Answer:
x=5
Step-by-step explanation:
step one: distribute to get rid of parentheses. this means multiplying -3 by the numbers inside of the parentheses next to it.
-3(-6)= 18 and -3(-4x)=12x
this makes the equation now 8x+38=18+12x
step two: move x to one side of the equation. we can do this by using inverse operations, so we're going to subtract 8x from both sides.
8x-8x=0, 12x-8x= 4x.
this makes the equation now 38=18+4x
step three: isolate x. this means getting rid of the 18. to do this, we are going to use inverse operations again. this means subtracting 18 from both sides.
18-18=0, 38-18=20.
this makes the equation now 20=4x
step four: divide to get x by itself. we don't want to know what 4x is, we just want to know what plain x is. so we're going to use inverse operations for the last time and divide both sides by 4 because 4x is the same thing as saying "four times x"
20/4= 5, 4x/4=x
this makes the equation now 5=x
that's your answer, x=5. hope this helped!
What is the range of this function?
a student was marked tardy five different time in a 40 day period. What percent of the times was the student tardy
Answer:
12.5%
Hope this helps!
Answer:
The percentage of times the students marked will be 12.5%.
Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
A student was marked tardy five different times in a 40-day period.
Percentage of 5 among 40 →
(5/40) x 100 = 12.5%
A forest ranger looking out from a ranger's station can see a forest fire at a 35 degree angle of depression. The ranger's position is 100 feet above the ground. How far is it from the ranger's station to the fire? Round your answer to the nearest tenth of a foot.
To find the distance from the ranger's station to the forest fire, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the forest fire, the height of the ranger's station above the ground, and the distance from the ranger's station to the forest fire to form a right triangle.
We can then use the tangent function to find the distance from the ranger's station to the forest fire as follows:
tan(35°) = opposite/adjacent
opposite = tan(35°) * adjacent
opposite = tan(35°) * 100 feet
opposite = 0.7392 * 100 feet
opposite = 73.92 feet
Therefore, the distance from the ranger's station to the forest fire is approximately 74 feet. To the nearest tenth of a foot, this is 73.9 feet.
To eliminate a variable in the system, should you add the equations or subtract the equations?
3x - 2y = 17
-3x - 4y = 7
Answer: You should add the equation
Step-by-step explanation: I see here that you already have perfect 3x and -3x, so the best way is to add them and eliminate the x to find the y first and then put the y back in the equation and solve for the x!
If you can, please give me a Brainliest, I only need one more to become an Ace, thank you!
give 3 examples each.
Answer:
see below
Step-by-step explanation:
You want examples of use of the rules of logarithms:
[tex]\begin{array}{ll}\vphantom{\dfrac{M}{gN}}1.&\log_b{(MN)}=\log_b{(M)}+\log_b{(N)}\\2.&\log_b{\left(\dfrac{M}{N}\right)}=\log_b{(M)}-\log_b{(N)}\\\vphantom{\dfrac{b}{g}}3.&\log_b{(M^a)}=a\cdot\log_b{(M)}\end{array}[/tex]
The point of these is that M and N and 'a' and 'b' can be anything. (Generally, 'b' will be a positive number greater than 1.) For the purpose here, we can let M ∈ {x^3y, (1+r)}, N ∈ {(x-4), r/n}, a ∈ {4, -3}, b ∈ {2, e}.
Using these values in various combinations, your examples could be ...
1. Product rule[tex]\log_2{((x^3y)(x-4))}=\log_2{(x^3y)}+\log_2{(x-4)}\\\\\ln{((1+r)(r/n))}=\ln{(1+r)}+\ln{(r/n)}\\\\ \log_2{((x^3y)(r/n))}=\log_2{(x^3y)}+\log_2{(r/n)}[/tex]
2. Quotient rule[tex]\log_2{\left(\dfrac{x^3y}{x-4}\right)}=\log_2{(x^3y)}-\log_2{(x-4)}\\\\\\\ln{\left(\dfrac{1+r}{r/n}\right)}=\ln{(1+r)}-(\ln{(r)}-\ln{(n)})\\\\\\ \log_2{\left(\dfrac{x^3y}{r/n}\right)}=\log_2{(x^3y)}-(\log_2{(r)}-\log_2{(n)})}[/tex]
3. Power rule[tex]\ln{(x^3y)^4}=4\ln(x^3y)=4(3\ln{(x)}+\ln{(y)}=12\ln{(x)}+4\ln{(y)}\\\\\log_2{(1+r)^{-3}}=-3\log_2{(1+r)}\\\\\log_2{(x^3y)^{-3}}=-3\log_2{(x^3y)}=-9\log_2{(x)}-3\log_2{(y)}[/tex]
Consider the graph of equation y=mx+b
How does changing the value of m affect the graph of the equation?
Let g(x)=x²-5 and h(x) = 3x + 2. Find (hog)(x)
The value of the composite function is (hog)(x) = 3x²- 13.
What is a composition function?
Function composition is an operation used in mathematics that takes two functions, f, and g, and creates a function, h = gof, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.
The functions are g(x)=x²-5 and h(x) = 3x + 2
The composition function (hog)(x) can be written as (hog)(x) =h(g(x))
Putting g(x)=x²-5 in (hog)(x) =h(g(x)):
(hog)(x) =h(x²-5)
Now putting x= (x²-5) in h(x) = 3x + 2:
h(x²-5) = 3(x² - 5) + 2
h(x²-5) = 3x² - 15 + 2
h(x²-5) = 3x² - 13
Therefore (hog)(x) = 3x² - 13.
To learn more about composition function, click on the below link:
https://brainly.com/question/4895631
#SPJ1
a set of 15 different integers has a median of 25 and a range of 25. what is the greatest possible integer that could be in this set? 32 37 ...
The greatest possible integer that could be in this set is 43.
The group of 15 different integers in this instance has a range of 25 and a median of 25. The greatest value that can be entered will be limited by that range.
With a median of 25, we can deduce that 7 numbers fall within the range of 25 and above, and 7 numbers fall within this range.
We must increase the smallest value in order to increase the largest value. Here's how to accomplish it:
18 19 20 21 22 23 24 25
With 18 as the lowest value and a range of 25, 43 would be the highest value.
To learn more about median
brainly.com/question/14532771
#SPJ4
CROSS CONDUCT PROPERTY
By cross multiplication, the result for each pair of rational numbers are listed below:
x = 14 x = 114 / 5 x = 97 / 19 x = 318 / 5 x = 27 / 4 x = 2 x = 109 / 5 x = 94 / 11How to use cross multiplication
Cross multiplication is a property involving multiplication and division between the terms of two rational numbers of the form:
a / b = c / d
Where a, b, c, d are real numbers. Combinations between a numerator and a denominator are multiplications and combinations between two numerators and two denominators are divisions. Now we proceed to solve on each case:
Case 11
4 / x = 2 / 7
4 · 7 = 2 · x
28 = 2 · x
x = 14
Case 12
19 / 10 = x / 12
19 · 12 = 10 · x
228 = 10 · x
x = 114 / 5
Case 13
(x - 1) / 6 = 13 / 19
(x - 1) · 19 = 13 · 6
(x - 1) · 19 = 78
x - 1 = 78 / 19
x = 1 + 78 / 19
x = 97 / 19
Case 14
5 / 17 = 19 / (x + 4)
5 · (x + 4) = 19 · 17
x + 4 = 323 / 5
x = 318 / 5
Case 15
10 / (2 · x - 9) = 20 / 9
10 · 9 = 20 · (2 · x - 9)
90 / 20 = 2 · x - 9
27 / 2 = 2 · x
27 / 4 = x
x = 27 / 4
Case 16
12 / 18 = (3 · x + 4) / 15
2 / 3 = (3 · x + 4) / 15
10 = 3 · x + 4
3 · x = 6
x = 2
Case 17
(x - 20) / 3 = (x - 11) / 18
18 · (x - 20) = 3 · (x - 11)
18 · x - 360 = 3 · x - 33
15 · x = 327
x = 109 / 5
Case 18
6 / (x + 16) = 7 / (3 · x + 3)
6 · (3 · x + 3) = 7 · (x + 16)
18 · x + 18 = 7 · x + 112
11 · x = 94
x = 94 / 11
To learn more on cross multiplication: https://brainly.com/question/15209325
#SPJ1
-5x=-35 cuánto es resultado
The Mid-High JV Team is playing in the state championship for football. In order
to beat their all-time points in a season record, they need to score more than 60
points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a
touchdown with an extra point (p) scores 7 points, which inequality best represents
the possible ways the team can score more than 60 points.
The inequality best represents the possible ways the team can score more than 60 points.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that, the Mid-High JV Team is playing in the state championship for football.
In order to beat their all-time points in a season record, they need to score more than 60 points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a touchdown with an extra point (p) scores 7 points.
We need to find the inequality best represents the possible ways the team can score more than 60 points.
3f+6t+7p>60
Hence, 3f+6t+7p>60 is the inequality best represents the possible ways the team can score more than 60 points.
To learn more on Inequality click:
https://brainly.com/question/28823603
#SPJ1
Find zeros of quadratic polynomial
x²+x -20
Answer:m,m,
Step-by-step explanation:
Answer:
Zeros:
x = -5x = 4Step-by-step explanation:
Given quadratic polynomial:
[tex]x^2+x -20[/tex]
The zeros of a function f(x) are the x-values that satisfy the equation f(x)=0.
Therefore, to find the zeros of the given function, set it to zero and solve for x.
Factor the quadratic:
[tex]\implies x^2+x-20=0[/tex]
[tex]\implies x^2+5x-4x-20=0[/tex]
[tex]\implies x(x+5)-4(x+5)=0[/tex]
[tex]\implies (x-4)(x+5)=0[/tex]
[tex]\boxed{\begin{minipage}{8.4 cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}[/tex]
Apply the Zero Product Property:
[tex]\implies x-4=0 \implies x=4[/tex]
[tex]\implies x+5=0 \implies x=-5[/tex]
Therefore, the zeros of the given quadratic polynomial are:
x = -5x = 4The force the attraction between two magnets is F Newtons. This force is inversely
proportional to the square of the distance, d centimetres, between the magnets.
(a) When the magnets are a certain distance apart, the force is 10 Newtons.
What is the force when the distance is doubled ?
(b) (i) Write down a formula connecting F,d and a constant k.
(ii) When the magnets are 3 cm apart, the force is 2 Newtons.
Find the force when they are 5 cm apart.
1a
f is inversely proportional to d² so when d is d f=10N and when d is doubled F is 5/2N
1bi K=Fd²
1bii
since K=fd² when d is 3cm and F is 2N k=18
then when d=5
F is 18/25N
Intermediate Value Theorem Help
According to the intermediate value theorem, every continuous function is a Darboux function.
Given that,
To discuss, what is Intermediate Value Theorem.
Darboux's theorem asserts that for a function f(x) that is differentiable on the domain [a, b], there exists some point c on the open interval (a, b) such that f′(c).
Here,
The intermediate value theorem is defined as that if the function is a continuous function over a domain [a, b] with domain values f(a) and f(b) at the interval's endpoints, then the function takes any value between f(a) and f(b) at any point inside the range.
Thus, According to the intermediate value theorem, every continuous function is a Darboux function.
Learn more about the intermediate value theorem here:
https://brainly.com/question/29436701
#SPJ1
What are the solutions of It - 2001 - 50 = 0?
O A. -250 and -150
OB. 40 and 50
O C. -150 and 250
OD. 150 and 250
Answer:
Step-by-step explanation:
d
Answer:
d
Step-by-stedp explanation:
On number 3 i need to find the following:
DF=
JH=
GJ=
m
m
please help and explain
Answer:
DF= 16m
JH= 14m
GJ= 19m
Step-by-step explanation:
turn the triangles until they overlap each other
since they are congruent, the measure of one angle will be the same for the other one
Answer:
DF= 16m JH= 14m GJ = 19m
Step-by-step explanation:
We know the two figures are equal to each other. So to find the missing sides just refer to the other figure with the included side.
Determine which situation is represented by the given dot plot. A. Billy bought between 0 and 6 shirts from each of his favorite 6 stores. B. Across the state, 15 cities were given a score between 0 and 15 regarding the cleanliness of their community. C. Henry has 15 classmates and each has between 0 and 6 pets. D. Each of Jessica's 6 friends has between $0 and $15 in his or her wallet.
The situation which can be used to represent the dot plot is "Henry has 15 classmates and each has between 0 and 6 pets".
The correct answer option is option C
Which situation represent the dot plot?A dot plot graph is a graph plotted by using small spots to represent data.
Henry has 15 classmates and each has between 0 and 6 pets
Each dot represent a pet
Total of Henry's classmates = 15Number of class mates with 0 pets = 2Number of class mates with 1 pets = 4Number of class mates with 2 pets = 2Number of class mates with 3 pets = 3Number of class mates with 4 pets = 2Number of class mates with 5 pets = 1Number of class mates with 6 pets = 1Consequently, the dot plot represent Henry's situation of having 15 classmates and each has between 0 and 6 pets
Read more on dot plot:
https://brainly.com/question/10639189
#SPJ1
I need help please i don’t understand
Alex went bowling. He managed to get 3 strikes after 15 attempts. If you were to suggest the probability that he gets a strike on his next attempt, what type of probability would you be using?.
Theoretical Probability because its what should happen but experimental is what happens
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
it is binomial probability p=3/15 = 1/5 = 0.2
or at the very least geometric
To learn more about Probability visit:https://brainly.com/question/11234923
#SPJ4
coach jenson bought 15 shirts for $180 for the basketball team. the unit rate for the shorts was 1.50 less than the unit rate for shirts. choach jenson bought the same number of shorts as shirts to complete each uniform. What was the total cost of the uniforms for the team? explain your answer
Answer:
$337.50
Step-by-step explanation:
To find the total cost of the uniforms, you will need to find the unit price of the shirts and the unit price of the shorts and then multiply each by the number of shirts and shorts, respectively.
The unit price of the shirts is the total cost divided by the number of shirts, or $180 / 15 shirts = 12/shirt.
The unit price of the shorts is
$12/shirt - $1.50/shirt = 10.5/shirt.
Since the coach bought the same number of shirts and shorts, the total number of shirts and shorts is 15 shirts + 15 shorts = 30 shirts and shorts.
The total cost of the shirts is $12/shirt * 15 shirts = $12*15 = 180.
The total cost of the shorts is $10.5/shirt * 15 shirts = 157.5
The total cost of the uniforms is the sum of the cost of the shirts and the cost of the shorts, or $180 + 157.5= 337.5.
Therefore, the total cost of the uniforms for the team is $337.5.
Breanne plans to invest her money into a simple interest savings account. Currently she has $14,374 to invest and the current market rate is 3.3% for annual interest yield. How long (in years) will Breanne need to leave the money in the account for it to earn $7,758 in interest? Round answer to the nearest hundredth (2 decimal places) of a year.
The intrest will be X=1293000/79057.
What is intest ?Interest is the price of you pay to borrow money or it is cost you charge to lend money.
Based on the given condition we know that
{P=14374
{R=3.3%
{I=7758
Formulate and substitute
Substitute {P=14374
{R=3.3%
{I=7758
These are into formula I=Prt
7758=14374rt
We have to solve the equation
14374×0.033x=7758
Multiply
474.342x=7758
Devide both sides
X = 7758/474.342
By calculating we can get
X =1293000/79057
To know more about intrest click-
https://brainly.com/question/25793394
#SPJ1
When dividing 80 by 9, what is the remainder?
Answer:
8
Step-by-step explanation:
The number 80 is called the numerator or dividend, and the number 9 is called the denominator or divisor.
The quotient (integer division) of 80/9 equals 8; the remainder (“left over”) is 8.
80 is the dividend, and 9 is the divisor.
What is the slope of a line perpendicular to the line whose equation is 3x-6y=90. Fully simplify your answer.
Answer:
the slope is 0.5 or 1/2
Step-by-step explanation:
3x - 6y = 90
-6y = -3x + 90
y = 0.5x + 90
Answer:
slope= 1/2
Step-by-step explanation:
3x-6y=90
rewrite the equation into slope intercept form
y=1/2x-15
subtracting is the same as adding the opposites
y=1/2x+(-15)
since the equation is written in slope intercept form, y=mx+b, identify the slope of the line as the coefficient next to the variable x
y=1/2x+(-15), m=1/2
identify the y intercept of the lines as the constant term
y=1/2x+(-15),m(slope)=1/2,b=-15
Which model represents a function?
Model III represents a function by vertical line test.
What is Vertical line test?
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
The vertical line test concludes that a curve in the plane represents the graph of a function if and only if no vertical line intersects it more than once.
According to the given question:
Graph I has vertical line intersections more than one on many points of the curve. Therefore, Graph I does not represents a function.
Model II has two values for the domain point that is -5 has two images 2 and 10. Hence it does not represents a function.
Graph III has only one intersection by vertical lines on the curve. Therefore, Graph III represents a function.
Graph IV has two intersection points if a vertical line passes through the curve. Hence, Graph IV does not represents a function.
To know more about vertical line test visit
https://brainly.com/question/17008719
#SPJ1
I need some step to solve this please
Answer:
MN = 50
Step-by-step explanation:
You want the length of the base segment MN in triangle MNO, where MN is marked 41+3x and parallel midsegment PQ is marked 49-8x.
MidsegmentThe midsegment is half the length of the parallel base segment. That means the base segment is double the length of the midsegment:
MN = 2·PQ
41 +3x = 2(49 -8x)
41 +3x = 98 -16x
19x = 57 . . . . . . . . add 16x-41
x = 3
MN = 41 +3x = 41 +3·3 = 50
The length of MN is 50 units.
how can confidence intervals help researchers attain their purpose of using a sample to understand a population?
The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .
In the question ,
we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,
we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .
the confidence interval are useful because ,
(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .
(ii) they make data analyses richer and help us to make more informed decisions about the research questions .
Therefore , the reason how confidence interval helps is mentioned above.
Learn more about Confidence Interval here
https://brainly.com/question/20309162
#SPJ4
Name each polynomial by degree and number of terms.
-6x^4-2x^2+2
A. quintic binomial
B. quadratic binomial
C. quartic trinomial
D. quartic monomial
Reason:
It's a quartic because the largest exponent is 4 (so the degree is 4).
It's a trinomial since it has 3 terms.
the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection.
For each binomial experiment described, find
A. the mean
B. the variance
C. the standard deviation
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
Learn more about probability visit:
brainly.com/question/11234923
#SPJ4
How many square inches of gift wrap will be needed to cover a box that is 5in x 7in x 3in?
Answer:
65 sq.inches
Step-by-step explanation:
To find the total surface area of a box, you need to calculate the area of each of its faces and add them together. In this case, the box has three faces with dimensions 5 inches by 7 inches, and three faces with dimensions 5 inches by 3 inches.
The total surface area of the box is therefore:
(5 * 7) * 2 + (5 * 3) * 2 = 35 + 30 = 65 square inches
This means that you will need 65 square inches of gift wrap to cover the box.
Hope this helps you
Answer: 142 squared inches of gift wrap
Step-by-step explanation:
To find how many square inches of gift wrap you would need, you would use the formula for the surface area of the box (rectangle)
Formula: 2 ( length x width + width x height + height x length ) = Surface AreaNow plug the numbers in from the given dimensions
2 ( 7 x 5 + 5 x 3 + 3 x 7 ) = Surface AreaNow solve...
2 ( 7 x 5 + 5 x 3 + 3 x 7 ) = 142Giving you the answer of 142 squared inches of gift wrap
Hope this is correct and helpful! ^^
PLEASE HELP!!!!!!!!!!!