Answer:
-4x+2
Step-by-step explanation:
rewright factor and reduce
The population of a town can be represented by the formula P (t) = 541 + 350, where P(t) represents the population, in thousands, and t represents the time, in
years, since 1970 (note: t = 0 for 1970).
A) what are t values when it is 1985 and 1990. B) what is p(t), when t=25? Explain the meaning in words.
Answer:
part A) see the explanation
part B) The population in 25 years since 1970 will be one million seven hundred thousand people (1,700,000)
Step-by-step explanation:
The correct equation is
[tex]P(t)=54t+350[/tex]
Part A) what are t values when it is 1985 and 1990.
we have
[tex]P(t)=54t+350[/tex]
This is the linear equation in slope intercept form
[tex]m=54\\b=350[/tex]
where
P(t) ----> is the population, in thousands
t ----> the time, in years, since 1970
Remember that
t = 0 for 1970
so
For the year 1985
[tex]t=1985-1970=15\ years[/tex]
For the year 1990
[tex]t=1990-1970=205\ years[/tex]
Part B) what is p(t), when t=25?
For t=25 years
substitute the value of t in the linear equation
[tex]P(t)=54(25)+350=1,700[/tex]
Remember that the population is in thousands
That means
The population in 25 years since 1970 will be one million seven hundred thousand people (1,700,000)
Which are the side lengths of a right triangle? Check all that apply. 3, 14, and StartRoot 205 EndRoot 6, 11, and StartRoot 158 EndRoot 19, 180, and 181 3, 19, and StartRoot 380 EndRoot 2, 9, and StartRoot 85 EndRoot
Answer:
a,c,e
Step-by-step explanation:
Correct me if I'm wrong!
Thank you
Tisa B Sora
The possible side lengths are:
3, 14, and √205
19, 180, and 181
Options A and C are the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
In a right triangle:
The square of the hypotenuse is equal to the sum of the other two sides.
Now,
We can apply the Pythagorean theorem in each case:
1)
3, 14, and √205
Hypotenuse² = 3² + 14²
Hypotenuse² = 9 + 169
Hypotenuse² = 205
Hypotenuse = √205
True.
2)
6, 11, and √158
Hypotenuse² = 6² + 11²
Hypotenuse² = 36 + 121
Hypotenuse² = 157
Hypotenuse = √157
Not possible
3)
19, 180, and 181
181² = 180² + 19²
181² - 180² = 19²
32761 - 32400 = 361
361 = 361
True.
4)
3, 19, and √380
Hypotenuse² = 3² + 19²
Hypotenuse² = 9 + 361
Hypotenuse² = 370
Hypotenuse = √370
Not possible
5)
2, 9, and 85
Hypotenuse² = 2² + 9²
Hypotenuse² = 4 + 81
Hypotenuse² = 85
Hypotenuse = √85
Not possible
Thus,
3, 14, and √205
19, 180, and 181 are possible side lengths.
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“I think I can make it. I’ll just jump.” says Denis, flashing a grin as he looks to the neighboring rooftop.
“Wait!” Vera exclaims. “First let's find the distance! Here, take a look at this diagram.”
“I’ve never much cared for math,” Denis frowns.
Vera rolls her eyes. “We know the distance between us, and we know the angles between ourselves and your target landing point. All we need to do is...”
Denis jumps.
“...apply the law of sines.” Vera gasps.
According to Vera's diagram, how far did Denis need to jump to reach the neighboring rooftop?
9514 1404 393
Answer:
5.3 m
Step-by-step explanation:
The angle opposite the given side is ...
180° -105° -40° = 35°
Then the law of sines tells us the unknown distance (d) is ...
d/sin(40°) = 4.7 m/sin(35°)
d = (4.7 m)sin(40°)/sin(35°) ≈ 5.267 m
Denis will need to jump about 5.3 m to reach the neighboring roof.
_____
Additional comment
Denis will need a running start. The world record for a standing broad jump is less than 4 m.
The vertex form of the equation of a parabola is y = 2(x + 4)2 - 21.
What is the standard form of the equation?
Answer:
y = 2x^2 + 16x + 11
Step-by-step explanation:
2(x + 4)^2 - 21
2(x + 4)(x + 4) - 21
2(x^2 + 8x + 16) - 21
2x^2 + 16x + 32 - 21
2x^2 + 16x + 11
Answer:
y = 2x^2 + 16x + 11
the other answer explains it much better
which of The following numbers is largest Try This question out and I’ll give you brainliest
Answer: 0.153 is the largest
Step-by-step explanation:
1/7=0.14, 1/12=0.08, and 15%= 0.150
1) 1336 = 8(-14x - 29)
Answer:
x = -14
Step-by-step explanation:
Step 1: Distribute
1336 = 8(-14x - 29)
1336 = -112x - 232
Step 2: Add 232 to both sides
1336 + 232 = -112x - 232 + 232
1568 = -112x
Step 3: Divide both sides by -112
1568 / -112 = -112x / -112
-14 = x
Answer: x = -14
Answer:
The solution is x = -14
Step-by-step explanation:
To solve for x, first perform the indicated multiplication. We get:
1336 = 8(-14x - 29) => 1336 = -112x - 232
Adding 232 to both sides isolates -112x:
1336 + 232 = -112x, or
1568 = -112x
Next, x = -1568/112 = -14
The solution is x = -14.
graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 1, and 3
Which of the following functions best represents the graph?
f(x) = (x + 3)(x − 3)(x − 9)
f(x) = (x + 3)(x − 3)(x + 9)
f(x) = (x + 3)(x − 3)(x − 1)
f(x) = (x + 3)(x − 3)(x + 1)
Answer:
The best is f(x) = (x + 3)(x − 3)(x + 1).
Step-by-step explanation:
The coefficient of x^3 will be positive because of where the graph rises and falls.
As one of the x intercepts is negative 3 one of the factors will be (x + 3).
By the same reasoning the other 2 factors will be (x - 3) and (x + 1).
Answer:
D is correct!
Step-by-step explanation:
I am with the same program.
What is the first operation to use to simplify the expression?
3,500÷(34+8×2)−4
Final answer:
To simplify the expression 3,500÷(34+8×2)−4, first simplify the expression inside the parentheses, then divide and subtract to get the final answer of 66.
Explanation:
To simplify the expression 3,500÷(34+8×2)−4, we need to follow the order of operations which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this case, we first simplify the expression inside the parentheses, which is (34+8×2). We perform the multiplication first, then the addition, resulting in 34+16. Next, we divide 3,500 by the sum of 34 and 16. Finally, we subtract 4 from the quotient.
Step-by-step:
1. Simplify (34+8×2) = 34+16 = 50
2. Divide 3,500 by 50 = 70
3. Subtract 4 from 70 = 66
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try?
A.1/7
B.1/12
C.1/24
D.1/64
About 8% of the U.S. population catches the flu each season. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?
A.1 in 8
B.1 in 12
C.1 in 18
D.1 in 80
Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws, and must make both to win the game. What is the probability that Kay's team will win the game?
A.64%
B.80%
C.88%
D.160% (so 100%)
Answer:
D.1/64
B.1 in 12
A.64%
Step-by-step explanation:
Each dial has 4 letters and only one of them is correct; the probability to choose the correct one is then 1/4. Selecting a letter in each dial is independent, then the probability of guessing the right combination in one try is 1/4 * 1/4 * 1/4 = 1/64
8% means a probability of 8/100 or an odds of 8 in 100. Dividing each term by 8 we get 8/8 = 1 in 100/8 = 12.5, which can be rounded to 1 in 12
80% means a probability of 80/100 = 0.8. Given that the 2 free-throws are independent, the probability that he makes both is 0.8*0.8 = 0.64 or 64%
please help
5 points up for grab
Answer:
197
Step-by-step explanation:
kk here we go
find the area of each side so:
5 x 5 = 25
5 x 5 = 25
9 x 5 = 45
6.4 x 5 = 32
trapezoid = 5 + 9 = 14
and then divide that 14 by 2 which is 7. multiply by height which is 5 again
that equals 35
double that bc there are 2 trapezoids = 70
add all together
197
there ya go:)
Type the Integer that makes the following addition sentence true.
Answer:
11
Step-by-step explanation:
3 + 38 - 63 + 33 = 11
Answer:
11
Step-by-step explanation:
I found the answer simply by doing trial-and-error, but here are the steps:
11 - 33 = -22
-22 + 63 = 41
41 + (-38) = 3
Polygon ABCDEF is a regular hexagon. Find the perimeter of the polygon. Round to the nearest hundredth. Round to give final answer only.
Answer:
12√2 ≈ 16.97
Step-by-step explanation:
Points A and B are on grid lines. The difference B-A is (2, 2), so the distance formula will tell you the length of that segment is ...
√(2²+2²) = 2√2
The regular hexagon has 6 sides all the same length. The perimeter is the sum of those lengths, so is ...
6 × 2√2 = 12√2 ≈ 16.97 . . . . units
Please help ASAP; it is based off of sequences
Answer:
[tex]a_n= - 1( - 2)^{n-1}[/tex]
Step-by-step explanation:
The given geometric sequence is :
-1,2,-4,8,...
The first term is
[tex]a_1=-1[/tex]
The common ratio is
[tex]r = \frac{2}{ - 1} = - 2[/tex]
The nth term is given by;
[tex]a_n=a_1(r^{n-1})[/tex]
We substitute the values of the first term and common ratio to get:
[tex]a_n= - 1( - 2)^{n-1}[/tex]
This is called the explicit formula.
If m/n =5, then m2−25n2 =
Answer:
(1) m > 0
(2) 2m + n= 26
Step-by-step explanation:
Answer:
its 0 trust me
Step-by-step explanation:
what is the equation of the line that passes through the points (0,4) and (3,-2)
Answer:
y= -2x + 4
Step-by-step explanation:
-2 - 4 = -6
3 - 0 = 3
-6 ÷ 3 = -2
-2x is the slope.
3 × -2 = -6
-2 - -6 = 4
4 is the y intercept
3/4 of m into an algebraic expression
The word OF means to multiply in math.
So, 3/4 of m becomes (3/4)m, which means 3/4 TIMES m.
We can also write the expression
this way: (3m)/4.
They both mean the same thing.
The requried 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.
To express 3/4 of a quantity, m, as an algebraic expression, we can multiply 3/4 by m.
The algebraic expression for 3/4 of m is (3/4)m.
To evaluate this expression, we simply multiply 3/4 by the value of m.
For example, if m = 10, we substitute m = 10 into the expression to find (3/4)(10) = (3/4) * 10 = 30/4 = 7.5.
Therefore, 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.
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please help. its very easy
Step-by-step explanation:
[tex]35\% \: of \: 40 \\ = \frac{35}{100} \times 40 \\ = 3.5 \times 4 \\ = 14[/tex]
Hence 14 students prefer American food.
Option B is the correct answer.
Solve for y.
-3=7(y-9/7)
Answer: Y= 6/7 or Y=0.86
Step-by-step explanation:
-3=7(y-9/7)
-3=7y-9
+9 +9
6=7y
divide both sides to get y by it self
6/7=y
Answer:
Y=6/7
Step-by-step explanation:
You have to isolate the variable by doing the opposite of PEMDAS to both sides of the equation.
Sienna earns $9.36 for each hour she works. This week she worked 15.67 hours. How much did Sienna earn this week?
Answer:
146.67 dollars
Step-by-step explanation:
9.36*15.67
Answer:
$146.67
Step-by-step explanation:
$9.36 per hour
15.67 hours
Multiply
$146.67
Hope this helps :)
Dexter has a gift card for $20.00 to an electronics store. He also has a coupon for 25% off his entire purchase, so he will be paying 75% of the total cost. He plans to buy a video game for $10.00 and batteries for $2.00. Select the equation that represents how much money will be left on his gift card after his purchases if x represents his remaining balance.
What is the equation that represents his remaining balance?
x = 20 + 0.75(10 + 2)
x = 20 – 0.75(10 + 2)
x = 20 + 0.25(10 + 2)
x = 20 – 0.25(10 + 2)
Answer: X=20-0.75(10+2)
Please mark brainliest!
Step-by-step explanation:
It would be B x=20-0.75(10+2)
because 20 is the amount of the gift card and 0.75 is the percent you will be paying so you subtract the total of 10 and 2 and subtract from 20 and thats the amount you have left!
Answer:
b. x = 20 – 0.75(10 + 2)
Step-by-step explanation:
I just know
--
Brianna Edwards
e d g e n u i t y things
Thanks and remember to always vote brainliest
dard
3. A soda pop company is running a bottle cap
contest where "WINNER" is printed
underneath random bottle caps. If the
probability of getting a winning bottle cap is
6 in 40, what is the probability of not winning?
Answer:
34 in 40
Step-by-step explanation:
6 in 40 is the probability of winning, so
34 in 40 is the probability of not winning.
simply do 40 - 6.
This answer can also be written as
[tex] \frac{34}{40} [/tex]
or 85%
The probability of not winning a bottle cap is 34/40.
What is probability?Probability is a field in mathematics that deals with the possibility of how an event is likely to occur or true.
The probability of favorable outcomes (winning) = 6The probability of unfavorable outcomes (not winning) = 40 - 6 = 34The total possible outcome = 40The probability of not winning = 34/40
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prove that :
1/sin^2A -1/tan^2A =1
To prove that:
[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]
LHS = [tex]\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}[/tex]
Using basic trigonometric identity, [tex]\tan (x)=\frac{\sin (x)}{\cos (x)}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\left(\frac{\sin A}{\cos A}\right)^{2}}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\frac{\sin^2A}{\cos^2 A}}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{\cos^2 A}{\sin^2A}[/tex]
[tex]$=\frac{1-{\cos^2 A}}{\sin ^{2}A}[/tex]
Using trigonometric identity: [tex]1-\cos ^{2}(x)=\sin ^{2}(x)[/tex]
[tex]$=\frac{\sin ^{2}A}{\sin ^{2}A}[/tex]
= 1
= RHS
LHS = RHS
[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]
Hence proved.
A system of equations that ended with the statement 5=5 has no solution? False or true
Answer: no solution
Step-by-step explanation:
In a system of equations, if the final equation simplifies to a statement that is always true, like 5=5, this indicates the system has in fact an infinity of solutions, not no solutions.
Explanation:The question given pertains to the solution of a system of equations. In a system of equations, if you simplify to a point where you end up with a statement that is always true, such as 5=5, this indicates that the system has an infinite number of solutions, not no solutions as suggested.
Let's imagine we have a system of two linear equations representing two lines on a graph. If the lines overlap perfectly (one is exactly the same as the other), every point on the line is a point of intersection, meaning it is a solution to the system. When we simplify such a system algebraically, we get an identity like 5=5 which is true no matter what values the variables may take, directly indicating that there are an infinite number of solutions.
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If MP = 6x – 5, QR = 3x + 1, and RN = 6, what is QN?
Answer:
19 units.
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure it is given that MN=PQ.
It is given that MP = 6x – 5, QR = 3x + 1, and RN = 6.
Since non parallel sides are equal, therefore it is an isosceles trapezoid.
The diagonals of an isosceles trapezoid are equal.
[tex]MP=QN[/tex]
[tex]MP=QR+RN[/tex]
Substitute the given values.
[tex]6x-5=3x+1+6[/tex]
[tex]6x-5=3x+7[/tex]
[tex]6x-3x=5+7[/tex]
[tex]3x=12[/tex]
[tex]x=4[/tex]
The value of x is 4.
[tex]QN=MP=6x-5=6(4)-5=24-5=19[/tex]
Hence, the measure of QN is 19 units.
To find QN, RN from the value of QR which is 3x - 5
Explanation:The value can be found using Algebraic expressions.
To find QN, we need to find the value of QR and subtract RN from it.
Given that QR = 3x + 1 and RN = 6, we can substitute these values into the equation.
So, QN = (3x + 1) - 6.
Simplifying further, QN
= 3x + 1 - 6
= 3x - 5.
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Multiply. Write your answer as a fraction in simplest form.
8(3/26)
Answer:
12/13
Step-by-step explanation:
I hope this helps!
Y=-2x^2+8x-8 What is the vertex
Answer:
Vertex is (2,0)
Step-by-step explanation:
The vertex of a parabola is x=-b/2a
Since a=-2 and b=8, we have:
x=-8/2(-2)
x=-8/-4
x=2
So the vertex is (2,0)
9. GO DEEPER Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday.
On Tuesday, she has the number of pens she had on Monday. On Wednesday, na
she has of the number of pens she had on Tuesday. How many packages of pens A
does she have on Wednesday?
Answer:
Mrs. Rodriguez has 6 packages of pens Wednesday
Step-by-step explanation:
how to find critical points
Answer:
look for places where the derivative is zero or undefined
Step-by-step explanation:
Find the derivative. Critical points are where the derivative is zero, and where it is undefined.
__
A polynomial function may or may not have points where the derivative is zero. It will never have points where the derivative is undefined (tangent lines are vertical).
A rational function, or one involving fractional exponents may have critical points where the derivative is undefined.
__
For example, the function ...
y = √(1 -x^2)
has the derivative ...
y' = -x/√(1 -x^2)
This has a zero at x=0 (tangent is horizontal). It is undefined at x = ±1, where the denominator is zero (tangent is vertical). Those values of x tell you the critical points are (-1, 0), (0, 1), (1, 0).
Critical points in a mathematical function are found by deriving the function, setting the derivative equal to zero, and solving for x. The x-values obtained are the x-coordinates of the critical points. An example is provided for the function f(x) = x3 - 3x2.
Explanation:To find the critical points in a function, you first need to identify the derivative of the function. Once you have obtained the derivative, you set it equal to zero and solve for x. The x-values you get are the x-coordinates of your critical points.
Let's illustrate with an example, using the function f(x) = x3 - 3x2.
First, let's find the derivative, f'(x) = 3x2 - 6x. Then set f'(x) = 0 and solve for x. This gives us x = 0 and x = 2. Therefore, (0, f(0)) and (2, f(2)) are the critical points of the function.
Please note, critical points are also the points where the derivative is undefined. However, in this case the derivative exists for all real numbers, so we do not have any such critical points here.
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Here is a system of two linear equations. Verify that the solution to this system is (3,4).
Equation A1: y = x + 1
Equation A2: y = -2x + 10
Answer:
The answer
x=3
y=4
Step-by-step explanation:
You use substitution to solve it:
x+1=-2x+10
3x+1=10
3x=9
x=3
y=4
plug in the solution to the equation to verify your answer.
If the rate 130 miles per 2 hours is reduced to a unit rate, the result is
miles per hour.
Answer here
Answer:
65 miles every 1 hour
Step-by-step explanation:
Unit rate is found once one of the units is 1. In this case we need to reduce the ratio so that it is 1 hour and we get a unit rate. We can do this by dividing both sided by 2 so that the hours are reduced to 1.
130=2
130/2=65 2/2=1
65=1
65 miles every hour
The unit rate of 130 miles per 2 hours is 65 miles per hour. This is calculated by dividing the number of miles (130) by the number of hours (2).
Explanation:In Mathematics, the term unit rate refers to the ratio of two measurements, in which the denominator is 1. In this situation, you are given the rate of 130 miles per 2 hours and need to reduce it to a unit rate. To do this, you divide the number of miles (130) by the number of hours (2).
The calculation would be 130 miles ÷ 2 hours = 65 miles per hour. Hence, the unit rate of 130 miles per 2 hours is 65 miles per hour. This means that if you travel at this rate, you would cover 65 miles in one hour.
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