Answer: x²-59x+114=0
explanation:
If the roots are 2 and 57, then:-
sum of roots = 2+57 = 59
and, product of roots = 2×57 = 114
the quadratic equation is given by,
x²-(sum of roots)x+(product of roots)=0
so, x²-59x+114=0 will be the desired quadratic equation.
so, none of the options are correct.
the correct answer is x²-59x+114=0.
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Applying the the properties of Congruence.
Quadrilateral GHJK = Quadrilateral LMNP.
Find the given side length or angle measure.
PLEASE HELP NO Scams pleaseeeee !!
Answer:
[tex]LM = 35cm[/tex] and [tex]m \angle H = 98^o[/tex]
Step-by-step explanation:
For this problem, it is critical to understand what the opening statement means.
[tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex] means that each pair of corresponding sides between shapes are congruent (they have equal length), and each pair of corresponding angles between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).
So, it's important to be able to determine which pairs are the corresponding parts. When the congruence is given like [tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex] the letters are in a particular order. That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.
So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc
In other words, point G and L correspond, point H and K correspond, etc.
Part 1 -- Find LMTo find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).
[tex]\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}[/tex]
While all of that is true, we only have a few sides with any information in them. Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written. So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent sides above, we see that [tex]\overline{GH} \cong \overline{LM}[/tex]
Since the sides (line segments) are congruent, their lengths are equal
[tex]GH = LM[/tex]
...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"
[tex]GH = LM\\(4x+3)=(6x-13)[/tex]
[tex](4x+3)+13=(6x-13)+13\\4x+16=6x[/tex]
[tex](4x+16)-4x=(6x)-4x\\16=2x[/tex]
divide both sides by 2
[tex]\frac{16}{2}=\frac{2x}{2}\\8=x[/tex]
So, to find the length, LM, we just need to look back at the expression for LM:
[tex]LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35[/tex]
remembering that the lengths are measured in centimeters (as indicated on the diagram): [tex]LM = 35cm[/tex]
Part 2 -- Find m∠HTo find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.
[tex]\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P[/tex]
While all of that is true, we only have a few angles with any information in them. Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written. So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent angles above, we see that
[tex]\angle H \cong \angle M[/tex]
Since the angles are congruent, their measures are equal
[tex]m\angle H = m\angle M[/tex]
...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"
[tex]m\angle H = m\angle M\\(9y+17)=(11y-1)[/tex]
subtract 1 from both sides
[tex](9y+17)+1=(11y-1)+1\\9y+18=11y[/tex]
subtract 9y from both sides
[tex]\\(9y+18)-9y=(11y)-9y\\18=2y[/tex]
divide both sides by 2
[tex]\frac{18}{2}=\frac{2y}{2}\\9=y[/tex]
So, to find angle H, we just need to look back at the expression for the measure of angle H:
[tex]m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98[/tex]
remembering that the angle is measured in degrees (as indicated on the diagram): [tex]m \angle H = 98^o[/tex]
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Write the recursive formula for the arithmetic sequence.
A(n)=(-1)+(n-1)(-5)
The recursive formula is [tex]a_n= a_{n-1} -5[/tex].
What is Arithmetic Progression?A set of numbers is an arithmetic progression (AP) or an arithmetic sequence such that the difference between successive words is unchanged.
Given:
A(n)=(-1)+(n-1)(-5)
A(n) = -1 - 5n + 5
A(n) = 4-5n
n=1
A(1)= 4-5= -1
n=2,
A(2) = -6
n=3
A(3)= -11
Hence, the recursive formula is [tex]a_n= a_{n-1} -5[/tex].
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G
Express as a percent.
4/5%
Answer:
80%
Step-by-step explanation:
I'm assuming you meant express 4/5 as a percent and not 4/5%. So simply evaluate 4/5 to get 0.80. Now multiply this value by 100 to get the percentage which gives you 80%
What are the soultions of the equation x^4 - 9x^2 + 8 = 0? Use u substitution to solve.
Step-by-step explanation:
Let u=x^2.
Notice that
[tex] {x}^{4} - 9 {x}^{2} + 8 = 0[/tex]
[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8 = 0[/tex]
[tex]u {}^{2} - 9u + 8 = 0[/tex]
[tex](u - 8)(u - 1) = 0[/tex]
[tex]u = 8[/tex]
[tex]u = 1[/tex]
Replace x^2= u
[tex] {x}^{2} = 8[/tex]
[tex]x = ±2 \sqrt{2} [/tex]
[tex] {x}^{2} = 1[/tex]
[tex]x = ±1[/tex]
So our answer is
[tex]±1 \: [/tex]
and
[tex]±2 \sqrt{2} [/tex]
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.
f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192
Answer:
the answer is f(x)=2x+192
Answer:
The answer is F(x)=2x+192
Which two activities are examples of data collecting?
A. Using the results of a race to predict who will win future races
B. Weighing dogs
C. Graphing the lengths of fish in a pond
D. Asking people what their favorite show is
Answer:
C and D.
Step-by-step explanation:
In option C, they are collecting data about the lengths of fish in a pond.
In option D, they are collecting data about people's favorite show.
Hope this helps!
If not, I am sorry.
X +4
2 - 16
lim
X→-4 X
I'm going to assume you meant to say
[tex]\displaystyle \lim_{x\to-4} \frac{x+4}{x^2-16}[/tex]
Factorize the denominator to reveal a removable discontinuity in the limand:
[tex]\dfrac{x+4}{x^2-16} = \dfrac{x+4}{(x+4)(x-4)}[/tex]
In the limit, we're considering values of x *near* -4, and not x = -4 itself. So we can cancel the factors of x + 4 and we're left with
[tex]\displaystyle \lim_{x\to-4} \frac{x+4}{x^2-16} = \lim_{x\to-4} \frac1{x-4} = \frac1{-4-4} = \boxed{-\frac18}[/tex]
Josefin is 32 years younger than Anette. How many years ago was Anette's age twice Josefin's age if Anette is 74 now?
2,753 people go to a concert and tickets cost $5 each. If it costs $8,000 to put on the concert, how much money was made?
Answer:
Money made by tickets=
2753 x $5 = $13765
We have to subtract the cost of the concert from the money made by tickets to get our profit. Therefore,
$13765 - $8000 = $5765
An IV solution of 120 mL at a drip rate of 5 gtt/min using a tubing factor of 20 gtt/mL has been ordered to be initiated at 1545. Calculate the infusion time. (Round your answer to the nearest tenth of an hour.
The infusion time for the IV solution that will be prescribed 480 mins.
What is IV infusion time?The time taken by the saline to be dripped in the infusion is called as the infusion time.
To calculate the infusion time the formula for IV drip rate is used which is;
Drip rate = volume/time × Drop factor
Drip rate = 5gtt/min
Volume = 120mL
Drop factor= 20 gtt/mL
Time = ?
From the formula above, make time the subject of the formula. That is,
Time = vol × drop factor/drip rate
Time = 120 × 20/5
Time= 120 x 4
Time= 480 mins
Therefore, the infusion time for the IV solution that was prescribed = 480 mins
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Determine the measure of each indicated angle. Show all necessary steps!
The measure of the unknown angle are; a) x = 89 degrees, b) p = 92 degrees.
What is the sum of all the angles of a regular polygon?
For a regular polygon of any number of sides, the sum of its exterior angle is 360°.
We already know that a 4-sided polygon's angles add up to 360 degrees.
So to find the value of x:
69 + 118 + 84 + x = 360
x = 360 - (69 + 118 + 84)
x = 89 degrees
b)
For a 4-sided polygon, we also know that the outside angles add up to 360 degrees.
So to find the value of p:
100 + 62 + 106 + p = 360
p = 360 - (100 + 62 + 106)
p = 92 degrees
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John is 36 years old now. 1/4 of his age is equal to 1/3 of sam's age. find their total age in 5 years time
Answer:
John = 41 years
Sam = 32 years
Step-by-step explanation:
On the second journey Ikbal drives at an average speed of 64km/h.
work out
(i) the distance he travels in 90minutes,
in km
Answer:
96Km
Step-by-step explanation:
l wrote 90/60 because the speed is given in hours.
so I had to deal with hours only not hours and minutes.
that's why I wrote 90/60 .
you can also choose to divide.
I mean to change the minutes to hours so that the formula can work.
good day.
C
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the
functions over the interval 0≤x≤1?
-1
-1
2
O The exponential grows at half the rate of the quadratic.
O The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic
The correct answer is option b which is the exponential grows at the same rate as the quadratic.
The complete question is given below with the graph attached:-
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval
a. The exponential grows at half the rate of the quadratic.
b.The exponential grows at the same rate as the quadratic.
c.The exponential grows at twice the rate of the quadratic.
d.The exponential grows at four times the rate of the quadratic.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval
a ≤ x ≤ b
is given by
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
0 ≤ x ≤ 1
is given by
[tex]\dfrac{f(1)-f(0)}{1-0}= \dfrac{2-1}{1}=1[/tex]
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
0 ≤ x ≤ 1
is given by
[tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{1-0}{1}=1[/tex]
Therefore, the exponential grows at the same rate as the quadratic in the interval .
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If f(x) = 2x – 5, find the inverse. This function passes the Horizontal Line Test which means it is a onetoone function that has an inverse. y = 2x – 5 Change f(x) to y. x = 2y – 5 Switch x and y. Solve for y by adding 5 to each side and then dividing each side by 2.
A function assigns the values. The inverse of the function is y = (x+5)/2.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To find the inverse of the function, the function is needed to be solved for x, and then replace x with y and vice versa. Therefore, the inverse of the function will be,
f(x) = y = 2x - 5
y = 2x - 5
y + 5 = 2x
x = (y+5)/2
y = (x+5)/2
Hence, the inverse of the function is y = (x+5)/2.
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An electronics store researched the TV sales in the last 6 months. The probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. Furthermore, 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty. A customer is randomly selected from among all those who bought a TV from the store. What is the probability that the selected customer purchased a Brand 1 model and an extended warranty
The probability that the selected customer purchased a Brand 1 model is 0.14.
Given that probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. and 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty.
The probability that a customer would purchase Brand 1 model TV P(A)=0.70.
The probability that a customer purchases the extended warranty given that the customer purchased the Brand 1 model TV is
P(B|A)=0.20
P(A and B)÷P(A)=0.20
P(A and B)÷0.70=0.20
P(A and B)=0.14
Hence, the probability that the selected customer purchases a Brand 1 model and an extended warranty is 0.14.
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In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained.
a. What is the ratio of the number of milk cartons taken to the total number of milk cartons?
b. What is the ratio of the number of milk cartons remaining to the number of milk cartons taken?
Answer:
a. 73:100
b. 27:73
Step-by-step explanation:
total: 100
number remaining: 27
number taken: 100 - 27 = 73
a. taken:total = 73:100
b. remaining:taken = 27:73
#a
total milk cartons used=100-27=73
Total=100So the ratio is
73:100#b
It's already mentioned in question
The ratio is 27:73find the area and perimeter of the figures
Answer:
6x+6 or 4x+10
Step-by-step explanation:
hope u like it
Answer:
a) 196cm^2
b) 225cm^2
c) 180 cm^2
Step-by-step explanation:
a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.
a = (14cm)^2
a = 196cm^2
b) a = (15cm)^2
a = 225cm^2
c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.
a = l x w
a = 18cm x 10 cm = 180 cm^2
:)
Add the following two numbers in scientific notation.
Answer:
3.31 x 10^4
Step-by-step explanation:
3.111 x 10^4 is 31110
2 x 10^3 is 2000
31110 + 2000 = 33100 or 3.31 x 10^4
Answer:
b) 3.31 × 10⁴
Explanation:
[tex]\sf \rightarrow \left(3.11\cdot 10^4\right)+ \left(2\cdot 10^3\right)[/tex]
remove parenthesis
[tex]\rightarrow \sf 3.11\cdot \:10^4+2\cdot \:10^3[/tex]
simplify
[tex]\rightarrow \sf 31100+2000[/tex]
add the numbers
[tex]\sf \rightarrow 33100[/tex]
convert to scientific form
[tex]\sf \rightarrow 3.31 \ x \ 10^4[/tex]
I need help please :3
Answer:
32ounces
Step-by-step explanation:
24/3=8pounds
8pounds=8x16=128ounces
but each 8 pounds is split into quarters so
8/4=2pounds=32ounces
can someone please help me
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = -3 [/tex]
[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]
[tex]\qquad \tt \rightarrow \: f(4) = 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
F(x) represents the value of y on curve for given value of x
[tex] \textsf{\large First -} [/tex]
[tex]\qquad \tt \rightarrow \: f(0) =( 0) {}^{2} - 3[/tex]
[ since 0 < 2 ]
[tex]\qquad \tt \rightarrow \: f(0) = 0 {}^{} - 3[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = - 3[/tex]
[tex] \textsf{\large Second} [/tex]
[tex]\qquad \tt \rightarrow \: f(2) = (2) {}^{2} - 3[/tex]
[ since 2 = 2 ]
[tex]\qquad \tt \rightarrow \: f(2) = 4{}^{} - 3[/tex]
[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]
[tex] \textsf{\large Third -} [/tex]
[tex]\qquad \tt \rightarrow \: f(4) = - 4 + 5[/tex]
[ since 4 > 2 ]
[tex]\qquad \tt \rightarrow \: f(4) = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please help! I am stuck on this
Answer:
c.
Step-by-step explanation:
Assuming we are not restricting the domain of f, the inverse isn't a function
[tex] \frac{1}{ {x}^{2} } - 7[/tex]
[tex]y = \frac{1}{ {x}^{2} } - 7[/tex]
[tex]x = \frac{1}{ {y}^{2} } - 7[/tex]
[tex]x + 7 = \frac{1}{ {y}^{2} } [/tex]
[tex] {y}^{2} = \frac{1}{x + 7} [/tex]
[tex]y = \sqrt{ \frac{1}{x + 7} } [/tex]
Since square root are Positve or negative, the function will not be a function.
The correct answer is c.
Hello hello :))) please help me with this problem
If a hotel decreases the price of its rooms from $80 to $40. As a result, the total quantity demanded of its service increased from 2000 to 4000. Which type of price elasticity of demand does the hotel room have?
a.
Elastic
b.
Inelastic
c.
Perfectly inelastic
d.
Unitary
PLEASE ANSWER ASAP!!!!!!!!!
How is the product of a complex number and a real number represented on the coordinate plane?
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° counterclockwise rotation of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a 90° counterclockwise rotation of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° clockwise rotation of the complex number.
The statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number:
= 6 + 4i
Multiplied by 3:
= 18 + 12i
If we plot on the coordinate plane there will be no rotation the scalar has changed by multiplying with a real number.
Thus, the statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
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A rectangle has perimeter 16 m. Express the area A (in m2) of the rectangle as a function of the length, L, of one of its sides.
The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
What is the perimeter of a rectangle?The perimeter of a rectangle is P = 2(L + W) where
L = length of the rectangle and W = width of the rectangleGiven that P = 16 m,
P = 2(L + W)
16 = 2(L + W)
16/2 = L + W
L + W = 8
So, W = 8 - L
What is the area of the rectangle?
The area of the rectangle, A = LW where
L = length of the rectangle and W = width of the rectangleSince W = 8 - L, substituting W into the equation for A, we have
A = LW
A = L(8 - L)
A = 8L - L²
So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
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a women is 34 years older than her dauhter eiht years ago she was 3 times as old as her daughter what is the age of her daughter now?
Answer:
The daughter is 14 years old
Step-by-step explanation:
34＋8＝42
42÷3=14
What is the value of x in the figure below? In this diagram, ABD ~ CAD.
Answer:
[tex] \sqrt{30} [/tex]
Step-by-step explanation:
altitude rule
10 / x = x / 3
x^2 = 30
x = sqrt(30)
Vivian and Noelle both leave the park at the same time, but in opposite directions. If Noelle travels 5 mph faster than Vivian and after 8 hours, they are 136 miles apart, how fast in mile per hour is each traveling
Vivian is traveling at 6 Noelle per hour and Noelle is traveling at x+5 = 11 Noelle per hour.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken.
Vivian and Noelle both leave the park at the same time, but in opposite directions, their total distance is the 136
Let Vivian's speed be = x
Let Noelle's speed be = x+5
They each can travel for 8 hours
so time = 8 hours
Distance = speed × time
136 = x(8) + (x+ 5) 8
136 = 8x + 8x + 40
96 = 16x
x = 6
So, Vivian is traveling at 6 Noelle per hour and Noelle is traveling at x+5 = 11 Noelle per hour.
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Sven makes bread rolls, he uses rye flour and wheat flour to the ratio 2:3. sven makes bread rolls using 250 g of rye flour, what mass of wheat flour does he use
