[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]
What is the function's decreasing in the interval?Generally, the equation for the function is mathematically given as
f(x) = -5x + 11 + 10
Therefore
When x >= -1, the function decreases because f(x) = -5(x+1)+10.
This means that the function is dropping throughout this range[tex](-1,\infty).[/tex]
b)
A look at the graph reveals a decreasing trend in the function over the timeframe (-2,2).
In conclusion, The number line will represent
Using the point where the intervals with decreasing functions overlap
[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]
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Answer:
see photos
Step-by-step explanation:
Plato/Edmentum
What is the quotient of the synthetic division problem below, written in
polynomial form?
3 -2 15
-22
-16
A.2xd 121xr 41
B=
2,219x15
C. 2y 1 9g
40
D
2y7 - 21x 40
The quotient of the synthetic division problem is "f(x) = -2x² + 9x + 5" (Option C).
What is Synthetic Division?
When a polynomial division is executed using the shorthand method, using a linear factor, one is said to have executed a Synthetic Division.
The synthetic division translates to
- 2 15 -22 -15
3 | -6 27 15
-2 9 5 0
Citing the coefficient of the quotient of the first three numbers:
- 2, 9, 5. The last number is given as the remainder.
Hence the remainder is zero.
Given that the coefficient of the quotient are three, the interpretation is that the polynomial greatest degree is 2.
Thus,
f(x) = -2x² + 9x + 5
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This table represents a quadratic function with a vertex at (1, 1). What is the
average rate of change for the interval from x = 5 to x = 6?
OA. 26
OB. 13
O C. 7
OD. 9
1
2
3
4
5
X
1
2
LO
5
10
17
y
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
How to find the average rate of change on the interval?
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
[tex]r = \frac{f(6) - f(5)}{6 - 5}[/tex]
[tex]f(x) = a*x^2 + b*x + c[/tex]
I we look at the table we see that:
[tex]f(1) = 1 = a + b + c[/tex]
[tex]f(2) =2 = 4a + 2b + c[/tex]
[tex]f(3) = 5 = 9a + 3b + c[/tex]
This is a system of equations.
If we subtract the second and first functions, we get:
[tex]2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c[/tex]
From that we take two relations:
[tex]1 - 3a = b\\2a = c[/tex]
Now we can replace these two in the last equations so we get:
[tex]5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1[/tex]
Now that we know the value of a:
[tex]c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2[/tex]
The quadratic equation is:
[tex]f(x) = x^2 - 2x + 2[/tex]
Evaluating this in x = 6 we get:
[tex]f(6) = 6^2 - 2*6 + 2 = 26[/tex]
And from the table we know that f(5) = 17, then the average rate of change is:
[tex]r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9[/tex]
The correct option is D.
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Solve using a formula. Please don't guess, I would like professionals to take a look
Let's take this problem step by step:
What we know:
[tex]x+y=4\\xy=-2[/tex]
Before we solve, let's do one thing that will help us out greatly later down the road:
[tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation
Let's rearrange the problem a little bit:
[tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]
Combine fractions of common denominators:
[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]
Now's let factor everything apart:
[tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]
Let's use what we know and our useful equation:
[tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]
The value is 440
Answer: 440
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X+1/2y=5 What is the rate of change of y with respect to x?
Answer:
I'll do it the answer to x is 5 0 the answer to y will be 0 10
Brandon is a running back for his local high school football team. In the last game, he carried the ball 8 times. In the first 5 carries, he gained 6 yards, 12 yards, and 4 yards before losing 2 yards and then losing additional yards. His last 7 carries combined for yards. What was his total net yardage for the game?
Using it's concept, it is found that Brandon's net yardage for the game was of 26.
How to find the net yardage?The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.
Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:
6 + 20 = 26.
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(11-8)x3+7+27-3
(18÷3)+6+(14-8)x5
(11-7)x6+4+32-4
The results of the arithmetic evaluations as given in the task content are; 40,42 and 62.
What are the results of the arithmetic evaluations?The arithmetic operations above can be evaluated and simplified as follows;
(11-8)x3+7+27-3 = (3×3)+7+27-3 = 40.
(18÷3)+6+(14-8)x5 = (6)+6+(6)x5 = 42.
(11-7)x6+4+32-4 = (5×6) +4 +32-4 = 62.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
3 days, 27
Step-by-step explanation:
After 3 days :
3³ = 27 belts4(3) + 15 = 12 + 15 = 27 beltsAfter 3 days, the number of belts and wallets sold will be the same, equal to 27.
After 3 days, the number of belts and wallets sold will be the same, equal to 27.
It is given that the number of belt sold s, x days after its online lunch s=3^x
and s=4x+15.
To find correct answer in each box.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers.
After 3 days :
3³ = 27 belts
4(3) + 15 = 12 + 15 = 27 belts
So, after 3 days, the number of belts and wallets sold will be the same, equal to 27.
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HELP ASAP/NOW...NO LINKS OR JOKING PLS
Answer:
D. 0 < x < 20
Explanation:
Domain is in the x axis, Range lies in the y axis.
Here it is seen that function's domain lies between 0 to 20.
Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'Here, as the circle's are open. Domain: 0 < x < 20
Additionally,
Range: -10 < f(x) < 04
12 + 17 < -18 *
True
False
can someone please help meee
Answer:
-10
Step-by-step explanation:
y2- y1 -7 -3
---------- ----------
x2 - x1 -6 6
Solve for B:
1/5b=d+f
Answer:
b=5d+5f
solve for b by simplifying both sides and then isolating the variable.
376
Step-by-step explanation:
C
2
1
3
A. 21
B. 23
C.24
D. 25
b7
#
5
4
In the figure, which angle has the same measure as /2?
Answer:
the angle that has the same measure as /2 is A
find the surface area of the pyramid
Answer:
20ft²
Step-by-step explanation:
Given the functions below, find g(5) + h(2).
g(x) = 2x - 5
h(x) = 4x + 5
Answer:
18
Step-by-step explanation:
substitute x = 5 into g(x) and x = 2 into h(x)
g(5) + h(2)
= 2(5) - 5 + 4(2) + 5
= 10 - 5 + 8 + 5
= 5 + 13
= 18
please place the dot for me(20 points will give brainliest!!!)
Answer:
Domain & Range are both all real numbers.
Step-by-step explanation:
i
If this was a traditional parabola, the range would be y<=4. However, the arrow on the left going back up means eventually y will go to both positive & negative infinity.
The heights of adult men in the united states are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. use this information together with the 68-95-99.7 rule to make three statements about the height of adult men in the united states.
Answer:
Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.
x + y = 152,
8.5x + 12y = 1,656
How many hats were sold?
hats
Step-by-step explanation:
a) 74.857% of adult men are shorter than Michael
b) 84.134% of adult men are taller than Jack
c) 58.991% of adult men are of height between Jack and Michael
What is 68-95-99.7 rule?Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.
Given:
µ = 70in, σ = 3in.
We know Z = (x-µ)/σ
a) Actor Michael B. Jordan is 6’0” (72”) tall.
Z = (72-70)/3 = 0.67
So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%
b. Comedian Jack Black is 5’7’ (67”) tall.
Z = (67-70)/3 = -1
The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.
But the percentage of those taller than jack is = 1 – .15866 = 0.84134
c) P(X < 72) – P(x < 67)
= 0.74857 – 0.15866
= 0.58991
= 58.991%
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The Question attached here is incomplete, the complete question is
a. Actor Michael B. Jordan is 6’0” (72”) tall. What percentage of adult men are shorter than Michael?
b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?
c. What percentage of adult men are of height between Jack and Michael?
Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.
Answer:
g = 24 - 1/25m
Step-by-step explanation:
Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.
This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.
This leads us to the equation:
g = 24 - 1/25m
where g is the amount of gas left, and m is the number of miles driven.
Translate each description into an algebraic expression. Then, evaluate the expression
using the value shown in the box for the variable.
EXAMPLE: the quotient of 112 and a added to 25 = (112 + a) + 25 = 53
a = 4
w = 10
b=3
x = 11
c = 9
y = 7
d=2
z = 5
1. the difference of 100 and the product of y and 12 =
2. b times the sum of 15 and 37 =
3. 27 added to the product of z and 12 =
4. 135 divided by the product of c and 5 =
5. w to the second power times the quotient of 12 and 4 =
6. 12 times d divided by the difference of 25 and 19 =
7. the product of x and 5 added to 13 =
The value of each algebraic expressions are:
1. 16
2. 156
3. 87
4. 3
5. 300
6. 4
7. 68
What is an Algebraic Expression?An algebraic expression is a mathematical statement involving variables and digits. It is evaluated by plugging in the value of the variables.
1. Product of y and 12 is 12y
100 - 12y
Plug in the value of y
100 - 12(7) = 16
2. b(15 + 37) = b(52) = 3(52)
= 156
3. Product of z and 12 is 12z
12z + 27 = 12(5) + 27
= 87
4. 135 ÷ 5c = 135/5(9)
= 3
5. w²(12/4) = 3w²
= 3(10²)
= 300
6. 12d ÷ (25 - 19)
12d/6 = 12(2)/6
= 4
7. 13 + 5x
13 + 5(11)
= 68
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vanessa deposited money into a bank account yhat earned 1.25% simple interest after each year. after 1/2 year she earned $5 in interest on the account. how much was her initial deposit
The initial amount is $800.
What is interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
Given:
Simple interest = 1.25% = 0.0125
So, interest in half a year.
=0.0125 ÷ 2
= 0.00625
Now,
=5 / 0.00625
= 800
Hence, the initial deposit was $800
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Domain of y=5x+2 help!!!!
in an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. can you find all angles of the triangles?
Answer:
all angles of the triangles is 60
Step-by-step explanation:
the perimeter = 2*side of an isosceles triangle + bottom edge
----> bottom edge = the perimeter - 2*side of an isosceles triangle =25
----> This is an equilateral triangle ----> all angles of the triangles is 60
Before opening night, the cast of Wicked put on a matinee and evening dress rehearsal at the Gershwin Theatre. At the Saturday matinee, 350 people attended the show. For the Saturday evening performance, 40% more people attended the performance. If the average cost of tickets was $182, how much money did the Gershwin Theatre collect from ticket sales of the Saturday performance?
The Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
At the Saturday matinee, 350 people attended the show.
The total number of people who watched the show on Saturday = 350
For the Saturday evening performance, 40% more people attended the performance.
350 x 40%
= 350 x 0.4
= 140
Total people will be = 350 + 140 = 490
If the average cost of tickets was $182
For 490 people = 490 x 182 = $89180
Hence, the Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.
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Can someone help me with this, it’s geometry and it’s so confusing
Answer:
Draw a line from one point A to B into the XY line in a angle
Draw a line parallel to the lines
Point a dot in the middle and name it O
Step-by-step explanation:
Hope it helps
Part 1: complete the operations geometrically. vector operations to draw the resultant vector draw 2u + 4v.
Vectors are elements of the vector space, and they can be illustrated by diagrams.
How to draw the vector 2u + 4v?The vector expression is given as:
2u + 4v
Split the vector expressions, as follows:
y1 = 2u
y2 = 4v
Next, we have:
y = y1 + y2
See the attachment for the graph of 2u + 4v.
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This probability distribution shows
the
typical grade distribution for a Geometry
course with 35 students.
Grade
B
F
Frequency
5
10
15
3
2
Find the probability that a student earns
a
grade of B or C.
p=[?]
Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
√m is an integer.
Given that the value of "m" lies between between 2929 and 3939
Write down the value of "m"
Answer:
There are 8 possible answers for the value of m
Step-by-step explanation:
3025 (55^2), 3136 (56^2), 3249 (57^2)...., 3844(62^2)
The square of the numbers 55-62 could be a solution set for m.
HELP! WILL GIVE BRAINLEST
Examine the following diagram: in the photo I attached of the question
What is the measure of DBC?
2°
6°
41°
49°
Answer:
Option C: 41
Step-by-step explanation:
<ABD+<CBD=90
<ABD=8x+1
<CBD=6x+5
(8x+1)+(6x+5)=90
Combine like terms
(8x+6x)+(1+5)=90
14x+6=90
14x=90-6
14x=84
divide both sides by 14
x=6
Now we plug that value into <DBC = 6x+5
6(6)+5=
36+5
41
Let's take this problem step by step:
∠ABC is 90 degrees
⇒ made up of two angles ⇒ ∠ABD and ∠DBC
⇒ in mathematical equation form:
[tex]ABD + DBC= ABC[/tex]
Since ∠ABD = 8x + 1 and ∠DBC = 6x+5
[tex]8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6[/tex]
Let's plug it into ∠DBC = 6x+5
∠DBC = 6x+5 = 6(6)+5=41
Answer: ∠DBC = 41
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Help me please I can’t do this and I need this for the exam tomorrow?
The value of the x will be 25. The force involved vertically to the surface of an object per unit area is pressure.
What is pressure?The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.
The given data in the problem is;
The base of the block of metal is a rectangle of 20 cm by x cm.
The block exerts a force of 1500 newtons on the ground. The pressure on the ground is 3 newtons/cm²
The area of the rectangle;
A = L × B
A=20 × x
[tex]\rm P = \frac{F}{A}\\\\ 3 N / cm^2 = \frac{1500 N}{20 \times x } \\\\ x= 25[/tex]
Hence the value of the x will be 25.
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Question 3(Multiple Choice Worth 5 points)
(06.03 LC)
Determine the equation of the graph, and select the correct answer below.
(-1, 3)
Millie needs a total of 7.8 feet of ribbon for a school project. She needs 0.7 more feet of ribbon. How much ribbon, in feet, did Millie already have? Write and solve an equation to find the answer.
6.9
7.1
7.5
8.5
Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,
Ribbon Millie had = Total Ribbon - ribbon that is needed
= 7.8 feet - 0.7feet
= 7.1 feet
Hence, the ribbon that Millie already had is 7.1 feet.
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