Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
Answers
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Related Questions
40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
Answers
But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.
To earn a profit of more than $2000, then s must be greater than 42
This makes the answer to be s > 42
The correct answer is the second option
The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answers
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
Cassie’s latest financial goal is to eliminate her credit card debt
Answers
Based on Cassie's financial goal to eliminate her credit card debt, the graph that would best model her situation in terms of scale and label is B. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)
How to model a graph?When modeling a graph, the time period is often the independent variable. This means that the time period which are in months (months that Cassie makes monthly payments) need to be on the x-axis and will be labelled from 0 to 12 months for the months of the year.
The amount of credit card debt would then be on the y-axis. It is best to have a scale that is larger than the maximum debt Cassie has to that the data can be included properly. So a limit of 0 - 8,000 is best and would properly incorporate the $5,000 she already owes.
Full question is:
Cassie's latest financial goal is to eliminate her credit card debt. She has about $5,000 in credit card debt. She determines that she can afford to make
monthly payments of about $500. To track her progress, she plans to create a graph to model her situation. How should Cassie label and scale her
graph?
A.X-axis scale, 0-8; label, Total Debt ($) y-axis scale, 0-5,000; label, MonthsB. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)C. X-axis scale, 0-8; label, Years y-axis scale, 0-5,000; label, Total Debt ($)D. x-axis scale, 0-12; label, Total Debt ($) y-axis scale, 0-8,000; label, YearsFind out more on models at https://brainly.com/question/22049822
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f(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x)
Answers
f(x) = -5x -4
g(x) = x^2+3
To find (g+f)(x) , simply add both equations:
(g+f)(x)= x^2+3 + (-5x -4 )
(g+f)(x)= x^2+3 -5x -4
Combine like terms
(g+f)(x)= x^2-5x+3-4
(g+f)(x)= x^2-5x-1
Suppose a person who jumps on Earth returns to the ground in 0.4 second. On Phobos, the same jumper will take 6.4 minutes to return to the ground. How many times longer would it be on Phobos than on Earth for the jumper to return to the ground? Explain.
Answers
The times longer would it be on Phobos than on Earth for the jumper to return to the ground is 16 times.
How to calculate the value?From the information, it was given that the person who jumps on Earth returns to the ground in 0.4 second and that on Phobos, the same jumper will take 6.4 minutes to return to the ground.
The number of times longer will be calculated by dividing the values that are given. This will be:.= Time on Phobos / Time on Earth
= 6.4 minutes / 0.4 minutes
= 16
This shows the concept of division of numbers.
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what is the area of the Shaded region used 3.14
Answers
In this problem, the area of the shaded region is equal to the area of the complete square, minus the area of the four circles
so
REmember that
The length side of the complete square is equal to two times the diameter of one circle
A=(2*12)^2-4*pi*(12/2)^2
assume pi=3.14
A=576-4(3.14)(36)
the area of the Shaded region is A=123.84 ft^2I have a bag, with some balls in it. All but four are blue, all but four are green, and all but four are red.
In total, how many balls are there in the bag?
Answers
===============================================
Explanation:
x = total number of balls
x-4 = number of blue
x-4 = number of green
x-4 = number of red
3(x-4) = 3x-12 = total number of blue, green, or red
x - (3x-12) = x-3x+12 = -2x+12 = number of other colors
If there are other colors, then we want this quantity to be larger than 0, so,
-2x+12 > 0
-2x > -12
x < -12/(-2)
x < 6
There are less than 6 balls in the bag.
At the same time, we want each x-4 to be greater than zero
x-4 > 0
x > 4
------------------
We found that x > 4 and x < 6
This combines to 4 < x < 6 which has us land on x = 5
This computes x-4 = 5-4 = 1, showing there's one of each blue, green and red. There are 5-1-1-1 = 2 balls of some other color not mentioned.
------------------
If x = 6, then,
x-4 = 2 each of blue, green and red
There wouldn't be any other color since 6-2-2-2 = 0
The sum of two numbers is 83. The difference of the 2 numbers is 13. What is the product of the two numbers?A.1632B.1650C.1666D.1680
Answers
Answer:
Let the first number be
[tex]=x[/tex]Let the second number be
[tex]=y[/tex]The sum of two numbers is 83 can be represented below as
[tex]x+y=83\ldots\ldots(1)[/tex]The difference of the 2 numbers is 13 can be represented below as
[tex]x-y=13\ldots\ldots\text{.}(2)[/tex]Step 1:
From equation (1) make x the subject of the formula to to give equation (3)
[tex]\begin{gathered} x+y=83\ldots\ldots(1) \\ x=83-y\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} x-y=13\ldots\ldots\text{.}(2) \\ x=83-y\ldots\text{.}(3) \\ 83-y-y=13 \\ 83-2y=13 \\ \text{collect similar terms,} \\ -2y=13-83 \\ -2y=-70 \\ \text{divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-70}{-2} \\ y=35 \end{gathered}[/tex]Step 3:
Substitute y= 35 in equation (3)
[tex]\begin{gathered} x=83-y\ldots\text{.}(3) \\ x=83-35 \\ x=48 \end{gathered}[/tex]Hence,
The product of the two numbers will be calculated as
[tex]\begin{gathered} =x\times y \\ =35\times48 \\ =1680 \end{gathered}[/tex]Hence,
The final answer is = 1680
OPTION D is the final answer
Alisa walks 3.5 miles in 30 minutes. At this rate, how many miles can she walk in 45 minutes?385.7 miles5 miles386 miles5.25 miles
Answers
Given:
Alisa walks 3.5 miles in 30 minutes.
To find:
The number of miles if she walks 45 mins.
Explanation:
The unit rate for speed is,
[tex]\begin{gathered} Speed=\frac{Distance}{Time} \\ =\frac{3.5}{30} \end{gathered}[/tex]The distance covered when she walks 45mins,
[tex]\begin{gathered} Distance=Speed\times Time \\ =\frac{3.5}{30}\times45 \\ =5.25miles \end{gathered}[/tex]Final answer:
The number of miles she walks in 45mins is 5.25miles.
Identify the explicit formula for the sequence given by the following recursive formula: A) f(n) = –2 + 4(n – 1)B) f(n) = –4 + 2(n – 1)C) f(n) = 4 – 2(n – 1)D) f(n) = 2 – 4(n – 1)
Answers
Given the recurssive formula;
[tex]f(n)=\begin{cases}f(1)=-2 \\ f(n)=f(n-1)+4\text{ if n>1}\end{cases}[/tex]Let's find the sequence using the recurssive formula, we have;
[tex]\begin{gathered} f(2)=f(2-1)+4 \\ f(2)=f(1)+4 \\ f(2)=-2+4 \\ f(2)=2 \\ f(3)=f(3-1)+4 \\ f(3)=f(2)+4 \\ f(3)=2+4 \\ f(3)=6 \\ f(4)=f(4-1)+4 \\ f(4)=f(3)+4 \\ f(4)=6+4 \\ f(4)=10 \end{gathered}[/tex]Thus, we have the sequence as;
[tex]-2,2,6,10,\ldots[/tex]We observed that the sequence is an arithmetic sequence with a common difference of 4 and first term of -2.
So, the recursive formula is;
[tex]\begin{gathered} f(n)=f(1)+d(n-1)_{} \\ f(n)=-2+4(n-1) \\ f(n)=-2+4n-4_{} \\ f(n)=4n-6 \end{gathered}[/tex]CORRECT OPTION: A
HELP PLEASEEEEE!!!!!!
Answers
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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Find the coordinates of the circumcenter of triangle PQR with vertices P(-2,5) Q(4,1) and R(-2,-3)
Answers
The given triangle has vertices at:
[tex]\begin{gathered} P(-2,5) \\ Q(4,1) \\ R(-2,-3) \end{gathered}[/tex]In the coordinate plane, the triangle looks like this:
There are different forms to find the circumcenter, we are going to use the midpoint formula:
[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Apply this formula for each vertice and find the midpoint:
[tex]M_{P,Q}=(\frac{-2+4}{2},\frac{5+1}{2})=(1,3)[/tex]For QR:
[tex]M_{Q,R}=(\frac{4+(-2)}{2},\frac{1+(-3)}{2})=(1,-1)[/tex]For PR:
[tex]M_{P,R}=(\frac{-2+(-2)}{2},\frac{5+(-3)}{2})=(-2,1)[/tex]Now, we need to find the slope for any of the line segments, for example, PQ:
We can apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-5}{4-(-2)}=\frac{-4}{6}=-\frac{2}{3}[/tex]By using the midpoint and the slope of the perpendicular line, find out the equation of the perpendicular bisector line, The slope of the perpendicular line is given by the formula:
[tex]\begin{gathered} m1\cdot m2=-1 \\ m2=-\frac{1}{m1} \\ m2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}_{} \end{gathered}[/tex]The slope-intercept form of the equation is y=mx+b. Replace the slope of the perpendicular bisector and the coordinates of the midpoint to find b:
[tex]\begin{gathered} 3=\frac{3}{2}\cdot1+b \\ 3-\frac{3}{2}=b \\ b=\frac{3\cdot2-1\cdot3}{2}=\frac{6-3}{2} \\ b=\frac{3}{2} \end{gathered}[/tex]Thus, the equation of the perpendicular bisector of PQ is:
[tex]y=\frac{3}{2}x+\frac{3}{2}[/tex]If we graph this bisector over the triangle we obtain:
Now, let's find the slope of the line segment QR:
[tex]m=\frac{-3-1}{-2-4}=\frac{-4}{-6}=\frac{2}{3}[/tex]The slope of the perpendicular bisector is:
[tex]m2=-\frac{1}{m1}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}[/tex]Let's find the slope-intercept equation of this bisector:
[tex]\begin{gathered} -1=-\frac{3}{2}\cdot1+b \\ -1+\frac{3}{2}=b \\ b=\frac{-1\cdot2+1\cdot3}{2}=\frac{-2+3}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Thus, the equation is:
[tex]y=-\frac{3}{2}x+\frac{1}{2}[/tex]This bisector in the graph looks like this:
Now, to find the circumcenter we have to equal both equations, and solve for x:
[tex]\begin{gathered} \frac{3}{2}x+\frac{3}{2}=-\frac{3}{2}x+\frac{1}{2} \\ \text{Add 3/2x to both sides} \\ \frac{3}{2}x+\frac{3}{2}+\frac{3}{2}x=-\frac{3}{2}x+\frac{1}{2}+\frac{3}{2}x \\ \frac{6}{2}x+\frac{3}{2}=\frac{1}{2} \\ \text{Subtract 3/2 from both sides} \\ \frac{6}{2}x+\frac{3}{2}-\frac{3}{2}=\frac{1}{2}-\frac{3}{2} \\ \frac{6}{2}x=-\frac{2}{2} \\ 3x=-1 \\ x=-\frac{1}{3} \end{gathered}[/tex]Now replace x in one of the equations and solve for y:
[tex]\begin{gathered} y=-\frac{3}{2}\cdot(-\frac{1}{3})+\frac{1}{2} \\ y=\frac{1}{2}+\frac{1}{2} \\ y=1 \end{gathered}[/tex]The coordinates of the circumcenter are: (-1/3,1).
In the graph it is:
Solve for x
4x = -5
Put the answer in its simplest form.
Answers
Answer:
[tex] \sf x=-1.25 [/tex]
[tex]\sf--------------------------------------------------------------------- [/tex]
Step-by-step explanation:
4x = -5
Divide both sides by 4 to single out the variable
4x/4 = -5/4
x = -1.25
Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
Answers
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbGrandma’s Guide to Cooking MeasurementsDried Seasonings 1 pinch = 2 smidgens1 dash = 2 pinches1 sprinkle = 3 pinches1 teaspoon = 8 dashesBased on Grandma's guide to cooking, how many smidgens are in one teaspoon?Do not include units with your answer.
Answers
32
Explanation:1 pinch = 2 smidgens
1 dash = 2 pinches
Therefore, 1 dash = 2 x 2 smidgens
1 dash = 4 smidgens
1 teaspoon = 8 dashes
1 teaspoon = 8 x 4 smidgens
1 teaspoon = 32 smidgens
There are 32 smidgens in 1 teaspoon
Patrice found airpods on sale for $84. The sale sales tax is 5%. What is the total Patrice will pay for the airpods?
Answers
To find the final cost with tax. You find the 5% of $84 and add that result to the initial cost:
[tex]84\cdot\frac{5}{100}=4.2[/tex][tex]84+4.2=88.2[/tex]Then, Patrice will pay $88.2 for the airpods
find the value of x for which r parallels s. then find the measures of angles 1 and 2 measure angle 1= 80-2xmeasure angle 2= 93-3xthe value of x for which r parallels s is....measure of angle 1 is.....°measure of angle 2 is.....°
Answers
Since the lines r and s are parallel the angles 1 and 2 must be equal
write an equation
[tex]80-2x=93-3x[/tex]solve the equation for x
[tex]\begin{gathered} 80-2x=93-3x \\ -2x+3x=93-80 \\ x=13 \end{gathered}[/tex]the value for x in which r and s are parallel must be 14
measure of angle 1 and 2 must be 54°
Please help me with this question! Will give brainliest !!! I need it ASAP
Answers
Answer:
The number is not a square number because the exponent is an odd number.
Step-by-step explanation:
Square numbers or perfect squares are any numbers that once put to the square root equals a whole number. Such as 4 is a square number because the square root of 4 is 2 or 2 to the second power. Numbers that are raised to even powers also fall under this rule. For example, 16 is a square number as it is equal to 2 to the fourth power, or 16 to the fourth root is 2. Since 1953125 can also be written by 5 to the ninth power it does not go under this rule due to the power being 9. 9 is an odd number. For it to be a perfect square the exponent would have to be an even number.
Determine the X intercepts of the para bola whose graph is given below write your answer as ordered pairs separated by a comma if necessary
Answers
The x-intercepts are (-1, 0) and (4, 0)
Explanation:Given:
A graph of a parabola
To find:
the x-intercepts of the parabola in ordered pairs
The x-intercept is the value of x when y = 0
On a graph, it is the value of x when the line crosses the x-axis
The line crosses the x axis at x = -1 and x = 4
The x intercept in ordered pairs will be in the form (x, y)
when x = -1, y = 0
when x = 4, y = 0
The x-intercepts are (-1, 0) and (4, 0)
9.) What type of relationship is indicated by the following set of ordered pairs (linear or quadratic)? Explain/Show
how you know by finding successive differences
X
-2
-1
0
1
2
3
Y=-4x-3
Y
14
-1
-6
-1
14
39
10.) Write the equation for question 9 showing all your work for full credit.
11.) Calculate fl-7) for the equation you wrote in Q10. Pls answer all 3 question will mark Brainliest
Answers
Step-by-step explanation:
9)
it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.
for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.
10)
so, since it is not linear, it is quadratic then (since that was our only given alternative).
y = ax² + bx + c
we know c from point (0, -6). c = -6.
for a and b we need to use 2 data points with their x and y coordinates.
let's start with the first (-2, 14)
14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6
we can simplify that
7 = 2a - b - 3
and then
10 = 2a - b
the next point is (-1, -1)
-1 = a×(-1)² + b×-1 - 6 = a - b - 6
5 = a - b
so, we have the 2 equations
10 = 2a - b
5 = a - b
from the second we get
a = 5 + b
and that we can use in the first equation
10 = 2×(5 + b) - b = 10 + 2b - b
0 = b
therefore
5 = a - b = a - 0 = a
a = 5
and the equation is
y = 5x² - 6
11)
f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239
Simplify the expression (3^1/4)^2 to demonstrate the power of a power property. Show any intermittentstepsthat demonstratehow you arrived at the simplified answer.
Answers
(3^1/4)²
= (3^1/4) x (3^1/4)
=(3)^1/4 + 1/4
=(3)^1/2
Which can also be expressed as
= √3
²
what is 6!3! over 2!5!
Answers
Answer:
16
Step-by-step explanation:
6!3!
-------
2!5!
(1 × 2 × 3 × 4 × 5 × 6)(1 × 2 × 3)
--------------------------------------------
(1 × 2)(1 × 2 × 3 × 4 × 5)
(720)(6)
-------------------
(2)(120)
4320
------------ = 18
240
I hope this helps!
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Answers
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
the net of a rectangular prism is shown below. the surface area of each face is labeled. which vakues represent the dimensions, in meters, of the rectangular prism.
Answers
The answer is 5, 9, 10
I need help on this question
Answers
Answer:
Real zeros are: x = 0, x = 1 and x =2
***Your graph is incorrect. See mine for the correct graph***
Step-by-step explanation:
We have the polynomial
[tex]$\displaystyle \:x^{4}-3x^{3}+2x^{2}\:=\:0$[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x^2:\\\\[/tex]
[tex]=x^2\left(x^2-3x+2\right)[/tex]
[tex]\mathrm{Factor}\:x^2-3x+2:[/tex]
For an expression of the form ax² + bx + c we can find factors if we find two values u and v such uv = c and u + v =b and factor into (ax +ux)+ (vx+c)
We have here a = 1, b = -3 c = 2
==> u = -1, v = -2
[tex]\:x^2-3x+2 = (x-1)(x-2)[/tex]
So the original expression becomes
[tex]\:x^2-3x+2 = x^2\left(x-1\right)\left(x-2\right)[/tex]
To find the zeros, set this equal to 0 and solve for x
[tex]x^2\left(x-1\right)\left(x-2\right)=0[/tex]
We end up with 3 roots corresponding to the 0 values for each of the three terms
[tex]x^2 = 0 == > x = \pm 0 = 0\\\\[/tex]
[tex](x - 1) = 0 == > x = 1\\\\(x - 2) = 0 == > x = 2\\\[/tex]
Answer real zeros are: x = 0, x = 1 and x =2
**** Your graph is incorrect. Check mine. The zeros happen where the curve intersects the x axis and these are at x = 0, x = 1, x =2
prove the formula sin 3 A + sin A = 4 sin A cos2A
Answers
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
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I'll send you the pic a
Answers
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answers
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
Answers
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
A store manager records a positive number to show when a deposit is made to the store's bank account and a negative number to show withdrawals.
Which equation could represent how the store manager records making 3 withdrawals of $36 each?
O 3 x 36 108
O 3x-36= -108
-3 x 36 108
O-3 x-36= -108
Answers
Answer:
03*36 108 the positive number
