Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
So, we are given:
[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]
First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.
[tex]x\neq 0[/tex]
Now, cross multiply.
[tex]3(x^2)=x(4x+3)[/tex]
[tex]3x^2=4x^2+3x[/tex]
Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).
[tex]3x=4x+3[/tex]
[tex]-x=3[/tex]
[tex]x=-3[/tex]
We didn't run into any possibilities for extraneous solutions.
Please help. I’ll mark you as brainliest if correct!
Answer:
8lb of the cheaper Candy
17.5lb of the expensive candy
Step-by-step explanation:
Let the cheaper candy be x
let the costly candy be y
X+y = 25.5....equation one
2.2x +7.3y = 25.5(5.7)
2.2x +7.3y = 145.35.....equation two
X+y = 25.5
2.2x +7.3y = 145.35
Solving simultaneously
X= 25.5-y
Substituting value of X into equation two
2.2(25.5-y) + 7.3y = 145.35
56.1 -2.2y +7.3y = 145.35
5.1y = 145.35-56.1
5.1y = 89.25
Y= 89.25/5.1
Y= 17.5
X= 25.5-y
X= 25.5-17.5
X= 8
given g(x)=3/x^2+2x find g^-1(x)
Answer:
A
Step-by-step explanation:
[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]
Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.
Determine whether 52c2y4 is a monomial, binomial, trinomial, or other polynomial.
Answer: Monomial.
Step-by-step explanation:
Ok, when we have a polynomial with only one term, this is a monomial.
If the polynomial has two terms, this is a binomial.
If the polynomial has 3 terms, this is a trinomial.
And so on.
In this particular case we have:
52*c^2*y^4
Where c and y may be variables.
We can see that here we have only one term, so this would be a monomial.
(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)
Answer:
binomial.
Step-by-step explanation:
The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.
Kirsten has 9 syrup containers from a local cafe. There are 6 milliliters of syrup per container.
Answer: 54 mL
Step-by-step explanation:
Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.
Hope it helps <3
Determine the zeros of r=2sin5theta
Answer:
[tex]\theta=\frac{n\pi}{5}[/tex]
Step-by-step explanation:
You have the following function:
[tex]r=2sin5\theta[/tex] (1)
In order to find the zeros of the function you equal to zero the equation (1), and then you solve for θ:
[tex]2sin5\theta=0\\\\sin5\theta=0\\\\5\theta=sin^{-1}(0)=n\pi;\ \ \ \ n=0,1,2,3,..\\\\\theta=\frac{n\pi}{5}[/tex]
Then, there are infinite zeros for the function of the equation (1), because n has infinite positive integers values.
Answer:
θ = 0, pi/5, 2pi/5, 3pi/5, 4pi/5 ,pi
Step-by-step explanation:
if my grade is 69% what will my grade be if i got a 3.3 of 4 on a essay and it's worth 25% of my grade?
Answer:
72.4%
Step-by-step explanation:
The essay is 25% of your grade, and the rest is 75% of your grade.
25 (3.3/4) + 75 (0.69) ≈ 72.4
plz help.... 2|x-3|-5=7
Answer:
x = -3 and x = 9.
Step-by-step explanation:
2|x - 3| - 5 = 7
2|x - 3| = 12
|x - 3| = 6
x - 3 = 6
x = 9
-(x - 3) = 6
-x + 3 = 6
-x = 3
x = -3
Hope this helps!
Answer:
x=9 x=-3
Step-by-step explanation:
2|x-3|-5=7
Add 5 to each side
2|x-3|-5+5=7+5
2|x-3|=12
Divide by 2
2/2|x-3|=12/2
|x-3|=6
There are two solutions to an absolute value equation, one positive and one negative
x-3 =6 x-3 = -6
Add 3 to each side
x-3+3 = 6+3 x-3+3 = -6+3
x=9 x = -3
please help!!!!!!!!!!!!
Answer:
csc B = 13/12
Step-by-step explanation:
csc B = 1 / sin B
The sin B is
sin B = opp/ hyp so
csc B = hyp /opp
csc B = 26 / 24
csc B = 13/12
Answer:
13/12
Step-by-step explanation:
sin θ = opposite/ hypotenuse
csc θ = 1/sinθ
csc θ = hypotenuse/opposite
csc (B) = 26/24
csc (B) = 13/12
What is 3/8 + 1/8 + 2/3 + 1/2 equal?
Answer:
5/3
Step-by-step explanation:
3/8 + 1/8 + 2/3 + 1/2
=> [ 3/8 + 1/8 ] + [ 2/3 + 1/2 ]
=> 1/2( or 4/8 ) + 7/6
=> 10/6 or 5/3
Answer:
[tex] \frac{3}{8} + \frac{1}{8} + \frac{2}{3} + \frac{1}{2} [/tex]
Add the fractions with the same common denominator
That's
[tex] \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2} [/tex]
So we have
[tex] \frac{1}{2} + \frac{2}{3} + \frac{1}{2} [/tex]
Add the fractions with the same common denominator
That's
[tex] \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1[/tex]
We have
[tex] 1 + \frac{2}{3} [/tex]
That's
[tex] \frac{1}{1} + \frac{2}{3} [/tex]
Find the common denominator
The common denominator is 3
[tex] \frac{1}{1} + \frac{2}{3} = \frac{3 + 2}{3} [/tex]
[tex] = \frac{5}{3} \: \: \: \: \: \: or \: \: \: \: \: \: \: 1 \frac{2}{3} [/tex]
Hope this helps you
When evaluating a multiple regression model, for example when we regress dependent variable Y on two independent variables X1 and X2, a commonly used goodness of fit measure is:
Answer:
Adjusted-R2
Step-by-step explanation:
When evaluating a multiple regression model, a commonly used goodness of fit is the adjusted-R2. It allows for a comparison of regression models with multiple predictors or independent variables. The addition of independent variables usually causes the model to be more reliable. The adjusted-R2 considers the effect of additional independent variables. It usually adjusts for the number of terms in the model.
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
Answer:
x>3
Step-by-step explanation:
The Cambridge Power and Light Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for electrical service last month:
53 49 54 50 21 46 75 45 63 76 61 63 36 34 54 63 37 62 66 62
(a) Compute the arithmetic mean.(Round your answer to 2 decimal places. Omit the "$" sign in your response.)
The mean is $
(b) Indicate whether it is a statistic or a parameter.
Answer:
a) the mean is $53.50
b) it is a statistic
Step-by-step explanation:
mean = ∑fx/∑f
∑f = 20
mean = (sum of the terms) ÷ (number of terms)
mean = (53+49+54+50+21+46+75+45+63+76+61+63+36+34+54+63+37+62+66+62) ÷ 20 = 1070/20
=$53.50
b) it is statistics because it is a random sample of 20 residential customers not the actual population
The slope of a line is 1/3 . What is the slope of a line perpendicular to this line? A. -3 B. 3 C. 1/3 D. -1/3
Answer:
The answer is option A
Step-by-step explanation:
Since the lines are perpendicular the slope perpendicular line is the negative inverse of the original line and when they are multiplied should give - 1
Let m be the slope of the perpendicular line
That's
1/3 × m = - 1
multiply through by 3
m = - 3
The slope of the perpendicular line is - 3
Hope this helps you
Answer:
-3
Step-by-step explanation:
A building feet tall casts a foot long shadow. If a person looks down from the top of the building, what is themeasure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)
do not know because my brain cant focus on this sorry :/
Help ASAP!!!!
Solve for X. Round to the nearest hundredth if necessary.
Answer:
11.47Step-by-step explanation:
Given : A right triangle
To do : Solve for x
Solution,
[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )
[tex]0.5736 = \frac{x}{20} [/tex]
multiply both sides of the equation by 20
[tex](0.5736) \times 20 = x[/tex]
Calculate the product
[tex]11.471 = x[/tex]
Swipe both sides of the equation
[tex]x = 11.471[/tex]
Round answer to nearest hundredth
[tex]x = 11.47[/tex]
Hope this helps...
Best regards!!
Question 12
<
>
1
The tank for a car holds 17 gallons. The gasoline gauge shows the tank is full. How much gas is still in
4
the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The tank for a car holds 17 gallons. The gasoline gauge shows the tank is 3/4 full. How much gas is still in the tank?
Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
Answer:
[tex]Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]
Step-by-step explanation:
The tank for a car holds 17 gallons.
The gasoline gauge of the car shows that the tank is 3/4 full.
We are asked to find the remaining gasoline in the tank.
[tex]Gas \: \:left = \frac{3}{4} \times 17 \\\\Gas \: \:left = \frac{51}{4} \\\\Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]
Therefore, the remaining gas in the tank is [tex]12\frac{3}{4}[/tex] gallons.
Alternatively:
[tex]1 - \frac{3}{4} = \frac{1}{4}[/tex]
Amount of gasoline consumed = [tex]\frac{1}{4} \times 17 = \frac{17}{4}[/tex]
Amount of gasoline left = total - consumed
Amount of gasoline left = [tex]17 - \frac{17}{4} = 12\frac{3}{4} \:\: gallons[/tex]
Identify the correct HYPOTHESES used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. H0: p = 12 vs. H1: p < 12
b. H0: ? = 12 vs. H1: ? < 12
c. H0: p = 12 vs. H1: p > 12
d. H0: ? = 12 vs. H1: ? > 12
Answer:
The null hypothesis is ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
Step-by-step explanation:
Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1
The null hypothesis is as follows ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
The number that is 75% of one less than a number n. As an expression THX!!!! i Promise to mark you brainliset
Answer:
x = [tex]\frac{3}{4}(n-1)[/tex]
Step-by-step explanation:
It's given in the question that '' The number is 75% of one less than a number n"
Let the number is 'x'.
One less than a number 'n' will be = (n - 1)
75% of one less than a number will be = 75% of (n -1)
= [tex]\frac{75}{100}(n-1)[/tex]
= [tex]\frac{3}{4}(n-1)[/tex]
Therefore, the desired expression to get the number 'x' will be,
x = [tex]\frac{3}{4}(n-1)[/tex]
Answer:
3/4(n-1)
Step-by-step explanation:
did it in rsm
Which would give a significantly smaller value than 1.19 x 10^-2 and which would give a significantly larger value?
1.19 x 10^-2 + 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 - 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 x 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 / 1.07 x 10^-2 (this problem is division) smaller or larger?
Answer:
a) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex]; b) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; c) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; d) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
Step-by-step explanation:
a) Is [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19+1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex]2.26 \times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex].
b) Is [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19-1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex][1.19+(-1.07)]\times 10^{-2}[/tex] Subtraction.
4) [tex]0.12\times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
c) Is [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 1.07)\cdot (10^{-2}\times 10^{-2})[/tex] Associative property/Commutative property.
3) [tex]1.27\times 10^{-4}[/tex] Multiplication/ ([tex]a^{b}\cdot a^{c} = a^{b+c}[/tex])/ [tex](-x)\cdot (-y) = x\cdot y[/tex] /Result.
[tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
d) Is [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})^{-1}[/tex] Division.
3) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{2})[/tex] ([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex](-x)\cdot (-y) = x\cdot y[/tex])
4) [tex](1.19\times 1.07)\cdot (10^{-2}\cdot 10^{2})[/tex] Associative property/Commutative property.
5) [tex]1.27[/tex] Multiplication/([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex]a^{0} = 1[/tex])/Modulative property/Result.
[tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
Which is the graph of linear inequality x - 2y 2-12?
10
10
10
1034
Help asappp!!!pls
It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.
also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.
dunno if I explained it very well
The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is the inequality as -
x - 2y² < 12
The given inequality is -
x - 2y² < 12
2y² - x < - 12
2y² < x - 12
y² < (x/2) - 6
[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]
[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]
and
[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]
Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.
Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
To solve more questions on inequality, visit the link-
https://brainly.com/question/11897796
#SPJ7
Write Given f(x)=2−4x−−−−−√ and g(x)=−3x, find the following: a. (g∘f)(x) the domain and range of the function using interval notation.
Answer:
If we have two functions g(x) and f(x)
I suppose that the functions here are:
f(x) = 2 - √(4*x)
g(x) = -3*x
First, let's analyze the functions:
g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.
f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.
The domain of f is D = x ∈ {0, ∞}
Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)
We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):
D = x ∈ {0, ∞}
Last week Holly took a math test. She got 98 out of 123 question correct. What percentage did Holly get correct? Round to the nearest hundredth.
Answer:
79.67%
Step-by-step explanation:
To find the percentage correct, take the number correct over the total
98/123
.796747967
Change to a percent by multiplying by 100 %
79.6747967%
Round to the nearest hundredth
79.67%
Answer:
79.67%
Step-by-step explanation:
percent = part/whole * 100%
percent = 98/123 * 100%
percent = 79.67%
CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
The adult ticket costs $18 and the children ticket costs $13.
Step-by-step explanation:
Let the price of the adult ticket be a.
Let the price of the children ticket be c.
Three adults and four children must pay $106. This implies that:
3a + 4c = 106 _______(1)
Two adults and three children must pay $75. This implies that:
2a + 3c = 75 ________(2)
We have two simultaneous equations:
3a + 4c = 106 _____(1)
2a + 3c = 75 ______(2)
Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):
6a + 9c = 225
- (6a + 8c = 212)
c = $13
Put this value of c in (2):
2a + 3*13 = 75
2a + 39 = 75
=> 2a = 75 - 39
2a = 36
a = 36/2 = $18
Therefore, the adult ticket costs $18 and the children ticket costs $13.
Does this graph show a function? Explain how you know.
O A. No; there are yvalues that have more than one x-value.
ОО
B. Yes; there are no y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
ОО
D. Yes; the graph passes the vertical line test.
It is possible to draw a single straight line to pass through more than one point on the red curve. Therefore, the graph fails the vertical line test. We have cases where one input leads to more than one output.
Which of the following functions is graphed below?
O A. y=x-4-2
O B. y=x+4-2
O C. y = x+4+2
D. y = x - 4+2
Answer:
Option (B)
Step-by-step explanation:
Given question is not complete; find the complete question in the attachment.
In the graph attached,
Parent function is an absolute value function,
f(x) = |x|
When this graph is shifted 4 units left, rule for the translation will be,
f(x) → f(x + 4)
Therefore, the new function of above translation will be,
g(x) = f(x + 4) = |x + 4|
Now the graph is shifted 2 units down so the translated function will be,
h(x) = g(x) - 2
h(x) = |x + 4| - 2
If we rewrite the function in the form of an equation, graph will be represented by
⇒ y = |x + 4| - 2
Therefore, Option (B) will be the answer.
You decide not to use your car and cycle to work every day.
You calculate that you will cycle 350 miles a month.
How many kilometres is this? (Use 5 miles to approximately 8 km).
km.
Answer:
560 km
Step-by-step explanation:
350x8/5=
350x1.6=
560
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
To learn more about the integers;
brainly.com/question/1768254
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Graph parallelogram ABCD on the graph
below with vertices A(2,0), B(7,0), C(10,3),
D (5,3). What is the area of parallelogram
ABCD?
Answer: 25 square units
Step-by-step explanation:
We mark the points, A(2,0), B(7,0), C(10,3), D (5,3). on a graph and then joined them to make parallelogram ABCD as provided in the attachment.
Area of parallelogram = Base x corresponding height
From the figure, base AB = 7 - 2 units = 5 units
corresponding height: h= 5 units
Now , Area of parallelogram ABCD = base AB x corresponding height
= 5 x 5 square units
= 25 square units
Hence, the area of parallelogram ABCD is 25 square units .
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem, and then find the values of the six trigonometric functions for angle B. Rationalize denominators when applicable. b=4, c=7
Answer:
Side a^2 = 49 + 16
Side a^2 = 65
Side a = 8.062
sin (B) = 4 / 8.062
cos (B) = 7 / 8.062
tan (B) = 4 / 7
cot (B) = 7 / 4
sec (B) = 8.062 / 7
csc (B) = 8.062 / 4
Step-by-step explanation:
What is x when: |3x–1|=8
Answer:
x=3 or/and x= -7/3
Step-by-step explanation:
3x-1= 8+1= +1
3x = 9
9 divided by 3 is x= 3
3x-1= -8+1= +1
3x = -7
-7 divided by 3 is x= -7/3
Answer:
[tex]\huge\boxed{x=3\ \vee\ x=-\dfrac{7}{3}}[/tex]
Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&\text{for}\ a\geq0\\-a&\text{for}\ a<0\end{array}\right\\\\|a|=k\to a=k\ \vee\ a=-k\ \text{for}\ k>0\\==========================\\\\|3x-1|=8\iff3x-1=8\ \vee\ 3x-1=-8\\\\\begin{array}{cccc}3x-1=8&\vee&3x-1=-8&\text{add 1 to both sides}\\3x-1+1=8+1&\vee&3x-1+1=-8+1\\3x=9&\vee&3x=-7&\text{divide both sides by 3}\\\dfrac{3x}{3}=\dfrac{9}{3}&\vee&\dfrac{3x}{3}=\dfrac{-7}{3}\\x=3&\vee&x=-\dfrac{7}{3}\\\end{array}[/tex]