The value for the quadratic equation is C(t) = t² + 3.
What is vertex?When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.
The standard form of the quadratic function is given as:
C(t) = at² + bt + c
Using different values of t from the table we have:
a(-2)² + b(-2) + c = 7
a(-1)² + b(-1) + c = 4
a(0)² + b(0) + c = 3
Simplifying the equations we have:
4a - 2b + c = 7
a - b + c = 4
c = 3
Substituting the value of c = 3 in equation 2:
a - b = 1
Further solving the equation for a and b we have:
a = 1
b = 0
Hence, the equation for the quadratic equation is C(t) = t² + 3.
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Find the LCM of:
x² - 3x + 2, x² + x + 2
Answer:
The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:
For x² - 3x + 2 = 0:
a = 1, b = -3, c = 2
x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2
x = 1 or x = 2
For x² + x + 2 = 0:
a = 1, b = 1, c = 2
x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2
x = (-1 ± i√7) / 2
Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:
(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))
What is the y intercept
Answer: (0, 48)
Step-by-step explanation:
To find the y-intercept, plug the x and y values in the equation y = -3x + b, and leave the b the same.
I will use (11, 15)
15 = -3(11) + b
15 = -33 + b
48 = b
The y-intercept is (0, 48)
Equation is y = -3x + 48
Hope this helps!
Based on the results in the table, about how
many times should Jaylon and Paula expect the
pointer to land on 4 out of a total of 130 spins
Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
What is the experimental probability?A probability calculated by a series of tests is known as experimental probability.
The given table is as follows:
1 2 3 4
Jaylon: 6 8 9 7
Paula: 8 5 7 10
To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:
Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)
= 7 / 30
Similarly,
Experimental probability for Paula:
= 10 / 30
Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)
For Jaylon: (7 / 30) × 130 = 30.33
For Paula: (10 / 30) × 130 = 43.33
Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
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The missing table has been attached below.
theres a picture of what I need help with thank you so much! Have an amazing day and will also mark brainliest <3
Answer:
5x4
Step-by-step explanation:
The dimensions of the rectangle are 20x16
The reducing factor is 0.25.
Multiple 20 * 0.25= 5
Multiple 16 * 0.25= 4
Therefore the new dimensions are 5x4.
If angle HIJ is congruent to angle JTS, then is
In the given triangle, using congruency, ∠JHI is congruent to ∠SJT.
What is Triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
In the given figure, we can see that there are two pairs of vertically opposite angles, which are opposite to each other at the intersection of two straight lines. These angles are:
What is the equation for triangle congruence?According to the ASA Rule, triangles are congruent to one another if any two angles and the side between them are comparable to the corresponding angles and side. According to the AAS Rule, the triangle's angles and excluded side are equal in the same way.
In the given triangle, using congruency, ∠JHI is congruent to ∠SJT
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In the diagram below of triangle
�
�
�
DEF,
�
G is the midpoint of
�
�
‾
DF
and
�
H is the midpoint of
�
�
‾
EF
. If m
∠
�
�
�
=
60
−
5
�
∠FDE=60−5x, and m
∠
�
�
�
=
46
+
2
�
∠FGH=46+2x, what is the measure of
∠
�
�
�
∠FGH?
The measure of ∠FGH is 28 - 4x.
What is triangle?A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.
Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.
Using angle sum property, we have:
m∠DEF + m∠FED + m∠FDE = 180
60 - 5x + 2(46 + 2x) + m∠FGH = 180
152 + 4x + m∠FGH = 180
m∠FGH = 180 - 152 - 4x
m∠FGH = 28 - 4x
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-15y-4
45
27
38%
十
15
24
Find X and
Find Y
Answer:
42
Step-by-step explanation:
you asding it all up
What is the profit for buying pencils for $2 each and selling them for $2,40 and manage to sell $40 and what is the profit and loss
The profit for buying pencils for $2 each and selling them for $2.40 is $6.40 and there is no loss.
The profit is the difference between the selling price and the cost price of the pencils. In this case, the profit per pencil is $2.40 - $2 = $0.40.
Since the total sales amount is $40, the number of pencils sold is $40/$2.40 = 16.67, which we can round down to 16 pencils. Therefore, the total profit is 16 * $0.40 = $6.40.
There is no loss in this scenario, as the selling price is higher than the cost price. Loss occurs when the selling price is lower than the cost price.
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Choose the correct answer from the drop-down menu. Use properties of operations to determine whether or not 3(x+2)+8 and 3x+14 are equivalent. Select... We can not determine whether the expressions are equivalent or not. The expressions are equivalent. The expressions are not equivalent.
"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.
First, let's apply the distributive property to the first expression:
3(x+2) + 8 = 3x + 6 + 8
Next, let's simplify the expression by combining like terms:
3x + 6 + 8 = 3x + 14
Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.
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A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.
We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.
A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.
Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.
Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.
Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.
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OBFW Publishers
Many fire stations handle more emergency calls for medical help than for fires. At one fire station, 81% of incoming calls are for
medical help. Suppose we choose 4 incoming calls to the station at random.
(a) Find the probability that all 4 calls are for medical help.
Round your answer to 4 decimal places.
Leave your answer in decimal form.
(b) What's the probability that at least 1 of the calls is not for medical help?
Round your answer to 4 decimal places.
Leave your answer in decimal form.
(c) Explain why the calculation in part (a) may not be valid if we choose 4 consecutive calls to the station.
The calculation in part (a) might not be valid because the 4 consecutive calls being medical may not be not be _____ events.
Answer:
(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where:
n is the number of trials (in this case, 4)
k is the number of successes (in this case, 4)
p is the probability of success on a single trial (in this case, 0.81)
Plugging in the values, we get:
P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)
P(X = 4) = 0.5314
Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.
(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:
P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)
We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:
P(at least 1 call not for medical help) = 1 - 0.5314
P(at least 1 call not for medical help) = 0.4686
Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.
(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.
Step-by-step explanation:
Use the following functions to: find, simplify, and identify the domain of each of the function combinations. f(x)=x^2−4x and g(x)=x+12 (a) (f+g)(x)=
Domain of (f+g)(x) : (b) (f−g)(x)= Domain of (f−g)(x) : (c) (fg)(x)= Domain of (fg)(x) : (d) (gf)(x)= Domain of (gf)(x) :
(a) The function combination (f + g)(x) is equal to x² - 3x + 12 and its domain are all real numbers.
(b) The function combination (f - g)(x) is equal to x² - 5x - 12 and its domain are all real numbers.
(c) The function combination (fg)(x) is equal to x³ + 8x² - 48x and its domain are all real numbers.
(d) The function combination (gf)(x) is equal to x³ + 8x² - 48x and its domain are all real numbers.
(a) To find the expression or value of the function combination (f + g)(x), we need to add f(x) and g(x).
(f + g)(x) = f(x) + g(x) = x² - 4x + x + 12 = x² - 3x + 12
Domain of (f + g)(x) : All real numbers
(b) To find the expression or value of the function combination (f - g)(x), we need to subtract g(x) from f(x).
(f - g)(x) = f(x) - g(x) = x² - 4x - (x + 12) = x² - 5x - 12
Domain of (f-g)(x) : All real numbers
(c) To find the expression or value of the function combination (fg)(x), we need to multiply the two functions.
(fg)(x) = f(x) * g(x) = (x² - 4x) (x + 12) = x³ + 8x² - 48x
Domain of (fg)(x) : All real numbers
(d) The function combination (gf)(x) is the same as (fg)(x).
(gf)(x) = g(x) * f(x) = (x + 12) (x² - 4x) = x³ + 8x² - 48x
Domain of (gf)(x) : All real numbers
In all cases, the domain is all real numbers because there are no restrictions on the values of x that can be used in the functions.
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Do Now 2 The table below shows ordered pairs of a linear function. Based on this data what is the slope of the line? a) 0.5 b) 1.5 c) 2.1 d) 3.1 X 0 -9 5 1.5 10 15 12 22.5
Based on the data showing the ordered pairs of a linear function, we can find the slope of the line, which will be: 2.4. The closest correct option is letter c.
How to calculate the slope of the line?We need to use the following formula to find the intended result:
Slope = (change in y) / (change in x)
To calculate slope, we can pick any two points from the table. Choosing the points (0, -9) and (10, 15) we have:
slope = (15 - (-9)) / (10 - 0) = 24 / 10 = 2.4Therefore, using two points from the table, we find that the slope of the line is 2.4. The option c) 2.1 is the closest to the result.
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An electronics manufacturer recorded the battery life of some different models
of mobile phone.
They have displayed some of their results in the incomplete histogram and
frequency table below.
Use this information to work out the missing value that completes the
frequency table.
The missing value that cοmpletes the frequency table is 174.
What is frequency distributiοn table?A frequency distributiοn table is a table that displays the number (οr frequency) οf οbservatiοns that fall within each interval after grοuping the data intο intervals. It is an effective tοοl fοr cοmprehending data distributiοn and spοtting patterns οr trends.
Typically, the table has twο cοlumns. The intervals, οr "bins," intο which the data is divided are listed in the first cοlumn. The frequency, οr quantity οf οbservatiοns, that fall intο each bin is displayed in the secοnd cοlumn. Depending οn the data and the level οf precisiοn required, the bins may be identical οr vary in width.
The analysis οf a variety οf data types, including numerical, categοry, and οrdinal data, can be dοne using frequency distributiοn tables. As well as calculating descriptive statistics like the mean, median, and mοde, as well as measures οf variability like the range and standard deviatiοn, they can alsο be used tο generate these statistics.
All things cοnsidered, frequency distributiοn tables οffer a quick and effective apprοach tο summarize a lοt οf data and learn mοre abοut its distributiοn and prοperties.
Tο cοmplete the frequency table, we need tο determine the frequency fοr the interval 28 ≤ x < 30.
We can see frοm the histοgram that the interval 28 ≤ x < 30 has a width οf 2. Since the tοtal frequency is the sum οf the frequencies in each interval, we can use the infοrmatiοn prοvided in the frequency table tο sοlve fοr the missing value:
110 + 36 + 180 + frequency fοr 28 ≤ x < 30 = tοtal frequency
We can simplify this expressiοn:
326 + frequency fοr 28 ≤ x < 30 = tοtal frequency
We knοw that the tοtal frequency is the number οf mοbile phοnes that were tested, sο we can assume that this is a knοwn quantity. Let's say that the manufacturer tested 500 mοbile phοnes. Then we can sοlve fοr the missing frequency:
326 + frequency fοr 28 ≤ x < 30 = 500
frequency fοr 28 ≤ x < 30 = 174
Therefοre, the missing value that cοmpletes the frequency table is 174. The cοmpleted frequency table is:
Battery life, x(hοurs) Frequency
15 < x < 20 110
20 ≤ x < 22 36
22 ≤ x < 28 180
28 ≤ x < 30 174
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Kendra bought a pair of $125 jeans for $93.75. What percent was taken off from the original price?
Answer:
25%
Step-by-step explanation:
p/w =x/100 for a percentage
93.75/125 = x/100
93.75×100= 9375
9375 = 125x
9375/125 =75
x=75
So she paid 75% of the original price, meaning the jeans were 25% off.
Airplane tickets to Fairbanks, Alaska will cost $958 each. Airplane tickets to Vancouver, Canada will cost $734. How much can the four members of the Harrison family save on airfare by vacationing to Vancouver
Answer:
The family will save $896 on airfare by vacationing to Vancouver
Step-by-step explanation:
Tickets to Fairbanks - $958 each (4 total people)
Total cost - 958 times 4 = $3832
Tickets to Vancouver - $734 each (4 total people)
Total cost - 734 times 4 = $2936
$3832 - $2936 = $896
Watch help video What are the roots of the equation x^(2)-12x+61=0 in simplest a+bi form?
The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.
The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.
The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.
Plugging in the values into the quadratic formula, we get:
x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))
Simplifying the equation, we get:
x = (12 ± √(144-244))/2
x = (12 ± √(-100))/2
Since the square root of a negative number is a complex number, we can write the equation as:
x = (12 ± 10i)/2
Simplifying further, we get:
x = 6 ± 5i
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What is the difference between point t and point v?
The difference between the two points is a vertical displacement of 5 units downward from point T to point V.
What is distance formula in graph?The distance formula is used to calculate the distance between two points in a two- or three-dimensional coordinate system. It is derived from the Pythagorean theorem and involves finding the square root of the sum of the squares of the differences between the corresponding coordinates of the two points.
The difference between point T(9, -4) and point V(9, -9) is 5 units in the y-direction. Specifically, the y-coordinate of point V is 5 units less than the y-coordinate of point T. This can be expressed as:
V - T = (9, -9) - (9, -4) = (0, -5)
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Please help. I can't seem to understand this one
Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)
Step-by-step explanation:
translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down
Fill in each blank to complete the following sentence. For 4x^(2)+6x+2=0,a=4,b= and c
The complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."
To complete the sentence, we need to identify the values of a, b, and c in the given equation. The equation is in the form of ax^(2)+bx+c=0, where a, b, and c are the coefficients of the respective terms.
Therefore, to fill in the blanks in the sentence, we can simply match the coefficients in the given equation with the corresponding letters:
a = 4, because the coefficient of the x^(2) term is 4
b = 6, because the coefficient of the x term is 6
c = 2, because the constant term is 2
So the complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."
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For g(x)=2x/3, find g(3) and g(12)
In response to the supplied query, we may state that Therefore, equation g(12) = 8.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
To find g(3), we substitute x=3 into the function g(x):
g(3) = 2(3)/3
g(3) = 6/3
g(3) = 2
Therefore, g(3) = 2.
To find g(12), we substitute x=12 into the function g(x):
g(12) = 2(12)/3
g(12) = 24/3
g(12) = 8
Therefore, g(12) = 8.
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Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.\\
The number line that shows the solution to the inequality y - 2 < -5 is:
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
What is inequality?
In mathematics, an inequality is a statement that compares two values, expressing that one value is less than, greater than, or less than or equal to, greater than or equal to, or not equal to another value.
The inequality is y - 2 < -5.
To graph the solution on a number line, we start by marking the point where y - 2 equals -5, which is y = -3. Then, since the inequality is less-than, we use an open circle to represent the point y = -3.
Next, we shade all the values of y that make the inequality y - 2 < -5 true. Since y is less than -3, we shade everything to the left of the open circle.
Therefore, the number line that shows the solution to the inequality y - 2 < -5 is:
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
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Describe all the x-values at a distance of 22 or less from the number
9.
Enter your answer in interval notation.
To enter [infinity], type infinity. To enter ∪, type U.
The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].
The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.
Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22
Step 2: Solve each inequality for x:
x≤31 and x≥-13
Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31
Step 4: Write the solution in interval notation:
[-13, 31]
So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:
x > 5.An open circle is at 5 and a bold line starts at 5 and is pointing to the right.What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.< x: amount less than x. -> to the left of x with an open dot at the number line. -> below the dashed horizontal line y = x on the coordinate plane.≥ x: amount at least x. -> to the right of x with a closed dot at the number line. -> above the solid horizontal line y = x on the coordinate plane.≤ amount at most x. -> to the left of x with a closed dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.The inequality for this problem is defined as follows:
–3(2x – 5) < 5(2 – x)
Expanding the operations, the solution is obtained as follows:
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
x > 5.
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Please I news help please send me the full explanation please
List three additional combos of length width and height that have a volume of 24 and please include the surface area too
The solution is then:
l = 6cm
w = 2cm
h = 2cm
What is the total surface area of cuboid?The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid
then, use the formula: surface area (SA)=2lw+2lh+2hw.
here, we have,
We know that the formula for the volume of a box is:
V = l*w*h
Where:
l = length
w = width
h = height
The formula of the surface area of a box is:
SA = 2(lw+lh+wh)
Based on the given we know the following:
24 = l*w*h
and
56 = 2(lw+lh+wh)
If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:
24 = 6*2*2
Let:
l = 6cm
w =2cm
h =2cm
Now let's try this on the surface area formula:
56 = 2(6*2+6*2+2*2)
so, 56 = 56
The answer is then:
l = 6cm
w = 2cm
h = 2cm
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Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds. (For example, they should do their first squat 30 seconds into the drill. ) How many times during the 200 second drill should the little monsters do an overhead press and a squat at the same instant?
The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
What do math operations entail?The process of calculating a value using operands and a math operator is referred to as a "operation" in mathematics. The math operator's symbol has predetermined rules that must be obeyed for the provided operands or integers. The five fundamental operations in mathematics are addition, subtraction, multiplication, division, and modular forms.
The prime factorizations of 12 and 30 are 2² x 3 and 2 x 3 x 5, respectively.
Hence, 2² x 3 x 5 = 60 is the smallest common multiple of 12 and 30.
This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.
To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:
200 ÷ 60 = 3 remainder 20
This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.
Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
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A company makes a single serving cereal box that contains a volume of 1. 2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain?
If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.
If the extra large box is a dilation of the single serving box with a scale factor of 4, then
The ratio of the volumes of the extra large box to the single serving box will be 4³,
We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.
So, the volume of the extra large box will be;
⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,
Therefore, the extra large box will contain 76.8 ounces of cereal.
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Use the Intermediate Value Theorem to show thatf has a zero
between a and b .
f(x)=2x 3 +6x 2
-3 a -2
There is a zero for f(x) between a and b.
How to calculateUsing the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.
The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.
Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.
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Help solve this question
The measure of angle FLI is 56=
What is sum of angle in triangle?The sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.
Therefore the sum of angle in a triangle is 180
Since FIL is right angle , then angle FLI =
180-(90+34)
= 180- 124
= 56°
therefore the measure of angle FLI is 56°
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