The solutions to quadratic equation are x = 1 and x = -8
Solution:
Given quadratic equation is:
[tex]x^2+7x = 8\\\\x^2 + 7x-8 = 0[/tex]
We have to find the solutions of equation
[tex]\mathrm{Quadratic\:Equation\:Formula:}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{Compare the given } x^2 + 7x - 8 = 0 \text{ with } ax^2 + bx + c = 0\\\\We\ get\\\\a = 1\\\\b = 7\\\\c = -8[/tex]
[tex]x=\frac{-7\pm \sqrt{7^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}\\\\x =\frac{-7 \pm \sqrt{7^2+4\cdot \:1\cdot \:8}}{2\cdot \:1}\\\\x = \frac{-7 \pm \sqrt{49 + 32}}{2}\\\\Simplify\ the\ equation\\\\x = \frac{-7 \pm \sqrt{81}}{2}\\\\x = \frac{-7 \pm 9}{2}[/tex]
Thus we get two solutions:
[tex]x = \frac{-7+9}{2} \text{ and } x = \frac{-7-9}{2}\\\\x = 1 \text{ and } x = -8[/tex]
Thus the solutions to quadratic equation are x = 1 and x = -8
3y + 6 divided by 2x
Answer:
3 (x^2 +1)/x
Step-by-step explanation:
To simplify the expression 3y + 6 divided by 2x, divide each term by 2x separately.
Explanation:The expression 3y + 6 divided by 2x can be simplified by dividing each term by 2x.
This can be done by dividing 3y by 2x and dividing 6 by 2x separately.
Simplifying further, the expression becomes:
(3y + 6)/2x
This is the simplified form of the given expression.
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Rabbits are released into the woods where there are no other rabbits of this species. The function f(t) can be used to model the population of this new species after t years. Below are four forms of the function that model this situation. Which form most clearly shows the monthly population growth?
Answer:
f(t)=15(1.0245)^12t
Step-by-step explanation:
It should be the first answer. Hope this helps:)
Final answer:
When modeling population growth, understanding functions like the logistic map and the Holling Type II functional response is crucial for accurate predictions of species dynamics.
Explanation:
Logistic Population Growth:
When modeling population growth with the logistic map, the most clear representation of monthly population growth is when the function includes a term that represents the rate of growth in relation to the existing population size. This is often seen as a term where the population in the next generation is a function of the population in the current generation multiplied by a constant, representing the fecundity of the species.
Holling Type II Functional Response:
In ecological situations, a commonly used model for predation is the Holling Type II functional response, where the rate of predation is described by a density-dependent function. This function accounts for increasing predation with higher prey density up to a saturation point, reflecting a more realistic portrayal of predator-prey dynamics.
Equilibrium and Growth Dynamics:
Equilibrium in population growth models can be explored using deterministic equations to find expectations, such as exponential growth when the birth rate exceeds the death rate. Understanding growth dynamics entails considering factors like carrying capacity, fecundity, and density-dependent functions to model population behaviors accurately.
Sallys basketball team played 6 games . They scored 76 points in the first game , 88 points in each of the next two games , and 92 points in each of the following two games . The team scored 515 points altogether . Write an expression and calculate the number of points they scored in the last game .
The expression is 436 + x = 515
The number of points they scored in the last game is 79
Step-by-step explanation:
Sally's basketball team played 6 games
They scored 76 points in the first game88 points in each of the next two games92 points in each of the following two gamesThe team scored 515 points altogetherWe need to write an expression and calculate the number of points they scored in the last game
Assume that the score of the last game is x
∵ Sally's basketball team played 6 games
∵ The score of the first game is 76 points
∵ The score of the next two games is 88 points each
∴ The score of the 2nd game is 88 points and the score
of the 3rd game is 88 points
∵ The score of each following two games is 92 points
∴ The score of the 4th game is 92 points and the score
of the 5th game is 92 points
∵ The score of the 6th game is x points
- Add all of them to find the total score of the 6 games
∴ The total score = 76 + 88 + 88 + 92 + 92 + x
- Add the like terms
∴ The total score = 436 + x
∵ The team scored 515 points altogether
- Equate the expression of the total by 515
∴ 436 + x = 515
- To find the value of x subtract 436 from both sides
∴ x = 79
∴ The score of the last game is 79 points
The expression is 436 + x = 515
The number of points they scored in the last game is 79
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We formulate an expression to represent the overall score of Sally's basketball team and solve for the final game's score. The outcome of the expression found that Sally's team scored 79 points in the last game.
Explanation:The subject of this question is regarding basketball scoring, which falls under the subject of mathematics, specifically algebraic expressions. The first step in finding out how many points were scored in the last game by Sally's basketball team is to write an expression that represents the total points scored in all games. This could be done as follows:
76 (first game score) + 88*2 (second and third game score) + 92*2 (fourth and fifth game score) + X (sixth game score) = 515 (total score)
To resolve this expression, you first do the multiplications and then the additions. This results in the partial sum of 436 points for the first five games.
Next, subtract this partial sum from the total score (515-436), the outcome is 79.
Therefore, Sally's basketball team must have scored 79 points in the last game.
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can somebody please let me know what the formula would be flipped?
Step-by-step explanation:
The flipped formula would be:
[tex]C = \frac{5}{9} (F - 32) \\ [/tex]
A spinner with 8 equal sections was spun 140 times. What is a reasonable prediction for the number of times the spinner will land on an even number? Show every step of your work
Answer:
If the spinner is spun 140 times then a reasonable prediction for the number of times the spinner will land on an even number = 0.5 [tex]\times[/tex] 140 = 70 times.
Step-by-step explanation:
The sections in the spinner are marked 1, 2, 3, 4, 5, 6, 7, 8
The even sections are 2, 4, 6, 8
There are 4 even sections and 4 odd sections among a total of eight sections.
Therefore the probability of the spinner landing on an even section is 1 / 2 or 0.5.
If the spinner is spun 140 times then a reasonable prediction for the number of times the spinner will land on an even number = 0.5 [tex]\times[/tex] 140 = 70 times.
1. Which figure has a circumference of
31.4 centimeters?
Figure A Figure C
Figure B. Figure D
Answer:
Figure B
Step-by-step explanation:
Circumference of a circle is simply the length of the boundary of the circle which can be measured by the formula of [tex]2\pi r[/tex]
In the figure B the given radius in the figure is 5
Putting 5 in the formula to find the circumference of the circle gives
[tex]2\pi *r[/tex]
= [tex]2*3.14*5[/tex] : [tex]\pi =22/7=3.14[/tex]
Circumference of the circle in fig B = 31.4 cm
So, Circle in the figure B will have the circumference of 31.4 cm. Also the Circumference of the fig A, C and D are different and are not equal to 31.4 cm
If n=3 then what is (4n-2) (7-2)
The value of equation when n = 3 is 50
Solution:
Given equation is:
[tex](4n -2)(7-2)[/tex]
We have to find the value of equation when n = 3
By plugging in n = 3 in given equation we can find the value of given equation
Substitute n = 3 in given equation
[tex]\rightarrow (4(3) -2)(7-2)\\\\Solve\ the\ above\ equation\\\\\rightarrow (12-2)(7-2)\\\\\rightarrow (12 - 2)(5)\\\\Simplify\ the\ above\ equation\\\\\rightarrow 10 \times 5 = 50[/tex]
Thus the value of equation when n = 3 is 50
simplify the expression 2a + 5b² - a - b - 3b²
Answer:
a+2b²-b (correct order is 2b²+a-b)
Step-by-step explanation:
combine like terms ( terms with the same variable and are to the same power) so thats 5b² and -3b² and 2a and -a. the -b doesnt have any like terms so leave that alone for now. combine like terms 5b²-3b² is 2b² and 2a-a is a. so you have 2b²+a and plug in the -b so you get 2b²+a-b.
Answer:
a-b+2b^2
Step-by-step explanation:
collect like terms
2a-a-b+5b^2-3b^2
a-b+2b^2
Loc weighs 14 pounds. The HCP prescribes an IV infusion of 5% dextrose in 1/4 normal saline to be infused at 8mL/kg/hr. How many mL of the prescribed solution should the nurse infuse each hour?
After converting the patient's weight from pounds to kilograms, it is multiplied by the prescribed infusion rate to calculate that approximately 50.88 mL of the IV solution should be infused each hour.
The question involves calculating the volume of IV fluid to infuse per hour based on the weight of the patient and an ordered flow rate. Given that Loc weighs 14 pounds, we need to convert his weight to kilograms to match the units given in the infusion rate (8mL/kg/hr). There are 2.2 pounds in one kilogram.
To find Loc's weight in kilograms, we divide his weight in pounds by 2.2:
Weight in kilograms =Weight in pounds / 2.2 = 14 pounds / 2.2 = 6.36 kilograms (rounded to two decimal places)
Next, we multiply Loc's weight in kilograms by the prescribed infusion rate to determine the flow rate:
Infusion volume per hour =
Weight in kilograms × Infusion rate = 6.36 kg × 8 mL/kg/hr = 50.88 mL/hr (rounded to two decimal places)
Therefore, the nurse should infuse approximately 50.88 mL of the prescribed solution each hour.
what is 2.99 times 0.150 ?
Answer:
0.4485
Step-by-step explanation:
2.99 times 0.150 = 0.4485
robin wants to find the area of the triangle below. to find the area of a triangle, multiple the base times the height and then divide by 2. the base and height of the triangle are shown. represent the area of the triangle with numerical expression.
Answer:
6
Step-by-step explanation:
Base = 4 in
Height = 3 in
Area= 1/2 Base * Height
Area = 1/2 * 4 * 3
Area = 1/2 * 12
Area = 6
8 inch by 6 inch retangular photo inside a 10 inch by 8 inch rectangular fram how much greater is the perimeter of the frame
The perimeter of frame is 1.29 greater
Step-by-step explanation:
Perimeter of a rectangular shape object is given by the formula;
2(l+w) when, l is length and w is width
Perimeter of the photo is;
2(8+6)= 2(14) =28 inches
Perimeter of the frame is;
2(10+8)= 2(18) =36 inches
Divide perimeter of frame by that of photo as;
36/28 =1.29
The perimeter of frame is 1.29 greater
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How to write a decimal
write a number and then put a point after it and then add more numbers after
Answer:
you can put a point basically a period after a number for instance 10.7 is a decimal or 0.66
Step-by-step explanation:
1/4 is = to 0.25 in decimal form
The drink dispenser in a fast food restaurant holds 250 liters
Question:
A drink dispenser in a fast-food restaurant holds 250 litres of lemonade. How many 0.6-litre drinks can be dispensed before a refill is needed?
Answer:
The number 0.6-litre drinks can be dispensed before a refill is needed is 416
Step-by-step explanation:
Given:
The capacity of the drink dispenser = 250 litres
To Find:
Number of 0.6-litre drinks can be dispensed before a refill is needed = ?
Solution
Let the number of 0.6-litre drinks can be dispensed before a refill is needed be x
Then
[tex]x = \frac{ \text{total capacity of the dispenser}}{\text{0.6-litre drinks}}[/tex]
On substituting the values we get
[tex]x = \frac{250}{0.6}[/tex]
x = 416. 667
Thus only 416 can be filled
Write a four digit number that is divisible by 3 and 5
Answer:
There are many numbers like 1005, 3000, and 2700.
Step-by-step explanation:
The divisibility rule for 3 is the sum of the numbers is divisible by 3. example is 111. well 1+1+1 is 3 so its divisible by three.
The divisibility rule for 5 is any number that ends in 5 or 0.
If you have any questions feel free to ask in the comments - Mark
PLS HELP WILL GIVE 10 PTS + BRAINLIEST THX SO MUCH
There are (4^3)^2 ⋅ 4^0 strawberries on a farm. What is the total number of strawberries on the farm?
a. 4^6
b. 4^8
c. 4^9
d. 4^16
TY! :D
Answer:4^9
Step-by-step explanation:
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for
full credit.
Total score:
of 15 points
(Score for Question 1: __of 4 points)
1. To go bowling, it costs $2.00 to rent shoes and $3.50 per game. The function t(x) = 3.5x + 2 is used to find the
total cost, 1, for x amount of games. Find the following and show all work:
(a) What is the charge to play 1 game?
(b) What is the charge to play 5 games?
Please help
Answer:
A). $5.50
B).19.50
Step-by-step explanation:
A). 3.5(1)+2=5.50
B). 3.5(5)+2=19.50
All you are are doing is inputing the number of games played (x) in for x in the function/equation.
Let f(x) = (x^2+3x-5)/(x^2-8x+15) What is the domain of f(x) ?
Answer:
So, Domain = {set of all the real numbers except 3, 5}
Interval notation = {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}
Step-by-step explanation:
The given function is f(x) = [tex]\frac{x^2 + 3x - 5}{x^2 - 8x + 15}[/tex]
Here we need to find the domain.
To find the domain, let's find the restricted domain.
If we set the denominator equal to zero and solve for x, we can find the restricted domain.
Here the denominator is [tex]x^2 -8x + 15 = 0[/tex]
Now we can factorize and solve for x.
(x - 3)(x - 5) = 0
(x - 3) or (x - 5) = 0
x -3 = 0 and x - 5 = 0
Solving the above equations, we get
x = 3 and x = 5
The restricted domains are x = 3 and x = 5.
Now we can find the domain.
Except 3 and 5, all the real numbers can be domain of this function.
So, Domain = {set of all the real numbers except 3, 5}
= {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}.
Answer: all real numbers except 3, 5
Step-by-step explanation:
What are the answers for a,b,c
Answer:
a=51
b=48
c=70
Step-by-step explanation:
C=180-110=70
a=180-110-19=51
b=180-70-62=48
In the diagram below lines H A and B C are parallel. If angle GEC = 135 degrees, what is angle angle HDF?
Answer:
The angle is 45
Step-by-step explanation:
I did this lol.
Does the example showing 1/2 × 2/5 support a similar rule when multiplying a fraction by a fraction less than 1
Final answer:
The multiplication of fractions, such as 1/2 × 2/5, follows the principle of multiplying the numerators and denominators to get the product. This supports the rule that the product of any two fractions is the quotient of the products of their numerators and denominators, which also holds true for fractions less than 1.
Explanation:
The multiplication of fractions, regardless of whether the fractions are less than 1 or not, follows the same basic principles. When multiplying two fractions, you multiply the numerators together and the denominators together. For example, when you multiply 1/2 by 2/5, you multiply the numerators (1 and 2) to get 2, and the denominators (2 and 5) to get 10. The result is 2/10, which simplifies to 1/5. This process supports the general rule of fractional multiplication.
Similarly, when dealing with a fraction such as 1/2 and a fraction less than 1, the product will be less than the original fraction (1/2 in this case). This is because you are multiplying by a number that is less than the whole. For instance, if you multiply 1/2 by 1/3, you get 1/6, which is indeed less than 1/2.
In the context of fractional exponents, the exponent represents the root of the number. So, an exponent of 1/2 would mean the square root.
How do simplify 4(x-3)+5(x-3)
Answer:
9x-27
Step-by-step explanation:
4(x-3)+5(x-3)=4x-12+5x-15=4x+5x-12-15=9x-27
log3 (7x - 1) = log2 (5x +17)
SOLVE.
Answer:
x=1.113317
Step-by-step explanation:
How do you write 40.545 in word form
The requried word form of the given number is forty and five hundred forty-five thousandth.
What is a number system?A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
Since the given number is of decimal form.
A word form of the given number 40.545 is given as,
40.545 = forty and five hundred forty-five thousandth.
Thus, the requried word form of the given number is forty and five hundred forty-five thousandth.
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What is -5/6 time -6/5
Answer:
1
Step-by-step explanation:
you are just multiplying by the reciprocal here which would make this equal to 1
What is (2x + 3y)^4?
Answer:
the answer is 8x+12y
Step-by-step explanation:
A bag contains 2 red, 5 blue, and 3 green balls. A ball is chosen at random. What is the probability of not choosing a red ball?
Answer:
Step-by-step explanation:
1. What is the fourth term of the
sequence 4, 8, 12, 16, 20, 24,
Answer:
16
Step-by-step explanation:
bruh, it's right there
Answer:
16
Step-by-step explanation:
it's the fourth number in the pattern
Kathy is paid a project fee of $70 plus $40 per hour. she wants to buy a new iPad and need $710. write an equation to represent how many hours(h) kathy needs to work to have the exact amount for the iPad
Answer:
70+40h=710
Step-by-step explanation:
Fill in the blank.
5.5 lbs. =___ oz.
Answer: 80 ounces
Step-by-step explanation: lbs is the abbreviation for pounds and oz is the abbreviation for ounces.
To convert 5.5 pounds into ounces, first find the conversion factor for pounds and ounces which is shown below.
16 ounces = 1 pound
Next, notice that we're going from a larger unit, pounds, to a smaller unit, ounces. When we go from a larger unit to a smaller unit we multiply.
So here, we multiply 5.5 pounds times the conversion factor, 16 to get 88 ounces. This means that 5.5 pounds is equal to 88 ounces.
5.5 lbs is equal to 88 oz because 1 pound is equal to 16 ounces.
To convert pounds (lbs) to ounces (oz), you need to know that 1 pound is equal to 16 ounces.
1 pound=16 ounces.
Now we have to find out how many ounces are in 5.5 pounds.
To find this we have to multiply 5.5 by 16.
5.5 lbs×16 oz/lb
= 88 oz
Therefore, 5.5 lbs is equal to 88 oz.
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