Answer: The answer is c)5
Answer:
c) 5
Step-by-step explanation:
If (x-y)^2=100 and xy=20. what's the value of x^2+y^2?
Answer: The value of [tex]x^2+y^2[/tex] is 140
Step-by-step explanation:
We are given an expression:
[tex](x-y)^2=100[/tex]
And,
xy = 20
Using the identity:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Solving the expression:
[tex]x^2+y^2-2xy=100[/tex]
Putting the value of 'xy' in above equation, we get:
[tex]x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140[/tex]
Hence, the value of [tex]x^2+y^2[/tex] is 140
Identify the equivalent trigonometric values. A sin 17°, cos 17° B cos 29°, sin 61° C sin 78°, cos 102° D cos 83°, cos 7°
Option B (cos 29° and sin 61°) contains equivalent trigonometric values, as the angles are complementary and adhere to the identity sin(90° - x) = cos(x).
The question asks us to identify equivalent trigonometric values out of the given pairs. The equivalent values will have the same numerical value if their angles are complementary (i.e., they add up to 90°) because of the identity sin(90° - x) = cos(x). Considering this, let's evaluate the provided pairs:
A: sin 17° and cos 17° are not complementary, so they are not equivalent.
B: cos 29° and sin 61° are complementary (29° + 61° = 90°), hence equivalent.
C: sin 78° and cos 102° are not complementary, and 102° is greater than 90°, so they are not equivalent.
D: cos 83° and cos 7° are not complementary, but they are both cosines of different angles, so they are not equivalent.
Thus, the pair with equivalent trigonometric values is B: cos 29° and sin 61°.
Hailey, a chemistry student, is measuring samples of a metallic substance for an experiment on density, using a balance that measures to 1/10 of a gram. Which is the most accurate measurement based on the limitations of the balance that might be found in her recorded data? A) 9.01 grams B) 9.2 grams C) 9.24 grams D) 9.244 grams
Answer:
B) 9.2 g
Step-by-step explanation:
The balance measures only to 0.1 g.
So, the best measurement Hailey can make is to the nearest 0.1 g.
The most precise measurement she can make is 9.2 g.
The accuracy depends on the balance and on how carefully she works.
What is the area of the rectangle shown on the coordinate plane? Enter your answer in the blank. Do not round at any steps.
12 units²
Step-by-step explanation:Counting half-squares around the perimeter of the rectangle, we find there are 10. Counting full squares inside the rectangle, we find there are 7. Then the total area is
... (1/2)·10 +7 = 12 square units
_____
Alternate calculation
The long side is the hypotenuse of a right triangle with legs 3, so has length 3√2. The short side is the hypotenuse of a right triangle with legs 2, so has length 2√2. The area is the product of these lengths, so is ...
.. area = (3√2)(2√2) = 6(√2)² = 6·2 = 12 . . . square units
Answer:
21
Step-by-step explanation:
Paul needs 8 equal-length sections of rope.After cutting these 8 sections,he has 28.9 inches of rope left over from an original length of 184.9 inches.What is the length of each of the sections?Be sure to define your variable(s)
19.5 inches
Step-by-step explanation:Let r represent the length of one of the sections of rope (in inches). Then the total length of the original rope is ...
... 8r +28.9 = 184.9
... 8r = 156 . . . . . . . . . . . . subtract 28.9; next, divide by 8
... 156/8 = r = 19.5
The length of each of the sections is 19.5 inches.
Proportional Relationships Please help :3
Worth 25 per answer (i think cause i put 50 points)
Answer:
6
Step-by-step explanation:
Since the relationship is proportional, when y is increased by a factor of 3 from 7 to 21, so is x—from 2 to 2×3 = 6.
What is the maximum Number of different sizes of faces that a rectangular Prism can have.
Answer:
3
Step-by-step explanation:
For a rectangular prism of dimensions L × W × H, pairs of opposite faces will have dimensions ...
L × WW × HH × LThese will be three different sets of dimensions if L, W, and H are all different lengths.
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) Find the percent decrease in the price of the laptop from 2007 to 2009.
B.) Find the percent decrease in the price of the laptop from 2009 to 2010 if the price decreased by $165 in 2010.
Given : The Cost of Laptop in 2007 is $1250
Given : The Cost of Laptop in 2009 is $1100
Decrease in Price of Laptop from 2007 to 2009 : (1250 - 1100) = $150
A) Percent Decrease in the Price of the Laptop from 2007 to 2009 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2007\;to\;2009}{Price\;of\;Laptop\;in\;2007} \times 100}[/tex]
[tex]\mathsf{\implies \frac{150}{1250} \times 100}[/tex]
[tex]\mathsf{\implies 12\%}[/tex]
Given : Decrease in Price of Laptop from 2009 to 2010 = $165
B) Percent Decrease in the Price of the Laptop from 2009 to 2010 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2009\;to\;2010}{Price\;of\;Laptop\;in\;2009} \times 100}[/tex]
[tex]\mathsf{\implies \frac{165}{1100} \times 100}[/tex]
[tex]\mathsf{\implies 15\%}[/tex]
The percent decrease in laptop prices, use the formula ((Original Price - New Price) / Original Price) x 100%. The percent decrease from 2007 to 2009 is 12%, and from 2009 to 2010 is 15% with a $165 decrease.
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) To find the percent decrease from 2007 to 2009, you use the formula: Percent decrease = ((Original Price - New Price) / Original Price) x 100%
Substitute the values: ((1250 - 1100) / 1250) x 100% = 12%
Therefore, the percent decrease in the price of the laptop from 2007 to 2009 is 12%.
B.) To find the percent decrease from 2009 to 2010 with a $165 decrease, you apply the same formula: Percent decrease = ((Price in 2009 - Price in 2010) / Price in 2009) x 100%.
Substitute the values: ((1100 - (1100 - 165)) / 1100) x 100% = 15%
Therefore, the percent decrease in the price of the laptop from 2009 to 2010 is 15%.
3. A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale to use for the y-axis? Explain your reasoning. (b) What is a good interval to use for the y-axis? Explain your reasoning. Answer:
The best way to plot them is by month.
170 - 110 = $60.
We are supposed to plot in months and the above calculation is in year, convert it into months
60/5 = $5 each month
So, the coordinates would be 0, 110 1, 115 2, 120 3, 125
The month will be in the x axis and your money will be the Y axis
A suitable y-axis scale to plot spending habits ranging from $110 to $170 would start at $100 and go up to $180, while a good interval for the y-axis would be $10 to allow for clear plotting of values in whole dollars.
To answer the student's question about how to plot spending habits on a coordinate grid:
A good scale for the y-axis when plotting the family's grocery bills that range from $110 to $170 would be one that fits the entire range of values without being too cramped or too spread out. For instance, a scale that starts at $100 and goes up to $180 would allow all points to be plotted clearly. Since these are monetary values, maintaining a scale that reflects currency would be logical.A good interval for the y-axis could be multiples of $10 since this allows for clear and precise plotting of bills that are likely to be in whole dollars, making the graph easier to read while still being detailed enough to discern differences of $10.Re-arrange the BMI formula for h, height.
Answer:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
Step-by-step explanation:
We have BMI formula that is body mass index formula which is:
[tex]\text{Body mass index}=\frac{weight}{height^2}[/tex]
Now, we have to arrange the formula for height:
we will rearrange the terms and derive the formula for height in terms of weight and height.
[tex]Height^2=\frac{weight}{\text{body mass index}}[/tex]
Hence, the required result is:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
pls help!!!
in which line is a mistake first made when solving the following system of equations by substitution? 2x - y =-4 3x + y = -9
line 1: 2x -y = -4
y= 3x-9
line 2: 2x-(3x-9)=-4
line 3: 2x-3x+9=-4
line 4: -1x + 9 = -4
line 5: -1x = -13
line 6: x = 13
Answer:
The very first line has an error.
Step-by-step explanation:
When you are solving the second system of equations for y, you need to subtract 3x from both sides and therefore it should be negative.
3x + y = -9
y = -3x - 9
Since the 3x isn't negative in the first line, there is an error.
on a road map of pennsylvania, the distance from philaephia to washington d.c. is 6.8 centimeters. whatis the actual distance between the cities if the mape scale is 2 centimeters = 40 miles.
Answer:
136 miles
Step-by-step explanation:
The map distance is 3.4 times 2 cm, so the road distance will be 3.4 times 40 miles, or 136 miles.
a damsel in distress is being
Check the picture below.
make sure your calculator is in Degree mode.
What numbers are on the nnumber line starting with the number 1 then it has 10 spaces then 1.01 then 10 spaces then 1.02 then 10 spaces then 1.03 then 10 spaces then 1.04.
You are referring to the thousandths spot.
1.00(0)000001
So, between any given number n to n.01 there are 10 numbers.
n.001, n.002, n.003, ..., n.01
Which graph represents f(x)=1/2x^2 ?
Answer:
See below.
Step-by-step explanation:
The one that looks like the attachment.
It is vertically shortened from f(x) = x^2, so appears wider than f(x) = x^2 does. The vertex is still at (0, 0), it still opens upward, and it remains symmetrical about the y-axis.
[tex]f(x)=\dfrac{1}{2}x^2\\\\for\ x=0\to f(0)=\dfrac{1}{2}(0)=0\to(0,\ 0)\\\\for\ x=\pm1\to f(\pm1)=\dfrac{1}{2}(\pm1)^2=\dfrac{1}{2}(1)=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right);\ \left(1;\ \dfrac{1}{2}\right)\\\\for\ x=\pm2\to f(\pm2)=\dfrac{1}{2}(\pm2)^2=\dfrac{1}{2}(4)=2\to(-2,\ 2);\ (2,\ 2)\\\\for\ x=\pm4\to f(\pm4)=\dfrac{1}{2}(\pm4)=\dfraC{1}{2}(16)=8\to(-4,\ 8);\ (4,\ 8)[/tex]
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A. (−5, 2)
B. (5, −2)
C. (−5, −2)
D. (5, 2)
Answer:
B. (5,-2)
Step-by-step explanation:
Plug in X and Y, verify accuracy
A basketball player attempts 15 baskets in a game, He makes 9 of the attempted basket. which ratio describe the number of basket the player made to the number of basket the player attempted?
Answer:
3:5
Step-by-step explanation:
We are looking for the ratio of baskets made to baskets attempted
made: attempted
9:15
We can divide each number by 3
9/3: 15/3
3:5
The ratio of baskets made: attempted is 3:5
The ratio that describes the number of baskets made to the number of baskets attempted by the basketball player is 9 to 15, which simplifies to 3 to 5.
The question pertains to the ratio of successful basket attempts to total attempts made by a basketball player in a game.
In this case, the player successfully made 9 baskets out of 15 attempts.
To express this as a ratio, we simply compare the number of made baskets to the total attempts,
thus the ratio is 9 to 15, which can also be simplified by dividing both numbers by their greatest common divisor, which is 3, resulting in a simplified ratio of 3 to 5.
Nikita knows the following information about her food club that has 1111 members: 33 members like neither fruit nor vegetables. 44 members like fruit but not vegetables. 55 members in total like fruit. Can you help Nikita organize the results into a two-way frequency table?
Answer:
[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]
Step-by-step explanation:
You are given such information:
food club has 1111 members;33 members like neither fruit nor vegetables;44 members like fruit but not vegetables;55 members in total like fruit.Then 55 - 44 = 11 members like fruit and vegetables. Thus,
1111 - 55 - 33 = 1023 members like vegetables but not like fruit.
A two-way frequency table will take look
[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]
Nikita can organize her data into a two-way frequency table showing members' preferences for fruit and vegetables. The table identifies how many members like only fruit, only vegetables, both, or neither accordingly.
Nikita has the following data about her food club consisting of 1111 members:
33 members like neither fruit nor vegetables.44 members like fruit but not vegetables.55 members in total like fruit.We can organize this information into a two-way frequency table. Here are the steps:
Calculate the number of members who like both fruit and vegetables. Since 55 members like fruit, 44 like only fruit, and 33 like neither, we subtract the 44 members who like only fruit from the total 55 fruit-likers to find those who like both: 55 - 44 = 11.
Calculate the number of members who like vegetables only. The number of members who like either fruit or vegetables or both can be found by subtracting those who like neither from the total number of members: 1111 - 33 = 1078. We already know 55 like fruit, so those who like vegetables only: 1078 - 55 = 1023 (1111 total members - 33 neither - 55 fruit).
The two-way frequency table looks like this:
Fruit No Fruit Total
Vegetables 11 1023 1034
No Vegetables 44 33 77
Total 55 1056 1111
At the community center nine boys and nine girls are playing singles at the community center nine boys and nine girls are playing singles table tennis. If each girl plays against east boys everyone’s how many games are played?
Answer:
81
Step-by-step explanation:
9girls x 9 boys to play each other
Find the value of the polynomial:
6a^3–a^10+4a^3+a^10–8a^3+a for a=−3
-57
Step-by-step explanation:We can collect terms to simplify the arithmetic.
... = a^3(6 +4 -8) +a^10(-1 +1) +a
... = 2a^3 +a
... = a(2a^2 +1)
For a = -3, this is
... -3(2(-3)² +1) = -3(2·9 +1)
... = -3·19 = -57
In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR.
Final answer:
To find the length of QR, we used the Pythagorean theorem on triangle PNQ to find NQ, then added it to PR, resulting in QR measuring 53 inches.
Explanation:
To find the length of side QR in △PQR, we can apply the Pythagorean theorem to one of the right triangles formed by the altitude PN. The triangle we'll use is △PNQ, where NQ is part of QR, and PN is given as 15 in.
Firstly, we can calculate NQ using the Pythagorean theorem:
PN² + NQ² = PQ²
15² + NQ² = 39²
NQ² = 39² - 15²
NQ² = 1521 - 225
NQ² = 1296
NQ = √1296
NQ = 36 in
Since PR = 17 in, we can conclude that NR is the difference between PR and NQ:
NR = PR - NQ
NR = 17 - 36
NR = -19 in
The negative value indicates a mistake since lengths cannot be negative. Therefore, we should use the entire length of PQ instead:
QR = NQ + NR
QR = 36 + 17
QR = 53 in
Thus, side QR measures 53 inches.
These prisms are similar. Find the volume of the larger prism in decimal form. Ratio 5:7. Volume of smaller Prism is 50 m3
Answer:
137.2 m³
Step-by-step explanation:
The ratio of volumes is the cube of the ratio of linear dimensions. The larger volume is ...
... V = (7/5)³ × 50 m³ = 2.744 × 50 m³
... V = 137.2 m³
The cost of an office chair is $159 and the markup rate is 24% of the cost. What is A. the dollar markup and B. the selling price?
A. The dollar amout of the markup is found by multiplying the markup rate by the dollar cost. "24% of cost" means "24% × cost". Of course, you know that 24% = 24/100 = 0.24.
... markup = 0.24 × cost = 0.24 × $159 = $38.16
B. The markup is the amount added to the cost to get the selling price. It is the amount by which the cost is marked up.
... selling price = cost + markup = $159.00 +38.16 = $197.16
Point D is between points S and T on ST. Given that SD = 2.9 and ST = 11.1, find the length of DT
D. 8.2
Step-by-step explanation:ST = SD + DT . . . . . segment addition theorem
11.1 = 2.9 + DT . . . . substitute the given lengths
8.2 = DT . . . . . . . . subtract 2.9
The length of segment DT is 8.2 units.
Answer:8.2
Step-by-step explanation:
I got it right on edginuity
In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?
Answer:
BE:EC= 1/3
Step-by-step explanation:
Given ABCD is a parallelogram, Point K is such that it belongs to diagonal BD so that BK:DK=1:4.
If we make an extension of AK which meets BS at point E, then using ΔDKA and ΔEKB, we have
∠DKA=∠EKB (Vertically opposite angles)
∠KDA=∠KBE (Alternate interior angles)
∠DAK=∠BEK (Alternate interior angles)
Thus by AAA similarity,ΔDKA≅ΔEKB
⇒[tex]\frac{AD}{BE}[/tex]= [tex]\frac{DK}{BK}[/tex],
Since, AD= BC,therefore
[tex]\frac{AD}{BE}[/tex]= [tex]\frac{BC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]
Now, BC= BE+EC, ⇒[tex]\frac{BE+EC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]
⇒1+[tex]\frac{EC}{BE} = \frac{4}{1}[/tex]
⇒[tex]\frac{EC}{BE}= 3[/tex]
Reciprocating on both the sides, we get
[tex]\frac{BE}{BC} = \frac{1}{3}[/tex]
you pay $2.76 for 6 bagels. what is the unit price?
a) $0.46 per bagel
b)$0.48 per bagel
c)$0.52 per bagel
d)$0.44 per bagel
Answer:
a) $0.46 per bagel
Step-by-step explanation:
When you are looking for a unit price, you have to divide the price in this instance by the amount of items that you have. For example, here you just have to divide $2.76 by 6 to get $0.46.
Hope I could help! :)
The graph of the function, f(x) = 3x^2 + x + 2, opens down/up and has a maximum/minimum value.
If the function has a ∪ shape (opens up), then it only goes so low—has a minimum value.
Any even-degree function with a positive leading coefficient will open up, so have a minimum. Your function is degree 2 (even) and has a leading coefficient of 3 (positive).
_____
Comment on other polynomial functions
If the leading coefficient of an even-degree function is negative, it will have an inverted-U shape (∩), so will have a maximum.
Any odd-degree function will have a generally rising (/) or generally falling (\) shape, depending on the sign of its leading coefficient. If positive, then rising; if negative, then falling.
PLZ HELP ME ASAP. I DONT UNDERSTAND
AND PLZ PLZ PLZ SHOW YOUR WORK
To find the rate of change, find the difference of people at the park at each given hour and divide that by the total number of hours in the given time frame.
Early Time interval:
Hour 1 there was 55 people.
Hour 3 there was 135 people.
The rate of change is 135 - 55 / 3-1 = 80/2 = 40 people per hour.
Late time interval:
Hour 3 had 135 people.
Hour 5 had 175 people.
The rate of change is 175 - 135 / 5-3 = 40/2 = 20 people per hour
20 is less than 40, so the late time interval had the smallest rate change.
Reid are 1/4 of pie. Vince ate 1/3 of same pie. How much of the pie is left?
Answer:
5/12
Step-by-step explanation: find common denominator
!!!!!!!!!!!! Helppppppp !!!!!!!!!!!!