The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
a)y=24x²+8x-2 at x=3.
b) y=(4x+2)/(6x-1) at x=3.
What is tangent?The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
Given
f at x=3 is y= 4x+2
g at x=3 is y=6x-1
f(3)= 4x+2 and g(3)=6x-1
y=f(x)g(x)
at x=3,
Solution for a:
y=f(3)g(3)
=(4x+2)(6x-1)
=24x²-4x+12x-2
=24x²+8x-2
So y=24x²+8x-2 at x=3.
Solution for b:
y=f(3)/g(3)
=(4x+2)/(6x-1)
So y=(4x+2)/(6x-1) at x=3.
Therefore y=24x²+8x-2 at x=3 for y = f(x)g(x) and y=(4x+2)/(6x-1) at x=3 for y = f(x)/g(x).
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Henry will paint 5 birdhouses with 1 quart of paint. How many quarts of paint will Henry use to paint 42 birdhouses?
Answer:
8
Step-by-step explanation:
because you can't count before 42 so eight
0.36 converted into a fraction
Answer:
9/25
Step-by-step explanation:
0.36 = 36/100
36 / 4 = 9
100 / 4 = 25
9/25
Baljeet invested $5500 at a simple annual rate of 4.8% for 6 years. What is the total future value of the investment?
State your answer in terms of dollars rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Answer:
[tex]a = p(1 + in) \\ = 5500(1 + 0.048 \times 6) \\ = 7084[/tex]
if log4^u - log8^v =1 find u in terms of v
u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
We are given that:
log 4 ^ u - log 8 ^ v = 1
This can also be written in another way using the logarithm properties. We get that:
u log 4 - v log 8 = 1
Subtract v log 8 from both the sides:
u log 4 = 1 + v log 8
v log 8 = u log 4 - 1
v = ( u log 4 - 1 ) / log 8
v = u log (- 4 ) - ( log 8) ⁻¹
Therefore, we get that, u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
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Write a slope-intercept equation for a line passing through the point (4,7) that is parallel to y=x+1. Then write a
second equation for a line passing through the given point that is perpendicular to the given line.
Answer:
y = x + 3
y = -x + 11
Step-by-step explanation:
When the slopes are parallel they are the same. When slopes are negative, the slope is the negative reciprocal.
Parallel: The slope is 1. This is the coefficient of the x in the equation given. If you do not see a number before the x like in y = x + 1, then number is 1.
Use this form:
y =mx + b Us the slope of 1 to put in for m. Use 4 for x and 7 for y
7 =(1)4 + b Solve for b.
7 = 4 + b Subtract 4 from both sides.
3 = b
The equation for the parallel line is
y = x + 3.
Perpendicular:
y = mx + b This time the slope is -1 Still use 4 for x and 7 for y
7 = (-1)4 + b
7 =-4 + b add 4 to both sides
11 = b
The equation would be y = -x + 11
Is it possible to calculate the square root of a negative number?
Answer: It is impossible to find the square root of negative one, or the square root of any negative number because no number times itself can equal a negative number.
Step-by-step explanation:
Answer:
It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.
Step-by-step explanation:
The square root of a negative number does not exist among the set of Real Numbers.
When problems with negatives under a square root first appeared, mathematicians thought that a solution did not exist. They saw equations such as x2 + 1 = 0, and wondered what the solution n3 really meant.
Why is adding two fractions different from multiplying the two fractions?
Answer:
Step-by-step: The reason we cross multiply fractions is to compare them. Cross multiplying fractions tells us if two fractions are equal or which one is greater. This is especially useful when you are working with larger fractions that you aren't sure how to reduce.
Answer:
adding two fractions is different than multiplying two fractions bc after adding the fractions, you have to simplify them and it is not easy but with multiplying, you multiply from left to right.
Step-by-step explanation:
example: 1/2+3/4
4/8+6/8=10/8=1 1/4
another example: 6/10*4/6=24/60
Cameron said that the y-intercept of a quadratic function always tells the maximum value of that function.
Explain Cameron's error.
The y-intercept is where the graph crosses the y-axis and is not necessarily where the maximum is. For instance, consider the graph of [tex]y=x^2 +2x+4[/tex].
If the average of 292, 305, 415, and x is 343, what is the value of x?
on average max makes 45 out of 60 shots with the basketball, write an equation to represent the average number of shots made out of x attempts
Answer:
See below
Step-by-step explanation:
Avg shots made = (45/60) x = (3/4 ) x = .75 x
Building A is 251 meters taller than building B. If the height of building A is subtracted from twice the height of building B, the result is 223 meters. How tall is each skyscraper?
Answer:
Step-by-step explanation:
write 25x + 2 as a verbal expression
The required verbal form of the expression is two more than 25 times of a number.
Given that,
An expression is given we have to determine the verbal expression of the given algebraic expression.
The algebraic expression consists of constant and variable. eg x, y, z etc.
Here,m
Given expression = 25x + 2
Where x is any variable number 25 times and further added 2.
So.
The verbal expression can be given as
two more than 25 times of a number.
Thus, the required verbal form of the expression is two more than 25 times of a number.
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On the graph f(x)=cos x and the interval [-2pie,0] for what value of x does the function cross the x-axis?
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
For what values does the cosine function cross the x-axis?
Cosine function is a function bounded between - 1 and 1 and whose period is 2π, all the values of x such that the cosine function crosses the x-axis is described by the following expression:
cos x = 0 (1)
Then, by inverse trigonometric functions:
x = cos⁻¹ 0
x = 0.5π ± π · i, where i is a non-negative integer.
If we know that i = 1 and i = 2, then the values of x within the interval [- 2π, 0] are, respectively:
x₁ = - 0.5π, x₂ = - 1.5π
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
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fraction numerator 8 over denominator 2.4 end fraction equals space 9 over x
Answer:
x = 2.7
Step-by-step explanation:
8/2.4 = 9/x
Cross multiply.
8x = 2.4 × 9
8x = 21.6
8x/8 = 21.6/8
x = 2.7
Find the slope of the regression line.
Shots on goal 22, 25, 28, 29, 33
Points scored 5, 7, 7, 9,8
A -0.561
B 0.283
C. 0.631
D. 0.794
Ten times the sum of a number and nine is 290. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
Step-by-step explanation:
10+290=x is the answer
x=290-10
x=280#
Find the circumference of the circle with area 1÷4πd² cm²
Answer:C=3.54
Step-by-step explanation:
Subtract Integers
1. FOOTBALL A team gained 5 yards on
their first play of the game. Then they
lost 6 yards. Find the total change in
yardage.
total change is -1
The total change in yard is -1
By this question we can get
The football A team gained 5 yard on their first day of the game
Then they lost 6 yards
The total change in yard is
We all know
The formula of find change is
Total-loss
So,
5-6=-1
Gain 5 yards
Lost 6 yards
Total change 5-6=-1 (ans)
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The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.
Answer:
The length of rectangle seven more than triple the width. If the perimeter 126 inches, find the dimensions The width inches. The length inches.
the cost of 1 dorzen of pencils is rs 80 find the cost of 18 pencil
Answer:
soln
given,
1dozen=rs 80
therefore,cost of 18 dozen pencils =80 × 18
=1440 Rs
Kim went to the store and bought three shirts.
She spent $26.30. One shirt cost $8.72, and
another cost $10.79. How much did the third shirt
cost?
Answer:
$6.79
Step-by-step explanation:
You add the cost of the first two then subtract that by the total she spent to get the answer
$10.79 + $8.72 = $19.51
$26.30 - $19.51 = $6.79
Graph the image of the figure after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer: (3, 3), (3, 9), (-6, 9), (-6, 3)
Step-by-step explanation:
With a dilation of 3 centered about the origin-
the point (1, 1) would go to (3, 3)
the point (1, 3) would go to (3, 9)
the point (-2, 3) would go to (-6, 9)
the point (-2, 1) would go to (-6, 3)
simply multiply the original coordinates all by 3.
One bar of candy A and two bars of candy B have 763 calories. Two bars of candy A and one bar of candy B contain 773 calories. Find the caloric
content of each candy bar
Candy bar A contains calories and candy bar B contains
(Simplify your answers.)
calories
Answer:
A = 261 calories. and B = 251 calories
Step-by-step explanation:
A + 2B = 763
2A + B = 773
---------------------------
-2(A + 2B = 763)
↓
-2A - 4B = - 1526
2A + B = 773
-----------------------------
-3B = - 753
B = 753/3
B = 251
Candy bar B has 251 calories
now let's find A
A + 2B = 763
A + 2 (251) = 763
A + 502 = 763
A = 763 - 502
A = 261
Candy bar A has 261 calories
Simplify the equation, [tex](x^{4})^{\frac{5}{6} }[/tex], to a simplified radical. Show work
The simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
The exponentiation is written as [tex]a^{n}[/tex], where a is the base and n is the exponent or power. We say as "a by n". Exponent means the number of times the base is used as a factor.
The expression = [tex](x^{4})^{\frac{5}{6} }[/tex]
Here we have to apply the exponent rule
We know,
The power rules for the exponent [tex](a^{m})^{n}=a^{mn}[/tex]
Here multiply the exponent times the power.
Simplify it
[tex](x^{4})^{\frac{5}{6} }=(x)^{4(\frac{5}{6}) }[/tex]
=[tex]x^{\frac{20}{6} }[/tex]
Divide both 20 and 6 by 2 to make it to simplest form, then the result
=[tex]x^{\frac{10}{3} }[/tex]
Hence, the simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
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If QS bisects PQR, m PQS = (10x-9), and m SQR= (4x+15), find x.
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
What is the numerical value of x?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
QS bisects PQRm PQS = (10x-9)m SQR= (4x+15)Value of x = ?Since QS bisects PQR, m PQS is the same as m SQR.
Hence;
m SQR = m PQS
We plug in the values
(4x+15) = (10x-9)
Remove parenthesis and solve for x.
4x + 15 = 10x - 9
15 + 9 = 10x - 4x
24 = 6x
x = 24/6
x = 4
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
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Steve has 6 3/4 pounds of ground beef to make hamburgers for a party it takes 3/8 of ground beef to make a hamburger how many burgers can Steve make
The number of burgers Steve can make = 18
In this question, Steve has 6 3/4 pounds of ground beef to make hamburgers for a party.
It takes 3/8 of ground beef to make a hamburger.
We need to find the number of burgers Steve can make.
First we convert the improper fraction 6 3/4 into a proper fraction.
6 3/4 = 27/4
For 1 hamburger 3/8 of ground beef is required.
Let n be the number of burgers Steve can make.
n = (27 / 4) / (3 / 8)
n = 27/4 × 8/3
n = 9 × 2
n = 18
Therefore, the number of burgers Steve can make = 18
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"divide 9 by p, then multiply 2 by the result" i need the expression for this, thank you
Answer: The expression would look like this p/9 (2)
Step-by-step explanation: You should make it a fraction by putting the p on top and 9 on bottom and in parentheses you put in the 2!
Hope this helped! :D
A patient's order is 70 milligrams of a drug. Available in stock is 80 milligrams in 1 milliliter of liquid. How many milliliters should be administered?
The required milliliters should be administered is 0.875 milliliter .
What is Volume?Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units. The definition of length is interrelated with volume.
Given:
A patient's order is 70 milligrams of a drug.
Available in stock is 80 milligrams in 1 milliliter of liquid.
According to given question we have
80 milligrams = 1 milliliter
70 milligrams =1*70/80 milliliter
70 milligrams = 0.875 milliliter
Therefore, the required milliliters should be administered is 0.875 milliliter .
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The line graph below shows the number of times Maria drove her car each day of the week.
How many times did Maria drive her car on day 4?
The number of times Maria drove the car on day 4 is 9 times.
How many times did Maria drive her car on day 4?A line graph is a graph that connects different data points on a graph using a straight line. A line graph is made up of a x-axis and a y-axis. In the line graph given, the number of days is on the x-axis and the number of times the car was driven is on the y-axis. A line graph is used to show quantitative data. Line graphs are used to visualise data.
In order to determine the number of times Maria drove the car on day 4, locate where day 4 is on the x-axis. Then trace 4 upward toward a data point. When the data point is located, trace it to the y-axis. When day 4 is traced to the y-axis, the value gotten is 9.
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Select the correct answer.
Why is the responsibility for maintaining roads and streets given to municipal governments?
O A.
The federal government would not have time to get to all the roads.
O B.
The local government has better knowledge about the needs in its area.
O C. The state government does not want to pay maintenance crews.
O D.
The county government does not have the power to pave roads.
Hurryyyyyyyy pls
Answer:
OA
Step-by-step explanation:
the federal government only manages the things about the country , that's why there are different types of government becuz each one of them has responsibilities