Distribute [tex]50[/tex] to every term inside the parentheses.
[tex]50\cdotx^2+50\cdot7x+50\cdot6[/tex]
Simplify with multiplication.
[tex]\huge\boxed{50^2+350x+300}[/tex]
You can't simplify further by adding, so leave the answer as-is.
Answer:
50x^2 + 350x + 300
Step-by-step explanation:
Original Equation:
50(x^2+7x+6)
Distribute 50 to all 3 #'s:
50x^2 + 350x + 300
Use the ratio test to determine whether the series is convergent or divergent. 1+3/1*2*3+5/1*2*3*4*5+…
The [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the series is evidently
[tex]\dfrac{2n-1}{(2n-1)!} = \dfrac{2n-1}{(2n-1)(2n-2)!} = \dfrac1{(2n-2)!}[/tex]
By the ratio test, the infinite series converges, since
[tex]\displaystyle \lim_{n\to\infty} \left| \frac{\frac1{(2(n+1)-2)!}}{\frac1{(2n-2)!}}\right| = \lim_{n\to\infty} \frac{(2n-2)!}{(2n)!} = \lim_{n\to\infty} \frac1{2n(2n-1)} = 0 < 1[/tex]
What is the range of y equals square root of x +7+5?
The range of a function are the dependent variables for which the function exists. The range of the function will be y ≥ 5
Range of a function
The range of a function are the dependent variables for which the function exists
Given the function below;
f(x) = √x+7 + 5
The function can only exist for values less than or equal to -7 that is x ≤ -7.
Substitute
f(-7) = √-7+7 + 5
f(-7) = 5
The range of the function will be y ≥ 5
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19) Find the surface area of the solid shown that has a square base. 9 in 7 in 3 in
The surface area of the composite shape is: 315 in.².
What is the Surface Area of the Composite Shape?Surface area = surface area of square pyramid + surface area of square prism - 2(base area)
Surface area of square pyramid = Area of base + 1/2(perimeter of base × slant height) = 9² + 1/2[4(9) × 7] = 207 in.²
Surface area of square prism = 2a² + 4ah = 2(9²) + 4(9)(3)
Surface area of square prism = 2(9²) + 4(9)(3) = 270 in.².
Base area = 9² = 81 in.².
Surface area of the composite shape = 207 + 270 - 2(81) = 315 in.².
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Answer:
315 in.²
Step-by-step explanation:
Recall:
area of rectangle = length × width
area of triangle = base × height / 2
Base of prism: 9 in. × 9 in. = 81 in.²
4 sides of prism: 4 × 9 in. × 3 in. = 108 in.²
Lateral area of pyramid: 4 × 9 in. × 7 in. / 2 = 126 in.²
Total area = 81 in.² + 108 in.² + 126 in.² = 315 in.²
Lisandro fabrica juguetes. Si tiene 100 ruedas ¿Cuantos autos puede armar?
Me aydan porfa
Answer:
25
Step-by-step explanation:
un carro tiene 4 ruedas, entonces divide 100 por 4
100÷4=25
9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.
Step-by-step explanation:
Let assume that
Cost of 1 burger = $ x
Cost of 1 doughnuts = $ y
According to statement, 9 burgers and 1 doughnut cost $ 31.30
[tex]\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}[/tex]
According to statement again, 3 doughnuts and 6 burgers cost $ 26.70
[tex]\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}[/tex]
On substituting the value of y from equation (1), we get
[tex]\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}[/tex]
So,
Cost of 2 burgers = 3.2 × 2 = $ 6.4
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
2 burgers cost $ 6.40[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
We need to make linear equations, to solve this problem.
let the cost of each burger be x, and that of each doughnut be y.
[tex] \qquad❖ \: \sf \:9x + y = 31 .30[/tex]
[tex] \qquad❖ \: \sf \:y = (31 . 30 - 9x)[/tex]
put value of y in other equation.
[tex] \qquad❖ \: \sf \:6x + 3y = 26.70[/tex]
[tex] \qquad❖ \: \sf \:6x + 3(31.3 - 9x) = 26.70[/tex]
[tex] \qquad❖ \: \sf \:6x + 93.90 - 27x = 26.70[/tex]
[tex] \qquad❖ \: \sf \:6x - 27x = 26.70 - 93.90[/tex]
[tex] \qquad❖ \: \sf \:27x - 6x = 93.90 - 26.70[/tex]
[tex] \qquad❖ \: \sf \:21x =67 .20[/tex]
[tex] \qquad❖ \: \sf \:x = 67.20 \div 21[/tex]
[tex] \qquad❖ \: \sf \:x = 3.20[/tex]
So, cost of each burger is x = $ 3.20
[tex] \qquad \large \sf {Conclusion} : [/tex]
Therefore, cost of two burgers is :
2 × 3.20 = $ 6.40The number of bacteria in a culture is expected to grow 82% per hour over the next several hours. The predicted change in the number of
bacteria can be represented by P= 120(1.82) where P is the predicted number of bacteria t hours from now.
To the nearest tenth of a percent, by what percent is the number of bacteria expected to grow by each minute?
O .1%
O 1.0%
O 1.1%
O 1.4%
A six sided die is rolled and a coin is tossed. Find P(odd and T).
The probability of getting tails and rolling an odd number is P = 0.25
How to get the probability?
The probability of getting tails on the coin is 0.5
On the dice, there are 6 numbers and 3 are odd, so the probability of rolling an odd number is:
p = 3/6 = 0.5
The joint probability (of getting tails and rolling an odd number) is equal to the product between the individual probabilities:
P(odd and T) = 0.5*0.5 = 0.25
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Use the Pythagorean identity
to find cos X.
15
19
?]√
sin x =
COS X =
Answer:
Step-by-step explanation:
So sin is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. and cosine is defined as [tex]\frac{adjacent}{hypoteunse}[/tex]. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: [tex]a^2+b^2 = c^2[/tex]
[tex]15^2 + b^2 = 19^2[/tex]
[tex]225 + b^2 = 361[/tex]
[tex]b^2 = 136[/tex]
[tex]b = \sqrt{136}[/tex]
[tex]b = \sqrt{4} * \sqrt{34}[/tex]
[tex]b = 2\sqrt{34}[/tex]
This is the adjacent side, so now plug this into the cosine equation and you get: [tex]\frac{2\sqrt{34}}{19}[/tex]
to solve the system of equations below, Becca isolated x^2 in the firs equation and then substituted it into the second equation
The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1
Equationx² + y² = 9
x²/25 - y²/36 = 1
From (1)
x² = 9 - y²
substitute x² = 9 - y² into (2)
x²/25 - y²/36 = 1
(9-y²) / 25 - y²/36 = 1
Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1
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Answer:
(9-y²) / 25 - y²/36 = 1
Step-by-step explanation:
The perimeter of an equilateral triangle is 38 centimeters. Find the length of an
altitude of the triangle. Round to the nearest tenth.
Answer:
11.0 cm
P=38 cm
38/3=12.67cm length of one side
Base of triangle = 12.67/2 =6.34 cm
Use formula [tex]a^2+b^2=c^2[/tex]
[tex]6.34^2+x^2=12.67^2\\\\=11.0 cm[/tex]
x = altitude of triangle
The following data set is the age of customers at the ice cream shop:
18, 52, 42, 36, 5, 31, 29, 22
Find the mean.
Answer: About 29
Step-by-step explanation: First you need to add all the numbers together. Then you divide the sum, 235, by however many numbers you have (8). And BOOM: you got your answer :)
PS: If you have a decimal number, just round it up or down ( 5 and above give it a shove; 4 and below let it lie low)!
A florist made 4 bouquets of flowers. each bouquet had "c" carnations and 9
daisies. 4(c+9) this expression can be used to represent the total number of flowers the florist used for the bouquets.
The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used is 4c + 36
How to find equivalent expression?The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used.
total number of flower the florist used for the bouquet = 4(c + 9)
Therefore,
total number of flower the florist used for the bouquet = 4c + 36
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Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x? (–[infinity], –8) (–[infinity], 8) (–8, [infinity]) (8, [infinity])
(-∞,8) is interval is the solution to set 0.35x – 4.8 < 5.2 – 0.9x.
How to solve the inequality?0.35x - 4.8 < 5.2 - 0.9x
Adding 0.9x to both sides of equation.
0.35x - 4.8 + 0.9x < 5.2 - 0.9x + 0.9x
1.25x - 4.8 < 5.2
Adding 4.8 to both sides of equation.
1.25x - 4.8 + 4.8< 5.2 + 4.8
1.25x < 10
Dividing both sides of equation by 1.25
x < [tex]\frac{10}{1.25}[/tex]
Hence x < 8
Thus, (-∞,8) interval is the solution to given set 0.35x – 4.8 < 5.2 – 0.9x.
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Anna has been studying a type of bacteria that triples every month. originally, there were 4 bacterial cells. she wants to know how many there will be after 15 months. which equation should she use?
Anna should use the following equation,
[tex]a_{15} = 4(3)^{15}[/tex]
Equation for Determining the Number of Bacterial Cells
Initially, the count of bacterial cells = 4
It is given that the bacterial cell triples every month.
Hence, the equation for the count of bacterial cells after first month is,
a₁ = 4(3)
This count of 4(3) triples again in the second month.
So, after the second month, the equation for the count of bacterial cells is given by,
a₂ = 4(3)(3) = 4(3)²
Calculating the Count of Bacterial Cells For Each Month
Again, this count triples in the third month.
Therefore, the equation for the count of bacterial cells after the third month becomes,
a₃ = 4(3)(3)(3) = 4(3)³
This count triples again in the fourth month and this process continues till 15 months.
Hence, the equation for determining the number of bacterial cells comes out to be as follows,
a₁₅ = 4(3)¹⁵
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Bryce grew 312 inches each year for the past 4 years. how many inches total has bryce grown in the past 4 years?
X=
Help me please! Thanks so much
In the given diagram, the value of x is 15
Circle GeometryFrom the question, we are to determine the value of x
From one of the circle theorems, we have that
Opposite angles of a cyclic quadrilateral are supplementary.
Thus, in the diagram
5x + 7x = 180°
12x = 180°
x = 180°/12
x = 15
Hence, the value of x is 15
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how do you find the angle of 2/5ths of a circle
Answer:
You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.
A customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full. How many different combinations of boxes can be used for the customer's 15 chocolate pieces
There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.
It is given that a customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full.
The coefficient of [tex]x^{15}[/tex] from the steps shown in the image is 20.
Hence, there are 20 possibilities.
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two numbers that multiply to equal 20 and that also equal -12
Answer:
-10 and -2
Step-by-step explanation:
ONLY IF ITS two number that mutiply to equal 20 and their sum is -12
PLEASE HELP thank you!!!!
Answer:
The answer is C: 3/4
Step-by-step explanation:
Your equation is equal to (3/2)/(4/2) due to absolute value (all numbers are positive even if negative symbol is infront of it) which is equal to 3/4.
Step-by-step explanation:
what is the real problem definition ?
is there now an absolute value around the top "-2", or not ?
in any case, remember, when we divide 2 rational numbers like this :
a/b / c/d
the result is
"outer multiplication" over "inner multiplication" :
a×d / b×c
as alternative you can always also say
a/b / c/d = a/b × d/c = a×d / b×c
so,
if the problem is
3/-2 / |-4/-2|
the result is
3×2 / 4×-2 = 6/-8 = - 3/4
if the problem is
3/|-2| / |-4/-2|
the result is
3×2 / 4×2 = 6/8 = 3/4
please pick the solution based on the actual problem.
I don’t know what to do pls help me
Answer:
35
Step-by-step explanation:
Basically, since the angle HGF consists of HGE and EGF, then that means that HGF = HGE + EGF, and since EGF and HGF is given we plug this into the equation to get: 145 = HGE + 110, so HGE = 35.
Answer: 35°
Step-by-step explanation:
Hi!
The total angle is 145°
part of the angle is 110°
to find the missing angle, do 145 - 110 = 35°
Hope this helped :)
Amy is x years old. Ben is 2 years older than Amy. Alice is six years younger than Amy.
a) Write an expression for Ben's age and Alice's age in terms of x.
Answer:
Step-by-step explanation:
Amy = x years
Ben = x + 2 (years)
Alice = x - 6 (years)
Answer:
a)
Amy's age is x.
• Ben's age is 2 more than Amy's age.
∴ Ben's age = x + 2
• Alice's age is 6 less than Amy's age.
∴ Alice's age = x - 6
If g(x) = 4x² - 16 were shifted 9 units to the right and 1 down,
what would the new equation be?
[tex]9 \: units \: to \: the \: right \: = x - 9[/tex]
[tex]1 \: unit \: down \: = - 1[/tex]
[tex]g(x) = 4x {}^{2} - 16 \\ h(x) = 4(x - 9) {}^{2} - 17[/tex]
Letter AIf you anwser the question i give you brainly
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
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take a deck of playing cards form following sets out of those
A=Set of playing cards
B=SET OF RED COLOURED FACE CARD
The information given about the probability shows that the cardinality of D is 18.
How to calculate the probability?From the complete information, the number of red-colored cards is 26.
Also, the number of red-colored number cards will be 18.
The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.
Here, the cardinality of set D is 18.
Here is the complete question:
Take a deck of playing cards. Form following sets out of those:
A = Set of Face Cards
B = Set of Red Coloured Face cards
C = Set of Black Coloured Face Cards
D = Set of Red Coloured Number Cards
Find the Cardinality of set D
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For which function is f(5) = 2?
By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.
What function contains a given relationship?
In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.
After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:
f(5) = 5 - 3
f(5) = 2
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Answer:A which is x-3
Step-by-step explanation:
Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change in your answer.
The average rate of change of the function given is 56
Rate of change of a functionThe formula for calculating the rate of change of a function is expressed as;
f'(x) = f(b)-f(a)/b-a
where
b = 4
a = 2
f(4) = 2(4)^3 +1
f(4) = 129
f(2) = 2(2)^3 + 1
f(2) = 17
Substitute
f'(x) = 129-17/4-2
f'(x) = 112/2
f'(x) = 56
Hence the average rate of change of the function given is 56
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Calculate XY, if UV=25 and WZ=39
Answer:
Step-by-step explanation:
UV = [tex]\frac{XY+WZ}{2}[/tex]
[tex]\frac{XY+39}{2}[/tex] = 25
XY + 39 = 50
XY = 11
Add: (-5u5 + 5) + 7u5
Answer:
2u^5+5
Step-by-step explanation:
Drop parenthesis and add like terms.
[tex]7u^{5}-5u^{5}+5=2u^{5}+5[/tex]
Hope this helps!
If not, I am sorry.
line L has a slope of 9/8 the line through which of the following pair of points is perpendicular to line L
A pair of points which is perpendicular to line L is: D. (3, -5),(-6, 3).
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For points A, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-9)}\\\\Slope = \frac{9}{12}[/tex]
Slope = 9/12.
For points B, we have:
[tex]Slope = \frac{6\;-\;(-2)}{-6\;-\;(-9)}\\\\Slope = \frac{8}{-3}[/tex]
Slope = -8/3.
For points C, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-5)}\\\\Slope = \frac{9}{8}[/tex]
Slope = 9/8.
For points D, we have:
[tex]Slope = \frac{3\;-\;(-5)}{-6\;-\;3}\\\\Slope = \frac{-8}{9}[/tex]
Slope = -8/9.
In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
9/8 × 8/9 = -1
Thus, points (3,−5) and (−6,3) are perpendicular to line L.
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Complete Question:
Line L has a slope of 9/8. The line through which of the following pair of points is perpendicular to L?
A. (−9,−6),(3,3)
B. (9,−2),(−6,6)
C. (−5,−6),(3,3)
D. (3,−5),(−6,3)