Evaluate the algebraic expression 3f + g,when f = 6, g = 8, h = 12 and j = 2. A. 30 B. 26 C. 17 D. 13
Answer: A.26
Step-by-step explanation:
= 3f+g
= 3 (6)+8
=26
negative 7 over 3, the whole multiplied by x minus 3 equals negative 52
Answer:
21
Step-by-step explanation:
4. Find the x-intercepts of the functions. (a) g(x)= 4x² +12x +9
Answer:
x = -3/2 or -1.5
Step-by-step explanation:
Factor function into (2x+3)(2x+3) Set 2x+3 equal to 0Solve 2x+3=02x=-3x = -3/2A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?
w2 = 3(243)
3w2 = 243
4w2 = 243
3w2 = 3(243)
Answer:
3w² = 243
Step-by-step explanation:
Width = w
Length = 3w
Area = 243 square units
length *width = 243
3w * w = 243
3w² = 243
The equation that you can used to determine the width of the rectangle with the given area is: 3w² = 243
What is the Area of a Rectangle?Area = (length)(width)
The given dimensions are:
Width = w unitsLength = 3w unitsArea of rectangle = 343 sq. unitsThe equation to se in finding the width (w) of the rectangle will be:
3w(w) = 243
3w² = 243
Learn more about area of a rectangle on:
https://brainly.com/question/25292087
#SPJ2
−3(3h−1)≤−7h−5
kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:
h<=4
Step-by-step explanation:
-9h+3<=-7h-5
-9h+7h<=-5-3
-2h<=-8
h<=4
Solve the following system of equations by substitution
2x – 3y = -1
y = x - 1
Answer:
(4, 3)
Step-by-step explanation:
Plug in x - 1 where y is. The equation will turn in 2x - 3(x - 1) = -1. Distribute, and you'll have 2x -3x + 3 = -1. Combine like terms (2x and -3x) and you'll have -x + 3 = -1. Subtract 3 from both sides, and you'll have -x = -4. Divide by -x (or -1) on both sides, and you'll have x = 4. Since y = x - 1, y = 3, since 4 - 1 = 3. Sorry if this sounds repetitive btw. Good luck :D
Another word one! Please help only if you know, thank you!
Answer:
Step-by-step explanation:
if C is the right angle,
AB is the hypotenuse
AB^2=AC^2+BC^2
AC^2=13^2-5^2
AC^2=169-25=144
AC=[tex]\sqrt{144}[/tex]=12
AC=12
How would you express the area of the rectangle using the Distributive Property?
Answer:
C. 3(x+5)
Step-by-step explanation:
hope this helps
Graph the inequality on the axes 2x-y>5
Answer: x>1/2y+5/2 look at the picture it going to be the graph
Step-by-step explanation: Hope this help :)
In the diagram below, AB = BD = BC, and mZA = 24°. Find
mZC.
Answer:
m∠C = 66°
Step-by-step explanation:
Since AB = BD, it means this triangle is an Isosceles triangle and as such;
∠BAD = ∠BDA = 24°
Thus, since sum of angles in a triangle is 180,then;
∠ABD = 180 - (24 + 24)
∠ABD = 180 - 48
∠ABD = 132°
We are told that BC = BD.
Thus, ∆BDC is an Isosceles triangle whereby ∠BCD = ∠BDC
Now, in triangles, we know that an exterior angle is equal to the sum of two opposite interior angles.
Thus;
132 = ∠BCD + ∠BDC
Since ∠BCD = ∠BDC, then
∠BCD = ∠BDC = 132/2
∠BCD = ∠BDC = 66°
PLZZZZ HELP ME WITH THIS QUESTION WITH AN EXPLANATION
Answer :
Given : A and B are complementary angles. B and C are complementary angles.
Prove : A C
I have attached a picture of me doing it. Hope this helps, thank you :) !!
5 nickles to 2 dollars
Answer:
1/8
Step-by-step explanation:
plz brainliest
I need help with these questions (see image). Please show workings.
Answer:
Inscribed angle is half of the intercepted arc.Central angle is the same size as the intercepted arc.As per above two statements we have:
y = 2*58° = 116°and
z = 90°/2 = 45°Answer:
y=58×2=116 central angle of the cyclic quadrilateral is double if inscribed angle
z=90/2=45
inscribed angle is half of central angle of the cyclic quadrilateral
Find m Help! Will mark brainliest!
Answer:
Answer is A! 38 degrees
Step-by-step explanation:
opposite side is the same
What is the answer this question is hard answer fast plz
Answer:
Step-by-step explanation:
I believe it is b
2400000 in standard form
Answer:
2.4 is the correct answer
if 24 golf balls weigh 2 1/4 pounds, how much would 60 golf balls weigh
Answer:
5.625 pounds or 5 5/8 pounds
Step-by-step explanation:
(2 1/4)/24 = weight of one golf ball = 0.09375
0.09375 x 60 = 5.625 pounds or 5 5/8 pounds
Answer:
5.625 pounds or 5 5/8 pounds as a fraction
Step-by-step explanation:
calculate average rate of change between n=1 and n= 11
Answer:
The ordered pairs for 1 and 3 are:
(1,2) (3,8)
Now use the slope formula:
(y2-y1)/(x2-x1)
(8-2)/(3-1)= 6/2 = 3
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 1 1 11
2 2 2 22
3 3
4 4
and now u see the first i think
A rectangular playground is 28m long and 15m wide. If all sides are
extended lm outward, what is the area of the enlarged playground ?
Answer:
464m^2
Step-by-step explanation:
Given data
Dimension of the regular playground
Length= 28m
Width= 15 m
We want to extend both sides by 1 m
Length= 28+1= 29m
Width= 15+1= 16m
Hence the area
Area=Length*Width
Area= 29*16
Area= 464m^2
The Area is 464m^2
D) 9. What is the solution to this equation?
2x + 10 = 28
Answer:
X=9
Step-by-step explanation:
I know this because you can find the answer by doing 28 - 10 which equals 18 and 2 times 9 gets you 18 and would make the equation
( 2 times 9) + 10= 28
18 + 10=28
1. What is the greatest common factor of
6x2 – 3x + 18?
a. 3
b. 3x
C. 6x
d. There is no GCF
Answer:
a. 3
Step-by-step explanation:
[tex]6 {x}^{2} - 3x + 18 \\ \\ = 3(2 {x}^{2} - x + 6) \\ \\ GCF = 3[/tex]
the greatest common factor of 6x2 – 3x + 18 is 3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life
Here, given that,
6x2 – 3x + 18
=3×(2x2-x+6)
Hence, the greatest common factor of 6x2 – 3x + 18 is 3.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ2
the mean of a group of students in 60 . if their marks 85 ,65,36 ,48 , X ,75 ,39,72 then find the value of x
Answer: 60
Step-by-step explanation:
Find the total number of students.
In this case, there are 8 total students. Multiply 60 * 8 = 480
Add all the numbers up.
85 + 65 + 36 + 48 + 75 + 39 + 72 = 420
480 - 420 = 60
x = 60
If we put money in an investment that increases 14% each year . what would be the multiplier?
Answer:
Step-by-step explanation:
1.14, just like 114%
Hi i have this class work of my cousing
but i need some help beacause i forgot this
the first question is 5_8
Answer:
5 < 8
-4 < 0
0 < 4
-5 < 5
-9 > -19
-5 > -8
Step-by-step explanation:
Remember, the "Alligator" or better known as the "Packman" symbol ( > < )
It will always want to "eat" the bigger number. so, 8 is bigger than five, so the "Packman" will want to go after the bigger number. 5 < 8
The perimeter of a rectangle is 104 meters. If the length of the
rectangle is 38 inches, find the area of the rectangle.
At any time t ≥ 0, in hours, the rate of growth of a population of bacteria is given by dy/dt = 0.5y. Initially, there are 200 bacteria.
(a) Solve for y, the number of bacteria present, at any time t ≥ 0.
(b) Write and evaluate an expression to find the average number of bacteria in the population for 0 ≤ t ≤ 10.
(c) Write an expression that gives the average rate of bacteria growth over the first 10 hours of growth. Indicate units of measure.
Answer:
(a) The equation for the number of bacteria at time t ≥ 0 is [tex]y = 200\cdot e^{0.5 \cdot t }[/tex]
(b) The average population in the bacteria for 0 ≤ t ≤ 10 is 29,482 bacteria
(c) The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour
Step-by-step explanation:
(a) The given rate of growth of the bacteria population is;
[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]
The initial amount of bacteria = 200
At time, t ≥ 0, we have;
[tex]\dfrac{dy}{y} = 0.5 \cdot dt[/tex]
[tex]\int\limits {\dfrac{dy}{y} } = \int\limits {0.5} \, dt[/tex]
ln(y) = 0.5·t + C
[tex]y = e^{0.5 \cdot t + C}[/tex]
[tex]y = C_1 \cdot e^{0.5 \cdot t }[/tex]
When, t = 0, y = 200, we have;
[tex]200 = C_1 \cdot e^{0.5 \times 0 } = C_1[/tex]
C₁ = 200
The equation for the number of bacteria at time t ≥ 0 is therefore given as follows;
[tex]y = 200\cdot e^{0.5 \cdot t }[/tex]
(b) The expression for the average number of bacteria in the population for 0 ≤ t ≤ 10 is given as follows;
[tex]y = \int\limits^t_0 {0.5 \cdot y} \, dt[/tex]
[tex]y = \int\limits^{10}_0 {0.5 \cdot 200\cdot e^{0.5 \cdot t }} \, dt = \left[200\cdot e^{0.5 \cdot t }\right]^{10}_0 \approx 2,9682.6 - 200 = 29,482.6[/tex]
The average population in the bacteria for 0 ≤ t ≤ 10 is therefore, y = 29,482
(c) The average rate of growth after 10 hours of growth is given as follows;
[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]
[tex]\dfrac{dy}{dt} = 0.5 \cdot 200\cdot e^{0.5 \cdot 10 } = 14,841.32 \ Bacteria/hour[/tex]
The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour
Population functions can either represent growth or decays.
The given parameter is:
[tex]\frac{dy}{dt}= 0.5y[/tex]
(a) Solve for y
We have:
[tex]\frac{dy}{dt}= 0.5y[/tex]
Integrate both sides
[tex]\int \frac{dy}{dt}= \int 0.5y[/tex]
Divide both sides by y, and multiply both sides by dt
[tex]\int \frac{dy}{y}= \int 0.5\ dt[/tex]
Integrate both sides of the equation
[tex]\ln(y) = 0.5t +c[/tex]
Take the exponent of both sides
[tex]y = e^{0.5t +c}[/tex]
This gives
[tex]y = ce^{0.5t}[/tex]
When t = 0, and y = 200.
So, we have:
[tex]200 = ce^{0.5 \times 0}[/tex]
[tex]200 = ce^{0}[/tex]
Evaluate the exponent
[tex]200 = c[/tex]
Rewrite as:
[tex]c = 200[/tex]
Substitute 200 for c in [tex]y = ce^{0.5t}[/tex]
[tex]y = 200e^{0.5t}[/tex]
Hence, the equation for y is [tex]y = 200e^{0.5t}[/tex]
(b) The average number of bacterial for 0 ≤ t ≤ 10.
The average value of the function is calculated as:
[tex]y' = y(10) - y(0)[/tex]
Calculate y(0) and y(10)
[tex]y = 200e^{0.5t}[/tex]
[tex]y(0) = 200e^{0.5(0)}= 200[/tex]
[tex]y(10) = 200e^{0.5\times 10} =29682.6318205[/tex]
So, we have
[tex]y' = y(10) - y(0)[/tex]
[tex]y' = 29682.6318205 - 200[/tex]
[tex]y' = 29482.6318205}[/tex]
[tex]y' = 29483[/tex]
Hence, The average number of bacterial for 0 ≤ t ≤ 10 is 29483
(c) The average rate over the first 10 hours of growth
We have:
[tex]\frac{dy}{dt}= 0.5y[/tex]
Substitute [tex]y = 200e^{0.5t}[/tex]
[tex]\frac{dy}{dt}= 0.5 \times 200e^{0.5t}[/tex]
[tex]\frac{dy}{dt}= 100e^{0.5t}[/tex]
When t = 10, we have:
[tex]\frac{dy}{dt}= 100e^{0.5 \times 10}[/tex]
[tex]\frac{dy}{dt}= 100e^{5}[/tex]
[tex]\frac{dy}{dt}= 14841[/tex]
Hence, the average rate over the first 10 hours of growth is 14841
Read more about population growth functions at:
https://brainly.com/question/20115298
Which property is represented by the equation below? (Lesson 1-4)
8•(5•3)=(8•5)•3
Answer:
associative property
Step-by-step explanation:
This is the associative property. The numbers and signs on both sides of the equation stay IN THE SAME ORDER, this is a big hint!
Answer:
associative property
Step-by-step explanation:
Here is an inequality: -2x>10.
List some values for x that would make this inequality true.
How are the solutions to the inequality -2x10 different from the solutions to -2x>10? Explain your reasoning.
Answer:
The difference is -2x10 is basically-2 times x times 10.
Step-by-step explanation:
Cuz i said so
The x values that makes the given inequality true are -10, -9, -8, -7 and -6.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -2x>10.
Divide -2 on both the sides of an inequality, we get
x<-5
So, the solution is {.......-10, -9, -8, -7, -6}
Hence, the x values that makes the given inequality true are -10, -9, -8, -7 and -6.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ3
find the area of the figure
Answer:
area = 92 yd²
Step-by-step explanation:
13x8 = 104
3x8x0.5 = 12
104 - 12 = 92 yd²
Answer:
Step-by-step explanation:
help please i rlly need it