X + 9 = 13
To know the value of x you have to subtract 9 from both sides of the equation
x+9-9= 13-9
x= 4
Usually it takes Mrs. Manny 5.2 hours to grade her students' assignments. Thisweekend, her daughter Lexi is home and has offered to help. If it would take Lexi 6.4hours to grade the papers alone, how long will it take the two to finish the task of grading,working together?
Mrs. Manny needs 5.2 hours to grade her students' assignments. It would take Lexi 6.4 hours to grade the assignments alone.
In one hour, Mrs. Manny completes 1 / 5.2 = 0.1923 of the work.
In one hour, Lexi completes 1 / 6.4 = 0.15625 of the work
Together, they complete 0.1923 + 0.15625 = 0.34856 of the work.
The full work would take them 1 / 0.34856 = 2.87 hours.
It would take 2.87 hours for them to finish the task together.
(4t^2-5u)^2What does this simplify to?What is the degree of the simplified answer?
Answer:
simplified expression = 16t⁴ - 40t²u + 25u²
degree = 4
Explanation:
The initial expression is:
[tex](4t^2-5u)^2[/tex]To simplify, we can solve the expression as:
[tex](4t^2-5u)(4t^2-5u)[/tex]Applying the distributive property, we get:
[tex]\begin{gathered} 4t^2(4t^2)+4t^2(-5u)-5u(4t^2)-5u(-5u) \\ 16t^4-20t^2u-20t^2u+25u^2 \end{gathered}[/tex]Adding the like terms, we get that the simplified expression is
[tex]16t^4-40t^2u+25u^2[/tex]Then, the degree of the simplified expression is 4 because it is the maximum exponent.
So, the answers are:
16t⁴ - 40t²u + 25u²
degree = 4
What are the solutions to the equation x- 8x = 10?1) 4 102) 4-263) 41104) 4+ 26
First, let's equal the expression to zero:
[tex]\begin{gathered} x^2-8x=10 \\ \rightarrow x^2-8x-10=0 \end{gathered}[/tex]Now, let's use the general formula for quadratic equations:
[tex]\begin{gathered} \text{For} \\ ax^2+bx+c=0 \\ \\ \rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-10)}}{2(1)} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{64+40}}{2} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{104}}{2} \\ \\ \rightarrow x=\frac{8\pm2\text{ }\sqrt[]{26}}{2} \\ \\ \Rightarrow x=4\pm\sqrt[]{26} \end{gathered}[/tex]Answer: Option 2
A right triangle has the lengths of the legs are 60 centimeters and 80 centimeters. what is the length, in cm, of the hypotenuse?
The following image shows a diagram (not to scale) of the triangle with the indicated measurements:
We will label them as "a" and "b" for reference:
And we need to find the hypotenuse of the triangle, which is the side that is opposite to the 90° angle. We will label the hypotenuse as "c":
To solve the problem we have to us The Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]Substituting the values of the legs a and b:
[tex]c^2=60^2+80^2[/tex]Since 60^2=3,600 and 80^2=6,400:
[tex]\begin{gathered} c^2=3,600+6,400 \\ c^2=10,000 \end{gathered}[/tex]Finally, to find the hypotenuse "c", take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{10,000} \\ c=\sqrt[]{10,000} \\ c=100 \end{gathered}[/tex]The length of the hypotenuse is 100 cm.
Answer: 100cm
9. A coin is tossed and a number cube is rolled. What is the probability of getting tails and rolling a two?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested probability, so we obtain the following:
Probability of getting tails and rolling a two=Probability of getting tails * Probability of getting a two
And basing ourselves on the fact that when tossing a coin there are two possible events and in this case a favorable one, and when tossing the die there are 6 possible events and one favorable for this case, we have:
Probability of getting tails and rolling a two=1/2*1/6
Probability of getting tails and rolling a two=1/12
Finally we obtain that the probability of getting tails and rolling a two is 1/12.
If point B, shown on the coordinate plane below, is reflected over the y-axis to create B’, what will be the coordinates of B’?(-5, 2)(5, 2)(-5, -2)(5, -2)
Solution
- The transformation for reflection over the y-axis is given below:
[tex](x,y)\to(-x,y)[/tex]- We have been given the coordinate of B to be (-5, -2) as shown below:
- Thus, applying the transformation formula given above, we have:
[tex]\begin{gathered} (x,y)\to(-x,y) \\ (-5,-2)\to(-(-5),-2)=(5,-2) \end{gathered}[/tex]- Thus, the reflected point B' is
[tex](5,-2)[/tex]- This is shown below:
Determine whether the function Y = 7- (3)represents exponential growth orexponential decay.a) exponential decayb) exponential growth
Given any exponential function in the form
[tex]y=ar^x[/tex]• If ,r >1, ,the function represents ,growth
,• If ,1 > r > 0,, the function represents ,decay
Notice that for
[tex]y=7\cdot(\frac{2}{3})^x[/tex]The exponential factor (2/3) is between 0 and 1 (0.66)
Therefore, the function represents decay.
Answer: Option A
Find the area of this irregular shape.
[Round off to the nearest whole number.]
sq. units
Answer:
Step-by-step explanation:
number of complete squares=14
number of half or more than half squares=4
whole squares=4/2=2
area≈14+2=16 sq. units
Rita is applying for a job as an engineer. Her starting salary at Company A will be $80,000 with an $800 yearly raise. Her starting salary at company B will be $65,000 with a 5% increase each year. If Rita is working at a company for 5 years. Which company should she pick?
Given:
In company A, starting salary is $80,000.
The yearly increment is $800.
So,
80,000+800=80,800
80,800+800=81,600
81,600+800=82,400
82,400+800=83,200
83,200+800=84,000
So, at the 5 year, she will get $84,000
In company B,
The initial salary is $65000 with a 5% increase each year.
So,
[tex]\begin{gathered} 65000\times\frac{105}{100}=68250 \\ 68250\times\frac{105}{100}=71662.5 \\ 71662.5\times\frac{105}{100}=75245.625 \\ 75245.625\times\frac{105}{100}=79007.906 \\ 79007.906\times\times\frac{105}{100}=82958.30 \end{gathered}[/tex]In the 5th year, she will get $82,958.30.
If Rita is working at a company only for 5 years, then she would choose company A. Because she will get salary in company A more than company B.
But, if she works for more than 5 years, she will get a salary in company B more than company A.
Acetone (fingernail polish remover ) has a density of 0.7857 g/cm^3.A) what is the mass in grams of 17.56 mL of acetone?B) what is the volume in milliliters of 7.22 g of acetone?
We can use density as a factor of conversion.
To find the mass in grams of the volume of acetone, multiply the volume by the density (always check the units, that in this case are consistent because 1cm^3=1mL):
[tex]17.56mL\cdot\frac{0.7857g}{mL}=13.79g[/tex]To find the volume of the mass of acetone, divide the mass by the density:
[tex]7.22g\cdot\frac{1mL}{0.7857g}=9.18mL[/tex](-5,-11) and (17,-22)
Find the slope
Answer:
-1/2
Step-by-step explanation:
CM Bookmarks Geometry Unit 11 Test Area of Plane Figures E CALCULATOR • colo a a noosa 12. Find the area of the shaded region of the figure
It is a trapezoid
[tex]\begin{gathered} \text{ Area = h}\frac{B\text{ + b}}{2} \\ \text{Area = 4}\cdot\text{ }\frac{16\text{ + 6}}{2} \\ \text{Area = 4}\cdot\frac{22}{2} \\ \text{Area = }\frac{88}{2} \\ \text{Area = 44 mm}^2 \end{gathered}[/tex]
3. For the sequence defined by tn = 3n + 8,find each indicated term.a) t1b) t7c) t14
The sequence is given by .
[tex]t_n=3n+8[/tex]a. The indicated term
[tex]t_1=3(1)+8[/tex][tex]t_1=3+8[/tex][tex]t_1=11[/tex]b. The indicated term
[tex]t_7=3(7)+8[/tex][tex]t_7=29[/tex]c. The indicated term
[tex]t_{14}=3(14)+8[/tex][tex]t_{14}=42+8[/tex][tex]t_{14}=50[/tex]
Cole's Ice Cream Shop sold 16 sundaes with nuts and 30 sundaes without nuts. What is the
ratio of the number of sundaes with nuts to the total number of sundaes?
Answer:
16:46
Step-by-step explanation:
-20 increased by 4
translating words to algebraic expressions
The algebraic expression is -20 +4.
What is algebraic expression?
An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.
Given, situation -20 increased by 4.
Translate the phrase -20 increased by 4 into an algebraic expression.
You probably already know that more than is associated with addition so the sign is not going to change. But what about the order of the terms?
Think about it this way: we have a number (some unknown value) and this phrase represents -20 increased by whatever that value is. So, in this case, you will start with the number -20 and add 4.
we get -20+4.
To know more about algebraic expression, visit:
https://brainly.com/question/24267361
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Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y).3x - 2y = -95x + 10y = - 5
Given,
[tex]\begin{gathered} 3x-2y=-9\ldots\ldots\ldots(1) \\ 5x+10y=-5\ldots\ldots\text{.}(2) \end{gathered}[/tex]Multiply 1st equation by 5.
[tex]\begin{gathered} 5(3x-2y=-9) \\ 15x-10y=-45\ldots\ldots\text{.}(3) \end{gathered}[/tex]Solve equations (2) and (3)
[tex]\begin{gathered} 20x=-50 \\ x=\frac{-5}{2} \end{gathered}[/tex]Put x =-5/2 in equation (1)
[tex]\begin{gathered} 3x-2y=-9 \\ 3\times\frac{-5}{2}-2y=-9 \\ \frac{-15}{2}-2y=-9 \\ -2y=-9+\frac{15}{2} \end{gathered}[/tex]Further solved as,
[tex]\begin{gathered} -2y=\frac{-45+15}{5} \\ -2y=\frac{-30}{5} \\ -2y=-6 \\ y=3 \end{gathered}[/tex]Therefore, the value of x and y is -5/2 and 3.
у 10 8 P 4 2 0 2 6 8 10 Which ordered pair represents the location of point P on the coordinate plane? a (5,6) b (6,5) (6,7) d (7,6)
The ordered pair that represents the location of point P is (6,5)
Explanation:
In order to determine the position of point P, we will need to trace its position to the x axis and also trace its position to the y axis.
Tracing its position to the x axis, we find it corresponds to 6 units
Tracing its position to the y axis, we find it corresponds to 5 units.
This because each line represents 1 units. After the 4 units, the next line is 5 units.
Using the coordinates (x,y):
The ordered pair that represents the location of point P is (6,5)
Write an expression in simplest form that represents the income from w women and m men getting a haircut and shampoo. Women: haircut $45 shampoo $12. Men: haircut $15 shampoo $7
Write an expression in simplest form that represents the income from w women and m men getting a haircut and shampoo. Women: haircut $45 shampoo $12. Men: haircut $15 shampoo $7
the income is equal to
45w+12w+15m+7m
combine like terms
57w+22m
total income=57w+22mwhere
w is the number of women
m is the number of men
the image is downloading nowabout 15%is too slowlyDo you can write the question?which expression means the same as an increase of 20%
ANSWER:
[tex]x+0.2x[/tex]STEP-BY-STEP EXPLANATION:
We have that an increase in 20% is the original value added to 20% of that original value, just like this:
[tex]x+\frac{20}{100}x=x+0.2x[/tex]how do i find the type of relationship of a table? whether it is linear or quadradic and how do i find the formula for either relationship?
By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs. If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic.
Also you can solve it by plotting the dots. If the graph seems a straight line it is linear and quadratic if it is a parabola.
For the data set given it is a linear relation
Line of best fit: y=3.18x+54.92
For x=7;
y=3.18*7+54.92
y=77.18
Could you please help me with this? I need to solve it.
Given: ( -100 ) + ( -4 ) + ( -2 + 6) ( 3 )
Required: Evaluation
Explanation:
We shall here use BODMAS rule.
First solve the brackets and the addition and subtraction
[tex]\begin{gathered} (-100)+(-4)+(-2+6)(3) \\ =-100-4+(4)(3) \end{gathered}[/tex]Further,
[tex]\begin{gathered} =-100-4+12 \\ =-104+12 \end{gathered}[/tex]Solving
[tex]-104+12=-92[/tex]Final Answer:
[tex]-92[/tex]Each month Mark‘s phone company charges a flat fee of $12 plus $0.05 per minute his bill for last month was $18 how many minutes did Marty talk on the phone last Month
Given:
Flat fee = $12
Per minute charge = $0.05
Total bill for last month = $18
To find the number of minutes, we have the equation:
18 = 12 + 0.05M
Where M represents number of minutes
Let's solve for M:
Subtract 12 from both sides:
18 - 12 = 12 - 12 + 0.05M
6 = 0.05M
Divide both sides by 0.05:
[tex]\begin{gathered} \frac{6}{0.05}=\frac{0.05M}{0.05} \\ \\ 120\text{ = M} \end{gathered}[/tex]Therefore, Marty spent 120 minutes talking on the phone last month.
ANSWER:
120 minutes
I need help with this math question all parts pleasePart 2: find y-interceptPart 3: find the zerosPart 4: Graph k(x)
Given the following function:
[tex]k(x)=x^3-5x^2[/tex]We will find the end behavior of the function.
the given function has a degree = 3 (odd)
And the leading coefficient is positive
the end behavior will be as follows:
[tex]\begin{gathered} x\to-\infty\Rightarrow k(x)\to-\infty \\ x\to\infty\Rightarrow k(x)\to\infty \end{gathered}[/tex]So, the answer will be:
The end behavior of the function is down to the left and up to the right.
===============================================================
Part (2), we will find the y-intercepts
The y-intercept is the value of y when x = 0
So, we will substitute x = 0 and then solve y
[tex]y=0^3-5(0^2)=0[/tex]So, the answer will be:
y-intercept = (0, 0)
================================================================
Part 3: we will find the zeros of k(x)
The zeros of the function are the values of x which make k(x) = 0
So, we will write the equation k(x) = 0 and then solve it for x.
[tex]\begin{gathered} x^3-5x^2=0 \\ x^2(x-5)=0 \\ x^2=0\to x=0 \\ x-5=0\to x=5 \end{gathered}[/tex]So, the answer will be:
Zeros of k: 0,5
===============================================================
Part 4: we will find the graph of k(x)
From the previous parts, we can conclude that
The graph of the function will be as shown in option D
accounts that earn 6% interest. If Emma’saccount earns simple interest and Paul’saccount earns compound interest, which is thevalue of each person’s account after 8 years?A. Emma – $2,960; Paul – $3,187.708. Emma – $960; Paul – $3,187.70C. Emma – $2,960; Paut- $ 1,187.70
So,
Remember that the simple interest of an initial amount after "t" years, can be found using the following formula:
[tex]A=P(1+rt)[/tex]Where A is the final amount, P is the initial amount, r is the rate and t are the years involved.
If we replace our values, Emma will has the following amount after 8 years:
[tex]\begin{gathered} A=2000(1+\frac{6}{100}(8)) \\ A=2960 \end{gathered}[/tex]So, Emma will has $2,960 after 8 years.
To find the amount that Paul will has, we should remember what the compound interest is.
Remember that the compound interest is given by the formula:
[tex]A=P(1+i)^n[/tex]Where A is the final amount, P is the initial amount, i is the rate and n are the years involved.
If we replace our values, Paul will has the following amount of money after 8 years:
[tex]\begin{gathered} A=2000(1+\frac{6}{100})^8 \\ A=3187.70 \end{gathered}[/tex]So, Paul will has $3187,70 after 8 years.
Therefore, the correct answer is A.
I will share a photo of the question it is to complicated to right
Answer : 6
We are given the above fraction to be
[tex]\frac{3}{4}\text{ divided by }\frac{1}{8}[/tex][tex]\begin{gathered} To\text{ proc}eed\text{ with this expression, we n}eed\text{ to find the reciprocal of }\frac{1}{8} \\ \text{Hence, the reciprocal of }\frac{1}{8}\text{ is 8} \\ \frac{3}{4}\text{ x }\frac{8}{1} \\ =\text{ }\frac{3\text{ x 8}}{4} \\ =\text{ }\frac{24}{4} \\ =\text{ 6} \end{gathered}[/tex]The answer is 6
Before you can change a division operator to a multiplication operator, we need to find the reciprocal of the left hand side fraction
The fraction at the left hand side is 1/8
The reciprocal of 1/8 is 8
I need help to find the indicated operation:g(n)= 2n-2h(n)= n^2+3nFind (g×h)(n)
Composition of functions:
You combine two functions bycomposition by using one of the functions to substitute the independient variable in the other one.
To find (g o h)(n) you substitute the n in the function g(n) for the function h(n):
[tex](g\circ h)(n)=2(n^2+3n)-2[/tex]Simplify:
[tex](g\circ h)(n)=2n^2+6n-2[/tex]The graph shows the equation x=y^2 use the slider for a to move the vertical line on the graph. According to the vertical line test, is this equation a function why or why not?
Explanation
We are given the equation:
[tex]x=y^2[/tex]We are to use the vertical line test to determine if the equation is a function or not
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 typical example below helps give a better explanation
So for the function
[tex]x=y^2[/tex]We can observe that the equation is not a function because the vertical line cuts the graph in more than one point
This is shown below for values of x = and x =8
Study PathsTestPlacement Test Williston State College 2018 Study PathTestInit: GeometryogressQuestion ID: 1191695The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answerFind the circumference of a circle with a diameter of 13 meters. Use 3.14 as an approximation for E. Round your answer to thenearest whole meter. Enter only the numberThe solution isSubmitPassDon't know answerSave and close
Explanation:
The question wants us to obtain the circumference of the circle given that the diameter of the circle is 13 meters.
To do so, we will use the formula:
[tex]\begin{gathered} Circumference=\pi D \\ Where \\ \pi=3.14 \\ D=diameter=13\text{ meters} \end{gathered}[/tex]Therefore, the circumference will be
[tex]Circumference=3.14\times13=40.82\text{ }meters[/tex]Rounding off to the nearest whole number, we will have 41 meters
The graph of f(x) = 4+ is shown below in blue. This graph in red is a transformation of f(x). Write a function thatdescribes the
Solution
Step 1:
Write the parent function
[tex]f(x)\text{ = 4}^x[/tex]Step 2:
Transformation of f(x) to g(x)
First, f(x) was reflected across the x-axis
[tex]f(x)\text{ }\rightarrow\text{ -4}^x\text{ }\rightarrow\text{ g\lparen x\rparen}[/tex]Step 3:
Then the function is later shifted 3 units vertically down.
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]Final answer
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]The graphs of functions f(x) and g(x) = f(x) + k are shown below:g(x)65432f(x))3-3The value of k is.(1 point)
Solution
We know that :
g(x) = f(x) + k
For this case the answer is:
the value of k is: 4