Answer:
[tex]\frac{1}{2} z[/tex]
Step-by-step explanation:
Taxi company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another if x represents the number of miles driven by taxi which linear equation can be used to solve this problem and how many miles did Isaac travel rounded to the nearest tenth
Answer:
The answer is B
Step-by-step explanation:
$2.50+$1.95=$27.46
-2.50
24.69
24.63/1.95
equal $12.80 or 12.8
Answer:
B) 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
Step-by-step explanation:
Convert 95 lbs to grams
Answer:
43091.3 or 43181.81(81 repeated)
Step-by-step explanation:
There are two answers because it depends on the method you use. You can get the second answer by plugging 95 into the equation gram*0.0022=pound or gram=(pound/0.0022). When you insert the 95, you get 43181.81(81 repeated).You can find the first answer by just looking it up on the conversion chart on google.
Answer:
43091.275 Grams
Step-by-step explanation:
95 pounds is equal to 43091.275 grams.
Multiply the mass value by 453.592
Which formula can be used to find the nth term of a geometric sequence where the first term is 8 and the common ratio is –3?
Answer:
f(n)=8(-3)^(n-1)
The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,
⇒ - 8/3 × (- 3)ⁿ
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
We have to given that;
The first term is, 8
And, the common ratio is –3
Now,
The nth term of a geometric sequence is:
⇒ T (n) = arⁿ⁻¹
Put a = 8 and r = - 3
⇒ T (n) = 8 (- 3)ⁿ⁻¹
⇒ T (n) = - 8/3 × (- 3)ⁿ
Thus, The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,
⇒ - 8/3 × (- 3)ⁿ
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Find the equation of the quadratic function with roots -8 and -6, "a" less than zero, and a vertex at (-7, 2).
ANSWER
[tex]y = - 2{x}^{2} -28x - 96[/tex]
EXPLANATION
We have that
[tex]x = - 8 \: \: and \: \: x = - 6[/tex]
are the roots of the quadratic function.
This implies that
[tex]x + 8 \: \: and \: \: x + 6[/tex]
are factors of the quadratic function.
The quadratic function will have an equation of the form:
[tex]y = a(x + 8)(x + 6)[/tex]
It was also given that, the vertex of the function is at
[tex](-7, 2)[/tex]
This point must satisfy the equation.
This implies that:
[tex]2= a( - 7 + 8)( - 7+ 6)[/tex]
This implies that,
[tex]2=-a[/tex]
[tex]a = - 2[/tex]
We substitute the value of 'a' to get the equation in factored form as:
[tex]y = - 2(x + 8)(x + 6)[/tex]
We expand the parenthesis to write the equation in standard form.
[tex]y = - 2( {x}^{2} + 6x + 8x + 48)[/tex]
[tex]y = - 2( {x}^{2} + 14x + 48)[/tex]
[tex]y = - 2{x}^{2} -28x - 96[/tex]
Or in vertex form, the equation is
[tex]y = - 2 {(x + 7)}^{2} + 2[/tex]
What is the slope of the line identified by 7Y= -2( X -4)?
Answer:
-2/7
Step-by-step explanation:
1. simplify the right side of equation by mult
2. divide by seven
3. whatever is being multiplied by x is the slope
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The slope of the linear equation 7Y= -2(X - 4) will be negative 2/7.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
7Y= -2(X - 4)
Simplify the equation in the slope-intercept form will be
7Y= -2X + 8
Y = (-2/7)X + 8/7
Then the slope of the linear equation 7Y= -2(X - 4) will be negative 2/7.
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4:x::5:15 SLOVE IT AND EXPLAIN
Answer:
x = 12
Step-by-step explanation:
Assuming you reqire the value of x that makes
4 : x equivalent to 5 : 15
Divide 5 by 4, that is 5 ÷ 4 = 1.25
Thus 1.25x = 15 ( divide both sides by 1.25 )
x = 12
Hence
4 : 12 = 5 : 15
A bookshop has 30816exercise books which were packed in cartons.Each carton contained 24 exercise books.The mass of an empty carton was 2kg and of a full carton is 12kg. What was the total mass of the empty cartons?
Answer:
2568 kg
Step-by-step explanation:
30816 divided by 24 gives us 1284 or the total number of cartons which can then be multiplied by 2 to give us the weight of the empty cartons.
To find the total mass of the empty cartons, divide the total number of exercise books by the number of exercise books in each carton and then multiply by the difference in mass between a full and empty carton.
Explanation:To find the total mass of the empty cartons, we need to determine how many cartons there are and the difference in mass between a full carton and an empty carton.
Given that each carton contains 24 exercise books and there are 30816 exercise books in total, we can calculate the number of cartons by dividing the total number of exercise books by 24.
So, there are 1284 cartons in total.
Now, we need to find the difference in mass between a full carton and an empty carton. The difference is 12 kg - 2 kg = 10 kg.
To find the total mass of the empty cartons, we multiply the number of cartons by the mass difference: 1284 cartons * 10 kg/carton = 12840 kg.
Therefore, the total mass of the empty cartons is 12840 kg.
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Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). Sketch the curves.
Answer:
3√3
Step-by-step explanation:
r = 3 cos θ
r = 2 - cos θ
First, find the intersections.
3 cos θ = 2 - cos θ
4 cos θ = 2
cos θ = 1/2
θ = -π/3, π/3
We want the area inside the first curve and outside the second curve. So R = 3 cos θ and r = 2 - cos θ, such that R > r.
Now that we have the limits, we can integrate.
A = ∫ ½ (R² - r²) dθ
A = ∫ ½ ((3 cos θ)² - (2 - cos θ)²) dθ
A = ∫ ½ (9 cos² θ - (4 - 4 cos θ + cos² θ)) dθ
A = ∫ ½ (9 cos² θ - 4 + 4 cos θ - cos² θ) dθ
A = ∫ ½ (8 cos² θ + 4 cos θ - 4) dθ
A = ∫ (4 cos² θ + 2 cos θ - 2) dθ
Using power reduction formula:
A = ∫ (2 + 2 cos(2θ) + 2 cos θ - 2) dθ
A = ∫ (2 cos(2θ) + 2 cos θ) dθ
Integrating:
A = (sin (2θ) + 2 sin θ) |-π/3 to π/3
A = (sin (2π/3) + 2 sin(π/3)) - (sin (-2π/3) + 2 sin(-π/3))
A = (½√3 + √3) - (-½√3 - √3)
A = 1.5√3 - (-1.5√3)
A = 3√3
The area inside of r = 3 cos θ and outside of r = 2 - cos θ is 3√3.
The graph of the curves is:
desmos.com/calculator/541zniwefe
The area of the region inside r=3cos(\theta) and outside r=2-cos(\theta) is obtained by integrating the square of each function times 1/2 over their intersection interval and subtracting the results.
Explanation:The student is tasked with finding the area of a region bounded by two polar curves r=3cos(\theta) and r=2-cos(\theta). This involves sketching the curves to identify the area that lies inside the first curve and outside the second one. To find the area of the region, we calculate the difference between the integrals of the two functions over the interval where they intersect. This requires setting up and evaluating definite integrals in polar coordinates. The integral calculation would involve integrating the function r^2/2 from the lower to the upper bound of \(\theta\) for each curve and then subtracting the area inside r=2-cos(\theta) from the area inside r=3cos(\theta).
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the sqaure of 9 less than a number is 3 less than the number
The student's mathematics problem requires solving a quadratic equation derived from the statement that the square of '9 less than a number' equals '3 less than the number'. By expanding, rearranging, and factoring the quadratic equation, we find that the number in question is 12.
Explanation:The student's question involves solving an algebraic equation to find an unknown number.
Let's denote the unknown number as x.
The problem states that the square of 9 less than the number is 3 less than the number itself.
This can be represented as the equation:
(x - 9)^2 = x - 3
To solve for x, we will follow these steps:
Expand the left side of the equation: x^2 - 18x + 81 = x - 3.Subtract x from both sides to set the equation to zero: x^2 - 19x + 84 = 0.Factor the quadratic equation: (x - 7)(x - 12) = 0.Find the values of x that make each factor equal to zero: x = 7 and x = 12.Therefore, the two possibilities for the unknown number are 7 and 12.
We must check which one satisfies the original equation, and we find that x = 12 is the correct solution.
=
factorise 4y^2 – 4y + 1
Answer:
[tex](2y-1)^{2}[/tex]
Step-by-step explanation:
[tex]4y^{2} -4y+1[/tex]
Sum = -4
Product = 1
Factors = -1 , -1
[tex](2y-1)^{2}[/tex]
what factorization of the binomial below 12x^2-x-35
Answer:
(3x + 5)(4x - 7)
Step-by-step explanation:
The most common factors of 35 are 5 and 7. The 12 is a nuisance.
We could try 6 and 2 or 3 and 4 or even 12 and 1. You just have to juggle a bit to get the difference to be - x.
I'm going to try 3 and 4 first with 5 and 7. The numbers you get for the middle term have to be quite close.
(3x 5)(4x 7) Oops. It's going to come out first try.
Now you need to get the middle term come to - 1
(3x - 5)(4x + 7)
Just to make it slightly harder, I'll do it the wrong way first.
-5*4x + 3x*7 = - 20x + 21x = x That is close. Only the signs are incorrect.
So try again.
(3x + 5)(4x - 7)
20x - 21x = - x
which of the following points are solutions to the system of inequalities shown below? can someone please answer now
check all that apply
y>6x+5
y<-6x+7
answers:
a. (-2,18)
b. (8,8)
c. (2,17)
d. (0,6)
e. (-2,19)
f. (2,18)
Answer:
(-2, 18)(0, 6)Step-by-step explanation:
A graph shows that only the points listed above are within the doubly-shaded area. Points on the boundary line are not solutions, since the inequalities do not include the "or equal to" case.
Which expression is equivalent to ( 256x^16 )^1/4
Answer: 4x^4
Step-by-step explanation:
Firstly, let's apply the ^1/4 to the 256
The fourth root of 256 is 4, that will be the coefficient in our answer
Next, let's apply the ^1/4 to the x^16
The power of powers property says we can multiply the two exponents as so:
(x^16)^1/4 = x^(16*1/4) = x^4
Now combine the 4 and x^4 to get: 4x^4
You need to buy 5 notebooks for your classes at school.Each notebook costs $2.79. What is the total cost before tax?
Answer:
$13.95
Step-by-step explanation:
You need to multiply the 5 notebooks with the costs of each notebook, which gives you the total costs before tax.
factor and solve to find roots
x squared -x - 90 =0
[tex]x^2-x-90=0\\x^2+9x-10x-90=0\\x(x+9)-10(x+9)=0\\(x-10)(x+9)=0\\x=10 \vee x=-9[/tex]
What is the solution of the equation 3x – 1 = 7? Round your answer to the nearest ten-thousandth
Answer:
x = 2.6667 (rounded)
Step-by-step explanation:
Move the constant to the right side and change its sign.
3x = 7 + 1.
Add the numbers.
3x = 8.
Divide both sides by 3.
x = 8/3 = 2.6667 (Rounded to the nearest ten-thousandth).
Hope this helps.
The solution of the equation, rounding the answer to the nearest ten-thousandth, is x = 2.6667.
Algebraic equationTo find the solution of the equation 3x - 1 = 7, we can follow these steps:
Step 1: Add 1 to both sides of the equation to isolate the term with x.
3x - 1 + 1 = 7 + 1
3x = 8
Step 2: Divide both sides of the equation by 3 to solve for x.
3x/3 = 8/3
x = 8/3
Step 3: Convert the fraction 8/3 to a decimal.
x ≈ 2.6667
Rounding the decimal to the nearest ten-thousandth, the solution of the equation is approximately x = 2.6667.
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How does the context of a data set affect how the data is interpreted?
Answer:
Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average.
Step-by-step explanation:
The standard deviation can never be a negative number, due to the way it’s calculated and the fact that it measures a distance (distances are never negative numbers).The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same.
The standard deviation is affected by outliers (extremely low or extremely high numbers in the data set). That’s because the standard deviation is based on the distance from the mean. And remember, the mean is also affected by outliers.
The standard deviation has the same units as the original data.
Final answer:
The context of a dataset influences its interpretation by providing background information that affects understanding. Different contexts can lead to varying interpretations of the same dataset. Understanding context is essential for accurate data interpretation and decision-making.
Explanation:
The context of a data set affects how the data is interpreted by providing background information and circumstances that influence the understanding of the data. For example, in statistics, when analyzing a dataset related to economic growth, the context of the data such as the time period or the country it represents can significantly impact the conclusions drawn.Context can lead to different interpretations of the same data set. For instance, a graph showcasing unemployment rates over time can be interpreted positively or negatively based on the context. If the data is during a recession, the interpretation would differ from a period of economic growth.Understanding the context of a data set is crucial for accurate interpretation and decision-making. It helps in avoiding misinterpretations and ensures that conclusions drawn are valid and relevant to the situation at hand.2 1/3 divided by 3 equal what
Answer:
7/6 is the answer, or as a mixed fraction, 1 1/6
Step-by-step explanation:
Turn 2 1/3 into an improper fraction. This gives 7/3. Since dividing by 3 is the same as multiplying by 1/2, 7/3 * 1/2 multiply top and bottom with each other to get 7/6 as your answer.
Hope this helps!
Answer:
[tex]\frac{7}{9}[/tex]
Step-by-step explanation:
2[tex]\frac{1}{3}[/tex] ÷3
= [tex]\frac{7}{3}[/tex] ÷3
= [tex]\frac{7}{3}[/tex] x [tex]\frac{1}{3}[/tex]
= [tex]\frac{7}{9}[/tex]
Which of the following is the slope and y-intercept of the graph -y= -0.9x + 4 ?
To find the slope and y-intercept of the equation -y = -0.9x + 4, multiply both sides by -1 to get y = 0.9x - 4, revealing a slope of 0.9 and a y-intercept of -4.
Explanation:To find the slope and y-intercept of the graph -y = -0.9x + 4, we first need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By multiplying both sides of the equation by -1, we get y = 0.9x - 4. Here, it's clear that the slope (m) is 0.9 and the y-intercept (b) is -4.
This means that for every increase of 1 on the horizontal axis (x), there is a rise of 0.9 on the vertical axis (y). Additionally, the point where the line intersects the y-axis is at y = -4.
If x=5-2√6 then find
1. 1/x
2. x-1/x
3. x+1/x
Answer:
[tex]\large\boxed{1.\ \dfrac{1}{x}=5+2\sqrt6}\\\boxed{2.\ \dfrac{x-1}{x}=-4-2\sqrt6}\\\boxed{3.\ \dfrac{x+1}{x}=6+2\sqrt6}[/tex]
Step-by-step explanation:
[tex]x=5-2\sqrt6\\\\1.\\\\\dfrac{1}{x}=\dfrac{1}{5-2\sqrt6}=\dfrac{1}{5-2\sqrt6}\cdot\dfrac{5+2\sqrt6}{5+2\sqrt6}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{5+2\sqrt6}{5^2-(2\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-2^2(\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-(4)(6)}=\dfrac{5+2\sqrt6}{25-24}\\\\=\dfrac{5+2\sqrt6}{1}=5+2\sqrt6\\\\2.\\\\\dfrac{x-1}{x}=\dfrac{x}{x}-\dfrac{1}{x}=1-\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x-1}{x}=1-(5+2\sqrt6)=1-5-2\sqrt6=-4-2\sqrt6[/tex]
[tex]3.\\\\\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x+1}{x}=1+5+2\sqrt6=6+2\sqrt6[/tex]
Please help.. part a & b
Answer:
Part A
to the 10th power will be positive and to the 11th power is negative. When the exponent is even it will be positive. When it is odd it will be negative
Part B
The one with the negative enclosed will be positive. The second one, the exponent is only effecting the number and not the sign. The outcome will always be negative.
Simone help me ASAP !! Please
a quadratic equation is an equation with a degree of 2.
well, is not 2x + x + 3 for sure, and is not 3x³ + 2x + 2 either, that one is a cubic, 3rd degree.
well, one would think is 0x² - 4x + 7, however 0x² is really 0, anything times 0 is 0, so the deceptive equation is really -4x + 7, which is not a quadratic.
5x² - 4x + 5 on the other hand is.
The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio? a. –16 b.–11 c. –4 d.–1
let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)[/tex]
Answer:
-11
Step-by-step explanation:
J =(–25, 10)
K=(5, –20)
Point L divides JK into a 7:3 ratio
To find the coordinates of L we will use section formula.
Formula : [tex]x=\frac{mx_2+nx_1}{m+n}[/tex] and [tex]y=\frac{my_2+ny_1}{m+n}[/tex]
m: n = 7: 3
[tex](x_1,y_1)=(-25,10)\\(x_2,y_2)=(5,-20)[/tex]
Substitute the values
[tex]x=\frac{7(5)+3(-25)}{7+3}[/tex] and [tex]y=\frac{7(-20)+3(10)}{7+3}[/tex]
[tex]x=-4[/tex] and [tex]y=-11[/tex]
Hence the y coordinate of L is -11
Solve 6y2-5y-6 = 0 using the quadratic formula.
A) y=- 3 over 2 or y =2 over 3
B) Y = -5 or y = -6
C) y or y=-2
D) y = 2 or y = 3
Answer:
Ay=3 over 2 or y=-2 over 3
Step-by-step explanation:
the quadratic formula: y={-b±√(b²-4ac)}/2a
In the equation 6y²-5y-6= 0, a=6, b=-5, c= -6
Substituting for the values in the formula we get:
{-(-5)±√[(-5²)-4(6)(-6)}/2(6)
{5±√169}12
={5±13}/12
(5+13)/12=3/2 or (5-13)/12= -2/3
Answer:
[tex]y=\frac{3}{2}[/tex] or [tex]y=-\frac{2}{3}[/tex]
Step-by-step explanation:
We have the expression
[tex]6y^2-5y-6 = 0[/tex]
For an equation of the form [tex]ay^2 +by +c[/tex] the quadratic formula is
[tex]y=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a = 6\\b= -5\\c =-6[/tex]
[tex]y=\frac{-(-5) \± \sqrt{(-5)^2 -4(6)(-6)}}{2(6)}[/tex]
[tex]y_1=\frac{3}{2}[/tex]
[tex]y_2=-\frac{2}{3}[/tex]
Which fraction is bigger 1/150 or 1/200? Why?
Answer:
1/150 is greater than 1/200. A general rule is that the larger the denominator is, the smaller the fraction.
The bigger fraction is,
⇒ 1 / 150
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
Two numbers are,
⇒ 1/150
⇒ 1/200
Since, We know that;
⇒ 1 / 150 = 0.0067
⇒ 1 / 200 = 0.005
Hence, The bigger fraction is,
⇒ 1 / 150
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Solve the exponential equation. (½)x = 32
Answer:
x = - 5
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Given
[tex](1/2)^{x}[/tex] = 32
[tex]\frac{1}{2^{x} }[/tex] = 32
[tex]2^{-x}[/tex] = [tex]2^{5}[/tex]
Since the bases are equal, both 5, equate the exponents
Hence x = - 5
an angle is formed by
It is formed by two rays lie in a plane.
To factor 4x2-25, you can first rewrite the expression as:
Answer:
(2x)^2-(5)^2
Step-by-step explanation:
Simplify the expression. 3−9 ∙ 36 ∙ 36
To simplify the expression 3−9 · 36 · 36, we understand that 36 is 3 raised to the power of 6. Multiplying 36 by itself means adding the exponents, resulting in 3¹². Subtracting 9 (the minus sign before 9) from 12 (the exponent in 36 · 36), we get 3³, which is equal to 27.
Explanation:To simplify the expression 3−9 · 36 · 36, we first need to understand the rules for cubing of exponentials and the operations of exponents.
To cube an exponential, you cube the base digit and multiply the exponent by 3.
For example, when cubing 3², we raise 3 to the power of 6 because the original exponent is multiplied by 3 (2×3=6), which gives us 3⁶, or in other words, 729.
In this case, however, we need to simplify the original expression.
We'll start by recognizing that 36 is 3 raised to the power of 6.
The expression states to multiply 36 by itself, which is essentially stating 3⁶ × 3⁶.
When multiplying exponents with the same base, we simply add the exponents, in this case, 6 + 6, which gives us 3¹².
Hence, the expression can be simplified to 3−9 · 3¹².
Now we are subtracting exponents (because of the minus sign), which means we take 9 away from 12 giving us 3³, or 3 cubed, which equals 27.
5+5+10+10+20+15-13+17