Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The pressure is given by:
P = 0.006A² - 0.02A + 120.
When the pressure is of 125 mmHg, we have that:
0.006A² - 0.02A + 120 = 125.
0.006A² - 0.02A - 5 = 0.
Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:
A = -30 and A = 27.
Age has to be positive, hence the man is 27 years old.
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Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd
Considering the result of the expression of the square of the sum, 2(2n² + 2) is always an even number, then when 1 is added it will always be an odd number.
What is the square of the sum notable product?It is given as follows:
(a + b)² = a² + 2ab + b².
In this problem, the expression is:
(2n + 1)² = (2n)² + 2(2n)(1) + 1²
= 4n² + 4n + 1
= 2(2n² + 2) + 1
The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an odd number squared is an odd number.
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Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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Choose the correct graph of the following condition. {(x, y) : x - y6}
The correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
What is a graph?
A graph is a diagram showing the relation between variable quantities each measured along one of a pair of axes at right angles.
In this case, the correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
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*30pts*What is the value of x in the triangle?
Answer:
A.4
Step-by-step explanation:
Using the sine rule
sin(α)/A equals sin(β)/B
From the question & inserting values,
sin(90°)/8 equals sin(30°)/x
∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8
∴x equals 4
You can learn more on the sine rule in case you get confused.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 8 ( divide both sides by 2 )
x = 4
What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
The value of x in the right angle triangle is 45 / 4 units
How to find the side of a right triangle?AB² = 20² - 15²
AB = √400 - 225
AB = √175
AB = √175 units
Hence, using similarity ratio,
x / 15 = 15 / 20
cross multiply
20x = 225
x = 225 / 20
x = 45 / 4
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I will give Brainliest
Which is a discrete random variable?
W = "exact time it takes for a computer to update its software"
Z = "results of flipping two coins"
X = "weight of the microprocessor inside your computer"
Y = "height of an emperor penguin on Antarctica"
Answer:
I believe that it should be Y; Height of an emperor penguin on Antarctica
Answer:
Z = "results of flipping two coins"
Step-by-step explanation:
A discrete variable is one which can take only certain values and usually represents values that are counted. The result of flipping two coins can only take a certain number of values of heads or tails (1 head and 1 tail, two heads, or two tails); therefore it is a discrete variable.
A continuous variable is one which can take any value, and usually represents values that are measured. The rest of the options provided (W, X, and Y) are all measurements, and are therefore continuous, not discrete.
Also, among the options presented, option Z is the only one which is "random".
Giving you the brainliest!
Answer:
The answer will be J
Step-by-step explanation:
Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.
Therefore the Answer Will Be J: 70,000 timed by 0.20.
Expert-Certifieder of Cousin.
file attached belowfile attached below
D − 37 = 40
D =
Check your solution.
− 37 = 40
Number of Potatoes
36
24
12
5
10
Number of Pounds
x
15
Use the graph to find the unit rate.
potatoes per pound
A recipe calls for 4 cups of peanuts for 5 cups of flour. Using the same recipe, how many cups of flour will you need for 3 cups of peanuts
I really need help
What is the equation for the following word problem: Hayden is selling snacks for $1.50 each. If he made $15, how many snacks did he sell?
Answer:
10
Step-by-step explanation:
15 ÷ 1.5 = 10
Which shows the first step in the solution to the
equation log₂x + log₂(x - 6) = 4?
log was used calculate big numbers before calculators
log is a re-arranged way to show a number with an exponent
example
log₂ 16 = 4 means 2^4 = 16
logx(Z) = y means x^y=Z
log(x-6)/log(2) + log(x)/log(2) = 4
(log(x-6)+ log(x))/log(2) = 4
(log(x-6)+ log(x)) = 4log(2)
(log(x-6)x) = log(16)
x=8
Question 5 of 10
Which function is shown in the graph?
Answer:
A
Step-by-step explanation:
By looking at the graph you can eliminate B as a choice since the denominator is 1+x which means it would have a vertical asymptote as x=-1 which doesn't correspond with the graph shown. You can also eliminate C since the function doesn't have a vertical asymptote as x=3 since the denominator of the function is 3-x meaning it would be undefined at x=3. It should be A since it appears to approaching 1 with a vertical asymptote at x=1 which corresponds with the denominator 1-x. If you plug in the value 0 as x you get 3 which is what is shown on the graph when x equals 0
Enter the amplitude of the function. f(x)=2sin x
Answer:
2
Step-by-step explanation:
In asin(bx - c) + d, a is the amplitude. In this case, it's 2.
Brainliest, please :)
A rectangular basketball court measures with a length of 82yds and
Width of 38 yards What is the perimeter and area?
Answer:
area:3116 perimeter:240
Step-by-step explanation:
the formula of area is always length x width=82x38 =3116the formula for the perimeter is always length+length+width+width=82+82+38+38 =240Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}\circ\leftharpoonup}}[/tex]
Pelet'rimeter =
Area = 3116 cm^2
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}\circ\leftharpoonup}}[/tex]
[tex]\bullet[/tex] Let's work out the perimeter
[tex]\twoheadrightarrow\sf P=2(a+b)[/tex]. a=length & b=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf P=2(82+38)[/tex]
[tex]\bullet[/tex] Perform the addition operation
[tex]\twoheadrightarrow\sf P=2\cdot120[/tex]
[tex]\bullet[/tex] Multiply and obtain the perimeter
[tex]\twoheadrightarrow\sf P=240cm[/tex]
[tex]\bullet[/tex] Now let's find the area
[tex]\twoheadrightarrow\sf A=lw[/tex] l=length w=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf A=82\cdot38[/tex]
[tex]\bullet[/tex] Multiply and obtain the area
[tex]\twoheadrightarrow\sf A=3116cm^2[/tex]
--
Hope that this helped! Best wishes.
[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]
--
What's the solution to –9x + 4 < 40? Question 4 options: A) No solutions B) All real numbers C) x > –4 D) x < –6
Hey there!
-9x + 4 < 40
SUBTRACT 4 to BOTH SIDES
-9x + 4 - 4 < 40 - 4
SIMPLIFY IT!
-9x < 40 - 4
-9x < 36
DIVIDE -9 to BOTH SIDES
-9x/-9 < 36/-9
SIMPLIFY IT!
x < 36/-9
x < -4
Therefore, the answer should be:
x < -4
(The graph is down below)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
You can make a tent by throwing a piece of cloth over a clothesline, then securing the edge to the ground with stakes so that an isosceles triangle is formed. How long would the cloth have to be so that the opening of the tent was 8 feet wide and 3 feet high?
Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.
How long should the length of the cloth be?The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.
That length - according to the Pythagoras theorem - would be:
= √(6² + (8 /2)²)
= √(36 + 16)
= 7.2 ft
As this is the length of one side of the cloth, the length of the entire cloth is:
= 7.2 x 2
= 14.4 ft
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14. What is the measure of ZABC in the image shown? OE A B 10x - 10 100 - 2x 2x + 10 C 14. What is the measure of ZABC in the image shown ? OE A B 10x - 10 100 - 2x 2x + 10 C
Answer: 110 degrees
Step-by-step explanation:
By the exterior angle theorem.
[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]
The power of an exponential expression raised to a power is the product of the exponents.
Answer:
[tex](y {}^{c} ) {}^{d } = y {}^{c \times d} \\ = y {}^{cd} \\ \\ \\ \\ \\ (v {}^{3} ) {}^{7 } \\ = v {}^{3 \times 7} \\ = v {}^{21} [/tex]HOPE THAT HELPS.Which point is a reflection of Z(5/1, 3) across the x-axis? Please I will give the brainliest
Answer: (5/1, -3)
Hope this helps :)
Answer:
Look at the attachment.
Step-by-step explanation:
Look at the attachment.
Examples for Continuous rv X
1. Given the pdf:
f(x) {1/4 e^-1/4x} x>0
0, otherwise
Find: a. E(X) and b. Var(X)
Use the definitions of expectation and variance.
Expectation[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]
Integrate by parts,
[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]
with
[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]
[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]
(since the integral of the PDF is 1, and this integral is 4 times that)
Variance[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]
Compute the so-called second moment.
[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]
Integrate by parts, with
[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]
[tex]E(X^2) = 8 E(X) = 32[/tex]
and the variance is
[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]
6x+2y=20 2x-3y=3 solve by substitution
The solution of the system of linear equation by substitution method is (3,1).
What is the method of substitution?The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.
Given here the linear equations are
Equation 1: 6x+2y=20
Equation 2: 2x-3y=3
in equation 1 the value of y will be
6x+2y=20
⇒2y=20-6x
⇒y=(20-6x)/2
⇒y=10-3x
substituting the value of y in the equation 2, we will get
2x-3y=3
⇒2x-3(10-3x)=3
⇒2x-30+9x=3
⇒11x-30=3
⇒11x=30+3
⇒11x=33
⇒x=33/11
⇒x=3
putting the value of x in value of y in equation 1
y=10-3x
⇒y=10-3(3)
⇒y=10-9
⇒y=1
The solution of the system of linear equation by substitution method is (3,1).
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Question 10 of 33
Which of the following is a characteristic of a regular tessellation?
O A. It uses only one type of regular polygon.
OB. It uses more than one type of regular polygon.
O C. It allows for overlaps and spaces between shapes.
OD. It does not cover a surface completely.
SUBMIT
A tessellation that uses only one type of regular polygon.
What is Polygon?
The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.
A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.
Hence, A is the correct option.
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determine if x-3 is a factor of f(x)=x^3-x^2-5x-3
Step-by-step explanation:
please mark me as brainlest
Answer:
(x - 3) is a factor of the given function
Step-by-step explanation:
Given function:
[tex]\implies f\:\!\:(x)=x^3-x^2-5x-3[/tex]
If (x - 3) is a factor of the given function then [tex]f\:\!\:(3) = 0[/tex]
Substitute x = 3 into the function and solve:
[tex]\implies f\:\!\:(3)=(3)^3-(3)^2-5(3)-3[/tex]
[tex]\implies f\:\!\:(3)=27-9-15-3[/tex]
[tex]\implies f\:\!\:(3)=0[/tex]
Therefore, as [tex]f\:\!\:(3) = 0[/tex] then (x - 3) is a factor of the given function.
Terick ran 2 3of a mile in 8 minutes. It took Chad 40 minutes to run 3 1 4miles. a. If Terick runs at that speed, how long will it take him to run one mile?
The time taken for Terick to run one complete mile is determined as 12 minutes
Speed of Chad
The speed of chad is calculated as follows;
s = distance/time
s = (3.25 miles)/(40)
s = 0.08125 miles/min
Total distance ran by Terick2/3 of a mile = 8 mins
1/3 of a mile = ?
1/3 of a mile = 4mins
1 mile = 8 mins + 4 mins = 12 mins
Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.
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Complete the following table using the equation: y = -2x²
The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The equation of the parabola will be
y = -x²
The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
The graph of the function is given below.
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if 200÷10=4×u then u=?
Answer:
The answer is 5
Because 200÷10 =20.
So I'm this case, 4x=20. Divide both sides by 4 and the answer is 5. So X=5
5
Answer:
u = 5Step-by-step explanation:
if 200÷10=4×u then u=?
200 : 10 = 4u
20 = 4u
u = 20 : 4
u = 5
---------------------------
check
200 : 10 = 4 * 5
20 = 20
the answer is good
If f(x) = 6x² - 4 and g(x) = 2x + 2, find (f- g)(x)
Step-by-step explanation:
[tex]f(x) = 6 {x}^{2} - 4[/tex]
[tex]g(x) = 2x + 2[/tex]
[tex] \: [/tex]
[tex] = (f - g)(x)[/tex]
[tex] = f(x) - g(x)[/tex]
[tex] = 6 {x}^{2} - 4 - (2x + 2)[/tex]
[tex] = 6 {x}^{2} - 4 - 2x - 2[/tex]
[tex] = 6 {x}^{2} - 2x - 4 - 2[/tex]
[tex] = 6 {x}^{2} - 2x - 6[/tex]
[tex](f - g)(x) = 6 {x}^{2} - 2x - 6[/tex]