Answer:
A. 6
Step-by-step explanation:
f(x) = x² − 12x + 7
To complete the square, we first factor the leading coefficient to make it 1 (which it already is).
Then, we take half the second coefficient, square it, and then add to both sides. So (-12/2)² = (-6)² = 36.
f(x) + 36 = x² − 12x + 36 + 7
Then we factor the perfect square:
f(x) + 36 = (x − 6)² + 7
Then solve for f(x) by subtracting and simplifying:
f(x) = (x − 6)² + 7 − 36
f(x) = (x − 6)² − 29
So the value of a is 6.
a segment has endpoints at (1, -2) The midpoint is at (-4, -2). What are the cooordinates of the other endpoint?
Answer:
coordinate of the other endpoint is (-9,-2)
Step-by-step explanation:
Given that a segment has endpoints at (1, -2). The midpoint is at (-4, -2).
Now we need to find about what are the coordinates of the other endpoint.
let the coordinates of other end points are (x,y)
Then mid point of (1,-2) and (x,y) is given by mid point formula:
[tex]\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]
[tex]\left(\frac{x+1}{2},\frac{y-2}{2}\right)=(-4,-2)[/tex]
[tex]\Rightarrow \frac{x+1}{2}=-4, \frac{y-2}{2}=-2[/tex]
[tex]\Rightarrow x+1=-8, y-2=-4[/tex]
[tex]\Rightarrow x=-9, y=-2[/tex]
hence coordinate of the other endpoint is (-9,-2)
Answer:
what the otherperson said
Step-by-step explanation:
just read what the other person said
Focus on number two ok
anwser is 5/12
dividing a fraction is the same as multiplying by a reciprocal
Each of 33 samples has a different standard deviation how many of the 33 samples could be from the same population A)33.
B)30.
C)31.
D)32
Answer:
A) 33
Explanation:
There are always chances so you never know where the samples could be from. The answer 33 makes the most logical sense.
·Hope I helped, -SunnySideHelper·A.33.sample population
a fish is 12 meters below the surface of the ocean what is its elevation
The surface of the ocean is 0 meters.
Because the fish is below the surface it would be a negative number. ( it is less than 0)
The elevation of the fish would be -12 meters.
Answer:
-12 meters
Step-by-step explanation:
Elevation is the height above a given level, most often the sea. Therefore, elevation is like a vertical numerical line. If the sea level is 0, and to the right of the 0 is positive numbers, then the left has to be negative.
Therefore, the fish is -12 meters below sea level.
Are the triangles congruent? If so, how do you know?
O yes, because all the angles of the triangles are
acute
yes, because the triangles have three congruent,
corresponding angles
yes, because of ASA or AAS
not enough information given
C.yes, because of ASA or AAS
I think of a number, double it and add 14. The result is 36. What is the number?
Answer:
11
Step-by-step explanation:
11*2=22, 22+14=36, quick maths
Answer:
11
Step-by-step explanation:
36-14 gives you the doubled-number you chose, 22.
Then since the number is doubled, divide it by 2. 22÷2=11
Evaluate the function below for x = 2.
f (x) = 4x^3 - x^2 - 5x+7
Answer: [tex]f(2)=25[/tex]
Step-by-step explanation:
You know that the given function is:
[tex]f(x)=4x^3-x^2-5x+7[/tex]
You know that you must evaluate this function for [tex]x=2[/tex].
Then, to evaluate the function for [tex]x=2[/tex], you need to substitute this value into the given function and simplify it.
Therefore, you get:
[tex]f(x)=4x^3-x^2-5x+7\\f(2)=4(2)^3-(2)^2-5(2)+7\\f(2)=4(8)-(4)-10+7\\f(2)=32-4-10+7\\f(2)=25[/tex]
So, the answer is: [tex]f(2)=25[/tex]
How might logarithmic functions relate to earthquakes?
Answer:
Step-by-step explanation:
The way that this function looks when graphed could be similar to the seismic waves recorded when an earthquake hits.
A logarithmic measure known as the Richter scale is used to quantify the overall energy generated during an earthquake. Each number higher on the Richter scale denotes a ten-times-stronger intensity. For instance, a magnitude 5 earthquake is ten times more powerful than a magnitude 4 earthquake.
What is logarithmic function?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
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Confused??? on how to prove the equation, the first part of the problem
Answer:
Asin(wt + φ) = c2sinwt +c1coswt
Step-by-step explanation:
Proof:
wt here is periodic where as φ is constant
taking left hand side
Asin(wt + φ)
Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ
Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]
= Asinwtcosφ +Asinφcoswt
Now as we know φ is constant
so will Asinφ and Acosφ will also be constant
let Asinφ= c1
and Acosφ=c2
Putting in above expression, we get
Asin(wt +φ) = c2sinwt +c1coswt !
!HELP!
I need to write an expression for the shaded region in its simplest form, showing all of my steps!
But it's late at night and I'm not entirely sure how to do this, so thank you so much in advance!!!
Answer:
x² + 23x + 49
Step-by-step explanation:
Area of the big rectangle
= (x + 10)(2x + 5)
= 2x² + 5x + 20x + 50
= 2x² + 25x + 50
Area of the small white rectangle
= (x + 1)(x + 1)
= x² + x + x + 1
= x² + 2x + 1
Area of the shaded area
= (2x² + 25x + 50) - (x² + 2x + 1)
= 2x² + 25x + 50 - x² - 2x - 1
= x² + 23x + 49
find the area of each triangle to the nearest tenth.
9. Area = 59.755[tex]cm^{2}[/tex] square cm. when the area to nearest tenth then, area = 60 square cm.
10. Area = 22.9813[tex]mi^{2}[/tex]. When the area to nearest tenth then, area = 20 square mi.
Area of the Triangle:
Area of the triangle is = half of (base x height)
=> (1/2) x (b x h)
Trigonometry:
sinθ = opposite side / hypotenuse
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The area of the triangles are 59.8 square cm and 23.0 square miles
How to determine the area of each triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
The area of each triangle is calculated using the following sine equation
Area = 1/2absin(C)
Using the above as a guide, we have the following
Area of triangle 1 = 1/2 * 11 * 11 * sin(99 degrees)
Area of triangle 1 = 59.8 square cm
Area of triangle 2 = 1/2 * 5 * 12 * sin(50 degrees)
Area of triangle 2 = 23.0 square miles
Hence, the area of the triangles are 59.8 square cm and 23.0 square miles
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What is the range of a cosine function?
Final answer:
The range of a cosine function is the set of output values the function can take, which is always between -1 and +1. This applies to the standard cosine function and is unaffected by horizontal or phase shifts. This range is consistent with the definition of the cosine function as the ratio of the adjacent side to the hypotenuse in a right triangle.
Explanation:
The range of a cosine function refers to the set of possible values that the function can output. In mathematical terms, the cosine function oscillates between +1 and -1 irrespective of any horizontal shifts or phase shifts. A horizontal shift, demonstrated in Figure 15.8 (b), where the function is shifted by an angle φ (phase shift), does not alter the range of values of the function, which remain – from its minimum value of -1 to its maximum of +1.
Similarly, in Figure 16.10, a sine function, which is related to the cosine function, also oscillates between +1 and -1 every 2π radians (a complete cycle). This oscillation represents the wave function amplitude, which in cases other than a cosine can fluctuate between +A and -A.
As illustrated in Figure 2.18, the cosine function can be visualized as the ratio of the adjacent side to the hypotenuse (Ax/A = cos A) in a right triangle, further highlighting that this ratio (and thus the range of the cosine function) is between -1 and 1.
For example, when √(1+1)* approaches 1, it is indicative that cos 0 = 1, representing one end of the cosine function's range.
Eric wants to find out the most popular after-school activity among high school seniors at his school. What is the population in Eric’s survey?
Answer: The population in Eric's survey is the high school seniors.
Answer:
all high school seniors at Eric’s school
Step-by-step explanation:
Which quantity is proportional to 18⁄3? Check all that are true. 90⁄16 36⁄6 72⁄12 6⁄1 36⁄12
A quantity is proportional to 18/3 if it simplifies to the same value, which is 6. The proportional quantities are 90/15, 36/6, 72/12, and 6/1, as they all simplify to 6. The quantity 36/12 is not proportional since it simplifies to 3.
To determine which quantities are proportional to 18/3, we need to find what 18 divided by 3 equals and then compare this to the given fractions to check for equivalence. Calculating 18/3 gives us 6. Now, let's examine each option:
90/15: This fraction reduces to 6, which is proportional to 18/3.
36/6: This fraction also equals 6 after simplification, so it is proportional to 18/3.
72/12: Simplifying 72/12 gives us 6, making it proportional to 18/3
6/1: 6 divided by 1 is just 6, so this too is proportional to 18/3.
36/12: Simplifying 36/12 results in 3, which is not equal to 6, so it is not proportional to 18/3.
The length of a rectangle is 6m more then the width. The area is 40m^2 . What is the length and the width?
let the width of the rectangle be x
area of rectangle is l*b
x * (x + 6) = 40^2
x^2 + 6x = 40^2
x^2 + 6x = 1600
x + 6x =√1600
x + 6x = 40
7x = 40
x = 5.7
Hope you found this useful
Find the solutions of the quadratic equation 14x^2+9x+10=014x
2
+9x+10=014, x, start superscript, 2, end superscript, plus, 9, x, plus, 10, equals, 0.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i
28
9
±
28
479
istart fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i
(Choice B)
B
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i−
28
9
±
28
479
iminus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i
(Choice C)
C
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}−
28
9
±
28
479
minus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction
(Choice D)
D
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}
28
9
±
28
479
Answer:
Option B. [tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]14x^{2}+9x+10=0[/tex]
so
[tex]a=14\\b=9\\c=10[/tex]
substitute in the formula
[tex]x=\frac{-9(+/-)\sqrt{9^{2}-4(14)(10)}} {2(14)}[/tex]
[tex]x=\frac{-9(+/-)\sqrt{-479}} {28}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
substitute
[tex]x=\frac{-9(+/-)\sqrt{479}i} {28}[/tex]
[tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]
use the factor theorem to determine whether the first polynomial is a factor of the second polynomial
x-3 ; 2x^2-4x+30
Answer:
not a factor
Step-by-step explanation:
If (x - 3) is a factor then f(3) = 0
f(x) = 2x² - 4x + 30
f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0
Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)
Kristina joined a health club. She paid an annual membership fee of $40 and $3.50 each time she worked out.
Part A
Write an equation to show the total amount, t, Kristina paid to go the health club z times.
Part B
Kristina spent a total of $110.00 before she stopped going to the health. How many times did she go to the health club?
Answer:
Part A) The equation is [tex]t=3.50z+40[/tex]
Part B) Kristina did go to the gym 20 times
Step-by-step explanation:
Let
t-----> the total amount
z----> the number of times that Kristina go the health club
Part A) Write an equation
we know that
The linear equation that represent this situation is
[tex]t=3.50z+40[/tex]
Part B) For [tex]t=\$110.00[/tex]
Substitute the value of t in the linear equation and solve for z
[tex]110.00=3.50z+40[/tex]
[tex]3.50z=110.00-40[/tex]
[tex]3.50z=70.00[/tex]
[tex]z=70.00/3.50[/tex]
[tex]z=20\ times[/tex]
Isabel received 4/7 of the 210 votes for cast for class treasurer. How many votes did she receive? Write your answer in simplest form
Answer:
120 votes
Step-by-step explanation:
So one way to solve this is by creating an equation to solve for x.
So we are given 4/7, that will be one side of the equation.
And we are trying to figure out how many votes out of the 210 she received, so on the other side of the equation we will have x/210, since we are solving for x.
So 4/7 = x/210
We want to get x alone, so we can multiply 4/7 by 210, which equals 120.
So x equals 120!
Isabel received 4/7 of the 210 votes for class treasurer, which equals 120 votes when the total is multiplied by the fraction.
The student is asking for help with a mathematics problem related to finding a fraction of a whole number. Isabel received 4/7 of the total votes cast for class treasurer, and the total number of votes cast was 210. To find how many votes Isabel received, we simply multiply 210 by 4/7:
Isabel's votes = (210) * (4/7)
Isabel's votes = 840 / 7
Isabel's votes = 120
Therefore, Isabel received 120 votes.
How did they get 0.97? Please show work, thank you!!
Answer:
see explanation
Step-by-step explanation:
0.97 is the value of cos14° to 2 dec. places
Use your calculator ( ensuring it is in degree mode )
press cos14 then = to obtain value 0.97
the product of x and the sum of 6 and 8 times the square of x
Answer:
x = 14; x = 0
Step-by-step explanation:
(x)(6 + 8) = x²
(x)(14) = x²
14x = x²
14x - x² = 0
(x)(14 - x) = 0
x = 14; x = 0
Find the height of a triangle with an area (a) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, a= 1/2bh
The height of rectangle is 10 inch
Answer:
10 inches
Step-by-step explanation:
HELP !!!!!!!!!!!!!!!!!!!
Hello There!
Your answer would be “B”
Forget about the -5 and just do 5 multiplied by 3 and you get a product of 15.
Then, make it negative and it would be 4^-15
the price of a meal was 29.85
the sales tax was 6% of the price of the meal
the tip was 15% of the meal and the sales tax
how much money did the smith family pay for the meal including the sales tax and tip
i believe they would spend $36.12
When point A( 3, 1) is translated 2 units to the right and 6 units up the coordinates of point A'
Answer:
A' = (5,7)
Step-by-step explanation:
So, we start with the original point A at (3,1), that means x = 3 and y = 1.
We move it 2 units to the right... so we're moving along the X-axis... and we're moving to the right.. so we're increasing the value of x. That means starting with x = 3, we go 2 more units... we then get to x = 5.
In the same way, we move 6 units up... so we move along the Y-axis. We go up, so we also increase the value of y. Starting with y = 1, we move up by 6 units... so we are now at y = 7.
A' point is then at (5,7).
Which of the following is an even function
Answer:
number2
Step-by-step explanation:
Answer:
f(x) = |x|
Step-by-step explanation:
function is even if and only if f(-x) = f(x)
f(x) = |x| ; regard to its sign f(x) = x
f(-x) = |-x| ; regard to its sign f(-x) = x
So answer is f(x) = |x| is the even function
What is 1 1/2 divided by 2?
Answer:
The answer is 3/4.
Step-by-step explanation:
1 1/2 is equal to 1.5.
1.5 divided by 2 is 0.75.
0.75 is equal to 3/4.
Answer:
Step-by-step explanation:
first you gotta make 1 1/2 an improper fraction then you put 2 over one to make a fraction to divide then swich 1 and 2 and multiply and the answer would be 3/4
The following equation represents the number of fish in a pond, F(x), after x number of weeks. F(x) = 500 (1.2)x. How many fish are in the pond after 4 weeks?
a. 600 fish
b. 1036 fish
c. 2000 fish
d. 2400 fish
How many fish are in the pond after 7 weeks?
a. 600 fish
b. 1036 fish
c. 1791 fish
d. 4200 fish
Answer:
1) d. 2400
2) d.4200
Step-by-step explanation:
As per given data:
F(x) represents number of fish
x represents number of weeks
Relation between F(x) and x is given as
F(x)= 500 (1.2)x
Now part 1:
How many fish are in the pond after 4 weeks=?
x=4
Putting in given equation F(x)= 500 (1.2)x
F(x)= 500(1.2)(4)
= 2400
Now part 2:
How many fish are in the pond after 7 weeks?
x=7
Putting in given equation F(x)= 500 (1.2)x
F(x)= 500(1.2)(7)
= 4200 !
Answer:
Correct choice is b. 1036 fish.
and c. 1791 fish.
Step-by-step explanation:
Given equation is [tex]f(x)=500(1.2)^x[/tex].
There x represents number of weeks. We need to find about wow many fish are in the pond after 4 weeks.
To find that we will plug x=4 into above formula and simplify
[tex]f(x)=500(1.2)^x[/tex]
[tex]f(x)=500(1.2)^{4}[/tex]
[tex]f(x)=500(2.0736)[/tex]
[tex]f(x)=1036.8[/tex]
Which is approx 1036
Hence correct choice is b. 1036 fish.
------
We can repeat same process with x=7 for 2nd problem
[tex]f(x)=500(1.2)^{7}=1791.5904[/tex]
Hence correct choice is c. 1791 fish.
A toy manufacturer uses 1,000 plastic wheels to make 250 toy trucks. If they use 3,584 plastic wheels in an 8 hour shift, how many toy trucks are made per hour?
Answer:
112 trucks
Step-by-step explanation:
so you take ratio:
1000-250
3584-x
x=896
and after you divide 896 by 8 hours and get 112
hope it helped you
In the given kite, AE = 6 ft, BE = 9 ft, and DE = 15 ft. Determine the area of the kite.
Answer:
72
Step-by-step explanation:
(24*6)/2 = 72
Answer:
[tex]144ft^2[/tex]
Step-by-step explanation:
For this problem, we can use the formula for the area of a kite.
[tex]A=\frac{pq}{2}[/tex]
Where p and q are the diagonals.
Since line AE starts at the edge of the kite and ends at the center, we can multiply its value by 2 to find the value of the p diagonal.
[tex]6*2=12[/tex]
So diagonal p is 12ft.
Now we can find the value of the q diagonal, which will be adding BE and DE.
[tex]9+15=24[/tex]
So diagonal q is 24ft.
Let's plug them into the area formula I mentioned earlier.
[tex]A=\frac{12*24}{2} \\ \\ A=\frac{288}{2} \\ \\ A=144[/tex]