PLEASE HELPS ME WITH MATHS I HAVE TIMER FOR 6mis!! :'(
Subash created the two-way table below. Teams Team A Team B Total Boys 15 18 33 Girls 17 31 Total 32 32 According to the table, how many girls were on team B? 14 15 17 18
Answers
Answer:
Step-by-step explanation:
the answer is 14 i already took the test
The answer is A) 14.
Based on the information provided in the table, the number of girls on team B is 31.
The table shows the breakdown of boys and girls on two teams, Team A and Team B, along with the total for each category and the overall total.
Looking at the "Girls" row, we see that a total of 31 girls are represented in the data.
Since the table specifies that this is a "two-way table," implying no other teams or categories beyond Team A and Team B, we can conclude that all 31 girls must be distributed between these two teams.
The "Girls" column further shows that Team A has 17 girls.
Therefore, the remaining 31 girls - 17 girls (Team A) = 14 girls must be on Team B.
Question:
Subash created the two-way table below. Team A and Team B. Total Boys are 33 and distributed in both the teams, where A has 15 and B has 18 boys. Total Girls are 31, where team A includes 17 girls. Both the teams have total 32 members. According to the table, how much girls were on team B?
A) 14
B) 15
C) 17
D) 18
Related Questions
Lance and Mary are buying a piece of property. The property cost $64,975. The bank is requiring a 20% down payment. About how much money will they need for a down payment?
Answers
Lance and Mary will need approximately $12,995 for a down payment on the property.
Explanation:To calculate the amount of money needed for a down payment, you need to find 20% of the property cost. In this case, the property cost is $64,975.
Step 1: Convert 20% to a decimal by dividing it by 100: 20/100 = 0.2
Step 2: Multiply the property cost by 0.2: $64,975 * 0.2 = $12,995
Therefore, Lance and Mary will need approximately $12,995 for a down payment on the property.
Plz help i can't figure this out for the life of me and it's due tmr
Answers
Answer:
D
Step-by-step explanation:
The diagram shows the rectangle with vertices at A(3,4), B(3,7), C(4,7) and D(4,4).
1. Rotate rectangle ABCD by 180° about the point (3,4) (vertex A). This rotation has the rule:
[tex](x,y)\rightarrow (6-x,8-y)[/tex]
So, the image points have the coordinates A'(3,4), B'(3,1), C'(2,1) and D'(2,4)
2. Dilate by a scale factor of 2 with the center of dilation at origin. This dilation has the rule:
[tex](x,y)\rightarrow (2x,2y)[/tex]
So, the image points have the coordinates A''(6,8), B''(6,2), C''(4,2) and D''(4,8)
3. Reflect it over the y-axis. This reflection has the rule:
[tex](x,y)\rightarrow (-x,y)[/tex]
So, the image points have the coordinates A'''(-6,8), B'''(-6,2), C'''(-4,2) and D'''(-4,8) that are exactly the coordinates of the second rectangle shown.
Thus, correct option is option D.
I need help solving this
Answers
Answer:
Area = 374.1 sq. in.
Step-by-step explanation:
A trick to solve this would be to know the area of a hexagon formula and plug the known information.
First, of all, if we count the number of sides, we see that we have 6 sides.
6 sided polygon is a HEXAGON, which has area formula of:
[tex]A=\frac{3\sqrt{3} }{2} a^2[/tex]
Where
a is the side length
Given, the side length is 12 inches ( a= 12), we simply substitute into formula and find area of hexagon shown:
[tex]A=\frac{3\sqrt{3} }{2} a^2\\A=\frac{3\sqrt{3} }{2} (12)^2\\A=\frac{3\sqrt{3} }{2}(144)\\A = 374.12[/tex]
Rounded to nearest tenth (1 decimal place)
Area = 374.1 sq. in.
Harper works at an electronics store as a salesperson. Harper earns a 6% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Harper made a total of $2600 in sales and earned $137 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Harper made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
Answers
Answer:
The system of equations are
x + y = 2600 …….equation (1)
and, 6x + 5y = 13700 ……equation (2)
Explanation:
Let x = amount of sales of phone;
y = amount of sales of computer
For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.
Similarly for computer,
5% of y = 0.05y
Given the total sales; x + y = 2600
And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700
Therefore the system of equations are
x + y = 2600 …….equation (1)
6 x + 5 y = 13700 ……equation (2)
all real numbers y that are less than 4 or greater than 9
Answers
Answer:
Y<4 or y>9
Hope this helps you out!
A women bought some large frames for $16 each and some small frames for $9 each at a close out sale. If she bought 16 frames for $165, find how many of each type she bought.
Answers
Answer:
3 large, 13 small
Step-by-step explanation:
large: x
small: y
x + y = 16
16x + 9y = 165
Multiply first equation by 9 and subtract the equations.
9x + 9y = 144
-(16x + 9y = 165)
-7x = -21
x = 3
Now substitute this x value into the first equation
x + y = 16
3 + y = 16
y = 13
Can someone help me with this problem? It’s Special Right Triangles: Decimal Answer. Round to the nearest tenth. Thank you ! 10 points
Answers
Answer:
h = 1.4
c = 2.8
Step-by-step explanation:
For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.
For the triangle with the variable h:
Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.
In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.
[tex]\frac{1}{\sqrt2} =\frac{h}{2} \\h = 2\frac{1}{\sqrt2} \\h = \frac{2}{\sqrt2} \\h = \frac{2\sqrt2}{2} \\h = \sqrt{2}[/tex]
h = √2
h ≈ 1.4
For the triangle with the variable c:
The is an equilateral triangle cut in half because the angles are 30 and 60.
The side ratio of altitude to hypotenuse is √3 to 2.
[tex]\frac{\sqrt{3} }{2} =\frac{c}{4} \\\sqrt{3} = \frac{c}{2}\\2\sqrt3 = c[/tex]
c = 2√2
c ≈ 2.8
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food. How many weeks can Keith withdraw money from his account?
Answers
Keith can withdraw money from his account for 12 weeks.
Step-by-step explanation:
Total savings = $500
Amount to be left in his account = $200
Withdrawal per week = $25
Let,
x be the number of weeks.
According to given statement;
Total savings - Withdrawal per week * no. of weeks = Amount to be left
[tex]500-25x=200\\-25x=200-500\\-25x=-300\\[/tex]
Dividing both sides by -25
[tex]\frac{-25x}{-25}=\frac{-300}{-25}\\x=12[/tex]
Keith can withdraw money from his account for 12 weeks.
Keywords: savings, linear expression
Learn more about linear expressions at:
brainly.com/question/4639731brainly.com/question/4655616#LearnwithBrainly
Final answer:
Keith can withdraw money from his account for food for 12 weeks before reaching his minimum account balance requirement of $200.
Explanation:
To determine how many weeks Keith can withdraw money from his account while maintaining a balance of at least $200, we need to perform a simple subtraction and division operation. First, we calculate the amount he needs to leave in the account:
$500 initial balance - $200 desired end balance = $300 available to spend.
Keith withdraws $25 per week for food. To find out how many weeks his money will last, we divide the total amount he can spend by the weekly withdrawal amount:
$300 \/ $25 per week = 12 weeks.
Therefore, Keith can withdraw money for food for 12 weeks before his account balance reaches his minimum requirement of $200.
Is (2,-5) a solution to the equation f(x)= -x - 3
Answers
Replace x in the equation with the x value of the given solution:
f(x) = -2 -3 = -5
Since replacing x with 2 , the equation equals -5, then (2,-5) is a solution.
Answer:
yes
Step-by-step explanation:
Question 1) Refer to the equation 2x-6y=12. A) Create a table of values for at least 4 points. Show your work. B) Use the table of values to graph the line. ( Question 2) I posted a picture of question 2. Will Mark Brainliest. Has to be turned in tonight
Answers
Answer:
Question 1)
Rearrange 2x-6y=12 to slope-intercept form by isolating y
y = (1/3)x - 2
Sub each x value to get the y value
x y
-3 -3
0 -2
3 1
6 0
y = (1/3)x - 2
y = (1/3)(-3) - 2
y = -3
Point (-3, -3)
y = (1/3)x - 2
y = (1/3)(0) - 2
y = -2
Point (0, -2)
y = (1/3)x - 2
y = (1/3)(3) - 2
y = 1
Point (3, 1)
y = (1/3)x - 2
y = (1/3)(6) - 2
y = 0
Point (6, 0)
See graph below
Question 2)
a) No, each support does not have the same starting coordinates. For example, the first support from the left starts at (0,0) and the second support from the left starts at (2,1).
b) No, each support does not have the same ending coordinates. For example, the first support from the left ends at (2,1) and the second support from the left ends at (6,3).
c) No, each support does not have the same change in x-values from the start to end.
The first support starts at the x-value 0 and ends at the x-value 2. It increased by 2.
The second support starts at the x-value 2 and ends at the x-value 6. It increased by 4.
d) No, each support does not have the same change in y-values from the start to end.
The first support starts at the y-value 0 and ends at the x-value 1. It increased by 1.
The second support starts at the y-value 1 and ends at the x-value 3. It increased by 2.
e) Yes, each support has the same change in the ratio of y-values over x-values. For the first support, the change is y-values is 1 and the change in x-values is 2. (1/2)
For the second support, the change in y-values is 2 and the change in x-values is 4. (2/4 = 1/2)
They both have the ratio of change in y-values over x-values 1/2.
y = x - 4
-2x + y = 18
Use elimination pls
Answers
Answer:
x = -22 , y = -26
Step-by-step explanation:
Solve the following system:
{y = x - 4 | (equation 1)
y - 2 x = 18 | (equation 2)
Express the system in standard form:
{-x + y = -4 | (equation 1)
-(2 x) + y = 18 | (equation 2)
Swap equation 1 with equation 2:
{-(2 x) + y = 18 | (equation 1)
-x + y = -4 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{-(2 x) + y = 18 | (equation 1)
0 x+y/2 = -13 | (equation 2)
Multiply equation 2 by 2:
{-(2 x) + y = 18 | (equation 1)
0 x+y = -26 | (equation 2)
Subtract equation 2 from equation 1:
{-(2 x)+0 y = 44 | (equation 1)
0 x+y = -26 | (equation 2)
Divide equation 1 by -2:
{x+0 y = -22 | (equation 1)
0 x+y = -26 | (equation 2)
Collect results:
Answer: {x = -22 , y = -26
Answer:
x = -22, y = -26Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x-4&\text{subtract}\ x\ \text{from both sides}\\-2x+y=18\end{array}\right\\\\\left\{\begin{array}{ccc}-x+y=-4\\-2x+y=18&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-x+y=-4\\2x-y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad x=-22\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\y=-22-4\\y=-26[/tex]
An electrolyte solution has an average current density of 111 ampere per square decimeter \left( \dfrac{\text{A}}{\text{dm}^2}\right)(
dm
2
A
)left parenthesis, start fraction, start text, A, end text, divided by, start text, d, m, end text, squared, end fraction, right parenthesis.
What is the current density of the solution in \dfrac{\text{A}}{\text{m}^2}
m
2
A
start fraction, start text, A, end text, divided by, start text, m, end text, squared, end fraction?
Answers
Answer:
The current density of the solution in [tex]m^2[/tex] is [tex]11100A/m^2[/tex]
Step-by-step explanation:
One square decimeter is equal to 0.01 square meter, Thus the current density in square meters is
[tex]\frac{111A}{dm^2} =\frac{111A}{0.01m^2} =\frac{111}{0.01}*\frac{A}{m^2}=\boxed{11100A/m^2}[/tex]
11100 Amperes per square meter.
Answer:
The numbers are messed up, don't copy and paste from khan.
The answer is 100
Step-by-step explanation:
I took the test
Image point B'(4,-8) was transformed using the translation (x - 2, y + 3). What were the coordinates of B?
Answers
Answer:
B(6, - 11 )
Step-by-step explanation:
Since the translation rule is (x - 2, y + 3 )
Then to go back the way do the opposite, that is
(x + 2, y - 3 ), thus
B(4 + 2, - 8 - 3 ) → B(6, - 11 )
Answer:(6, -11)
Step-by-step explanation:
how many pumpkin plants would be in 2 rows
Answers
Answer:
If a vine tear is occurs after the fruit, cover it with soil and it should produce secondary roots. Number of Fruit on a Vine: A single pumpkin plant normally produces two to five pumpkins. Miniature varieties will produce up to a dozen or so.
Step-by-step explanation:
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets-2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
Answers
Answer:
Number of Adult's tickets sold on Saturday = 3,356
Number of Children's tickets sold on Saturday = 2, 928
Total number of tickets sold over these two days is 8,938.
Step-by-step explanation:
Here, the number of tickets sold on FRIDAY:
Adult Ticket sold = 1,678
Children's Tickets sold = 976
So, the total number of tickets sold on Friday
= Sum of ( Adult + Children's ) tickets = 1,678 + 976 = 2,654 .... (1)
The number of tickets sold on SATURDAY:
Adult Ticket sold = 2 times the number of adult tickets sold on Friday
= 1,678 x 2 = 3,356
Children's Tickets sold = 3 times the number of children's tickets sold on Friday.
= 976 x 3 = 2, 928
So, the total number of tickets sold on Saturday
= Sum of ( Adult + Children's ) tickets = 3,356 + 2,928 = 6, 284 .... (2)
Now, the total number of tickets booked in these two days :
Sum of tickets booked on (Friday + Saturday)
= 2,654 + 6, 284 = 8,938
Hence, total number of tickets sold over these two days is 8,938.
A box of cereal has a net weight of 42 ounces. If you buy three of these boxes, how much cereal will you have?
Answers
Answer:
126 ounces of cereal
Step-by-step explanation:
42*3=126
Answer:
7 lb and 14 oz
Step-by-step explanation:
42 oz × 3 = 126 oz
126 oz = 7 lb and 14 oz
ALOT OF POINTS IF YOU HELP ME PLEASE EXPLAIN
Answers
Answer:
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Step-by-step explanation:
Misha's group was asked to write an expression equivalent to
7y²z + 3yz² - 3
When Mr. Chen checked their answers, he found only one to be correct.
And she was Helena.
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Because, (7y²z + 6yz²- 5 - 3yz² + 2)
= 7y²z + (6yz² - 3yz²) - (5 - 2)
= 7y²z + 3yz² - 3 (Answer)
240 grams of a 25% alcohol solution was mixed with 160 grams of a 40% alcohol solution. What is the percentage of alcohol in the new solution?
Answers
Answer:31%
Step-by-step explanation:look the pic
Answer:
31%
Step-by-step explanation:
The cost function for a company is C(x) = 90x + 1,800, where x is the number of bicycles produced at a cost of $90 each. How many bicycles can be produced for $3,780?
Answers
Answer:
22
Step-by-step explanation:
If the total cost of production can be explained with the function [tex]C(X)=1.800+90X[/tex], then when this total cost equals $3.780, we know that [tex]3.780=1.800+90X[/tex].Subtracting 1.800 both sides of the equation yields [tex]1.980=90X[/tex].Finally, dividing both sides by 90 gives us the value of X=22.Then, with $3780 we can produce 22 bicycles.you begin with $90 in your savings account and your friend begins
with $35 in her savings account. You deposit $10 in savings each
week, and your friend deposits $15 in savings each week.
a. Write and graph a system of linear equations that
represent the amounts in each of your savings
accounts
b. Your friend says that in 10 weeks you will both
have the same amount of money in your savings
accounts. Is your friend correct? Use the graph
from part (a) to explain your answer.
Answers
Answer:
F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.
F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.
When you graph the equations, plugging in different values for t, you can see that the graphs intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200. They will not have the same amount of money in 10 weeks.
Answer:
a. [tex]y=10x+90[/tex][tex]y=15x+35[/tex]
b. Your friend is wrong.Step-by-step explanation:
If you begin with $90 and add $10 each week, then we express it as
[tex]y=10x+90[/tex]
Where [tex]x[/tex] refers to weeks and [tex]y[/tex] refers to the total amount of money in you savings account.
On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is
[tex]y=15x+35[/tex]
Therefore, the sytem of linear equation that models this situation is
[tex]y=10x+90[/tex]
[tex]y=15x+35[/tex]
The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.
Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.
What is the answer to, (4-1) . n = n . _
Answers
Answer:
(4-1)•n=n•(4-1)
Step-by-step explanation:
It should equal each other so no matter what n equals it will equal each other :3
Step-by-step explanation:
Commutative property: a · b = b · a
(4 - 1) · n = n · (4 - 1)
Brandi jogged 2 1\2 miles in 30 minutes. Sharma jogged 3 1\2 miles in 3\4 hour. who jogged at slower rate
Answers
Answer:
The speed of Sharma is slower than the speed of Brandi
I.e ∵ 4.67 miles per hour [tex]<[/tex] 5 miles per hour
∴ [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]
Step-by-step explanation:
Given as :
The distance cover by Brandi = [tex]D_1[/tex] = 2 [tex]\frac{1}{2}[/tex] =[tex]\frac{5}{2}[/tex]
The Time taken by Brandi for jogging = [tex]T_1[/tex] = 30 minutes =[tex]\frac{1}{2}[/tex] hour
Let the speed of Brandi = [tex]S_1[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]
or, [tex]S_1[/tex] = [tex]\dfrac{\textrm [tex]D_1[/tex] }{\textrm [tex]T_1[/tex] }[/tex]
Or. [tex]S_1[/tex] = [tex]\frac{\frac{5}{2}}{\frac{1}{2}}[/tex]
∴ [tex]S_1[/tex] = 5 miles per hour
Again
The distance cover by Sharma = [tex]D_2[/tex] = 3 [tex]\frac{1}{2}[/tex] =[tex]\frac{7}{2}[/tex]
The Time taken by Sharma for jogging = [tex]T_2[/tex] = [tex]\frac{3}{4}[/tex] hour
Let the speed of Sharma = [tex]S_2[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]
or, [tex]S_2[/tex] = [tex]\dfrac{\textrm [tex]D_2[/tex] }{\textrm [tex]T_2[/tex] }[/tex]
Or. [tex]S_2[/tex] = [tex]\frac{\frac{7}{2}}{\frac{3}{4}}[/tex]
∴ [tex]S_2[/tex] = [tex]\frac{14}{3}[/tex] = 4.67 miles per hour
Now, ∵ 4.67 miles per hour [tex]<[/tex] 5 miles per hour
∴ [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]
So, Sharma jogged at slower late
Hence The speed of Sharma is slower than the speed of Brandi Answer
11. The sum of two numbers
is 29 and the difference of the
same two numbers is 15.
What are the two numbers?
Answers
Answer:
(22, 7)
Step-by-step explanation:
Let x and y be the unknown two numbers.
x+y=29
x-y=15
----------
2x=44
x=44/2
x=22
----------
22+y=29
y=29-22=7
x=22, y=7.
A groundskeeper needs grass seed to cover a circular field 290 feet in diameter
A store sells 50 pins bags of grass seed. One pound of grass seed covers about 400 square feet of field.
What is the smallest number of bags the groundskeeper must buy to cover the circular field?
Answers
Answer:
165
Step-by-step explanation:
First we need to find the area of the field, A = r^2 * pi
The radius is 290 / 2 = 145 feet
A = 145 * 145 * 3.14 = 66018.5 sqr feet
One bag covers 400 sqr feet
Divide the Area by 400 sqr feet to find number of bags needed.
66018.5 / 400 = 165
He will need at least 165 bags to cover the field
Answer:
4 bags
Step-by-step explanation:
We need to find the area of the circular field. To do this, we use the formula
A=piR^2 (pi multiplied by radius squared)
The radius is going to be 290/2 which is 145 which we plug into the equation.
A=pi145^2
The next step is to square 145, getting 21025. But now we need to multiply that by pi (3.14). We get 66018.5 as the answer.
Now we need to figure out how many square feet one bag can cover. To do this, we multiply 400 by 50 (because one pound can cover 400ft and one bag has 50 pounds). We get 20000 as the amount one bag of grass seed can cover. Now we need to divide 66018.5 by 20000. We get 3.300925. But the groundskeeper can't buy a decimal of a bag so we have to round up to 4 bags of grass seed.
we need to solve for Y
xy=5
Answers
Answer:
y=5/x
Step-by-step explanation:
Just divide by x on both sides to isolate y
Answer:
=2.5
Step-by-step explanation:
1.25×4+3×2 divided By (1/2) third power
Answers
Answer:
(1.25×4+3×2 )/((1/2)^3) = 88
Step-by-step explanation:
The solution to the equation 1.25×4+3×2 divided By (1/2) third power is 53 applying the order of operation PEMDAS.
Explanation:To solve 1.25×4+3×2 divided By (1/2) third power, we first have to follow the order of operation, that is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), also known as PEMDAS.
Step 1: Solve the expressions in parentheses and the exponent. As there's none, we move to the next step.
Step 2: Solve the multiplication and division.
1.25×4 equals 5, then 3×2 equals 6, and then 1/2, to the third power, equals 0.125.
So our equation now reads 5+6 divided by 0.125.
Step 3: Execute the division operation. 6 divided by 0.125 equals 48.
Our equation now reads 5 + 48.
Step 4: The last step is addition. 5 + 48 equals 53. So, the answer to the equation 1.25×4+3×2 divided By (1/2) third power is 53.
Learn more about Order of Operation here:https://brainly.com/question/15840745
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A rubber of length 89m is cut into 3 equal pieces. What is the length of each piece.
a) 8 /3. b)24/9
c)4 1/9 d) 8/27
Answers
Answer: i dont see the answer listed. The answer is 29 ²/₃m
Step-by-step explanation:
89m long piece of rubber is cut into 3 pieces. In other words, divided into 3 pieces.
89m ÷ 3 = 29.66666666m
Which concerts to 29²/₃m
A flock of 20 seagulls merges with a flock of cardinals. The new flock is bigger than either of the original ones, but still, it is no larger than 100 birds. How many birds were in the flock of cardinals?
Answers
There are 80 birds in the flock of cardinals.
Solution:Given:- A flock of 20 seagulls or we can say
Number of seagulls in a flock = 20
The new flock is no larger than 100 birds
So, let Total number of birds of new flock = 100
To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.
Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock
Number of birds in cardinal = 100 – 20 =80
Hence there are 80 birds in the flock of cardinals.
The answer explains how to determine the number of birds in the flock of cardinals based on the given conditions.
The number of birds in the flock of cardinals can be calculated as follows:
Let x be the number of birds in the flock of cardinals.
Since the new flock is no larger than 100 birds, the total number of birds after merging is 20 (seagulls) + x (cardinals).
Therefore, the equation to represent this situation is x + 20 ≤ 100, and solving for x, we get x ≤ 80. Thus, there were at most 80 birds in the flock of cardinals.
Name two pairs of congruent angles in the figure. Justify the answer.
Answers
Answer:
A and D
Step-by-step explanation:
Statement (A) and statement (D) are the two pairs of congruent angles in the figure.
What is the congruent figures?Congruent figures are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that:
The angles are shown in the picture.
It is required to name the two pairs of congruent angles in the figure.
From the figures:
According to the right angles congruent theorem, angle DIB and angle CIA
The right angles congruent theorem states that angle BIA and angle CIB are congruent.
Angle DIB and angle CIA according to the right angles congruent theorem
Angle BIA and angle CIB according to the right angles congruent theorem
Thus, statement (A) and statement (D) are the two pairs of congruent angles in the figure.
Learn more about the congruent figures here:
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If f(x)=2x^6+x^5+32x+32, is (x+2) a factor of f(x).
Answers
Answer:
No
Step-by-step explanation:
By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0
f(- 2)
= 2[tex](-2)^{6}[/tex] + [tex]-2)^{5}[/tex] + 32(- 2) + 32
= 2(64) - 32 - 64 + 32
= 128 - 32 - 64 + 32
= 64 ≠ 0
Hence (x + 2) is not a factor of f(x)
Answer: By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0
f(- 2)
= 2(-2)^{6} + -2)^{5} + 32(- 2) + 32
= 2(64) - 32 - 64 + 32
= 128 - 32 - 64 + 32
= 64 ≠ 0
Hence (x + 2) is not a factor of f(x)