Answer:
53 bagels
Step-by-step explanation:
The number of bagels, y sold is a function of the square of the time (x) plus 4.
Therefore:
[tex]y=x^2+4[/tex]
Number of Hours from 12.00 am to 7:00 am =7
At x=7
The number of bagels sold,
[tex]y=7^2+4\\=49+4\\=53\\[/tex]
The bagel shop sold 53 bagels from 12: 00 am to 7: 00 am.
The equations 2 x minus y = negative 2, 3 x + 2 y = 5, 4 x minus y = 2, and 22 x + 10 y = 7 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2.5) and (1.75, 0). Blue line goes through (0.5, 0) and (1, 2). Pink line goes through (negative 1, 0), and (0, 2). Purple line goes through (negative 0.75, 2.5) and (0, 0.75). Which system of equations has a solution of approximately (–0.3, 1.4)? 2 x minus y = negative 2 and 22 x + 10 y = 7 3 x + 2 y = 5 and 4 x minus y = 2 4 x minus y = 2 and 22 x + 10 y = 7 2 x minus y = negative 2 and 3 x + 2 y = 5
Answer:
2 x - y = - 2 and 22 x + 10 y = 7
Step-by-step explanation:
To find the equation to produce a solution of approximately (–0.3, 1.4), we have to solve the equations simultaneously.
a) For line 2 x - y = - 2 and 22 x + 10 y = 7
Multiply line 1 by 10 to give : 20x - 10y = -20
Add 20x - 10y = -20 and 22 x + 10 y = 7 to get:
42x = -13
x = -13/42 = -0.3
Put x = -0.3 in 2 x - y = - 2 to get:
2(-0.3) - y = - 2
-0.6 - y = -2
y = 2 - 0.6 = 1.4
x = - 0.3 and y = 1.4
This is the correct option
b) For line 3 x + 2 y = 5 and 4 x - y = 2
Multiply line 2 by 2 to give : 8x - 2y = 8
Add 8x - 2y = 48 and 3 x + 2 y = 5 to get:
11x = 13
x = 13/11 = 1.2
Put x = 1.2 in 3 x + 2 y = 5 to get:
3 (1.2) + 2 y = 5
y = 1.4
x = 1.2 and y = 1.4
c) For line 4 x - y = 2 and 22 x + 10 y = 7
Multiply line 1 by 10 to give : 40x - 10y = 20
Add 40x - 10y = 20 and 22 x + 10 y = 7 to get:
62x = 27
x = 0.44
Put x = 0.44 in 4x - y = 2 to get:
y = -0.24
d) For line 2 x - y = - 2 and 3 x + 2 y = 5
Multiply line 1 by 2 to give : 4x - 2y = -4
Add 4x - 2y = -4 and 3x + 2 y = 5 to get:
7x = 1
x = 0.14
Put x = 0.14 in 2 x - y = - 2 to get:
y = 2.28
Answer:
it's A
Step-by-step explanation:
i took the test
Check all that apply. (pi/3) is the reference angle for:
1. 15pi/3
2. 2pi/3
3. 7pi/3
4. 19pi/3
Answer:
2π/3, 7π/3 and 19π/3 are the reference angles.
Step-by-step explanation:
Given the angle π/3, the reference angle to this angle is the angle similar to the given angle.
The angle similar to the angle is derived by adding 2πk to each resulting angle where k is integers from 1 and above
Given initial angle of π/3
The following are the reference angles:
When k = 1
theta(k) = π/3 + 2πk
theta(1) = π/3 + 2π(1)
=(π+6π)/3
= 7π/3
When k = 2
theta(2) = π/3 + 2π(2)
= π/3 + 4π
=(π+12π)/3
= 13π/3
When k = 3
theta(2) = π/3 + 2π(3)
= π/3 + 6π
=(π+18π)/3
= 19π/3
Note that π-theta is also a reference angle where theta us the given angle.
π-theta= π-π/3
= 3π-π/3
= 2π/3
From the calculation above, 2π/3, 7π/3 and 19π/3 are the reference angles.
Answer:
π/3 is the reference angle for 2π/3, 7π/3, and 19π/3
Rosa thinks of a number. She rounds it to the nearest thousand and gets 35,000. When rounded to the nearest hundred, the rounded value is greater than the original number. Which choice could be Rosa's number?
Hey there! The answer will be below
B is the correct answer
Because in B the last 3 numbers are 500 (estimate) so 34,500 would be rounded to 35,000.Plus B makes the most sense.
Hope that helps!
By: xBrainly
Darryl has a daily goal of earning $100 in profit. His profit is $0.72 per sandwich, and he sold 150 sandwiches today. Explain how Darryl can use the profit rate to determine how much profit he earned. Did Darryl meet his daily goal? PLEASE HELP ASAP
Answer:
Step-by-step explanation:
Hello,
His profit is $0.72 per sandwich
so for 150 sandwiches his profit is 0.72 * 150 = $ 108
He does meet his daily goal as 108 > 100
Hope this helps
Lisa is currently taking physics as one of her electives in school. Her grade at the end of the year is determined by the average of four exams, each worth 100 points. On her first test she got an 84, on her second she got a 92, and on her third an 80. What must she score on her fourth exam to get exactly 80% in the course?
Answer: 64
Step-by-step explanation:
From the question, we are informed that Lisa is currently taking physics as one of her electives in school and that her grade at the end of the year is determined by the average of four exams, each worth 100 points.
First test = 84,
Second test = 92
Third test = 80
Forth test = y
The fourth test is denoted by y.
Since we are told that she must get exactly 80% in the course and she took 4 exams, that means her total score will be: = 80 × 4 = 320
Therefore,
84 + 92 + 80 + y = 320
256 + y = 320
y = 320 - 256
y = 64
The fourth exam's score is 64
The Owens family has saved up $50,000 for a down pay
saved up $50,000 for a down payment on a house. They are
going to use this money as the 10% down payment their lender is req
make to purchase the house. What is the price of the ne
eune house. What is the price of the house that the Owens family
is buying?
Answer:
Step-by-step explanation:
Let the price of the house be P .
10 % of P is demanded as down payment
10 % of P = P x 10 / 100
= P / 10
This down-payment = 50000
P / 10 = 50000
P = $5,00,000 .
Price of house = $5,00,000
Why is x^4 - 16 when factored not just (x^2 + 4) (x^2 - 4)?
Answer:
[tex] (x - 2)(x + 2)( {x}^{2} + 4)[/tex]
Step-by-step explanation:
[tex] {x}^{4} - 16 \\ = ({x}^{2})^{2} - ({2}^{2})^{2} \\ = ( {x}^{2} - {2}^{2} )( {x}^{2} + {2}^{2} ) \\ = (x - 2)(x + 2)( {x}^{2} + 4)[/tex]
Because [tex] (x^2 - 4) = (x^2-2^2) [/tex] can further be factorised as (x - 2) (x + 2).
Can you guys help me answer these questions?
Answer:
1 and 2 have already been done.
See below for the answers to 4 to 6.
Step-by-step explanation:
7. Finding the limit as x --> 2 of the function:
(2^(x + 2) - 16) / (4^x -16)
= 4(2^x - 4) / (2^x -4)(2^x + 4)
= 4 / (2^x + 4)
When x = 2 this = 4/8 = 0.5
The limit is the same whether you approach 2 from below or above.
So k = 0.5.
Please help!!!!!!!!!!!!Thanks
Answer:
The answer is option B.
Step-by-step explanation:
The prime number is 2
Since 1 + 1 = 2
And 1 is an odd number
Hope this helps you
What is the value of r in the equation?
-1.5(4-1)=-12
-6
Answer:
-4
Step-by-step explanation:
-1.5 (4-r) = -12 Distribute the -1.5.
-6 - 1.5r = -12 Add 6 to both sides.
-1.5r = 6 Divide both sides by -1.5.
r = -4
Answer:
[tex] \boxed{\sf r = - 4} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: r: \\ \sf \implies - 1.5(4 - r) = - 12 \\ \\ \sf Divide \: both \: sides \: of \: - 1.5(4 - r) = - 12 \: by \: - 1.5 : \\ \sf \implies \frac{ - 1.5(4 - r)}{ - 1.5} = \frac{ - 12}{ - 1.5} \\ \\ \sf \frac{ \cancel{ - 1.5}}{ \cancel{ - 1.5}} = 1 : \\ \sf \implies 4 - r = \frac{ - 20}{ - 1.5} \\ \\ \sf \frac{ - 20}{ - 1.5} = 8 : \\ \sf \implies 4 - r = 8 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies (4 - \boxed{ \sf 4}) - r = 8 - \boxed{ \sf 4} \\ \\ \sf 4 - 4 = 0 : \\ \sf \implies - r = 8 - 4 \\ \\ \sf 8 - 4 = 4 : \\ \sf \implies - r = \boxed{ \sf 4} \\ \\ \sf Multiply \: both \: sides \: of - r = 4 \: by \: - 1: \\ \sf \implies - r \times ( - 1) = 4 \times ( - 1) \\ \\ \sf - r \times ( - 1) = r : \\ \sf \implies r = 4 \times ( - 1) \\ \\ \sf \implies r = - 4[/tex]
20 points and brainliest!
Tree Diagrams
1. For what type of situation is a tree diagram a suitable way to organize information?
2. Explain how to read a tree diagram to determine the possible outcomes for that situation.
Answer: Use a tree diagram for conditional probability
The first branch lists the elements in the starting field-- how many items or outcomes. Like heads or tails, how many of each color of marbles or socks, etc. The next branch shows the set of outcomes from the first event and what is available for the next event. The branches are labeled with fractions to tell the chances of each outcome.
Step-by-step explanation:
A tree diagram is good for determining probability when there are multiple steps in the "draw" and multiple outcomes-- sometimes chances of event a and b "this and that" or event a or b "this or that"
You use the fractions on each branch to calculate the final outcome. If it's a and b, you multiply the fractions on each "trail" you follow through the branches to get the defined final outcome.
If it is a or b, you add the fractions to get the probability of the defined final outcome.
pleassseeeeee help pleaseeeeeeeeeeeee help
Answer:
The picture is attached!
Step-by-step explanation:
For c, the last bracket said (y=6) and I assumed that it is (y+6).
If it is (y-6), the answer would change, so please tell me if I am wrong.
But the rest, I hope it helps, if you have any questions, please feel free to ask me:)
BRAINLIEST would help me a lot:)
The local hospital offers an incentive for nurses to work longer shifts. After a regular 8-hour shift, they can make double time on the remainder of their shift. That is, they make twice their salary for each hour they work over 8 hours. Nurse Jane works 12 hour shifts Monday through Friday. Her weekly gross income is $2136.00, what is her base salary?
Answer:
$26.70/hour
Step-by-step explanation:
Let's look at 1 day.
She works a 12 hour shift. For the first 8 hours, she receives her regular hourly salary. That means 8 hours of pay at her regular hourly salary.
Then she works another 4 hours at her overtime pay. Her overtime pay is twice her regular salary, so the extra 4 hours at overtime pay are paid as if they were 8 hours of regular work. In effect, she is earning 16 hours of regular pay per day.
Monday through Friday means 5 days of work per week.
5 days/week * 16 hours/day = 80 hours/week
She is earning as if she were working 80 hours of regular pay per week.
base salary = (gross weekly income)/(effective number of hours in 1 week)
base salary = $2136/80
base salary = $26.70/hour
Which equation can be used to find the measure of angle BAC? tan−1(StartFraction 5 Over 12 EndFraction) = x tan−1(StartFraction 12 Over 5 EndFraction) = x cos−1(StartFraction 12 Over 13 EndFraction) = x cos−1(StartFraction 13 Over 12 EndFraction) = x
Answer:
tan−1(StartFraction 12 Over 5 EndFraction) = x
Step-by-step explanation:
The measure of the angle x in the right triangle ABC is equal to
Scenario A) Using cos
Cos x=adjacent/hypotenuse
=AC/AB
=5/13
x=cos x^-1=5/13
Scenario B) using sin
Sin x=opposite/hypotenuse
=BC/AB
=12/13
x=sin x^-1=12/13
Scenario C). Using tan
tan x=opposite/adjacent
=BC/AC
=12/5
x=tan x^-1=12/5
tan−1(StartFraction 12 Over 5 EndFraction) = x
The correct answer is option B which is [tex]tan^-1(\dfrac{12}{5})=x[/tex]
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The measure of the angle x in the right triangle ABC is equal to
Scenario A)
Using cos
Cos x =adjacent/hypotenuse
Cos x = AC/AB
Cos x = 5/13
x = cos x^-1 = 5/13
Scenario B)
using sin
Sin x = opposite/hypotenuse
Sin x = BC/AB
Sin x = 12/13
x=sin x^-1=12/13
Scenario C).
Using tan
tan x =opposite/adjacent
tan x =BC/AC
tan x =12/5
x = tan x^-1=12/5
From the figure attached, we can see that the angle BAC will be[tex]tan^-1(\dfrac{12}{5})=x[/tex].
Therefore the correct answer is option B which is [tex]tan^-1(\dfrac{12}{5})=x[/tex]
The complete image of the triangle is attached with the answer below.
To know more about trigonometry follow
https://brainly.com/question/24349828
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In order to clear out room for new merchandise, James decided to mark down some of the items for sale in his electronics store. He marked down DVD players by 36%, and he marked down stereo tuners by 22%. If DVD players cost $41.60 after the markdown and stereo tuners cost $69.42 after the markdown, which item’s price was reduced by more, and by how many dollars more was it reduced? Round all dollar values to the nearest cent.
Answer:
a) Which item’s price was reduced by more, and by how many dollars more was it reduced?
The DVD player's price was reduced more by $3.82 than the stereo tuner's price.
b) Round all dollar values to the nearest cent.
Rounding $3.82 dollars to the nearest cents
$1 = 100 cents
$3.82 =
3.82 × 100 cents
= 382 cents
The DVD player's price was reduced by 382 cents more than the stereo tuner's price
Step-by-step explanation:
Lets day the original price of the DVD player was $100
We are told the price was marked down to 36%
36% of $100 = $36
$100 - $36 = $64
We are told the DVD cost $41.60 after the markdown.
Original cost of DVD =
$41.60/$64 × 100 = $65
Lets the original price of the Stereo player was $100
We are told the price was marked down to 22%
22% of $100 = $22
$100 - $22 = $78
We are told the DVD cost $69.42 after the markdown.
Original cost of Stereo =
$69.42/$78 × 100 = $89
DVD = $65 - $41.60 = $23.40 less
Stereo = $89 - 69.42 = $19.58 less
Difference between the DVD and the Stereo is
$23.40 - $19.58 = $3.82
Therefore,the DVD player's price was reduced by $3.82 more than the stereo tuner's price
Rounding $3.82 dollars to the nearest cents
$1 = 100 cents
$3.82 =
3.82 × 100 cents
= 382 cents
Answer:
The answer is A on edg 2020
Step-by-step explanation:
Find the equation of the median shown:
Hey there! I'm happy to help!
The median is the line cutting the triangle in this graph. In general, a median connects any of the triangle points to halfway across the side opposite to that point. This median connects R to halfway across the side across from R.
We want to find the equation of this median. We see that T is at (-2,3) and R is (3,-3). The first thing to do when looking for the equation of the line is to find the slope, or incline. Since we have two points, we can do this very easily. You simply divide the difference in the y-values by the difference in the x-values.
DIFFERENCE IN Y-VALUES
3-(-3)
3+3
6
DIFFERENCE IN X-VALUES
-2-3
-5
Now, we divide the two answers, giving us -6/5.
So, we have our slope, which gives us the equation so far y=-6/5x+b. We just need to find the b, which is our y-intercept. Well, to do this, we plug in one of our points and we can solve for b. We will use (3,-3)!
-3=-6/5(3)+b
-3=-3 3/5+b
We add 3 3/5 to both sides to isolate the b.
b=3/5
This means that this median should hit the y-axis at (0,3/5), and it looks like it does. Therefore, the equation of this median is y=-6/5x+3/5.
Now you can find the slope of a median! Have a wonderful day! :D
Thirty equally spaced points on the circumference of a circle are labelled in order with the
numbers 1 to 30. Which number is diametrically opposite to 7?
Answer:
22 is diametrically opposite of 7
Step-by-step explanation:
A circle has a total of 360º
The circumference of the circle has 12 equally spaced points
Each point on the circumference=360°/30
= 12º per point
A point (n) opposite to 7 on the circumference will form 180° line on the circle, that is half of the circle.
Half of the circle=30 points/2
=15 points
Therefore,
15+7=22
22 is diametrically opposite 7
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 1818 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.140.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 12.0212.02 oz and 12.6612.66 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.160.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.160.16 oz. Use a 0.010.01 significance level. Complete parts (a) through (d) below.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 18 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population.
If the workers want the filling process to work so that almost all cans have volumes between 12.02 oz and 12.66 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.01 significance level. Complete parts (a) through (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic.
c. Find the p-value.
d. State the conclusion.
Answer:
Null hypotheses = H₀: σ = 0.16 oz
Alternate hypotheses = H₁: σ < 0.16 oz
Critical value = 6.408
Chi-square value = [tex]\chi^2[/tex] = 13.016
Reject H₀ Since [tex]\chi^2[/tex] > Critical value
Reject H₀ Since p-value ≤ α
We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.
Step-by-step explanation:
Set up hypotheses:
The null hypotheses is that the population of volumes has a standard deviation of 0.16 oz
Null hypotheses = H₀: σ = 0.16 oz
The claim to be tested is that the population of volumes has a standard deviation of less than 0.16 oz
Alternate hypotheses = H₁: σ < 0.16 oz
Determine type of test:
Since the alternate hypothesis states that the population of volumes has a standard deviation of less than 0.16 oz, therefore we will use a lower-tailed chi-square test.
Determine the Critical value:
Given level of significance = 0.01
Since it is a lower-tailed test, the areas given in the chi-square table are the areas to the right of the critical value. To get the areas on the left, subtract it from one, and then look it up
α = 1 - 0.01 = 0.99
degree of freedom = df = n - 1 = 18 - 1 = 17
The critical value from the chi-square table at α = 0.99 and df = 17 is found to be
Critical value = 6.408
Using an online “chi-square p-value calculator”
The left tail p-value for df = 17 and Critical value = 6.408 is found to be
p-value = 0.01
Set up decision rule:
Reject H₀ If > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
OR
Reject H₀ If p-value ≤ α
Compute the test statistic:
[tex]$ \chi^2 = \frac{(n-1) s^2}{\sigma^2} } $[/tex]
[tex]$ \chi^2 = \frac{(18-1) 0.14^2}{0.16^2} } $[/tex]
[tex]\chi^2 = 13.016[/tex]
Conclusion:
We reject H₀
Since [tex]\chi^2[/tex] > Critical value
13.016 > 6.408
Also
p-value ≤ α
0.01 ≤ 0.01
We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.
Shawn the builder estimated that it would cost $12,000 to build a new conservatory. In fact it cost $13,200 What was the percentage error?
Answer:
10%Solution,
Measured value= $ 13200
True value = $ 1200
Now,
Percentage error:
[tex] \frac{measured \: value - true \: value}{true \: value} \times 100 \: percent\\ = \frac{13200 - 12000}{12000} \times 100 \: percent \\ = \frac{1200}{12000} \times 100 \: percent \\ = 10 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Let y=5x_1+3x_2+〖9x〗_3 find Mean and variance of y. Where x_1,x_2 and〖 x〗_3 are independent uniform random variable with parameter of x_(1 ) as [2:4] for x_2 as [5:10] and for x_3 as [0:4]?
Answer:
Mean value = 55.5
Step-by-step explanation:
Y = 5X1 + 3X2 + 9X3
CASE 1:
X1 = 2, X2 = 5, X3 = 0
Y = 5(2) +3(5) + 9(0) = 10 + 15 + 0 = 25
CASE 2:
X1 = 4, X2 = 10, X3 = 4
Y = 5(4) + 3(10) + 9(4) = 20+30+36 = 86
The mean value of Y is (25 + 86)/2 = 55.5
The variance from the mean is 30.5
Denise bought a box of 560 pieces of candy.4/5 of the pieces of the candy were fruity and 1/4 of the remaining pieces of candy were mint.How many of candy of the other flavors were there?
Answer:
Number of Other flavor candy is 84.
Step-by-step explanation:
Given that
A total of 560 pieces of candy are there in the box.
[tex]\frac{4}{5}[/tex] of the pieces are fruity.
Number of Fruity pieces:
[tex]\dfrac{4}{5} \times 560\\\Rightarrow 4 \times 112 =448[/tex]
Now, remaining pieces = Total pieces - Fruity pieces
remaining pieces = 560 - 448 = 112
Also given that [tex]\frac{1}4[/tex] of the remaining pieces are mind.
Number of mint pieces:
[tex]\dfrac{1}{4}\times 112 = 28[/tex]
Other flavors remaining = Total pieces - Fruity pieces - Mint pieces
Other flavors remaining = 560 - 448 - 28
Other flavors remaining = 112 - 28 = 84
Number of Other flavor candy is 84.
The sum of the interior angles of a polygon is 9x³. If x is 3 greater than the number of sides of the polygon, how many sides does the polygon have?
Answer:
n = 7
Step-by-step explanation:
The sum of the interior angles of a polygon is 9[tex]x^2[/tex]. If x is 3 greater than the number of sides of the polygon, how many sides does the polygon have?
The sum of the interior angles of a concave polygon can be found using the formula S = (n - 2)*180.
n= number of sides of the polygon
n-2 * 180 = the sum of the interior angles
9[tex]x^2[/tex]= the sum of the interior angles
9[tex]x^2[/tex]= (n-2) *180
x= 3+ n
9 [tex](3+n)^{2}[/tex]=(n-2) *180
9 (9+6n+n^2) = (n-2) *180
81+54n+9n^2 = (n-2) *180
n = 7
What is the rate of discount if a pair of shoes is regularly $145.00 and the sales price is $108.75?
Answer:
25%
Step-by-step explanation:
You set up the proportion 108.75/145 is x/100 to find out what percentage of 145 108.75 is. You can then use this proportion to find that percentage with cross multiplying, by doing this you get the equation 108.75 times 100 is equal to 145x. Then you simplify to get 10,875=145x. Then you solve like regular by dividing both sides by 145 to get x=75. Now we know that 108.75 is 75% of 145, but we aren't done yet. Now in order to find the discount price you subtract 75 from 100 to get 25, so you're finding the difference between 100 and the x-value we just found. The final answer is 25%
Vikas is the head of student council this year at his high school in London. He is responsible for planning the annual graduation trip to Canada’s Wonderland. The students will spend one full day at the park and return late that evening. The school has rented a bus for transportation. The entry fee into the park is $50 and the bus costs $600. Write an equation to relate the cost, C, in dollars to the number of student, s, who participate in this fun trip.
Answer:
C = 600 + 50s
Step-by-step explanation:
The students are planning to visits the Canada's wonderland. The students will spend a full day at the park.
The entry fee for each student is $50 and the bus cost is $600. Each student will pay $50 for entry into the park.
Let
the number of student = s
cost of the trip = C
Relating the variable C and s
The total amount of money the student will pay for entry fee = 50 × s = 50s
Therefore, cost of the trip can be expressed as follows
C = 600 + 50s
Pleas answer this in two minutes
Answer: x=5, y=7
Step-by-step explanation:
Since ΔEFG and ΔHIJ are congruent, we can set the corresponding sides equal to each other.
y+14=3y [subtract both sides by y]
14=2y [divide both sides by 2]
y=7
------------------------------------------------------------------------------------
10x=x+45 [subtract both sides by x]
9x=45 [divide both sides by 9]
x=5
can i have help with these questions
Answer:
(-3, 5), (-1, -1), (5, -3)
Step-by-step explanation:
Each pair of vertices can be one of the diagonals. Then the missing point will be found at the coordinates that are the sum of those, less the coordinates of the third point.
Given points are ...
A(-2, 2), B(1, 1), C(2, -2)
For AB a diagonal, D1 is ...
A+B-C = (-2+1-2, 2+1-(-2)) = (-3, 5)
For AC a diagonal, D2 is ...
A+C-B = (-2+2-1, 2-2-1) = (-1, -1)
For BC a diagonal, D3 is ...
B+C-A = (1+2-(-2), 1-2-2) = (5, -3)
_____
For a lot of parallelogram problems I find it easiest to work with the fact that the diagonals bisect each other. This means they both have the same midpoint, so for quadrilateral ABCD, we have (A+C)/2 = (B+D)/2. Multiplying this by 2 gives the equation we used above, A+C = B+D, so D=A+C-B. Remember, in ABCD, AC and BD are the diagonals.
Answer:
Answer:
(-3, 5), (-1, -1), (5, -3)
Step-by-step explanation:
Each pair of vertices can be one of the diagonals. Then the missing point will be found at the coordinates that are the sum of those, less the coordinates of the third point.
Given points are ...
A(-2, 2), B(1, 1), C(2, -2)
For AB a diagonal, D1 is ...
A+B-C = (-2+1-2, 2+1-(-2)) = (-3, 5)
For AC a diagonal, D2 is ...
A+C-B = (-2+2-1, 2-2-1) = (-1, -1)
For BC a diagonal, D3 is ...
B+C-A = (1+2-(-2), 1-2-2) = (5, -3)
_____
For a lot of parallelogram problems I find it easiest to work with the fact that the diagonals bisect each other. This means they both have the same midpoint, so for quadrilateral ABCD, we have (A+C)/2 = (B+D)/2. Multiplying this by 2 gives the equation we used above, A+C = B+D, so D=A+C-B. Remember, in ABCD, AC and BD are the diagonals.
Thanks for everything have a good day
Increase £16870 by 3%
Give your answer rounded to 2 DP.
Answer:
£17376.10
Step-by-step explanation:
Percentage increase.
16870 × (1 + 3%)
16870 × 1.03
= 17376.1
Answer:
£17376.10
Step-by-step explanation:
100% + 3% = 103%
103% into a decimal = 1.03
16870 × 1.03
= £17376.1
In 8 years, a girl will be 3 years older than twice her present age. How old is she now
Answer:
5
Step-by-step explanation:
You can express this as a system of equations:
x in this instance will be her present age.
x + 8 = 2x + 3
simply solve for x after this by subtracting three and x from both sides, and you’ll find that x is 5.
Sam has some red and yellow cubes. She has 20 cubes in total. She has 8 more yellow cubes than red ones. How many red cubes does she have?
Answer:
12
Step-by-step explanation:
because if she has 8 more red cubes that yellow than that would mean it would become 12
Answer:
20-8=12
Step-by-step explanation:
let the red cubes be x,
total cubes=20
yellow cubes=x+8
according to question,
x+8=20
x=20-8
x=12
hence, sam has 12 cubes
one day the town of waterville had an afternoon rainstorm that lasted 90 minutes. the rainstorm started at 4:15 pm. when did it end?
Answer:
Hey there!
90 mins= 1 hr 30 mins.
4:15+ 1 hr 30 mins= 5:45
The rainstorm ended at 5:45 PM
Hope this helps!