If AC denote the ladder and B be foot of the wall the length of the ladder AC be x metres then the length of the ladder exists 5 m.
What is meant by trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
Let AC denote the ladder and B be foot of the wall. Let the length of the ladder AC be x metres.
Given that ∠ CAB = 60° and AB = 2.5 m In the right Δ CAB,
cos 60° = AB / AC
simplifying the above equation, we get
⇒ AC = AB / (cos 60°)
x =2 × 2.5 = 5 m
Therefore, the length of the ladder exists 5 m.
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Question 19 of 25Which of the following equations is an example of inverse variation betweenthe variables x and y?O A. y -O B. y = 8xO C. y -OD. y=x+8SUBMIT
Where 8 is the constant
The Final answerOption CRearrange the formula 5w-3y +7=0 to make w the subject.
Please help me on #1 Please show your work so I can follow and understand
Answer:
Between markers 3 and 4.
Explanation:
We know that each student runs 2 / 11 miles. Given this, how many miles do the first two students run?
The answer is
[tex]\frac{2}{11}\cdot2=\frac{4}{11}\text{miles}[/tex]Now, we know that the course has markers every 0.1 miles. How many markers are ther in 4 /11 miles?
The answer is
[tex]\frac{2}{11}\text{miles}\times\frac{1\text{marker}}{0.1\; miles}[/tex][tex]=3.6\text{ markers}[/tex]This is between markers 3 and 4. Meaning that the second student finishes between markers 3 and 4.
Find the distance between the pair of points. (16,0) and (1, -7) The distance is. (Round to the nearest thousandth as needed.)
Solution
For this case we can use the formula for the distance between two points:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]and replacing we got:
[tex]d=\sqrt[]{(-7-0)^2+(1-16)^2}=\sqrt[]{274}[/tex]And the correct answer after round would be:
16.553
I need help with part b, c ii, and d
Recall that:
[tex]\text{average speed=}\frac{total\text{ distance}}{total\text{ time}}.[/tex](b) Since Marcos traveled for 2 hours and 17 minutes a distance of 155 miles, then Marco's average speed for the 155 miles trip is:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](c ii) Since Devon also traveled the 155 miles in 2hours and 17 minutes but at a constant speed, then the constant speed at which he traveled is equal to his average speed, which is equal to:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](d) Marco needs to drive 2 miles in 5 minutes to be able to complete the 155 miles trip in 2 hours and 17 minutes, then he must drive at a constant speed of:
[tex]\frac{2mi}{5\min }=\frac{2mi}{\frac{5}{60}h}=\frac{120mi}{5h}=24\text{miles per hour.}[/tex]Answer:
(b) 67.89 miles per hour.
(c ii) 67.89 miles per hour.
(d) 24 miles per hour.
f(x) = x2 + 4 and g(x) = -x + 2Step 2 of 4: Find g(d) - f(d). Simplify your answer.Answer8(d) - f(d) =
Answer:
[tex]\begin{equation*} g(d)-f(d)=-d^2-d-2 \end{equation*}[/tex]Explanation:
Given:
[tex]\begin{gathered} f(x)=x^2+4 \\ g(x)=-x+2 \end{gathered}[/tex]To find:
[tex]g(d)-f(d)[/tex]We can find g(d) by substituting x in g(x) with d, so we'll have;
[tex]g(d)=-d+2[/tex]We can find f(d) by substituting x in f(x) with d, so we'll have;
[tex]f(d)=d^2+4[/tex]We can now go ahead and subtract f(d) from g(d) and simplify as seen below;
[tex]\begin{gathered} g(d)-f(d)=(-d+2)-(d^2+4)=-d+2-d^2-4=-d^2-d+2-4 \\ =-d^2-d-2 \\ \therefore g(d)-f(d)=-d^2-d-2 \end{gathered}[/tex]Therefore, g(d) - f(d) = -d^2 - d -2
If the given is -3x+20=8 What should the subtraction property of equality be?
Given the equation
[tex]-3x+20=8[/tex]To apply the subtraction property of equality, we subtract 20 from both sides.
[tex]-3x+20-20=8-20[/tex]The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?
Answer:
300 in²
Step-by-step explanation:
Hello!
Because the diagonal forms right triangles, we can use the Pythagorean Theorem to find the missing length of the rectangle.
a² + b² = c²
a = legb = legc = hypotenuseIn this case, 25 is c, and 15 is a. We can solve for b using the formula.
Solve for ba² + b² = c²15² + b² = 25²225 + b² = 625b² = 400b = 20So the missing length of the rectangle is 20. We can find the area by multiplying 15 and 20
15 * 20 = A300 = AThe area is 300 in².
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
Write an equation of the line containing the given point and parallel to the given line.
(9,−6); 4x−3y=2
Answer:
y=4/3x-18
Step-by-step explanation:
4x-2=3y
y=4/3x-2/3
to parallel slope has to be the same
-6=9*(4/3)+b
b=-18
y=4/3x-18
The data for numbers of times per week 20 students at Stackamole High eat vegetables are shown below. A dotplot shows 4 points above 1, 4 points above 3, 5 points above 2, 3 points above 4, 3 points above 5, and 1 point above 9.
Considering the given dot plot for the distribution, it is found that:
a) The distribution is right skewed.
b) There is an outlier at 9.
c) Since there is an outlier, the best measure of center is the median.
Dot plotA dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:
1, 1, 1, 1, 2, 2, 2, 2, 2 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 9.
To find the skewness of the data-set, we need to find the mean and the median.
The mean is the sum of all values divided by the number of values of 20, hence:
Mean = (4 x 1 + 5 x 2 + 4 x 3 + 3 x 4 + 3 x 5 + 9)/20 = 3.1.
The median is the mean of the 9th and the 10th elements(even cardinality) of the data-set, hence:
Median = (2 + 3)/2 = 2.5.
The mean is greater than the median, hence the distribution is right skewed.
To identity outliers, we need to look at the quartiles, as follows:
First quartile: 0.25 x 20 = 5th element = 2.Third quartile: 0.75 x 20 = 15th element = 4.The interquartile range is:
IQR = 4 - 2 = 2.
Outliers are more than IQR from the quartiles, hence:
4 + 1.5 x 2 = 4 + 3 = 7 < 9, hence 9 is an outlier in the data-set, and hence the median will be the best measure of center.
Missing information
The questions are as follows:
Part A: Describe the dotplot. (4 points)
Part B: What, if any, are the outliers in these data? Show your work. (3 points)
Part C: What is the best measure of center for these data? Explain your reasoning. (3 points) (10 points)
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The function h (t) = -4.9t² + 19t + 1.5 describes the height in meters of a basketball t secondsafter it has been thrown vertically into the air. What is the maximum height of the basketball?Round your answer to the nearest tenth.1.9 metersO 19.9 meters16.9 metersO 1.5 meters
Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:
[tex]\begin{gathered} h(t)=-4.9t^2+19t+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t)+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t+(\frac{19}{9.8})^2)+1.5+4.9(\frac{19}{9.8})^2 \\ =-4.9(t+\frac{19}{9.8})^2+19.9 \end{gathered}[/tex]Hence the function can be written as:
[tex]h(t)=-4.9(t+1.9)^2+19.9[/tex]and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m
Write an explicit formula that represents the sequence defined by the following recursive formula: a1=7 and an=2a_n-1
Answer:
[tex]a_n=7(2^{n-1})[/tex]Explanation:
Given the sequence with the recursive formula:
[tex]\begin{gathered} a_1=7 \\ a_n=2a_{n-1} \end{gathered}[/tex]First, we determine the first three terms in the sequence.
[tex]\begin{gathered} a_2=2a_{2-1}=2a_1=2\times7=14 \\ a_3=2a_{3-1}=2a_2=2\times14=28 \end{gathered}[/tex]Therefore, the first three terms of the sequence are: 7, 14 and 28.
This is a geometric sequence where:
• The first term, a=7
,• The common ratio, r =14/7 = 2
We use the formula for the nth term of a GP.
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7\times2^{n-1} \end{gathered}[/tex]The explicit formula for the sequence is:
[tex]a_n=7(2^{n-1})[/tex]Please help me with this problem so my son can better understand I have attached an image of the problem
We have to solve for c:
[tex](c+9)^2=64[/tex]When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.
We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.
Then, taking that into account, we can solve this expression as:
[tex]\begin{gathered} (c+9)^2=64 \\ c+9=\pm\sqrt[]{64} \\ c+9=\pm8 \end{gathered}[/tex]We then calculate the first solution for the negative value -8:
[tex]\begin{gathered} c+9=-8 \\ c=-8-9 \\ c=-17 \end{gathered}[/tex]And the second solution for the positive value 8:
[tex]\begin{gathered} c+9=8 \\ c=8-9 \\ c=-1 \end{gathered}[/tex]Then, the two solutions are c = -17 and c = -1.
We can check them replacing c with the corresponding values we have found:
[tex]\begin{gathered} (-17+9)^2=64 \\ (-8)^2=64 \\ 64=64 \end{gathered}[/tex][tex]\begin{gathered} (-1+9)^2=64 \\ (8)^2=64 \\ 64=64 \end{gathered}[/tex]Both solutions check the equality, so they are valid solutions.
Answer: -17 and -1.
triangle HXI can be mapped onto troangle PSL by a reflection If m angle H = 157 find m angle S
From the information provided, the triangle HXI can be mapped onto triangle PSL. This means the vertices of the reflected image would now have the following as same measure angles;
[tex]\begin{gathered} \angle H\cong\angle P \\ \angle X\cong\angle S \\ \angle I\cong\angle L \end{gathered}[/tex]Measure of angle S cannot be determined from the information provided because there is insufficient information given to determine the measure of angle X, hence the angle congruent to it (angle S) likewise cannot be determined.
Question 34: Find the polar coordinates that do NOT describe the point on the graph. (Lesson 9.1)
Notice that the polar coordinates of the point on the simplest form are (2,30). Then, the only option that does not match a proper transformation of coordinates is the point (-2,30)
According to projections through the year 2030, the population y of the given state in year x is approximated byState A: - 5x + y = 11,700State B: - 144x + y = 9,000where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?The two states will have the same population in the year
The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.
The year in which both states would have the same population can be determined by the value of x which satisfies both equations.
We would now solve these system of equations as follows;
[tex]\begin{gathered} -5x+y=11700---(1) \\ -144x+y=9000---(2) \\ \text{Subtract equation (2) from equation (1);} \\ -5x-\lbrack-144x\rbrack=11700-9000 \\ -5x+144x=2700 \\ 139x=2700 \\ \text{Divide both sides by 139} \\ x=19.4244 \\ x\approx19\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]Note that x = 19 represents the year 2019
ANSWER:
The two states will have the same population in the year 2019
andrew went to the store to buy some walnuts. the price pee walnut is $4 per pound and he has a coupon for $1 off the final amount. with the coupon, how much would andrew have to pay to buy 4 pounds of walnuts? what is the expression for the cost to buy p pounds of walnuts , assuming at least one pound is purchased.
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
4. Martin was asked to solve the following system of equations. Hegraphed the two equations below, and decided that the answer was"infinitely many solutions". Do you agree with Martin? Why or why not? Ifyou disagree, what should the answer be?*y=-x-3y=-***+3
Types of solutions in a system of equations:
Based on this image, we can see that when they are parallel lines (same slope), there is no solution because the lines never touch.
The type of solution Martin was describing is when the lines are the same (letter b in the image) and it looks like one line when graphed.
Answer: We disagree with Martin because the lines never touch, meaning that the system has no solutions.
A chemist has 30% and 60% solutions of acid available. How many liters of each solution should be mixed to obtain 570 liters of 31% acid solution? Work area number of liters | acid strength | Amount of acid 30% acid solution 60% acid solution 31% acid solution liters of 30% acid liters of 60% acid
Let the amount of 30% acid solution be a
Let the amount of 60% acid solution be b
Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:
[tex]0.3a+0.6b=0.31(570)[/tex]Also, we know 30% acid and 60% acid amounts to 570 liters, thus:
[tex]a+b=570[/tex]The first equation becomes:
[tex]0.3a+0.6b=176.7[/tex]We can solve the second equation for a:
[tex]\begin{gathered} a+b=570 \\ a=570-b \end{gathered}[/tex]Putting this into the first equation, we can solve for b. The steps are shown below:
[tex]\begin{gathered} 0.3a+0.6b=176.7 \\ 0.3(570-b)+0.6b=176.7 \\ 171-0.3b+0.6b=176.7 \\ 0.3b=176.7-171 \\ 0.3b=5.7 \\ b=\frac{5.7}{0.3} \\ b=19 \end{gathered}[/tex]So, a will be:
a = 570 - b
a = 570 - 19
a = 551
Thus,
551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.
estimate 328 divided by 11=?
Answer:
30
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Given: Kite ABDC with diagonals AD and BC intersecting at E
Prove: AD L BC
A
C
E
LU
D
B
Determine the missing reasons in the proof.
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
What is Kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.
Given,
ABCD is a kite, with the diagonal AD and BC
We have,
AC = AB
and
CD = BD [Property of Kite]
In ΔACD and ΔABD
AC = AB
and
CD = BD [Property of Kite]
AD = AD [Common]
By rule SSS Criteria [Side Side Side ]
ΔACD ≅ ΔABD
∴ ∠CDA = ∠BDA [CPCT]
Now,
In ΔCDE and ΔBDA
CD = BD
∠CDE = ∠BDE
DE = DE [Common]
By rule SAS Criteria [Side Angle Side]
ΔCDE ≅ ΔBDA
∴ CE = BE [CPCT]
Hence, AD bisects BC into equal parts
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
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Frankenstein was in charge of bringing punch to the Halloween party. He brought 36 liters of his famous eyeball punch. How many gallons was this?
Answer: 9.5112
Step-by-step explanation:
There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]
Help me please Circle describe and correct each error -2=-3+x/4-2(4)-3+x/4•48=-3+x+3X=11
Answer
The error in the solution is circled (red) in the picture below.
The equation can be solved correctly as follows
[tex]\begin{gathered} -2=\frac{-3+x}{4} \\ \\ Multiply\text{ }both\text{ }sides\text{ }by\text{ }4 \\ \\ -2(4)=\frac{-3+x}{4}\cdot4 \\ \\ -8=-3+x \\ \\ Add\text{ }3\text{ }to\text{ }both\text{ }sides \\ \\ -8+3=-3+x+3 \\ \\ x=-5 \end{gathered}[/tex]what times what equals 38
Simplify 17(z-4x)+2(x+3z)
Answer:
23z-66x
Step-by-step explanation:
Look at the attachment please :D
how do I know where which choices below go into the correct blanks for number 1-4?
For 1, we have the following triangle:
Using the cosine function to get the hypotenuse we get:
[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:
[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]Therefore, the value of the remaining side is 7.
The width of a rectangle measures (5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The most appropriate choice for perimeter of rectangle will be given by -
Perimeter of rectangle = (22v + 14w) cm
What is perimeter of rectangle?
At first it is important to know about rectangle.
Rectangle is a parallelogram in which every angle of the parallelogram is 90°.
Perimeter of rectangle is the length of the boundary of the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by
Perimeter of rectangle = [tex]2(l + b)[/tex]
Length of rectangle = (5v - w) cm
Breadth of rectangle = (6v + 8w) cm
Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]
= 2(11v + 7w)
= (22v + 14w) cm
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Complete Question
The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
the inside diameter (I.D.) and outside diameter (O.D.) of a pope are shown in the figure. The wall thickness of the pope is the dimension labeled t. Calculate the wall thickness of the pipe if its I.D. is 0.599 in. and its O.D. is 1.315 in.
Given:
The inside diameter of the pope, I.D.=0.599 in.
The outside diameter of the pope, O.D.=1.315 in.
The inside radius of the pope is,
[tex]IR=\frac{ID}{2}=\frac{0.599}{2}=0.2995\text{ in}[/tex]The outside radius of the pope is,
[tex]OR=\frac{OD}{2}=\frac{1.315}{2}=0.6575\text{ in}[/tex]The wall thickness of the pope can be calculated as,
[tex]t=OR-IR=0.6575-0.2995=0.358\text{ in}[/tex]Therefore, the wall thickness of the pope is t=0.358 in.
4) What is perimeter of this shape? * 4 cm 2 cm
the perimeter is the sum of the outside sides. So in this case is 4+4+2+2+2+2=16
so the answer is 16cm