Answer:
4. two real solutions
Step-by-step explanation:
[tex]x^2 - x = 1[/tex] (Given)
[tex]\implies x^2-x-1=0[/tex]
Equating it with [tex]ax^2+bx+c=0[/tex]We find: a = 1, b = -1, c = -1Next, we calculate the discriminant of the given quadratic equation by plugging the values of a, b and c in the formula [tex]\implies b^2-4ac[/tex][tex]b^2-4ac\\=(-1)^2-4(1)(-1)\\=1+1=2>0\\\implies b^2-4ac >0[/tex]
-> Given quadratic equation has two real solutions.
Find the nth term of this number sequence
7, 10, 13, 16, ...
help please !!
Answer:
[tex]a_{n}[/tex] = 3n + 4
Step-by-step explanation:
there is a common difference between consecutive terms , that is
10 - 7 = 13 - 10 = 16 - 13 = 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = 3 , then
[tex]a_{n}[/tex] = 7 + 3(n - 1) = 7 + 3n - 3 = 3n + 4
Answer:
The nth term = 3n + 4.
Step-by-step explanation:
The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d.
So this breaks down simply to,
a(n) = dn + a(1) - d a(n) = 3n + 7 - 3 a(n) = 3n + 4
The speedometer on Leona's car
ws the speed in both miles per
and kilometers per hour. Using
the mile per hour rate that is
valent to 40 kilometers per hour.
Answer: 24.86miles/hr
Step-by-step explanation: Divide the speed by 1.609 to convert
what is the answer to In 3/4 of an hour Ryan codes 3/5 of his game. At this rate, how much of the game can he code in 1 hour?
Answer:
4/5 of game
Step-by-step explanation:
Rate = 3/5 g / (3/4 hr) = 12/15 = 4/5 game per hour
LEMON SQUASH
1 part concentrate
to 2 parts water
If you put 140 ml of water in a glass,
how much concentrate should be added?
PLEASE HELP ASAP
NEEP HELP
Answer:
x = 14
Step-by-step explanation:
We have alternate interior angles that are congruent.
[tex]5x + 5 = 4x + 19[/tex]
[tex]x = 14[/tex]
help me to solve this problem
Answer:
(More than an hour) Three times as many
(Less than an hour) Two times as many
Step-by-step explanation:
Which expression is a factor of 21x2 + 13x – 20?
A 3x – 4
B 72 - 5
C 7x +4
D 30 + 5
Answer: A
Step-by-step explanation:
This seems to be the only applicable answer
Find the sum. 5/2x + 4/3y
A. 9/2x + 3y
B. 15y + 8x/6xy
C. 23xy/6xy
D. 3/2xy
Answer:
B
Step-by-step explanation:
[tex]\dfrac{5}{2x} + \dfrac{4}{3y}=\dfrac{15y+8x}{6xy}[/tex]
Find the next number in the 4; 2; 1; 2 .......
Answer:
The answer is 3
let me know if im wrong :)
find the area of the composite figure
Answer:
84 square inches
Step-by-step explanation:
An art gallery wants to display 4 pieces of art in the front window. If there are 8 pieces to choose from, how many distinct displays are
possible?
A. 40,320
B. 10,080
OC. 1,680
D. 70
Answer: 70
Step-by-step explanation:
you would do 8C4
If there are 8 pieces to choose from, there are 1,680 different ways distinct displays are possible.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
To find the Ways can 8 pieces of art in the front window be arranged in the display window.
Let us use permutation to find the number of ways can 8 pieces of art in the front window be arranged in the display window.
here we have
n= 8
r= 4
substituting the values,
[tex]^nC_r = \dfrac{n!}{ (n-r)!}\\\\^8C_4 = \dfrac{8!}{ (8-4)!}\\\\^8C_4 = \dfrac{8!}{ (4)!}\\\\^8C_4 = 8 \times 7 \times 6\times 5\\\\^8C_4 =1680[/tex]
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
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paragraph explaining how the volume of a sphere in real world and mathmatical problems
Answer:
We can find the volume of a sphere using the volume of a cylinder. Cylinder is a solid which has a circular base. We know the fact that the volume of any solid is equal to the product of base area and height of the solid. So, the volume of a right circular cylinder of base radius ‘r’ and height ‘h’ is given by
Step-by-step explanation:
(2a-16)+(3a+18)=17 what is a?
Hope this is the right answer .
A triangle has sides with lengths of 51 miles,68 miles and 85 miles. Is it a right triangle.?
Answer: YES
Step-by-step explanation: It is
Suppose that 19 inches of wire costs 76 cents. At the same rate, how much (in cents) will 14 inches of wire cost?
Answer:
10.64
Step-by-step explanation:
2. Select the two graphs with a negative slope.
Answer:
2nd one on the top row
last one on the bottom row
(left to right)
Step-by-step explanation:
the negative slopes are the lines that go down towards the right side
so that would be the second one on the top row and the last one on the bottow row
Factor 9p² +6p-8
Step 1: multiply a x c and write the new equation
Step 2: Divide by "a" and simplify the fractions. Write the new equation n factored form.
Step 3: Bottoms up and write the new equivalent equation in factored form.
The diameter of a circle is 5 cm. Find its area to the nearest whole number.
Answer:
79cm
Step-by-step explanation:
Area of a circle = πr^2
Plug in r: π(5)^2 = 79cm
You deposit $2500 into a bank account that pays 7.5% annual interest, compounded continuously. Find
the amount in the account after 6 years?
Answer:
16,125
Step-by-step explanation:
The original version of a song is 270 seconds long.
The remix is 20% shorter. How many seconds long is
the remix of the song?
Answer:
The remix is 216 seconds long.
Step-by-step explanation:
Answer:
216 seconds
Step-by-step explanation:
270/5 =54
54*4=216 seconds.
Just need the answer fast pls help
Answer:
121/49 a^8 b^2
Step-by-step explanation:
the answer is the last option
Give me an example of how you would solve 1+1 in the worst way possible
Answer:
add 20 subtract 20 multiply by 3 divide by 3 add 1
Please help!!!!!!!! How do I type?
Answer:
Keyboard fam
Step-by-step explanation:
Answer:
You press the buttons in the keyboard.
Step-by-step explanation:
hope it helps
sorry if I'm wrong
lol
Find the quotient of 2/5 and 4/5
Answer:
10/20 or 1/2
Step-by-step explanation:
Heres a picture to explain:
whats the biggest ten you can multiply by 3 but dont go over 42
Answer:
14
Step-by-step explanation:
3x14=42 it dosen't go over 42
Answer: 14
Step-by-step explanation:
3,6,9,12,15,18,21,24,27,30,33,36,39,42
3x14=42
A graph titled Fast Freddy has time (minutes) on the x-axis and Distance (miles) on the y-axis. A line goes through points (0, 0) and (4, 1). A 2-column table with 3 rows titled Speed Sam. Column 1 is labeled Time (minutes) x with entries 4, 20, 32. Column 2 is labeled Distance (miles) y with entries one-half, 2 and one-half, 4.
Find the slope from the graph and from the table to compare the speeds of two marathon runners.
What is the constant speed of Fast Freddy?
What is the constant speed of Speedy Sam?
Who ran faster?
Using linear function concepts, it is found that:
The constant speed of Fast Freddy is of 0.25 miles per minute.The constant speed of Speedy Sam is of 0.125 miles per minute. Hence, due to the higher speed, Fast Freedy ran faster.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For Fast Freedy, we have that he run one mile in four minutes, hence the slope is given by:
mF = 1/4 = 0.25 miles per minute.
The constant speed of Fast Freddy is of 0.25 miles per minute.
For Speedy Sam, when the the time changes by 16 minutes, the distance changes by 2, hence his slope is given by:
mS = 2/16 = 1/8 = 0.125 miles per minute.
The constant speed of Speedy Sam is of 0.125 miles per minute. Hence, due to the higher speed, Fast Freedy ran faster.
More can be learned about linear function concepts at https://brainly.com/question/24808124
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Answer:
1/4 1/8 and Freddy was faster
Step-by-step explanation:
How do you find the answer for surface area?
Answer:
720 m²
Step-by-step explanation:
The surface area of the prism is the sum of the areas of its 5 surfaces.
Area of triangle= ½ ×base ×height
Area of front face
= ½(6)(8)
= 24 m²
Area of back face= 24 m²
Area of rectangle= length ×breadth
Area of base
= 8(28)
= 224 m²
Area of right surface
= 10(28)
= 280 m²
Area of left surface
= 6(28)
= 168 m²
Total surface area
= 24 +24 +224 +280 +168
= 720 m²
if a=3,b=−1 and c= −2,3ac-4c²/ 5ab
Step-by-step explanation:
Given expression,
[tex]\\ \longrightarrow \qquad \sf \frac{3ac-4c²}{ 5ab} \\ \\ [/tex]
Now, when a = 3, b = -1 and c = -2 we get,
[tex]\\ \longrightarrow \qquad \sf \frac{3.3.( - 2)-4. {( - 2)}^{2} }{ 5.3.( - 1)} \\ \\ [/tex]
[tex] \longrightarrow \qquad \sf \frac{3.( - 6)-4. 4 }{ 5.( - 3)} \\ \\ [/tex]
[tex]\longrightarrow \qquad \sf \frac{ - 18-16 }{ - 15} \\ \\ [/tex]
[tex]\longrightarrow \qquad \sf \frac{ - 34 }{ - 15} \\ \\ [/tex]
[tex]\longrightarrow \qquad \sf \frac{ 34 }{ 15} \\ \\ [/tex]
The population of a city is modeled with the function P = 250,000e^0. 013t, where t is the number of years since 2000. In what year will the population reach 450,000
[tex]P=250000e^{0.013t}\implies \stackrel{P}{450000}=250000e^{0.013t}\implies \cfrac{450000}{250000}=e^{0.013t} \\\\\\ \cfrac{9}{5}=e^{0.013t}\implies \log_e\left( \cfrac{9}{5} \right)=\log_e(e^{0.013t})\implies \ln\left( \cfrac{9}{5} \right)=0.013t \\\\\\ \cfrac{\ln\left( \frac{9}{5} \right)}{0.013}=t\implies 45.21\approx t\qquad \textit{about 45 years, 2 months and a half}[/tex]
PLS HELP FAST !!!
The chart below shows the results of survey taken by a movie theater. The theater asked what genre the mover goers preferred to see. If the theater owner asked 100 people, how many people would prefer Drama? Round to the nearest whole number
Using proportions, it is found that if the theater owner asked 100 people, 47 would prefer Drama.
What is a proportion?A proportion is a fraction of a total amount.
From the table, out of the 7 + 18 + 7 + 6 = 38 people surveyed, 18 prefered drama. Hence the proportion is given by:
p = 18/38 = 0.47.
Out of 100 people, the amount would be given by:
A = 0.47 x 100 = 47.
More can be learned about proportions at https://brainly.com/question/24372153