solve for b:
take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{4(3b+2)^2}=\sqrt[]{64} \\ \sqrt[]{4}\cdot\sqrt[]{(3b+2)^2}=\pm8 \\ 2(3b+2)=\pm8 \\ 6b+4=\pm8 \\ so\colon \\ b=\frac{\pm8-4}{6} \end{gathered}[/tex]therefore:
[tex]\begin{gathered} b=\frac{2}{3} \\ or \\ b=-2 \end{gathered}[/tex]Answer: b=2/3 and b=-2
Step-by-step explanation:
1
Suppose Vanessa can clean her bedroom in 30
minutes. Steven can clean the same room in only
15 minutes. If they work together, how long
will it take them to clean the bedroom ?
How long will it take them to clean the bedroom? 10 minutes
How to calculate the time of the work done together?
Given:
Vanessa (A)= 30 minutes
Steven (B) = 15 minutes
The total time taken if both work together is given by,
[tex]A+B=\frac{AB}{A+B} \\\\=\frac{30*15}{30+15}\\\\=\frac{450}{45}\\\\= 10[/tex]
So, it would take 10 minutes to clean the bedroom, if they work together
What is the time - work concept ?
Time and work is concerned with the amount of time it takes a person or a group of people to complete a task and the effectiveness of the work performed by each of them. The rate of work and the amount of time required are inversely proportional. Time taken = 1 / The rate of work.To learn more about time and work , refer:
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Pls help I’m close finishing this assignment
A. No, Alexandra made a mistake going from the given expression to Step 1. Alexandra should have added 18 and 3 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate exponents.
B. No, Alexandra made a mistake going from Step 1 to Step 2. Alexandra should have divided 9 by 9 before adding. The order of operations says to divide before you add.
C. Yes, Alexandra's work is correct.
The expression illustrates that C. Yes, Alexandra's work is correct.
What is an expression?The expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The expression is given as:
= (18 + 3²) ÷ 3²
= (18 + 9) ÷ 9
= 27 ÷ 9
= 3
In this case, the work is correct.
Therefore, the correct option is C.
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Convert 489 degrees into radians.10.54 radians9 radians8.53 radians15.73 radians
To convert the degree to radian use this rule
[tex]x(radian)=\frac{x^{\circ}}{180}\times\pi[/tex]Substitute x by 489 and pi by 22/7
[tex]\begin{gathered} x(radian)=\frac{489}{180}\times\frac{22}{7} \\ \\ x(radian)=8.53 \end{gathered}[/tex]The answer is 8.53 radians the 3rd choice
I was explained this by another tutor but it didn't make too much sense
Given a right angle triangle
The hypotenuse of the triangle = x
The adjacent side to the angle 50 = 6
We will find x using the cosine function as follows:
[tex]\begin{gathered} \cos 50=\frac{adjacent}{hypotenuse} \\ \\ \cos 50=\frac{6}{x} \\ \\ x=\frac{6}{\cos 50}=9.334 \end{gathered}[/tex]Rounding to the nearest tenth
So, the answer will be x = 9.3
Which graph represents this equation?y = 3:2 - 61ОА.+X-4No26-24-6B.24N- 2C.
To determine which one is the graph of the equation:
[tex]y=\frac{3}{2}x^2-6x[/tex]We can finc the x-intercepts of the equations, we know that this happens when y=0, then we have:
[tex]\frac{3}{2}x^2-6x=0[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{3}{2}x^2-6x=0 \\ x(\frac{3}{2}x-6)=0 \\ \text{then} \\ x=0 \\ or \\ \frac{3}{2}x-6=0 \\ \frac{3}{2}x=6 \\ x=\frac{2}{3}\cdot6 \\ x=4 \end{gathered}[/tex]This means that the the graph have to cross the x axis in the values x=0 and x=4.
Looking at the options we notice that the only graph that do this is option B, therefore the gaprh of the equation is shown on B.
x + y = 5 17x + 4y = 46 ) Find the solution to the system of equations. Write it as an ordered pair below.
we have
x + y = 5 -----> equation A
17x + 4y = 46 ------> equation B
Solve the system by substitution
step 1
isolate the variable x in equation A
x=5-y ------> equation C
step 2
substitute equation C in equation B
17(5-y)+4y=46
solve for y
85-17y+4y=46
17y-4y=85-46
13y=39
y=3
Find the value of x
x=5-y
x=5-3=2
thereforethe solution is the ordered pair (2,3)If f(x)=x²-3x+5 and g(x)=-2x, find the following composition.
(f ° g)(2)
(f ° g)(2) = ____ (Simplify your answer.)
The value of the composite function (fog)(2) is equivalent to 0
Composite functionsA mathematical procedure called "function composition" combines two functions, f and g, to produce a third function, h, where g is the sum of f and
Given the functions below;
f(x) = x^2-3x+5
g(x) = -2x
Determine the composite function (gof)(2)
(fog) = f(g(x))
f(g(x)) = g(x^2-3x+5)
f(g(x)) = -2(x^2-3x+5)
f(g(2)) = -2(2^2-3(2)+2)
f(g(2)) = -2(0) = 0
This gives the equivalent composite value
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If Volume = 216 cm^3, what is the length of one edge of Julie's jewelry box?
The volume of a cube = Side³
The length of one edge of Julie's Jewelry box is 6 cm.
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges.
The volume of a cube = Side³
We have,
The volume of the Jewelry box = 216 cm³
The length of one edge of the box = L
The volume of a cube is given as:
V = L³
216 = L³
[ 6 x 6 x 6 = 216 ]
L = ∛216
L = ∛6³
L = 6
Thus,
The length of one edge of Julie's Jewelry box is 6 cm.
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Triangle J is shown below. James drew a scale version of Triangle J using a scale factor of 4 and labeled it Triangle K. What is the area of triangle K
James used a scale factor of 4 to draw a scale representation of Triangle J and named it. Triangle K’s surface area is 10.
What are the triangle’s three main components?Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides.
Any one of a triangle’s three sides might serve as its foundation, although most frequently it is the bottom side.
Below, Triangle J is depicted. James used a scale factor of 4 to create a scale version of Triangle J that he dubbed Triangle K.
How big is triangle K’s surface area?Area= 1/2 bh
=(1/2)*4*5
=10In such a case, K’s triangle’s area is 10.
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Note: The question is incomplete in the portal. Here is the total question,
Question: Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of and labeled it Triangle K. What is the area of Triangle
tommie works at a local store on the weekends. He earns $11.50 per hourr. tommie will get a 10% raise after working 4 weeks. How much will he make per hour after his raise?
Tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is tommie who earns $11.50 per hour and he will get a 10% raise after working 4 weeks.
The amount tommy will earn after 10% raise can be calculated as follows-
10% of 11.50
10/100 x 11.5
1.15
Earnings per hour after raise = 11.5 + 1.15 = $12.65
Therefore, tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
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Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at arate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this induchange from 2008 to 2018?a. 70%b. -27%C. -17%d. -75%
The inicial number of jobs is 63.1 thousand, and each year this number will decrease by 1.7 thousand.
So the change from 2008 to 2018, that is, 10 years, will be:
[tex]10\cdot(-1.7)=-17[/tex]To find the change in percentage, we need to divide the change (-17) by the inicial amount of jobs (63.1), then we have that:
[tex]\frac{-17}{63.1}=-0.27=-27\text{\%}[/tex]So the change in this period is -27%, therefore the answer is B.
Build Understanding ACTIVITY When two lines are cut by a third line, the third line is called a transversal. The intersections of the lines form eight angles, including five special types of angle pairs. When the two lines cut by a transversal are parallel, as shown, the angles in any of the special pairs will be either congruent or supplementary. 1/2 3/4 5/6 7/8 1 The term alternate means that two angles are on opposite sides of the transversal. A. Alternate interior angles are angles on opposite sides of the transversal inside the parallel lines. Measure a pair of alternate interior angles with a protractor. Name the angles you found. Are they congruent or supplementary?
Answer
First of, let us explain what congruent and supplementary mean.
Congruent angles are equal to each other.
Supplementary angles add up to give 180 degrees.
A) Alternate interior angles are congruent. Examples of alternate interior angles from the image include
- angles 3 and 6.
- angles 4 and 5.
B) Alternate exterior angles are congruent. Examples of alternate exterior angles from this image include
- angles 1 and 8.
- angles 2 and 7.
C) Same-side interior angles are supplemetary. Examples of same-side interior angles from the image include
- angles 3 and 5.
- angles 4 and 6.
D) Same-side corresponding angles are also supplementary. Examples of same-side exterior angles from the image include
- angles 1 and 7.
- angles 2 and 8.
E) Corresponding angles for two parallel lines are congruent. Examples of corresponding angles from the image include
- angles 1 and 5.
- angles 2 and 6.
- angles 3 and 7.
- angles 4 and 8.
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The diameter of Mars is about 9^4 kilometers. Write 9^4 as a product. Then find the value of the product.
HELP PLEASE AND THANK YOUMelinda and Paul ran in a marathon. this this graph shows the relationship between the distance and the time they each run. Melinda ran a constant speed of 5 mph. Paul ran at a ____ constant speed than Melinda. an equation that could represent the relationship between Paul's distance and his time is y = _____x, where x is the time in hours and y is the distance in miles Paul ran.THE ANSWER CHOICES ARE 1) FASTER OR SLOWER 2) 1 , 3 , 5 , 7 to complete the sentence !
When a line is steeper than other one it means it has a greater slope. In this case the slope represents the speed of Melinda and Paul. As shown in the picture, the line that represents Paul's movement has a greater slope than the one that represents Melinda's, it means Paul ran at a faster constant speed than Melinda.
If Melinda ran at a constant velocity of 5mph and Paul ran faster than her, an equation that could represent the relationship between Paul's distance an his time has to have a greater slope than 5, which is 7.
what is the displacement of a hiker who first walks 1.5 km north, then walked back 0.45 km south, then walks 3.2km north?
Answer:
5.0 km.
Step-by-step explanation:
Answer: 4.25 Km
Step-by-step explanation:
First you're going to consider the first number given as the main one to start with. (1.5 km)
The question told you that the hiker first went north so you can consider north positive, then he walked back south 0.45 km.
So far your calculation should be 1.5 - 0.45 = 1.05
Then the hiker walks again north with a distance of 3.2 km
so now add that to your value (1.05) as 1.5 and 3.2 are going to the same direction and 0.45 is only opposing them
Final calculation: 1.05 + 3.2 = 4.25 (1.5 - 0.45 + 3.2)
Another way of explaination if you didn't get this one:
The two values 1.5 and 3.2 are mentioned to be in the same direction (north), while 0.45 is mentioned to be opposing them going south, so you can either consider it as
(+)1.5 + 3.2 - 0.45 (But this one would make more sense)
Or
- 1.5 - 3.2 + 0.45
Hope you understood and good luck with your studies :D
A line passes through the point (4,-7) and has a slope of -6 write an equation in slope intercept form for this line
i only need the answer THANK YOU!
The trigonometry expression is cos Ф = 3√5/7 , sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2
sin Ф = perpendicular(p) / hypotenuse(h)
= 2/7
base(b) = √(h²-p²)
=[tex]\sqrt{7^{2} - 2^{2} }[/tex]
= √45
= 3√5
cosФ = b/h
= 3√5/7
sec Ф = h/b
= 7/3√5
cosec Ф = h/ p
= 7/2
tan Ф = p/b
= 2/3√5
cot Ф = b/p
=3√5/ 2
Therefore cos Ф = 3√5/7, sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2.
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Question 1 (10 points)
Listen ▶
Twelve major Earthquakes had Richter magnitudes shown here.
6.8 6.0 7.5 6.8 6.2 6.0 7.0 5.2 6.2 6.3 7.0 5.2
Find Mean
5.35
6.35
7.35
6.95
How do I turn the contents of the passage into an equation?Her phone bill, the cost of diapers, and the subscriptions and pizza for her son. I guess I have to give her an amount to start with, so I’ll go with she started with $100.What if the subscriptions and pizza were 65. The diapers were 30. And her phone bill is 150. Can you show how much she paid toward the diapers and phone bill?
Let G be the cost os monthly game subscriptions, P the cost of a wekly phone bill, D = $30 the cost of a package of 42 diapers, F the cost of pizza on fridays and W the amount she receives each workday.
Then, for a initial amount I = $100, the money M she still have after the events in the text is given by:
[tex]\begin{gathered} M=(W+I)-(G+P+D+F) \\ M=(W+100)-(G+P+30+F) \\ M=W+70-G-P-F \end{gathered}[/tex]If F + G = $65 and P = $150, we have:
[tex]\begin{gathered} M=W+70-65-150 \\ M=W-145 \end{gathered}[/tex]If we are considering only how much she payed for the diapers and the phone bill, we have:
[tex]D+P=30+150=\text{ \$}180[/tex]
Adding: If the two values have the same sign, then?
And use the same sign.
and use the same sign
Using the addition rule with different signs, we know that the resultant answer will have the same sign.
What is Addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.Same Sign - When adding absolute values, use the same sign for the result.Different Signs - Denote the result with the same sign as the number with the bigger absolute value after subtracting the smaller absolute value from the larger absolute value.Subtracting signs - The opposite of an integer number is added when subtracting an integer.A general example to help you recognize patterns:
Adding Integers:
(−3)+2=−121+(−28)=−79+(−9)=0Subtracting Integers:
−3−(−9)=−3+9=6−7−8=−7+(−8)=−15Therefore, using the addition rule with different signs, we know that the resultant answer will have the same sign.
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12y=28x+609y=21x+45A.) no solution B.) many solutions C.) one solution
Step 1: Name the equation
12y = 28x + 60 ....... equation 1
9y = 21x + 45 ........... equation 2
Step 2: Eliminate one of the variables (either x or y ) in the two equations
To do this,
(12y = 28x + 60) multiply by 9
=> 108y = 252x + 540 ........ equation 3
(9y = 21x + 45 ) multiply by 12
=> 108y =252x + 540....... equation 4
step 4
equate equations 3 and 4
252x + 540 = 252x + 540
step 5 :solve the equation
252 x -252x = 540
0 = 0
Hence, the Equations has no solution
option A i
Which of the following equations describes the line shown below? Check allthat apply.(-5,6)(-1,-1)
Options E and F are the correct options
Here, we need to get the equation of the line that passes through the two points given
Mathematically, the equation of a line can be generally expressed as ;
y = mx + c
where m is the slope of the line and c is the y-intercept of the lien ( where it crosses the y-axis)
To get the slope m , we are goint to use the formula below;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_{2\text{ - }}x_1} \\ \\ x_{1\text{ }}=-5,x_2=-1,y_1\text{ = }6,y_2\text{ = -1} \end{gathered}[/tex]Substituting these values into the slope equation , we have
m = (-1-(6))/(-1-(-5)) = -7/4
The equation is now in the form;
y = -7x/4 + c
what is left is to get the y-intercept
We can get the value of the y-intercept by substituting for x and y using any of the points
Let us use the second point
Here, x = -1 and y = -1
Thus;
-1 = -7(-1)/4 + c
-1 = 7/4 + c
c = -1-7/4 = -11/4
So the complete equation of the line is;
y = -7x/4 - 11/4
To properly answer the questions, we need the forms in the options that looks like or can be manipulated arithmetically to look like what we have as our answer
We proceed with each of the options one after the other to see if they can be written in the form of our answer
Option A
y - 5 = -7/4 ( x + 6)
Opening the bracket and evaluating;
y - 5 = -7x/4 - 42/4
y = -7x/4 -42/4 + 5
y = -7x/4 -22/4
we can see this is not a correct option
Option B
y - 6 = -4/7 (x + 5)
Multiply through by 7
7y - 42 = -4x - 20
7y = -4x - 20 + 42
7y = -4x + 22
divide through by 7
y = -4x/7 + 22/7
We can see this is incorrect also
Option C
y - 1 = -4/7(x-1)
Multiply through by 7
7y - 7 = -4x + 4
7y = -4x + 4 + 7
7y = -4x + 11
divide through by 7
y = -4x/7 + 11/7
This is incorrect too
Option D
y + 1 = -4/7 ( x + 1)
Multiply through by 7
7y + 7 = -4x - 4
7y = -4x -4 -7
7y = -4x - 11
y = -4x/7 - 11/7
This is incorrect also
Option E
y - 6 = -7/4 (x + 5)
Multiply through by 4
4y - 24 = -7x - 35
4y = -7x - 35 + 24
4y = -7x -11
y = -7x/4 - 11/4
This is a correct option
Option F
y + 1 = -7/4 ( x + 1)
Multiply through by 4
4y + 4 = -7x - 7
4y = -7x - 7-4
4y = -7x - 11
y = -7x/4 - 11/4
This is a correct option too
Assume the random variable X is normally distributed with mean μ = 50 and standard deviation o=7. Find the 78th percentile
The 78th Percentile is 55.402
What is Percentile?
A Percentile (or centile) is a statistic measure that indicates the value below which a given percentage of observations in a group fall. The 20th percentile, for example, is the value (or score) below which 20% of the observations can be found.
The terms Percentile and Percentile rank are frequently used in the reporting of norm-referenced test scores. For example, a score in the 86th percentile, where 86 is the percentile rank, corresponds to a value below which 86% of the observations can be found. In contrast, a score in the 86th percentile indicates that it is at or below the value at which 86% of the observations can be found.
We know that,
μ = 50,
and σ = 7,
First, we need to find the z-score associated to this percentile.
We need to find the value [tex]Z_{p}[/tex] that solves the equation below.
[tex]Pr(Z < Z_{p}) = 0.78[/tex]
The value of [tex]Z_{p}[/tex] that solves the equation above cannot be made directly, it is solved either by looking at a standard normal distribution table or by approximation.
Based on this, we find that that the solution is [tex]Z_{p}[/tex] 0.772, because from the normal table we see that
Pr(Z<0.772)=0.78
Therefore, the percentile we are looking for is computed using the following formula:
[tex]P_{78}[/tex] = μ+ [tex]Z_{p}[/tex] × σ
= 50+0.772×7
= 55.405
Therefore, it is concluded that the corresponding 78-th percentile is found to be [tex]P_{78}[/tex] is 55.405.
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Use the vertex (0,3) and a point on the graph (2,7) to find the general form of the equation of the quadratic function.
The line which is passing through the point on the graph (2,7) and with vertex (0,3) having equation is [tex]x^{2}[/tex] -y +3 = 0
The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c are R and a [tex]\neq[/tex] 0, are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).
The general equation of the quadratic equation if (h, k) is the vertex and (x, y) is a point on the curve is given by
y = [tex]a(x-h)^{2} + k[/tex] ......eqn 1
In the situation where a must be determined at position (h, k) and (x, y)
In the above question, it is given that,
vertex is (h,k) = (0,3) and the point on the graph is (x,y) = (2,7)
Now we'll put the points in the general equation of the quadratic equation to get the desired equation
y = [tex]a(x-h)^{2} + k[/tex]
y = [tex]a(x-0)^{2}[/tex] + 3 .....eqn 1
Now putting the value of (x,y)
7 = [tex]a(2-0)^{2}[/tex] + 3
7 = 4a + 3
4a = 4
a = 1
putting the value of a in the equation 1, we get
y = [tex]1(x-0)^{2}[/tex] + 3
y = [tex]x^{2}[/tex] + 3
[tex]x^{2}[/tex] -y +3 = 0
Hence, the equation of the line passing through a point on the graph (2,7) with the vertex (0,3) is [tex]x^{2}[/tex] -y +3 = 0
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Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.
In the given figure we have that
AC=AD -----> by the radius of the circle
Δ ACO -------> is a right triangle
Δ ADO -------> is a right triangle
Applying the Pythagorean Theorem in both triangles
AC^2=CO^2+AO^2
AD^2=DO^2+AO^2
Remember that
AC=AD ----> radius of the circle
so
CO=DO
Δ ACO≅Δ ADO -----> by SSS
therefore
is proved that the radius that bisects the chord is a perpendicular bisector
Find the 11th term of the sequence: 32805, 10935, 3645...
first term a=32805
common ration: r=10935/32805=1/3
11th term:
[tex]\begin{gathered} a_{11}=32805(\frac{1}{3})^{11-1} \\ a_{11}=32805(\frac{1}{3})^{10} \\ a_{11}=32805(\frac{1}{59049}) \\ a_{11}=0.555 \end{gathered}[/tex]So the 11th term is 0.555
hhhelpppppppppppppppppp meeeeeeeee
Answer: she does an average of -0.07
Step-by-step explanation:
add the all up which equals -0.35 divide that by how many there are which equals -0.07
Evaluate f(3) for f(x)=2x+6
for the first week of January,Patricia Morgan worked 46 hours. Patricia earns $9.70 an hour. her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. calculate the following for the first week of January ( round your responses to the nearest cent if necessary) regular pay amount, overtime pay, gross pay
Answer
Regular pay = $388
Overtime pay = $87.3
Gross pay = $388 + $87.3
= $475.3
Explanation
During the first week of January, Patricia Morgan worked 46 hours at a rate of $9.70 per hour for regular hours.
For overtime, the pay is 1.5 times the normal rate. That is, 1.5 × $9.70 = $14.55
So, working for 46 hours, that is, 40 hours regular pay rate, and 6 hours overtime pay rate.
Regular pay = 40 × $9.70 = $388
Overtime pay = 6 × $14.55 = $87.3
Gross pay = Regular pay + Overtime pay
= $388 + $87.3
= $475.3
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Simplify completely: cos/1−sin
There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.
cot θ = 1/tan θ = Base/Perpendicular
sec θ = 1/cos θ = Hypotenuse/Base
cosec θ = 1/sin θ = Hypotenuse/Perpendicular
Given:
cos x/ 1- sin x
Using Trigonometric identities
1-sin²x = cos²x
So, on rationalizing
= (cos x) /(1-sinx) x (1+sinx)/(1+sinx)
= (cos x) (1+sinx) /(1²-sin²x)
= (cos x) (1+sinx) /(1-sin²x)
= (cos x)(1+sinx)/(cos²x)
= (1+sinx)/(cos x)
=1/ cos x + sin x / cos x
=sec x + tan x
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