Answer:
x = [tex]\frac{1}{3}[/tex] y = -1
Step-by-step explanation:
x = 0 to solve for y
[tex]y=3x-1[/tex]
[tex]y=3(0)-1[/tex]
[tex]y=-1[/tex]
y = 0 to solve for x
[tex]y=3x-1[/tex]
[tex]0=3x-1[/tex]
Add 1 to both sides
[tex]1=3x[/tex]
Divide by 3 to isolate x
[tex]\frac{1}{3} =x[/tex]
John buys 20 bunches of bananas for 5naira. He sells them for 6.50. what is his percentage profit?
To paint interior walls, a person charges 50¢ per square foot plus the cost of the paint. For a recent job, the paint cost $100 and the total bill was $475.
The person must have painted ____ ft^2.
Answer: [tex]750\ ft^2[/tex]
Step-by-step explanation:
Given
Rate of painting 50¢ per square foot
Cost of paint is $100
If the total bill is $475
We can write,
[tex]\Rightarrow 475=100+0.5\times x\quad [x=\text{area in square foot}]\\\Rightarrow 375=0.5x\\\Rightarrow x=750\ ft^2[/tex]
Thus, [tex]750\ ft^2[/tex] must be painted.
Paula, Adam, and Jessica are siblings. Adam is half the age of Paula, and Jessica is one quarter of Paula's age. In six years' time, Jessica will be 75% of Adam's age.
a How old is each sibling now?
b How old will each sibling be in six years' time?
c In how many years' time will Jessica be 75% of Paula's age?
Step-by-step explanation:
answer is in photo above
f(x)=3x-3
g(x) 3x^3+5
Find F(-3) and g(-2)
Answer:
f(-3) = -12
g(-2) = -19
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 3x - 3
g(x) = 3x³ + 5
f(-3) is x = -3 for function f(x)
g(-2) is x = -2 for function g(x)
Step 2: Evaluate
f(-3)
Substitute in x [Function f(x)]: f(-3) = 3(-3) - 3Multiply: f(-3) = -9 - 3Subtract: f(-3) = -12g(-2)
Substitute in x [Function g(x)]: g(-2) = 3(-2)³ + 5Exponents: g(-2) = 3(-8) + 5Multiply: g(-2) = -24 + 5Add: g(-2) = -19Answer:
f(-3) = -12
g(-2) = -19
Step-by-step explanation:
1.
f(x) = 3x - 3
One is asked to find (f(-3)), substitute (-3) into the given function (f) in place of (-3), and solve to evaluate,
f(-3) = 3(-3) - 3
Simplify,
= -9 - 3
= -12
2.
g(x) = [tex]3x^3+5[/tex]
The problem asks one to find (g(-2)), subtitute (-2) into the function in place of (x) and solve to find tis value,
g(-2) = [tex]3(-2)^3+5\\[/tex]
Remember any number raised to an exponent is equal to the base (the number that is being raised to the exponent) times itself the number of times that the exponent indicates,
[tex]=3(-8)+5\\=-24+5\\=-19[/tex]
The vertices of a trapezoid are located at (1, 2), (3, 1), (3, 5), (1, 4). The trapezoid is translated 4 units to the right. What are the coordinates of the image of the trapezoid?
Answer:
Suppose that we have a given point (x, y)
If we translate this point N units to the right, then the new coordinates of the point are:
(x + N, y)
Ok, now if we know that the vertices of the trapezoid are:
(1, 2), (3, 1), (3, 5), (1, 4)
And we move the whole figure 4 units to the right, then all the vertices are moved 4 units to the right.
Then the new vertices of the figure will be:
(1 + 4, 2) = (5, 2)
(3 + 4, 1) = (7, 1)
(3 + 4, 5) = (7, 5)
(1 + 4, 4) = (5, 4)
Then the coordinates of the image of the trapezoid (of the new vertices) are:
(5, 2), (7, 1), (7, 5), (5, 4)
the temperature of a cup of coffee obeys newton's law of cooling. The initial temperature of the coffee is 150F and 1 minute later it is 135F. The temperature of the room is 70F. If T(t) represents the temperature of the coffee at time T the correct differential equation for the temperature for this condition is
Answer:
Newton's law of cooling says that:
T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)
or:
[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]
in the differential form.
where:
T is the temperature as a function of time
Tₐ is the ambient temperature, in this case, 70F
T₀ is the initial temperature of the object, in this case, 150F
k is a constant, and we want to find the value of k.
Then our equation is:
T = 70F + (150F - 70F)*e^(k*t)
Now we also know that after a minute, or 60 seconds, the temperature was 135F
then:
135F = 70F + (150F - 70F)*e^(k*60s)
We can solve this for k:
135F = 70F + 80F*e^(k*60s)
135F - 70F = 80F*e^(k*60s)
65F = 80F*e^(k*60s)
(65/80) = e^(k*60s)
Now we can apply the Ln(x) function to both sides to get:
Ln(65/80) = Ln(e^(k*60s))
Ln(65/80) = k*60s
Ln(65/80)/60s = k = -0.0035 s^-1
Then the differential equation is:
[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]
. How much time, in minutes, did she spend studying Spanish?
The time Kathleen spent studying Spanish is
SEE IMAGE BELOW AND ONLY ANSWER IF YOU KNOW THE ANSWER
The ratio between boys and girls in a class is 3 : 1. Find the number of boys in the class is the total number of students is 40.
Answer: 30 boys
Step-by-step explanation:
Boys:Girls
3 : 1
Let no. of girls =x
⇒ no. of boys =3x.
⇒ no. of students in class =4x
= 4/3×3x
= 4 /3 ×no. of boys
40=4/3* no.of boys
40* (3/4)=no.of boys
30=no of boys
Calculus chapter7 (Transcendental Functions)
Answer:
1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } \approx 1.665[/tex]
2) [tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]
3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } \approx 1.317[/tex]
Step-by-step explanation:
1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} }[/tex]
This integral can be solved easily by using algebraic substitutions:
[tex]u = \ln x[/tex], [tex]du = \frac{dx}{x}[/tex]
Then, the integral can rewritten as follows:
[tex]\int {\frac{dx}{2\cdot x\cdot \sqrt{\ln x}} } = \frac{1}{2}\int {\frac{du}{u^{1/2}} } = \frac{1}{2}\int {u^{-1/2}} \, du[/tex]
[tex]\int {u^{-1/2}} \, du = 2\cdot u^{1/2} + C = 2\cdot \sqrt{\ln x} + C[/tex]
Where [tex]C[/tex] is the integration constant.
[tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } = F(16) - F(2)[/tex]
[tex]F(16) - F(2) = 2\cdot (\sqrt{\ln 16}-\sqrt{\ln 2})[/tex]
[tex]F(16) - F(2) \approx 1.665[/tex]
2) Let be [tex]y = \cosh^{-1} (2\cdot \sqrt{x+1})[/tex], then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:
[tex]\frac{dy}{dx} = \pm\frac{1}{\sqrt{4\cdot x + 3}}\cdot \left(\frac{1}{\sqrt{x+1}} \right)[/tex]
[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{(4\cdot x + 3)\cdot (x+1)}}[/tex]
[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]
3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} }[/tex]
This integral can be solved by the following trigonometric substitutions:
[tex]\frac{2}{\sqrt{4 + x^{2}}} = \cos \theta[/tex]
[tex]\frac{1}{\sqrt{4+x^{2}}} = \frac{\cos \theta}{2}[/tex]
[tex]\frac{x}{2} = \tan \theta[/tex]
[tex]x = 2\cdot \tan \theta[/tex]
[tex]dx = 2\cdot \sec^{2}\theta \,d \theta[/tex]
[tex]\int {\frac{dx}{\sqrt{4+x^{2}}} } = \int {\left(\frac{\cos \theta}{2} \right)\cdot (2\cdot \sec^{2}\theta)} \, d\theta = \int {\sec \theta} \, d\theta[/tex]
[tex]\int {\sec \theta}\,d\theta = \ln |\sec \theta + \tan \theta| + C[/tex]
[tex]\ln \left|\frac{\sqrt{4+x^{2}}}{2} + \frac{x}{2} \right| + C[/tex]
Where [tex]C[/tex] is the integration constant.
[tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } = F(2\sqrt{3}) - F(0)[/tex]
[tex]F(2\sqrt{3}) - F(0) = \ln \left|2+\sqrt{3}\right|-\ln \left|1\right|[/tex]
[tex]F(2\sqrt{3}) - F(0) \approx 1.317[/tex]
What is the range of g(x) = -2 [X + 3] + 2?
Answer:
A.
Step-by-step explanation:
When x = -3 g(x) = + 2 and this is the maximum value of g(x).
All other values of x give a value of g(x) < 2.
The range is (-∞, 2]
mark all statements that are true . help !
Answer:
C D E
Step-by-step explanation:
They are the options that are clear enough
Which expression represents the area in square centimeters of the new cup opening? Use A=2
Answer:
A = πx² - 2πx + π
Step-by-step explanation:
The area of the new cup opening :
We are given the area formula to use :
Area, A = πr²
r = Radius = x-1
Area = π(x - 1)²
A = π(x - 1)(x - 1)
A = π(x² - x - x + 1)
A =π(x² - 2x + 1)
A = πx² - 2πx + π
Find the area of the parallelogram below
Step-by-step explanation:
area of the parallelogram = 7 × 14
=98 cm²
A triangle has side lengths of 24 centimeters and 35. The third side has a length of x centimeters. Complete the inequality to show all the possible values of x.
*2 answers*
Answer: [tex]11<x<59[/tex]
Step-by-step explanation:
Given
The side of the triangle are [tex]24\ \text{and }35[/tex]
Suppose the third side is [tex]x[/tex]
Also, the sum of the two sides of the triangle is always greater than the third
[tex]\therefore x<24+35\\\Rightarrow x<59\quad \ldots(i)[/tex]
Similarly,
[tex]\Rightarrow x+35>24\\\Rightarrow x>-11[/tex]
Also,
[tex]\Rightarrow x+24>35\\\Rightarrow x>11\quad \ldots(ii)[/tex]
From (i) and (ii) we get
[tex]\Rightarrow 11<x<59[/tex]
please solve fast please
Answer:
3/6 =1/25/6pls give me brainliest plzzzzz
Find the mean for the following data set: 5, 3, 6, 8, 1, 1 *
Answer:
add all the numbers
which will get you 24
then divide by how many numbers you got which will give you 6
the answer is six
Step-by-step explanation:
Hope this helps :D
Answer:
The mean is equal to 4.
Step-by-step explanation:
To find the mean of any set of numbers, you have to add all of those numbers and divide the result by however many numbers their are.
For example, the mean of 2,5,6, and 7 would be the following: 2+5+6+7/4
The mean of 5,3,6,8,1, and 1 is the following: 5+3+6+8+1+1/6=24/6=4
The mean is equal to 4.
solve for x 6(x-3)=8(x-4)
Answer:
7=x
Step-by-step explanation:
6(x-3)=8(x-4)
Distribute
6x -18 = 8x-32
Subtract 6x from each side
6x-18 -6x = 8x-32-8x
-18 = 2x-32
Add 32 to each side
-18+32 = 2x-32+32
14 = 2x
Divide by 2
14/2 =2x/2
7=x
[tex]\sf\purple{x= 7}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
[tex]➺\:6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6x - 18 = 8x - 32[/tex]
[tex]➺ \: 6x - 8x = - 32 + 18[/tex]
[tex]➺ \: - 2x = - 14[/tex]
[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the value of [tex]x[/tex] is 7.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]
[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]
[tex]➺ \: 24 = 24[/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
Are these triangles congruent?
Answer:
yes...
Step-by-step explanation:
its a congrate triangle
Lydiagrace33
Image attached
A) 1 point Write an inequality for this graph . Use the shift key and the key or key to type the < or > symbol . *
B) Water boils when the temperature is at least 212 degrees F. Which inequality shows this situation ?
C) When the temperature drops below 50 degrees F , crickets usually stop chirping . Which inequality shows this situation ?
D) Explain the difference between the meaning of a closed
circle and an open circle on a graph of an inequality .
which is an irrational number
Answer:
The irrational number is [tex]\sqrt{\frac{5}{3}}[/tex].
__________________________________
Definition : In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
Answer:
Step-by-step explanation:
I'm not sure but I think it's A
I'm not sure!!
(pls do not vote ..)
Bye!
It is A (45). Hope this helps!
Can someone please help me?
Answer:
The Answer for your question is B
Answer:
78%
Step-by-step explanation:
They are asking for spotted animals and dogs so
Spotted animals=40%
Dogs=38%
So just add them to get 78%
(Don’t get confused by the 12% spotted dogs those are from the 38%)
Find the lowest common multiple of 10 and 12
At a basketball game, a vender sold a combined total of 101 sodas and hot dogs. The number of sodas sold was 37 more than the number of hot dogs sold. Find
the number of sodas sold and the number of hot dogs sold.
Answer:
101 - 37 = 64
I hope this is correct
How many natural numbers are there between 8² and 9² ?
Answer:
19
Step-by-step explanation:
Answer:
i think the answer 17
81-64 =17PLEASE HELP ME WILL MARK YPU IF YOU HELP ME
ok check image file in the image is answers with color code
Choose the inequality that repersents the following graph
Answer:
B. x</=-3
Step-by-step explanation:
the arrow is pointed to the left which means less than and the end is shaded which means or equal to
What is 6 divided by 3/8
Answer:
16 (sixteen) is 6 divided by 3/8.
Help need help fast
Answer:
Answer is in bold form
Step-by-step explanation:
Given
radius = 3feet
Height = 6feet
Volume of the cylinder = πr²h
Volume of the cylinder = 3.14 * 3² * 6
Volume of the cylinder = 169.56ft³
volume of the cone = Volume of cylinder/3
volume of the cone = 169.56/3
volume of the cone = 56.52ft³
Volume of the sphere = 4/3πr³
Volume of the sphere = 4/3*3.14*(3)³
Volume of the sphere = 4 * 3.14* 9
Volume of the sphere = 113.04ft³
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 7500 households, and the data collected today will be used to determine the proportion of households tuned to a particular sports program. Which type of observational study is described in the problem statement?
Answer:
Cross sectional study
Step-by-step explanation:
Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).