Answer:
Inequality Form: -5<x<2
Interval Notation: (-5,2)
Find the equation of the linear function represented by the table below in slope-intercept form.
pls help me
The equation of the linear function in slope intercept form is y = 2x -6
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope of the linear function using (0, -6)(1, -4).
m = -4 + 6 / 1 - 0
m = 2 / 1
m = 2
Therefore, the y-intercept of the linear function can be calculated using (0, -6) and the lope.
y = 2x + b
-6 = 2(0) + b
b = -6
Therefore, the equation of the line is y = 2x -6
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I am attaching pages 3-5 for context. I just need help with Question 4 on page 5. I have also attached my answers to page 3 (spreadsheet) and page 4 (screenshot).
We are given the initial function to be
[tex]\begin{gathered} A=A_0e^{-0.316t} \\ \text{where} \\ A_0=550mg \end{gathered}[/tex]Page 5
Question 4
We are told to use the function above to estimate how long it will take for the amount in the body to be 175mg.
This simply translates to making A= 175 in the equation so that we will obtain
[tex]175=550e^{-0.316t}[/tex]So we will make t the subject of the formula
To do so, we can follow the steps below
Step 1: Divide both sides by 550
[tex]\begin{gathered} \frac{175}{550}=\frac{550e^{-0.316t}}{550} \\ 0.318=e^{-0.316t} \end{gathered}[/tex]Next, we will take the natural logarithm to both sides
[tex]\begin{gathered} ln(0.318)=\ln (e^{-0.316t}) \\ \ln 0.318=-0.316t \\ -0.316t=\ln 0.318 \end{gathered}[/tex]Next, we will divide both sides by -0.316
[tex]\begin{gathered} t=\frac{\ln (0.318)}{-0.316} \\ t=3.6256 \end{gathered}[/tex]
Thus, the value of t = 3.6256 hours.
What is the equation of a circle with diameter endpoints of (-14, 1) and (-10, 9)
Given data:
The first end point of the diameter is (-14, 1).
The second end point of the diameter is (-10, 9).
The centre of the circel is,
[tex]\begin{gathered} x=\frac{-14-10}{2} \\ =\frac{-24}{2} \\ =-12 \\ y=\frac{1+9}{2} \\ =5 \end{gathered}[/tex]The diameter of the circle is,
[tex]\begin{gathered} d=\sqrt[]{(-10+14)^2+(9-1)^2} \\ =\sqrt[]{16+6}4 \\ =4\sqrt[]{5} \end{gathered}[/tex]The radius is,
[tex]\begin{gathered} r=\frac{4\sqrt[]{5}}{2} \\ =2\sqrt[]{5} \end{gathered}[/tex]The equation for the circle is,
[tex]\begin{gathered} (x-(-12))^2+(y-5)^2=(2\sqrt[]{5})^2 \\ (x+12)^2+(y-5)^2=20 \end{gathered}[/tex]Thus, the equation for the circle is (x+12)^2 +(y-5)^2 =20.
find the area of the equilateral triangle. round to the nearest tenth
the The area of the triangle is 35.1
We can get the height of the triangle using Pythagorean theorem
a^2+b^2=c^2
the height is 7.8
the area of the triangle is 1/2 * base * height
1/2 * 9 *7.8 = 35.1
Isabell will rent a car for a day. The rental company offers two pricing options: Option A and option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below. It’s Isabell drive the rental car 200 miles which option cost more?How much more does it cost than the other option?For what number of miles driven do the two options cost the same?If Isabell drives more than this amount, which option cost more?
From the graph of miles driven and pricing, it can be observed that for 200 miles option A price is $100 and option B price is $70.
So option A cost more than option B.
Determine the difference between $100 and $70 to obtain how much option A cost more than option B.
[tex]100-70=30[/tex]So option A cost $30 more than option B.
From the graph, it can be observed that lines of option A and option B intersect each other at (50,40). So option A and option B cost same for 50 miles.
Given Rhombus ABCD, Solve for X
The value of x for the rhombus sides will be equal to 7 units.
What is a rhombus?A rhombus is a quadrilateral with four equal-length sides. The term equilateral quadrilateral refers to the fact that all of its sides are the same length. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.
Given that there is a rhombus ABCD, and the sides are AB = 2x - 3, BC = 5y + 1, CD = 11, and AD = 20 - z.
The value of x will be calculated by equating the sides AB and CD
AB = CD
2x - 3 = 11
2x = 11 + 3
2x = 14
x = 7
Therefore, the value of x for the rhombus sides will be equal to 7 units.
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WILL GIVE BRAINIEST!!!!
The value of x for functions f(x)=(1+2x)/x and g(x)=2+x is 1 or -1
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
f(x)=(1+2x)/x
g(x)=2+x
f(x)=g(x)
Plug in values of f(x) and g(x)
(1+2x)/x=2+x
1+2x=x(2+x)
Apply distributive property on RHS
1+2x=2x+x²
1+2x-2x=x²
x²=1
x=±1
The value of x is 1 or -1.
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What is the solution of x^2+3x-28
Let's solve for x by factoring this quadratic equation.
We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).
The two numbers that multiply to -28 and add to 3 are 7 and -4.
Therefore, we can factor this equation like so:
[tex](x+7)(x-4)[/tex]Now, we can set this equation to 0 and solve for x.
[tex](x+7)(x-4)=0[/tex]If we look at each factor individually, we can determine the values of x:
[tex](x+7)=0[/tex]Subtract 7 from both sides of the equation.
[tex]x=-7[/tex]Now, let's look at the other factor:
[tex](x-4)=0[/tex]Add 3 to both sides of the equation.
[tex]x=4[/tex]The solution of x^2 + 3x - 28 is x = -7, x = 4.
This morning Justin’s car had 19.17 gallons of fuel.now, 2.6 gallons are left.how much fuel did Justin use?
Answer:
16.57
Step-by-step explanation:
19.17 - 2.6 = 16.57
The table shows the number of books donated to a library each month. Suppose the growth continues exponentially.How many books were donated to the library in Month 8?Round to the nearest whole number.Enter your answer in the box.
The general exponential function is,
[tex]f(x)=a\cdot(b)^x[/tex]For x = 0, f(x) = 80. So,
[tex]\begin{gathered} 80=a\cdot(b)^0 \\ 80=a\cdot1 \\ a=80 \end{gathered}[/tex]For x = 1, f(x) = 100 and a = 80. So,
[tex]\begin{gathered} 100=80\cdot(b)^1 \\ b=\frac{100}{80} \\ =1.25 \end{gathered}[/tex]So exponential function is,
[tex]f(x)=80\cdot(1.25)^x[/tex]Substitute 8 for x in the function to determine the number of books in 8th month.
[tex]\begin{gathered} f(8)=80\cdot(1.25)^8 \\ =476.83 \\ \approx477 \end{gathered}[/tex]So in 8th month number of book denoted is 477.
The average height of students at uh from an srs of 19 students gave a standard deviation of 3. 2 feet. Construct a 95% confidence interval for the standard deviation of the height of students at uh. Assume normality for the data.
The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)
How to find the confidence interval for standard deviation?
The formula for the confidence interval for the standard deviation is given by the formula;
CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
We are given;
Sample size; n = 19
D F = n - 1 = 19 - 1 = 18
Standard Deviation; s = 3.2
Confidence Level; CL = 95% = 0.95
Significance level; α = 1 - 0.95 = 0.05
Thus, using Chi-square distribution table online we have;
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
CI = √[(18 * 3.2²/(24.736)], √[(18 * 3.2²/(5.01)]
CI = (1.81, 4.03)
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A line has an x-intercept of 8 and a y-intercept of 3. What is the equation of the line?
Answer
y = (-3/8)x + 3
Multiply through by 8
8y = -3x + 24
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we just need to solve for the slope of this line.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question, the x and y intercepts are given. Since these are points where the line crosses the x and y axis, we can write them in coordinates form as
x-intercept = (8, 0)
y-intercept = (0, 3)
(x₁, y₁) and (x₂, y₂) are (8, 0) and (0, 3)
[tex]\text{Slope = }\frac{3-0}{0-8}=\frac{3}{-8}=-\frac{3}{8}[/tex]y = mx + b
m = slope = -(3/8)
b = y-intercept = 3
y = mx + b
y = (-3/8)x + 3
Multiply through by 8
8y = -3x + 24
Hope this Helps!!!
Please help I will crown you
The value of b in the given angle is 25°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.Six Different Angles
Acute Angles.Obtuse Angles.Right Angles.Straight Angles.Reflex Angles.Full Rotation.So, the balance of b is:
We can easily tell that the angle is a 90°.And ∠90° is divided into two portions which are:
b + 7 2b + 8Now, calculate for b as follows:
b + 7 + 2b + 8 = 903b = 15 = 903b = 90 - 153b = 75b = 75/3b = 25°Therefore, the value of b in the given angle is 25°.
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Farmer Joogh wanted to sell some dubbles and gespils at the market.
She expected to sell no more than 11 units. She planned to charge $7
per dubble and $4 per gespil. She expected to make no less than $56.
She expected to sell at least 3 gespils.
Write a system of statements, in standard form, modeling the
relationships between amount of dubbles (x) and amount of gespils
(Y)
The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
No more than 11
x + y ≤ 11
Total earning ≥ $56
7x + 4y ≥ 56
At least 3 gospels
y ≥ 3
Hence "The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3".
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Graph the equation on a coordinate grid:y=-1/2x
In this case you have a linear equation of the form:
y=mx+b
To graph a line we only need to specify two points of the line and then join them.
b the intercept is zero in this case, and the slope of your line is -1/2. Since the intercept is zero, this means that the line crosses the origin, so the point (0,0) is included in the line, to find other poin of the line we just have to replace a value of x and calculate the value of y, for example let's take x equals 2.
[tex]y(2)=-\frac{1}{2}2=-\frac{2}{2}=-1[/tex]Now, we know that the line crosses the points (0,0) and (2,-1), let's graph them.
Michael and his sister Mel share the job of mowing the grass in their yard. Michael mows 1/3 of the yard, and Mel mows the rest. Mel can mow 3/4 of the entire yard in an hour. 1. How long will it take Mel to finish mowing her part of the yard?2. After Michael mows 1/3 of the yard, what fraction of the yard does Mel need to mow? Explain.3. Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard.4. How long will it take Mel to finish mowing the yard? Show your work.
Michael mows 1/3 of the yard, and the remaining is for Mel,
Note that 1 whole yard is 1
So the remaining is 1 - 1/3 = 2/3
Mel can mow 3/4 of the entire yard in 1 hour :
So in 1 whole yard, Mel can mow it for :
[tex]\frac{1hr}{\frac{3}{4}}=\frac{4}{3}hr\text{ per yard}[/tex]Mel's rate in mowing 1 yard is 4/3 hrs
Since Mel will mow 2/3 of the yard, multiply it by her rate will be :
[tex]\frac{2}{3}\times\frac{4}{3}=\frac{8}{9}[/tex]8/9 or 0.89 hour
Note that multiplication can be expressed as division,
The number of hours Mel can finish mowing the yard is :
[tex]\begin{gathered} \text{hours}=\frac{\text{part of yard}}{\text{Mel's rate}} \\ \text{hours}=\frac{\frac{2}{3}}{\frac{4}{3}} \\ \text{hours}=\frac{8}{9} \end{gathered}[/tex]Since the answer is same, 8/9 hour is correct.
To summarize the answers :
1. 8/9 hr or 0.89 hr
2. 2/3, as explained above.
3. The division problem is :
[tex]\frac{2}{3}\div\frac{3}{4}[/tex]4. 8/9 hr or 0.89 hr
[tex]\frac{2}{3}\div\frac{3}{4}=\frac{2}{3}\times\frac{4}{3}=\frac{8}{9}[/tex]Question
If the cost of filing a floor is $1.75 per square foot, how much will it cost to file a rectangular floor that is 9
foot by 12 feet?
(Area Length x Width)
Answer:
[tex]3x - 6 = 9[/tex]
solve forWhen comparing two decimal numbers, you should always line up the decimals and then compare the digits from left to right.
TrueFalse
Answer:True
example:
89 and 84, 8 are equal, but next 9 is bigger than 4
A spinner is divided into five colored sections that are not of equal size: red, blue,green, yellow, and purple. The spinner is spun several times, and the results arerecorded below:Spinner ResultsColor Frequency718RedBlueGreenYellowPurple569Based on these results, express the probability that the next spin will land on green asa decimal to the nearest hundredth.
Answer:
0.11
Explanation:
First, find the total of the color frequency:
[tex]\begin{gathered} \text{Total}=7+18+5+6+9 \\ =45 \end{gathered}[/tex]The Frequency with which it lands on Green = 5
Therefore, the probability that the next spin will land on the green:
[tex]\begin{gathered} =\frac{5}{45} \\ \approx0.11 \end{gathered}[/tex]The required probability is 0.11 (to the nearest hundredth).
What is the difference of -3 multiplied by a number and the product of two and another number
Let a number be "a" and the other number be "b".
-3 multiplied by a number "a" is:
[tex]-3\cdot a[/tex]The product of two and another number "b" is:
[tex]2\cdot b[/tex]And the difference between the numbers is:
[tex]-3a-2b[/tex]Answer: - 3a - 2b.
Translate the sentence into an equation.
Twice the difference of a number and 2 is 6.
Use the variable w for the unknown number.
Answer: 2(x-2)=6
Step-by-step explanation: when they say twice, so you make is times 2, then it said the difference of a number which would be a variable, or x, and 2, is 6, so one part is =6, next is the variable -2, so you can use x-2, then in order to multiply everything, you need to make parenthesis. So, it would be x-2=6, but you forgot the parathesis, so 2(x-2)=6
hello. i just need a little helping hand on this thank you
As given by the question
There are given that the expression
[tex]\sqrt[]{45}[/tex]Now,
The value of the given expression is:
[tex]\begin{gathered} \sqrt[]{45}=\sqrt[]{5\times9} \\ =\sqrt[]{9}\times\sqrt[]{5} \\ =3\sqrt[]{5} \end{gathered}[/tex]Hence, the correct option is C.
Find the geometric mean of the sequence: 2112,______,33
The sequence first term is a = 2112 and last term is b = 33.
The formula for the geometric mean is,
[tex]\sqrt[]{a\cdot b}[/tex]Determine the geometric mean of 2112 and 33.
[tex]\begin{gathered} \sqrt[]{2112\cdot33}=\sqrt[]{69696} \\ =264 \end{gathered}[/tex]So geometric sequence is 264.
Answer: 264
it is one of the 4 answers
The rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.
What is the rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Other instances of changing rates are as follows: 40 more rats are added to the colony every week.
So, the rate of change is:
The point is given at 1.5 with respect to the y-axis.
And we can clearly see that it has been decreased to 1 with respect to the y-axis.
So, the rate of change:
1.0 - 1.5 - = -0.5
Therefore, the rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.
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How do I do this my teacher just assigned this and I don’t know what to do ?
We need to subtract both expressions, then simplify it and make only one expression:
First, subtract both expressions:
[tex](-3x+9y)-(8x-6y)[/tex]Then:
[tex]-3x+9y-8x+6y[/tex]Now, simplify like terms:
[tex]-11x+15y[/tex]Therefore, the result expression is -11x+15y.
How you solve this problem?
t^2/20+8=15
Answer: t=2*±√(35)=±11.8322
Step-by-step explanation: STEP
1
:
t2
Simplify ——
20
Equation at the end of step
1
:
t2
(—— + 8) - 15 = 0
20
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 20 as the denominator :
8 8 • 20
8 = — = ——————
1 20
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
t2 + 8 • 20 t2 + 160
——————————— = ————————
20 20
Equation at the end of step
2
:
(t2 + 160)
—————————— - 15 = 0
20
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 20 as the denominator :
15 15 • 20
15 = —— = ———————
1 20
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(t) = t2 + 160
Polynomial Roots Calculator is a set of methods aimed at finding values of t for which F(t)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers t which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 160.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,5 ,8 ,10 ,16 ,20 ,32 ,40 , etc
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 161.00
-2 1 -2.00 164.00
-4 1 -4.00 176.00
-5 1 -5.00 185.00
-8 1 -8.00 224.00
Note - For tidiness, printing of 15 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
3.3 Adding up the two equivalent fractions
(t2+160) - (15 • 20) t2 - 140
———————————————————— = ————————
20 20
Trying to factor as a Difference of Squares:
3.4 Factoring: t2 - 140
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 140 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
3
:
t2 - 140
———————— = 0
20
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
t2-140
—————— • 20 = 0 • 20
20
Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
t2-140 = 0
Solving a Single Variable Equation:
4.2 Solve : t2-140 = 0
Add 140 to both sides of the equation :
t2 = 140
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
t = ± √ 140
Can √ 140 be simplified ?
Yes! The prime factorization of 140 is
2•2•5•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 140 = √ 2•2•5•7 =
± 2 • √ 35
The equation has two real solutions
These solutions are t = 2 • ± √35 = ± 11.8322
Three more than the square of the sum of five times a number and two. written as a math problem is?
Let the number be x.
The mathematical expression for the statement is,
[tex]3+(5x+2)^2[/tex]help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.
What is a rectangle?A rectangle is a type of parallelogram that has equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
The dimensions of the given rectangle is (650 - 2x) and x.
Then, the area of the given rectangle is A(x) = x(650 - 2x)
In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,
(660 - 2x) - 2x = 0
=> 4x = 660
=> x = 660 / 4
=> x = 115
Now, the maximum area is the value of A(x) at x = 115 as below,
= 115 × (650 - 2×115)
= 115 × 320
= 36800
The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.
Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width labeled in the figure is given as 115 meter.
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Square ABCD has vertices at A(-1, 2) and B(3, -3).
What is the slope of segment BC?
Answer:
BC=OB-OA
BC=(3/-3) - (-1/2)
BC= -1-3/2--3
-4/5=BC
Y=50-3.5x continuous or discrete
By continuity of polynomial function, y = 50 - 3.5x is a continuous function.
What is a continuous function?
A function is said to be continuous if the graph of the function has no breakage or no discontinuity at any point
y = 50 - 3.5x is a polynomial function.
All polynomial functions are continuous function.
y = 50 - 3.5x is a continuous function.
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