Answer:
Option B is correct.
Value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
Step-by-step explanation:
Using the formula:
[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]
Given the values:
[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]
Using trigonometric identity:
[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]
or
[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]
or
[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]
Find the value of sin a and cos B;
Using trigonometric identity:
[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]
[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]
Similarly;
[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]
[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]
Substitute these given values equation [1] we have;
[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]
[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]
then;
[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]
Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.
Explanation:To find cos(a + B), we can use the formula:
cos(a + B) = cos(a)cos(B) - sin(a)sin(B)
Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:
cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)
To find cos(B), we can use the Pythagorean identity:
cos²(B) + sin²(B) = 1
Substituting the given value of sin(B), we can solve for cos(B):
cos(B) = √(1 - (5/13)²)
Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):
cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)
Simplifying this expression gives us the final answer: cos(a + B) = 16/65.
The area of a rhombus is given by the formula A=1/2xy,where x and y are the lengths of the diagonals. If the diagonals of a rhombus have lengths 10cm and 20cm, find the area of the rhombus.
how to do 5,745 / 66
Answer:
1915/22
Step-by-step explanation:
5745 / 66
Factor the numbers:
5745 = 3 * 1915
66 = 3 * 22
(3 * 1915) / (3 * 22)
Cancel the common factor:
1915/22
To divide 5,745 by 66, first determine how many times 66 fits into 574, then bring down the next digit and repeat. The result is 87 with a remainder of 3 or 87.068 as a decimal. The answer to 5,745 ÷ 66 is 87.068.
To find the result of 5,745 ÷ 66, follow these steps:
Set up the division problem: 5745 ÷ 66.Determine how many times 66 can fit into the first part of 5745, which is 574. Perform the subtraction: 574 - 528 = 46.Bring down the next digit, which is 5, to make 465.Now see how many times 66 fits into 465. Perform the subtraction: 465 - 462 = 3.Since there are no more digits to bring down, the result of 5,745 ÷ 66 is 87 with a remainder of 3, or 87.068 when expressed as a decimal.The answer to 5,745 ÷ 66 is 87.068.
Given the rectangle ABCD, AB has a slope of 2/3, what is the slope of BC?
Answer:
slope = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
note that BC is perpendicular to AB, hence the slope of BC is the negative reciprocal of the slope of AB
[tex]m_{BC}[/tex] = - [tex]\frac{1}{2/3}[/tex] = - [tex]\frac{3}{2}[/tex]
At 1:00 the water level in a pool is 13 inches. At 2:30 the water level is 28 inches what is the rate of change?
A: 15/90
B: 1/10
C: 10/1
Answer:
b:1/10
Step-by-step explanation:
In 1 hour and 30 minutes the water level increased by 15 inches. If we simplify that, we get 10 inches for every hour. The correct answer is b.
Hope this helps!
Can I please have brainliest? I only need one more!
what is the horizontal asymptote of f(x)= 3 / x-2
Answer: y = 0
Step-by-step explanation: Since the degree of the numerator is lower than the degree of the denominator, the horzontal asymptote is 0.
1.Let x = 6.
What is the value of the expression 5x2+x−7 ? the x is x/2
Enter your answer in the box.
2.Which values from the specified set make up the solution set of the inequality?
4n<16 ; {1,2,3,4}
Select each correct answer.
3.Let m = 3.
Enter > , < , or = to compare the expressions.
4m−1______5m−4
4.Diana writes this inequality:
15>w
4.
Is the given value of w a solution to the inequality?
Select Yes or No for each value.
Solution? Yes No
w = 15
w = 21
w = 14
5.Which value in the replacement set is a solution to this equation?
2n + 5 = 27
Replacement set: {11, 12, 13}
Drag the solution into the box.
options 11,12,13
6.
Which situation can be represented by the inequality?
x<3
The ceiling is lower than 3 m.
The movie is longer than 3 h.
The child is 3 years old.
The backpack is heavier than 3 kg.
7.
Solve for g.
5.1g = 35.7
Enter your answer in the box.
g =
8.Solve for c.
36+c=54
Enter your answer in the box.
c =
9.Cassandra works at a bookstore. Yesterday, she sold 18 hardcover books. The rest of the books she sold were paperback books. She sold a total of 41 books. How many paperback books did she sell?
Use the variable p to represent the number of paperback books Cassandra sold yesterday.
Which equation represents this situation and its solution?
p + 18 = 41; p = 23
p + 41 = 18; p = 23
41p = 18; p = 23
18p = 41; p = 23
10.The table show the total distance d, in kilometers, a truck traveled after t hours.
Time in hours (t) Distance in kilometers (d)
0 0
1 100
2 200
3 300
Which equation shows the relationship between d and t?
d=t+300
d=t+100
d=100t
d=300t
Answer:
1: 6
2: 1,2,3
3: 4m-1>5m-4
4: Not enough data
5: n = 11
6: The ceiling is lower than 3m
7: G = 7
8: C = 18
9: p + 18 = 41; p = 23
10: D = 100t
Step-by-step explanation:
Question 1:
5*2+x/2-7
5*2+6/2-7
10+6/2-7
10+3-7
13-7
6
Question 2:
4*2<16
8<16 True
4*1<16
4<16 True
4*3<16
12<16 True
4*4<16
16<16 False
Question 3:
Let's plug in 1 for m
4*1-1____5*1-4
4-1_____5-4
3_____1
3>1
Question 4:
You did not give an equation, so I cannot answer.
Question 5:
2*11 + 5 =27
22 + 5 = 27
27 = 27
So n = 11
Question 6:
x<3
The ceiling is lower than 3m because x<3
Question 7:
5.1g = 35.7
5.1g/5.1=35.7/5.1
g = 7
Check: 5.1 * 7 = 35.7
Question 8:
36 + c = 54
36 + c -36 = 54 - 36
c = 18
Check: 36 + 18 = 54
Question 9:
p + 18 = 41; p = 23 is correct because the number of paperback books plus the number of hardcover books would equal the total number of books sold. Check: 23 + 18 = 41
Question 10:
d=100t is correct because each time t goes up one it goes up 100. Example: if it is at one hour, than it is 100, if it is at 3 hours, than d = 100*3 = 300, which is the same pattern as the table.
Hope this helps!
The expression 5x² + x - 7 is calculated by substituting x with 6. Inequality and equation solving techniques are used to find the solutions to 4n < 16, 4m - 1 compared to 5m - 4, and other given problems, resulting in specific numerical solutions and identifying suitable real-world scenarios like a ceiling height represented by x < 3.
To solve the expression 5x² + x
- 7 where x equals 6, we substitute and get 5(3)² + (3) - 7 = 45 + 3 - 7 = 41.
The solutions to the inequality 4n < 16 from the set {1,2,3,4} are 1, 2, and 3, since 4 times each of these is less than 16.
Comparing the expressions when m = 3, we get 4m - 1 and 5m - 4. Substituting we have 12 - 1 < 15 - 4, thus 11 < 11, which is false, so 4m - 1 = 5m - 4.
The inequality 15 > w is only true for w = 14. Values w = 15 and w = 21 do not satisfy the inequality.
In the equation 2n + 5 = 27, solving for n within the replacement set gives n = 11 as the correct solution.
The inequality x < 3 represents a situation where The ceiling is lower than 3 m.
To solve 5.1g = 35.7, divide both sides by 5.1 to find g = 7.
For the equation 36 + c = 54, subtract 36 from both sides to get c = 18.
Cassandra's situation is best represented by the equation p + 18 = 41, resulting in p = 23 paperback books sold.
The relationship between the distance d and time t from the truck table is d = 100t, since distance is increasing by 100 kilometers every hour.
Rachael’s patio has an area of 290 square feet. If the patio is shaped like a square, what is the approximate side length?
A. about 72.5 feet
B. about 145 feet
C. about 17 feet
D. about 24 feet
To find the side length of Rachael's square patio with an area of 290 square feet, you have to take the square root of the area. The square root of 290 is approximately 17. So, the side length of the patio is approximately 17 feet.
Explanation:The subject at hand pertains to the geometry and area calculation of a square. In a square, all sides are equal. Thus, to find the side length when only given the area, you can simply take the square root of the area. The square root of 290 is approximately 17. Therefore, Rachael's patio has a side length of approximately 17 feet, making option C the correct answer.
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what is the median of this data set
Answer:
The median is four.
Step-by-step explanation:
First you put the numbers in order from least to greatest and write the number as many times as indicated.
2 2 2 3 4 4 4 4 6 6 7 7 7 8 9
then start from one side then go to the other crossing out numbers. So cross out a two, then nine, then another two, then eight, then the last two, then the first seven and so on. When your done you should be left with one middle number, in this case it's four.
Answer is provided in the image attached
I NEED HELP someone plz help meh
Three of the choices are ways to express 0.25. Which is NOT?
A. 25 hundredths
B. 2 tenths and 5 hundredths
C. 1 fourth
D. 25 tenths
Answer:the last one, 25 tenths
Step-by-step explanation:
Write an equation to determine Sarah’s age
A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked
Answer:
The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
Step-by-step explanation:
The student's question involves choosing between a flat rate of $500 or an hourly rate of $20 for a contractor's job. The better option depends on the number of hours worked compared to the flat rate. Calculations must be made to determine which method yields a higher payment.
Explanation:The student's question is related to making a decision on a contractor's billing method.
The decision involves choosing between a flat rate of $500 or billing at an hourly rate of $20 per hour for a completed job. To determine which option is more advantageous, the contractor would need to calculate the total earnings based on the number of hours worked and compare it against the flat rate.
For instance, if the contractor works 10 hours, the payment at the hourly rate would be 10 hours × $20/hour = $200. Since $200 is less than the flat rate of $500, the hourly rate would be the better choice in this case. However, if the contractor works for 30 hours, the payment at the hourly rate would be 30 hours × $20/hour = $600, which is more than the flat rate, making the flat rate the better option.
Soup cost 10 for 3 cans. Josh spent $40 on soup.How many can did he buy
Answer:
He bought 12 cans of soup
Step-by-step explanation:
We can use a ratio to solve this problem.
$10 $40
----------- = --------------
3 cans x cans
Using cross products
10* x = 3 * 40
10x = 120
Divide by 10
10x/10 = 120/10
x = 12
Annie can make 18 baskets out of 30 attempts. Her younger brother Cameron can make half as many in the same number of attempts. How many baskets can Cameron make in 50?
Answer:
Cameron will make 15 baskets out of 50 tries.
Step-by-step explanation:
Since Annie can take out 18 baskets out of 30 and her brother can take out half as much, then we know that 18:2 is 9, so we know that Cameron can take out 9 baskets out of 30. Since this is our proportion( 9:30 ), we can simplify it which brings us to 3:10. And since we must find how much he will take out in 50 tries, We multiply the proportion by 5 which is 15:50, meaning he will make 15 baskets.
Final answer:
Cameron can make 15 baskets out of 50 attempts based on his success rate, which is half of his sister Annie's success rate of 60%.
Explanation:
Annie can make 18 baskets out of 30 attempts, which means her success rate is 60% (since 18 is 60% of 30). Her younger brother Cameron can make half as many baskets in the same number of attempts, so Cameron's success rate is 30% because half of 18 is 9, and 9 is 30% of 30. If Cameron were to attempt 50 shots, we would calculate the number of baskets he can make by applying his success rate to these 50 attempts. Therefore, 30% of 50 is 15. This means Cameron can make 15 baskets out of 50 attempts.
Mrs.o’brien purchases 112 ounces of laundry detergent for $13.44. Mr. o’brien purchases a 17.5 pound container of laundry detergent for $19.60. What is the difference in the unit price per ounce for the laundry detergent mr. and mrs. o’brien Purchase?
Final Answer:
The difference in the unit price per ounce for the laundry detergent Mr. and Mrs. O’Brien purchased is $0.045 per ounce, with Mr. O’Brien's detergent being the more cost-effective option.
Explanation:
To find the unit price per ounce for each type of laundry detergent, we first determine the cost per ounce by dividing the total cost by the total weight. For Mrs. O’Brien's detergent, which is 112 ounces for $13.44, the unit price per ounce is $13.44/112 = $0.12 per ounce. For Mr. O’Brien's detergent, which is 17.5 pounds for $19.60, we convert pounds to ounces (1 pound = 16 ounces) and calculate the unit price per ounce as $19.60/(17.5 * 16) = $0.165 per ounce.
The difference in unit price per ounce is then found by subtracting Mrs. O’Brien's unit price from Mr. O’Brien's unit price, resulting in $0.165 - $0.12 = $0.045 per ounce. The positive value indicates that Mr. O’Brien's detergent is more cost-effective on a per-ounce basis.
This mathematical approach provides a clear comparison of the unit prices, allowing consumers to make informed decisions based on cost-effectiveness. The calculated difference highlights the savings per ounce associated with Mr. O’Brien's laundry detergent.
plz help 20 points!!! The length of the Titanic was 882 feet. Porter's history class is building a model of the Titanic. The model is 1/100(fraction) of the actual length of the ship. How long is the model?
8+1/82, 882/100 so you get 8 and 1/82
Which input value produces the same output value for the two functions on the graph?x = x= –3
x = –1
x = 1
x = 3
Answer:
x=3
Step-by-step explanation:
Basically the question is asking what value of x gives the same value for y
(or where do the 2 lines cross)
the input is x=3, the out put is y =-1
Answer:
x = 3
Step-by-step explanation:
X - LINE: Horizontal
Y - LINE: VERTICAL
The reason why it's x = 3 is because it's where both line up to, where they both intersect.
Input (x) is 3 & output (y) is -1
Hope this helps you!!! :)
−3 1/3÷9
PLEASE HELP ME!!!
Answer:
-.37
Step-by-step explanation:
PLZZZZ MARK BRANIEST I REALLY NEED IT!!!!
Answer:
-.37
Step-by-step explanation:
that 3 /1 is 3 that
X/7-3=-6/7
How do I solve this
Answer:
Alright well solve by cross multiplying
x = 15 Hope this helps have a nice day :)
Step-by-step explanation:
Now if u want i can explain with detail.
PLEASE HELP!!!!!!!! 100 POINTS!!!!! I need a step by step simple explanation and answer
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
The formula of a volume of a cylinder:
[tex]V_{cylinder}=\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in and height H = 9 in.
[tex]d=2r\to r=d:2\to r=8\ in:2=4in[/tex]
Substitute:
[tex]V_{cylinder}=\pi(4^2)(9)=\pi(16)(9)=144\pi\approx144\cdot3.14=452.16\ in^3[/tex]
The formula of a volume of a cone:
[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in → r = 4 in and the height H = 18 in.
Substitute:
[tex]V_{cone}=\dfrac{1}{3}\pi(4^2)(18)=\pi(16)(6)=96\pi\approx96\cdot3.14=301.44\ in^3[/tex]
[tex]\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{452.16}{301.44}=1.5[/tex]
The volume of the cylinder is one and a half times larger than the volume of the cone.
If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.
[tex]V_{cone}=\pi r^2H\\\\V_{cylinder}=\dfrac{1}{3}\pi r^2H\\\\\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{\pi r^2H}{\frac{1}{3}\pi r^2H}=\dfrac{1}{\frac{1}{3}}=3[/tex]
The formula of a volume of a cylinder:
r - radius
H - height
We have the diameter d = 8 in and height H = 9 in.
Substitute:
The formula of a volume of a cone:
r - radius
H - height
We have the diameter d = 8 in → r = 4 in and the height H = 18 in.
Substitute:
The volume of the cylinder is one and a half times larger than the volume of the cone.
If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.
Plz Mark me BRAINLIEST
Which equation in parallel to 3x-5y=10
3x-5y=n
3x-5y=1
----------------------------
describe whether the triangles are similar for 30 points
[tex]Similar:\\\\\triangle STU\sim\triangle QPR\qquad \boxed{SAS}\to side-angle-side\\\\m\angle SUT=m\angle QRP\\\\\dfrac{10}{4}=\dfrac{20}{8}\\\\L_s=\dfrac{10}{4}=\dfrac{10\cdot2}{4\cdot2}=\dfrac{20}{8}=R_s\\-------------------------------[/tex]
[tex]\text{Not similar or not necessarily similar}\\\\180^o-(90^o+30^o)=180^o-120^o=60^o\neq50^o\\\\\text{different angles}\\-------------------------------[/tex]
[tex]Similar:\\\\\triangle ABC\sim\triangle FED\qquad\boxed{SSS}\to side-side-side\\\\\dfrac{15}{5}=\dfrac{12}{4}=\dfrac{9}{3}\\\\3=3=3\\-------------------------------[/tex]
A 15ft ladder leans against the side of a house. The top of the ladder is
13ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
Answer:
Angle x = 60.1 degrees
Step-by-step explanation:
Given : height of the ladder is 15 ft that is the hypotenuse
The top of the ladder is 13ft off the ground.
That is the oppposite side of angle x
Since this forms a right angle triangle we use trigonometric ratios to find x
We know the opposite side and the hypotenuse
sin(x) = opposite / hypotenuse
[tex]sin(x) = \frac{13}{15}[/tex]
[tex]x = sin^{-1}(\frac{13}{15})[/tex]
x= 60.073565
Angle x = 60.1 degrees
check the picture below.
make sure your calculator is in Degree mode.
Morgan needs to earn $16.31 more to have $40.00. Four students wrote and solved equations to find m, the amount of money that Morgan has now. Which student wrote and solved the equation correctly?
The equation for the amount of money that Morgan has now is 16.31+m = 40
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, Morgan needs to earn $16.31 more to have $40.00, we need to establish an equation to find the amount of money Morgan need,
Let the required money be m,
So, the equation will be
16.31+m = 40
m = 40-16.31
m = 23.69
Hence the equation for the amount of money that Morgan has now is 16.31+m = 40
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Morgan currently has $23.69. An equation m + 16.31 = 40.00 is set up and solved by subtracting $16.31 from $40.00 to find the value of m.
We can set up the equation m + 16.31 = 40.00. This equation translates the fact that Morgan needs $16.31 more to have $40.00. Therefore, by performing a basic subtraction (40.00 - 16.31), we can solve for m.
Step 1: Write the equation: m + 16.31 = 40.00.
Step 2: Subtract 16.31 from both sides of the equation to isolate m: m = 40.00 - 16.31.
Step 3: Perform the subtraction to find m: m = 23.69.
This method is a straightforward way to solve for the current amount of money that Morgan has.
Consider the piecewise-defined function.
What is f(6)?
A 6
B 12
C 18
D 26
Answer:
B 12
Step-by-step explanation:
Since f(6) means we want to evaluate the function when x=6
We will want to use f(x) =2x because 5<= 6 <10
f(6) = 2*6
f(6)=12
f(x) = x when 2 ≤ x < 5
So you can use this function if "x" is greater than or equal to 2 and less than 5
f(x) = 2x when 5 ≤ x < 10
You can use this function if "x" is greater than or equal to 5 and less than 10
f(6) This means that x is 6, so you can plug in 6 for "x" in the equation.
You use the second function because 6 is greater than 5 and less than 10
f(x) = 2x
f(6) = 2(6)
f(6) = 12 Your answer is B
Your friend is starting a small business baking and decorating cakes and wants to make a profit of at least $250 for the first month. The expenses for the first month are $155. What are the possible revenues that your friend can earn in order to meet the profit goal?
Answer: The revenue can be $405 or it can be larger than this value.
In short, the revenue must be at least $405.
======================================
Explanation:
Let R be the possible revenue. We want the profit to be at least $250, so we want the profit to be 250 or more
Recall that profit is equal to revenue minus expenses, so
Profit = Revenue - Expenses
Profit = R - 155
The expression R - 155 represents the profit (R is just a placeholder for a number). We want R - 155 to be 250 or larger, so,
[tex]R - 155 \ge 250[/tex]
[tex]R - 155 \ge 250[/tex]
[tex]R - 155+155 \ge 250+155[/tex] add 155 to both sides
[tex]R \ge 405[/tex]
As long as the revenue is $405 or higher, then the profit will be at least $250
Final answer:
To meet a profit goal of at least $250 with expenses of $155, the friend must generate revenues of at least $405 in the first month.
Explanation:
To calculate the possible revenues needed to achieve at least a $250 profit for the first month, we need to consider both the expenses and desired profit. The calculation is straightforward: Revenue = Expenses + Desired Profit. Here, the expenses are $155, so the calculation is Revenue = $155 + $250, which equals $405. Therefore, to meet the profit goal of at least $250, your friend must generate revenues of at least $405 in the first month.
20 POINTS PLEASE SOMEONE ANSWER What is the equation of the line with m = 3 and b = 8.25? a. y = 3x – 8.25 b. y = 3x 8.25 c. y = 3x 8.25 d. y = 3x 8.25
Answer:
Equation of the line with m=3 and b = 8.25 is y=3 x+8.25
Step-by-step explanation:
m = 3 and b = 8.25
To get equation of line we use y=mx+b
Where m represents the slope = 3
b represents the y intercept = 8.25
Plug in the values in y=mx+b
y= 3x + 8.25
Equation of the line with m=3 and b = 8.25 is y=3 x+8.25
Answer:
y = 3x + 8.25
Step-by-step explanation:
y = mx + b
y = 3x + 8.25
solve the system of linear equations
-x=-6y+19
4=-4x-12y
(x, y) = (-7, 2)
Step-by-step explanation:Divide the second equation by 4 and add it to the first.
... (-x) +(4)/4 = (-6y+19) +(-4x -12y)/4
... -x +1 = -9y -x +19 . . . . simplify
... 9y = 18 . . . . . . . add 9y +x -1
... y = 2 . . . . . . . . . divide by 9
... -x = -6·2 +19 = 7
... x = -7
The solution is (x, y) = (-7, 2).
SHOPPING Sera went to the mall and made four purchases. She spent $2.85, $5.11, $7.89, and $4.15. Use mental math to determine how much money Sera spent at the mall.
Answer:
She spent around 20$
Step-by-step explanation:
add all whole numbers and estimate the cents.
Answer:
$20.00
Step-by-step explanation:
$2.85 = 3.00 - 0.15
$5.11 = 5.00 + 0.11
$7.89 = 8.00 + 0.11 Mentally cancel the 0.11s
$4.15 = 4.00 + 0.15 Mentally cancel the 0.15s
TOTAL = 20.00 + 0.00
TOTAL = $20.00
Diagonal AC divides the trapezoid ABCD (with bases AD and BC , AD>BC) into two similar triangles, △ABC and △DCA. Find AC if BC=4 cm and AD=9 cm.
Answer:
AC= 6 cm
Step-by-step explanation:
It is given that ABCD is a trapezoid
Also AC divides the trapezoid into two similar triangles
ΔABC≈ΔDCA
The ratio of corresponding sides of similar triangles are equal, so we have
[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now we can take
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
[tex]\frac{4}{AC} =\frac{AC}{9}[/tex] ( since BC=4 and AD= 9)
now we cross multiply
[tex]4(9)=AC^{2}[/tex]
[tex]AC^{2}=36[/tex]
[tex]AC=\sqrt{36}[/tex] (taking square root )
AC= 6 cm