Answers
Answer:
y = 2x - 1
Step-by-step explanation:
gradient is defined as rise over run.
we need coordinates that are both whole numbers. from looking at the graph, I have (0, -1) and (1, 1)
for the run, 1 - 0 = 1
for the rise, 1 - -1 = 2
2 / 1 = 2
it crosses the y-axis at -1
therefore in the form y = mx + b, the equation is y = 2x - 1
Related Questions
Find the simplified product 2 square root 5x^3(-3 square root 10x^2
Answers
The simplified product of [tex]2\sqrt{5x^{3} }[/tex] and -3[tex]\sqrt{10x^{2} }[/tex] is -30[tex]x^{5/2} \sqrt{2}[/tex].
Given Two expressions: -3[tex]\sqrt{10x^{2} }[/tex] and 2[tex]\sqrt{5x^{3} }[/tex].
We have to multiply both the expressions and it can be done as under:
-3[tex]\sqrt{10x^{2} }[/tex] *2[tex]\sqrt{5x^{3} }[/tex]
Firstly we have to multiply -3 with 2 to get
=-6[tex]\sqrt{10x^{2} }\sqrt{5x^{3} }[/tex]
Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.
=[tex]-6x^{3/2} x\sqrt{10}\sqrt{5}[/tex]
Now we have to multiply both the numbers in the root to get the answer;
=-6[tex]x^{5/2} \sqrt{50}[/tex]
Square root of 50 is 5 root 2.
=-6*5[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]
=-30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]
Hence the simplified product is -30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex].
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Emily works at a local restaurant. She made $200 in tips last night. She shared 15 percent of her tips with the crew that cleans the tables. How much did she give to the clean-up crew?
$
Answers
A percentage is a way to describe a part of a whole. The amount Emily shared is $30.
What are percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,
15% of $200
= 0.15 × $200
= $30
The amount Emily shared is $30.
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Which of the following is a Recursive Formula for an Arithmetic Sequence?
an = 6n – 9
an = -3 + 6(n – 1)
a1 = -3, an = an-1 + 6
a1 = -3, an = 6an-1
Pls I require assistance.
Answers
The Recursive formula for an Arithmetic Sequence is a1 = -3, an = an-1 + 6.
What is Arithmetic sequence ?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
Given:
an = -3 + 6(n – 1)
a1= -3
a2= 3
a3 = 9
Here the common difference is 6 and first term is -3
Hence, the recursive formula is a1 = -3, an = an-1 + 6.
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HELP NOW PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASE
Answers
Answer:
-3/2
Step-by-step explanation:
First, you divide by taking the reciprocal of -2/5 which is -5/2.
Second, you get the answer which is -5/4.
Add that with -1/4 and you will get -6/4.
Simplify to get the answer which is -3/2.
Answer:
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{\dfrac{1}{2}}{-\dfrac{2}{5}}+\left(-\dfrac{1}{4}\right)[/tex]
To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies \dfrac{1}{2} \times -\dfrac{5}{2}+\left(-\dfrac{1}{4}\right)[/tex]
To multiply the fractions, multiply the numerators and multiply the denominators:
[tex]\implies \dfrac{1 \times (-5)}{2 \times 2} +\left(-\dfrac{1}{4}\right)[/tex]
[tex]\implies -\dfrac{5}{4} +\left(-\dfrac{1}{4}\right)[/tex]
Apply the rule -a + (-b) = -a - b :
[tex]\implies -\dfrac{5}{4} -\dfrac{1}{4}[/tex]
As the denominators are the same, subtract the numerators and put the answer over the same denominator:
[tex]\implies \dfrac{-5-1}{4}[/tex]
[tex]\implies -\dfrac{6}{4}[/tex]
Simplify by dividing the numerator and denominator by the highest common factor:
[tex]\implies -\dfrac{6 \div 2}{4 \div 2}[/tex]
[tex]\implies -\dfrac{3}{2}[/tex]
Alex, jas and stef each get a student loan to help with living expenses. they decide to allocate two fifths of their loans for food, and one-sixth for travel. what fraction of their student loan will be left to spend?
Answers
The fraction of their student loan will be left to spend is half of their loan.
A number expressed quotient, in which numerator is divided by denominator is called a fraction.
Let the loan amount be $100.
Expenses for food is given that two fifths of their loan
i.e.
= 2/5 × 100
= $40
Now,
Remaining part will be = $100- $40 = $60
So,
Expenses for travel are given that one sixth of their loan,
i.e.
= 1/6 × 60
= $10
So,
Remaining part will be = $60 - $10 = $50
Hence, the fraction of their student loan will be left to spend is half of their loan.
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Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
Answers
Answer:
4 secs
Step-by-step explanation:
Since they have to be synchronized, their parabolic equations must be equal to one another
3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0
2t^2 - 9t + 4
(2t - 1)(t - 4) = 0
t = 1/2, 4
From the options, the answer is 4
The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
so, correct option is: C.
Here, we have,
To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.
The given equations are:
y = –(x – 5)² + 3
y = –3(x – 3)² + x + 1
Setting the two equations equal, we have:
–(x – 5)² + 3 = –3(x – 3)² + x + 1
Expanding the squared terms:
–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1
Simplifying the equation:
–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1
Combining like terms:
–x² + 10x – 22 = –3x² + 19x – 26
Rearranging the equation:
2x² - 9x + 4 = 0
To solve this quadratic equation, we can factor it:
(2x - 1)(x - 4) = 0
Setting each factor equal to zero:
2x - 1 = 0 or x - 4 = 0
Solving for x:
2x = 1 or x = 4
Dividing by 2:
x = 1/2 or x = 4
Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
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please help need it asap
Answers
Answer:
195
Step-by-step explanation:
87+38+40=165
360-165=195
Hope this helps!
If not, I am sorry.
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
and the equation will have
.
Answers
Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50
Points given for every correct Answer = +3
Points deducted for every Incorrect Answer = -1
For every question unanswered ,
points Deducted = -0.5
Total Points Obtained by Desiree after Answering all the questions = 110
Number of Answers that Desiree answered correctly = x questions
Number of Incorrect Answers = (50 - x) questions
Then,the Equation representing above situation
→ 3 × x + ( -1 ) × ( 50 - x ) = 110
⇒3x - 50 + x = 110 ----------- equation that represents the given situation
⇒ 4x - 50 = 110
Adding 50, on both sides
→ 4x - 50 + 50 = 110 + 50
⇒ 4x = 160
Dividing both sides by, 4 we get
x = 40
Number of correct answers given by Desiree= 40 questions
Number of Incorrect Answers = 50 - 40
= 10 Questions .
Answer:
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
3(50 - x) + x = 110
and the equation will have
no solution
.
Step-by-step explanation:
Which currency is it
Answers
Answer:
pounds (£)
Step-by-step explanation:
pounds are used in countries such as the UK and South Georgia
Using a standard deck of cards, find the probability of selecting a jack, replacing the card, and then selecting a king.
please explain
Answers
The probability of selecting a jack, replacing the card, and then selecting a king is 1/169
How to determine the probability?In a standard deck of cards, we have:
Total = 52
Jack = 4
King = 4
The probability of each is:
P(Jack) = 4/52
P(King) = 4/52
So, we have:
P = 4/52 * 4/52
Simplify
P = 1/13 * 1/13
Evaluate
P = 1/169
Hence, the probability is 1/169
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Deon has bought 18 pounds of dog food. He feeds his dog
Write your answer in simplest form.
2|3
pounds for each meal. For how many meals will the food last?
Answers
Answer:
6 to 9 meals
Step-by-step explanation:
9 If he feeds 2 pounds per meal. 18÷2 =9
6 if he feeds 3 pounds per meal. 18÷3=6
The graph of a system of inequalities shown
Answers
how many sets of 5 students can be selected out of 30 students?
Answers
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]
[tex]=142506[/tex]
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]
[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]
[tex]\mathbf{^nC_r = 142506}[/tex]
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(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answers
Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.
Linear function that is represented by the graph is f(x)= -1/2 x+1.
Here, we have,
From the graph,
y - intercept of the linear function is 1 , i.e. c = 1
and there are two points on the line (-4, 3), (4, -1)
We can get the equation of line by applying slope-intercept formula,
Slope of the line,
m = y₂ -y₁ / x₂-x₁
so, we get,
m = -1 -3 / 4 + 4
= -4/8
= -1/2
Now applying slope-intercept formula,
y = mx+c
Putting the values,
=> y = -1/2 x + 1
=>f(x) = -1/2 x + 1.
Therefore, linear function that is represented by the graph is
f(x) = -1/2 x + 1.
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Suppose you know the slope of a linear relationship and one of the points that it’s graph passes through how can you determine if the relationship is proportional or not?
Answers
Answer:
I exactly don't have or know the answer
Use the graph and the given point to determine the second point. Connect the two points by a straight line. If the graph passes through the origin, the relationship is proportional and if the graph does not pass through the origin, the relationship is non-proportional.
Need Help Fast!!!!!! The graph of the piecewise function f(x) is shown. f(x) What is the range of f(x)?
Answers
Answer:
The second option
Step-by-step explanation:
If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4
What is the results of
4-³ × (¼)²
Answers
Answer:
4^-3*(1/4)^2
(1/64)*(1/16)
=(1/1024)
Answer:
0.00025
Step-by-step explanation:
hope it'll help I'll ask . if you feel that it's not that correct please comment so that I can ask my sister who I'm sure she'll help although she's far good day.
If u(x) = -2x²+3 and v(x)=
X'
what is the range of (uv)(x)?
Answers
The answer is option D which is the range will be ( -∞, ∞ ).
What is the range?After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).
Given function is
u(x) = -2x²+3 and v(x) = ( 1 / x ).
The product of the function will give uv(x).
uv(x) = (-2x²+3 ) x [tex]\dfrac{1}{x}[/tex]
uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]
When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.
Therefore the answer is option D which is the range will be ( -∞, ∞ ).
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True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.
Answers
The given statement is false.
What is the effect of a row operation on a determinant?
The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.
Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.
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Describe the solution of f(x) shown in the graph. a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero All real solutions All solutions that lie on f(x) All positive solutions All whole number solutions
Answers
A quadratic equation is in the form of ax²+bx+c. The correct option is C, All the positive solutions.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the question is given below. Since a quadratic equation has only two solutions, and this two solutions can be found by observing the graph. The coordinate at which the graph of the equation intersect the x-axis are the solution of the equation.
As it can be observed in this graph, that the graph intersect the x-axis at (1,0) and (2,0).Therefore, the solutions of the graph are 1 and 2.
Thus, both the solutions are positive or it can be concluded that all the solutions are positive.
Hence, the correct option is C, All the positive solutions.
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Answer:
B. All solutions that lie on f(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
A dilation maps (9, 12) to (3, 4). Find the coordinates of the point (8, 4) under the same dilation
Answers
Assuming the dilation is centered at the origin, the scale factor is 1/3.
This means the coordinates of the point (8,4) are [tex]\boxed{\left(\frac{8}{3}, \frac{4}{3} \right)}[/tex]
PQ = 15cm and QR = 17cm. Calculate the perimeter of PQR.
Answers
can u please tell if the figure is a right angled triangle??...cuz in order to find the perimeter, Pythagoras theorem must be applied but it's only for right angled triangle...so specify please
Hi! So, I know I got this answer wrong, but I wasn't sure how to solve an equation with signs like: [brackets] in it, I've included my problem as an example, but can someone please teach me what those brackets mean, and how do I go about solving an equation (using this problem as an example) with brackets like these?
Answers
Step-by-step explanation:
Brackets is the bigger version of parentheses, you first solve the questions inside the parentheses, then move onto brackets.
For example, this question:
[tex]x=-1\\y=-2\\z=3[/tex]
[tex]5x-y[7-4(z-y)][/tex]
plug in x, y, and z.
[tex]5(-1)-(-2)[7-4(3-(-2))][/tex]
[tex]5(-1)-(-2)[7-4(5)][/tex]
[tex]5(-1)-(-2)[7-20][/tex]
[tex]5(-1)-(-2)[-13][/tex]
[tex]-5-(-2)[-13][/tex]
[tex]-5-26[/tex]
[tex]-31[/tex]
I hope you understand better now.
If m varies directly with n , and m = 8 when n = 24 . what is the value of n when m = 12
Answers
Answer:
the answer will be 36
Step-by-step explanation:
if you divide 24 by 8 it will be 3 so then you multiply 12 times 3 and it's 36
x(3y - 2)
Multiply this problem
Answers
Answer:
3xy-2x
Step-by-step explanation:
Distribute x to both 3y and -2: 3y*x-2*x.
Order these fractions from smallest to lowest
1[tex]\frac{1}{2} \frac{7}{12} \frac{2}{17}[/tex]
Answers
Answer: [tex]\frac{1}{2} \frac{2}{17} \frac{7}{12}[/tex]
Step-by-step explanation:
Solve for x using quadratic formula :
abx^2 + (b^2 - ac)x - bc = 0
Answers
[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]
Explanation:
Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0
Here given:
a = abb = b² - acc = -bcApply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]
Insert values:
[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Apply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
solve X-2=7 answer the question pls pls
Answers
Answer:
x = 9
Step-by-step explanation:
x-2 = 7
you solve by adding 2 to both sides to maintain equality. and you add by 2 to cancel out the -2 to isolate the x.
x = 9
if you remove the X with 9 it would be 9-2=7
(c) (i) A new truck costs $15 000 and loses 23% of its value each year. Calculate the value of the truck after three years. ( c ) ( i ) A new truck costs $ 15 000 and loses 23 % of its value each year . Calculate the value of the truck after three years .
Answers
Answer:
$6847.955
Explanation:
Use the compound interest formula, but the value decreases over time.
[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]
where 'A' is final amount, r is rate, t is time
Inserting P = $15,000, r = 23, t = 3 years
[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]
[tex]\sf A = 6847.995[/tex]
Hence the value of truck after three years will be $6847.955.
How many square feet of outdoor carpet will we need for this hole.
Answers
Step-by-step explanation:
area of rectangle= 12×6
=72ft^2
A2=9ft^2 whereby the base of the hole is 3ft
height is 6ft
therefore the square is 18 ft
