Answer:
∠ 3 = 90°
Step-by-step explanation:
∠ 3 and ∠ 4 are adjacent angles on a straight line and sum to 180° , then
∠ 3 + ∠ 4 = 180°
∠ 3 + 90° = 180° ( subtract 90° from both sides )
∠ 3 = 90°
What is the quotient of the synthetic division problem below, written in polynomial form?
-1| 1 7 15 9 7
Answer:
Step-by-step explanation:
If we have 5 terms to the right of the -1 outside the box thing, that means that our original polynomial is a 4th degree (the degree is one lower than the number of terms in order to allow for the constant which has no variable). Set up the synthetic division as shown in the problem. The rule is to bring down the first term, the 1 to the right of the box, multiply it by the number outside, -1, and put that product up under the next number in line inside the box. Like this:
-1 | 1 7 15 9 7
-1
1
Now add straight down, multiply the sum by -1 and put that product up under the next term in line, the 15:
-1 | 1 7 15 9 7
-1 -6
1 6
Then add straight down again, multiply the sum by -1 and put that product up under the next term in line, the 9:
-1 | 1 7 15 9 7
-1 -6 -9
1 6 9
Then do the same thing. Add straight down, multiply the sum by -1 and put the product up under the next term in line, the 7:
-1 | 1 7 15 9 7
-1 -6 -9 0
1 6 9 0 7
This is the final result. The last number, the 7 is the remainder, but the rest of it makes up what we call the depressed polynomial and is a polynomial that is one degree less than the degree we started with. So this depressed polynomial is a 3rd degree. The numbers are the coefficients on the x terms:
[tex]1x^3+6x^2+9x+0R7[/tex] or more simply stated:
[tex]x^3+6x^2+9xR7[/tex]
How many index laws are there?
Answer:
There are three laws of indices.
Samuel played a video game. He gained some points, lost 87 points, and
finished with less than 320 points, Which of the following inequality
represents the given situation?
A.) n-87 < 320
B.) N + 87 < 320
C.) N-87 = 320
D.) n +87= 320
Answer:
A
Step-by-step explanation:
The correct inequality that represents the given situation is: A.) n - 87 < 320.
How to explain the equationThe situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.
Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.
Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.
This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.
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F={(-1, 2), (3, 2), (4,2), (0, 2)} Is Fa function and why/why not?
Answer:
yes it is a function A
Step-by-step explanation:
A ball is thrown vertically with a velocity of18 m/s. It’s height, h, in meters above the ground after t seconds is given by the equation: h= -5t2+10t+35. Algebraically, determine the following.
Find The maximum height of the ball and the time it takes to reach that height
The time it takes the ball to hit the ground.
PLEASE HELP!
Answer:
Step-by-step explanation:
First of all, something is wrong with either the wording in the problem or the equation that you wrote; if the upward velocity is 18, we should see 18t in the equation, not 10t. I solved using 10t.
To find the max height of the ball and the time it took to get there, we need to complete the square on this quadratic and solve for the vertex. That will give us both of those answers in one!
To complete the square, set the quadratic equal to 0 and then move over the constant, like this:
[tex]-5t^2+10t=-35[/tex] The rule is that we have to have a 1 as the leading coefficient, and right now it's a -5, so we factor that out, leaving us with:
[tex]-5(t^2-2t)=-35[/tex] and now we are ready to begin the process to complete the square.
The rule is: take half the linear term, square it, and add it to both sides. Our linear term is a -2 (from the -2t); half of -2 is -1, and -1 squared is 1. We add in a one to both sides. BUT when we put the 1 into the set of parenthesis on the left, we didn't just add in a 1, we have that -5 out front that is a multiplier. That means that we actually added in a -5 after it's all said and done.
[tex]-5(t^2-2t+1)=-35-5[/tex] and we'll clean that up a bit. The right side is easy, that's a -40. The left side...not so much.
The reason we complete the square is to put this quadratic into vertex form. Completing the square creates a perfect square binomial on the left, which for us is, along with the simplification on the right:
[tex]-5(t-1)^2=-40[/tex]
Lastly, we move the -40 back over by adding and setting the quadratic back to equal y:
[tex]-5(t-1)^2+40=y[/tex] and we see that the vertex is (1, 40). That translates to a height of 40 meters at 1 second after launch. That's the vertex which, by definition, is the max or min of the parabola. Because our parabola is negative, the vertex for us is a max.
To find out how long it takes the ball to hit the ground, set the quadratic equal to 0 and factor however it is you are currently doing this in class. You can continue to factor from the vertex form we have the equation in if you'd like. Let's do that, since we are already most of the way there. Begin here:
[tex]-5(t-1)^2=-40[/tex] and divide both sides by -5 to get
[tex](t-1)^2=8[/tex] and take the square root of both sides to "undo" that squaring on the left:
t - 1 = ±√8. Now add 1 to both sides to isolate the t:
t = 1 ± √8. In decimal form:
t = 1 + √8 is 3.828 seconds and
t = 1 - √8 is -1.828 seconds.
Since we all know that time will NEVER be a negative value, the time it takes the ball to hit the ground is 3.828 seconds.
Lucia gave Brenda half of the cash she had in the store counter at the end of the day. Brenda put the money in her purse and added one half of the amount she had from her own savings. Brenda had saved half of what Lucia earned in the store that day. Brenda took her purse and went to the dog shelter and brought food and treat packet for 5 dogs. Each packet cost her $15. How much money did Lucia earn at the store that day?
Answer:
$100
Step-by-step explanation:
The amount Lucia gave Brenda = Half the amount in the store counter
The amount Brenda added to the money Lucia gave her = Half the amount in her (Brenda) savings
The amount Brenda had saved = Half of the amount Lucia earned in the store that day
The number of food and treat packets Brenda bought = 5
The cost of each packet = $15
Let x represent the amount Lucia earned and let y represent the amount Brenda saved
We have;
x/2 = y
x/2 + y/2 = 15 × 5 = 75
Therefore, we get;
y + y/2 = 75
(3/2)·y = 75
y = 75 × 2/3 = 50
y = 50
From x/2 = y, we have;
x/2 = 50
x = 2 × 50 = 100
The amount Lucia earned in her store that day, x = $100
1 by 8 of the passenger of a train where children is there where 40 children traveling in the train on a Saturday how many Abbott were there in that that day?
Answer:
200 adults
Step-by-step explanation:
1/8 of the passengers (children) is 40
Total passengers in the train is 8/8
Therefore to get the total number of passengers is given by
(8/8) × 40 × (8/1)
= 240 passengers
Adults in the train = Passengers - Children
= 240 - 40
= 200 adults
If you roll a standard number cube 42 times, how many times do you expect the cube to show a five?
Round your answer to the nearest whole number if needed.
Answer:
5
Step-by-step explanation:
this is probability
probability of 5 occuring once is = 5/42=0.119
therefore, probability of 5 occuring in 42 times is;
42 x 0.119=4.998
approximately 5
There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that
the first horse selected is tan and the second horse selected is brown?
20/81
5/18
2/9
1/20
Answer:
5/18
Step-by-step explanation:
The total number of horses present is 9
The probability that the first selected horse is tan is 4/9
So , now for the second choice , we are left with 8 total horses of which 5 is brown
The probability is 5/8
So the joint probability is the product of this two
That will be;
5/8 * 4/9 = 5/18
To make a disinfecting solution, Alana mixes 2 cups of bleach with 5 cups of
water. What is the ratio of water to the total amount of disinfecting solution?
Answer:
Step-by-step explanation:
Ok
Second time posting this. Please help!! :)
Answer:
Step-by-step explanation:
[tex]\frac{480+24(x-40)}{x}[/tex]
The numerator of the rational expression the money he earned for 'x' hours
The rate at which William is paid for each hour in excess of 40 hours 24.
x = 50 hours = (40 + 10 ) hours
The amount paid for excess 10 hours = 24 *10 = 240
Total amount earned for the week = 480 + 240 = 720
A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet
Answer:
Step-by-step explanation:
starting point: 140 feet below sea level.=-140
she then decends= 7(4.5)=31.5
-140-31.5=-171.5
finally she ascends 112.2 feet
-171.5+112.2=-59.3 feet or 59.3 feet below sea level
Answer:
It's B
Step-by-step explanation:
Three events A, B and C are defined over a sample space, S. Events A and B are independent. Events A and C are mutually exclusive. Given that P(A)= 0.04, P(B)=0.25, P(C)=0.20 and P(B/C)=0.15. Find for P(C/B)
Answer:
[(b/c)=0.15)]
Step-by-step explanation:
===================================================
Work Shown:
P(B/C) = P(B and C)/P(C) ... conditional probability formula
P(B and C) = P(C)*P(B/C)
P(B and C) = 0.20*0.15
P(B and C) = 0.03
------------
P(C/B) = P(C and B)/P(B) .... note the swap of B and C
P(C/B) = P(B and C)/P(B)
P(C/B) = (0.03)/(0.25)
P(C/B) = 0.12
------------
Extra notes:
The fact that events A and B are independent is not relevant.The fact A and C are mutually exclusive isn't used here either.This problem can be solved through Bayes' Theorem.Another alternative you can do is to set up a 3 by 3 contingency table to help solve this problem.Solve the proportion.
14
y +9
-
10
15
y = [?]
Answer:
y=12
Step-by-step explanation:
14 10
----- = --------
y+9 15
Using cross products
14*15 = 10 (y+9)
210 = 10(y+9)
Divide by 10
210/10 = 10(y+9)/10
21 = y+9
Subtract 9
21-9 = y
12 =y
A rectangle is twice as long as it is wide. Its width is 51⁄2 cm. Find the area of the rectangle.
Step-by-step explanation:
The are of rectangle is 1300.5cm2
In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be
chosen for early release. How many 4-person groups are possible?
two because there is 11 people in total and you have two 4 person groups so that would leave 3 people left and you cant make a 4 person group w 3 people
Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.
If in a jail cell, there are 5 Democrats and 6 Republicans, the possible ways to form a group of 4 is 330.
The number of possible groups is 330.
What is combination?Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.
It is given as:
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
We have,
The total number of people:
5 Democrats and 6 Republicans = 5 + 6 = 11.
The number of persons in a group = 4.
The number of groups possible are:
= [tex]^{11}C_4[/tex]
= 11! / 4! ( 11-4)!
= 11! / 4! 7!
= 11 x 10 x 9 x 8 / 4 x 3 x 2
= 330
Thus,
The number of possible groups is 330.
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please help i will give brainliest (check both images)
Answer:
Amanda's box holds more popcorn.
Amanda's box holds 70 m³ more than Mary's.
Step-by-step explanation:
Find the volume of both boxes.
13.5 x 10 x 10 = 1350.
20 x 8 x 8 = 1280.
As clearly shown, Amanda's box holds more popcorn.
To find how much more, subtract 1,280 from 1,350 to get 70 m³.
Hope this helps!
If there is something wrong, please let me know.
Make a documentary on the “Journey of Coronavirus” OR Conservation of Plants and Animals. Give an appropriate name for your documentary.
PLSS REPLY FAST
Answer:
Explanation is as follows;
Step-by-step explanation:
Fundamentals to Plant and Animal Preservation
Plants and animals are the foundation of life on Earth; it is critical to protect them from extinction by maintaining a healthy population that contributes to global biodiversity, or the variety of flora and wildlife.
Everyone in the area must actively participate in planting additional trees and preventing countless trees from being chopped down. Deforestation is the practise of chopping down trees and making a forestland barren and unsuitable for animals and birds to live in.
Shelley drove from New Haven, Connecticut, to New York City in 90 minutes. Which equation relates the distance she traveled to her speed?
a.distance = speed + 90
b.distance = speed × 90
c.distance − speed = 90
d.distance × 90 = speed
Answer:
b
Step-by-step explanation:
d = r * t
None of them are really correct, but the closest one is B. Look at the equation. Rate is multiplied by time. The result is distance.
The 90 minutes should be changed to hours. No speedometer on a car is rated in feet per second.
PLEASEEEE HELP, how do i draw this ?
Answer:
/ - - - - - - - - -- - - -
/ \
/ \
/ \ _________
/
_/
What is the factored form of
Answer:
C
Step-by-step explanation:
You can distribute the values or even plug in x=2 and see which one matches.
Which expression is a sum of cubes
Answer: what is the rest of the question?
Step-by-step explanation:
need help solving the equation, trying to figure whether I multiply or divide.
Answer:
m∠B = 43°
b = 26.1
c = 38.3
Step-by-step explanation:
By applying triangle sum in the given triangle,
47° + 90° + m∠B = 180°
137° + m∠B = 180°
m∠B = 43°
By applying sine ratio to the angle measuring 47°.
sin(47°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{28}{c}[/tex]
c = [tex]\frac{28}{\text{sin}(47^{\circ})}[/tex]
c = 38.28
c ≈ 38.3
By applying cosine rule,
cos(47°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{b}{c}[/tex]
= [tex]\frac{b}{38.3}[/tex]
b = 38.3[cos(47°)]
b = 26.1
The radius of the circle below intersects the unit circle at (3/5 • 4/5)What is the approximate value of e?
Answer:
do you have a pic of it but i think its 15.75
Step-by-step explanation:
What are the restrictions on the domain of the following function?
f(x)=x-3/(x-3)(x-4)(x-5)
Answer:
Step-by-step explanation:
C
Identify the segments that are parallel, if any, if ∠DCB and ∠CDA are supplementary.
Answer:
C
Step-by-step explanation:
We are given that
[tex]\angle[/tex]DCB and [tex]\angle[/tex]CDA are supplementary.
We have to identify the parallel segments if [tex]\angle[/tex]DCB and [tex]\angle[/tex]CDA are supplementary.
Supplementary angles: If the angles are supplementary then the sum of two angles is 180 degrees.
Therefore,
[tex]\angle DCB+\angle CDA=180^{\circ}[/tex]
Therefore, angle DCB and angle CDA are interior angles .
Because CA is a transversal line and sum of interior angles is 180 degrees.
When the sum of interior angles formed between two lines and on same side of transversal line is 180 degrees. Then the lines are parallel.
Therefore, angle DCB and angle CDA are formed between line AD and BC.
Hence, AD is parallel to BC.
Option C is correct.
Answer:
c
Step-by-step explanation:
i had the same question
Which value is equivalent to x +4/4+x?
–4
–1
1
4
Hi! Please help me im really confused >.< tysm
g² - 4g = -3
Answer:
g = 1, 3
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
g² - 4g = -3
Step 2: Solve for g
[Addition Property of Equality] Add 3 on both sides: g² - 4g + 3 = 0Factor: (g - 1)(g - 3) = 0Solve: g = 1, 3How do I do this question
Answer:
Graph:
Solution: (1, 1)
Check:
y = -3x +4
1 = -3 +4
1 = 1
y = 3x -2
1 = 3 -2
1 = 1
Renata moved to her new home a few years ago. Back then, the young oak tree in her back yard was 190190190 centimeters tall. She measured it once a year and found that it grew at a constant rate. 333 years after she moved into the house, the tree was 274274274 centimeters tall.
Answer:
I know the answer...
Step-by-step explanation:
but i dont know the question (i also dont know how to comment so i have to do it as an answer)... thanks
