Answer:
1
Step-by-step explanation:
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In 1995, the population of a town was 33,500. It is decreasing at a rate of 2.5% per decade.
a. Identify whether the function is a growth or decay function.
b. Write the function, f(n), that expresses the population of the town after (n) decades.
c. What is the population in the year 2025 to the nearest hundred?
Answer:
See belowStep-by-step explanation:
Initial date = 1995Initial population = 33500Decrease rate = 2.5% per 10 yearsa. It is a decay function as number of population is decreasing over time
b. f(n) = 33500*((100 - 2.5)/100)^n = 33500*(0.975)^n
c. In year 2025, n = (2025 - 1995)/10 = 3
f(3) = 33500*(0.975)^3 = 31100 rounded up
The distance between two stars is 9.0 x 10 to the power of -3 light years. A light year is equal to
5.88 x 10 to the power of 12 miles. What is the distance, in miles, between the two stars
Answer:
The distance between the two stars in miles is 5.292 * 10^10 miles
Step-by-step explanation:
Here, we want to make a conversion from light year to miles
To make this conversion, we simply are going to multiply the light year by the miles
Mathematically, we have this as;
9 * 10^-3 * 5.88 * 10^12
= 52.92 * 10^9
= 5.292 * 10^10 miles
From the top of tower, the angle of depression to a stake on the ground is 60°. The top of the tower is 80 feet above the ground. How far is the stake from foot of the tower?
Answer:
The stake is 80√3 ft or 138.56ft away
Step-by-step explanation:
let the distance from the stake to the foot of the tower=x
tan(60°)=x/80
x=80tan(60°)
x=80√3 ft
The distance of the stake from the foot of the tower is 46.189 feet.
What are trigonometric functions?Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the angle of depression is 60°
60° is the angle from the stake to the top of the tower due to alternative angles,
height of tower = 80 feet
let the distance of the stake from tower be x
using tangent to find the distance,
tanФ = perpendicular/base
perpendicular = 80 feet
base = x
Ф = 60°
tan60 = √3
tan60 = 80/x
x = 80/1.732
x = 4.189 feet
hence stake is 46.189 feet from the tower.
Learn more about trigonometric functions;
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Find the slope of the line that passes through the pair of points ? (5, 6), (7, –2)
Answer:
[tex]m=-4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (5, 6)
Point (7, -2)
Step 2: Find slope m
Substitute [SF]: [tex]m=\frac{-2-6}{7-5}[/tex]Subtract: [tex]m=\frac{-8}{2}[/tex]Divide: [tex]m=-4[/tex]Find the measure of QS.
S9T 10 R 21 F 4x+5 Q
A. 35 B, 20 C. 27 D. 29
Answer:
C. 27
Step-by-step explanation:
((4x + 5) + 10)*10 = (21 + 9)*9 (two secants intersecting)
(4x + 5 + 10)*10 = (30)*9
(4x + 15)*10 = 270
40x + 150 = 270
40x = 270 - 150 (subtraction property of equality)
40x = 120
Divide both sides by 40
40x/40 = 120/40
x = 3
✔️QS = (4x + 5) + 10
Plug in the value of x
QS = 4(3) + 5 + 10
QS = 12 + 5 + 10
QS = 27
Select the correct answer which function is increasing at the highest rate?
Answer:
for anyone who needs it: the answer was C.
Step-by-step explanation:
i got it correct on plato test
Solve for X
-2(5x-5.5) + 8= -9x+2-(-5)
Answer:
x = 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesCombining Like TermsStep-by-step explanation:
Step 1: Define
-2(5x - 5.5) + 8 = -9x + 2 - (-5)
Step 2: Solve for x
Distribute: -10x + 11 + 8 = -9x + 2 + 5Combine like terms: -10x + 19 = -9x + 7Add 10x to both sides: 19 = x + 7Subtract 7 on both sides: 12 = xRewrite: x = 12What is the definition of equation
Answer: a definition of an equation can be defined as a mathematical statement consisting of an equal symbol between two expressions that have the same value.
Step-by-step explanation:
If the gas station is selling 5 bottles of water for $10, what is the unit price of each bottle of water?
Answer:
2
Step-by-step explanation:
5 bottles = 10 dollars
divide by 5 to get 1 bottle
now divide 10 by 5 that will be 2
2$ for 1 bottle
write in simplest form 1/3 times 1 1/3
Answer:
3 2/3
Step-by-step explanation:
Use a calculator please
what is this equation -3 +9 +-3
Answer:
3
Step-by-step explanation:
sorry its a little blurry but what is it
Answer:
C
Step-by-step explanation:
I really need help with this question.
Write the equation of the line that pass through the points below. Write your answer in Point-Slope Form or Slope-Intercept Form. Do NOT use any spaces in your answer.
(2, 17), (4, 7)
Equation:
Answer:
Please check the explanation.
Step-by-step explanation:
Given the points
(2, 17)(4, 7)Finding the slope between (2, 17), (4, 7)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:17\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)[/tex]
[tex]m=\frac{7-17}{4-2}[/tex]
[tex]m=-5[/tex]
We know the Point-Slope Form of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Here:
m is the slope(x₁, y₁) is the pointsubstituting the values m = -5 and the point (2, 17) in the Point-Slope Form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 17 = -5 (x-2)[/tex]
Thus, the answer Point-Slope Form is
[tex]y - 17 = -5 (x-2)[/tex]
It can be further simplified to write into the Slope-Intercept Form
[tex]y - 17 = -5 (x-2)[/tex]
y-17 = -5x+10
y = -5x+10+17
y = -5x+27
Thus, the answer in the Slope-Intercept Form (y=mx+b)
y = -5x+27 ∵Slope-Intercept Form → y=mx+b
Calculate the discriminant and determine the type and number of solutions for each quadratic equation. 2x2−28x=−48 discriminant: Number of solutions: Type of Solutions: Rational or irrational:
Answer:
Discriminant = 100
Number of solutions = 2
Type of solution = Real and Unique
Rational or Irrational: Rational
Step-by-step explanation:
Given the quadratic expression;
[tex]2x^2 - 28x= - 48 \\[/tex]
Rewrite in standard form
[tex]2x^2 - 28x+ 48= 0 \\[/tex]
Divide through by 2;
[tex]x^2 - 14x + 24 = 0[/tex]
From the expression;
a = 1, b = -14 c = 24
Discriminant determines the nature of the root of the quadratic equation;
Discriminant D = b² - 4ac
Substitute the given values;
D = (-14)² - 4(1)(24)
D = 196 - 96
D = 100
Since the discriminant is greater than zero this means that the solution will be real and unique values.
Get the number of solutions;
Using the formula;
x = -b±√D/2a
x = -(-14)±√100/2(1)
x = 14±10/2
x = 14+10/2 and 14-10/2
x = 24/2 and 4/2
x = 12 and 2
Hence the equation has 2 solutions.
The solutions are rational since we can write then as a ratio of two integers
what is it??,,,,,,,,,,,,
Answer:
99,000
Step-by-step explanation:
since 3 times 10 to the power of 3 is 1000 and 10 to the power of 5 is 100000 the answer is 99,000
Answer: 97000 more
Step-by-step explanation:
10*10*10*10*10=100000 10⁵
10*10*10=1000*3=3000 10³
So 100000-3000= 97000 more
Hope this helped!
If tan 0 = -5, find the cot 0
Answer:
Step-by-step explanation:
cot(theta) = 1 / tan(theta)
cot(theta) = 1 / -5
cot(theta) = - 0.2
Find the x-intercept and the y-intercept of the line 2x-5y= -6
Answer:
Step-by-step explanation:
2x - 5y = 6
5y = 2x - 6
y = 2/5x - 6/5
y-intercept is -6/5
x-intercept is when you say that y = 0
and so 6/5 = 2/5x
x = 6/2 = 3
PLEASE HELP THANK U!
Answer:
the fist one
Step-by-step explanation:
Hope it helps
f(x) = x + 2x + 12
for the following function, select the x-intercepts and y-intercept
Answer:
Y intercept is 12 x intercept is -4
Step-by-step explanation:
Isaac works as a cook at a restaurant. He started this week with 800 potatoes. On Monday, he used 380 potatoes. On Tuesday, he used 270 potatoes. How many potatoes were left at the end of Tuesday?
Answer:
The number of Potatoes remaining is = 150
Step-by-step explanation:
From the information given above,
On first day of the week (Sunday),
Total potato = 800
The number used include:
Monday = 380
Tuesday = 270
Total potato used = Monday + Tuesday
= 380 + 270 = 650
Remaining Potato = 800 - 650 = 150
Answer plsss
I’m on the 7th question from my math packet help plsss
And I’m almost done so pls
Answer: First step would be to do whatever is inside the parentheses.
Step-by-step explanation:
PEMDAS
Solve the following system of equations:
-2x + y = 1
-4x + y = -1
A: (3, 1)
B: (-1, 3)
C: (-1, -3)
D: (1, 3)
Answer:
x=1,y=3
correct answer is (1,3)
Step-by-step explanation:
We can quickly eliminate y by subtracting one equation from the other
(-2x+y=1)-(-4x+y=-1)
2x=2
x=1
plug x=1 into equation 1
-2(1)+y=1
y=1+2=3
Please! Find the values of x,y and Z
Answer:
x = 24
y = 10
z = 17
Explanation:
It's long to explain, so heres a picture of how solved each. hope this helps!! :)
James started an apple orchard with the trees he already had and then planted 25 more. Now his orchard contains 44 trees. How many trees did James start out with?
x/5 - g = a for x
how can i find x?
Answer:
X = 5a+5g
Step-by-step explanation:
Adding g on both sides gives:
X/5 = a+g
Now dividing 5 on both sides gives us the value of x which is:
X = 5(a+g)
Hence X=5(a+g) or X=5a+5g( multiplying by 5 gives us 5a and 5g)
What is half of 2+2 First answer gets Brainliest
Answer:
Half is 2
Step-by-step explanation:
Bob and Cheryl are taking a road trip that is 181.60 miles. Bob drove
3
4
of the total distance.
How many miles did Bob drive?
what is 1 7/8 + 2/8 ???
Answer:
The answer is 2.375.
Step-by-step explanation:
17 / 8 = 2.125.
2 / 8 = 0.25.
2.125 + 0.25 = 2.375.
Which mathematical statement represents "17 more than a number is 26"?
O 17 > 26
On+17 - 26
017-26
26+n=17
Answer:
n +17 = 26
Step-by-step explanation:
Let the number be 'n'
17 more than 'n' = n + 17
n + 17 = 26
Answer:
n +17 = 26
Step-by-step explanation:
I got a 100 on the test ed2021
If (x-2,6)=(4,y+2)then the value of x=_____and y=____
x=6 , y = 4
Step-by-step explanation:
( x-2,6)=(4,Y+2)
this means; (x-2) &( 4) stands for" x "axis.
and( 6 )& (y+2) stands for y axis.
So, we can say( x-2)=X1 & (4)=X2 , (6)=Y1 & (y+2)=Y2
then; to Solve The Equation we use The Formula: X1=X2 for "X" And Y1=Y2 for "Y".
Solution: for "X" ; X1=X2
x-2= 4
x=4+2
x=6
For "Y" ; Y1=Y2
6 = y+2
y=6-2
y=4
finally check ; ( (x-2),6) = (4,(y+2) )
(6-2),6 = (4,(4+2) )
( (4),6) = (4,(6) )
(4,6) = (4,6)
so, X1 =X2 ; 4 = 4
Y1 = Y2 ; 6 = 6