Given:
h(n)=-2n+3
g(n)=4n
The objective is to find
[tex](h\cdot g)(-2)[/tex]Let's rewrite the required function as
[tex]\begin{gathered} (h\cdot g)=h\lbrack g(n)\rbrack \\ h\lbrack g(n)\rbrack=-2(4n)+3 \\ h\lbrack g(n)\rbrack=-8n+3 \\ (h\cdot g)(-2)=-8(-2)+3 \\ (h\cdot g)(-2)=16+3 \\ (h\cdot g)(-2)=19 \end{gathered}[/tex]Hence the value of (hog)(-2)=19
Consider the following quadratic equation:35x2 = 13x + 12Step 1 of 2: Using the standard form ax² + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
Given: The quadratic equation below
[tex]35x^2=13x+12[/tex]To Determine: The two linear factors of the given equation using standard form of a quadratic equation
The standard form of a quadratic equation is given as
[tex]ax^2+bx+c=0[/tex]Re-write the given equation in the standard form as shown below
[tex]\begin{gathered} 35x^2=13x+12 \\ 35x^2-13x-12=0 \end{gathered}[/tex]Factor the left hand side as shown below
[tex]35x^2-28x+15x-12=0[/tex][tex]\begin{gathered} 7x(5x-4)+3(5x-4)=0 \\ (5x-4)(7x+3)=0 \\ \text{Therefore} \\ 35x^2-13x-12=0,in\text{ factored form is} \\ (5x-4)(7x+3)=0 \end{gathered}[/tex]Hence, the two linear factors of the given equation is
(5x -4)(7x + 3) = 0
2/5 x 3/7 in simple form
Answer:
2/5*3/7= 6/35
Step-by-step explanation:
Write 60% as afraction in lowest terms.
60% as a fraction is 3/5
To solve this, first we need to conver the percentage to decimal:
[tex]undefined[/tex]Consider the equation: 0=x^2– 10x + 101) Rewrite the equation by completing the square.Your equation should look like (x+ a)^2= b or (x – c)^2= d.
1) Considering the equation x²-10x +10 let's rewrite it completing the square
1.1 Let's divide the coefficient of the term 10x by 2. To find the most closer term of the perfect square. As 10 :2 = 5
Then:
(x-5)² =x²-10x +25
2) Since there was added 25 on the left side, we need to add 25 on the right side to keep this identity:
x² -10x +25 +10 = 0 +25
(x-5)² +10=25
(x-5)² =25-10
(x-5)² = 15
3) Since the question does not ask us to solve it. Then we can stop it here.
A well-known pizza franchise sells over 4×10 to the power of 11 pizzas age in the US well well-known fast food chain sells about 2×10 to the power of nine taco city in the US proximately how many times greater are there any pizza sales in that taco sales
A. create an expression to represent how many times greater the annual pizza sales are than the annual taco sales
Pizza sales are 200 times greater than taco sales.
What are exponent?Exponent tells us how many times a number is multiplied by itself.
For example : [tex]2 ^ 4 = 2 \times 2 \times 2 \times 2[/tex]. Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times..... \times a[/tex] (m times), a is the base and m is the index.
Here,
Number of pizzas sold = [tex]4 \times 10^{11}[/tex] pizzas
Number of Taco sold = [tex]2 \times 10^9[/tex] tacos
By the problem,
[tex]2 \times 10^9 \times x = 4 \times 10^{11}\\x = \frac{4 \times 10^{11}}{2 \times 10^9}\\ x = 2 \times 10^2\\x = 200[/tex]
Pizza sales are 200 times greater than taco sales.
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I Need help with this question.
How do you rewrite -8 - 4 = -12 in two different ways?
Answer:
Step-by-step explanation:
-4 - 8 = -12
-4 + 12 = 8
Susan said, "Venus is more than twice as far from the sun as Mercury is."
Is Susan correct? If so, write yes. If she is wrong, rewrite the statement to make it true.
You could change more to less, change the planets-do whatever you need to do to
make a TRUE statement for Susan.
Answer:
Venus bigger then mercury so it would be no so just change her answer
The temperature in Phoenix, Arizona is 97 degrees. The temperature on Antarctica can be -3 degrees.How far apart are the temperatures of these two cities?
Answer:
100 degrees
Explanation:
Given that:
The temperature in Phoenix, Arizona = 97 degrees.
The temperature on Antarctica = -3 degrees.
To determine how far apart the temperature of the two cities are, we find the difference in temperature.
[tex]\begin{gathered} \text{Difference }=97^0-(-3^0) \\ =97^0+3^0 \\ =100^0 \end{gathered}[/tex]The temperature in the two cities is 100 degrees apart.
Is the relationship between Climate Change and Forest Fires causal or it a correlation?
PHS AND FUNCTIONSg local maxima and minima of a function given the graph
A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but maybe) a global minimum
(a) The function h(x) has two local minimums. The values at which h has a local minimum is :
[tex]\text{0, 4}[/tex](b) The local minimum values of h:
[tex]=\text{ -2}[/tex]Where do the graphs of f of x equals cosine of the quantity x over 2 and g of x equals square root of 2 minus cosine of the quantity x over 2 intersect on the interval [0, 360°)?
Given the functions f(x) and g(x) defined as:
[tex]\begin{gathered} f(x)=\cos (\frac{x}{2}) \\ g(x)=\sqrt[]{2}-\cos (\frac{x}{2}) \end{gathered}[/tex]The intersection of the graphs will be at f(x) = g(x):
[tex]\begin{gathered} \cos (\frac{x}{2})=\sqrt[]{2}-\cos (\frac{x}{2}) \\ 2\cos (\frac{x}{2})=\sqrt[]{2} \\ \cos (\frac{x}{2})=\frac{\sqrt[]{2}}{2}=\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]This is true for:
[tex]\begin{gathered} \frac{x}{2}=45\degree\Rightarrow x=90\degree \\ \frac{x}{2}=315\degree\Rightarrow x=630\degree \end{gathered}[/tex]But only x = 90° is within the interval [0°, 360°)
Answer: 90°
9zxaA14ePolynomialThe parallelogram shown below is transformed. Identify the type of transformation thatoccurred, then write the algebraic rule that describes the transformation. Use a table like theone shown to help you.(5) = ?Copy the text below into the answer space and then replace the _ with your answer.Expression23-(1-1)Op 1 OpType of Transformation:Algebraic Representation: *Get reald67850.0 mLITGGPre-ImageImageWhathappensto x?Whathappensto y?E'HX3FHIG'GEH'9.Enter your answer
Given the parallelogram and its image
For the point E'
Pre image is E = (2 , 5 )
Image is E' = ( -2 , -5 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of F' ;
Pre - image is F = (4 , 8 )
Image is F' = ( -4 , -8 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of G' :
Pre - image is G = ( 6 , 5 )
Image is G' = ( -6 , -5 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of H' :
Pre - image is H = ( 4 , 2 )
Image is H' = ( -4 , -2 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
so,
As shown, Type of Transformation: is reflection over the point ( 0 , 0 )
Or can be written reflection Through the origin
Algebraic Representation: ( -x , -y )
the rule of translation
(x , y ) → ( -x , -y)
which inequality can be used to determine x the maximum number of outfits scarlett can purchase while staying within her budget?
Answer
Option C is correct.
The inequality that can be used to determine x, the maximum number of outfits Scarlett can purchase while staying within her budget is
640 ≥ 74.2x + 504.91
Hope this Helps!!!
What is the slope of the line passing through the points (2,
-5) and (4, 1)?
Answer: 3
Step-by-step explanation:
We can use the slope formula to calculate the slope of the line passing through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{1--5}{4-2} =\frac{1+5}{4-2} =\frac{6}{2} =3[/tex]
Suppose that an individual has a body fat percentage of 17.3% and weighs 151 pounds. How many pounds of his weight is made up of fat? Round your answer
to the nearest tenth.
14
Answer:26.1
Step-by-step explanation: This probably isn't the most efficient way to do it bus this is how I do percentages: Divide the number by 100 (151) and multiply it by the percentage (17.3) 151/100*17.3 is 26.123 and rounding it is 26.1
Please help with the Geometry question.
The numerical values of x and y are 16 and 63 respectively, where line m and n are parallel to each other.
What are the numerical values of x and y?From the diagram;
Angle (8x - 2)° as a vertical angle of (2y)° forms a same side exterior angle with ( 4x - 10 )°.
Note that, same side exterior angle are supplementary.
Hence;
(8x - 2)° + ( 4x - 10 )° = 180°
Solve for x
8x - 2 + 4x - 10 = 180
Collect like terms
8x + 4x - 10 - 2 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192/12
x = 16
Therefore, the numerical value of x is 16.
Next, angle (8x - 2)° forms a vertical angle with angle (2y)°.
Note that, vertical angles are equal.
Hence
(8x - 2)° = (2y)°
Plug in x = 16 and solve for y.
8x - 2 = 2y
8( 16 ) - 2 = 2y
128 - 2 = 2y
126 = 2y
2y = 126
y = 126/2
y = 63
Therefore, the numerical value of y is 63.
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6 4/5 divided by 3 2/9
Answer:
Step-by-step explanation:
[tex]6 \frac{4}{5}=\frac{34}{5}[/tex]
[tex]3 \frac{2}{9} = \frac{29}{9}[/tex]
[tex]\frac{34}{5} : \frac{29}{9} = \frac{34}{5}*\frac{9}{29} = \frac{306}{145} \\[/tex]
[tex]\frac{306}{145}=2\frac{16}{145} \\[/tex]
The table below shows the relationship between the number of water bottles at a park that are thrown away and the number of water bottles at the park that are recycled for each of five months. Which statement correctly descrīdes the relationship between the number of water bottles that are thrown away and the number of water bottles that are recycled at the park each month? Water Bottles at a Park Water Bottles Water Bottles Thrown Away Recycled 40 12 15 24 80 110 A. The relationship is proportional. For every 3 bottles that are thrown away each month, 10 bottles are recycled. B. The relationship is proportional. For every 10 bottles that are thrown away each month, 3 bottles are recycled. c. The relationship is not proportional. The number of water bottles that are thrown away increases more from month to month than the number of water bottles that are recycled. D. The relationship is not proportional. The difference between the number of bottles that are thrown away and the number of bottles that are recycled is not the same for each month.
EXPLANATION
As we can see in the picture, there is a proportional relationship between the bottles that are thrown away each month and those recycled.
Considering two ordered pairs as for instance, (x_1,y_1)= (40,12) and (x_2,y_2)= (50,15) give us the appropiate rate.
[tex]\text{rate}=\frac{y_2-y_1}{x_1-x_1}[/tex]The rate is as follows:
[tex]rate=\frac{(15-12)}{(50-40)}=\frac{3}{10}\frac{bottles\text{ recycled}}{\text{bottles thrown away}}[/tex]In conclusion, for each 10 bottles thrown away, there are 3 bottles recycled.
The answer is the option B.
wSubmit your answer as an exact fraction or a decimal rounded to thehundredths place.You're a player in a video game and have theoption to choose from 5 character options (elf,dwarf, human, ranger, wizard) and 4 weaponsoptions (axe, shield, spear, staff).What is the probability that you will not be aelf or use a axe?Show your work here
we know that
5 character options and 4 weapons options
so
Total outcomes =5*4=20
step 1
Not be an ef
P=16/20
step 2
use an axe
P=5/20 ------> (include 4/20 of the previous probabilty)
so
The probability is equal to
(16/20)+(5/20)-(4/20)=17/20
The answer is 17/20Find an equation for the linear function which has f(300)=1200 and f(800)=4300
f(x)=
The equation of the linear function is f(x) = (31/5)x - 660.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
Let the equation be:
f(x) y = ax + m
Now,
The linear function:
f(300) = 1200
f(800) = 4300
This can be written as:
1200 = 300a + m ____(1)
4300 = 800a + m ______(2)
From (1) we get,
m = 1200 - 300a _____(3)
Putting (3) in (2) we get,
4300 = 800a + 1200 - 300x
4300 = 500a + 1200
4300 - 1200 = 500a
3100 = 500a
a = 31/5
Now,
m = 1200 - 300a
m = 1200 - 300 x 31/5
m = 1200 - 60 x 31
m = 1200 - 1860
m = - 660
The equation can be written as:
f(x) = (31/5)x - 660
We can cross-check:
f(300):
= (31/5) x 300 - 660
= 31 x 60 - 660
= 1860 - 660
= 1200
Thus,
The equation of the linear function is f(x) = (31/5)x - 660.
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Find the equation of the line through the points (3,6) and (-1, 1).
Let's begin by listing out the information given to us:
(x, y) at point 1 = (3, 6)
(x, y) at point 2 = (-1, 1)
The equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-6}{-1-3}=\frac{-5}{-4} \\ m=\frac{5}{4} \end{gathered}[/tex]Substitute the slope (m) into the equation, we have:
[tex]\begin{gathered} y=mx+b \\ m=\frac{5}{4} \\ y=\frac{5}{4}x+b \\ \text{Substitute the value of x \& y into the equation from (}3,6) \\ 6=\frac{5}{4}\cdot3+b\Rightarrow6=\frac{15}{4}+b \\ b=6-\frac{15}{4}=6-3\frac{3}{4} \\ b=2\frac{1}{4}=2.25 \\ \\ \therefore y=\frac{5}{4}x+2.25 \end{gathered}[/tex]Which statement must be true if ARST = AXYZ?
OA LT = LX
OB. RS=XY
OC. RT = XY
OD. ZS = LX
RS = XY ,Because ΔRST & ΔXYZ are congruent .option c is correct .
What does the word "congruent" signify in mathematics?
If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence.SSS (three sides the same), RHS (right-angled triangle, hypotenuse, and a side the same), ASA or AAS (two angles and a side the same), and SAS are examples of similar triangle shapes (side-angle-side, two sides and the included angle the same).Are cogent means equivalent?
If and only if the measurements of two angles are equivalent, they are congruent. If and only if the two segments have equal measurements, they are congruent. A pair of triangles are identical if and only if their corresponding angles and sides are identical.In ΔRST & ΔXYZ are congruent so, ΔRST ≅ ΔXYZ
RS = XY Because ΔRST ≅ ΔXYZ .
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State all integer values of x in the interval (1 less than or equal to x less than or equal to 8 ) that satisfy the following inequality:
-3x+9 > 1
The inequality is -3x+9>1. The inequality value of x is greater then 8/3.
Given that,
The inequality is -3x+9>1
We have to find the x value.
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. When two values are not equal, we typically use the "not equal symbol ()".But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Take the inequality is greater then symbol,
-3x+9>1
-3x>1-9
-3x>-8
x>-8/-3
x>8/3
Therefore, the inequality value of x is greater then 8/3.
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When 91 is divided by 1 1/9 the quotient is closest to what whole number?
Justify your answer.
When 91 is divided by 1 1/9 the quotient is closest to 81.
What is a quotient?
When we divide a number by the dividend the result of the division is known as quotient.
We are given a number as 91
We have to divide 91 by 1 1/9
We get, [tex]\frac{91}{\frac{10}{9} }[/tex]
On simplifying the above equation we get,
[tex]\frac{91}{10}[/tex]·[tex]9[/tex]
[tex]=\frac{819}{10}[/tex]
=81.9
This can be rounded off as this value is close to 82.
Hence when 91 is divided by 1 1/9 the quotient is closest to 82.
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Convert the standard equation 9x + 3y =18 to slop intercept form.Covert the point slope equation y= 1/3 (x-3) -8 to slop-intercept form.
14.) Convert the standard equation 9x + 3y = 18 to slope-intercept form.
Converting the given equation into standard form means we will be transforming the given equation into the following form: y = mx + b.
We get,
[tex]9x+3y=18[/tex][tex]9x+3y-9x=18-9x[/tex][tex]\text{ 3y = 18 - 9x}[/tex][tex]\text{ }\frac{\text{3y}}{3}\text{ = }\frac{\text{18 - 9x}}{3}[/tex][tex]\text{ y = 6 - 3x}[/tex][tex]\text{ y =-3x + 6}[/tex]Therefore, the slope-intercept form of the equation 9x + 3y = 18 is y = -3x + 6.
15.) Covert the point slope equation y = 1/3 (x-3) - 8 to slope-intercept form.
From the point-slope equation y = 1/3 (x-3) - 8,
y = 1/3 (x-3) - 8
(y + 8) = 1/3(x - 3)
We get,
Slope = m = 1/3
x₁ = 3
y₁ = -8
To convert it to a slope-intercept form, let's first find the y-intercept (b).
Substitute m = 1/3 and x,y = 3, -8 in y = mx + b.
y = mx + b
-8 = 1/3(3) + b
-8 = 1 + b
-8 - 1 = 1 + b - 1
-9 = b
b = -9
Let's now complete the equation, substitute m = 1/3 and b = -9 in y = mx + b.
y = mx + b
y = (1/3)x + (-9)
y = 1/3(x) - 9
In summary,
The answer to question 14 is:
[tex]\text{ y =-3x + 6}[/tex]The answer to question 15 is:
[tex]y=\frac{1}{3}x-9[/tex]Let f(x)= sqrt x. Find (g)x, the function that is f(x) shifted up 2 units and left 5 units
The function f(x) becomes [tex]g(x)=\sqrt{x+5} +2[/tex] after shifting up 2 units and left 5 units.
How is a function vertically and horizontally shifted?Vertical shift: A new function g(x)=f(x)+k, where k is a constant, is a vertical shift of the function f(x), given a function f(x). The output values are all altered by k units. The graph will shift to the right if k is positive. If k is negative, the graph will shift downward.
Horizontal shift: A new function g(x)=f(x-h), where h is a constant, is a horizontal shift of the original function f, where f is a function. Graph shifts to the right if h is positive. If h is negative, the graph will shift to the left.
It is given that [tex]f(x)=\sqrt{x}[/tex].
The graph is shifted up 2 units first.
So, the function becomes [tex]\sqrt{x} +2[/tex]
Now the function is shifted 5 units to the left.
So, the new function. [tex]g(x)=\sqrt{x+5} +2[/tex]
So, the function f(x) becomes [tex]g(x)=\sqrt{x+5} +2[/tex] after shifting up 2 units and left 5 units.
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find the equation of the parabola with its focus at -5,0 and it's directrix y = 2
Recall that a parabola is a curve where any point is at an equal distance from the focus and the directrix, if (x,y) is a point on the parabola then:
[tex]\sqrt[]{(-5-x)^2+(y-0)^2}=2-y\text{.}[/tex]Solving for y we get:
[tex]\begin{gathered} (-5-x)^2+y^2=(2-y)^2, \\ (x+5)^2+y^2=4-4y+y^2, \\ -4y=(x+5)^2-4, \\ y=-\frac{1}{4}(x+5)^2+\frac{4}{4}, \\ y=-\frac{1}{4}(x+5)^2+1. \end{gathered}[/tex]Answer: Second option.
Which is the graph of g(x) = (0.5)^x+3 -4?
The graph of the function g(x) = (0.5)ˣ +3 -4 is shown (refer the graph attached below.)
What do we mean by the graph of the functions?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.So, the graph of the function g(x) = (0.5)ˣ +3 -4 will be:
(Refer to the graph attached below.)Therefore, the graph of the function g(x) = (0.5)ˣ +3 -4 is shown.
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The correct question is given below:
What is the graph of g(x) = (0.5)^x+3 -4?
What is the missing leg in the following expression below?
The figure shows a right triangle with a hypotenuse of lengths c = 65 and one of the legs of length a = 60.
The other leg can be calculated by using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]Solving for b:
[tex]b=\sqrt{c^2-a^2}[/tex]Substituting:
[tex]b=\sqrt{65^2-60^2}[/tex]Calculating:
[tex]\begin{gathered} b=\sqrt{4225-3600} \\ \\ b=\sqrt{625}=25 \end{gathered}[/tex]The missing leg is 25
What number should be placed in the box to help complete the division calculation
There is the number 224 should be placed in the box.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
As per the given division calculation,
It is 3200 and subtracted 226 - 224 to get 4, so if you try to divide 16 into 226 you will get 3 for the quotient, and then 224 for the product in the box. Then, subtract 226- 224 to go on with the division.
Hence, there is the number 224 should be placed in the box.
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