A population of flies grows according to the function p(x) = 5(2)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 3x + 2. What is the population of flies after three weeks with the introduced spider?
x = 3 weeks
Growth: 5(2)(3) = 30 flies in 3 weeks
eaten: 3(3) +2 = 9+2 =11 flies eaten in 3 weeks
30-11 = 19 flies ( population after 3 weeks)
Why do elephants have pointy tails
∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 . What is the value of x? Enter your answer in the box.
Answer:
x = 5
Step-by-step explanation:
We need to remember that vertical angles are opposite to each other when two lines cross. The vertical angles that result from two lines crossing have the same measure.
In this problem we have angle E which measures 8x + 8 and angle F which measure 2x + 38.
Since they are vertical angles, we know that they have the same measure and therefore we can equal them both and solve for x:
[tex]8x+8=2x+38\\8x-2x=38-8\\6x=30\\x=5[/tex]
Therefore, x = 5 (and ∠E = ∠F = 48)
How is the distance formula like the pythagorean theorem explain?
The distance formula is
simply a variation of the theorem. The method is the same with the Pythagorean
however we are now dealing with 2 sets of points instead of 2 lengths.
In the distance formula, the lengths are derived from the
(x1,y1)->(x2,y2) coordinate points and the formula simplified. We still
square the difference of x’s and difference of y’s to get our two squares then
square root the sum to give our length. While the Pythagorean theorem is
directly the sum of the square of the other two sides.
Nevertheless, both formulas work on the same principle.
Answer:
Both formulas can be used to find the distance between two points on the coordinate plane. The vertical leg of the right triangle represents the difference in the y values of the two points. The horizontal leg of the right triangle represents the difference in the x values of the two points. The hypotenuse of the right triangle represents the distance between the two points.
Step-by-step explanation:
Consider the system of equations
{ -2x + 6y = -8
{ cx + 3y = -4
What value of c would produce a system that has an infinite number of solutions?
Justify your answer.
Explain why there is no value of c that would produce a system with no solution.
Enter your answer, justification, and explanation in the box provided.
With calculations please
Find the measure of angle e.
A. 70°
B. 130°
C. 100°
D. 110°
Which of the following measurements is equivalent to 5 quarts? 25 cups 40 fl. oz. 10 pt. 1 gal.
So I’m doing test corrections and I need help on the problem
HELP PLEASE APPRECIATED Margarita is driving at the speed of s-4/ s^2- 9s + 20 miles per hour.
The distance Margarita covers in s-5/4 hours is ___ miles.
Give the answer in simplest form.
Only correct answers and please show your work so I can refer to it on my other problems. thank you.
The distance Margarita covers in [tex]\( \frac{s-5}{4} \)[/tex]hours is [tex]\( \frac{1}{4} \)[/tex] miles.
Given that Margarita is driving at the speed of [tex]\( \frac{s-4}{s^2 - 9s + 20} \)[/tex] miles per hour, we can express the distance function as:
[tex]\[ d(s) = \text{speed} \times \text{time} = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times s \][/tex]
[tex]\[ d\left(\frac{s-5}{4}\right) = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times \frac{s-5}{4} \][/tex]
Let's simplify this expression:
[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{(s-4)(s-5)}{4(s^2 - 9s + 20)} \][/tex]
[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{s^2 - 9s + 20}{4(s^2 - 9s + 20)} \][/tex]
[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{1}{4} \][/tex]
In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?
Factor this expression completely.
mr + ns - nr - ms
What is the value of x?
a. -16
b. 120
c. 60
d. 16
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
the triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
Fencing costs $10.15/ft. A customer purchases 8 3/8 ft of fencing for his yard. How much did the customer pay for the fencing? Round to the nearest cent.
You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95, what percentage discount is he offering you?
Answer:
Find out the what percentage discount is seller offering you .
To prove
Formula
[tex]Discouunt\ percentage = \frac{Discount\times 100}{Marked\ price}[/tex]
Discount = Marked price - Selling price
As given
You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95 .
Here
Marked price = $19.95
Selling price = $17.85
Discount = 19.95 - 17.85
= $2.1
Put in the formula
[tex]Discouunt\ percentage = \frac{2.1\times 100}{19.95}[/tex]
[tex]Discouunt\ percentage = \frac{210}{19.95}[/tex]
Discount percentage = 10.5% (Approx)
Therefore the discount is seller offering you is 10.5 % .
4=3/4m-6
find the value of m
4 = 3/4m -6
add 6 to both sides
10 = 3/4m
divide both sides by 3/4
m = 10 / 3/4 = 10 *4 = 40 /3 = 13 1/3
Which of the following numbers is not part of the solution to x > 1?
1
1.2
4
8
Answer:
the answer is 1
hpoe this helps
Branliest offered
Decide which of the two points on the graph of the line
X=0
A. 0,7
B. -4,0
Large reusable bottles cost $4 more than small ones. 8 large bottles cost $24 less than 12 small ones. How much does one small bottles cost?
how do u solve using the ratios !
The scale on a map of Texas shows that 1 inch represents 20 miles. The actual distance from Austin to Dallas is 195 miles. On the map, how many inches apart are the two cities?
To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.
Explanation:To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.
Cross-multiply to solve for x:
(1 inch) * (195 miles) = (20 miles) * (x inches)
195 inch-miles = 20x inch-miles
Now, divide both sides by 20 miles to solve for x:
x = 195 inch-miles / 20 miles
x = 9.75 inches
So, on the map, Austin and Dallas would be 9.75 inches apart.
If be bisects abd find x and m angle abe
Write the equation in slope -intercept form with slope of 4 that contains (-3, -6).
The measure of each interior angle of a regular polygon is 140 degrees, how many sides does the polygon have
The regular polygon with an interior angle of 140 degrees has 9 sides. This conclusion can be reached by using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides.
Explanation:
The number of sides in a regular polygon can be determined using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides. This formula comes from the fact that a polygon can be divided into (n-2) triangles, each of which has angles summing up to 180 degrees.
In this particular case, an interior angle of 140 degrees is given. So we will set up an equation: 140 = (n-2)*180/n. Solving for 'n', we get a value of 9.
Therefore, the regular polygon with an interior angle of 140 degrees has 9 sides.
Learn more about Interior angles of polygons here:https://brainly.com/question/35498523
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You claim to have a magic coin that will land on heads whenever you want. Your friend dares you to prove it by tossing 4 heads in a row. Assuming the coin is fair, what is the probability that your magic will fail?
A) 50%
B) 62.5%
C) 75%
D) 93.75%
Convert the radian measure to degree measure. use the value of π found on a calculator and round answers to two decimal places. five pi divided by six
One canned juice drink is 30 percent orange juice, another is 10 percent orange juice. how many liters of each should be mixed together in order to get 20l, that is 12 perfect orange juice
Find the value of X, can someone help me?
Which expression can be used to change 75 kilometers per hours to meters per minute?