8c + 3 = 5c + 12
5c is adding on the right, then it will subtract on the left
3 is adding on the left, then it will subtract on the right
8c - 5c = 12 - 3
3c = 9
3 is multiplying on the left, then it will divide on the right
c = 9/3
c = 3
Suppose angles a and B are the two acute angles in a right triangle and that b < a. Apply the relationship between sine and cosine todetermine which statements are correct.sin(6x - 10) = cos(4x + 10)A)x = 9B)a = 46°a = 48°D)B = 42°E)B = 44
The right statements are: A, B and E
Sin(A)=cos(B)
then we check if using x=9 this holds true:
sin(6x-10)=cos(4x+10)
sin((6*9)-10) = sin(44º)
cos(4x+10)=cos(46)
Sin(44)=0.694=cos(46)
then a is true
Now, we know that b
2+2=im in kendergardenin. pls help.
The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:
We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.
Answer:
the answer is 11
duuuh
Step-by-step explanation:
Could you explain to me on what to do for this question
1. First you need to know the value of the three internal angles in the triangle:
The mising thriangle cam be find as follow:
The angle in green is 180º
You have the value of a part of that angle (6+25x) then the other part of the angle is:
[tex]180º-(6+25x)=180º-6-25x=174º-25x[/tex]Then you have the three internan angles:
44
18x-3
174-25x
You must know that the internal angles of a triangle always gonna sum 180º, then:
[tex]180=44+(18x-3)+(174-25x)[/tex]You can clear the x, as follow:
[tex]180=44+18x-3+174-25x[/tex][tex]180=215-7x[/tex]Then so, x=5the cake is regular price at $9 and is on sale for 25%. how much would you save with the discount
Let be "x" the amount of money (in dollars) you would save with the discount.
By definition, a percent can be converted to a Decimal number by dividing it by 100. Then, since the cake store is having 25% off sale on all cakes, this can be written as:
[tex]\frac{25}{100}=0.25[/tex]According to the information given in the exercise, the regular price of the cake you want is $9. Based on this, you can set up the following expression for price of the cake with the discount (in dollars):
[tex]9-(9)(0.25)[/tex]Evaluating, you get:
[tex]=6.75[/tex]Knowing this value, you can set up that:
[tex]x=9-6.75[/tex]Finally, evaluating, you get:
[tex]x=2.25[/tex]The answer is: You would save $2.25 with the discount.
what is the most important piece of the software in a computer
Answer:
Step-by-step explanation:
the operating system
Answer:
An operating system is the most important software that runs on a computer. It manages the computer's memory and processes, as well as all of its software and hardware. It also allows you to communicate with the computer without knowing how to speak the computer's language.
Brainliest please?
Hope this helps
2. Two of your classmates are arguing over the solution to a problem. Rhonda believes that the only method to solving the following theequation below is by using the quadratic equation. Max believes that you can use the quadratic formula but you can also factor theequation. Explain if Rhonda or Max is correct.2x^2-5x=88Some words/phrases to consider using in your response would be:factorFOIL MethodZero-Product PropertyStandard Formquadratic expressionquadratic equationscoefficientperfect square
Given data:
The given expression is x^2 -6x-7=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-6x=7 \\ x^2-6x+(\frac{6}{2})^2=7+(\frac{6}{2})^2 \\ x^2-2(x)(3)+3^2=7+3^2 \\ (x-3)^2=16 \end{gathered}[/tex]Thus, the number 9 is added on both sides to complete square.
In college, we study large volumes of information- information that, unfortunately, we go not often retain for very long. The function f(x) = 80e +20 describes the percentage of information, fx), that a particular person remembers x weeks after learning the information. a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for x and find the percentage of information remembered after 1 week C. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after 1 year.
a)
[tex]f(0)=80\cdot e^{-0.5\cdot0}+20=100[/tex]b)
[tex]f(1)=80\cdot e^{-0.5}+20=68.52[/tex]c)
[tex]f(4)=80\cdot e^{-0.5\cdot4}+20=30.82[/tex]d)
[tex]f(48)=80\cdot e^{-0.5\cdot48}+20=20[/tex]The half-life of a radioactive kind of iodine is 21 hours. How much will be left after 42 hours,if you start with 19,296 grams of it?In grams
The half-life of a radioactive material is the time that it takes to reduce to half
In this case, the half-life is 21 hs, and since 42hs is twice the half-life, the material will reduce to half after 21 hours and then to half again.
one half of one half is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Then we multiply by the initial amount:
[tex]19,296\cdot\frac{1}{4}=4824gr[/tex]The amount left after 42 hours is 4824 grams.
Find the value of each variable.All answers must be in simplest radical form
Radical
x = √10 • tan 45° = √10• 1 = √10
then
x= √10
y= √x^2 + 10 = √ 10 +10 = √20
Then answer is
x=√10
y= √20
-2(k - 5) + 2K = 5k +5A)k=0B)k=4C)k1D)k=2
The equation we have is:
[tex]-2(k-5)+2k=5k+5[/tex]Now we can simply the equation by multiply the -2 into the parenthesis
[tex]\begin{gathered} -2k+10+2k=5k+5 \\ 10=5k+5 \end{gathered}[/tex]now we can solve for k
[tex]\begin{gathered} 10-5=5k \\ 5=5k \\ \frac{5}{5}=k \\ 1=k \end{gathered}[/tex]pleaseee help meeee For questions 9 - 10, answer the question about inverses. 9. The function m(d) below relates the miles Bob can drive his rental car and the numbers of dollars it will cost. 10. The function a(h) below relates the area of a triangle with a given base 7 and the height of the triangle. It takes as input the number of dollars spent and returns as output the number of miles. It takes as input the height of the triangle and returns as output the of the triangle. m(d) = 40(d- 35) ain= Write the equation that represents the inverse function, d(m), which takes the number of miles driven, m, as input and returns the number of dollars owed, d. Write the equation that represents inverse function, h(a), which takes triangle's area as input and returns height of the triangle.
First problem:
Find the inverse of the function
m = 40 (d - 35)
Recall that for the inverse function we need to solve for d in terms of m (reverse the dependence), so we proceed to isolate d on the right hand side of the equation:
divide both sides by 40
m/40 = d - 35
now add 35 to both sides:
m/40 + 35 = d
The inverse function (dollars in terms of miles) is given then by:
d(m) = 1/40 m + 35
Second problem:
a = 7 * h / 2
in order to find the inverse function (as h in terms of a) we solve for h on the right hand side of the equation as shown below:
multiply both sides by 2:
2 * a = 7 * h
now divide both sides by 7 in order to isolate h on the right
2 a / 7 = h
So our inverse function of height in terms of area is given by:
h(a) = (2 a) / 7
The function f(t) = 2(2.25)^t models the growth of bacteria cells, where f(t) is the number of bacteria cells and t is time in days. After 10 days, approximately how many bacteria cells are there?
Step 1
write out the function
[tex]\begin{gathered} f(t)=2(2.25)^t \\ \end{gathered}[/tex]Step 2
for every input, an input produce unique output
t = 10days is the input
Step 3
substitute t = 10 in the function
[tex]\begin{gathered} f(t)=2(2.25)^{10} \\ =\text{ 2 }\times2.25^{10} \\ =\text{ 2 x 3325.25673} \\ =\text{ 6650.51} \\ =\text{ 6651} \end{gathered}[/tex]The number of cities in a region over time is represented by the function
For this question, in order to find T(x), we need to multiply the two given functions.
[tex]T(x)=(C\cdot P)(x)[/tex][tex]T(x)=C(x)\cdot P(x)[/tex][tex]=(2.9)(1.05)^x\cdot(1.05)^{3x+5}[/tex][tex]=(2.9)(1.05)^{x+3x+5}[/tex][tex]T(x)=2.9(1.05)^{4x+5}[/tex]Therefore, the answer must be option A.
in 3 years Donald wants to buy a bicycle that costs 600.00 if he opens a savings account that earns 4% interest compounded quarterly how much will he have to despoit as principal to have enough money in 3 years to buy the bike
We want the future value to be $600. With an interest of 4% quarterly in 3 years, we have the following information:
[tex]\begin{gathered} FV=600 \\ i=0.04 \\ t=3 \\ n=4 \end{gathered}[/tex]Then we apply the following formula:
[tex]PV=\frac{FV}{(1+\frac{i}{n})^{n\cdot t}}[/tex]therefore, we have that:
[tex]PV=\frac{600}{(1+\frac{0.04}{4})^{4\cdot3}}=\frac{600}{(1.01)^{12}}=532.46[/tex]therefore, Donald would have to deposit $532.46 as principal.
Ingrid is preparing a budget. She is first calculating her income. She makes $2,000 a month as a tutor, but she is going to school to become a lawyer who will eventually make close to $10,000 a month. What is the BEST thing for Ingrid to do to prepare an accurate budget?A. She should use the difference between both incomes--$8,000.B. She should average both incomes and use $6,000.C. She should use her future income of $10,000.D. She should use her current income of $2,000.
Given:
Ingrid is preparing a budget. She is first calculating her income.
She makes $2,000 a month as a tutor.
And she is going to school to become a lawyer.
Eventually, she will make close to $10,000 a month
So, the best thing is to calculate her earnings when she becomes a lawyer.
So, the answer will be option A
She should use the difference between both incomes--$8,000.
Which of these shows the result of using the first equation to substitute for y?
D) 9x=18
Explanationgiven
[tex]\begin{gathered} y=3x\Rightarrow equation(1) \\ 3x+2y=18\Rightarrow equation(2) \end{gathered}[/tex]Step 1
substitute the y value from equation (1) into equation(2)
so
[tex]\begin{gathered} 3x+2y=18\operatorname{\Rightarrow}equat\imaginaryI on(2) \\ replace \\ 3x+2(3x)=18 \\ 3x+6x=18 \\ add\text{ like terms } \\ 9x=18 \end{gathered}[/tex]therefore, the answer is
D) 9x=18
I hope this helps you
Enter a range of values for x.1416202x+109/15-5
26
Here, we want to write a range of values for x.
The shape we have is not a parallelogram but we have two equal sides
If it was a complete parallelogram, the two marked angles will be equal
But since what we have is not a complete parallelogram,
then;
[tex]\begin{gathered} 2x\text{ + 10 < 62 } \\ 2x\text{ < 62 - 10} \\ \\ 2x\text{ < 52} \\ \\ x\text{ < }\frac{52}{2} \\ \\ x\text{ < 26} \end{gathered}[/tex]you are packing for a road trip and want to figure out how much you can fit in your rectangular suitcase the suitcase has the following dimensions list length2 1/3ft width 1/3ft 1 1/2ft what is the volume of your suitcase in cubic feet
The Volume of the suitcase is given by the formula:
Length x width x height = L X W X H
L= 2 1/3ft
W= 1/3ft
H= 1 1/2ft
[tex]\begin{gathered} \text{Volume = 2}\frac{1}{3\text{ }}\text{ x }\frac{1}{3}\text{ x 1}\frac{1}{2}ft^3 \\ V\text{ = }\frac{7}{3}\text{ x }\frac{1}{3}\text{ x}\frac{3}{2}ft^3 \\ V\text{ = }\frac{21}{18}ft^3 \\ V=\text{ }\frac{7}{6}ft^3 \\ V=\text{ 1}\frac{1}{6}ft^3 \end{gathered}[/tex]Volume of the suitcase is 1 1/6 cubic feet
76. A company has hired 10 new employees, I men and 3 women. The company mustassign 5 of them to the morning shift, 3 of them to the swing shift, and the restof them to the graveyard shift.(a) (2 points) Find the prob that at least one man is assigned to the swing shift?
Answer:
[tex]\frac{2519}{2520}[/tex]Explanation:
Here, we want to get the probability that at least one man is assigned to the swing shift
From the question, 3 of the employees are assigned to the swing shift
Thus we have to calculate the probability of:
1 man , 2 men or 3 men
Mathematically, we have that as:
1 - p(all of the swing shift employees are women)
For the swing shift, for all them to be women, we will be selecting 3 out of 3 so the combination here is 3 C 3 which is 1
We now calculate the probability by dividing this value by the total number of possible ways
Mathematically, we have that as follows:
[tex]\frac{1}{10\text{ C 5 }\times\text{ 5 C 3 }^\times\text{ 1}}\text{ = }\frac{1}{2520}[/tex]This is the probability of placing all of the women on the swing shift
So, the probability that at least 1 man is assigned will be:
[tex]1-\text{ }\frac{1}{2520}\text{ = }\frac{2519}{2520}[/tex]Two functions are shown. f(x) = 29(0.5)* g(x) = 18x + 14 What is the value of f(2) + g(4)?
Answer:
93.25
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=29(0.5)^x \\ g(x)=18x+14 \end{gathered}[/tex]To be able to find the value of f(2) + g(4), we have to 1st determine the value of f(2) and f(4) as shown below;
[tex]\begin{gathered} f(2)=29(0.5)^2=29\ast0.25=7.25 \\ g(4)=18(4)+14=72+14=86 \end{gathered}[/tex]Let's go ahead and find the value of f(2) + g(4);
[tex]f(2)+g(4)=7.25+86=93.25[/tex]Two lines are shown on the grid below.Read the statements below about the graph of the two lines.Which statements are true about the two lines on the graph?A.I,II, and IV onlyB.II,III, and IV onlyC.II and III only D.I,II,III,and IV
Answer:
B. II, III, and IV only
Explanation:
Vertical lines have an undefined slope and the equation of these lines is x = c, where c is a constant value
Horizontal lines have a slope equal to 0 and the equation of these lines is y = c, where c is a constant value.
Therefore, the statements that are true about the graph are:
The equation of line b is y = -5
Line b has a slope of 0
The equation of line a is x = 3
I need help with this assignment
In this problem the big angle will be equal to two times the smaller angle so the correct expression is:
[tex]\angle TUV=2\angle VUW[/tex]Now we can rewrite the equation so:
[tex]\angle VUW=\frac{1}{2}\angle TUV[/tex]Simplify the following expression. Assume variables are positive. Express your answer using rational exponents.
Let's simplify the expression:
[tex]\begin{gathered} (x^{-\frac{1}{2}}\cdot y^{-\frac{2}{3}}\cdot z^{-2})^{-\frac{1}{2}}=x^{(-\frac{1}{2})(-\frac{1}{2})}y^{(-\frac{2}{3})(-\frac{1}{2})}z^{(-2)(-\frac{1}{2})} \\ =x^{\frac{1}{4}}y^{\frac{1}{3}}z \end{gathered}[/tex]Therefore the answer is:
[tex]x^{\frac{1}{4}}y^{\frac{1}{3}}z[/tex]What is the value of the expression shown? 5 – a(3² + (ab + 2)² – 7) when a = 2 and b = –3
The expression has a value of -31 when a = 2 and b = –3
How to evaluate the expression?From the question, the expression is given as
5 – a(3² + (ab + 2)² – 7)
Also, we have the values of the variables to be
a = 2 and b = –3
Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)
So, we have the following equation
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)
Evaluate the expressions in the bracket
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)
Evaluate the exponents
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)
So, we have
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18
This gives
5 – a(3² + (ab + 2)² – 7) = 5 – 36
Evaluate the difference
5 – a(3² + (ab + 2)² – 7) = -31
Hence, the value of the expression is -31
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Find the median:1,4,2,7,3,9,5,12,4,8
Take into account that the median of a data set is given by the element of the set that is at the center of the ordered list of elements. If there is no possible to determine a central element in the list, then, you take two elements of the center and calculate the average value in between such elements.
Then, first order the elements, as follow:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
THe number of elements is 10, then, you conisder the two elements at the center of the list, that is, the 5th and 6th elements:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
and calculate the average in between these numbers:
median = (4 + 5)2 = 9/2 = 4.5
Hence, the median of the given data set id 4.5
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x)=230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
The cost at the break-even point is $
The revenue at the break-even point is
units.
www
The break-even point=30, The cost of producing x units of tile =6900$, revenue from the sale of x units of tile at the break-even point=6900$.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What is revenue?Revenue is the total amount of money made from the sale of products and services that are essential to the business's core operations. Sales or turnover are other terms used to describe commercial revenue. Some businesses make money from royalties, interest, or other fees.
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile is given by R(x)=230x.
C(x) = 200x + 900
R(x)=230x
200x+900=230x
30x=900
x=30
C(x)=200*30+900
=6900
R(x)=230*30=6900
30 is the break-even point; At the break-even point, the cost of producing 30 units of tile is $6900, and the revenue from those sales is $6900.
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Need help pleaseI was bad at math in school so lwant to learn
The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/tex]TRIGONOMETRY Given a unite circle what is the value for y?
Let's put more details in the given figure:
To find y, we will be using the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{r}^2=x^2+y^2 \\ \end{gathered}[/tex]Where,
r = radius
x = 1/3
y = uknown
We get,
[tex]\text{r}^2=x^2+y^2[/tex][tex]\begin{gathered} y^2\text{ = r}^2\text{ - }x^2 \\ y^{}\text{ = }\sqrt{\text{r}^2\text{ - }x^2} \end{gathered}[/tex][tex]\text{ y = }\sqrt[]{1^2-(\frac{1}{2})^2}\text{ = }\sqrt[]{1\text{ - }\frac{1}{4}}[/tex][tex]\text{ y = }\sqrt[]{\frac{3}{4}}\text{ = }\frac{\sqrt[]{3}}{\sqrt[]{4}}[/tex][tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Therefore, the answer is:
[tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]The area of a circle is about 167.3306 square inches. The circle's circumference is ____ inches.Use 3.14 for π.
The area of a circle can be calculated using this formula:
[tex]A=\pi r^2[/tex]Where "r" is the radius of the circle.
The circumference of a circle can be found using this formula:
[tex]C=2\pi r[/tex]Where "r" is the radius of the circle.
In this case you know that the area of this circle is:
[tex]A\approx167.3306in^2[/tex]Then, you can substitute this value into the first formula and solve for "r". Use:
[tex]\pi=3.14[/tex]Then:
[tex]\begin{gathered} (167.3306in^2)=(3.14)r^2 \\ \\ \frac{(167.3306in^2)}{3.14}=r^2 \\ \\ r=\sqrt[]{(\frac{167.3306in^2}{3.14})} \\ \\ r=7.3in \end{gathered}[/tex]Now you can substitute this value into the formula for calculate the circumference of a circle:
[tex]\begin{gathered} C=(2)(3.14)(7.3in) \\ \end{gathered}[/tex]Finally, evaluating, you get:
[tex]C=45.844in[/tex]The answer is:
[tex]45.844in[/tex]I am canfusing in this question can you solve it.
Answer:
Step by step explanation:
