The x - intercept of the line passing through the points (-3,5) and (5,1) is
x - intercept:
x intercept means the value of the x coordinate of the point where the graph cuts the x-axis, or x-intercept is the value of the x coordinate of a point where the value of y coordinate value is equal to zero.
Given,
Here we have the points (-3,5) and (5,1).
And we need to find the x intercept of the line passing through the points.
In order to find the x-intercept of a line of the form
y = mx + b,
substitute y = 0.
But the value of m is also unknown.
So, Let the line be
y=mx + b
The line passes through two points (-3,5) and (5,1)
5 = m × (-3) + b
-3m +b = 5 ------------------ (i)
1 = m × (5) + b
5m + b = 1 --------------------(ii)
While we subtracting (ii) from (i) we get,
=> (5m + b) - (-3m + b) = 1 - 5
=> 8m = -4
=> m = -1/2
Substitute the value in (i) we get,
=> -3(-1/2) + b = 5
=> b = 5 - 3/2
=> b = 7/2
Now, the equation of the line is
y = mx + b
when we apply the value then we get,
y = -3/2x + 7/2
When we apply the value of y = 0, then we get,
0 = -3/2x + 7/2
-3/2x = -7/2
x = 7/2 x 2/3
x = 7/3
Therefore, the x intercept is 7/3.
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The sales tax rate is 10%. If Bill buys a globe priced at $14.80,
what will be the total cost including tax?
a rectangle is h units wide it length is 3 units more than the width
Answer:
I think that you have to find the length and width of the rectangular
Can you answer this? ASAP
Answer:
h = 5m
Step-by-step explanation:
A = 1/2bh
15 = 1/2(6)h
15 = 3h
h = 5
what is 121 divided by 12.75
Answer:
9.49
Step-by-step explanation:
this is the answer hope it helps
what color is your buggati?
Answer: yellow
Step-by-step explanation:
ITS THE RIGHT ANSWER IMAOAO
Answer:
Bugatti veyron is available in 10 different colours
Step-by-step explanation:
Light blue pear,black-M,mocca brown, black blue-M ,lemon and Light red.
The Safari Restaurant is giving away gift bags. They have 24 magnets and 36 pencils. They want all the bags to be the same so that each bag has the same number of magnets and the same number of pencils. What is the greatest number of gift bags that the restaurant can make using all of the supplies?
Answer: 18
Step-by-step explanation:
Remove 2 from 36 and remove 1 from 24 until you get to 0.
In his spare time, Kim likes to go cycling. He cycles partly on paved surfaces and partly off-road, through hilly and wooded areas. He cycles at 25km/h on paved surfaces and at 10 km/h off-road. One day, he cycled 41 km in 2 hours. How far did he cycle on the paved road and how far off-road?
Kim travelled 35 km on a paved surface and 6 km off-road which took 1.4 hours and 0.6 hours respectively
Speed of Kim when cycling on paved surfaces: 25 km/hr
Speed of Kim when cycling off-road = 10 km/hr
Distance covered by Kim = 41 km
Time is taken by Kim = 2 hours
Let x be the time Kim travels on a paved surface, and y represents the time off-road
Using the formula:
Speed = Distance/Time
Distance travelled by Kim on paved surface = 25*x
Distance travelled by Kim off-road = 10*y
x + y = 2-------(1)
25x + 10y = 41-------(2)
Multiplying equation (1) with 25 and equating with (2) we get:
25x + 25y = 50
25x + 10y = 41
15y = 9
y = 0.6 hours
x = 1.4 hours
Distance travelled on paved surface = 25*1.4 = 35 km
Distance travelled off-road = 10*0.6 = 6km
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What is the equivalent expression of 4.32÷0.16?
The equivalent expression of 4.32÷0.16 is 0.27.
What are equivalent expressions?Equivalent expressions are expressions that perform the same function notwithstanding their appearance. In mathematics, equivalent expressions are expressions that are the same even if they appear to be different. When the values are entered into the expression, however, both formulations produce the same result. If the terms in both expressions are identical, the expressions are equal.Given:
Expression = 4.32÷0.16
We have to determine the equivalent expression of 4.32÷0.16.
4.32÷0.16 (multiply both the terms by 100 to remove decimals)
432 ÷ 16
= 0.27
Therefore, the required equivalent expression is 0.27 respectively.
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-2 1/2 - 5 3-4 as a mixed number
Answer:
The distance between -2 1/2 and -5 3/4 Is
13/4.
Solve the equation 5+10(x-9)<-103-(7-5x)
we have the inequality
5+10(x-9) < -103-(7-5x)
solve for x
apply distributive property left side and remove the parenthesis right side
5+10x-90 < -103-7+5x
Combine like terms
10x-85 < 5x-110
Group terms
10x-5x < -110+85
5x < -25
x< -25/5
x < -5
the solution is the interval (-inf, -5)
set builder notation
x| x < -5
Help please it's going to be due soon):
Answer:
(2,1)
Step-by-step explanation:
Its the only pair that when plugged in would give you 13
3(2) + 7(1) =13
6 + 7 = 13
Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven.
Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.
Explain about the consecutive odd integers?The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11.
Three consecutive odd numbers that are 3, 5, and 7 are all prime. Three successive odd numbers that are not all prime are 109, 111, and 113 (111=37 times 3).
Answer
Let x - 2, x, and x + 2 be the three odd numbers.
x - 2 + x = 3(x + 2) + 7
2x - 2 = 3x + 6 + 7
2x - 2 = 3x + 13
3x - 2x = -2 - 13
x = -15
The three successive odd numbers are 17, 15, and 13, respectively.
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Solve for x with zero product propertyX^2 + 4x -27 = 5
Answer
[tex]\begin{gathered} Given\text{ }x^2+4x-27=5 \\ x^2+4x-27-5=5-5 \\ x^2+4x-32=0 \end{gathered}[/tex]Using factorization method
[tex]\begin{gathered} x^2+8x-4x-32=0 \\ x(x+8)-4(x+8)=0 \\ (x+8)(x-4)=0 \end{gathered}[/tex][tex]\begin{gathered} x+8=0\text{ }or\text{ }x-4=0 \\ x=-8\text{ }or\text{ }x=4 \end{gathered}[/tex]Therefore, x = -8 or x = 4
3. What are the approximate zeros of the function f(x) = x³ - 2x²-3x+1?
(round to tenth place)
The approximate zeros of the function f(x) = x³ - 2x²-3x+1 (round to tenth place) are -1.2 and 0.3.
What are Zeros of a Function?A function's zeros are the values of its variables that result in the function equaling 0. (f(x) = 0). The zeros of a function are the points on the x-axis where the graph intersects the x-axis. To put it another way, the zeros of a function are the x-intercepts of its graph.
Given:
We have f(x) = x³ - 2x²-3x+1
To determine the real zeros of the function f(x), we have f(x) = 0.
Using a graph to find the solutions for x(round to tenth place) are,
x₁ = -1.199 ≈ -1.2
x₂ = 0.286 ≈ 0.3
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answer choices are 100, 80, 117, 63.
Answer:
117
[tex]100[/tex]
by taking the interior angle sum as 360
Simplify the ratio of 4 :12
the answer Is 1:3
Step-by-step explanation:
reduce 4:12 to the lowest term and you will have 1:3
Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
The point that divides the directed line segment YX so that the ratio of YP to PX is 5 to 3 is P.
According to the question,
We have the following information:
Point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5.
Now, when the line segment XY is inverted to call the line segment YX then the point P is still there.
And the point P divided the line segment in the same way but the difference is that the measurement are taken from the other side. But the point P has not been removed because it is common in YP and PX and YX (as we observe even from the name of these smaller segments) is the line segment.
Hence, P is the point dividing the line segment YX into the given ratio.
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What % of 55 is 20?
Answer:
is 11
Step-by-step explanation:
A bicycle travels at a speed of 2,808 inches
per minute. The radius of each tire on the
bicycle is 3 feet. Approximately how many
revolutions does one of these tires make in 2 minutes?
(Use the approximation 22/7 for π.)
A. 12
B 25
C. 32
D. 46
Answer:
in a complete turn the wheel will travel the
expressed 2pi x radius or 2 x 3.14 x 28 or 175.84
circumference of the wheel. The circumference is cm x 3 (turns) = 527.52 cm or 572.52cm x 1in/2.54 cm x 1ft/12in or 18.78 ft or if you prefer meters 572.52 cm x 1m/100cm = 5.73 m
What is the equation in standard form has a graph that passes through the point (5,-3) and has a slope of 6/5
Considering the definition of a line, the equation of the line that passes through the point (5, -3) and has a slope of 6/5 is y= 6/5x -9.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 6/5.The line passes through the point (5, -3).Substituting the value of the slope m, the line has the form: y=6/5x +b
Substituting the value of the point in the previous expression, the value of the ordinate to the origin b can be obtained:
-3= 6/5×5 + b
-3= 6 + b
-3 - 6= b
-9= b
Finally, the equation of the line is y= 6/5x -9.
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Please help me with this problem!
The length of the indicated lines segments are as follows:
HI = 10 unitsHJ = 20 unitsHow to find length of a line segment?The line segment is given and we are ask to find the length HI and HJ in the line segment.
Therefore, let's find HI
13.
HI = x - 2
GI = 13
HJ = 2x + 2
GJ = 4x - 19
Hence,
GH = 4x - 19 - (2x + 2)
GH = 13 - (x - 2)
Therefore,
4x - 19 - 2x - 2 = 13 - x + 2
2x - 21 = 15 - x
2x + x = 15 + 21
3x = 36
x = 36 / 3
x = 12
Therefore,
HI = x - 2 = 12 - 2 = 10
12.
Let's find HJ
HJ = x + 30
IJ = 2x + 26
HK = x + 33
IK = 9
Therefore,
JK = x + 33 - (x + 30) = x + 33 - x - 30 = 3
JK = 9 - (2x + 26) = 9 - 2x - 26 = -2x - 17
Therefore,
-2x - 17 = 3
-2x = 3 + 17
-2x = 20
x = 20 / - 2
x = - 10
Therefore,
HJ = -10 + 30 = 20 units
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Evaluate the expression.
12−{1+2[−1(3−8)]2}
What is the value of the expression?
Answer:
13
Step-by-step explanation:
12-{1+2[-1(3-8]2}
12-{1+2[-1-5]2}
12-{1+2[-6]2}
12-{3-4}
12-(-1)
12+1
13
Answer: -39 is the answer
Step-by-step explanation:
Henry went shopping for a new pair of pants because of a sale. The store was offering a 10% discount. If the price on the tag was $21, what would be the price after the discount but before tax, to the nearest dollar and cent?
Answer:
Discount:
$2.10
Final Price:
$18.90
Step-by-step explanation:
Answer:
Step-by-step explanation:
$30.4
Step-by-step explanation:
fist we figure out what 5% of 32 is which is 1.6 then we subtract it from the total cost 32 - 1.6 = 30.4
x + 3/4 > - 1/3 Solve the inequality for x.
Simplify your answer as much as possible.
Answer:
x > -13/12
Step-by-step explanation:
x + 3/4 > - 1/3
x + 9/12 > -4/12
x > -13/12
-1/3 = -4/12
3/4 = 9/12
Answer:
x > - 13
12
Step-by-step explanation:
[tex]x + \frac{3}{4} > - \frac{1}{3} \\ x + \frac{3}{4} - \frac{3}{4} > - \frac{1}{3} - \frac{3}{4} \\ x > \frac{ - 4 - 9}{12} \\ x > - \frac{13}{12} [/tex]
Rebecca needs 10 1/2 yards of fabric to make a quilt. she has one piece of fabric that is 2 1/2 yards and another piece of fabric that is 4 1/4 yards. how many more yards of fabric does does Rebbeca need to make a quilt
pls put step by step
The most appropriate choice for fraction will be given by -
Rebeca still needed [tex]3\frac{3}{4}[/tex] yards of fabric to make a quilt.
What is a fraction?
Suppose there is a collection of objects and a part of collection has been taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of fraction is called numerator and the lower part of fraction is called denominator.
Here,
Length of fabric needed to make a quilt = [tex]10\frac{1}{2}[/tex] yards = [tex]\frac{21}{2}[/tex] yards
Length of one piece of fabric = [tex]2\frac{1}{2}[/tex] yards = [tex]\frac{5}{2}[/tex] yards
Length of another piece of fabric = [tex]4\frac{1}{4}[/tex] yards = [tex]\frac{17}{4}[/tex] yards
Total length of fabric Rebeca has = [tex]\frac{5}{2} + \frac{17}{4}\\[/tex]
= [tex]\frac{10 + 17}{4}\\[/tex]
= [tex]\frac{27}{4}[/tex] yards
Length of Fabric Rebeca still needed to make a quilt = [tex]\frac{21}{2} - \frac{27}{4}\\[/tex]
= [tex]\frac{42 - 27}{4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3\frac{3}{4}[/tex] yards
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Work out the missing number
a) 0.36 ÷
= 0.09
Graph the equation y=1/3x-2
Answer:
Start by putting a dot on -2 on the y-axis. Then go up 1 square and go across to the right three squares. Continue to do that to graph the equation.
Step-by-step explanation:
Start by putting a dot on -2 on the y-axis. Then go up 1 square and go across to the right three squares.
Answer:
Step-by-step explanation:
can someone help me here please! thankyou
Answer:
AUB = {0,1,2,3,4,6,8}
B∩C = Nil
Xc∩Yc = {February, April, August, September, November, December}
(YUZ)c= {February, March, April, May, August}
the symbol c stands for complement in the solution.
Step-by-step explanation:
union is combining all the elements of sets A and B
AUB = {0,1,2,3,4,6,8}
intersection is combining only the common elements present in both B and C
B∩C = Nil
complement of a set is the number of elements that are not present in the set.
Xc = {January, February, April, August, September, November, December}
Yc= {February, March, April, May, August, September, October, November, December}
Xc∩Yc = {February, April, August, September, November, December}
Y∪Z = {January, June, July, September, October, November, December}
(YUZ)c= {February, March, April, May, August}
the symbol c stands for complement in the solution.
Answer:
A⋃B = {0, 1, 2, 3, 4, 6, 8} B⋂C = { } . . . (the empty set) X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec} (Y⋃Z)' = {Feb, Mar, Apr, May, Aug}Step-by-step explanation:
Given various set definitions, you want to find the union and the intersection of specific pairs of sets.
We find it convenient to list the set contents in such a way that we can readily identify elements in one set or another, neither, or both. That is what we have done in the attachment.
1. A⋃BThe union of sets A and B will be the list of elements in either set. That is, if an element is included in set A or in set B, it is included in their union. An element is only listed once, even if it appears in both sets.
A⋃B = {0, 1, 2, 3, 4, 6, 8}
2. B⋂CThe intersection of sets B and C will be the list of elements contained in both sets. Set B is even digits, and set C is odd digits. Since there are no digits that are both even and odd, their intersection is the empty set.
B⋂C = { } . . . (the empty set)
3. X'⋂Y'The intersection of the complements of sets X and Y is the list of elements of U that are not in either set.
X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec}
4. (Y⋃Z)'The complement of the union of Y and Z is the list of elements of U that are not in either of sets Y or Z. This is effectively the same as Y'⋂Z'.
(Y⋃Z)' = {Feb, Mar, Apr, May, Aug}
__
Additional comment
We have elected to abbreviate the month names for problems 3 and 4. Your answer may need to spell them out completely to match the problem statement.
Find the indicated value using the given functions
The correct option is b: 2 ∛(5 - 1) , is the value of the composite inverse function.
What is meant by the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question,
The functions as given as;
f(x) = x/3 + 1
g(x) = x³
Now, the find the composite function f o g (x).
Put the value of g(x) at the place of x in f(x).
f o g (x) = x³/8 + 1
Let the obtained composite function be y.
y = f o g (x) = x³/8 + 1
Find the value of x in terms of y.
y = x³/8 + 1
y - 1 = x³/8
8(y - 1) = x³
taking cube root.
x = 2 ∛(y - 1)
Now, substitute the value of x in place of y.
(f o g )⁻¹(x) = 2 ∛(x - 1)
Now, put the value of x as 5.
(f o g )⁻¹(x) = 2 ∛(x - 1)
(f o g )⁻¹(5) = 2 ∛(5 - 1)
Thus, the value of the composite inverse function is obtained as 2 ∛(5 - 1).
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Heleine wants to save up for a Macbook during the 4 years of high school so she can have a computer to take to college. She wants to save $3,000. How much must she deposit monthly into an account that pays 1.54 % interest, compounded monthly, in order to have enough money?
Here is a formula for figuring out loan interest payments. Divide the annual payment amount, typically 12 months, by the interest rate you are being charged. Divide that sum by your loan's initial balance, which should be set at the full amount you borrowed.
How much would a loan for $30,000 per month be?Depending on the APR and length of the loan, the monthly payment for a $30,000 loan can vary from 64.48. For instance, your monthly payment would be $3095.21 if you took out a $30,000 loan for one year with an APR of 1.54%.
Example
Amount of Loan: = $3,000
monthly payment = 64.48
interest = 1.54
term equals 48 months
The total amount paid, including interest, was $305.21.
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