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the function is
[tex]y=-10x+3[/tex]we must replace the value of x and obtain y
x=-5
[tex]\begin{gathered} y=-10(-5)+3 \\ y=50+3 \\ y=53 \end{gathered}[/tex]x=-1
[tex]\begin{gathered} y=-10(-1)+3 \\ y=13 \end{gathered}[/tex]x=0
[tex]\begin{gathered} y=-10(0)+3 \\ y=3 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=-10(1)+3 \\ y=-7 \end{gathered}[/tex]Related Questions
solve a system of equations to solve the problem question 8
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Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Determine m such that the line through points (2m,4) and (m-3,6) has a slope of -5.
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We have to use the formula of the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=2m,x_2=m-3,y_1=4,y_2=6,m=-5[/tex]Replacing all these values, we have
[tex]-5=\frac{6-4}{m-3-2m}[/tex]Now, we solve for m
[tex]\begin{gathered} -5=\frac{2}{-m-3} \\ -m-3=\frac{2}{-5} \\ -m=-\frac{2}{5}+3 \\ m=\frac{2}{5}-3=\frac{2-15}{5}=\frac{-13}{5} \end{gathered}[/tex]Therefore, m must be equal to -13/5 in order to meet the given characteristics.Someone help me please
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Approximately 5 meters long.
a number, twice that number, and one-third of that number added. the result is 20. what is the number?
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Answer:
6
Step-by-step explanation:
Let x = the number
2x = twice the number
1/3 x = one-third of the number
x + 2x + 1/3 x = 20
Combine like terms.
3 1/3 x = 20
Change 3 1/3 to an improper number.
10/3 x = 20
Times by 3/10 on both sides.
3/10 • 10/3 x = 20•3/10
x = 60/10
x = 6
Check:
6 + 2(6) + 1/3(6)
= 6 + 12 + 2
= 20 check!
x+2x+(1/3)x=20...multiply terms by 3
3x+6x+x=60
10x=60
x=6
4. Which of the following rules is the composition of a dilation of scale factor 2 following (after) a translation of 3 units to the right?
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ANSWER
A. (2x + 3, 2y)
EXPLANATION
Let the original coordinates be (x, y)
First, there was a dilation of scale factor 2.
This means that the coordinates become:
2 * (x, y) => (2x, 2y)
Then, there was a translation of 3 units to the right. That is a translation of 3 units on the horizontal (or x axis).
That is:
(2x + 3, 2y)
So, the answer is option A.
If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
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The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
Dave has a collection of 60 DVDs. One quarter of them are action mc
What is the ratio of the number of action DVDs to all ofner genres?
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Answer:
15:45 i think
Step-by-step explanation:
25% of 60 is 15
60-15=45
15:45
I'm trying to solve this problem. I went wrong somwhere.
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I am trying to solve this equation using Synthetic Division. I got the answer wrong, I would like to see where I made a mistake.
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The result for the division is:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]Explanation:Step 1: Write the coefficients of the numerator on the right-hand side, and the opposite of the constant term in the denominator on the left-hand side.
20..............2 || 3 || 5 || 9
..................2
Step 2: Multiply 20 by 2 and add the result to 3
20..............2.......................|| 3 || 5 || 9
..................2*20 = 40
....................2 || 3 + 40 = 43
Step 3: Multiply 43 by 20, and add the result to 5
20..............2 || 3 .........................|| 5 || 9
...................... 40.......20*43 = 860
....................2||43 .......5+860=865
Step 4: Multiply 865 by 20, and add the result to 9
20..............2 || 3 || 5 ..........................|| 9
...................... 40 ||860......20*865=17300
....................2||43||865...9 + 17300=17309
The coefficients are 2, 43, 865, 17309
The quotient is:
[tex]2x^2+43x+865[/tex]and the remainder is 17309
So, we can write:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]i inserted a picture of the question please state whether the answer is a b c or d please don’t ask questions, yes i’m following.
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Solution
- We are asked to find the complement of rolling a 5 or 6 given a cube numbered 1 - 6.
- The complement of an event is defined as every other event asides the event in context.
- Other than rolling a 5 or 6, we can also roll a 1, 2, 3, or 4. This constitutes the complement of rolling 5 or 6.
Final Answer
The complement of rolling a 5 or 6 is:
{Rolling a 1, 2, 3, or 4} (OPTION B)
What is the measure of m?n20m5m = [?]✓=Give your answer in simplest form.Enter
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STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]Cross-multiply
[tex]m^2=25\times5[/tex]Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]James types 50 words per minute. He spends 20 minutes typing his homework. What is the domain of this situation?
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Answer:
You answer is B, from 0 to 20 and including 0 and 20.
Step-by-step explanation:
given a quadratic equation in standard form f(x) = ax^2 + bx + c. explain how to determine if there is one real solution, two real solutions, or no real solutions (use the discriminant b^2 - 4ac)
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As per given by the question,
There are given that a general form od quadratic equation.
The equation is,
[tex]f(x)=ax^2+bx+c[/tex]Now,
For determine the one real solution, two real solution, and no real solution;
There are apply the condition for all these three.
So,
First for one real solution.
If
[tex]b^2-4ac=0,\text{ then}[/tex]The given quadratic equation has one real solution.
If,
[tex]b^2-4ac>0,\text{ then;}[/tex]The given quadratic equation has two real solution.
And,
If,
[tex]b^2-4ac<0,\text{ then;}[/tex]The given quadratic equation has no real solution.
3.) Write the explicit formula for the arithmetic sequence. 50, 47, 44, 41,...
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all the terms are 3 less than its preceding term, simple!
So, the formula would be:
[tex]a_n=a+(n-1)d[/tex]Where
a is the first term
d is the common difference (diff in 2 terms)
From the sequnce,
first term (a) is 50
common difference (d) = 47 - 50 = -3
So, we have:
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=50+(n-1)(-3_{}) \\ a_n=50-3n+3 \\ a_n=53-3n \end{gathered}[/tex]Explicit Formula:
[tex]a_n=53-3n[/tex]which fraction remains in the quotient when 4,028 is divided by 32
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We get that
[tex]\frac{4028}{32}=\frac{1007}{8}=\frac{1000}{8}+\frac{7}{8}=125+\frac{7}{8}[/tex]so the fractions that remains is 7/8
Eight less than a number n is at least 10
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Answer:
n - 8 ≥ 10
n ≥ 18
Step-by-step explanation:
Hello!
8 less than the number n can be represented as n - 8.
To be atleast 10, we can have values greater than 10 and equal to 10, but cannot be less than 10 . We can use the ≥ symbol to represent this.
The inequality would be n - 8 ≥ 10
Solving for n:n - 8 ≥ 10n ≥ 18n has to be greater than or equal to 18
Suppose a certain company sells regular keyboards for $82 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,415, how many of each type were sold?how many regular keyboards?how many wireless keyboards?
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Given:
A set 3 regular and 1 wireless keyboard,
Regular keyboards = $ 82
Wireless keyboards = $ 115
Total keyboards sales = $ 5415
Find-:
(a) how many regular keyboards?
(b) how many wireless keyboards?
Explanation-:
A set of 3 regular and 1 wireless keyboard would sell for:
[tex]\begin{gathered} =3\times82+115 \\ \\ =246+115 \\ \\ =361 \end{gathered}[/tex]For, the given sales, the number of sets sold:
Total keyboard sales = $5415
[tex]\begin{gathered} =\frac{5415}{361} \\ \\ =15 \end{gathered}[/tex]Since there are 3 regular keyboards in each set,
The regular keyboard is:
[tex]\begin{gathered} =3\times15 \\ \\ =45\text{ Regular Keyboards} \end{gathered}[/tex]The regular keyboard is 45.
Wireless keyboard is 15.
7. Find the perimeter of the rectangle with length 33 yards and width 59 yards.A.92 ydB.1,947 ydC.125 ydD.184 yd
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Solution
We are given
Length (l) = 33 yards
Width (w) = 59 yards
To find the perimeter
Note: Perimeter of a Rectangle
[tex]Perimeter=2(l+w)[/tex]what is the area of the triangle below with a side length of 4
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All angles of triangles is equal means that that triangle is equailateral triangle with side of a = 4 in.
The formula for the area of equilateral triangle is,
[tex]A=\frac{\sqrt[]{3}a^2}{4}[/tex]Substitute 4 for a in the formula to determine the area of the triangle.
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}\cdot(4)^2 \\ =4\sqrt[]{3} \end{gathered}[/tex]So area of triangle is,
[tex]4\sqrt[]{3}[/tex]the value of y is directly proportional to the value of x. if y = 45 when x = 180 what is the value of y = 90
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We have a direct proportionality between y and x.
If "k" is the constant of proportionality, the equation for this situation is:
[tex]y=kx[/tex]To find the constant of proportionality, we solve that equation for k:
[tex]k=\frac{y}{x}[/tex]And since when y=45, x=180, substituting these values to find k:
[tex]\begin{gathered} k=\frac{45}{180} \\ k=0.25 \end{gathered}[/tex]Now, we substitute the value of k into the equation of proportionality:
[tex]y=0.25x[/tex]And in this equation, we can substitute any value of the variables, and find the value of the other variable.
In this case, we have y=90, so we substitute that value and solve for x:
[tex]\begin{gathered} 90=0.25x \\ \frac{90}{0.25}=x \\ 360=x \end{gathered}[/tex]Answer: when y=90, x=360
Find the 52nd term.16, 36, 56, 76,…
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Answer:
[tex]\text{ a}_{52}\text{ = 1,036}[/tex]Explanation:
Here, we want to find the 52nd term of the sequence
What we have to do here is to check if the sequence is geometric or arithmetic
We can see that:
[tex]\text{ 36-16 = 56-36=76-56 = 20}[/tex]Since the difference between the terms is constant, we can say that the terms have a common difference and that makes the sequence arithmetic
The nth term of an arithmetic sequence can be written as:
[tex]\text{ a}_n\text{ = a +(n-1)d}[/tex]where a is the first term which is given as 16 and d is the common difference which is 20 from the calculation above. n is the term number
We proceed to substitute these values into the formula above
Mathematically, we have this as:
[tex]\begin{gathered} a_{52}\text{ = 16 +(52-1)20} \\ a_{52}\text{ = 16 + (51}\times20) \\ a_{52}\text{ = 16 + 1020 = 1,036} \end{gathered}[/tex]Solve the equation. Select the correct answer below, and, if necessary, fill in the answer box to complete your choice.
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Explanation
[tex]\begin{gathered} \frac{4}{y}+\frac{3}{4}=\frac{4}{4y} \\ Multiply\text{ through by the lowest common multiple }\Rightarrow4y \\ 4y\times\frac{4}{y}+\frac{3}{4}\times4y=\frac{4}{4y}\times4y \\ 16+3y=4 \\ 3y=4-16 \\ 3y=-12 \\ y=-\frac{12}{3} \\ y=-4 \end{gathered}[/tex]Answer= y=-4
solve using the quadratic formulax^2+2x-17=0
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957.55x8042x6/4x6=??
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6930553.9
1) Let's rewrite and solve the expression, note that since Multiplication and Division are on the same level of priority according to PEMDAS acronym for the order of operations:
[tex]\begin{gathered} 957.55\times8042\times\frac{6}{4}\times6= \\ 957.55\times8042\times\frac{3}{2}\times6= \\ 957.55\times8042\times\frac{3}{1}\times3= \\ 69305553.90= \end{gathered}[/tex]Notice that we simplified 6/4 to 3/2 and then 6 by 2. In addition to this, note that the 2 decimal places were kept, we can write 69305553.90 or simply 69305553.9
2) Hence, the answer is = 6930553.9
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
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Answer: [tex]\frac{5}{2\sqrt{5x+3\\} }[/tex]
Step-by-step explanation:
First, use the chain rule to quickly find the answer so that you can check after you go through the ridiculous process that is the bane of every calculus 1 student's existence.
f(x) = (5x + 3)^(1/2)
(d/dx) (5x + 3)^(1/2) =
(1/2)(5x + 3)^(-1/2) * (5) =
5/[2(5x+3)^(1/2)]
Now, we enter the first gate of hell:
f'(x) = the limit as h approaches 0 of [(f(x+h) - f(x))/h]
lim as h -> 0 of [(5(x+h)+3)^(1/2) - (5x+3)^(1/2)/h]
lim as h -> 0 of [(5x+5h+3)^(1/2) - (5x+3)^(1/2) / h]
Multiply numerator and denominator by the conjugate of the numerator, which is (5x+5h+3)^(1/2) + (5x+3)^(1/2).
lim as h -> 0 of
[√(5x+5h+3) - √(5x+3) ] [√(5x+5h+3) + √(5x+3) ]
______________________________________
h[√(5x+5h+3) - √(5x+3) ]
Simplify the numerator via FOIL:
5x+5h+3 + √(5x+5h+3)√(5x+3) - √(5x+3)√(5x+5h+3) - (5x+3)
The remaining radicals in the numerator cancel each-other, giving us:
5x + 5h + 3 - 5x - 3
Simplify Further:
5h
Now that we have simplified our numerator, let's continue:
lim as h -> 0 of (5)(h)/[(h)((5x+5h+3)^(1/2) + (5x+3)^(1/2))]
The h in the numerator cancels the h in the denominator.
lim as h -> 0 of 5/[(5x+5h+3)^(1/2) + (5x+3)^(1/2)]
Now, we directly substitute h with 0 in the equation.
5/[ (5x+3)^1/2 + (5x+3)^(1/2) ]
In the denominator, both sides of the addition sign are the same, so we can simplify it further to:
5/[ 2(5x+3)^(1/2) ]
This is the same answer we received using the chain rule, so it is correct!
If d - 243 = 542, what does d-245 equal? CARA GOIECT CH 1UJAINRIகபட்ட RE Lien Answer: Your answer
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Given the following expression:
[tex]d-243=542[/tex]if we add 243 on both sides of the equation we get the following:
[tex]\begin{gathered} d-243+243=542+243=785 \\ \Rightarrow d=785 \end{gathered}[/tex]thus, d = 785
NO LINKS!! Show all work where necessary to get full credit
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16. Circle F
You name a circle using the center.17. BF
A radius connects the center to a point on the circumference of the circle.18. CD
A chord is a segment connecting two points on the circumference of the circle.19. BE
A diameter is a segment that passes through the center while also connecting two points on the circumference of the circle.20. FA
See 17 and 19.Answer:
16. F
17. FA
18. CD
19. BE
20. FA
Step-by-step explanation:
Question 16
A circle is named by its center.
The center of the given circle is F, therefore the name of the given circle is F.
Question 17
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
FA, FB and FE.Question 18
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
BE and CD.Question 19
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameter of the given circle is:
BE.Question 20
As the diameter is BE, it contains the radii FB and FE.
Therefore, the radius that is not contained in the diameter is:
FA.Evaluate the function for the indicated values of x. (2x + 1, x 5 f(-10) = F(2) = f(-5) = f(-1) = f(8) =
Answers
Explanation
[tex]f(x)f(x)=\mleft\{\begin{aligned}2x+1\text{ if x}\leq-5\text{ } \\ x^2\text{ if -5}Step 1you need to select the correct function depending on the number
i)f(-10)
[tex]-10\leq-5,\text{ then you n}eed\text{ apply}\Rightarrow f(x)=2x+1[/tex]Let x= -10, replacing
[tex]\begin{gathered} f(x)=2x+1 \\ f(-10)=(2\cdot-10)+1 \\ f(-10)=-20+1 \\ f(-10)=-19 \end{gathered}[/tex]Step 2
Now
ii) f(2)
[tex]\begin{gathered} 2\text{ is in the interval} \\ -5Letx=2,replacing
[tex]\begin{gathered} f(x)=x^2 \\ f(2)=2^2=4 \\ f(2)=4 \end{gathered}[/tex]Step 3
iii) f(-5)
[tex]\begin{gathered} -5\text{ is smaller or equal than -5} \\ -5\leq5,\text{ then apply}\Rightarrow f(x)=2x+1 \end{gathered}[/tex]Let
x=-5,replace
[tex]\begin{gathered} f(x)=2x+1 \\ f(-5)=(2\cdot-5)+1=-10+1 \\ f(-5)=-9 \end{gathered}[/tex]Step 4
iv)f(-1)
[tex]\begin{gathered} -1\text{ is in the interval} \\ -5<-1<5 \\ \text{then apply}\Rightarrow f(x)=x^2 \end{gathered}[/tex]let
x=-1,replace
[tex]\begin{gathered} f(x)=x^2 \\ f(-1)=(-1)^2 \\ f(-1)=-1\cdot-1=1 \\ f(-1)=1 \end{gathered}[/tex]Step 5
Finally
F(8)
[tex]\begin{gathered} 8\text{ is greater or equal than 5, then apply} \\ 8\ge5\Rightarrow apply\text{ f(x)=3-x} \\ f(x)=3-x \end{gathered}[/tex]Let
x=8,replace
[tex]\begin{gathered} f(x)=3-x \\ f(8)=3-8 \\ f(8)=-5 \end{gathered}[/tex]I hope this helps you
Reflects the given the coordinates points across the y - axis
Answers
Answer:
Explanation:
The reflection over the line y = x gives the following transformation of coordinates
[tex](x,y)\to(y,x)[/tex]therefore, for our case the transformation gives
[tex]\begin{gathered} S(-2,5)\to S^{\prime}(5,-2) \\ T(-3,0)\to T^{\prime}(0,-3) \\ U(1,-1)\to U^{\prime}(-1,1)_{} \end{gathered}[/tex]which are our answers!
The graphical representation of a point and its reflection about the line y =x is the following:
Graph the line that passes through the points (9,4) and (9,1) and determine the equation of the line.
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Both points of the given points have the same x-coordinate. This is only possible if we have a vertical line. The vertical line have the format
[tex]x=k[/tex]Where k represents the x-coordinate of all points of the line. The x-coordinate of our points is 9, therefore, the equation of the line is
[tex]x=9[/tex]And its graph is