Calculate x from: Log (x + 4) + log (3x + 2) = log 100 - 2log 2
Answer: x = 1
Step-by-step explanation:
Given that
Log (x + 4) + log (3x + 2) = log 100 - 2log 2
Log (x + 4) + log (3x + 2) = log 100 - log2^2
Log (x + 4) + log (3x + 2) = log 100 - log4
According to the laws of logarithms,
LogA + logB = log AB
Also,
Log A - logB = log A/B
Apply the law to left hand side and the right hand side of the equation
Log (x+4)(3x+2) = log(100/4)
Open the bracket in the left hand side
Log(3x^2 + 2x +12x + 8) = log25
Log(3x^2 + 14x + 8) = log25
The two log will cancel out
3x^2 + 14x + 8 = 25
3x^2 + 14x + 8 - 25 = 0
3x^2 + 14x - 17 = 0
Factorise the above equation
3x^2 - 3x + 17x - 17 = 0
3x( x - 1 ) + 17( x - 1 ) = 0
3x + 17 = 0
3x = - 17
X = -17/3
Or
X - 1 = 0
X = 1
Therefore, x = -17 or 1
Substituting 1 back into the equation give the solution to the equation. While -17 does not.
Which graph shows the system of equations 4 x + y = 3 and 2 x minus 3 y = 3? On a coordinate plane, a line goes through (0, negative 1) and (3, 1) and another line goes through (0, 3) and (1, negative 1). On a coordinate plane, a line goes through (0, 3) and (1, negative 1) and another line goes through (0, negative 3) and (3, negative 1). On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 3) and (3, negative 1). On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 1) and (3, 1).
Answer:
A is the correct answer
Step-by-step explanation:
Graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
The system of equations
4x + y = 3 and
2x - 3y = 3
In the first line, the slope is -4, and the y-intercept at (0,3)
In the second line, the slope is 2/3, and the y-intercept at (0,-1)
Thus, graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Ten students take a test. Five students get a 50. Four students get a 70. If the average score is 55, what was the last student’s score?
Answer:
20%
Step-by-step explanation:
50x5 + 70x4 = 530. 530 divided by 9 equals 58.89. When you add 20 to 530 you get 550. 550 divided by 10 equals 55. The student got a 20%.
Answer:20
Step-by-step explanation:
average= total/number of items/students/whatever you take. So, here its ((5x50)+(4x70)+m)/10=55 and if you solve m you get 20 as the answer!
I will give brainliest to simplest explanation! There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
117,600 ways
Step-by-step explanation:
This problem can be solved using fundamental principle of counting , according to which , if there are m different things and n different things,
then there m*n ways to combine.
Example: if there 5 shirts and 3 ties,
then number of ways in which different combination shirt and tie can be worn is
5*3 = 15 ways.
____________________________________
In the problem,\
number of states is 50,
let those states be
A1, A2, A3, A4 ......A50
in each state there are 2 senate
Condition
3-Senator committee in which no two members are from the same state.
then
first member can be chosen from any of the 50 state,
hence first member can be chosen in 50 ways
for simplicity lets take state A1, you can choose any one you wish
second member cannot be from state A1, then number of state left = 49
second member can be chosen from any of 49 state left
hence second member can be chosen in 49 ways
for simplicity lets take state A2,
Third member cannot be from state A1 and A2, then number of state left = 48
Third member can be chosen from any of 48 state left
hence Third member can be chosen in 48 ways
for simplicity lets take state A3,
Hence no. of ways of choosing 3-Senator committee be formed such that no two Senators are from the same state = 50*49*48 = 117,600 ways
How do you do this [tex]||x-3|-2| ≤1[/tex]
What is the equation of the following graph in vertex form? parabolic function going down from the left through the point zero comma five and turning at the point two comma one and contin Courtesy of Texas Instruments (2 points) y = (x - 2)2 + 1 y = (x - 1)2 + 2 y = (x + 2)2 + 1 y = (x + 2)2-1
Answer:
y = (x - 2)² + 1
Step-by-step explanation:
Gnerela equation of a parabola in vertex form:
y = a(x - h)² + k
where (h, k) is the vertex
From the description of the graph:
the parabola passes through (0,5)the parabola has a vertex at (2,1)Replacing into the general equation:
y = a(x - 2)² + 1
5 = a(0 - 2)² + 1
5 - 1 = a*4
4/4 = a
1 = a
Then, the equation is: y = (x - 2)² + 1
Answer:
The correct answer is A, "y = (x - 2)² + 1"
Step-by-step explanation:
I just completed the test and got full credit using this option.
A rectangular wall has length 3 less than 4 times the width . I wish to put a silver line along the corners of the wall. The lining costs 25 cents per foot and I spent a total of $18.50 for the lining on the corners of the wall. If painting costs 20 cents per square foot , how much dose it cost to paint the wall? PLEASE ANSWER correctly. I WILL GIVE BRAINLIEST ANSWER TO U IF U DO
Answer:
Step-by-step explanation:
Let width = w units
Length = 4w - 3
Cost for lining corners of wall = $ 18.50
Perimeter of the wall = 18.50/0.25 = 74 ft
2*(length +width ) = 74
2*(4w - 3 + w) =74
2*(5w - 3) =74
10w - 6 = 74 {Add 6 to both sides}
10w - 6 + 6 = 74 + 6
10w = 80
Divide both sides by 10
10w/10 = 80/10
w = 8 ft
Length = 4w - 3 = 4*8 - 3 = 32 - 3
Length = 29 ft
Area of the wall = length * width
= 29 * 8
= 232 square ft
Cost of painting the wall per square feet = 20 cents = 0.20
Cost of painting 232 square feet = 232 * 0.20
= $ 46.40
From the equation, find the axis of symmetry of the parabola.
y = 4x+ 32x+ 61
a. x= 3
x=-4
C.
b. X= 4
d. X=-3
Sketch graph y=-4x+4
Answer:
I hope this helps you! Have a great rest of your day.
Find the number of 4-digit numbers that contain exactly two even and two odd digits.
Answer:
2,435
Step-by-step explanation:
find two even and two odd
I'm confused can somebody help me ASAP?!?!??!?!
Answer:
part 2 it should be 20 minutes
Step-by-step explanation:
40 = 8 add another 40= 16 half of 40 is 20 so half of 8 is 4 so add 8+8+4
that equals 20
part 1 even d on't understand
1. Which of the following figures is not a polygon?
Answer:
the cricle is not a polygon since it does not have any sides and a polygon has to have striaght sides
Step-by-step explanation:
Answer:b
Step-by-step explanation:
When graphed, which parabola opens downward?
Answer:
A
Step-by-step explanation:
Edge 2020
PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!
Find the measure of the line segment indicated. Assume that lines which appear
tangent are tangent.
Find DA (SEE PICTURE)
Answer:
DE = 8
Step-by-step explanation:
EF * DF = FG * FJ
6 * (6 + x + 3) = 7 * (7 + 5)
6(x + 9) = 7 * 12
x + 9 = 7 * 2
x + 9 = 14
x = 5
DE = x + 3 = 5 + 3 = 8
Which ordered pairs are solutions to the inequality –2x+y>-4?
Select each correct answer.
(3, -1)
0 (-1, 1)
(0, -5)
(1, - 2)
0 (0,1)
Answer:
answer is (0,1)
Step-by-step explanation:
check
by substituting x=0 and y=1 in the equation above
- 2(0)+1> -4
1> -4
Thereby (0,1) is the required solution to the inequality
How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these similarities or differences important when looking for intersections between rational functions and other types of functions? Be sure to cite examples as you explain your ideas.
Answer:
See explanation below for further details.
Step-by-step explanation:
A rational consist of two real numbers such that:
[tex]\frac{a}{b} =c[/tex]
If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.
If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example:
If [tex]a = x^{2}[/tex] and [tex]b = x[/tex], then:
[tex]c = \frac{x^{2}}{x}[/tex]
[tex]c = x[/tex]
If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example
If [tex]a = 3\cdot x^{3}[/tex] and [tex]b = x[/tex], then:
[tex]c = \frac{3\cdot x^{3}}{x}[/tex]
[tex]c = 3\cdot x^{2}[/tex]
But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.
Example
If [tex]a = 10^{2x}[/tex] and [tex]b = 3\cdot 10^x[/tex], then:
[tex]c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}[/tex]
[tex]c = \frac{1}{3}\cdot 10^{2\cdot x -x}[/tex]
[tex]c = \frac{1}{3}\cdot 10^x[/tex]
Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.
If [tex]a = 5\cdot e^{x}[/tex] and [tex]b = -3\cdot e^{x}[/tex], then:
Example
[tex]c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}[/tex]
[tex]c = -\frac{5}{3}[/tex]
It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.
Example
[tex]5\cdot a^2\cdot x -9[/tex]
What is the domain of F(x) = x?
Answer:
All real numbers
Step-by-step explanation:
The equation F(x)=x is an identity function. If you plot this on a graph, you notice that it is a diagonal line that always passes through (0,0), making the domain all real numbers.
Find the area of a circle with a diameter of 12 inches. Use 3.14 for pi
Answer:
A =113.04 in ^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
The radius is 1/2 of the diameter
r = 1/2 (12) = 6
A = pi (6)^2
A = 36 pi
Using 3.14 for pi
A = 36 (3.14)
A =113.04 in ^2
Randy Johnson was a baseball pitcher for the Arizona Diamondbacks during the 2002 season. He had a record of 24 wins and 5 losses at the end of the regular season. To find his Won‐Loss percentage, divide the number of games won by the total number of decisions (games he either won or lost). What was Randy Johnson’s Won‐Loss percentage for the 2002 regular season?
Answer:
The won percentage is 24 / 29 ≈ 83% (24 + 5 = 29 games total) and the loss percentage is 5 / 29 ≈ 17%.
A department store stocks pants and shorts in the colors black and blue. The relative frequency of their orders for blue pants is half the relative frequency of their orders for black shorts. Which two-way frequency table could represent the data from the store's orders?
Answer:
Table 2
Step-by-step explanation:
The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.
We are interested in the number of blue pants and black shorts.
If we name them as p and b respectively, then we are looking for a table where s/p=2
Let's verify relevant data in all tables:
Table 1:
p= 82, s= 41 ⇒ s/p= 41/82 ≠ 2, no, not this oneTable 2:
p= 57, s= 114 ⇒ s/p= 114/57 = 2, yes, it is the oneTable 3:
p= 78, s= 110 ⇒ s/p= 110/78 ≠ 2, no, not this oneTable 4:
p= 44, s= 150 ⇒ s/p= 150/44 ≠ 2, no, not this oneSo only one of tables- the second one from top represents the required data.
Answer:
The second table
Step-by-step explanation:
I did the test.
* DIFFICULT QUESTION , PLS ANSWER * Write an equation for the circle whose graph is shown.
Answer:
D
Step-by-step explanation:
The formula of a circle is [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex] where the vertex is (h,k).
The vertex is (4,-2) and the radius is 5, so substitute the numbers in and you get the solution.
Answer:
D
Step-by-step explanation:
PLS HELPPPP MEEEE!!!
Answer:
No
Step-by-step explanation:
We have to check if 3/5 = 6/25. If we convert 3/5 into a fraction with denominator of 25 so that we can compare the two we get 15/25 and this is clearly not equal to 6/25. Therefore, the answer is no.
PLEASE HELP Order these numbers from least to greatest. 2 1/10, 61/10, 3.122, 3.19
Answer: 2 1/10, 3.122, 3.19, 61/10
Step-by-step explanation:
Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)
2.1, 6.1, 3.122, 3.19. Obviously, the smallest number is 2.1, because it has a 2 in the ones place. Next, we see a tie in the ones place between 3.122 and 3.19. Then we look at the tenths place and see another tie. Then, at the hundredths place, we see that 3.19 is greater that 3.122. Thus, the order of the numbers is 2.1,3.122,3.19,6.1.
Hope it helps <3
Need help finding the missing length to the attached triangle.
Answer:
Estimated answer 80
Step-by-step explanation:
I believe its 84 or some where in 80. Because the estimated value I got by solving this geometrical question is somewhere in 80. HOPE this helps! :D
Find the factors of the polynomial 45 x2 - 20 y2
Answer:
The factors of the polynomial are 5, ( 3x - 2y), and (3x + 2y)
Step-by-step explanation:
The given polynomial is 45x² - 20y²
45x² - 20y² = 5 (9x² - 4y²)
45x² - 20y² = 5 [ (3x)² - (2y)² ]
Using difference of two squares, (3x)² - (2y)² = ( 3x - 2y)(3x + 2y)
45x² - 20y² = 5 ( 3x - 2y) (3x + 2y)
The factors of the polynomial are 5, ( 3x - 2y), and (3x + 2y)
Answer:
5(3x - 2)(3x + 2)
Step-by-step explanation:
Please indicate exponentiation with " ^ " : 45 x^2 - 20 y^2.
Identify the GCF and factor it out: 5(9x^2 - 4y^2)
Recognize that (9x^2 - 4y^2) is the difference of two squares, which factors into (3x - 2y)(3x + 2y)
Then 45 x^2 - 20 y^2 = 5(3x - 2)(3x + 2)
What is the ratio of 76,000 and 100,000
Answer:
19 : 25
Step-by-step explanation:
PLS give answer ASAP
Answer: 3.5 pi.
Step-by-step explanation: Since we know the circumference formula of a circle is 2*pi*radius, we just have to substitute 7 in there, and divide by 4. So here ya go, 3.5 pi.
Work out the equation of a line when the gradient is 1/2 and it passes through the point (4,-2)
Answer:
The equation of the line is
[tex]y = \frac{1}{2} x - 4[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where m is the gradient
c is the y intercept
Gradient = 1/2
Equation of the line using point ( 4 , -2) is
[tex]y + 2 = \frac{1}{2} (x - 4) \\ y + 2 = \frac{1}{2} x - 2 \\ y = \frac{1}{2} x - 2 - 2 \\ y = \frac{1}{2} x - 4[/tex]
Hope this helps you
Solve: 20/x=2 a. x = 40 c. x = 20 b. x = 10 d. x = 15 Please select the best answer from the choices provided A B
Answer:
B. x=10
Step-by-step explanation:
We are given the equation:
20/x=2
To solve this, we must get x by itself. First, let's cross multiply.
20/x= 2/1
Multiply the denominator of the first fraction by the numerator of the second. Then, multiply the numerator of the first and the denominator of the second.
x*2= 20*1
2x=20
x is being multiplied by 2. The inverse of multiplication is division. So, divide both sides of the equation by 2.
2x/2 = 20/2
x= 20/2
x=10
Therefore, the answer is B. x=10
Can someone please help with this maths
Hey there! :)
Answer:
C. (0, 5)
Step-by-step explanation:
Where the equation crosses the y axis is known as the y-intercept.
In the equation y = mx + b, the b value represents the y-intercept where x = 0. Therefore:
Rearrange the equation pictured:
y = 5 - 3x --> y = -3x + 5
The b value in this equation is 5, so
The y-intercept of this equation is (0, 5).
Answer:
(0,5)Option C is the correct option.
Here,
y=5-3xWhen X=0
y= 5-3*0
= 5-0
=5
x=0
y=5
Hope this helps...
Good luck on your assignment..