Answer:
Step-by-step explanation:
Hello, the sum of the roots is -9=-4-5 and the product is 20=(-4)*(-5) so we can write
[tex]x^2+9x+20=(x+4)(x+5)[/tex]
thanks
Answer:
( x + 4 ) ( x + 5 )
Step-by-step explanation:
For this polynomial, we will factor the coefficient of the x^2 term and the constant.
The coefficient of x^2 is 1, which just factors to 1.
The constant 20 factors into 2 * 2 * 5.
Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9. 4 + 5 = 9, so we will choose that.
Using the standard binomials, we will factor the polynomial:
( x^2 + 9x + 20 )
= ( x + 4 ) ( x + 5)
We can check by performing foil:
= ( x + 4 ) ( x + 5 )
= ( x * x + x * 5) + ( 4 * x + 4 * 5)
= ( x^2 + 5x ) + ( 4x + 20 )
= ( x^2 + 9x + 20 )
Thus, we have successfully factored our polynomial.
Cheers.
Type a simplified fraction as an answer. PLEASE ANSWER ASAP!!!!
Answer:
0.06944444444 as a fraction equals 6944444444/100000000000
Express the following expression in the form of a + bi: (39 + 34i) + (76 + 89i) - (47 +26i).
Answer:
68+97i
Step-by-step explanation:
work shown and pictured
Answer:
68+97i
Step-by-step explanation:
(39 + 34i) + (76 + 89i) - (47 +26i).
Distribute the minus sign
(39 + 34i) + (76 + 89i) + (-47 -26i)
Combine like terms
(39+76-47)+(34i+89i-26i)
68+97i
PLEASE HELPPPPP ASAPPPPPP
Answer:
2208
Step-by-step explanation:
So first we can write this as 4(500+50+2)
Then we distribute it 4*500+4*50+4*2
Multiply to get 2000+200+8
So the answer is 2208
One side of a triangle is one-fourth the longest side. The third side is 8 feet less than the longest side. The perimeter is 73. Find all three sides.
The sides gave lengths of __,__, and __
Answer:
b/4 +b + b-8 =73
2b + b/4 = 81
9b/4 = 81
9b =81 * 4
b = 9* 4
b = 36
The sides of the triangles are 9 inch, 28 inch and 36 inch respectively
Step-by-step explanation:
There are 12 peaches in a bananas in a fruit basket you get a snack for yourself and three of your friends by choosing four of the pieces of fruit at random .what is the probability that all four peaches ?
Answer:
10.2% chance
Step-by-step explanation:
There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.
So we can write it:
[tex]\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}[/tex] = [tex]\frac{11880}{116,280}[/tex] = .102 or 10.2% chance
For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.
12 * 11 * 10 * 9 = 11880
20 * 19 * 18 * 17 = 116,280
We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.
Answer:
10.2% probability
Step-by-step explanation:
12 peaches
8 bananas
Chance of getting a peach the first time is 12/20 the second time is 11/19, third 10/18, and fourth 9/17
11880/116280 = .1022 = 10.2% probability
what's the answer for p2 when p=25
Answer: p^2 = 25 ^2 = 625
Refer to the figure below. (Remember: The sum of the thre
Find a if A = 75°.
Answer:
15°
Step-by-step explanation:
The sum of three interior angles in a triangle is 180.
180-90-75=15°
Hi, what is the answer to 4 • 7 – 62 ÷ 3
Answer:
22/3
Step-by-step explanation:
[tex]4\times\:7-\frac{62}{3}\\\\\mathrm{Multiply\:the\:numbers:}\:4\times\:7=28\\=28-\frac{62}{3}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:28=\frac{28\times\:3}{3}\\=\frac{28\times\:3}{3}-\frac{62}{3}\\\\=\frac{28\times\:3-62}{3}\\\\28\times\:3-62=22\\\\=\frac{22}{3}[/tex]
PLEASE HELP ILL PICK YOUR ANSWER AS THE BRAINLIEST FOR POINTS! Jaime flipped a coin 20 times, and it landed on heads 15 out of the 20 times. Which would be the BEST way for Jaime to change his experiment so that his experimental probability of the coin landing on heads is closer to the theoretical probability? * 1 point He could use 20 different coins and flip each coin once. He could use 10 different coins and flip each coin twice. He could flip the coin only 2 times. He could flip the coin 100 times.
Answer:
the first one im pretty sure
Step-by-step explanation:
Answer:
The First one is correct im pretty sure.
Use the figure below. Find the value of KL. KL = 4x - 8 and KM = 6x − 4
Answer:
Equation:
LM = (1/2)KM
2x+4 = (1/2)(5x-6)
Hoped I helped
put a brainiest for me pls
The length of KL will be equivalent to 16.
What is the mid - point of the line segment?In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints. It bisects the segment.Given is to that KL = 4x - 8 and KM = 6x − 4
Since [M] is the midpoint, so we can write -
KL = (1/2)KM
(4x - 8) = (1/2)(6x - 4)
4x - 8 = 3x - 2
4x - 3x = 8 - 2
x = 6
So -
KL = (1/2)(6 x 6 - 4)
KL = (1/2) x 32
KL = 16
Therefore, the length of KL will be equivalent to 16.
To solve more questions on mid - points, visit the link below -
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PLS HELP FOR BRAINLIEST ANSWER
Answer:
Point C which is 1.
Step-by-step explanation:
A = -6
E = 8
M = (A + E)/2
M = (-6 + 8)/2 = 2/2 = 1
The midpoint is 1 which is point C.
8y=(5y+24) find the value of y
[tex]8y=5y+24[/tex] collect like-terms
[tex]8y-5y=24[/tex] subtract
[tex]3y=24[/tex] now divide
[tex]y = \frac{24}{3}\\[/tex]
[tex]y=8[/tex]
plug in the value of [tex]y[/tex] to check if the answer is correct:
[tex]8y=5y+24\\8(8)=5(8)+24\\64=40+24\\64=64[/tex]
ergo, [tex]y = 8[/tex]
50. Error Analysis for each of the past four years, Paulo has grown 2 in. every year, He is now 16 years old and is 5 ft 10 in. tall. He figures that when he is 22 years old he will be 6 ft 10 in. tall. What would you tell Paulo about his conjecture?
Answer:
I'd say that it's a good start, but he is assuming that his rate of growth will remain the same.
Since there are relatively few people 6'10" tall, it's likely that his extrapolation is too high.
Maybe if he could study the growth rates and heights at various ages of people who did achieve 6'10" height, he would have a sounder basis for his theory.
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = x3/2 y = 27 x = 0.
Volume of the solid generated by revolving the plane region about the y-axis is [tex]\frac{6561 \pi}{7}[/tex] .
Given, that y = x3/2, y = 27, x = 0
So, the volume of the solid generated by revolving the region about y axis will be,
[tex]V=\int_0^92\pi(x)(27-y)dx[/tex]
[tex]V=\int_0^92\pi x(27-x^{\frac{3}{2}})dx[/tex]
[tex]V=\left [ 27{\pi}x^2-\frac{4{\pi}x^\frac{7}{2}}{7} \right ]_0^9[/tex]
[tex]V=\left [ \frac{{\pi}\left(189x^2-4x^\frac{7}{2}\right)}{7} \right ]_0^9[/tex]
[tex]V=\frac{6561 \pi}{7}[/tex]
The image of the region bounded by plane is attached below.
Know more about volume of solid,
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The volume of the solid generated by revolving the plane region about the y-axis is approximately 6863.01 cubic units.
To use the shell method to find the volume of the solid generated by revolving the plane region about the y-axis, we need to express the limits of integration and the height of the infinitesimally thin cylindrical shells.
Given the equations:
y = x^(3/2)
y = 27
x = 0
To determine the limits of integration, we need to find the intersection points between the two curves: y = x^(3/2) and y = 27.
Setting the equations equal to each other:
x^(3/2) = 27
Taking the square root of both sides:
x = 27^(2/3)
x = 9
Therefore, the limits of integration are x = 0 and x = 9.
Now, let's consider an infinitesimally thin cylindrical shell with height "h" and radius "r" at some x value between 0 and 9.
The height of the shell, "h", is the difference between the y-values of the two curves:
h = 27 - x^(3/2)
The radius of the shell, "r", is the x-value.
The volume of the shell can be expressed as:
dV = 2πrh dx
To find the total volume, we integrate this expression from x = 0 to x = 9:
V = ∫[0, 9] 2π(27 - x^(3/2))x dx
Now, let's evaluate this integral:
V = 2π ∫[0, 9] (27x - x^(5/2)) dx
Integrating term by term:
V = 2π [(27/2)x^2 - (2/7)x^(7/2)] evaluated from 0 to 9
Plugging in the limits of integration:
V = 2π [(27/2)(9)^2 - (2/7)(9)^(7/2)] - 2π [(27/2)(0)^2 - (2/7)(0)^(7/2)]
Simplifying and evaluating the expression:
V = 2π [(27/2)(81) - (2/7)(3√(9))] - 0
V = 2π [1093.357] ≈ 6863.01 cubic units
for such more question on volume
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-7/10 is at least twice a number k minus 4. Write an inequality.
Answer:
-7/10 >= 2k - 4
Step-by-step explanation:
For this problem, we can simply follow the wording to write the inequality.
-7/10 is at least twice a number k minus 4
-7/10 >= 2k - 4
We use >= since is says at least, meaning it could be equal or greater than
We multiply k by 2 since it states the number is twice k
And we subtract 4 from the 2k since the number is "minus 4" from the twice k.
Thus, we have our inequality, -7/10 >= 2k - 4.
Cheers.
Lynne was making cookies and she
wanted to double the recipe. If the
recipe requires 2 cups of flour, how
much flour will Lynne need?
Answer:
4 cups of flour
Step-by-step explanation:
We just need to double 2. The phrase "double" means to multiply by 2 so the answer is 2 * 2 = 4 cups of flour.
Mark is a nurse anesthetist. He administers medication that puts people to sleep for surgeries and other invasive medical procedures. For healthy adults, the manufacturer recommends using a dose of 0.6mcg/kg, which means that Mark must give his patients 0.6mcg of medication for each kg they weight. If Mark's patient weights 60kg, how much medication should he administer?
Answer:
Quantity of medicine provide to patient = 36 mcg
Step-by-step explanation:
Given:
Quantity recommend = 0.6 mcg / kg
Weight of patient = 60 kg
Find:
Quantity of medicine provide to patient
Computation:
Quantity of medicine provide to patient = Weight of patient × Quantity recommend
Quantity of medicine provide to patient = 60 × 0.6
Quantity of medicine provide to patient = 36 mcg
The cost of renting a car is $75/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y = 75 + 0.25x, where x is the number of miles traveled. If your cost was $96.25, how many miles were you charged for traveling?
Answer:
We know we have to pay $75 per weel plus $0.25 for each mile we traveled, from that, if we call x the miles we have travelled, the total cost would be:
[tex]C = 75 + 0.25x[/tex]
As each mile we travel costs $0.25. Now that we have that expression, they ask us how many miles did we travel if we had to pay $96.25.
The only thing we have to do is replacing the C (our total cost) per $96.25 and solve the equation we get:
[tex]96.25=75+0.25x[/tex]
[tex]96.25-75=0.25x[/tex]
[tex]21.25=0.25x[/tex]
[tex]\frac{21.25}{0.25} = x[/tex]
[tex]85 = x[/tex]
We hve traveled 85 miles.
Divide 200cm in the ratio 5:3
Answer:
125 cm and 75 cm
125:75 = 5:3
Step-by-step explanation:
Let the number be 5x and 3x
we are taking these value because in ratio
a:b = ax:bx
that is if we multiply both part of ratio by a same number ratio remains same.
____________________________________________________
Since we have divided 200 cm in two parts with value 5x and 3x
Thus,
sum of 5x and 3x will be equal to 200 cm
5x+3x = 200cm
8x = 200cm
x = 25 cm
Thus,
first part = 5x = 5*25 = 125 cm
other part = 3x = 3*25 = 75cm
midpoint (-4.-27), endpoint (-5, -19)
Answer:
(-3,-35), and the slope is -8/1
Step-by-step explanation:
If you're trying to find the other endpoint, that's it, and the slope is -8/1
I need help with this
Show the steps to get full credit
3 (22 + 2) = 18 + 4(x – 5)
Answer:
[tex] \boxed{ \bold{ \huge \boxed{ \sf{x = 18.5}}}}[/tex]
Step-by-step explanation:
[tex] \sf{3(22 + 2) = 18 + 4(x - 5)}[/tex]
Add the numbers : 22 and 2
⇒[tex] \sf{3 \times 24 = 18 + 4(x - 5)}[/tex]
Multiply the numbers : 3 and 24
⇒[tex] \sf{72 = 18 + 4(x - 5) }[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{72 = 18 + 4x - 20}[/tex]
Calculate the difference
⇒[tex] \sf{72 = - 2 + 4x}[/tex]
Swap the sides of the equation
⇒[tex] \sf{ - 2 + 4x = 72}[/tex]
Move 2 to right hand side and change it's sign
⇒[tex] \sf{4x = 72 + 2}[/tex]
Add the numbers : 72 and 2
⇒[tex] \sf{4x = 74}[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{74}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 18.5}[/tex]
Hope I helped!
Best regards!!
Answer:
x=18.5
Step-by-step explanation:
3(22+2) =18 + 4(x-5)
3(24) = 18 + 4(x-5)
72=18+4(x-5)
4(x-5)+18=72
4x-20+18=72
4x= 72-18+20
4x=72+2
4x=74
x=74/4
x=18.5
3
En el numeral 341, 427,538 ¿Cuál dígito está
en el lugar de la centena de
millón? *
(1 Punto)
O A. 2
B. 7
O
C, 4
O
D. 3
Answer:
The answer is D. 3
Step-by-step explanation:
A number refers to the expression of a quantity or a magnitude. In mathematics, a number represents a fixed quantity of something or generally of a number system.
The numbers have a fixed order that determines their value.
The numbers are in order of:
Unit = 8
Ten = 3
Hundred = 5
Unit of thousand = 7
Ten thousand = 2
Hundred thousand = 4
Million unit = 1
10 million = 4
And a hundred million represented by = 3.
Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza. Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
Amount of money left on Keith's card in dollars = __________
Amount of money left on Mary's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
Answer:
a)Amount of money left on Keith's card in dollars = $90 - $15x
= $(90 - 15)
b) Amount of money left on Mary's card in dollars= $110 - $20x
= $(110 - 20x)
c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
$90 - 15x = $110 - 20x
Step-by-step explanation:
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
For Keith
Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza.
x numbers of pizza costs = $15x
Hence, the amount of money left on Keith's card after purchasing x pizzas =
$90 - $15x
For Mary,
Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.
Hence, x number of pizzas cost =$20 × x
= $20x
Therefore, the amount of money left on Mary's card after she buys x pizzas =
$110 - $20x
Amount of money left on Keith's card in dollars = __________
Amount of money left on Mary's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
To find the equation that shows that the two cards have the same amount of money =
Equation 1 = Equation 2
$90 - 15x = $110 - 20x
Collect like terms
-15x + 20x = $110 - $90
5x = 20
x = 20/5
x = 4
Hence, anytime Keith and Mary buys 4 pizzas their gift card will have the same amount of money left on them.
Which represents the solution set of the inequality 5x-9<21?
Answer:
Step-by-step explanation:
5x - 9 < 21
5x < 30
x < 6
1/2(30)-(40) this is on integers math maze freebie to search up
Answer:
hey thanks for ur points too
Step-by-step explanation:
maths:Mr John thinks of a number he double it he' result is 58 what is Mr John number
Answer:
Let x the number Mr John thinks
He double it so 2×x=2x ( double = multiplying by 2 )
The result is 58
So 2x=58
We solve the equation
2x=58
So x =58/2
x=19
So it's 19 the number Mr John thinks
pls help i give BRAINLIEST AND 50 POINTS
Answer:
60= per hour ....which is 1 hrs
so 120= 2 hrs
60+60
120
2hr is the answer
Answer:
3.5 hours
Step-by-step explanation:
[tex]speed \: = 60 \\ distance = 210 \\ time = \\ speed \: = \frac{distance}{time} [/tex]
[tex]time = \frac{distance}{speed} \\ time = \frac{210}{60} \\ time = \frac{7}{2} [/tex]
[tex]time = 3.5 \: hours[/tex]
Given <1 and <2 are a linear pair, find the value of x if m<1 = 2x-5 and m<2 = 4x-7
This is geometry, and I need help because I don't know if it adds up to 90 or 180 degrees.
Answer:
32
Step-by-step explanation:
Linear pair means they form a line, or add to 180°.
2x − 5 + 4x − 7 = 180
6x − 12 = 180
6x = 192
x = 32
g 1.32 Two points on a sphere of radius 3 are given as P1(3,0,30) and P2(3,45,45): (a) Find the position vectors of P1 and P2. (b) Find the vector connecting P1 (tail) to P2 (head). (c) Find the position vectors and the vector P1P2 in cylindrical and Cartesian coordinates.
Answer:
a) P.V of is OP₁ = [ 1.5i + 0j + 2.6k ], P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]
b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]
c) cylindrical coordinates are (1.5, π/2, 0.48)
Step-by-step explanation:
Given that;
r = 3
P₁ ( 3, 0°, 30° ), P₂ ( 3, 45°, 45° )
a)
P.V of P₁
x = rcos∅sin∅ = 3(cos0°) ( sin30°) = (3 × 1 × 0.5) = 1.5
y = rsin∅sin∅ = 3(sin0°) (sin30°) = (3 × 0 × 0.5) = 0
z = rcos∅ = 3(cos30°) = ( 3 × 0.866) = 2.6
∴ P.V of is OP₁ = [ 1.5i + 0j + 2.6k ]
P.V of P₂
x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5
y = rsin∅sin∅ = 3(sin45°) (sin45°) = (3 × 0.7071 × 0.7071) = 1.5
z = rcos∅ = 3(cos45°) = ( 3 × 0.7071) = 2.12
∴ P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]
b)
Vector connecting P₁ to P₂ is given by
OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]
= [ 0i + 1.5j + 0.48k ]
c)
P₁P₂ → = [ 0i + 1.5j + 0.48k ] = [ 1.5j + 0.48k ]
so in a cylindrical coordinate, it should be
r = √(o² + 1.5²) = 1.5
∅ = tan⁻¹[y/π] = π/2
z = 0.48
cylindrical coordinates are (1.5, π/2, 0.48)