Answer:
x=16
Step-by-step explanation:
Simplifying
3x + 16 = 4x
Reorder the terms:
16 + 3x = 4x
Solving
16 + 3x = 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
16 + 3x + -4x = 4x + -4x
Combine like terms: 3x + -4x = -1x
16 + -1x = 4x + -4x
Combine like terms: 4x + -4x = 0
16 + -1x = 0
Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16
Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16
Combine like terms: 0 + -16 = -16
-1x = -16
Divide each side by '-1'.
x = 16
Simplifying
x = 16
3. Pentagon PENTA with P(0, 2), E(4,6), N(8,-1), T(6,-3), and A(2,-4); reflect across y-axis. /1a. What is the "arrow rule" to show this transformation? 15 b. What are the vertices of the image after the transformation?
1a) The arrow will be (-x,y) for reflection
1b)The vertices are P(-(0),2), E(-4,6), N(-8,-1), T(-6,-3), A(-2/-4) = P(0,2), E(-4,6), N(-8,-1),T(-6,-3), A(-2,-4)
what is the inequality on a graph with the boundary line x+3y=-15
Solution
To graph the inequality,
we make y the subject of the formula;
[tex]\begin{gathered} x+3y\ge-15 \\ \\ \Rightarrow3y\ge-x-15 \\ \\ \Rightarrow y\ge-\frac{1}{3}x-\frac{15}{3} \\ \\ y\ge-\frac{1}{3}x-5 \end{gathered}[/tex]The inequallity is;
[tex]\begin{gathered} \ge \\ \\ That\text{ is} \\ x+3y\ge-15 \end{gathered}[/tex]The art teacher mixed 12 ounces of yellow paint with 5 ounces of blue paint to make green. How many ounces of blue would be needed if you used 20 ounces of yellow ?
The relation is 12 ounces of yellow paint with 5 ounces of blue paint. To find how many ounces of blue would be needed if you used 20 ounces of yellow, we can use the next proportion:
[tex]\frac{12\text{ ounces of yellow}}{20\text{ ounces of yellow}}=\frac{5\text{ ounces of blue}}{x\text{ ounces of blue}}[/tex]Solving for x,
[tex]\begin{gathered} 12\cdot x=5\cdot20 \\ 12\cdot x=100 \\ x=\frac{100}{12} \\ x=\frac{25}{3} \end{gathered}[/tex]You would need 25/3 ounces of blue paint
find the probability of rolling a die five times and getting no threes 
Answer:
5/5
Step-by-step explanation:
since its 5 times u re rolling the dice and u have 5 chances or 5 possibilities of getting 5
Answer:
Step-by-step explanation:
1) Set an equation
Getting a three on the dice is 1/6. So the opposite is 5/6.
5/6 * 5/6 * 5/6 * 5/6 * 5/6
2) Solve
3125/7776
0.4018
40.18%
Write an algebraic expression for the sum of 3 coins and c coins.
Oc+3
Oc/3
O3c
Oc-3
Answer:
c+3
Step-by-step explanation:
The word 'sum' means addition, so the equation would be c+3
In developing her science project, Leigh learned that light travels at a constant rateand that it takes 500 seconds for light to travel the 93 million miles from the Sun toEarth. Mars is 142 million miles from the Sun. About how many seconds will it takefor light to travel from the Sun to Mars?A. 235 secondsB. 327 secondsC. 642 secondsD. 763 seconds
D. 763 seconds
Explanation:
Data:
Seconds light travels distance between Sun and Earth : 500 seconds
Distance between Sun and Earth: 93 million miles
Distance between Sun and Mars: 142 million miles
Formula: (see image below)
Solution:
From Sun to Mars the light takes (142 * 500) / 93 = 763 seconds
NB:
The tactic is to first put the data given in a table like in the image above, to first multiply diagonally then divide horizontally. (starting from the data that his paired data).
Here the paired data missing is the time it takes for the light to travel from the Sun to Mars, therefore you'll multiply the distance between the Sun to Mars (known data missing a pair) by the time it takes light to travel from the Sun to Earth (known data with its pair), then divide the result by the distance between the Sun and earth (pair of the former mentioned known data)
15) Cost of a computer game: $4.99
Markup: 40%
Discount: 55%%
Tax: 1%
Answer:
$3.18
Step-by-step explanation:
(4.99×0.4)+4.99=6.986
6.986-(6.986×0.55)=3.1437
(3.147×0.01)+3.147=3.175137
Use the binomial theorem to expand the binomial.(x – 3)^5
The binomial theorem tells us how to expand an expression of the form (a + b)^2 like this:
[tex](a+b)^n=nC_0a^nb^0+nC_1a^{n-1}b^1+\cdots nC_na^0b^n[/tex]And nCr is given by the following formula:
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, for this polynomial, we can apply the binomial theorem with a = x, b = -3 and n = 5 to get:
[tex](x-3)^5=5C_0x^5(-3)^0+5C_1x^4(-3)^1+5C_2x^3(-3)^2+5C_3x^2(-3)^3+5C_4x^1(-3)^4+5C_5x^0(-3)^5[/tex][tex]\begin{gathered} 5C_0=1 \\ 5C_1=5 \\ 5C_2=10 \\ 5C_3=10 \\ 5C_4=5 \\ 5C_5=1 \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} (x-3)^5=(1)x^5(-3)^0+(5)_{}x^4(-3)^1+(10)_{}x^3(-3)^2+(10)x^2(-3)^3+(5)x^1(-3)^4+(1)x^0(-3)^5 \\ (x-3)^5=x^5+(5)_{}x^4(-3)^{}+(10)_{}x^3(9)+(10)x^2(-27)+(5)x^1(81)^{}-243 \\ (x-3)^5=x^5-15_{}x^4^{}+90_{}x^3-270x^2+405x^{}^{}-243 \end{gathered}[/tex]Then, the expanded polynomial is:
x⁵ - 15x⁴ + 90x³ - 270x² + 405x - 243
I might not respond for a little while, please don’t end the session! Need help on #3 and 4
We have a right triangle with a 15m hypotenuse and a 8m leg. If we use x for the missing leg then the Pythagorean Theorem states that:
[tex]15^2=8^2+x^2[/tex]Then we have to solve that equation for x:
[tex]\begin{gathered} x^2=15^2-8^2=225-64 \\ x^2=161 \\ x=\sqrt[]{161} \end{gathered}[/tex]So the answer is the square root of 161.
Final and of the non side round your answer to the nearest 10th 18 and 4
In the right triangle, there is a relation between its sides
(hypotenuse)^2 = (leg1)^2 + (leg2)^2
The hypotenuse is the side opposite to the right angle
leg1 and leg 2 are the sides of the right angle
In the given figure
The hypotenuse = 18
leg1 = 4
(18)^2 = (4)^2 + (leg2)^2
324 = 16 + (leg2)^2
Subtract 16 from both sides
324 - 16 = 16 - 16 + (leg2)^2
308 = (leg2)^2
Take square root for both sides
17.54992877 = leg2
Round it to the nearest tenth
leg2 = 17.5
how can i get an elimination out of this equation? i think its c but im not sure
We have the system of equations
[tex]\begin{cases}x+8y=2 \\ -2x+8y=20\end{cases}[/tex]We can solve it subtraction, the first equation minus the second equation
[tex]\begin{gathered} x+8y-(-2x+8y)=2-20 \\ \\ x+8y+2x-8y=-18 \\ \\ x+2x=-18 \\ \\ 3x=-18 \\ \\ x=\frac{-18}{3}=-6 \end{gathered}[/tex]Therefore x = -6, we can now find the value of y
[tex]\begin{gathered} x+8y=2\Rightarrow-6+8y=2 \\ \\ -6+8y=2 \\ \\ 8y=8 \\ \\ y=1 \end{gathered}[/tex]Therefore the solution is
[tex](-6,1)[/tex]The table below shows the educational attainment of a country's population, aged 25 and over. Use the data in the table, expressed in millions, to find the probability that a randomly selected citizen, aged 25 or
over, had 4 years of college.
Male
Female
Total
Less Than
4 Years
High School
15
19
34
4 Years
High School
Only
25
32
57
Some College
(Less Than
4 Years)
18
26
44
4 Years
College
(or More)
24
20
44
Total
82
97
179
The probability that a randomly selected citizen, aged 25 or
over, had 4 years of college : 0.2458
From the table
Total number of citizens aged 25 or above = 179 million.
number of citizens aged 25 or above, had 4 years of college = 44 million
Therefore, probability = 44/179 = 0.2458
What is probability ?Probability is a branch of mathematics that deals with calculating the probability of a given event, expressed as a number between 1 and 0. An event with a probability of 1 can be considered certain: for example, the probability of a coin toss. a toss that results in either "heads" or "tails" is 1 because there are no other options, assuming the coin lands flat. An event with probability 0.5 can be considered equally likely to occur or not to occur: for example, the probability that a coin toss results in heads is 0.5, because the toss is equally likely to result in tails." An event with probability 0 can be considered impossible: for example, the probability that the a coin lands (uniformly) without both sides up is 0, because either "heads" or "tails" must be up.
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Solve the systems of equations. List variables a, b, and c.
a-2b+c=8
2a+b-c=0
3a-6b+ 3c = 24
a = 2b-c+8
b = (-a-c+8)/ 2
c = -a+2b+8
variable a ,b & c for 2a+b-c=0
a = (-b+c) / 2
b=-2a+c
c = 2a+b
variable a ,b & c for 3a-6b+ 3c = 24
a=2b-c+8
b = - (-a-c+8)/ 2
C = -a+2b+8
How to find variables a,b,c ?
1) Finding variable a ,b & c for a-2b+c=8
Finding a=(a-2b+c) + (2b-c)=8+ (2b-c)
a -2b+c+2b-c=8+2b-c
a-2b+2b+c-c=2b-c+8
a = 2b-c+8
Finding b =a-2b+c=8
(a-2b+c) + (−a − c) = 8+ (-a-c)
a-2b+c-a-c=8-a-c
b = (-a-c+8)/ 2
Finding c =a-2b+c8
(a-2b+c)+(-a+2b)=8+(-a+2b)
c = -a+2b+8
2) Finding variable a ,b & c for 2a+b-c=0
Finding a=2a+b-c=0
(2a+b-c)+(-b+c) = -b+c
2a+b-c-b+c = -b+c
a = (-b+c) / 2
Finding b =2a+b-c=0
(2a + b-c) + (-2a + c) = -2a + c
b=-2a+c
Finding c =2a+b-c=0
(2a+b-c) + (-2a - b) = -2a-b
c = 2a+b
3) Finding variable a ,b & c for 3a-6b+ 3c = 24
Finding a=3a-6b+3c = 24
(3a-6b+3c) + (6b-3c) = 24 + (6b- 3c)
3a-6b+3c+6b-3c = 24 + 6b-3c
a=2b-c+8
Finding b =3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
3a-6b+3c-3a-3c-24-3a-3c
3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
b = - (-a-c+8)/ 2
Finding c =3a-6b+3c=24
(3a-6b+3c) + (-3a+6b)=24+ (-3a+6b)
3a-6b+3c-3a+6b-24-3a+6b
C = -a+2b+8
System of equations :In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.A system of equations is a set of one or more equations involving a number of variables.The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. A system of equations can be classified in a similar manner as single equations.The following set of equations is an example of system of equations,2x - y = 12
x - 2y = 48
Solving a system of equations means finding the values of the variables used in the set of equations.We compute the values of the unknown variables still balancing the equations on both sides.The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.To learn more about System of equations refer :
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The amount Lins sister earns at her part time job is proportional to the number of hours she works. She earns 9.60 dollars per hour1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.2. is y a function of x? explain how you know.3. Write an equation describing x as a function of y
The amount Lins sister earns at her part-time job is proportional to the number of hours she works.
She earns 9.60 dollars per hour.
1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.
$9.60 per hour means that y = 9.60 and x = 1
[tex]\begin{gathered} y=kx \\ 9.60=k(1) \\ k=\frac{9.60}{1} \\ k=9.60 \end{gathered}[/tex]Since we found the value of constant k, so the relation becomes
[tex]y=9.60x[/tex]2. is y a function of x? explain how you know
y is a function of x means that the value of y depends on the value of x.
In the above function, when the value of x changes then the value of y will also change.
3. Write an equation describing x as a function of y
To write the equation describing x as a function of y, make x the subject of the equation.
This simply means to separate out the variable x.
[tex]\begin{gathered} y=9.60x \\ 9.60x=y \\ x=\frac{y}{9.60} \end{gathered}[/tex]The diagonal of a square measures 12 inches. What is the length of the sides
It is given that the diagonal of a square is 12 inches.
The square is given by the diagram shown below:
In the triangle ABC by pythagorean theorem it follows:
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ 2AB^2=12^2 \\ AB^2=\frac{144}{2} \\ AB^2=72 \\ AB=\sqrt[]{72}=6\sqrt[]{2} \end{gathered}[/tex]Hence the side is given by:
[tex]s=6\sqrt[]{2}\text{ inches}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
function of f(-5) is equal to the same value of y in an equation y= f(x).
therefore x value is -5 on x-axis and on this point it gives the value of y-axis which is -2
Expand using binomial theorem(4x-7y)^4
Answer:
Recall that the binomial theorem states that:
[tex](a+b)^n=\sum ^n_{k=0}{\binom{n}{k}}a^{n-k}b^k\text{.}[/tex]Then:
[tex](4x-7y)^4=\sum ^4_{k=0}{\binom{4}{k}}(4x)^{4-k}(-7y)^k\text{.}[/tex]Therefore:
[tex]\begin{gathered} (4x-7y)^4={\binom{4}{0}(4x)^{4-0}(-7y)^0}+{\binom{4}{1}(4x)^{4-1}(-7y)^1}+{\binom{4}{2}(4x)^{4-2}(-7y)^2} \\ +{\binom{4}{3}(4x)^{4-3}(-7y)^3+{\binom{4}{4}(4x)^{4-4}(-7y)^4\text{.}}} \end{gathered}[/tex]need help asappppppp
a.
Consider that the volume (V) of a cone with radius 'R' and height 'H' is given by,
[tex]V=\frac{1}{3}\pi R^2H[/tex]Substitute the values,
[tex]\begin{gathered} V=\frac{1}{3}\pi(4)^2(3) \\ V=16\pi \end{gathered}[/tex]Therefore, option b is the correct choice.
b.
Consider that the volume (V') of a cylinder with radius 'R' and height 'H' is given by,
[tex]V^{\prime}=\pi R^2H[/tex]Solve for the ratio of volume of cone to that of cylinder as,
[tex]\frac{V}{V^{\prime}}=\frac{(\frac{1}{3}\pi R^2H)}{(\pi R^2H)}=\frac{1}{3}[/tex]Therefore, option c is the correct choice.
The test scores for the analytical writingsection of a particular standardized test canbe approximated by a normal distribution, asshown in the figure.(a) What is the maximum score that can be inthe bottom 10% of scores?(b) Between what two values does the middle80% of scores lie?
Solution:
Given:
Recall that the z-value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{where} \\ \mu\Rightarrow\operatorname{mean}\text{ value} \\ \sigma\Rightarrow s\tan dard\text{ deviation} \end{gathered}[/tex]Thus,
[tex]z=\frac{x-3.7}{0.91}\text{ ---- equation 1}[/tex]A) maximum score that can be in the bottom 10% of scores
using the table of z-values,
for the bottom 10% scores, we have
[tex]z=-1.28155156554[/tex]To evaluate x, substitute the value of z into equation 1.
Thus,
[tex]\begin{gathered} -1.28155156554=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5337895 \end{gathered}[/tex]Thus, the maximum score that can be in the bottom 10% of scores is 2.5
B) Two values for which the middle 80% of scores lie.
From the z score values shown below:
The z scores of the value are
[tex]\begin{gathered} z_1=-1.28 \\ z_2=1.28 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{when z=-1.28, we have} \\ -1.28=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5352 \\ \text{when z=1.28, we have} \\ 1.28=\frac{x-3.7}{0.91} \\ \Rightarrow x=4.8648 \end{gathered}[/tex]Thus, the two values for which the middle 80% of scores lie are 2.5 and 4.86.
Use the distributive property to write an equivalent expression to y(6+15)
The most appropriate choice for distributive property of algebraic expression will be given by-
21y is the required equivalent expression
What is distributive property of algebraic expression?
At first it is important to know about algebraic expression.
Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division.
Distributive property is a property which connects both addition and multiplication.
Suppose a, b and c are three numbers. Distributive property implies
a [tex]\times[/tex] (b + c) = a [tex]\times[/tex] b + a [tex]\times[/tex] c
Here,
y(6 + 15)
y [tex]\times[/tex] (6 + 15)
6 [tex]\times[/tex] y + 15 [tex]\times[/tex] y
6y + 15y
21y
This is the required equivalent expression
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Kara wants to order lunch for her friends. She'll order 8 cups of soup and a $4 child’s meal for her brother. Kara has $28. How much can she spend on each cup of soup if they are all the same price?
Choose two answers: one for the inequality that models this situation and one for the correct answer.
A.
Inequality: 4x + 8 ≥ 28
B.
Answer: $3 or less
C.
Inequality: 8x + 4 ≥ 28
D.
Inequality: 8x + 4 ≤ 28
E.
Answer: $5 or less
F.
Inequality: 4x + 8 < 28
The inequality that represents the equation is 8x+4<=28. The money spent on each cup is $3 or less. So, B and D are the correct options
Number of cups ordered by Kara = 8 cups
Money spent on the child's meal by Kara = $4
Total money with Kara = $28
Let x represent the money Kara will spend on each cup of soup
In formulation of the equation we get the following:
Number of cups*Money she can spend on each cup + Money spent on child's meal <= 28
8x + 4<=28
Solving the inequality:
8x<=24
x<= $3
So, the cost of a cup is $3 or less
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math question #12solve for the missing value x 1/2: 4 = 1/3 : x
To find the value of x we need to write the equation in another form that tells us what to do; both sides of the equations are ratios then we have:
[tex]\begin{gathered} \frac{1}{2}:4=\frac{\frac{1}{2}}{4} \\ \text{ and} \\ \frac{1}{3}:x=\frac{\frac{1}{3}}{x} \end{gathered}[/tex]Then the equation is:
[tex]\frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x} \\ \frac{1}{8}=\frac{1}{3x} \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}[/tex]Therefore, the value of x is 8/3
if d=3, does d+d+d =3d?
Yes, d + d + d = 3d
Explanations:d + d + d can also be written as:
1d + 1d + 1d
which equals to 3d
Therefore, no matter what the value of d is,
d + d + d = 3d
Find the y-intercept of the line on the graph.
Answer:
-2
Step-by-step explanation:
This is where the line crosses the y axis. It is at point (0,-2)
What is what is 156.4÷23
Answer:
156.4 ÷ 23 = 6.8
Step-by-step explanation:
hope this helps
Reese is selling lemonade at the parade. He gets to keep 10% of the money he collects. A large lemonadeis $4.00 and a small lemonade is $3.00.The expression represents 10% of the money he collects.0.10(4/ +35)Use the Distributive Property to expand the expression.The simplified expression is
ANSWER
[tex]0.40l+0.30s[/tex]EXPLANATION
We want to use the distributive property to expand the expression:
[tex]0.10(4l+3s)[/tex]To do this, use the term outside the bracket to multiply each of the terms in the bracket:
[tex]\begin{gathered} (0.10\cdot4l)+(0.10\cdot3s) \\ 0.40l+0.30s \end{gathered}[/tex]That is the simplified expression.
j(x) = 2x² - 2
Find j(-1)
Your answer would be 0, hope this helps.
I need help with this question please and thank you
Answer:
[tex]x(x+3)[/tex]Step-by-step explanation:
The least common denominator of a and b is the smallest multiplier that is divisible by both a and b. In this case, for:
[tex]\begin{gathered} \frac{x+4}{x}+\frac{x}{x+3}=\frac{(x+3)(x+4)+x\cdot x}{x(x+3)} \\ \end{gathered}[/tex]4. Which equation does NOT have like terms to collect?
3y - 2(y-1) + y = −42
-8(b-3) = -56 - 6
15t+19r = 2
8.5d +7.5 10d +3
Answer:
15t + 19r = 2
Step-by-step explanation:
None of the unknowns are common
Урна содержит 10 белых и 10 черных шаров. Вынимают 5 раз по два шара (без возврата). С какой вероятностью каждый раз вынимали по 2 шара разного цвета?
An urn contains 10 white and 10 black balls. Two balls are taken out 5 times (without return). What is the probability that 2 balls of different colors were drawn each time?
Answer:
≈4,365%.
Step-by-step explanation:
1) для нахождения требуемой вероятности необходимо найти вероятность каждого из пяти выниманий, а затем перемножить их;
2) при каждом вынимании вероятности:
[tex]P_1=\frac{C^1_{10}*C^1_{10}}{C^2_{10}}=\frac{10}{19};\\P_2=\frac{C^1_9*C_9^1}{C^2_{18}}=\frac{9}{17};\\P_3=\frac{C^1_8*C_8^1}{C^2_{16}}=\frac{8}{15};\\P_4=\frac{C^1_7*C^1_7}{C^2_{14}}=\frac{7}{13};\\P_5=\frac{C^1_6*C^1_6}{C^2_{12}}=\frac{6}{11};[/tex]
3) требуемая вероятность:
P=P₁*P₂*P₃*P₄*P₅≈0,04365.
