The quadratic equation that describes the function is
f(x) = x² + 4x + 1
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is the table that describes the quadratic function h(x) as follows -
{x} h{x}
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
The quadratic equation is of the form given -
y = ax² + bx + c
For the point (0, 1), we can write -
1 = c ..... Eq{1}
For the point (1, 6), we can write -
6 = a + b + 1
a + b = 5 ...... Eq{2}
For the point (2, 13), we can write -
13 = 4a + 2b + 1
4a + 2b = 12 ...... Eq{3}
From Eq{2}, we can write -
a = 5 - b
So, the equation 3 can be written as -
4(5 - b) + 2b = 12
20 - 4b + 2b = 12
20 - 2b = 12
2b = 8
b = 4 ...... Eq{4}
then
a = 1 ...... Eq{5}
So, we can write the quadratic equation as -
f(x) = x² + 4x + 1
Therefore, the quadratic equation that describes the function is
f(x) = x² + 4x + 1
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Dana's survey showed that 3 out of 8 students preferred pepperoni pizza and
1 out of 8 preferred cheese pizza. How many more of the 72 students surveyed by
Dana preferred pepperoni pizza than preferred cheese pizza?
Answer:
18 more students preferred pepperoni pizza over cheese pizza in the survey.
Step-by-step explanation:
[tex]\frac{3}{8}[/tex] x [tex]\frac{72}{1}[/tex] Can be rewritten
[tex]\frac{3}{1}[/tex] x [tex]\frac{9}{1}[/tex] = [tex]\frac{27}{1}[/tex] = 27 I cross canceled the 8 and 72. They have a common factor of 8. 8 goes into 8 once and 8 goes into 72 9 times.
27 students preferred pepperoni pizza.
[tex]\frac{1}{8}[/tex] x [tex]\frac{72}{1}[/tex] = [tex]\frac{1}{1}[/tex] x [tex]\frac{9}{1}[/tex] = 9
9 students preferred cheese pizza.
27 - 9 = 18
what is the closest estimate of x where f(x) = g(x)?
g(x) = (2 (x+3))^3 + 4
.....................................
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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What Is the slope for these two points (3,-2) and (5,6)?
Answer:
4
Step-by-step explanation:
m = Δy/Δx = (6-(-2))/(5-3) =8/2 = 4
A student wants to write an expression for, all of the elements which are in set A AND all of the elements in set B.” Which expression below matches the statement? (A ‘U B’). (A U B). (A n B) P(A n B)
A student wants to write an expression for, all the elements which are in set A and all the elements in set B. Then, the expression matches the statement is (A n B), which is read as A intersection B. Thus, option B is correct.
What is intersection?The intersection of two sets A and B, denoted by display by (A ∩ B). It is the set containing all elements of A that also belong to B, or, alternatively, all elements of B that also belong to A. The symbol is sued for the intersection is ∩. This is defined as that the element of A and B are is a single set.
Therefore, option B is correct.
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A band expects to put 15 songs on their next CD. The band wriand records 60% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD
Answer:
18 songs
Step-by-step explanation:
15 x 1.6 = 24
24 x 0.75 - 18
Solve the following simultaneous equations by elimination
A) x+y=2
x-y-1=0
B) x+y=5
x-y=7
C) x+y=17
x-y=1
D) 5x+y=29
5x-y=11
Answer:
0
8
0
9
0
9
9
098098809667906432
Find the sum and express it in simplest form.
(-7n² - 8n - 8) + (-n² + 9n + 9)
008
Clear all
Enter the correct answer.
+ BO
DONE
The simplest form of the given expression is (- 8n² +n +1)
What is simplification?Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.
There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.
How to find the sum and express in simplest form?We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)
In order to simplify, we first remove the parenthesis and get
- 7n² - 8n -8 - n² + 9n +9
in the next we will collect like terms
- 7n² - n² -8n +9n - 8 +9
We now add or subtract like terms
- 8n² + n+1
this is the simplest form of the given expression.
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Use triangles to find the sum of the interior angle measures of the polygon.
SHOW YOUR WORK.
The sum of the interior angle measures of the polygon is 900 degrees
How to determine the sum of interior angles
From the image shown, we can see that the polygon has 7 sides.
A polygon with seven sides is called a heptagon
It is important to note that the number of triangles in a heptagon is 5.
Also, the sum of angles in a triangle is 180 degrees.
Now, the formula for calculating the sum of interior angles of a polygon is expressed as;
= (n - 2) 180
Where; n is the number of sides of the polygon
Substitute the value
= (7-2)180
Subtract the value
= 5(180)
= 900 degrees
Hence, the sum is 900 degrees
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Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
5 quarts 4 pints =____ pints
Answer:
14
Step-by-step explanation:
5 quarts = 10 pints
10 pints + 4 pints = 14 pints
3) Mr. Johnson uses 2.34 yards of yarn to knit a scarf. If Mr. Johnson has a total of 30.42 yards of yarn, how many scarfs will he be able to knit?
she will be able to knit 13 scarfs
Given ,
Mr. Johnson uses 2.34 yards of yarn to knit a scarfMr. Johnson has a total of 30.42 yards of yarnTo Find : Scarfs Mr John will be able to make if he has 30.42 yards of yarn
2.34 yards of yarn = 1 scarf
30.42 yards of yarn = [tex]\frac{30.42}{2.34}[/tex]
= 13 scarfs
Hence , the number of scarfs Mr John will make with 30.42 yards of yarn is 13
What does (AM) represent to segment [BC]? Justify.
AM is a perpendicular bisector of BC.
What is a bisector example?A ray that divides an angle into two equal parts is known as an angle bisector or the bisector of an angle. For instance, each measurement will be equal to 30 degrees if ray AX divides an angle of 60 degrees into two equal parts. There is an angle bisector for each angle.
A line's bisector is defined.To divide a segment or an angle into two congruent parts is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
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A woman leaves home at 7 am and drives to New York City 200 miles away. If she averages 50 miles per hour, what time will she arrive at the city
Answer:
11 AM
Step-by-step explanation:
Mile Calculation:
200 miles away and 50 miles per hour.
200 divided by 50 is equal to 4
Answer:
Now, 7 am + 4 hours is equal to 11 AM.
Bridgette has drawn a representation of a sphere with a
radius of 3 units, using the graphs of a circle and an ellipse,
as shown in the picture below on the left.
She needs to determine the equations of the graphs that
will generate the representation of the 3D sphere, as
shown in the picture below on the right.
What are possible equations of the circle and ellipse that
Bridgette can use to create her 3D drawing?
Answer:
C
Step-by-step explanation:
You want the equations of the circle and ellipse in the given figure.
EquationsThe standard form equation for an ellipse is ...
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.
You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...
[tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]
ApplicationHere, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...
[tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]
Anyone read tgcf/heaven officials blessing??
Dan is training his puppy, Lola, to sit. Dan holds a treat 5 feet above the ground until Lola
sits. As soon as she does, he drops the treat, and Lola catches it in her mouth 1.5 feet above
the ground.
To the nearest tenth of a second, how long does the treat fall before Lola catches it?
Hint: Use the formula h = -16t² + s.
The distance the treat falls before Lola catches the treat is 3.5 feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distance of the treat from the ground = 5 feet.
The distance the dog jumps to catch the treat from the ground = 1.5 feet.
Now,
The distance the treat fall before Lola catches.
= 5 - 1.5
= 3.5 feet
Thus,
The treat falls for 3.5 feet.
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How many triangles can be formed with the angle measures: 20, 100, and 60 degrees?
There are infinite many triangles that can be formed with the angle measures 20, 100, and 60 degrees
How to determine the number of trianglesFrom the question, we have the following parameters that can be used in our computation:
Angles = 20, 100, and 60 degrees
The above parameters are angles
When only angles are given, the triangle can have as many side lengths as possible
This means that there are infinite many triangles
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(1,0) m=-5
Formula
Y-Y1 = m(x-x1)
Slope form
Slope form -
y - y1 = m(x - x1)
y - 0 = -5(x - 1)
y = -5x + 5
Corin measures the apparent height of a tower 800 feet away by holding a ruler in front
of her eye and observing that the tower appears to be 9 inches tall. The apparent height h
(in inches) varies inversely with Corin's distance d (in feet) from the tower. Write an
equation that gives d as a function of h. How tall would the apparent height of the tower
be if she was standing 2000 feet away from the tower? Show your work.
Answer:
Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:
hd = k
where k is a constant.
We can find the value of k by substituting the known values of h and d:
9 inches * 800 feet = k
Solving for k, we find that k = 7200 inches * feet.
Since h and d are inversely proportional, we can write the inverse relationship as:
d = k / h
Substituting the value of k that we found earlier, we have:
d = 7200 inches * feet / h
To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:
h = 7200 inches * feet / 2000 feet = 3.6 inches
Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.
Step-by-step explanation:
What is the inverse of the function [tex]y=x^{2} +4x+4[/tex]
Answer:
y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)
Step-by-step explanation:
Given the quadratic function:
[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]
We can rewrite the function above using perfect square form:
[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]
Finding an inverse, we swap the terms of x and y:
[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]
Square root both sides, solving for y:
[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]
Subtract both sides by 2:
[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]
Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.
Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.
Which expression is equivalent to 4(x + 2)?
12x
6x
4x + 2
4x + 8
Answer:
4x +2
Step-by-step explanation:
4( x + 2)
= 4*x +4*2
= 4x +2
Change this radical to an algebraic expression with fractional exponents.
3√a
The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical expression [tex]\sqrt[3]a[/tex].
We know this describes the cube root of a or one-third root of a.
This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].
Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
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4 out 18 students will ride in a car instead of a van
why do the hands on the clock form an angle?
Answer:
The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)
I hope this helps you!
Compare 8.002 to 8.20. Which is greater?
Answer:
8.20
Step-by-step explanation:
8.20 is greater than 8.002 due to 0.20 being greater than 0.002
What is the range of f(x) = 3* + 9?
O {yly<9}
O {yly>9}
O {yly> 3}
O {yly<3}
On solving the provided question, we can say that - the range [tex]|x + 1| = 0[/tex] [tex]x + 1 = 0 = > x = -1[/tex] and [tex]y = 3[/tex]
What is range?Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
The regions where the absolute values are zero are known as the vertex points of an absolute value function.
[tex]|x + 1| = 0\\x + 1 = 0\\x = -1[/tex]
[tex]y = |-1 + 1| + 3\\y= 0 + 3\\y = 3[/tex]
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40mph in feet per secend
Answer:
58.8 feet per second
CONVERTING MPH TO FPS
If you are moving at the rate of 40MPH, how many feet do you travel in a second? At 40 miles per hour, you are traveling 58.8 feet per second. To convert miles per hour to feet per second, multiply the miles per hour figure by 1.47. There are 5280 Feet in a mile and 3600 Seconds in an hour.
6. Which of the following is true about the line given by 8x - 2y = 24?
A) The slope is negative.
B) The y-intercept is negative.
C) The x-intercept is 8.
D) The line does not pass through quadrant III.
Answer:
B
Step-by-step explanation:
put equation in slope-intercept formula (y=mx+b)
8x-2y=24
-8x -8x
-2y=-8x+24
divide each side by -2
y=4x-12
the "b" in the formula is the y-intercept which is -12, therefore B is correct
Which expression is equivalent to 10 ?
0 x²(√²)
Ox2.2
O
**(√)
5
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The expression 10+(-8) is equivalent to 10 - 8.
What is expression?Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.
Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).
Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.
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Full question
What expression is equivalent to 10-8?