Answers
SOLUTIONS
Solve the equations. Show the solution sets on a number line.
\(|3x-7|-4=0\)
Related Questions
What’s 6 and 2/3 divided by 8
Answers
Answer: 5/6
Step-by-step explanation:
Answer:
6 divided by 8 is 3/4 (.78)
2/3 divided by 8 is 1/12 (0.083)
6 2/3 divided by 8 is 5/6 (0.83)
please answer this question
Answers
As it is given :
Present age of mom : Present age of son = 6 : 1
Therefore let :
Mother's age be 6xSon's age be xPart two :Ages after 10 year :
Mom's age = 6x + 10Son's age = x + 10Part three :The ages after 10 years are given in rational of 8 : 3.
Which means :
Mom's age after 10 years : Son's age after 10 years = 8 :3.
Now :
\( \scriptsize \purple{ \boxed{ \scriptsize \dfrac{ \text{Mom's age after 10 years}}{ \text{son's age after 10 years}}= \dfrac{8}{3} }} \star\)
\( \\ \\ \)
So :
\( \small\sf \dashrightarrow \dfrac{6x + 10}{x + 10} = \sf \dfrac{8}{3} \)
\( \\ \\ \)
\( \small\sf \dashrightarrow \dfrac{3(6x + 10)}{x + 10} = \sf \dfrac{8}{1} \)
\( \\ \\ \)
\(\small \sf \dashrightarrow \dfrac{18x +30}{x + 10} = \sf \dfrac{8}{1} \)
\( \\ \\\)
\( \small\sf \dashrightarrow \dfrac{18x +30}{1} = \sf \dfrac{8(x + 10)}{1} \)
\( \\ \\ \)
\(\small \sf \dashrightarrow 18x +30= \sf 8(x + 10)\)
\( \\ \\ \)
\( \small\sf \dashrightarrow 18x +30= \sf 8x + 80\)
\( \\ \\ \)
\( \small\sf \dashrightarrow 18x - 8x +30= \sf 80\)
\( \\ \\ \)
\(\small \sf \dashrightarrow 10x +30= \sf 80\)
\( \\ \\ \)
\(\small \sf \dashrightarrow 10x = \sf 80 - 30\)
\( \\ \\ \)
\(\small \sf \dashrightarrow 10x = \sf 50\)
\( \\ \\ \)
\(\small \sf \dashrightarrow \dfrac{10x}{10} = \sf \dfrac{50}{10} \)
\( \\ \\ \)
\(\small \sf \dashrightarrow \dfrac{1\cancel0x}{1\cancel0} = \sf \dfrac{5\cancel0}{1\cancel0} \)
\( \\ \\ \)
\( \small\bf \dashrightarrow x = \pink 5\)
\( \\ \)
Part four :We know :
\( \footnotesize \hookrightarrow \sf Son's \: age = x\)
\( \footnotesize \hookrightarrow \sf Son's \: age = \red{5 \: years}\)
\( \\ \\ \)
\( \footnotesize \hookrightarrow \sf Mother's \: age = 6x\)
\( \footnotesize\hookrightarrow \sf Mother's \: age = 6 \times 5\)
\( \footnotesize \hookrightarrow \sf Mother's \: age = \bf \red{30 \: years}\)
━━━━━━❃━━━━━━And all we are done ! ㋛
~\(\pmb{\cal W\frak{indy}M\frak{int}}\)༄In this table, x is directly proportional to y. What is the missing number?
Answers
Answer:
36
Step-by-step explanation:
The numbers on the bottom are always equal to 1.5 times the number on top.
3 x 1.5 = 4.5, 10 x 1.5 = 15, and so on. 24 x 1.5 = 36, so the missing number is 36.
1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?
Ans: years
2. The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other
number is ….
Answers
Answer:
1) 48 years.
2) Question incorrect.
11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Step-by-step explanation:
Let the ages of Kissi, Esinam and Lariba be x, y and z respectively.
Ratio of the ages of Kissi and Esinam is 3:5
x:y = 3:5
(x/y) = (3/5)
5x = 3y
x = (3y/5) (eqn 1)
Ratio of the ages of Esinam and Lariba is 3:5
y:z = 3:5
(y/z) = (3/5)
5y = 3z
z = (5y/3) (eqn 2)
The sum of their 3 ages is 147
x + y + z = 147 (eqn 3)
Substituting the values of x and z from eqn 1 and 2 into eqn 3, we have
(3y/5) + y + (5y/3) = 147
(49y/15) = 147
y = (147×15/49) = 45.
x = (3y/5) = (3×45/5) = 27
z = (5y/3) = (5×45/3) = 75
The ages of Kissi, Esinam and Lariba are then 27, 45 and 75 respectively.
The difference in the ages of the oldest amf the youngest is thus, 75 - 27 = 48 years.
2) This question seems to be faulty and incorrect as 11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Hope this Helps!!!
i will mark brainliest please help me on this question!
Answers
Answer:
C
Step-by-step explanation:
You can determine this by the third and fourth quartiles.
Answer:
C
Step-by-step explanation:
1,4,4,9,10,10,14
We know the smallest number is 1 and the largest number is 14, so they are left and right whiskers
1,4,4, 9, 10,10,14
The middle number is the 4th number, which is 9 so it is the middle number of the box
Taking the numbers on the left
1,4,4
The middle number is 4 so it is the left hand side of the box
Taking the numbers on the right
10,10,14
10 is the middle number so it is the right hand side of the box
5 [11 marks] Question 4 - Exponents 1. A factory makes 1 000 000 000 yo-yos. Write the number of yo-yos in exponential form. (1) 2. Mrs. Penn has a vegetable garden. There are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. Work out the number of small squares, each 1cm by 1cm in the grid and write it in exponential form. (1) [2 marks]
Answers
1.) The exponential form for the number of yo-yos, 1,000,000,000, is \(10^9\). This represents 10 raised to the power of the number of zeros in the original number.
2.) For Mrs. Penn's vegetable garden, with 8 rows and 8 columns of 1cm squares, the total number of small squares is 64. This can be expressed as \(2^6\) , where 2 is the base number and 6 represents the exponent obtained from repeated multiplication.
1.) To write the number of yo-yos in exponential form, we can use the base 10 since we have a decimal system. The given number of yo-yos is 1,000,000,000. We can express it as 10 raised to the power of a certain exponent that represents the number of zeros in the original number.
In this case, the number has 9 zeros, so we can write it as \(10^9\). The exponential form for the number of yo-yos is \(10^9.\)
2.) In Mrs. Penn's vegetable garden, there are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. We need to calculate the number of small squares, each measuring 1cm by 1cm, in the grid.
Since there are 8 rows and 8 columns, we can multiply these two numbers together to find the total number of small squares. 8 multiplied by 8 equals 64.
The exponential form represents repeated multiplication of the base number. In this case, the base number is 64 since we have 64 small squares. To write it in exponential form, we need to determine the exponent that represents the number of times 64 is multiplied by itself.
Since 64 is 2 raised to the power of \(6 (2^6)\), we can express it as \((2^6)^1\). Simplifying this, we get \(2^(6*1)\) which equals \(2^6.\)
Therefore, the exponential form for the number of small squares in the grid is \(2^6.\)
In summary, the number of yo-yos in exponential form is \(10^9\), and the number of small squares in the grid is \(2^6.\)
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What is the volume of this prism?
Answers
Answer:
The answer is 13 1/8ft3
Explanation:
Substitute into the formula:
Volume = 3 1/2 x 2 1/2 x 1 1/2
= 7/2 x 5/2 x 3/2
= 105/8
= 13 1/8 ft3
rotate the figure 90 degrees clockwise then translate 4 units left
Answers
Answer:
If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)
Answer:
For each of the following equations determine the output values Corresponding to the input value
(-2;-1;0;1;2;3)
Find the missing number in this proportion. 24/36= 8/?
Answers
Answer: i think the answer is 9
Step-by-step explanation:
Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
1. f(x) is exponential; an exponential function increases more slowly than a linear function.
2. f(x) is exponential; f(x) increased more overall than g(x).
3. g(x) is exponential; g(x) has a higher starting value and higher ending value.
4. g(x) is exponential; an exponential function increases faster than a linear function.
Answers
Hi there!
\(\large\boxed{\text{Choice 4}}\)
We can look at each function, f(x) and g(x), to determine which is exponential.
Use slope formula: m = y2-y1/x2-x1
f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.
g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.
Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.
What is the answer to this combination lock
Answers
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
QRS has been dilated to form TUV. What is the length of QS?
Answers
Answer:
C. 2
Step by step explanation:
In this case, you can use the similarity of triangles.
\(\frac{x}{a}=\text{ }\frac{y}{b}\text{ = }\frac{z}{c}\)X= 35
Y = 5
a =14
b = ?
Then we replace.
\(\frac{35}{14}=\frac{5}{?}\)\(\text{? = }\frac{5\cdot14}{35}\)\(\text{? = 2}\)
Help to solve x and Y
Answers
Solving steps:
1. Solve for x
Look at picture
2. Find y
(10x-6)+(9y-5)=180
(10(11)-6)+(9y-5)=180
104+(9y-5)=180
9y-5=76
9y=81
y=9
how do u get the range of a function for example in question 8 explain the range for like a and f
Answers
Explanation:
We are to sketch the graph of the function and also state the intercepts, range, and domain of the function
Question 8a
\(y=|x^2-4|\)To answer the question
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
The domain of a function is the complete set of possible values of the independent variable
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain
For the question, we will have to plot the graph which is shown below
From the above
\(\mathrm{X\:Intercepts}:\:\left(-2,\:0\right),\:\left(2,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:4\right)\)From the graph, we can observe the value of y ranges from 0 to positive infinity. therefore, we can represent this as:
\(\begin{gathered} Range \\ \\ \begin{bmatrix}\mathrm{Solution:}\: & \:y\ge\:0\: \\ \:\mathrm{Interval\:Notation:} & \:[0,\:\infty\:)\end{bmatrix} \end{gathered}\)For the Domain, we can observe that the values of x span from negative infinity to positive infinity, therefore, we can represent this as:
\(\begin{gathered} Domain \\ \\ \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:Question 8f
\(h(x)=|-3(x+2)^2-4|\)The graph is shown below
\(\mathrm{Y\:Intercepts}:\:\left(0,\:16\right)\)\(\begin{gathered} Domain \\ \\ \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:\(\begin{gathered} Range \\ \begin{bmatrix}\mathrm{Solution:}\: & \:y\ge\:4\: \\ \:\mathrm{Interval\:Notation:} & \:[4,\:\infty\:)\end{bmatrix} \end{gathered}\)
A radioactive compound with mass 260 grams decays at a rate of 3.8% per hour. Which equation represents how many grams of the compound will remain after 8 hours?
Answers
Approximately 138.3 grams of the compound will remain after 8 hours. The decay of a radioactive compound is an exponential process, which can be modeled by the equation:
N(t) = N₀ * e^(-λt)
where N(t) is the amount of the compound remaining at time t, N₀ is the initial amount of the compound, λ is the decay constant, and e is the mathematical constant known as Euler's number.
To find the amount of the compound remaining after 8 hours, we need to plug in the given values into the equation above. We know that the initial mass of the compound is 260 grams, and the decay rate is 3.8% per hour, which means that the decay constant λ is equal to 0.038. Therefore, the equation becomes:
N(8) = 260 * e^(-0.038 * 8)
Simplifying this equation gives:
N(8) = 260 * e^(-0.304)
N(8) ≈ 138.3 grams
Therefore, approximately 138.3 grams of the compound will remain after 8 hours.
It's important to note that this calculation assumes that the decay rate remains constant over time, which may not always be the case in reality. Additionally, the actual amount of the compound remaining may vary due to experimental error or other factors.
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The price of a necklace was increased by 10% to £121. What was the price before the increase.
Answers
Answer:
£110
Step-by-step explanation:
Adding 10% to something is the same thing as multiplying by 1.1 (1.1 is the decimal form of 110%). This has already happened so we divide by 1.1 instead.
121 / 1.1 = 110
Answer:
110
Step-by-step explanation:
10% of 110 = 11
110 + 11 = 121 :)
Please show work thank you math experts
Answers
Answer:
1. 35 - 176 = -141
2. 0.55 × 1.79 = 0.9845
3. 11.38 × 5.46 = 62.1348
Hope it helps and have a great day! =D
~sunshine~
Solve for x
x^2 - 8x = -3
Answers
The solutions for the quadratic equation:
x^2 - 8x = -3
Are:
x = 7.6x = 0.4How to solve the quadratic equation?Here we want to solve the quadratic equation:
x^2 - 8x = -3
First we can move all the terms to the left side so we get:
x^2 - 8x + 3 = 0
Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:
\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)
Then the two solutions for the quadratic equation are:
x = (8 + 7.2)/2 = 7.6
x = (8 - 7.2)/2 =0.4
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Write the linear equation that gives the rule for this table.
X
4
5
6
7
Y
24
30
36
42
Write your answer as an equation with y first, followed by an equals sign.
Answers
The equation of the line passing through the given points is y = 6x
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (4, 24) and (5, 30),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),
Therefore, the required equation is =
y-24 = 30-24/5-4 (x-4)
y-24 = 6(x-4)
y-24 = 6x-24
y = 6x
Hence, the equation of the line passing through the given points is y = 6x
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An octopus weighed 3 5/6 kilograms.After two weeks,its weight was increased by 1 4/5 kilgrams.But afterwards,it got sick and lost 2 7/15 kilograms.what is the current weight?
Answers
I think it's 3 1/6 kilograms
Step-by-step explanation:
3 5/6 + 1 4/5 since it increased
find the LCD (Least Common Denominator)
that would be 30
3 25/30 + 1 24/30
=4 49/30
= 5 19/30
Then we do subtraction since it lost some weight
5 19/30 - 2 7/15
find LCD again
5 19/30 - 2 14/30
=3 5/30
simplify
3 1/6 kilograms. That's what I think.
A diver is 15 feet below sea level.
Enter an integer that represents this situation in the box.
ft
Answers
Answer:
-15
Step-by-step explanation:
Find the measure of < 6.
Answers
Answer:
Angle 6 = 70
Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.
55% of the cookies Joel baked had chocolate chips.If joel baked 77 cookies with chocolate chi[s.How many cookies did hs bake
Answers
Answer:
140 cookies
Step-by-step explanation:
77=55%
55/5=11
77/11=7
7=5%
it's 45% away from 100%
45/5= 9
9x7=63
63+77=140
help me please please please
Answers
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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How many paths are there from $A$ to $B,$ if you travel along the edges? You can travel along each edge at most once, but you can pass through the same point more than once. (You can pass through $B,$ as long as you end up at the point $B.$)
Answers
Answer:
9
Step-by-step explanation:
You don't need to pass through each edge once.
If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:
A-1-B
A-B
A-2-B
A-1-B-A-2-B
A-2-B-A-1-B
A-B-1-A-2-B
A-B-2-A-1-B
A-1-B-2-A-B
A-2-B-1-A-B
Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.
Hope this helps!
How did you do this question?
Answers
Answer:
R = ∞
I = (-∞, ∞)
Step-by-step explanation:
Use the ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│
lim(n→∞)│x 2n! / (2(n+1)!)│
lim(n→∞)│n! / (n+1)!││x│
lim(n→∞) (1 / (n+1))│x│
0
The series converges if the limit is less than 1.
The limit is always less than 1, so the radius of convergence is infinite.
So the interval of convergence is (-∞, ∞).
Which table or graph shows the value of y going down as the value of x goes
up?
Answers
Answer:
A
Step-by-step explanation:
That's your answer...
dang u fail gonna fail i feel baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad.......
just look at the one that has the letter x going up it is c or d
oak trees are shady. shady things are not to be trusted. therefore, oak trees are not to be trusted. group of answer choices O amphiboly O equivocationO compositionO division
Answers
The fallacy in the given statement "oak trees are shady, shady things are not to be trusted, therefore oak trees are not to be trusted" is equivocation. So, second option is accurate.
Equivocation is a type of fallacy in logic and rhetoric where a word or phrase is used with multiple meanings or ambiguous terms, leading to misleading or false conclusions. It occurs when a word or phrase is used in different senses within the same argument or context, resulting in confusion or deception.
Equivocation often involves exploiting the ambiguity of words or phrases to create a deceptive or misleading impression. It can occur in various forms, including:
Ambiguous language: Using words or phrases that have multiple meanings or interpretations, and switching between them to suit the argument.Shifting definitions: Changing the definition or understanding of a term or concept within the argument to support a particular conclusion.Vague or imprecise language: Using language that is intentionally vague or lacks clarity, allowing for multiple interpretations and leading to misleading conclusions.To learn more about Equivocation refer to:
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Consider the following relation. y= 2x-4
Find four points contained in the inverse. Express your values as an integer or simplified fraction.
ASAP PLEASE¡
Answers
Four points that are contained in the inverse function include the following:
Point = (0, 4).Point = (1, 4.5).Point = (2, 5).Point = (4, 6).What is an inverse function?An inverse function refers to a type of function that is obtained by reversing a mathematical operation in a given function (f(x)).
In order to determine the inverse of the given function, we would interchange both the input value (x) and output value (y) as follows:
y = 2x - 4
x = 2y - 4
Subtracting 4 from both sides, we have:
x + 4 = 2y - 4 + 4
2y = x + 4
Dividing both sides by 2, we have:
y = (x + 4)/2
y = x/2 + 4
When x = 0, we have:
y = x/2 + 4
y = 0/2 + 4
y = 4
Point = (0, 4).
When x = 1, we have:
y = x/2 + 4
y = 1/2 + 4
y = 4.5
Point = (1, 4.5).
When x = 2, we have:
y = x/2 + 4
y = 2/2 + 4
y = 5
Point = (2, 5).
When x = 4, we have:
y = 4/2 + 4
y = 0/2 + 4
y = 6
Point = (4, 6).
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3
4 and 2i are zeros
f(1)=-30
Answers
The function for the given zeros is f(x)=2x³-8x²+8x-32.
What are the zeros of the polynomial function?The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.
Given that, n=3.
x=4 and x=2i
We then know that the third root must be x=-2i
Now, f(x)=a(x-4)(x-2i)(x+2i)
= a(x-4)(x²-(-2i)²)
= a(x-4)(x²-(-4))
= a(x-4)(x²+4)
= ax²(x-4)+4(x-4)
f(x)= a(x³-4x²+4x-16)
f(1)=a(1³-4×1²+4×1-16)
-30=a(1-4+4-16)
a=2
Now, f(x)=2(x³-4x²+4x-16)
f(x)=2x³-8x²+8x-32
Therefore, the function is f(x)=2x³-8x²+8x-32.
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