Answer:
Ste(x−5)2=x2−10x 25
step-by-step explanation:
The standard form of a polynomial in one variable is a sum of terms in decreasing order of degree.
For brevity, terms with negative coefficients are usually written as subtractions rather than adding the additive inverses. That is, we would write
x
2
−
3
x
+
2
rather than
x
2
+
(
−
3
)
x
+
2
In order to express
(
x
−
5
)
2
in standard form, we need to multiply it out, combining terms of like degree. We can use the FOIL mnemonic to help:
(
x
−
5
)
2
=
(
x
−
5
)
(
x
−
5
)
(
x
−
5
)
2
=
First
(
x
)
(
x
)
+
Outside
(
x
)
(
−
5
)
+
Inside
(
−
5
)
(
x
)
+
Last
(
−
5
)
(
−
5
)
(
x
−
5
)
2
=
x
2
−
5
x
−
5
x
+
25
(
x
−
5
)
2
=
x
2
−
10
x
+
25
Alternatively, we can recognise a pattern and use it.
For example:
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
So we could take the second of these and put
a
=
x
,
b
=
5
to find:
(
x
−
5
)
2
=
x
2
−
2
(
x
)
(
5
)
+
5
2
(
x
−
5
)
2
=
x
2
−
10
x
+
25
The standard form is: [tex]x^2+10x+25[/tex].
We expand the given expression.
[tex](x + 5)^2\\=x^2+2(x)(5)+5^2\\=x^2+10x+25[/tex]
So the standard form is: [tex]x^2+10x+25[/tex].
Learn more: https://brainly.com/question/13769924
What should you do? Jason collects baseball cards. He has 33 cards. He wants to put 4 cards on each page of his book. How many pages will he need to put all of his cards in the book? Should you.. Ignore the remainder Ignore the remainder Increase the quotient by one Increase the quotient by one Remainder as the answer
Answer:
Increase the quotient by one
Step-by-step explanation:
Since in the question it is mentioned that There is a total of 33 cards and wants to put 4 cards on each page
So for determining the number of pages for put all of his cards
We should do increment in the quotient by 1 as there is a requirement of an additional page for the left cards
Therefore the above is the answer
(-1,2) (1,8)
Find the slope
Lucas buys sandwiches for the boys' basketball team. At the first game, he paid $85 for 17 sandwiches. At the second game, he will have to buy 21 sandwiches at the same cost per sandwich
How much will Lucas have to pay? Use any strategy to solve this problem.
O $90
O $105
O $110
O $120
Answer:
$105
Divide 85 by 17 which equals 5 so each sandwich cost $5. Then multiply 21 by 5 which is 105.
Write an equation of the line that passes through (2,-4) and is perpendicular to the line
y = -2x + 5 in slope intercept form
Answer:
y = (1/2)x - 5
Step-by-step explanation:
The slope of the line y = -2x + 5 is -2. The slope of any straight line perpendicular to this line is therefore the negative reciprocal of -2, which comes out to +1/2.
Using this fact, and the point (2, -4), we write out the slope-intercept form y = mx + b, and substitute the appropriate values:
-4 = (1/2)(2) + b
Then:
-4 = 1 + b, which yields b = -5
Thus, the desired equation is y = (1/2)x - 5
Use the expression $100 + 5n to find the total price for n students to take a field trip to the science museum. If 175 students go on the field trip, how much will total cost?
Answer:
Total cost= $975
Step-by-step explanation:
Giving the following information:
Total cost= 100 + 5*n
n= number of students
The $100 is a fixed cost. It remains constant no matter the number of students. The $5 is the unitary variable cost. The total variable cost increases with the number of students.
Total cost for 175 students:
Total cost= 100 + 5*175
Total cost= $975
If f(x) = 2x² then when x = 3, y will equal
Answer:
y = 18
Step-by-step explanation:
Given
f(x) = 2x² ( substitute x = 3 )
y = f(3) = 2(3²) = 2(9) = 18
What is the slope of the line passing through the points (-1, 3) and (4, - 7)?
A. -4/3
B. 3/4
C. 2
D. -2
Answer:
D
Step-by-step explanation:
-1,3
4,-7
-7-3=-10
4--1=5
-10/5=-2
PLSS HELP!! NEED ASAP!!! MARKING BRAINLIEST!!! PLS EXPLAIN!!! At the produce store you can buy 4 bags of bananas for $22.52. How much would it cost if you were to buy 2 bags?
Step-by-step explanation:
4 bags of bananas for $22.52
=> 2 bags of bananas for $22.52 * 2/4 = $11.26.
Hence it would cost $11.26.
In the accompanying diagram. altitude CD is
drawn to the hypotenuse of right triangle ABC. If
AD - 9 and AB = 13. find CD.
Someone help me please
To Find :
The value of side CD.
Solution :
Applying Pythagoras theorem in ΔABC :
[tex]AC^2 + CB^2=AB^2 \\\\AC^2 + CB^2 = 13^2[/tex] ....1)
Applying Pythagoras theorem in ΔACD and ΔCDB :
[tex]AD^2 + CD^2 = AC^2[/tex] ....2)
[tex]CD^2 + DB^2 = CB^2[/tex] ....3)
Adding equation 2 and 3, we get :
[tex]AC^2 + CB^2 =AD^2 + 2CD^2 + DB^2[/tex] ...4)
Solving equation 1) and 4), we get :
[tex]AD^2 + 2CD^2 + DB^2 = 13^2\\\\9^2 + 2CD^2 + ( 13 - 9 )^2 = 13^2\\\\2CD^2 = 72\\\\CD = 6[/tex]
Therefore, length of CD is 6 .
Jackson is buying a new TV for $650. He will also be
charged 7.5% in sales tax. What will be Jackson's total bill?
Is the answer 48.75
Answer:
his total bill would be 698.75
Step-by-step explanation
you only did half of the problem lol.
48.75 is just the sales tax. to get the total bill, you need to add 650 to 48.75 because 650 is the actual price of the TV
hope this helps :)
Answer:
This is an percentage change question to calculate this, simply:
7.5% * 650 is 48.75 (You are correct here)
But the question
asks for) "Jackson' total bill) therefore its 48.75 + 650 = 698.75
Cheers! :)
Escribe la ecuación: Un balón de baloncesto cuesta 10€ menos que uno de fútbol. Si 10 balones de fútbol y 4 de baloncesto cuestan 310€.
Responder:
14x - 40 = 310
Explicación paso a paso:
Dado que:
El baloncesto cuesta 10 € menos que un balón de fútbol
10 balones de fútbol y 4 de baloncesto cuestan 310 €
Para formar una ecuación:
Deje que el costo de:
Balón de fútbol = x
Costo del baloncesto = x - 10
Por lo tanto,
Costo de 10 balones de fútbol = 10 * x = 10x
Costo de 4 pelotas de baloncesto = 4 * (x - 10) = 4x - 40
Coste total :
Coste del balón de fútbol + coste del baloncesto = 310 €
10x + 4x - 40 = 310 €
14x - 40 = 310
14x = 310 + 40
14 veces = 350
x = 25 € = coste del balón de fútbol
Coste del baloncesto = 25 € - 10 € = 15 €
What is the probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32? Round your answer to the nearest
tenth of a percent.
A. 84.3%
B. 82.3%
C. 83.3%
D. 81.3%
Please tell me how to do this in my calculator
Answer:
The probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32 is 81.3%
Option D is correct.
Step-by-step explanation:
We need to find the probability that a data value in a normal distribution is between a z-score of -1.32 and a z score of 1.32.
We can write it as P(-1.32 < Z < 1.32)
It is equal to : [tex]P(-1.32 < Z < 1.32)= P(Z<1.32)-P(Z<(-1.32))[/tex]
Looking at z-score tables to find value of z=1.32 and z=-1.32
P(Z<1.32)= 0.90658
P(Z<-1.32) = 0.09342
Putting values and finding answer
[tex]P(-1.32 < Z < 1.32)= P(Z<1.32)-P(Z<(-1.32))\\ P(-1.32 < Z < 1.32)=0.90658-0.09342\\P(-1.32 < Z < 1.32)=0.81316\\P(-1.32 < Z < 1.32)=81.3\%[/tex]
So, the probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32 is 81.3%
Option D is correct.
i need help can someone plz solve this 20x-24y= -144
Answer:
if you are solving for x, x=-36/5+6y/5
if you are solving for y, y=6+5x/6
Step-by-step explanation:
Al considerar 52 m como la distancia entre dos puntos situados realmente 53.06 m
please help me brainliest for correct answer the sides of a triangle are as follows; (3x - 2), (-5x) and (8x + 7). what is the expression of the perimeter?
Answer:
Perimeter = 6x + 5.
Step-by-step explanation:
The perimeter is the sum of the three sides.
Perimeter = 3x - 2 + (-5x) + 8x + 7
= 3x - 2 - 5x + 8x + 7
= 3x - 5x + 8x - 2 + 7
= 6x + 5.
what is 1093 + 28478
Answer:
29571 is the answer welcome!!
Please help me I cant figure it out.
Answer:
24 possibilities
Step-by-step explanation:
3 colors X 8 numbers = 24 possibilities
If u = <5, -5>, v = <1, -4>, and w = <4, -9>, which operation gives the result represented in the graph?
Answer:
-2u+w
Step-by-step explanation:
Which would produce a larger balance: an annual interest rate of 8.05% compounded monthly or an annual interest rate of 8% compounded continuously? Explain.
Answer:
8% compounded monthly has higher yield
Step-by-step explanation:
Here, we want to compare which of the two options would give a higher yield
An interest rate of 8% compounded monthly or 8% compounded annually
Let us say we are looking at a time frame of two years
If compounded monthly, since there are 12 months in a year, there would have been a compounding of 12 * 2 = 24 times
While if it is annual, we would have only twice
The higher the number of times we compound, the more the return
helicopter is flying at an elevation of 450 feet. It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘. Find the distance between a point on the ground directly below the helicopter and the landing pad. Round your answer to the nearest whole number.
Answer:
138 feets
Step-by-step explanation:
Given that :
Angle of depression (α) = 16°
Elevation = height = 450 feets
Appling trigonometry :
From the picture attached :
Height / elevation = 450 feets (Adjacent)
Distance = d (opposite)
Tan α = opposite / Adjacent
Tan 17 = d / 450
450 tan17 = d
450 * 0.3057306 = d
d = 137.57880
Hence, distance between a point on the ground directly below the helicopter and the landing pad 138 feets
The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.
Given that,
The helicopter is flying at an elevation of 450 feet.
It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘.
We have to determine,
The distance between a point on the ground directly below the helicopter and the landing pad.
According to the question,
The angle of depression = 16°,
Elevation = height = 450 feet
And d is the distance,
The angle of depression is an important component used in trigonometric operations.
The angle of depression is formed when the observer stands on a ground higher than the object which he is trying to observe.
Therefore, The angle of depression is,
[tex]Tan16 = \dfrac{d}{450}\\\\0.28 = \dfrac{d}{450}\\\\d = 450 \times 0.28\\\\d = 129.03 \ feet[/tex]
Hence, The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.
To know more about Trigonometry click the link given below.
https://brainly.com/question/13760328
Find the value of x and y in the parallelogram. Helpp
Answer:
The answer is D.
Step-by-step explanation:
In a parallelogram, lengths are parallel to each other so we can assume that AB is parallel to CD and AD is parallel to BC. In order to find the value of x and y, you have to compare the expressions :
AB // CD
x - 2 = 24
x = 26
AD // BC
y = 11
Help pls o answers asap
Answer:
17 to 12
Step-by-step explanation:
it's monkeys to chimps
How long would it take me to earn $139.50 of interest at 6% interest rate if i started with $930
Answer:
I think 0.06
Step-by-step explanation:
Fractions help me please
Answer: the first one
Step-by-step explanation: 9/15 is indeed less than 4/5 which u can make 12/15
find the exact perimeter of square whose side length is 5∛16 cm
Answer:
P = 50.39 cm
Step-by-step explanation:
It is given that,
The side of a square, a = 5∛16 cm
We need to find the perimeter of the square.
Perimeter = sum of all sides.
All sides of a square are equal. Its perimeter is given by :
P = 4a
[tex]P=4\times 5\sqrt[3]{16} \\\\P=50.39\ cm[/tex]
So, the exact perimeter of the square is 50.39 cm.
Lines / and mare parallel. Line / can be represented by the equation 3x + 4y = 8. If line m passes through the po
m?
y-5= -
(x+2)
y +5 = -
44-2)
y-5= f «+2)
y+5 = ģ«-2)
Answer:B
Step-by-step explanation:
Answer:
B y-5=- 3/4(x-2)
Step-by-step explanation:
The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 25° angle with the water. To the nearest foot, how far is the boat from the cliff?
Group of answer choices
75 feet
129 feet
141 feet
27 feet
The distance between a boat and a cliff is 129 feet.
TrigonometryThe trigonometric functions are used to determine the distance and angle in real-life situations.
How to find the distance between a boat and a cliff using trigonometry?Consider the following diagram.
Let the distance between a boat and a cliff be [tex]x[/tex].
[tex]tan25^{o}=\frac{40}{x}[/tex]
[tex]x=\frac{35+25}{tan25}[/tex]
[tex]x=\frac{60}{0.4663}[/tex]
[tex]x=128.67[/tex]
Therefore, the distance between a boat and a cliff is 129 feet.
Learn more about trigonometry here-
https://brainly.com/question/26719838
#SPJ2
Please answer this question.
Answer:
Step-by-step explanation:
It’s 88
A box with inside area of 1.1m2 is covered with an unknown 0.163m of insulation material. Determine the thermal conductivity for the insulating material if a 62 W bulb is used to heat the box. The bulb maintains the inside temperature at 23oC higher than the outside temperature.
9514 1404 393
Answer:
0.40 W/(m·K)
Step-by-step explanation:
Units of thermal conductivity are ...
W/(m·K)
The length dimension in the denominator comes from the ratio of area to thickness. That is, we can compute the thermal conductivity from ...
(62 W)(0.163m)/(1.1 m²·23K) ≈ 0.40 W/(m·K)
Jim wants to make 2.7 quarts of a 60% alcohol solution by mixing together a 80% alcohol solution and a 20% alcohol solution. How much of each solution must Jim use?
Answer:
1.8 quartz of 80% solution and
0.9 quarts of 20% solution.
Step-by-step explanation:
Given that:
Total alcohol solution to be made = 2.7 quarts of 60% solution
Alcohol concentration in first solution= 80%
Alcohol concentration in second solution = 20%
To find:
How much of each solution must Jim use?
Solution:
Let amount of first solution to be used = [tex]x[/tex] quartz
Total amount is given as = 2.7 quarts
So, amount of second solution to be used = (2.7 - [tex]x[/tex]) quartz
As per question statement, we can write the following equation:
[tex]80\%\ of\ x +20\%\ of\ (2.7-x) = 60\%\ of\ 2.7\\\Rightarrow \dfrac{80}{100} x +\dfrac{20}{100} (2.7-x) = \dfrac{60}{100}\times 2.7\\\Rightarrow 4x+2.7-x =3\times 2.7\\\Rightarrow 3x=2\times 2.7\\\Rightarrow \bold{x =1.8\ quartz}[/tex]
First solution, 80% solution to be used = 1.8 quartz
Second solution, 20% solution to be used = 2.7 - 1.8 = 0.9 quartz