Let k be the number in the blank, so that:
[tex]7x+3=7x-k[/tex]Substract 7x from both sides:
[tex]3=-k[/tex]These two equations are equivalent regardless the value of x. We can change the conclusions that we may obtain by choosing different values for k.
Then, the equation:
[tex]7x+3=7x-0[/tex]Is true for no values of x.
If we want the equation to be false regardless of the value of x, then set k so that -k is different from 3. For example, set k=0:
[tex]\begin{gathered} 3=-0 \\ \Rightarrow3=0 \end{gathered}[/tex]Since this is contradictory, then there are no values of x that make the equation true.
If we want the equation to be true for all values of x, then 3=-k must be an identity. Then, let k=-3:
[tex]\begin{gathered} 3=-(-3) \\ \Rightarrow3=3 \end{gathered}[/tex]Then, the equation:
[tex]7x+3=7x-(-3)[/tex]Is true for all values of x.
If we want the equation to be true for only one value of x, we have to bring back x into the equation 3=-k. So, we can take k=x. This way, we would have:
[tex]\begin{gathered} 7x+3=7x-x \\ \Rightarrow3=-x \\ \Rightarrow x=-3 \end{gathered}[/tex]Which function in vertex form is equivalent to f(x) = x² + x +1?
Answer:
f(x) = (x + 1/2)² + 3/4
===============================
Vertex form of quadratic equation:
f(x) = a(x - h)² + kConvert the given expression into vertex form by completing the square:
f(x) = x² + x + 1 = x² + 2*(1/2)x + (1/2)² + 1 - (1/2)² = (x + 1/2)² + 1 - 1/4 = (x + 1/2)² + 3/4Answer:
[tex]f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To find the vertex form of the given function, complete the square.
Given function:
[tex]f(x)=x^2+x+1[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+x+\left(\dfrac{1}{2}\right)^2+1-\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+1-\dfrac{1}{4}[/tex]
[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}[/tex]
Factor the perfect square trinomial formed by the first three terms:
[tex]\implies f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]
Help me to answer 1b, solve the problem in detail, thank you
Hello
we are given a function and asked to find the reminder when it is divided by a binomial
According to the remainder theorem, f(a) would be the remainder from dividing f(x) by x -a
[tex]\begin{gathered} x-a=x-2 \\ a=2 \end{gathered}[/tex]but our f(x) is given as
[tex]\begin{gathered} f(x)=2x^3+7x^2-8x+3 \\ a=2 \\ \end{gathered}[/tex][tex]f(a)=f(2)=2(2)^3+7(2)^2-8(2)+3=31[/tex]From the calculation above, the answer to this question is 31
If you have 10 white slips of paper, 6 red slips of paper, and 4 blue slips of paper, writing the ratio of red slips compared to the total number of slips. How many red slips do you have? How many slips of paper do you have?
Answer:
6:20 - 2:4 (simplified)
Step-by-step explanation:
20 total slips
6 red slips
please help. I don't understand this
The answer of the expression is 3 -4 and the sum is -1
Given,
In the figure, given a number line.
And, write an addition expression represented by number line. Then find the sum.
Now, According to the question:
To solve for an expression is:
Calculate the principle based on the number line .
We can figure out the formula .
= 3 - 4
[Moving to the right is positive and moving to the left is negative ]
To find the sum:
3 - 4 = -1
According to the figure , the end point of the movement is -1 and the answer is correct.
Hence, The answer of the expression is 3 -4 and the sum is -1
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A shop has a sale that offers 20% off all prices. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day
Work out the overall percentage reduction on the price of the radio.
The overall percentage reduction in the price of the radio is 40%.
What is the overall decline?Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentages is %.
Let's assume that that initial price of the radio is 100.
Price of the radio after the 20% decline in price = (1 - 0.2) x 100
0.8 x 100 = 80
Price of the radio after the 25% decline in price = (1 - 0.25) x 80
0.75 x 80 = 60
The percentage decline in price = (initial price / final price) - 1
(60 / 100) - 1 = 0.4 = 40%
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Write the quadratic equation whose roots are 3 and 6, and whose leading coefficient is 2.
For right triangle ABC, find the sine ratio of angle θ.Opition - three fifthsthree fourthsfour fifthsfour thirds
For any given angle in a right triangle that is not the 90° angle its sine is given by the quotient between its opposite side and the hypotenuse. For triangle ABC the hypotenuse is BC and the opposite side to theta is AB. Then the sine of this angle is given by the following equation:
[tex]\sin\theta=\frac{AB}{BC}=\frac{4}{5}[/tex]AnswerThen the answer is the third option, 4/5.
4.5 un 5.5 6 y 0.5 0.6 0.8 Which is most likely the equation of the line of best fit for the data given in the table? A y = 0.34 x - 09 B y = 0.25x - 0.7 y =0.45x-1 D y = 0.50x -0.6
The Solution.
The correct answer is y = 0.34x - 0.9 (option A ).
Step 1:
First, we shall determine the slope of the line by picking two coordinates from the table.
pls help l need to finish this
Answer:
y = 3x+3
Step-by-step explanation:
The rate of change, or slope, in this case, is 3, as we can either count the increase in y-values or perform the Δy/Δx (slope equation: [tex]\frac{9-3\\}{2-0}[/tex])to yield three, meaning that the (3x) in this equation would be the slope. Since the y-intercept is the constant in the equation and the y-intercept is always when x=0 (when the graph crosses the y-axis) on the XY plane, we can just subtract 3 from the x=1 coordinate, meaning that the y-intercept/x=0 coordinate would be (0, 3), leaving 3 as the constant.
Therefore,
the equation is y = 3x+3.
Is the sequence described as 3,5,8,12,17...... arithmetic. Explain your answer
Based on the sequence given of 3,5,8,12,17, it would be incorrect to say that the sequence is arithmetic. The sequence is not arithmetic.
What is an arithmetic sequence?In an arithmetic sequence, one would find that the number that separates each of the figures in the sequence is the same. In other words, the common difference between each figure is the same.
For instance, 2, 5, 8, 11, 14 has the common difference of 3 so this is an arithmetic sequence.
The sequence given of 3,5,8,12,17 is not arithmetic because the difference between each number is not common and instead increases.
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how many minutes does it take Julian to ride School
Given data:
The time taken by Amy is A=30 min.
The expression for the time taken by Julian is,
[tex]\begin{gathered} J=A+\frac{60}{100}A \\ =(1.6)A \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} J=1.6(30\text{ min)} \\ =48\text{ min} \end{gathered}[/tex]Thus, the time taken by Julian is 48 minutes.
find the domain of f(x)=ln(cosx)
x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
The domain of f(x)=ln(cosx) = x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
Solution:The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f (x). A function's range is the set of values that the function can take.Given function,
f(x)=ln(cosx)
When cos(x) is positive, the domain is.
(cos(x)) > 0
since,
cos0 = 1
cos π/2 = 0
cos π = -1
cos 3π/2 = 0
cos 2π = 1
cos 3π/2 = 0
The values of cos(x) are then between -1 and 1.
That is domain of f(x)=ln(cos x)
= cos x ∈ (0;1] -> x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
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1. You will receive $100 per year for 10 years. The discount rate is 10%. What is the
present value of this stream?
Answer:
100 ×10 =1000
Step-by-step explanation:
10% of 1000 is 100 that's the final answer if am wrong let me know
help me please is when all The sides are right
Not true, true, true, true, true, true, true, not true, true, true
See explanation below
Explanation:From the diagram, we noticed a change in lengths when all four vertex was dragged.
This means the 4 sides will not always be the same (congruent).
Not always true: The four sides are congruent
From both diagrams. we found the opposite sides are the same (congruent)
Always true: The opposite sides are congruent
Since they opposite sides arecongruent, this also means the opposite sides are parallel
Always true: opposite sides are parallel
All four angles from both diagrams are equal (congruent)
Always true: all four angles are congruent
SInce all four angles areequal, then the angles opposite each other will also be equal.
Always true: opposite angles are congruent
The diagonals of both shapes bisect each other. Hence, they are congruent.
Always true: Diagonals are congruent
Always true: diagonals bisect each other
Diagonals of a square (the shapethat has all sides equal ) intersect at a right right angle.
Diagonals of a rectangle ( the shape with opposite sides equal) don ot intersect at right angle.
Not always true: Diagonals intersect at a right angle
The interior angles were split by the two diagonals in both shapes.
Always true: Diagonals bisect interior angles
The sum of angles in a quadrilateral is equal to 360°
Both shapes are quadrilaterals. Hence, the sumof their angles is 360°.
Always true: sum of all angles equal 360°
find the derivative of [tex]\sqrt({x^{2}*6^x})^9[/tex]
Answer: [tex]9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
Step-by-step explanation:
[tex]w=\sqrt{(x^2 6^x)^9}=(x^2 6^x)^{9/2}=x^9 6^{9x/2}\\\\[/tex]
Using the product rule,
[tex]\frac{dw}{dx}=6^{9x/2}\frac{d}{dx} (x^9)+x^9 \frac{d}{dx}(6^{9x/2})\\\\=9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
How many solutions can be found for the linear equation? 3(x+4)=3x+7
Answer:
there is no solution because there aren't any nubmer of X to get linear equation
3X-3X= 12-7
0=5
there aren't solutions so it will be 0
Whats the answer I DONT het how to do this At all
Given that the radius r of a circle is written as a function of the area A with the following equation:
[tex]r=\sqrt[]{\frac{A}{\pi}}[/tex]The domain of the above function is the area A of the circle.
This is because, in this context, the area is an independent and unique variable.
A is the input value.
I need help with this
[tex] { 3 }^{ - 1} \times {3}^{x + 1} - { 3}^{x - 2} + {3}^{ - 2} \times { 3}^{x + 3} = 35 \\ {3}^{ - 1 + x + 1} - {3}^{x - 2} + {3}^{ - 2 + x + 3} = 35 \\ {3}^{x} - {3}^{x - 2} + { 3}^{ - 2 + 3 + x} = 35 \\ { 3 }^{x} - {3}^{x - 2} + {3}^{x + 1} = 35 \\ {3}^{x} - {3}^{x} \times {3}^{ - 2} + {3}^{x} \times {3}^{1} = 35 \\ {3}^{x} (1 - {3}^{ - 2} + 3) = 35 \\ {3}^{x} (3 + 1 - \frac{1}{9}) = 35 \\ \\ {3}^{x} (4 - \frac{1}{9} ) = 35 \\ {3}^{x} ( \frac{35}{9} ) = 35 \\ \frac{ {3}^{x}( \frac{35}{ 9 } )}{ \frac{35}{9} } = 35 \div ( \frac{35}{9} ) \\ {3}^{x} = 9 \\ {3}^{x} = { 3 }^{2} \\ x = 2[/tex]
ATTACHED IS THE SOLUTION.
I USED THE LAWS OF EXPONENTS.
GOODLUCK.
Please help me ASAP!! I will not hesitate to give brainliest to the best answer!!
Answer:
The correct answers are below, if you want a more in depth explanation let me know and I will provide
Step-by-step explanation:
- The Diver surfaced 3 min before the Watcher
- When the noticed was received, the Diver was 20 ft deeper than the watcher
- 3 Min after receiving the notice, the diver and the watcher are at the same depth
Connor deposited $84 into his checking account. If his new balance is $51. what was his balance before the deposit?'
Answer: -33
Step-by-step explanation: I guess he had like debt to pay lol but he would've had to have -33 dollars and added $84 to get a total of $51
HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 90 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
1. 6 units
2. 13 units
3. 5 units
Step-by-step explanation:
6 in. 4 in 6 in 10 in
we have that the figure of a rectangle and a triangle. So the area of this figure is:
[tex]A=6\cdot10+\frac{4\cdot4}{2}=60+8=68[/tex]so the answer is 68 in^2
Which point shown in the graph below is the image of point P after a counterclockwise rotation of 90° about the origin? Please help me
We can see that if we rotate P 90° counterclockwise it would be located in the first quadrant. So it can be A or B. But A forms a 90° with the position of point P. So, the answer is A.
If Amy Van swam her recordbreaking 50 m by swimming to one end of the pool, then turning around and swimming back to her starting position, what would her average velocity be
Answer:
zero
Step-by-step explanation:
You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.
Average velocityAverage velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...
Vave = (change in position)/time = 0/time = 0
Her average velocity is zero.
The sum of a number and five more than the number is 17.
The number is 6.
What is a number?
A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
Let the number be n.
Then according to que, n + (5+n) = 17
or, 2n = 17 - 5
or, n = 12/2 = 6
Hence the number is 6.
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Which best describes the relationship between the line that passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8)?A. same lineB. parallelC. neither perpendicular nor parallelD. perpendicular
Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).
To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.
For point A and B with coordinates:
[tex]A(x_1,y_1),B(x_2,y_2)[/tex][tex]\text{Gradient, m= }\frac{y_2-y_1}{x_2-x_1}[/tex]For points (2, 3) and (5,8)
[tex]\text{Gradient, m= }\frac{8-3}{5-2}=\frac{5}{3}[/tex]For the points (-7, 5) and (-12, 8)
[tex]\text{Gradient, m= }\frac{8-5}{-12-(-7)}=\frac{3}{-5}=-\frac{3}{5}[/tex]• Two lines are said to be ,parallel, ,if their gradients are the same.
,• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.
Product of the two gradients
[tex]\begin{gathered} =\frac{5}{3}\times-\frac{3}{5} \\ =-1 \end{gathered}[/tex]Since the product of the gradients is -1, the two lines are said to be perpendicular.
The correct option is D
what is a relation function?
Answer: A relation is just a relationship between x and y-coordinates. It maps inputs to outputs. A function is just a special kind of relation: any input has exactly one output.
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
What is a constant rate of change
Answer:A rate of change is a rate that describes how one quantity changes in relation to another quantity. Constant rate is also called as uniform rate which involves something travelling at fixed and steady pace or else moving at some average speed. For example, A car travels 3 hours.
Step-by-step explanation:
Write a mixed number and an improper fraction for the model below.
The mixed fraction can be 3 2/3 and the improper fraction would be 11/3 for the same mixed fraction.
What is mixed fraction?A mixed fraction is one that is represented by its quotient and remainder. 2 1/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number and a proper fraction.
What is improper fraction?An improper fraction is one in which the numerator (top number) exceeds or equals the denominator (bottom number). Fractions like 651/14 are "incorrect." They are simply another way to write a mixed number.
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