Greetings from Brasil...
Rewriting the problem sets
A = {-7, 4, 2, 14, 21, 34, 42}
B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}
C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}
So, according to the statement, it is desired:
A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....
Looking at the sets we conclude that
A ∩ B ∩ C = {14; 42}What is the Factor:X^2-x-12 ?
Start by setting up your two sets of parenthses.
Inside, we have the terms that compose each binomial.
Since x² breaks down into x · x, we use an x in each binomial.
The second term is the factors of -12 that add to the coefficient
of the middle term but what is the coefficient of the middle term?
If there is nothing written there, it's understood to be 1.
So factors of -12 that add to -1 are 4 and -4.
So we have (x + 4)(x - 3) which is our answer.
Answer:
x = 4 , x = -3
Step-by-step explanation:
x^2 - x - 12 = ( x - 4) ( x + 3)
x - 4 = 0 or x + 3 = 0
x = 4 or x = -3
Find the sum and Express it in simplest form. (-8n^3 + 4n - 8) + (7n^3 - 2n + 6)
Please Help !
Answer:
n^3 + 2n -2
Step-by-step explanation:
Remove the parentheses and simplify:
-8n^3 + 4n - 8 + 7n^3 - 2n + 6
n^3 + 2n -2.
Answer:
Step-by-step explanation:
We have to add the like terms. Like terms are with variables of same power.
-8n³ and 7n³ are like terms , now add the coefficient of n³ , -8 + 7 = -1
-8n³ + 7n³ = -1n³
(-8n³ + 4n - 8) + (7n³ - 2n + 6 )
Combine like terms
= -8n³ + 7n³ + 4n - 2n - 8 + 6
= -1n³ + 2n - 2
Find the measure of APBˆ. A. 130 B. 63 C. 50 D. 230
Answer:
65
Step-by-step explanation:
TAB is an isosceles triangle by the point to tangent theorem theorem.
BAT and BAT are congruent because of the isosceles triangle definition.
CAT and ABT are right angles by the tangent theorem.
Thus, CAB and CBA are both 90 - 65 = 25.
ACB is 130 because triangles' angles add up to 180.
APB is one half of ACB by the inscribed angles theorem.
The measure of the arc APB will be 230°. Then the correct option is D.
What is a circle?
It is the circle of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
We know that the tangents are equal.
Then triangle ΔATB is an isosceles triangle.
Then the angle ∠TAB and angle ∠TBA are congruent.
We know that the angle sum of a triangle is 180°.
∠TAB + ∠TBA + ∠ATB = 180°
65° + 65° + z = 180°
z = 50°
We know that the radius and tangent of circle make 90°.
And the angle sum of quadrilateral is 360°.
∠TAC + ∠TBC + ∠ATB + ∠ACB = 360°
90° + 90° + 50° + y = 180°
y = 130°
Then the measure of the arc APB will be
x = 360° – 130°
x = 230°
The measure of the arc APB will be 230°.
Then the correct option is D.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
What’s the value of X in this triangle
Answer:
x = 85
Step-by-step explanation:
Step 1: Solve x
∠x = 180 - 27 - 68
∠x = 85
Therefore angle x equals 85
Answer:
85 degrees
Step-by-step explanation:
The sum of the angles of a triangle always add up to 180 degrees.
Here, we have two angles already given, so we can write:
27 + 68 + x = 180
95 + x = 180
Subtract 95 from both sides:
x = 180 - 95 = 85
The answer is thus 85 degrees.
~ an aesthetics lover
Use the x-intercept method to find all real solutions of the equation.
x^3-6x^2+3x+10=0
Answer:
x=-1 or 5 or 2
Step-by-step explanation:
x³-6x²+3x+10=0
(x+1)(x-5)(x-2)=0
x+1=0 ⇒ x=-1
x-5=0 ⇒x=5
x-2=0 ⇒ x=2
Which statement is NOT true about elements of
the set of rational numbers?
F All integers are elements of the set.
G Elements of the set include repeating and
terminating decimals.
H All elements of the set can be written as a
ratio , where b# 0.
J The numbers i and V3 are elements of the
set.
Answer:
The numbers i and V3 are elements of the set.
Step-by-step explanation:
The rational numbers are those which can be written as fractions. These are the numbers which can be repeating elements and terminating decimals. All integers can be set of rational numbers. The statements which is not true is statement which states that numbers i and V3 are elements of the set.
Keiko sold 3 less than three-fourths of his sister's sales. Which expression represents what Keiko sold? Three-fourths x minus 3 Three-fourths x + 3 3 x + three-fourths 3 x minus three-fourths
Answer:
Step-by-step explanation:
Given that:
Keiko sold 3 less than three-fourths of his sister's sale.
To find:
Expression that represents what Keiko sold ?
[tex]1.\ \dfrac{3}{4} x - 3 \\2.\ \dfrac{3}{4} x + 3 \\ 3.\ 3 x + \dfrac{3}{4} \\4.\ 3x - \dfrac{3}{4}[/tex]
Solution:
First of all, let the sales done by Keiko's sister = [tex]x[/tex]
Now, let us consider the Keiko's sale word by word.
3 less than three-fourths of his sister's sale.
Three fourth of his sister's sale i.e. [tex]\frac{3}{4}x[/tex] 3 lessi.e. subtract 3 from the expression obtained in 1st line.
[tex]\dfrac{3}{4}x-3[/tex]
So, sales done by Keiko = [tex]\dfrac{3}{4}x-3[/tex]
So, correct answer is:
[tex]1.\ \dfrac{3}{4}x-3[/tex]
[tex]\frac{3}{4}x-3[/tex]
An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.
Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.
Let [tex]x[/tex] denotes sale of sister of Keiko.
As Keiko sold [tex]3[/tex] less than three-fourths of his sister's sales,
Sales of Keiko [tex]=\frac{3}{4}x-3[/tex]
For more information:
https://brainly.com/question/19585043?referrer=searchResults
Find t12 for a geometric sequence where t1=2+2i and r=3
Answer:
[tex]T_{12} = 354294 + 354294i[/tex]
Step-by-step explanation:
Given
Geometric Sequence (GP)
[tex]T_1 = 2 + 2i[/tex]
[tex]r = 3[/tex]
Required
Determine T₁₂
The nth term of a GP is calculated as thus;
[tex]T_n = ar^{n-1}[/tex]
In this case;
[tex]n = 12[/tex]; [tex]r = 3[/tex] and [tex]a = T_1 = 2 + 2i[/tex]
Substitute these values in the above formula
[tex]T_{12} = (2 + 2i) * 3^{12-1}[/tex]
[tex]T_{12} = (2 + 2i) * 3^{11}[/tex]
[tex]T_{12} = (2 + 2i) * 177147[/tex]
Open the bracket
[tex]T_{12} = 177147 * 2 + 177147 * 2i[/tex]
[tex]T_{12} = 354294 + 354294i[/tex]
Hence, the 12th term of the sequence is [tex]T_{12} = 354294 + 354294i[/tex]
What’s 1/3 times 2/5
Answer:
[tex] \boxed{ \bold{ \huge{ \sf{ \frac{2}{15} }}}}[/tex]Step-by-step explanation:
[tex] \sf{ \frac{1}{3} \times \frac{2}{5} }[/tex]
▪️To multiply one fraction by another , multiply the numerators for the numerator , and multiply the denominators for its denominator.
⇒[tex] \sf{ \frac{1 \times 2}{3 \times 5} }[/tex]
⇒[tex] \sf{ \frac{2}{15} }[/tex]
Hope I helped!
Best regards!
why are halves a good choice for benchmark fractions for 1 1/3
Answer:
Following are the answer to this question:
Step-by-step explanation:
For calculating, matching, or arranging certain fractions, the benchmark fraction can be described as common fractions, that can be calculated or judged. It is most useful when measuring fractions to comparisons in a number line.
Given value:
[tex]\to 1 \frac{1}{3}[/tex] [tex]= 1+\frac{1}{3} \\[/tex]
[tex]= 1+ \frac{1}{6}+\frac{1}{6}\\[/tex]
Find the value of a. Then find the angle measures of the polygon.
a =
26
(2aº caº
a
Sum of angle
measures: 360°
Answer:
In the given quadrilateral, two angles measure 60° and other two angles measure 120°.
Step-by-step explanation:
As we know sum of all interior angles of a polygon with 'n' sides is,
Sum of interior angles = (n - 2) × 180°
= (4 - 2) × 180° [for a polygon with n = 4]
= 360°
a + a + 2a + 2a = 360°
6a = 360°
x = 60°
Measure of angles = a° = 60°
And angles having measure = 2a° = 2(60)°
= 120°
Therefore, in the given quadrilateral, two angles measure 60° and other two angles measure 120°.
1.1.17
Question Help
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
6/7
Answer:
whole number is the answer
How are the ratios 30:12 and 40:16 equivalent
Answer:
see explanation
Step-by-step explanation:
Given the ratio 30 : 12 ( divide both parts by 6 )
= 5 : 2
Given the ratio
40 : 16 ( divide both parts by 8 )
= 5 : 2
Thus the 2 ratios are equivalent and simplify to 5 : 2
Please help as soon possible! :'(
Answer:
BC = 1/2 AC
2m angle DBC = m angle ABC
Angle ABC is bisected by ray BD
m∠WUT = 38°
Step-by-step explanation:
For both questions, we use the Angle Bisector Theorem.
Question 1:
We know since ray DB bisects ABC, AB and BC are congruent. They are split into 2 equal parts. Therefore, we know that if we take half of mAC, we should get either mBC or mAB. Therefore, the 1st statement is correct.
Since it is ray DB bisecting ABC, it created 2 right angles. If angle DBC was bisected, it would create 2 new angles that were 45° each, so the 2nd statement is incorrect.
We know that line ABC is equal to 180°. So if we add m∠ABD and m∠DBC (they both are 90°, as denoted in the picture) together, we should get 180°. Also, since they are congruent angles, one angle multiplied twice would also be 180°. Therefore, the 3rd statement is correct.
The Angle Bisector Theorem doesn't state that the bisector and one segment would be congruent. The length of the bisector could be anything and is not marked congruent to the other segments. Therefore, the 4th statement is incorrect.
Since we see that there is a bisector DB bisecting line ABC, creating 2 congruent segments and angles, we know that the 5th statement is correct.
Question 2:
The Angle Bisector Theorem states that a bisector that bisects 2 angles will become 2 smaller but congruent angles. So,
Step 1: Find x
4x + 6 = 6x - 10
6 = 2x - 10
16 = 2x
x = 8
Step 2: Find m∠WUT
m∠WUT = 6x - 10
m∠WUT = 6(8) - 10
m∠WUT = 48 - 10
m∠WUT = 38°
HELP WILL GIVE 40 POINTS AND BRAINLIEST!!!! Solve these two (second-degree) quadratic equations by factoring. [tex]2x^{2}+6x=0[/tex] & [tex]x^{2}+9x+14=0[/tex]
Answer:
Step-by-step explanation:
First equation: 2x^2 + 6x = 0 factors into 2x(x + 3) = 0, so either x = 0 or x = -3.
Second equation: x^2 + 9x + 14 = 0 factors into (x + 2)(x + 7) = 0. Thus, either x = -2 or x = -7
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------------
Answer for [tex]2x^{2} + 6x = 0[/tex]: x = 0x = -3|
|[tex]2x^{2} + 6x = 0[/tex]
|
|First we factor out x
\/
[tex]x(2x+6)=0[/tex]
To find equation solutions, solve [tex]x = 0[/tex] and [tex]2x+6 = 0[/tex]
|
\/
[tex]x = 0[/tex]
[tex]x = -3[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer for [tex]x^{2}+ 9x + 14 = 0[/tex]:x = -2x = -7|
|
|[tex]x^{2}+ 9x + 14 = 0[/tex]
|
|To solve the equation, factor [tex]x^{2}+ 9x + 14[/tex] using formula [tex]x^{2} + (a + b)x + ab = (x+a) (x+b).[/tex] To find [tex]a[/tex] and [tex]b[/tex], set up a system to be solved.
|
\/
[tex]a + b = 9[/tex]
[tex]ab = 14[/tex]
|
\/
Since [tex]ab[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] have the same sign. Since [tex]a + b[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] are both positive. List all such integer pairs that give product 14.
1, 14
2, 7
|
\/
Calculate the sum for each pair.
1 + 14 = 15
2 + 7 = 9
|
\/
The solution is the pair that gives sum 9.
[tex]a = 2[/tex]
[tex]b = 7[/tex].
|
\/
Rewrite factored expression [tex](x+a)(x+b)[/tex] using the obtained values.
[tex](x+2)(x+7)[/tex]
|
\/
To find equation solutions, solve [tex]x + 2 = 0[/tex] and [tex]x + 7 = 0[/tex].
|
\/
[tex]x = -2[/tex]
[tex]x = -7[/tex]
1. Name the vertex of angle 2.
2. Name the sides of angle 4.
3. Write another name for angle 3.
4. Classify each angle.
-angle YTW
-angle XTU
-angle YTU
-angle WTX
5. Name an angle bisector.
Answer:
1) YTW
2) WT, TZ
3) UTZ
4) Right angle
Acute angle
Obtuse angle
Right angle
5) TU
You spend 30 minutes reading emails. You then spend 2 hours playing video games . Write the ratio of the amount of time reading emails to the amount of time spent playing on video games as a fraction in a simple form.
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Step 1: State what is given
2 hours playing games or 120 minutes
30 minutes reading email
Step 2: Put information into fraction
[tex]\frac{email}{games} = \frac{30}{120}[/tex]
Step 3: Simplify the fraction by 30
[tex]\frac{30}{120}=\frac{1}{4}[/tex]
Therefore the fraction representing how long he plays games and reads email is [tex]\frac{1}{4}[/tex]
What is the value of 9 packs of Sweets if one pack of sweet cost Rs 120.5?
Answer:
1084.5
Step-by-step explanation: 120.5*9 = 1084.5
Answer:
One pack = Rs 120.5
→ Multiply both the brackets and price by 9
9 packets = Rs 1084.5
what is 6, 400 written in scientific nation?
Answer:
6.4 x 10 to the power of 3
Step-by-step explanation:
always have 1 number after the decimal point and then times by ten to the power of 3.
Answer:
64x10²
Just move it to the left 2 times.
Hi . I'm kinda stuck on this question .
Help please.
Workings please
Answer:
[tex]\large \boxed{\text{Q31, D. 6.00 F; 32. C. N21.75; Q33. A. 168.00 F}}[/tex]
Step-by-step explanation:
Your graph is hard to read, so I re-drew it as best I could.
You must first develop an equation relating francs and naira.
The line goes through the origin, so the general equation is
y = kx
One of the points is (40,240).
[tex]\begin{array}{rcl}F & = &k \times N\\240 & = &k \times 40\\k & = & \dfrac{240}{40}\\\\k&=&\textbf{6 F/N}\\\end{array}\\\text{The equation is $\large \boxed{\mathtbf{F = 6 N}}$}[/tex]
Q 31.
[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 1.00\\& = & \mathbf{6.00}\end{array}\\\text{The equivalent value of N1.00 is $\large \boxed{\textbf{6.00 F}}$}[/tex]
Q 32.
[tex]\begin{array}{rcl}F & = &6N\\130.5& = & 6 N\\N&=& \dfrac{130.5}{6}\\\\& = & \mathbf{21.75}\\\end{array}\\\text{The equivalent value of 130.5 F is $\large \boxed{\textbf{N21.75}}$}[/tex]
Q 33.
[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 28.00\\& = & \mathbf{168.00}\end{array}\\\text{An amount of N28.00 is $\large \boxed{\textbf{168.00 F}}$}[/tex]
What is two and one-fourth subtracted by one-eighth?
how to do this question plz answer me step by step plzz
Answer:
Not enough tables.
Step-by-step explanation:
Circumference is 2*pi*r
The diameter is 2 times the radius or 2r, if the table diameter is 180cm. All we need to do is multiply by pi (3.14159) to get the circumference.
180*pi = 556.48cm
If each guest needs 70cm then we divide the circumference by 70
556.48/70 = 8.08 but we cant have a portion of a person so we can fit 8 people per table.
18 tables with 8 at a table is 8 x 18 = 144
If 145 guests are attending then there aren't enough tables, you are 1 table short.
Find the center of a circle with the equation:
x² + y² + 2x -20y – 20 = 0
===============================================
Explanation:
If we had x^2+2x + ___, then 1 must go in the blank so that we have x^2+2x+1 = (x+1)^2
So we must add 1 to both sides to complete the square for the x terms. To find this value '1' we take half of the x coefficient 2 to get 1, then square it to get 1^2 = 1.
We have
x^2+y^2 + 2x - 20y - 20 = 0
x^2+y^2 + 2x - 20y - 20 + 1 = 0 + 1
(x^2+2x+1) + y^2 - 20y - 20 = 1
(x^2+2x+1) + y^2 - 20y = 1 + 20
(x+1)^2 + y^2 - 20y = 21
After completing the square for the x terms. Repeat for the y terms. Take half of -20 to get -10, which squares to 100. Add this to both sides
(x+1)^2 + y^2 - 20y = 21
(x+1)^2 + y^2 - 20y + 100 = 21+100
(x+1)^2 + (y - 10)^2 = 121
The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where
h = -1k = 10r = 11The center is (h, k) = (-1, 10). The radius is r = 11.
PLEASE HELP ME ASAP ILL MARK BRIANLIEST!!!!!!!!! ANSWER THE QUESTIONS AND DO THE STEPS TOO PLEASEE
Answer:
1). t ≥ -[tex]\frac{3}{2}[/tex]
2). k ≥ [tex]\frac{16}{3}[/tex]
3). y < -[tex]\frac{1}{2}[/tex]
4). b > [tex]\frac{250}{9}[/tex]
5). w ≤ 0
Step-by-step explanation:
1). [tex]14(\frac{1}{2}-t)\leq 28[/tex]
[tex]\frac{14}{14}(\frac{1}{2}-t)\leq \frac{28}{14}[/tex]
[tex]\frac{1}{2}-t\leq 2[/tex]
[tex]-t\leq 2-\frac{1}{2}[/tex]
[tex]-t\leq \frac{3}{2}[/tex]
t ≥ -[tex]\frac{3}{2}[/tex]
2). 15k + 11 ≤ 18k - 5
15k - 18k ≤ -5 - 11
-3k ≤ - 16
3k ≥ 16
k ≥ [tex]\frac{16}{3}[/tex]
3). 44y > 11 + 88y - 22y
44y > 11 + 66y
44y - 66y > 11
-22y > 11
22y < -11
[tex]\frac{22y}{22}<-\frac{11}{22}[/tex]
y < [tex]-\frac{1}{2}[/tex]
4). [tex]\frac{7}{9}(b - 27) > \frac{49}{81}[/tex]
[tex]\frac{7}{9}(b - 27)\times \frac{9}{7} > \frac{49}{81}\times \frac{9}{7}[/tex]
(b - 27) > [tex]\frac{7}{9}[/tex]
b > [tex]\frac{7}{9}+27[/tex]
b > [tex]\frac{250}{9}[/tex]
5). 11w - 8w ≥ 14w
3w - 14w ≥ 0
-11w ≥ 0
w ≤ 0
simplify- 13= 7x + 4 - 4x simplify- b - 6 + 6b = 27 simplify- 5(5x - 2) = 65 URGENT please answer i will give brainliest
Step-by-step explanation:
1: - 13= 7x + 4 - 4x
Isolate variables.
- 13= 7x + 4 - 4x
-13 = 3x + 4
-3x = 13+4
-3x = 17
x = -17/3
2: - b - 6 + 6b = 27
5b - 6 = 27
5b = 33
b = 33/5
3: - 5(5x - 2) = 65
-25x + 10 = 65
-25x = 55
x = -55/25
x = -11/5
the ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. if the first number of the ratio is 10, what is the second number? justify your reasoning.
Answer:
10:40
Step-by-step explanation:
3x4 = 12
4 x 4 = 16
5 x 4 = 20
so 10 x 4 = 40 (10:40)
Answer:
10:40
Step-by-step explanation:
Step 1: Reduce ratio to lowest value
3 : 12 = 1 : 4
*Divide by 3
Step 2: Solve ratio
Let 'x' represent the second number
1 : 4 = 10 : x
Multiple the left side by 10
10 : 40 = 10 : x
Therefore the second number in the ratio with 10 is 40
What are the next three terms in this arithmetic sequence? 33, 27, 21,...
A: 15, 9, 3
B: 14, 8, 2
C: 15, 9, 2
D: 15, 10, 5
Answer:
15,9,3
Step-by-step explanation:
4. Using the digits 1 to 9, at most one time each, fill in the boxes to
make a result that has the greatest value possible. HELP PLEASE
Answer:
9^3
Step-by-step explanation:
9x9x9= 729
1. Simplify the following a) 4√12 - √50 -5√48 b) √8 × √5 ×√10 c) √45 + √180 + √80
Answer:
-12√3 - 5√22013√5Step-by-step explanation:
1.
[tex]4\sqrt{12}-\sqrt{50}-5\sqrt{48}\\\\4\sqrt{12}=8\sqrt{3}\\\\\sqrt{50}=5\sqrt{2}\\\\5\sqrt{48}=20\sqrt{3}\\\\=8\sqrt{3}-5\sqrt{2}-20\sqrt{3}\\\\\mathrm{Add\:similar\:elements:}\:8\sqrt{3}-20\sqrt{3}=-12\sqrt{3}\\\\=-12\sqrt{3}-5\sqrt{2}[/tex]
2.
[tex]\sqrt{8}\sqrt{5}\sqrt{10}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{a\times b}\\\\=\sqrt{8\times \:5\times \:10}\\\\=\sqrt{400}\\\\\mathrm{Factor\:the\:number:\:}\:400=20^2\\\\=\sqrt{20^2}\\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a\\\\\sqrt{20^2}=20[/tex]
3.
[tex]\sqrt{45}+\sqrt{180}+\sqrt{80}\\\\\sqrt{45}=3\sqrt{5}\\\\\sqrt{180}=6\sqrt{5}\\\\\sqrt{80}=4\sqrt{5}\\\\=3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\\mathrm{Add\:similar\:elements:}\:3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\=13\sqrt{5}[/tex]
What is the maximum value of this function? f(x)=−16x²+32x+20
Answer: The maximum value is 35.94
Step-by-step explanation:
We have the function:
f(x) = -16*x^2 + 34*x + 20
This is a quadratic equation, and the first thing we can see is that the leading coefficient is smaller than zero, which means that the "arms" of the graph will go downwards, which means that the maximum of our function will be at the vertex.
First, we know that the vertex of a quadratic function is when f'(x) = 0.
f'(x) = 2*(-16*x) + 34 = 0.
x = -34/(-2*16) = 34/32 = 17/16.
Now we evaluate our function in the point x = 17/16.
f(17/16) = -16*(17/16)^2 + 32*(17/16) + 20 = 35.94
The maximum value is 35.94
Using the vertex, it is found that the maximum value of the function is of 36.
The function is given by:
[tex]f(x) = -16x^2 + 32x + 20[/tex]
Which is a quadratic function with coefficients [tex]a = -16, b = 32, c = 20[/tex].
The maximum value of a quadratic function with [tex]a < 0[/tex] is at the vertex, in which the value is:
[tex]f_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Hence, in this problem:
[tex]f_{MAX} = -\frac{(32)^2 - 4(-16)(20)}{4(-16)} = 36[/tex]
The maximum value of the function is of 36.
A similar problem is given at https://brainly.com/question/16858635