The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?
Answers
Work Shown:
f(x) = 50(0.952)^x
f(9) = 50(0.952)^9
f(9) = 32.1146016801717
f(9) = 32 approximately
Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.
Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.
Answer:
32
Step-by-step explanation:
The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...
about 32 feral cats
_____
You can evaluate f(9) to choose the same answer:
f(9) = 50(0.952^9) ≈ 32.114 ≈ 32
Related Questions
88 feet/second = 60 miles/hour. How many feet per second is 1 mile? (Hint: divide both side of the equation by the same amount.)
Answers
Answer:
1 mile/hour is equivalent to 1.47 feet/seconds
Step-by-step explanation:
Given
[tex]88 ft/s= 60 miles/hr[/tex]
Required
Determine the equivalent of 1 mile/hour
[tex]88\ ft/s= 60\ miles/hr[/tex]
Express 60 as 60 * 1
[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]
Divide both sides by 60
[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]
[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]
Reorder
[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]
Divide 88 by 60
[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]
Approximate to 3 significant figures
[tex]1\ mile/hr = 1.47\ ft/s[/tex]
Hence;
1 mile/hour is equivalent to 1.47 feet/seconds
The office building is 111ft high. About how tall is this in meters.?
Answers
Answer:
Hey there!
11 meters is about 36 feet tall.
Let me know if this helps :)
Answer:
you answer is :33.8328
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
Answers
Answer:
is it 2
Step-by-step explanation:
Can someone please help me with these 7 questions please?
Answers
The solution to each of the question takes different approach, as the questions are taken from different concepts; however, a common operation among all questions, is factorization.
[tex](1)\ (-xy)^3(xz)[/tex]
Expand
[tex](-xy)^3(xz) = (-x)^3* y^3*(xz)[/tex]
[tex](-xy)^3(xz) = -x^3* y^3*xz[/tex]
Rewrite as:
[tex](-xy)^3(xz) = -x^3*x* y^3*z[/tex]
Apply law of indices
[tex](-xy)^3(xz) = -x^4y^3z[/tex]
[tex](2)\ (\frac{1}{3}mn^{-4})^2[/tex]
Expand
[tex](\frac{1}{3}mn^{-4})^2 =(\frac{1}{3})^2m^2n^{-4*2}[/tex]
[tex](\frac{1}{3}mn^{-4})^2 =\frac{1}{9}m^2n^{-8[/tex]
[tex](3)\ (\frac{1}{5x^4})^{-2}[/tex]
Apply negative power rule of indices
[tex](\frac{1}{5x^4})^{-2}= (5x^4)^2[/tex]
Expand
[tex](\frac{1}{5x^4})^{-2}= 5^2x^{4*2}[/tex]
[tex](\frac{1}{5x^4})^{-2}= 25x^{8[/tex]
[tex](4)\ -x(2x^2 - 4x) - 6x^2[/tex]
Expand
[tex]-x(2x^2 - 4x) - 6x^2 = -2x^3 + 4x^2 - 6x^2[/tex]
Evaluate like terms
[tex]-x(2x^2 - 4x) - 6x^2 = -2x^3 -2x^2[/tex]
Factor out x^2
[tex]-x(2x^2 - 4x) - 6x^2 = (-2x-2)x^2[/tex]
Factor out -2
[tex]-x(2x^2 - 4x) - 6x^2 = -2(x+1)x^2[/tex]
[tex](5)\ \sqrt{\frac{4y}{3y^2}}[/tex]
Divide by y
[tex]\sqrt{\frac{4y}{3y^2}} = \sqrt{\frac{4}{3y}}[/tex]
Split
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{\sqrt{4}}{\sqrt{3y}}[/tex]
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}}[/tex]
Rationalize
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}} * \frac{\sqrt{3y}}{\sqrt{3y}}[/tex]
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2\sqrt{3y}}{3y}[/tex]
[tex](6)\ \frac{8}{3 + \sqrt 3}[/tex]
Rationalize
[tex]\frac{8}{3 + \sqrt 3} = \frac{3 - \sqrt 3}{3 - \sqrt 3}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{(3 + \sqrt 3)(3 - \sqrt 3)}[/tex]
Apply difference of two squares to the denominator
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{3^2 - (\sqrt 3)^2}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{9 - 3}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{6}[/tex]
Simplify
[tex]\frac{8}{3 + \sqrt 3} = \frac{4(3 - \sqrt 3)}{3}[/tex]
[tex](7)\ \sqrt{40} - \sqrt{10} + \sqrt{90}[/tex]
Expand
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4*10} - \sqrt{10} + \sqrt{9*10}[/tex]
Split
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4}*\sqrt{10} - \sqrt{10} + \sqrt{9}*\sqrt{10}[/tex]
Evaluate all roots
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =2*\sqrt{10} - \sqrt{10} + 3*\sqrt{10}[/tex]
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =2\sqrt{10} - \sqrt{10} + 3\sqrt{10}[/tex]
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =4\sqrt{10}[/tex]
[tex](8)\ \frac{r^2 + r - 6}{r^2 + 4r -12}[/tex]
Expand
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r^2 + 3r-2r - 6}{r^2 + 6r-2r -12}[/tex]
Factorize each
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r(r + 3)-2(r + 3)}{r(r + 6)-2(r +6)}[/tex]
Factor out (r+3) in the numerator and (r + 6) in the denominator
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{(r -2)(r + 3)}{(r - 2)(r +6)}[/tex]
Cancel out r - 2
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r + 3}{r +6}[/tex]
[tex](9)\ \frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14}[/tex]
Cancel out x
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 5x - 14}[/tex]
Expand the numerator of the 2nd fraction
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 7x+2x - 14}[/tex]
Factorize
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x(x - 7)+2(x - 7)}[/tex]
Factor out x - 7
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{(x + 2)(x - 7)}[/tex]
Factor out 4 from 4x + 8
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4(x + 2)}{x} \cdot \frac{1}{(x + 2)(x - 7)}[/tex]
Cancel out x + 2
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x} \cdot \frac{1}{(x - 7)}[/tex]
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x(x - 7)}[/tex]
[tex](10)\ (3x^3 + 15x^2 -21x) \div 3x[/tex]
Factorize
[tex](3x^3 + 15x^2 -21x) \div 3x = 3x(x^2 + 5x -7) \div 3x[/tex]
Cancel out 3x
[tex](3x^3 + 15x^2 -21x) \div 3x = x^2 + 5x -7[/tex]
[tex](11)\ \frac{m}{6m + 6} - \frac{1}{m+1}[/tex]
Take LCM
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m(m + 1) - 1(6m + 6)}{(6m + 6)(m + 1)}[/tex]
Expand
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 + m- 6m - 6}{(6m + 6)(m + 1)}[/tex]
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 - 5m - 6}{(6m + 6)(m + 1)}[/tex]
[tex](12)\ \frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}}[/tex]
Rewrite as:
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} \div \frac{2}{y^2 - 9}[/tex]
Express as multiplication
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 9}{2}[/tex]
Express y^2 - 9 as y^2 - 3^2
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 3^2}{2}[/tex]
Express as difference of two squares
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{(y - 3)(y+3)}{2}[/tex]
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{1} * \frac{(y+3)}{2}[/tex]
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{y+3}{2}[/tex]
Read more at:
https://brainly.com/question/4372544
In the function f(x) = 4(x2 − 6x + ____) + 20, what number belongs in the blank to complete the square?
Answers
Answer:
9
Step-by-step explanation:
6x=2*x*(a number), (a number)^2=the number we need. A number=3, the number is 3^2=9
The ratio of boys and girls in the class is 4:3. How many boys and girls are in the class if there are 35 students?
Answers
Explanation:
Boy = 35 x 4/7 = 20
Girl = 35 x 3/7 = 15
Answer:
20boys and 15girls
Step-by-step explanation:
Let no of boys be 4x
no of girls be 3x
4x+3x=35
7x=35
x=35/7
x=5
no of boys=4×5=20
no of girls=3×5=15
20+15=35 students
Find the coordinates of U' after a reflection across parallel lines; first across the line x=-2 and then across the line x=-1 write your answer in form (a,b)
Answers
Answer:
U in the line x=-2: (-4,0)
U in the line x=-1: (-2-0)
Step-by-step explanation:
...............
Assignment: Counting Investigation Dakota and Karen noticed that there were a bunch of combinations available in their school cafeteria. Think about a meal at your school, or maybe a favorite restaurant. How many combinations of choices do you have? Create a tree diagram listing the possible combinations, and count the results. 1. For what will you find the number of combinations? ______________________________________________________________________________________________________________________ 2. List at least three categories to consider. ______________________________________________________________________________________________________________________ 3. List the choices within each category. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4. Assign each choice a symbol. Ex. juice = (diamond shape) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 5. Create a tree diagram to determine the number of combinations available. 6. List all possible combinations and count the total number of possibilities. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Answers
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------------
Q1: (For what)"Will you find the number of combinations?"
Answer: (I unfortunately don't understand this very well so I'm giving it my best, and take this with a grain of salt.) I will be able to find combinations using a school cafeteria!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Q2: "List at least three categories to consider."
My choices:
Answer: Fruits, Vegetables, Protein.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Q3: "List the choices within each category."
Answer:
Fruits: Apples, Bananas, and Grapes.
Vegetables: Cauliflower, Carrot, and Corn.
Protein: Green beans, Salmon, and Almonds.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Q4: "Assign each choice a symbol. Ex. juice = (diamond shape)"
Answer:
Fruits: Apples, Bananas, and Grapes.
Vegetables: Cauliflower✨, Carrot, and Corn.
Protein: Green beans, Salmon, and Almonds.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Q5: "Create a tree diagram to determine the number of combinations available."
(I'm not very familiar with a tree diagram so here is my interpretation at the bottom.)
(You can rewrite this and do it your way if you want).
Q6: "List all possible combinations and count the total number of possibilities."
There are 27 combinations possible!
All of my possible combinations:
Apples, Cauliflower, Green beans.Apples, Cauliflower, SalmonApples, Cauliflower, Almonds.Bananas, Cauliflower, Green Beans.Bananas, Cauliflower, Salmon.Bananas, Cauliflower, Almonds.Grapes, Cauliflower, Green bean.Grapes, Cauliflower, Salmon.Grapes, Cauliflower, Almonds.Apples, Carrot, Green beans.Apples, Carrot, Salmon.Apples, Carrot, Almonds.Bananas, Carrot, Green beans.Bananas, Carrot, Salmon.Bananas, Carrot, Almonds.Grapes, Carrot, Green beans.Grapes, Carrot, Salmon.Grapes, Carrot, Almonds.Apples, Corn, Green beans.Apples, Corn, Salmon.Apples, Corn, Almonds.Bananas, Corn, Green beans,Bananas, Corn, Salmon.Bananas, Corn, Almonds.Grapes, Corn, Green Beans.Grapes, Corn, Salmon.Grapes, Corn, Almonds.The last image below is for Qestion 5.
cuantos son 4 elevado a 4???
Answers
Answer:Answer and Explanation:
When a number is said to be 'to the fourth power,' that just means that you need to multiply the number by itself four times. For example, 7 to the...
Step-by-step explanation:
Which pairs of polygons are congruent?
Answers
Answer:
pair3
Step-by-step explanation:
it is when they have same number of sides .
Answer:
1 and 3.
Step-by-step explanation:
Pair 1 and pair 3.
If we reposition one of them we see that it exactly fits onto the other.
What is the equation for the line of symmetry in this figure?
Answers
Answer:
x = -1
Step-by-step explanation:
the line of the simetry is x = -1
Answer:
Its x = -1 because it splits the diamond shape perfectly at x -1
Step-by-step explanation:
look at picture and solve
Answers
Answer:
79°
Step-by-step explanation:
PQO is straight angle with measure of 180°
the given angles' sum makes 101° and we need 79 to complete it to 180° therefore the angle STQ = 79°
Find the missing angle. Round your answer to the nearest tenth. PLS HURRY.
Answers
Answer:
x = 24.4°
Hope this helps... Have a good day!!
A number if that number and the number b sum to 40.
Answers
Answer:
40-b
Step-by-step explanation:
x is the unknown number
x+b = 40
We want to find x
Subtract b from each side
x+b-b = 40 -b
x = 40-b
The unknown number is 40-b
Answer:
[tex]\huge \boxed{40-b}[/tex]
Step-by-step explanation:
[tex]\sf Let \ x \ be \ that \ number.[/tex]
[tex]x+b=40[/tex]
[tex]\sf Solve \ for \ x.[/tex]
[tex]\sf Subtract \ b \ from \ both \ sides.[/tex]
[tex]x+b-b=40-b[/tex]
[tex]\sf Simplify \ the \ equation.[/tex]
[tex]x=40-b[/tex]
Question 5 10 pts Which function represents the inverse of f(x) = (x + 6)2 - 5? of 1(1) = V1 + 5 - 6 of '(x) = (x + 5)2 - 6 of '(x) = V1 – 6 + 5 Of '(x) = (x + 6 – 5
Answers
Answer:
f(x)^-1(x) =sqrt(x+5) -6
Step-by-step explanation:
f(x) = (x + 6)^2 - 5
y = (x + 6)^2 - 5
Exchange x and y and solve for y
x = (y + 6)^2 - 5
Add 5 to each side
x+5 = (y + 6)^2 - 5+5
x+5 = (y + 6)^2
Take the square root of each side
sqrt(x+5 )= sqrt( (y + 6)^2 )
sqrt(x+5 )=(y + 6)
Subtract 6 from each side
sqrt(x+5 ) -6=y + 6-6
sqrt(x+5) -6 = y
square root of 3x^4 times square root of 5x^2 times square root of 10.
Multiply and remove all perfect squares from inside the square roots. Assume x is positive.
Answers
Answer:
[tex]5x^3\sqrt{6}[/tex]
Step-by-step explanation:
We need to simplify
[tex]\sqrt{3x^4}\times\sqrt{5x^2}\times\sqrt{10}[/tex]
Right away we can take out the perfect squares. Remember a perfect square is the result of multiplying any value by itself.
[tex]= x^2\sqrt{3}\times x\sqrt{5}\times\sqrt{10} \\= x^3\sqrt{3\times 5 \times 10}\\= x^3\sqrt{3 \times 5 \times 5 \times 2 }\\= 5x^3\sqrt{6}[/tex]
The square root of 3x⁴ times square root of 5x² times square root of 10, the product of all the term is, 5x³ [tex]\sqrt{6}[/tex]
What is square root?In mathematics, square roots is a concept in which, if we multiply square roots of any number by itself then it will give us an original number.
if 'a' is square root of 'b' then it will represent as, a = √b.
Given that,
three terms,
[tex]\sqrt3{x^{4} }[/tex]
[tex]\sqrt{5x^{2} }[/tex]
[tex]\sqrt{10}[/tex]
by multiplying all the three terms,
⇒ [tex]\sqrt3{x^{4} }[/tex] × [tex]\sqrt{5x^{2} }[/tex] × [tex]\sqrt10} }[/tex]
⇒ √(3x⁴×5x²10)
⇒ √ 150x⁶
⇒ 5x³ [tex]\sqrt{6}[/tex]
Hence, the product is 5x³ [tex]\sqrt{6}[/tex]
To know more about square root check:
https://brainly.com/question/29286039
#SPJ2
Katie brought 5/6 pounds of candy to a slumber party tori brought 1/3 pound of candy how much candy did the girls have altogether
Answers
Answer:
1 [tex]\frac{1}{6}[/tex] pounds of candy
Step-by-step explanation:
Add together the fractions by creating a common denominator of 6:
[tex]\frac{5}{6} + \frac{1}{3}[/tex]
[tex]\frac{5}{6} + \frac{2}{6}[/tex]
= [tex]\frac{7}{6}[/tex]
Simplify into a mixed fraction:
= 1 [tex]\frac{1}{6}[/tex]
So, the girls had 1 [tex]\frac{1}{6}[/tex] pounds of candy
Use the distributive property to clear parentheses
Answers
Answer:
18z + 24
Step-by-step explanation:
The distributive property is the multiplication of the number outside the parenthesis with the numbers inside.
All you need to do to solve this is to multiply 6 with 3z, and 6 with 4.
6 × 3 = 18 =
18z
6 × 4 = 24
Put them together:
18z + 24
Another way to do this:
how do I do this and what is the answer?
Answers
Answer:
4
plug in -1 for all the x's
3 + 2 + 7 = 12 (remeber that -1 *-1 = + 1 and that -2*-1 = + 2
-2+ 5 = + 3
12/3 = 4
Step-by-step explanation:
Find the formula for the 4th of the following A.P.S a)3,7,11........ b)12,7,2.......
Answers
Answer:
A = 15
B = -3
Step-by-step explanation:
3 ,7,11..... You add 4 each time so 11+4 is 15
12,7,2.... You take 5 each time so 2-5 is -3
Vertices name in triangle A B C
Answers
Answer:
The answer is B.
I think I answered the wrong answer.
6 times a number increased by 11 is equal to 17. What is the number?
Answers
Let the no be x
ATQ
[tex]\\ \sf\longmapsto 6x+11=17[/tex]
[tex]\\ \sf\longmapsto 6x=17-11[/tex]
[tex]\\ \sf\longmapsto 6x=6[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{6}{6}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Answer:
1
Step-by-step explanation:
let the number be x
and solve it
I need help ASAP!!! Please explain how to solve the answer.
Answers
Answer:
Does the answer help you?
Please choose my answer as a brainliest answer and please rate.
It take a few minutes to solve your question.
3. Solve 2log4y - log4 (5y - 12) = 1/2
Answers
Answer:
y = 4 or y = 6
Step-by-step explanation:
2log4y - log4 (5y - 12) = 1/2
2log_4(y) - log_4(5y-12) = log_4(2) apply law of logarithms
log_4(y^2) + log_4(1/(5y-12)) = log_4(/2) apply law of logarithms
log_4(y^2/(5y-12)) = log_4(2) remove logarithm
y^2/(5y-12) = 2 cross multiply
y^2 = 10y-24 rearrange and factor
y^2 - 10y + 24 = 0
(y-4)(y-6) = 0
y= 4 or y=6
Find the product of all real values of $r$ for which $\frac{1}{2x}=\frac{r-x}{7}$ has exactly one real solution.
Answers
Answer:
-14
Step-by-step explanation:
Observe first that $x=0$ is not a solution to the equation since it makes the denominator of $\frac{1}{2x}$ equal to 0. For $x\neq 0$, we may multiply both sides by both denominators and move all the resulting terms to the left-hand side to get $2x^2-2rx+7=0$. Observe that there are two ways the original equation could have exactly one solution. Either $2x^2-2rx+7=0$ has two solutions and one of them is 0, or else $2x^2-2rx+7=0$ has exactly one nonzero solution. By trying $x=0$, we rule out the first possibility.
Considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the solutions of $ax^2+bx+c=0$, we find that there is exactly one solution if and only if the discriminant $b^2-4ac$ is zero. Setting $(-2r)^2-4(2)(7)$ equal to 0 gives $4r^2-4(14) = 0$. Add 4(14) and divide by 4 to find $r^2=14$. The two solutions of this equation are $\sqrt{14}$ and $-\sqrt{14}$, and their product is $\boxed{-14}$.
The value of r from the given equation is r=(2x²+7)/2x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is [tex]\frac{1}{2x}=\frac{r-x}{7}[/tex].
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
By cross multiplication, we get
7=2x(r-x)
7=2rx-2x²
2rx=7+2x²
r=(2x²+7)/2x
Therefore, the value of r from the given equation is r=(2x²+7)/2x.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
1. Solve the equation: - 2x + 8 = 3x + 14
Answers
-2x + 8 = 3x + 14
-2x - 3x = 14 - 8
-5x = 6 / : (-5)
x = -1,2
Answer: x = -6/5
Step-by-step explanation:
Given equation
-2x + 8 = 3x + 14
Subtract 3x on both sides
-2x + 8 - 3x = 3x + 14 - 3x
-5x + 8 = 14
Subtract 8 on both sides
-5x + 8 - 8 = 14 - 8
-5x = 6
Divide -5 on both sides
-5x / -5 = 6 / -5
[tex]\boxed{x = -\frac{6}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Plug in the values from the set {12, 15, 18, 19} to find the value of x. The value that holds true for the equation is . So, Jenny is years old and her mother is years old.
Answers
Answer:
Jenny´s age is 19 and her mother is 43.
Step-by-step explanation:
Given that
x + 2x + 5 = 62
where,
x = Jenny’s age
Now the following cases occured
a.
x = 12
Now put the x value to the above equation
12 + 2(12) + 5 = 62
12 + 24 + 5 = 62
41 = 62
It is not equaled so the Jenny age is not 12
b.
x = 15
Now put the x value to the above equation
12 + 2(15) + 5 = 62
15 + 30 + 5 = 62
50 = 62
It is not equaled so the Jenny age is not 15
c.
x = 18
Now put the x value to the above equation
18 + 2(18) + 5 = 62
18 + 36 + 5 = 62
59 = 62
It is not equaled so the Jenny age is not 12
d.
x = 19
Now put the x value to the above equation
19 + 2(19) + 5 = 62
19 + 38 + 5 = 62
62 = 62
It is equaled so the Jenny age is 19
Now the mother age is
as we know that
x + y = 62
19 + y = 62
y = 62 - 19
= 43
Also it proved that if we doubles the jenny age i.e 38 and then add 5 so the total is 43 i.e. equivalent to her mother age
Simplify the expression. (6x – 5) + (4x2 – 3x + 4)
Answers
[tex](6x - 5) + (4x^2- 3x + 4)=\\6x-5+4x^2-3x+4=\\4x^2+3x-1[/tex]
Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
Answers
Answer:
9 hours
11 hours
19 hours
Step-by-step explanation:
The graph represents the percentage of battery life remaining after a certain number of hours is attached below.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hours
Answer: From the graph, the line segment with negative slope (that is decreasing value) shows that the phone is not plugged but being used while the line segment with positive slope (increasing value) or stays at 100% shows that the phone is plugged to the charger.
As shown, from 0 to 8 hours their is a decreasing value, the phone is not plugged. From 8 to 10 hours their is an increasing value therefore the phone is plugged also from 10 to 12 hours the phone is plugged since it is constant. From 12 to 16 hours it is not plugged. From 16 to 18 hours it is plugged and from 18 to 20 hours it is plugged.
From the options it is plugged at 9 hours, 11 hours and 19 hours
Answer:
B - 9 HOURS
C - 11 HOURS
E - 19 BHOURS
Step-by-step explanation:
i took the test
Find the difference between8/15 and −2/3. Show all calculations in your final answer.
Answers
Answer:
6/5
Step-by-step explanation:
8/15 - (-2/3)
8/15 + 2/3
24 + 30/45
54/45 = 6/5
Thus, the difference between 8/15 and -2/3 is 6/5
Start by changing the minus a negative to plus a positive.
So we have 8/15 + 2/3.
To add these two fractions together, we need a common denominator.
The common denominator is simply the
least common multiple for the two denominators.
You should find that the least common multiple is 15.
Since 8/15 already has 15 as its denominator, leave it.
To get a denominator of 15 in 2/3, we multiply top
and bottom of 2/3 by 5 to get 10/15.
So we have 8/15 + 10/5.
This simplifies to 18/15.
Now reduce to get 6/5.