Answer: Square root of x+3
Step-by-step explanation:
Insert the denominator to 3
ANSWER
The graph of the function starts from (1,4) and moves up right.
EXPLANATION
The given rational function is
[tex]y = \sqrt{x - 1} + 4[/tex]
The base of this function is
[tex]y = \sqrt{x} [/tex]
The -1 under radical sign means the graph of the base function is shifted 1 unit right.
The +4 shows that base function is shifted up by 4 units.
The graph of the function therefore starts from (1,4) and moves up right.
Taylor rides her bicycle for 3 hours and is 32 miles from her house. After riding for 6 hours, she is 62 miles away.
What is Taylor's average rate during her trip?
_____ miles per hour
Step-by-step explanation:
10.44 is correct as we have to add both dis and divide by both hrs
In this case, Taylor's average rate is 10 miles per hour.
To calculate Taylor's average rate during her trip, we can use the formula for average speed:
Calculate the total distance traveled: 62 miles - 32 miles = 30 miles.
Calculate the total time taken: 6 hours - 3 hours = 3 hours.
Divide the total distance by the total time to find the average speed: 30 miles / 3 hours = 10 miles per hour.
Are the equations |x-3|=7 and |x|-3=7
Answer:
1. x=4 or x=10
2. x=-10 or x=10
No equivalent
Step-by-step explanation:
1. |x-3|=7 and x-3=7
Absoulte rules.
x-3=-7 and x-3=7
Add 3 both sides.
x-3+3=-7+3
Simplify.
-7+3=-4
x=-4
x-3=7
Add by 3 both sides.
x-3+3=7+3=10
x=10
X=-4, and X=10 is the correct answer.
________________________________
2. |x|-3=7
Add by 3 both sides.
|x|-3+3=7+3
Simplify.
7+3=10
X=10
X=-10 and X=10 is the correct answer.
______________________________
The two equations |x-3|=7 and |x|-3=7, are solved differently. For |x-3|=7, the possible solutions are x=10 and x=-4. For |x|-3=7, the possible solutions are x=10 and x=-10.
Explanation:The two equations you're looking at are: |x-3|=7 and |x|-3=7. They look very similar but they're solved differently because absolute value symbols affect all values inside them together.
For the first equation, |x-3|=7, we solve this by considering the two situations, x-3 = 7 and x-3 = -7. Solve each of these two equations separately, so you get x = 10 and x = -4.
For the second equation, |x|-3=7, firstly, we need to eliminate '-3' from the right-hand side by adding 3 to both sides, leading to |x| = 10. This is then broken down into the two possible situations as before: x = 10 and x = -10.
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Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.
Answer:
y + 12 = 3(x - 2)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. Since both lines contain have to have similar rate of changes [slopes], we do not go any further.
Choose two angles that are each separately alternate exterior angles with 412.
41 and 210
112
41 and 26
11
25 and 26
42 and 45
43 and 2
Answer:
∠2 and ∠5
Step-by-step explanation:
we know that
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal
In this problem
∠12 and ∠2 are alternate exterior angles
∠12 and ∠5 are alternate exterior angles
therefore
∠2 and ∠5 are each separately alternate exterior angles with ∠12
area of shaded segment
Answer:
N/A
Step-by-step explanation:
Which area of shaded segment?
Answer:
Area Of Shaded Segment =
In Pictures
If X/7=Y/5 then what does 5X equal
Answer:
7y
Step-by-step explanation:
By cross multiplication
[tex] \frac{x}{7} = \frac{y}{5} \\ 5x = 7y[/tex]
Answer:
[tex]5x=7y[/tex]
Step-by-step explanation:
We have the following relationship
[tex]\frac{x}{7}=\frac{y}{5}[/tex]
Based on the relationship between the variables X and Y that we know, we must find out what the expression "5x" is in terms of the variable y.
Then we solve the equation for x
[tex]x=\frac{7y}{5}[/tex]
Now multiply by 5 both sides of equality
[tex]5x=\frac{5*7y}{5}[/tex]
[tex]5x=7y[/tex]
Finally we have that 5x equals 7y
In the triangle below, what is the length of the side opposite the 60° angle?
Answer:
What triangle below?
Step-by-step explanation:
Im confused sorry
Triangle ABC has vertices at A(-2, 3), B(-3,-6), and C(2,-
1). Is triangle ABC a right triangle? If so, which angle is the
right angle?
w Ano
A(-2,3)
O No, the triangle has no right angles.
O Yes, the right angle is angle A.
O Yes, the right angle is angle B.
O Yes, the right angle is angle C.
6
5
4 -3 3-2 -1,5
2
6
x
3 4 5
C (2,-1)
B(-3,-6)
Answer:
Yes, the right angle is angle B
Step-by-step explanation:
we have
[tex]A(-2, 3), B(-3,-6),C(2,-1)[/tex]
Plot the vertices
see the attached figure
we know that
If triangle ABC is a right triangle
then
Applying the Pythagoras Theorem
[tex]AB^{2} =AC^{2}+BC^{2}[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(-2, 3), B(-3,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(-1)^{2}}[/tex]
[tex]AB=\sqrt{82}\ units[/tex]
Find the distance BC
[tex]B(-3,-6),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1+6)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(5)^{2}}[/tex]
[tex]BC=\sqrt{50}\ units[/tex]
Find the distance AC
[tex]A(-2, 3),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(2+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]AC=\sqrt{32}\ units[/tex]
Verify the Pythagoras theorem
[tex](\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}[/tex]
[tex]82=82[/tex] ---> is true
therefore
Is a right triangle and the right angle is B
Factor completely. If a polynomial is prime, state this.
2t^2-19-6t
ANSWER
Prime
EXPLANATION
The given quadratic expression is
[tex] {2t}^{2} - 19 - 6t[/tex]
We rewrite in standard form to obtain
[tex]{2t}^{2} - 6t - 19[/tex]
Comparing to the standard quadratic function in t,
[tex]a {t}^{2} + bt + c[/tex]
We have
[tex]a = 2[/tex]
[tex]b = - 6[/tex]
[tex]c = - 19[/tex]
We find that the product
[tex]ac = 2 \times - 19 = - 38[/tex]
There are no two factors of -38 that sums up to -6.
This means that, the given polynomial does not have rational factors.
Therefore the polynomial is prime.
a solution consisting of 52 mg of dopamine in 26 mL of solution at a rate of 10 mL/hr what is the flow rate in mg of dopamine per hour
Answer:
20 mg / hour
Step-by-step explanation:
The first step is to find the mg/mL of dopamine.
If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).
If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.
You can also do this using dimensional analysis.
[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]
Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.
The first step is to find the mg/mL of dopamine.
If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).
If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.
You can also do this using dimensional analysis.
[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]
Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.
What four numbers can equal 15?? Please help!!
Answer:
1,3,5,15
Step-by-step explanation:
these are the factors of 15
Answer:
Step-by-step explanation:
I must assume that you meant, "the sum of which four numbers equals 15?"
15 = 6 + 9
= 3 + 3 + 9
= 3 + 3 + 3 + 6
All of these sets (on the right side) add up to 15. There are four numbers in the last set.
What is the domain of the function shown in the table?
X y
-2 0
-1 1
0 2 1 3
Answer:
{-2,-1,0}
Step-by-step explanation:
The domain of a function is defined as the set of x values for which the function is real and defined. The x values represent independent or predictor variable.
The domain of the function is thus;
{-2,-1,0}
These are basically the x values of the function
White shapes and black shapes are used in a game. Some of the shapes are circles. All the other sahpes are squares.
The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles.
Answer:
9/32
Step-by-step explanation:
BC = black circle
BS = black square
WC = white circle
WS = white square
Given:
(WC + WS) / (BC + BS) = 5 / 11
WC / WS = 3 / 7
BC / BS = 3 / 8
Find: (BC + WC) / (BC + BS + WC + WS)
Solve for WC and BC in the last two equations, then substitute into the first:
WC = 3/7 WS
BC = 3/8 BS
WC + WS = 5/11 (BC + BS)
3/7 WS + WS = 5/11 (3/8 BS + BS)
10/7 WS = 5/8 BS
WS = 7/16 BS
Therefore:
WC = 3/7 WS
WC = 3/16 BS
Substitute:
(BC + WC) / (BC + BS + WC + WS)
(3/8 BS + 3/16 BS) / (3/8 BS + BS + 3/16 BS + 7/16 BS)
(9/16 BS) / (2 BS)
9/32
30 points
What is the opposite of cosine called and what is its triangle ratio
Answer: Answer is below
Step-by-step explanation: The answer is that the opposite of a cosine is called a hypotenuse. The ratio of the triangle is called a tangent.
I hope this info helps! :V
Four Representations: Equations, Tables, Words,
WARM-UP and Graphs
Select the words that best describe the given
equation Y = X-1
DONE
w the following questions, look at different ways to
represent the relation given by the
equation y = x2 - 1.
Which graph represents the relationship?
The table below shows some values for the given
equation. Find the values of a and b.
a =
Nyt
Intro
Equations are used to represent the relationships between variables. In [tex]y=x^2 -1[/tex], the variables are x & y and the following observations are true for the given equation:
The words that describe [tex]y=x^2 -1[/tex] are: y is 1 less than the square of xThe values of a and b are 3 and 0, respectively.Given that:
[tex]y=x^2 -1[/tex]
[tex]x^2 \to[/tex] the square of x
So, means that: the y is 1 less than the square of x
From the attached table, we have:
[tex]x = -2; y = a[/tex]
This means that:
[tex]a = (-2)^2 - 1[/tex]
[tex]a = 4 - 1[/tex]
[tex]a =3[/tex]
Also, we have:
[tex]x = b; y = -1[/tex]
This means that:
[tex]-1 = b^2 - 1[/tex]
Collect like terms
[tex]b^2 =1-1[/tex]
[tex]b^2 =0[/tex]
Take square roots
[tex]b = 0[/tex]
Hence, the values of a and b are 3 and 0, respectively.
The graph options are not made available. So, I will plot the graph of [tex]y=x^2 -1[/tex].
See attachment for graph of [tex]y=x^2 -1[/tex]
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Answer: In short for ed2020 :
1. 3rd answer
Graph: A
Table: A=3 B=0
one number is 7 more than twice another number, the sum of the numbers is 22. what is one of the numbers?
Answer:
One of the numbers is 5
The other number is 17
Step-by-step explanation:
You could do this just by guessing numbers. But I think you are intended to do it with algebra.
x + y = 22
y = 2*x + 7 Substitute the y value in this equation into the first equation
x + 2x + 7 = 22 Combine the xs on the left.
3x + 7 = 22 Subtract 7 from both sides.
3x+7-7=22- 7 Combine
3x = 15 Divide by 3
3x/3 = 15/3 Combine
x = 5
x + y = 22 Substitute 5 for x
5 + y = 22 Subtract 5 from both sides.
5-5+y = 22-5
y = 17
Answer:
17 or 5
Step-by-step explanation:
I took the test
the perimeter of a rectangle is 11 inches. the width is 2 inches shorter than the length. find the length of the rectangle.
The perimeter is 11 inches.
One side is 2 inches shorter, so two sides would be 4 inches shorter total.
Subtract 4 from 11 to get 7 inches.
Divide 7 by 4 ( the number of sides):
7 / 4 = 1.75
The shorter side is 1.75 inches.
Now add 2 inches to that for the longer side:
1.75 + 2 = 3.75 inches.
Check: 3.75 + 3.75 + 1.75 + 1.75 = 11
The longer side is 3.75 inches.
1/3x^2+2 what does the graph look like
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]\frac{1}{3}x^{2} +2[/tex]
This is a vertical parabola open upward with the the vertex at (0,2)
The vertex is a minimum
The y-intercept is the point (0,2) (value of y when the value of x is equal to zero)
The graph does not have x-intercepts, therefore the solutions of the quadratic equation are complex number
using a graphing tool
see the attached figure
how many terms does the polynomial x^2 y^2 have
Final answer:
The polynomial ₓ2y² has 1 term.
Explanation:
A polynomial is an algebraic expression consisting of terms that are variables raised to non-negative integer powers, multiplied by coefficients. The number of terms in a polynomial is determined by counting the number of distinct combinations of variables and exponents in the expression.
In the given polynomial, ₓ2y², there is only one term because there is only one combination of variables (x and y) raised to their respective exponents (2 and 2).
Therefore, the polynomial ₓ2y²has 1 term.
Which relation is a function?
Answer: c
Step-by-step explanation:
What is the equation in slope intercept form of the perpendicular bisector of the given line segment?
Answer:
y = -4x - 6
Step-by-step explanation:
The equation of a line in point-slope form.
[tex] y - y_1 = m(x - x_1) [/tex]
is the equation of the line containing point (x1, y1) and having slope, m.
The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.
We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.
Now we use the equation above and our values.
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-2) = -4(x - (-1)) [/tex]
[tex] y + 2 = -4(x + 1) [/tex]
[tex] y + 2 = -4x - 4 [/tex]
[tex] y = -4x - 6 [/tex]
Answer:
Step-by-step explanation:
y = -4x - 6
What is the perimeter of the square in terms of x? The length of each side is 2x-1in.
Answer:
Perimeter of the square = 8x - 4 in
Step-by-step explanation:
Perimeter of the square = 4 * side
= 4 * (2x - 1)
= 8x - 4 in
Given this equation in slope-intercept form…
y = 2x + 5
Identify or solve for the following:
Slope
y-intercept
x-intercept
Independent variable
Dependent variable
Domain
Range
Answer:
Slope = 5
y-intercept = (0, 5)
x-intercept = (-2.5, 0)
Independent variable = x
Dependent variable = y
Domain = Any real #
Range = I believe it's any real #
Step-by-step explanation:
The slope of the equation is 2.
The y-intercept is 5.
The x-intercept is -5/2.
The independent variable is x.
The dependent variable is y.
The domain of the equation is any real number.
The range of the equation is any real number.
What is the slope-intercept form?The graph of the linear equation y = mx + c is a line with m as slope, and m and c as the y-intercept.
The equation in slope-intercept form is;
y = 2x + 5
1. The slope of the equation is;
y = mx + c
y = 2x + 5
On comparing m = 2
The slope of the equation is 2.
2. The y-intercept is;
y = mx + c
y = 2x + 5
On comparing c = 5
The y-intercept is 5.
3. The x-intercept is;
y = 0
y = 2x + 5
0 = 2x +5
2x = -5
x = -5/2
The x-intercept is -5/2.
4. The independent variable is x.
5. The dependent variable is y.
6. The domain of the equation is any real number.
7. The range of the equation is any real number.
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What is the solution to the system of equations? 3x + 10y = -47 5x- 7y = 40
Please and thank u
Answer:
x=1, y=-5
Step-by-step explanation:
Given equations are:
[tex]3x+10y=-47\ Eqn\ 1\\and\\5x-7y=40\ Eqn\ 2[/tex]
In order to solve the equation
Multiplying Eqn 1 by 5 and eqn 2 by 3 and subtracting them
So,
Eqn 1 becomes
15x+50y=-235
Eqn 2 becomes
15x-21y=120
Subtracting 2 from a
15x+50y - (15x-21y) = -235-120
15x+50y-15x + 21y = -355
71y = -355
y = -355/71
y =-5
Putting y= -5 in eqn 1
3x+10(-5) = -47
3x -50 = -47
3x = -47+50
3x = 3
x = 3/3
x = 1
Hence the solution is:
x=1, y=-5
Answer: x=1; y=-5
Step-by-step explanation: To solve this system we can use differente methods, in this case we are going to use substitution:
first equation: 3x+10y=-47
second equation: 5x-7y=40
we are going to isolate x from the first equation:
3x=-47-10y
[tex]x=\frac{-47-10y}{3}[/tex]
now we replace it in the second equation:
[tex]5*\frac{-47-10y}{3}-7y=40[/tex]
and now we solve for y:
[tex]\frac{-235-50y}{3} -7y=40[/tex]
[tex]\frac{-235-50y-21y}{3}=40[/tex]
[tex]-235-71y=40*3[/tex]
[tex]-235-71y=120[/tex]
[tex]-71y=120+235[/tex]
[tex]y=-355/71[/tex]
y=-5
now we replace the value of y in the first equation and solve for x:
[tex]x=\frac{-47-10y}{3}[/tex]
[tex]x=\frac{-47-10(-5)}{3}[/tex]
[tex]x=\frac{-47+50}{3}[/tex]
[tex]x=\frac{3}{3}[/tex]
x=1
A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind.
What was the speed of the wind?
miles per hour
Answer:
20 miles per hour
Step-by-step explanation:
traveling against the wind was 160mph (400/2.5)
traveling with the wind was 200mph (400/2)
going against the wind is going in the negative direction of the wind speed, and going with the wind is going in a positive direction of the wind speed, therefore the wind speed is |direction1-direction2|/2, which would be |200-160|/2 = |40|/2 = 20mph
(180mph is neutral speed with no wind, with wind affecting this neutral speed ±20mph)
Final answer:
To determine the wind speed, we used the distances and times provided for the flights against and with the wind to set up equations for the airplane's effective speeds. Solving these equations, we found that the wind speed is 20 miles per hour.
Explanation:
To solve for the wind speed, we first need to establish the speed of the airplane without the influence of the wind. Let's denote the speed of the airplane in still air as A, and the speed of the wind as W. When the plane is flying into the wind, its effective speed is A - W, and while flying with the tailwind, its effective speed is A + W.
From the first part of the trip, we have:Distance = 400 milesTime = 2.5 hoursSpeed against the wind = (A - W) = 400 / 2.5 = 160 mph
From the return trip, we have:Distance = 400 milesTime = 2 hoursSpeed with the wind = (A + W) = 400 / 2 = 200 mph
We now have two equations based on the effective speeds:
A - W = 160A + W = 200By adding these two equations, we eliminate W:
2A = 360 mphThus, the speed of the airplane in still air (A) is 180 mph. We can now find the wind speed by subtracting this value from the effective speed with the wind:
A + W = 200 mph180 + W = 200 mphW = 200 - 180W = 20 mphTherefore, the speed of the wind is 20 miles per hour.
Help me on this one
Answer:
[tex]\large\boxed{3\div\dfrac{1}{5}}[/tex]
Step-by-step explanation:
Each 1 was divided into five equal parts. Each of these parts is 1/5. We calculate how many times 1/5 is in 3.
Use the rule y=-x+7to fill in the blank (1,y) is on the graph,then y=
Answer:
y=6
Step-by-step explanation:
y = -x+7
We have the point (1,y)
That means x=1 and we want to find y
Let x=1
y = -1+7
y = 6
The point is (1,6) where x=1 and y =6
What is the equation of the line that passes through (7, 4) and (4, -2)?
Answer:
y=2x-10
Step-by-step explanation:
First step: Let's compute the slope. You can directly use the formula for slope given two points here but I just like to like them up and subtract vertically. Make sure you put 2nd difference on top of 1st difference (yes, like a fraction).
(7 , 4)
-(4 , -2)
=======
3 6
So the slope is 6/3 =2.
So we know our line is in the form y=2x+b.
We have to find the y-intercept now. To find b we will use a point that we know is on the line (you know two-just choose one of them) . I will plug in (4,-2) giving me this equation -2=2(4)+b
Solving: -2=8+b
So b=-10
The answer is y=2x-10
simplify this expression 6m/18(m+n)
Answer
[tex]\frac{m^{2}+mn }{3}[/tex]
Step-by-step explanation:
Reduce the numbers with the greatest commen divisor 6
Then calculate the product
Credit card companies use negative balances to represent when the credit card company owes the customer money and positive balances to represent when the customer owes the credit card company money.
Mya has a balance of 0 dollars with her credit card company.
What does a balance of 0 dollars represent?
Answer:
she owes nothing and the credit card company owes her nothing.
Answer:
It represents that the bank owes her nothing and she doesn't owe the bank anything. So it is neither postive or negative
Step-by-step explanation: