria. B) If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram. C) If a quadrilateral is a rectangle with 4 equal sides, then it is a square. Quadrilateral ABCD is a rectangle with 4 equal sides. Therefore, quadriateral ABCD is a square. D) Sally goes to the mall every Saturday. Today is Saturday. Therefore, Sally will go to the mall today.
Answer:
The correct answer is: (just took the test)
if a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram
if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria
Step-by-step explanation:
For the given answers the answers that follow the law of syllogism is options A and B.
Given that,
4 statement is given, and we have to pick the statement that follows the low of syllogism.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here
There are only two statements that are following the law of syllogism. ie.
A. If there is a children's movie playing at the cinema, Maria's mother will take her to see it. When Maria's mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children's movie playing at the cinema, Maria's mother will buy popcorn for Maria.
B. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.
C. and D. are invalid statement because it does not follow the Law of Syllogism.
Thus, for the given answers the answers that follow the law of syllogism is options A and B.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
What is the domain in interval notation?
Answer:
The answers are all real numbers where x<2 or x>2. We can use a symbol known as the union, ∪,to combine the two sets. In interval notation, we write the solution:(−∞,2)∪(2,∞). In interval form, the domain of f is (−∞,2)∪(2,∞).
Fill in the next number in the list.
5. 6. 11. 17. 28. 45
5. 6. 11. 17. 28. 45 . 73
Here,5 &6 are given,
Then,
5+6=11
6+11=17
11+17=28
17+28=45
So,
28+45=73
Answer:
73
Step-by-step explanation:
We are adding the two numbers before
5+6 = 11
6+11 = 17
11+17 = 28
17+28 = 45
28+45 =73