Answer:
[tex]\theta\text{ = 115.67}\degree[/tex]Explanation:
Here, we want to find the angle between the two vectors
Mathematically, we have that as:
[tex]cos\text{ }\theta\text{ = }\frac{a.b}{|a||b|}[/tex]The denominator represents the magnitude of each of the given vectors as a product while the numerator represents the dot product of the two vectors
We have the calculation as follows:
[tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{(1\times8)+(-9\times5)}{\sqrt{1^2+(-9)\placeholder{⬚}^2}\text{ }\times\sqrt{8^2+5^2}} \\ \\ cos\text{ }\theta\text{ = }\frac{8-45}{\sqrt{82}\text{ }\times\sqrt{89}} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{-37}{\sqrt{82}\text{ }\times\sqrt{89}} \\ cos\text{ }\theta\text{ = -0.4331} \\ \theta\text{ = }\cos^{-1}(-0.4331) \\ \theta\text{ = 115.67}\degree \end{gathered}[/tex]Which of the following would be the best equation for the function of the values for Janet’s reading?A) p = 6hB) p = 20hC) h = 20pD) 20 + p = h
In order to obtain the best equation for the function of the values for Janet’s reading, we will apply the equation of a straight line between two points.
The formula to calculate the equation of a line between two points is,
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let us now pick any two points from the table given
[tex]\begin{gathered} (x_1,y_1)=(1,20) \\ (x_2,y_2)=(6,120) \end{gathered}[/tex][tex]\begin{gathered} \text{where,} \\ p=y \\ h=x \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{120-20}{6-1} \\ \end{gathered}[/tex]Simplify
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{100}{5} \\ \frac{y-20}{x-1}=20 \\ y-20=20(x-1) \\ y=20(x-1)+20=20x-20+20=20x \\ y=20x \\ \therefore p=20h \end{gathered}[/tex]Hence, the answer is
[tex]p=20h\text{ (OPTION B)}[/tex]Solve the equation.5/6=1/3+d
We have the following equation
[tex]\begin{gathered} \frac{5}{6}=\frac{1}{3}+d \\ \end{gathered}[/tex]We substract 1/3 each side:
[tex]\begin{gathered} -\frac{1}{3}+\frac{5}{6}=-\frac{1}{3}+\frac{1}{3}+d \\ -\frac{1}{3}+\frac{5}{6}=0+d \\ -\frac{1}{3}+\frac{5}{6}=d \\ \end{gathered}[/tex]We multiply each side of the fraction 1/3 by 2:
[tex]-\frac{1}{3}=-\frac{1\cdot2}{3\cdot2}=-\frac{2}{6}[/tex]Then
[tex]\begin{gathered} -\frac{1}{3}+\frac{5}{6}=d \\ -\frac{2}{6}+\frac{5}{6}=d \\ \frac{3}{6}=\frac{1}{2}=d \end{gathered}[/tex]Answer: d = 1/2Use prime factorization to reduce each fraction 1. 22/165 2. 35/210
Lets find the prime factorization of 22, 165, 35 and 210. Prime factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number.
The prime factorization of the number 22 is:
[tex]22=2\times11[/tex]Similarly, for 165, 35 and 210 we have
[tex]\begin{gathered} 165=3\times5\times11 \\ 35=5\times7 \\ 210=2\times3\times5\times7 \end{gathered}[/tex]Then, we can solve the given questions.
Question 1.
[tex]\frac{22}{165}=\frac{2\times11}{3\times5\times11}[/tex]so we can cancel out the number 11 and get
[tex]\frac{22}{165}=\frac{2}{3\times5}=\frac{2}{15}[/tex]Then, the answer is
[tex]\frac{2}{15}[/tex]Question 2.
[tex]\frac{35}{210}=\frac{5\times7}{2\times3\times5\times7}[/tex]and we can cancel out the number 5 and 7, then we obtain
[tex]\frac{35}{210}=\frac{1}{2\times3}[/tex]then, the answer is
[tex]\frac{1}{6}[/tex]3(2x - 5) – 4x > 7x + 10.Please help
EXPLANATION.
To solve the inequality we must follow some steps:
1.1.the number 3 must multiply the values that are inside the parentheses
Which problem could be solved with the expression 5 (2 + 4) = 6?Choose 1 answer:Hayden made 2 bracelets before school and 4 after school each day for 5 days. Then he split thebracelets into 6 equal groups. How many bracelets did Hayden have in each group?(вShadi is building a new back deck. He puts 2 nails and 4 screws in each board. He did this to 5boards. How many total screws and nails did he use?Khai, the dog, ate 2 bones on Monday, 4 bones on Tuesday and 6 bones on Wednesday. OnThursday, she ate 5 times more bones than the other days combined. How many bones did Khai eaton Thursday?Stuck? Review related articles/videos or use a hint.Report a problem
Let us attempt to solve the options to check which one will give the expression
[tex]5\times(2+4)\div6[/tex]OPTION A:
If Hayden makes 2 bracelets before school and 4 after school daily, then the bracelets she makes daily is gotten by
[tex]2+4[/tex]In 5 days, the number of bracelets will be the expression above multiplied by 5:
[tex]5\times(2+4)[/tex]If she breaks the total bracelets into 6 groups, this means that we divide the expression above by 6:
[tex]5\times(2+4)\div6[/tex]This tallies with the expression in the question.
Hence, OPTION A is correct.
A recipe that uses 1/2 pound of almonds makes 5/6 cup of almond butter. Which is a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds?What amout of almond butter does the recipe make per pound of almonds?____ cup(s) of almond butter per pound of almonds
The given information is:
1/2 pound of almonds makes 5/6 of almond butter.
Since 1 pound is double of 1/2 pound, we will need to multiply the amount of almond butter by 2 to find the almond butter that 1 pound can make.
Multiply the amount of almond butter by 2:
[tex]2\times\frac{5}{6}[/tex]The reason for this multiplication is that to find the amount of almond butter that 1 pound makes, we need double of what 1/2 can make.
Solving the multiplication:
[tex]2\times\frac{5}{6}=\frac{2\times5}{6}[/tex]Since 2x5 is equal to 10:
[tex]2\times\frac{5}{6}=\frac{10}{6}[/tex]1 pound of almonds makes 10/6 cups of almond butter.
Answer: 10/6 cups of almond butter per pound of almonds
Can you please throughly explain this question. I don't get it.
In graphing y > 2x - 7, a dashed line is used.
Answer: True
Explanation
Whenever we graph > or < , the boundary line is not inclusive of the range of solutions. Hence, we use a dashed line on the boundary.
On the other hand, whenever we have the inequality <= or >= , the
answer: true
explanation: my teacher just did it
Solve the equation x(x+6) = 91 using completing the square, finding the square root, and solving. Put the equivalent equations in the appropriate order. |x+3 = 10 7 x² + 6x = 91 x= 7 or x = -13 x² - 6x +9 = 91 +9 x + 3 = 10 or x + 3 = -10 (x+3)² = 100
Solution
Given the equation below:
[tex]x(x+6)=91[/tex]Using the completing the square:
[tex]\begin{gathered} x(x+6)=91 \\ x^2+6x-91=0 \\ half\text{ the coefficient of x, square and add to both side} \\ x^2+6x=91 \\ x^2+6x+(3)^2=91+(3)^2 \\ (x+3)^2=91+9 \\ (x+3)^2=100 \end{gathered}[/tex]Square root both side of the equation
[tex]\begin{gathered} (x+3)^2=100 \\ \sqrt{(x+3)^2}=\pm\sqrt{100} \\ x+3=\pm10 \\ x=\pm10-3 \\ x=7,x=-13 \end{gathered}[/tex]Therefore the equivalent equations in the appropriate order is
Can you please help me out with a question
To find the point S we first need to find the equation of the circle which is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case we don't have the radius but we know that the radius is the distance between the center and any point on the circle, then the radius is equal to the distance:
[tex]\begin{gathered} r=d(A,R)=\sqrt[]{(5-3)^2+(4-(-1))^2} \\ =\sqrt[]{4+25} \\ =\sqrt[]{29} \end{gathered}[/tex]hence the equation of the circle is:
[tex](x-3)^2+(y+1)^2=29[/tex]Now that we have this equation we need to determine which of the options given fullfil the equation. From the options given we conclude that the only point that fullfils the equation is the point D, this come from the fact that:
[tex]\begin{gathered} (1-3)^2+(-6+1)^2=29 \\ 4+25=29 \\ 29=29 \end{gathered}[/tex]Therefore this point is in the circle. Therefore we conclude that the coordinates of point D are (1,-6) and the answer is D.
This can be seen in the graph below:
At a flea market, used computer games are sold at the prices shown in the table below.Number of Games/Price ($)2/9.005/22.507/31.50Do the number of games and price form a proportional relationship?Choose the correct response.A.Yes. There is a constant of proportionality of $11.25.B.Yes. There is a constant of proportionality of $4.50.C.No. There is not a constant of proportionality.D.No. The slope is 4.5.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where k is the constant of proportionality
where k is the constant of proportionality
so
Verify
Let
x -----> numb
Find out the value of k in each case
er of games
y ----> price
Find out the value of k in each case
For x=2, y=9
k=y/x
k=9/2=$4.5 per game
For x=5, y=22.50
k=22.5/5=$4.50 per game
For x=7, y=31.50, because the value ok is the smaamef K
k=31.50/7=$4.50 per game
that means
Yes , Irs a proportional relationship
the answer is the option BWhat is the solution to the equation -6 = x/8
Given equation is
[tex]\frac{x}{8}=-6[/tex]Performing the cross multiplication,
[tex]\begin{gathered} x=(-6)\times8 \\ =-48 \end{gathered}[/tex]Hence, the solution of the given equation is x=-48.
Factor completely 6x^2 -7x-20
Solution:
Given the expression;
[tex]6x^2-7x-20[/tex][tex]\begin{gathered} 6x^2-7x-20=6x^2-15x+8x-20 \\ \\ 6x^2-7x-20=3x(2x-5)+4(2x-5) \\ \\ 6x^2-7x-20=(2x-5)(3x+4) \end{gathered}[/tex]FINAL ANSWER:
[tex]\begin{equation*} (2x-5)(3x+4) \end{equation*}[/tex]Last year, Jenny opened an investment account with $7400. At the end of the year, the amount in the account had decreased by6.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?
if the decreasing amount is 6.5% the r in our decay function will be:
[tex]1-0.065=0.935[/tex]and in one yeat t=1 so the equation will be:
[tex]\begin{gathered} y=7400(0.936)^1 \\ y=6925.4 \end{gathered}[/tex]john ran at a pace of 3.5 miles per hr for a distance of 10.5 miles. how many minutes did it take them to run 10.5miles? use the distance formula: d= rt to where d is total distance, r is rate and t is time
d=rt
divide both-side of the equation by r
t =d/r
distance = 10.5 miles
we will go ahead and find the rate r
r = 3.5/60
r=0.05833
substituting into t= d/r
t = 10.5 / 0.05833
t=180 minutes
Elizabeth is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over t months is given by the equation C = 25t + 100. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
The y-intercept of the equation is 100
For this problema the y-intercep is equal to the one-time fee
2 by 6 rectangle is inscribed in circle 5 by 6 rectangle is inscribed in circle 2 by 15 rectangle is inscribed in circle 1 by 12 rectangle is inscribed in circle what is the circumference?
21:51
it seems that your questions has multiple questions in it. Unfortunately, the tutoring app is meant to answer only one problem per session. So, I encourage you to start another session with your the remainder of the questionsk, so one of my colleague can help you out.
can you see what I'm writing?
Write a equivalent unit rate to running 5/4 a mile in 9 minutes
To determine the unit rate to running 5/4 a mile in 9 minutes you have to determine the distance in miles run in one minute.
You can use corss multiplication to do the calculation:
9min____5/4miles
1min_____xmiles
[tex]\begin{gathered} \frac{\frac{5}{4}}{9}=\frac{x}{1} \\ x=\frac{5}{36} \end{gathered}[/tex]The unite rate is 5/36miles/minute, expressed as a decimal value is 0.14miles/min
Find a best-fit linear model for the following data:xy−3196−2139−1820251−322−893−146y = −57xy = 57xy = 57x + 25y = −57x + 25
Explanation
We are given a set of x and y values in the table
To compute the best-fit model for the data, we will use the graphing calculator
From the graph above, we have the function to be
[tex]y=-57x+25[/tex]Thus, the answer is y= -57x +25
I need help with math
a)
3000x - 2000 = 10 000
Add 2000 to both-side of the equation
3000x - 2000 + 2000 = 10 000 + 2000
3000x = 12000
Divide both-side of the equation by 3000
3000x/3000 = 12000/3000
x = 4
b) -2x/3
[tex]\frac{-2x}{3}-\frac{x}{7}=\text{ 17}[/tex]Multiply through the equation by 21
[tex]21(\frac{-2x}{3})-21(\frac{x}{7})=\text{ 17(21)}[/tex][tex]7(-2x)\text{ - 3x =357}[/tex]-14x - 3x = 357
-17x = 357
Divide both-side of the equation by -17
x = -21
c)
[tex]\frac{5}{2}x-\frac{1}{3}=\text{ 13}[/tex]Add 1/3 to both-side of the equation
[tex]\frac{5x}{2}=13\text{ +}\frac{1}{3}[/tex][tex]\frac{5x}{2}=\text{ }\frac{39+1}{3}[/tex][tex]\frac{5x}{2}=\frac{40}{3}[/tex]cross-multiply
15x = 80
Divide both-side of the equation by 15
x= 5.33
d)
[tex]\frac{3}{10}+\frac{2x}{5}=\frac{1}{2}[/tex]multiply through the equation by 10
[tex]10(\frac{3}{10})+10(\frac{2x}{5})=10(\frac{1}{2})[/tex]3 + 2(2x) = 5
3 + 4x = 5
subtract 3 from both-si
Find Sec A and Cot B exactly if a=8 and b=7
The given triangle is right angle triangle with side a = 8 and b 7
Apply pythagoras theorem for the side c;
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Hypotenuse² = Perpendicular² + Base²
Here, perpendicular, a =8 and Base b = 7
[tex]\begin{gathered} c^{2}=a^{2}+b^{2} \\ c^{2}=8^{2}+7^{2} \\ c^2=113 \\ c=\sqrt[]{113} \end{gathered}[/tex]The trignometric ratio for sec of an angle define as the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
[tex]\begin{gathered} \sec A=\frac{Hypotenuse}{Adjacent\text{ side of angle A}} \\ \sec A=\frac{c}{b} \\ \sec A=\frac{\sqrt[]{113}}{7} \end{gathered}[/tex]The trignometric ratio for cosine of angle define as the ratio of the adjacent side to the the opposite side of the angle,
[tex]\begin{gathered} CotB=\frac{\text{Adjacent side to angle B}}{\text{Opposite side to angle B}} \\ CotB=\frac{a}{b} \\ CotB=\frac{8}{7} \end{gathered}[/tex]Answer; a)
[tex]\text{SecA}=\frac{\sqrt[]{113}}{7},\cot B=\frac{8}{7}[/tex]
At Fry's supermarket, each 12-1b bag of apples costs $4. Write an equation to represent the relationship between the number of pounds of apples, p, and cost, c I
if a 12 lb bag costs $4, then a 1 lb bag costs $4/12, which is equal to $1/3 dollars, so if we let p be the number of pounds that we are going to buy and c the amount that we must pay
[tex]c=\frac{1}{3}p[/tex]that is the relation between c and p
Find bc if your answer is not an integer, leave it in simplest radical form
Hello!
We know that this is a right triangle and the angle C is 45º.
Knowing it, we have:
Considering the information above, we must use the sine of 45º to calculate the value of side BC, look:
[tex]\sin(45\degree)=\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}[/tex]As we know, the sine of 45º is:
[tex]\sin(45)=\frac{\sqrt{2}}{2}[/tex]Let's replace all the values in the formula:
[tex]\begin{gathered} \sin(45\operatorname{\degree})=\frac{\mathrm{oppos\imaginaryI te}}{\mathrm{hypotenuse}} \\ \\ \dfrac{\sqrt{2}}{2}=\frac{10}{\mathrm{BC}} \\ \\ \mathrm{BC}\sqrt{2}=10\cdot2 \\ \mathrm{BC}\sqrt{2}=20 \\ BC=\frac{20}{\sqrt{2}} \\ \\ BC=\frac{20\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\frac{20\sqrt{2}}{\sqrt{4}}=\frac{20\sqrt{2}}{2}=\boxed{10\sqrt{2}\text{ ft}} \end{gathered}[/tex]Answer:Alternative B.
if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<15=?
Step 1: Quoting the theorem of a straight line
The theorem of a straight line says Total angles on a straight line is equal to 180°.
Step 2:
m<16 and m<15 are angles on a straight line from the diagram given,
[tex]\begin{gathered} \text{where} \\ m<16=139^0 \\ m<15=\text{?} \\ \text{therefore,} \\ m<16+m<15=180^0 \\ 139^0+m<15=180^0 \\ \text{Collecting like terms} \\ m<15=180^0-139^0 \\ m<15=41^0 \end{gathered}[/tex]Hence the value of m<15= 41°.
With the enthusiasm for statistics at an all-time high, students were found sprinting from their vehicle to the classroom just to be the first person to grab a seat. The times of the students were recorded (in seconds) and given in the stemplot below.What is the 9th fastest time a student took to go from his/her vehicle to a seat in the classroom? Make sure to use labels and avoid the use of abbreviations
The 9th fastest time is 28 seconds
Explanation:We have been given a stem plot diagram of the time it took the students to grab a seat.
We need to find the 9th fastest time
To do this, we first need to list out the time in seconds:
13, 14, 15, 19, 19
21, 27, 27, 28
32
45, 49, 49
Since the right side is empty, there is no list of 50 plus
62, 62
combining the list (all in seconds):
13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62
The lower the number, the faster the time. Since the list is ordered in ascending order, we will count to the 9th place
The ninth place on the list = 28
The 9th fastest time a student took to go from his/her vehicle to a seat in the classroom is 28 seconds
Prove #8Given: PR congruent to TR angle P is congruent to angle T
Reason: Given
[tex]\angle P\cong\angle T[/tex]Reason: Given
[tex]m\angle PRQ\cong m\angle SRT[/tex]Reason: Definition of Vertical angles
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent by ASA (Angle-Side-Angle).
I am confused. Please help. Give answer options and simple explanation. Thanks!
Given the functions
[tex]\begin{gathered} f(x)=2x^2+4x-5 \\ g(x)=6x^3-2x^2+3 \end{gathered}[/tex][tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =2x^2+4x-5-(6x^3-2x^2+3) \\ =2x^2+4x-5-6x^3+2x^2-3 \\ =-6x^3+2x^2+2x^2+4x-5-3 \\ =-6x^3+4x^2+4x-8 \end{gathered}[/tex]The final answer is OPTION C
The markings on the number line are evently spaced. Label the other markings on the number line. + + А B C -30 0 F 45 A= B = C = D = E = F=can someone please tell me the answers
The points are evenly spaced at a distance of 15 units between each other, then when we go to the right side of the graph from 0 we increase 15 units until we reach the point E, 15 units further we get to the point F, then we have the following labels:
E = 15
F = 15 + 15 = 30
As we got the left side from 0, we subtract 15 units for each marking, then we get:
D = 0 -15 = -15
C = -30 -15 = -45
B = -45 - 15 = -60
A = -60 - 15
Pressure (torr)Volume (mL)Which statement accurately represents the relationshipbetween pressure and volume ?75030O As pressure increases, volume increases.As pressure decreases, volume decreases.95022O As pressure increases, volume decreases.As pressure increases, volume stays constant.115019135015150013165010
The equation that describes the relationship between pressure and volume is
[tex]P=\frac{n\cdot R\cdot T}{V}[/tex]As you can observe, the pressure and the volume are inversely proportional, which means, as pressure increases, volume decreases.
Therefore, the answer is As pressure increases, volume decreases.Celine is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a fair 12-sided die labeled with the numbers 1 through 12. How many outcomes are in the sample space for pulling a marble out of the box and rolling the die?4832168
Multiply the number of possible outcomes of pulling a marble out times the number of possible outcomes o rolling the die to find the total amount of outcomes in the sample space.
There are 4 different possibilities of pulling a marble out of a box: white, green, blue and orange. Since the die has 12 outcomes, then the total amount of outcomes in the sample space is:
[tex]4\times12=48[/tex]An angle measures 83∘. Find a. its supplement and b. its complement.
Let
A = Angle (83°)
S = Supplement of A
C = Complement of A.
1) Finding the Supplement of A.
Supplementary angles are the angles whose sum is equal to 180°.
Then,
A + S = 180
Substituting A, we can find S.
83 + S = 180
S = 180 - 83
S = 97°
2) Finding the Complement of A.
Complementary angles are the angles whose sum is equal to 90°.
Then,
A + C = 90
83 + C = 90
C = 90 - 83
C = 7 °C.
Answer:
Supplement = 97 °C
Complement = 7 °C