[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]
Can someone help me with 1-3
The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon with two sides of length 3.
The first hexagon: 2, 2, 3, 4, 6, 7
The second hexagon: 3, 3, a, b, c, d
The hexagons are similar. Therefore the sides are in proportion.
[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex] multiply both sides by 3
[tex]a=\dfrac{3}{2}=4.5[/tex]
[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex] multiply both sides by 4
[tex]b=\dfrac{3}{2}\cdot4=6[/tex]
[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex] multiply both sides by 6
[tex]c=\dfrac{3}{2}\cdot6=9[/tex]
[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex] multiply both sides by 7
[tex]d=\dfrac{21}{2}=10.5[/tex]
The perimeter:
[tex]P=4.5+6+9+10.5=30[/tex]
Answer:
36
Step-by-step explanation:
The previous answerer forgot to add the two 3's to the sum so the correct answer it 36
Which Expression are equivalent to -12(2-3x)-5x
Answer:
-24-36x-5x
-24-41x
or -41x-24
Step-by-step explanation:
WILL GIVE BRAINLIEST
What is the domain of the function below?
A. -5 ≤ y ≤ 2
B. -3 ≤ x ≤ 3
C. -2 ≤ y ≤ -2
D. -5 ≤ x ≤ 6
Answer:
D
Step-by-step explanation:
The domain is the set of all x-values. We know the domain by finding the start and stop point of the function on the x-axis. The domain is all the values in between if the function is continuous without any breaks.
Here the function begins at x=-5 and ends at x=6.
We write the domain as [tex]-5\leq x\leq 6[/tex].
Answer is D.
You have 10 batteries sitting on your desk, three of which are dead. You choose 2 batteries are random for you calculator. What is the expected number of good batteries that you get?
A) 0
B) 1
C) 1.4
D) 2
Answer:
C) 1.4
Step-by-step explanation:
The probability of choosing 2 good ones is 7/10·6/9 = 42/90.
The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.
The probability of choosing 0 good ones is 3/10·2/9 = 6/90
The expected value is the sum of the product of number of good ones and their probability:
... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4
Ali caught a fish that weighted 9 and 1/2 lb. Lisa caught a fish that weighed 5 and 1/ 3 lb. How much more did ali fish weight.
Final answer:
Ali's fish weighs 25/6 lb more than Lisa's fish.
Explanation:
To find out how much more Ali's fish weighs compared to Lisa's fish, we need to subtract the weight of Lisa's fish from the weight of Ali's fish.
Ali's fish weighs 9 and 1/2 lb, which can be rewritten as 19/2 lb. Lisa's fish weighs 5 and 1/3 lb, which can be rewritten as 16/3 lb.
Now, subtracting the weight of Lisa's fish from Ali's fish, we have:
Ali's fish weight - Lisa's fish weight = (19/2) lb - (16/3) lb = (57/6) lb - (32/6) lb = 25/6 lb.
Therefore, Ali's fish weighs 25/6 lb more than Lisa's fish.
In a basketball game,Carolyn made 14 out of 20 shots. Anna made 16 out of 24 shots. Explain how you can tell if the two players made a proportional number of shots.
Answer:
You will want to set up the ratio for each and set them equal to each other. Then you can cross multiply to verify if you get the same answer. Another strategy is to set up each ratio and then reduce to lowest terms to see if you get the same fraction.
Step-by-step explanation:
how do you do this? solve for b1
[tex]\dfrac{1}{2}h(b_1+b_2)=A\qquad\text{multiply both sides by 2}\\\\h(b_1+b_2)=2A\qquad\text{divide both sides by }\ h\neq0\\\\b_1+b_2=\dfrac{2A}{h}\qquad\text{subtract}\ b_2\ \text{from both sides}\\\\\boxed{b_1=\dfrac{2A}{h}-b_2}\to\boxed{F.}[/tex]
Indicate the method you would use
Answer:
SSS can be used to prove that the given triangles are congruent.
Step-by-step explanation:
In the given two triangles ΔADC and ΔABC,
AD = AB = 7 units,CD = BC = 8 units,AC is common to both triangles,Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.
SSS congruence-
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. After how many weeks will Gina have exactly $700 in her account, excluding interest?
Answer:
After 33 weeks.
Step-by-step explanation:
Let w be number of weeks.
We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.
To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.
[tex]20w+40=700[/tex]
Let us subtract 40 from both sides of equation.
[tex]20w+40-40=700-40[/tex]
[tex]20w=660[/tex]
Upon Dividing both sides of our equation by 20 we will get,
[tex]\frac{20w}{20}=\frac{660}{20}[/tex]
[tex]w=\frac{660}{20}[/tex]
[tex]w=33[/tex]
Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.
Help me please lots of points
Answer:
In your first picture
7) -40
14) 200
Step-by-step explanation:
The symbol in the picture is asking for multiplication. Typically for these, teachers encourage the use of the multiplication button on a calculator, but otherwise you need to know the basic steps of multiplication.
Answer:
7) -40
14) 200
Step-by-step explanation:
Someone help plz (20 points)
Answer:
The answer is C)
Step-by-step explanation:
In order to fully solve a system of equations, you need both variables, x And y. Therefore he has to go back and solve for x
What is the value of x?
Answer:
x = 22 tan 31
x is approximately equal to 13.22
Step-by-step explanation:
We know from trigonometric functions that
tan A = opposite side/ adjacent side
tan 31 = x / 22
Multiply each side by 22
22 tan 31 = x
13.2189332
x is approximately equal to 13.22
1950, the U.S. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. Find an exponential function to model this data
Let's do the usual thing and make t the years since 1950. We'll just abbreviate a billion B.
f(1950-1950)=39.4 B
f(2000-1950) =2025.2 B
Our exponential form for f will be
[tex]f = a e^{kt}[/tex]
[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]
[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]
Dividing
[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]
[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]
[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]
Our function is
[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]
Since [tex]e^{0.0787932} \approx 1.08198[/tex]
[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]
around 8.2 % annualized growth.
Final answer:
An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]
Explanation:
We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.
From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:
f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.
f(50) = 2025.2 = 39.4 × b^50.
To find the value of 'b', we solve the second equation:
2025.2 = 39.4 × [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]
Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:
[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]
Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.
Which of the following points is a solution of the inequality y < -|x|?
A) (1, -2)
B) (1, -1)
C) (1, 0)
Answer: choice A only
(1,-2) is the only solution (from the list of choices)
====================================
Explanation:
Let's go through each answer choice. We'll plug the coordinates in one at a time.
-------------
Choice A has the point (1,-2) so x = 1 and y = -2 pair up together
y < -|x|
-2 < -|1|
-2 < -1
This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.
-------------
Choice B) plug in (x,y) = (1,-1)
y < -|x|
-1 < -|1|
-1 < -1
False. A number is not smaller than itself. So we can cross B off the list.
-------------
Choice C) plug in (x,y) = (1,0)
y < -|x|
0 < -|1|
0 < -1
This is false because -1 is smaller than 0. Cross choice C off the list.
-------------
Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.
The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.
After evaluating each point against the inequality y < -|x|, only point A (1, -2) satisfies the condition, making it the correct answer.
Explanation:To determine which point is a solution for the inequality y < -|x|, we need to check if the y-value of each point is less than the negative absolute value of its corresponding x-value.
For point A (1, -2), we check if -2 < -|1|. Since |-1| = 1, we are checking if -2 < -1, which is true. So, point A is a solution.For point B (1, -1), we check if -1 < -|1|. Since |-1| = 1, we are verifying if -1 < -1, which is not true. Therefore, point B is not a solution.For point C (1, 0), we check if 0 < -|1|. Since |-1| = 1, we are verifying if 0 < -1, which is not true. Hence, point C is not a solution.Therefore, the correct answer is point A (1, -2), as it is the only point where the y-value is less than the negative absolute value of the x-value.
An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly on 5 hours?
Greetings!
Answer:
2370 miles can be travelled
Step-by-step explanation:
If 474 miles can be travelled in 1 hour, this means that to find the total amount in 5 hours we can simply multiply this value by 474:
474 * 5 = 2370
So it can travel 2370 miles!
Dana can jump a rope 264 times in 4 minutes. How many jumps can Dana make in one minute?
A) 55 jumps
B) 60 jumps
C) 66 jumps
D) 72 jumps
Whoever can answer it right, gets brainliest too!
Answer:
66
Step-by-step explanation:
divide 264/4=66
Answer:
C) 66 jumps
Step-by-step explanation:
Dana can jump 264 times in 4 minutes
Divide 364 by 4 to see how many times she can jump in one minute
264/4 = 66
Help please !Algebra Two!!
Answer:
a. -1, odd; 2, even
b. [tex](x+1)(x-2)^2[/tex]
c. odd likely 3
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -1,2
We can write them in intercept or factored form as (x+1) and (x-2).
Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.
The graph is ends up and is a sideways s so is positive with an odd degree.
This means the function has a degree of 3 or higher with the degree being odd.
Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equation?
1 THROUGH 4 ARE THE ANSWERS
Answer:
Correct choice is D
Step-by-step explanation:
Given the system of two equations:
[tex]\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..[/tex]
Fro mthe first equation
[tex]y=8-4x.[/tex]
Substitute into the second equation [tex]8-4x[/tex] instead of y:
[tex]6x-9(8-4x)=12.[/tex]
Note that [tex]8-4x=-4x+8,[/tex] then the second equation will take look
[tex]6x-9(-4x+8)=12.[/tex]
Evaluate the infinite sum
Answer:
It does not converge.
Step-by-step explanation:
Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.
The series ∑a·rⁿ converges if we have |r| < 1.
And the series ∑a·rⁿ diverges if we have |r| > 1.
But we can easily check that |r| = 7/6 > 1.
It means the given series diverges, i.e. does not converge.
Hence, option D is correct answer, i.e. It does not converge.
Answer:
D. it does not converge
Which is equivalent to 80 1/4 ?
Hey there!
"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"
In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator
So,
[tex]80\frac{1}{4}[/tex]
[tex]80(4) = 320[/tex]
[tex]320 +1 = 321[/tex]
[tex]4[/tex] stays the same
[tex]\boxed{Answer: \frac{321}{4}}[/tex]
If you want the decimal form, simplify the the mixed to a improper then you should get a outcome of: [tex]80.25[/tex]
For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.
The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex]. To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.
Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.
Using the substitution method, make y the subject in the first equation
y = 5x + 26
substitute into the second equation
2x -7(5x + 26) = 16
-33x - 182 = 16
-33x = 16 + 182
-33x = 198
x = 198/-33
x = -6
since y = 5x + 26
y = 5(-6) + 26
= -30 + 26
= -4
hence (x,y) = (-6,-4)
Hector went shopping for a computer. At RST store, a computer originally prices at $955 had a price reduction of 40%. What was the sale price?
Answer:
$573
Step-by-step explanation:
955* 0.60=573
or
10% of 955= 95.5
50% of 955=477.5
477.5=95.5=573
The sale price of the computer is given by the equation A = $ 573
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the sale price of the computer after the price reduction be A
Now , the equation will be
The initial sale price of the computer = $ 955
The price reduction percentage on computer = 40 %
So , the sale price after reduction A = initial sale price of the computer - ( price reduction percentage x initial sale price of the computer )
Substituting the values in the equation , we get
The sale price after reduction A = 955 - ( 40/100 ) x 955
On simplifying the equation , we get
The sale price after reduction A = 955 - 382
The sale price after reduction A = $ 573
Therefore , the value of A is $ 573
Hence , the price of the computer is $ 573
To learn more about equations click :
https://brainly.com/question/19297665
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Which equation is in point-slope form for the given point and slope?
Answer: y-7 = 4(x+3), choice B
============================================
Point slope form is generally
y-y1 = m(x-x1)
we have m as the slope and (x1,y1) as the point this line goes through. In this case,
m = 4
(x1,y1) = (-3,7) so x1 = -3 and y1 = 7
So,
y-y1 = m(x-x1)
y - 7 = 4(x - (-3))
y - 7 = 4(x + 3)
which is why choice B is the answer
Point-slope form:
y - y₁ = m(x - x₁) "m" is the slope
Since you know:
m = 4
(x₁ , y₁) = (-3,7)
You can plug it into the equation
y - y₁ = m(x - x₁)
y - 7 = 4(x - (-3))
y - 7 = 4(x + 3)
Your answer is the 2nd choice
A 20-foot piece of string is cut into two pieces so that the longer piece is 5 feet than twice the shorter piece
A rectangular field is 115 yards long and 75 yards wide.
Give the length and width of another rectangular field that has the same perimeter but a smaller area
Final answer:
To create a rectangular field with the same perimeter but a smaller area than the original 115 yards by 75 yards field, one could have a field that is 130 yards long and 60 yards wide.
Explanation:
To find the length and width of another rectangular field that has the same perimeter as a 115 yards by 75 yards field but a smaller area, we first calculate the perimeter of the original field:
Perimeter = 2(length + width) = 2(115 yd + 75 yd) = 2(190 yd) = 380 yd
To have a smaller area, the new field cannot be a square (which would maximize the area) and the sides need to have a greater difference in their measurements while still adding up to half of the original perimeter:
Let's assume the new length is 130 yards, to find the new width: 380 yd / 2 - 130 yd = 60 yd
Therefore, a new rectangular field could be 130 yards long and 60 yards wide.
For the following functions, (a) describe the domain and range, and (b) sketch the graph.
f(x)=(1/2)^x(-3)
line A and line B are parallel. If line A is 2x + 3y =10, what is the equation for line B if it passes through the point (-6,8)
Let us Represent the Line A in the Standard form : y = mx + c
where : m is the Slope of the Line and c is the y-intercept
Given : Equation of Line A is 2x + 3y = 10
[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]
Comparing with the Standard form, We can notice that :
Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]
We know that : Parallel lines have Same Slope
Given : Line A and Line B are Parallel
⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]
Given : Line B passes through the Point (-6 , 8)
We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)
Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]
Equation of Line B is :
[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]
⇒ 3y - 24 = -2x - 12
⇒ 2x + 3y = 12
Find the exact values of the six trigonometric functions for angle in standard position if a point with the coordinates (-6, 6) lies on its terminal side.
Answer:
sin = √2/2, cos = -√2/2, tan = cot = -1
csc = √2, sec = -√2
Step-by-step explanation:
Angle runs around unit circle (where x^2+y^2=1)
from (1,0) to (-√2/2,√2/2)
An initial population of 8 wolves increases by 9% each year. The function f(x) = abx models this situation. Which value does x represent in the function when determining the population after 6 years?
A value which x represent in the function when determining the population after 6 years is 6.
In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x)=a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents the time or x-variable.b represents the rate of change or common ratio.In this context, we can reasonably infer and logically deduce that the variable x in the standard form of the equation of an exponential function represent time, which can either be measure in years, months, days, hours, minutes, or seconds.
In conclusion, x represents 6 in the exponential function when determining the population after 6 years.
Complete Question:
An initial population of 8 wolves increases by 9% each year. The function [tex]f(x) = ab^x[/tex] models this situation. Which value does x represent in the function when determining the population after 6 years?