recall your d = rt, distance = rate * time.
s = Samantha's speed rate
one thing to bear in mind is that, when Samantha is going upstream, she's not really going "s" mph fast, because she's going against the current, and the current's rate is 4 mph and subtracting speed from her, then she's really going "s - 4" fast.
Likewise, when she's going downstream because she's going with the current, the current is adding speed to her, so she's going "s + 4" fast.
Now, let's say the distance she covered both ways was the same "d" miles.
Let's recall that since there are 60 minutes in 1 hour, 12 minutes is 12/60 = 1/5 of an hour.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&d&s-4&1\\ Downstream&d&s+4&\frac{1}{5} \end{array}\qquad \implies \begin{cases} d=(s-4)(1)\\ d=(s+4)\left( \frac{1}{5} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{from 1st equation}}{\boxed{d}=s-4}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}~\hfill }{\boxed{s-4}=\cfrac{s+4}{5}\implies 5s-20=s+4} \\\\\\ 4s-20=4\implies 4s=24\implies s=\cfrac{24}{4}\implies s=6[/tex]
Answer:
6 mph
Step-by-step explanation:
Let the the total distance is D and the speed of Samantha's speed in still water is x ( in mph ),
Here, speed of stream = 4 mph,
Thus, the speed in upstream = (x - 4) mph,
Speed in downstream = (x + 4) mph,
We know that,
[tex]Speed =\frac{Distance}{Time}\implies Time =\frac{Distance}{Speed}[/tex]
∴ Time taken in upstream = [tex]\frac{D}{x-4}[/tex]
And, time taken in downstream = [tex]\frac{D}{x+4}[/tex]
According to the question,
[tex]\frac{D}{x-4}=1\implies D = x-4-----(1)[/tex]
[tex]\frac{D}{x+4}=\frac{12}{60}\implies \frac{D}{x+4}=\frac{1}{5}\implies 5D=x+4----(2)[/tex]
Equation (1) - 5 equation (2),
0 = x + 4 - 5x + 20
0 = -4x + 24
4x = 24
⇒ x = 6 mph.
Hence, Samantha swims with the speed 6 mph.
n triangle ABC, m∠A = 35° and m∠B = 40°, and a=9. Which equation should you solve to find b?
Answer:
[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex] should be used to find b.
Step-by-step explanation:
We are given that in a triangle ABC, ∠A = 35°, ∠B = 40° and side a = 9 and we are to find the side length b.
Now using sine rule to find b:
[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex]
[tex]\frac{sin 40}{b} = \frac{sin 35}{9}[/tex]
[tex]b=\frac{sin 40 \times 9}{sin 35}[/tex]
b = 10.1
Answer:
The equation is 9/sin(35) = b/sin(40) , The length of b = 10.086
Step-by-step explanation:
* Lets explain how to solve the triangle
- In ΔABC
- a, b, c are the lengths of its 3 sides, where
# a is opposite to angle A
# b is opposite to angle B
# c is opposite to angle C
- m∠A = 35°
- m∠B = 40°
- a = 9 ⇒ the side opposite to angle A
* To solve the triangle we can use the sin Rule
- In any triangle the ratio between the length of each side
to the measure of each opposite angle are equal
- a/sinA = b/sinB = c/sinC
∴ The equation which used to find b is a/sinA = b/sinB
∵ a = 9 , m∠A = 35° , m∠B = 40°
∴ 9/sin(35) = b/sin(40) ⇒ by using cross multiplication
∴ b = 9 × sin(40) ÷ sin(35) = 10.086
* The length of b = 10.086
Find the vertex of the parabol whose equatio is y =3x^2+6x+1
Answer:
(-1,-2)
Step-by-step explanation:
y=ax^2+bx+c
Find -b/(2a) and you will have found the x-coordinate of the vertex of this parabola.
You can find the y-coordinate that corresponds to it by plugging in your into the original equation.
-b/(2a)=-6/(2*3)=-6/6=-1
Now replace x with -1
3(-1)^2+6(-1)+1
3-6+1
-3+1
-2
So the vertex is (-1,-2)
What is the approximate area of the circle shown below? 17.5 in
A.962 m2
B.55 m2
C. 110 m2
D. 3848 m2
Answer:
No, the answer is actually a) 962
Step-by-step explanation:
In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population had increased to
approximately 1884 bears. If this trend continues and the bear population is increasing exponentially,
how many bears will there be in 2018?
Answer:
[tex]8,101\ bears[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
x ----> is the number of years since 2009
y ----> is the population of bears
a ----> is the initial value
b ---> is the base
step 1
Find the value of a
For x=0 (year 2009)
y=1,570 bears
substitute
[tex]1.570=a(b)^{0}[/tex]
[tex]a=1.570\ bears[/tex]
so
[tex]y=1.570(b)^{x}[/tex]
step 2
Find the value of b
For x=1 (year 2010)
y=1,884 bears
substitute
[tex]1,884=1.570(b)^{1}[/tex]
[tex]b=1,884/1.570[/tex]
[tex]b=1.2[/tex]
The exponential function is equal to
[tex]y=1.570(1.2)^{x}[/tex]
step 3
How many bears will there be in 2018?
2018-2009=9 years
so
For x=9 years
substitute in the equation
[tex]y=1.570(1.2)^{9}[/tex]
[tex]y=8,101\ bears[/tex]
Answer:
Step-by-step explanation:
Question 15
1 / 1 pts
In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population had increased to approximately 1884 bears. If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?
ANSWER = 8,101 GOT IT RIGHT ON TEST
(this is my sister on my acc I'm letting her) True or False? When you use a pulley you use less force to pull up a load.Explain your thinking below. btw im in grade four so no fancy words.
Answer:
True depending on what you are comparing it to.
Step-by-step explanation:
A pulley would help lighten the load that you are trying to pull up, which may make it easier for you to get the load to your designated area. The more complicated it is, usually the more 'lighter' it becomes, or the less force you have to exert.
For example, you will have to give a 100% energy in trying to life a heavy box. However, if you use a simple pulley (only one), you may only have to exert 75% more energy, for the weight is significantly lower.
~
If you run for 4 hours at 8 miles an hour and walk 8 hours at 2 miles an hour, how far will you have gone at the end
of 12 hours?
Make a Selection:
A. 48 miles
B. 50 miles
C. 32 miles
D. 60 miles
Answer:
4 hours at 8 miles an hour: 8(4) = 32 miles in total
8 hours at 2 miles an hour: 2(8) = 16 miles in total
Miles in total: 32 + 16 = 48
The answer is A. 48 miles
Answer: 48
Step-by-step explanation:
8 (MPH) x 4 (H) = 32 miles covered in 8 hours.
2(MPH) x 8 (H) = 16 miles covered in 8 hours.
32 + 16 = 48 MPH
Find the solution set of this inequality. Enter your answer in interval notation using grouping symbols. |8x-4| ≤ 12
[tex]|8x-4|\leq12\\4|2x-1|\leq12\\|2x-1|\leq3\\2x-1\leq3 \wedge 2x-1\geq-3\\2x\leq 4 \wedge 2x\geq-2\\x\leq 2 \wedge x\geq-1\\x\in \langle -1,2\rangle[/tex]
The solution set of the inequality |8x-4| ≤ 12 is [-1, 2]. The solution was found by breaking down the absolute value into two separate inequalities and solving them.
Explanation:To solve the inequality |8x-4| ≤ 12, we use the property that |a| ≤ b is equivalent to -b ≤ a ≤ b. So, the inequality can be rewritten as -12 ≤ 8x-4 ≤ 12. We then solve these two inequalities separately.
For -12 ≤ 8x-4, first add 4 to both sides to get -8 ≤ 8x, then divide by 8 on both sides to get x ≥ -1.
For 8x-4 ≤ 12, add 4 to both sides to get 8x ≤ 16, and then divide by 8 on both sides to get x ≤ 2.
Since x has to satisfy both these inequalities, the solution set is x ≥ -1 and x ≤ 2. In interval notation, this is represented as [-1, 2].
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y = x – 6 x = –4 what is the solution to the system of equations? (–8, –4) (–4, –8) (–4, 4) (4, –4
Answer:
(- 4, - 10 )
Step-by-step explanation:
Given the 2 equations
y = x - 6 → (1)
x = - 4 → (2)
Substitute x = - 4 into (1) for corresponding value of y
y = - 4 - 6 = - 10
Solution is (- 4, - 10 )
Answer:
the answer is b (-4,-8)
Step-by-step explanation:
i got it right top one is wrong
Find an equation for the line that passes through the point (-3,7) and is perpendicular to 3x-5y=80. Give your answer in point-slope form. Show as much work as possible to support your answer.
Answer:
y-7=-(5/3)(x+3)
Step-by-step explanation:
step 1
Find the slope of the line that is perpendicular to 3x-5y=80
we have
3x-5y=80
5y=3x-80
y=(3/5)x-16
The slope of the given line is m1=3/5
Remember that
If two lines are perpendicular, then the product of their slopes is equal to -1
so
m1*m2=-1
Find m2
(3/5)*m2=-1
m2=-5/3
step 2
Find the equation of the line into point slope form
y-y1=m(x-x1)
we have
m=-5/3
point (-3,7)
substitute
y-7=-(5/3)(x+3) ----> equation of the line into point slope form
Solve the equation: -3(h+5)+2=4(h+2)-9
For this case we must solve the following equation:
[tex]-3 (h + 5) + 2 = 4 (h + 2) -9[/tex]
We apply distributive property to the terms of parentheses:
[tex]-3h-15 + 2 = 4h + 8-9[/tex]
We add similar terms:
[tex]-3h-13 = 4h-1[/tex]
We add 13 to both sides of the equation:
[tex]-3h = 4h-1 + 13\\-3h = 4h + 12[/tex]
Subtracting 4h on both sides of the equation:
[tex]-3h-4h = 12\\-7h = 12\\h = - \frac {12} {7}[/tex]
ANswer:
[tex]h = - \frac {12} {7}[/tex]
Answer:
[tex]h=-\frac{12}{7}[/tex]
Step-by-step explanation:
To solve the equation for h follow the next steps
[tex]-3(h+5)+2=4(h+2)-9[/tex]
Subtract 4(h+2) on both sides of the equality
[tex]-3(h+5)+2-4(h+2)=4(h+2)-4(h+2)-9[/tex]
[tex]-3(h+5)+2-4(h+2)=-9[/tex]
Subtract 2 on both sides of the equality
[tex]-3(h+5)+2-4(h+2)-2=-9-2[/tex]
[tex]-3(h+5)-4(h+2)=-11[/tex]
Apply the distributive property
[tex]-3h-15 -4h-8=-11[/tex]
[tex]-7h-15 -8=-11[/tex]
[tex]-7h-23=-11[/tex]
Sum 23 on both sides of equality
[tex]-7h-23+23=-11+23[/tex]
[tex]-7h=12[/tex]
Divide by -7 on both sides of the inequality
[tex]\frac{-7}{-7}h=-\frac{12}{7}[/tex]
[tex]h=-\frac{12}{7}[/tex]
(دل) +
(2/5x+5/8)+(1/5+-1/4)
Answer:
[2x + 1\5] + ⅜
Step-by-step explanation:
Simply combine like-terms, then evaluate.
what number should be added to both sides of the equation to complete this square? x^2-10x=7
Answer:
The number is 25
Step-by-step explanation:
we have
[tex]x^{2} -10x=7[/tex]
we know that
[tex]10/2=5[/tex]
so
Adds [tex]5^{2}[/tex] both sides
[tex]x^{2} -10x+5^{2}=7+5^{2}[/tex]
[tex]x^{2} -10x+25=7+25[/tex]
[tex]x^{2} -10x+25=32[/tex]
Rewrite as perfect squares
[tex](x-5)^{2}=32[/tex]
What is the answer for this
Answer: [tex]y=\frac{1}{30}x+1[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
You need to find slope of the line with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Pick to points of the given line. You can choose the point (60,3) and the point (30,2).
Then, substituting into the formula:
[tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]
You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:
[tex]b=1[/tex]
Substituting the slope and the y-intercept found into [tex]y=mx+b[/tex], you get the equation of this line:
[tex]y=\frac{1}{30}x+1[/tex]
Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.
The officer stepped off 20 paces from E to G. If his pace is 2 1/2 feet long. How wide was the river?
Answer:
The wide of river is [tex]50\ ft[/tex]
Step-by-step explanation:
In this problem we know that
Triangles DEG and DEF are congruent by ASA (Angle-Side-Angle) Congruence
therefore
EG=EF
[tex]EG=20*(2\frac{1}{2})=20*\frac{5}{2}=50\ ft[/tex]
Simplify 9x + 12 –x + 4.
Answer:
8x+16
Step-by-step explanation:
What is the slope of the line y+2=-2(x-3)
Answer:
m = -2
Step-by-step explanation:
This equation is in point-slope form
The numbers added or subtracted by a variable are a coordinate point.
y + 2 --> (0,-2)
x - 3 --> (3,0)
(3,-2)
The slope is represented by the number outside of the parentheses.
Therefore, the slope of the line is -2
Answer:
-2
Step-by-step explanation:
This equation is written in point slope form
y-y1 = m(x-x1)
where (x1,y1) is a point on the line and m is the slope
y- -2 = -2(x -3)
A point on the line is (-3, -2) and the slope is -2
julie has $80 in her savings account and plans to save $x each month for 8 months.The expression $8x+$80 represents the total amount in the account after 8 months.Factor this expression
Answer:
[tex]8(x+10)[/tex]
Step-by-step explanation:
we have the expression
[tex](8x+80)[/tex]
we know that
[tex](8x+80)=(8x+8(10))[/tex]
Factor the number 8
[tex](8x+8(10))=8(x+10)[/tex]
therefore
The expression factored is [tex]8(x+10)[/tex]
The factorization of the given expression is given as:
[tex]8(x+10)[/tex]
Step-by-step explanation:To factor a algebraic equation means to represent it as the multiplication of the simple expressions.
( i.e. if the expression has a common multiple in each of the terms then we take it out and represent the rest of the expression in brackets.
Also, we can express a algebraic equation by the multiplication of the factors of the expression )
We are given a expression as:
[tex]8x+80[/tex] which represents the total amount in the account after 8 months.
and x represents the amount saved each month.
Since both the terms i.e. 8x and 80 have a common multiple as: 8
Hence, we take it out of the expression and write the resulting expression as follows:
[tex]8x+80=8(x+10)[/tex]
A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile.
How many deer live in the county? Round to the nearest whole number, if necessary.
deer
Answer:
5852 deer.
Step-by-step explanation:
That would be 11 * 532
= 5852 (answer).
Answer:
There are 5852 deer live in the county.
Step-by-step explanation:
The population density of deer in the county is 11 deer per square mile.
That means, there are 11 deer in 1 square mile in that county.
Given that, the total area of that county is 532 square miles.
For getting the total number of deer, we just need to multiply the 'population density' by the 'total area'.
So, the total number of deer [tex]=(11\times 532)= 5852[/tex]
how many weeks are in 3 years
Answer:
156.429
Step-by-step explanation:
52.1428571 in one year x 3
What is the sine ratio for
Remember:
SOH-CAH-TOA
(Sine = [tex]\frac{opposite}{hypotenuse}[/tex] - Cos = [tex]\frac{adjacent}{hypotenuse}[/tex] - tan = [tex]\frac{opposite}{adjacent}[/tex])
For angle H the sin ratio is...
side FG (5) is opposite angle H
side HF (13) is the hypotenuse
so...
sinH = [tex]\frac{5}{13}[/tex]
For angle F the sin ratio is...
side HG (12) is opposite angle F
side HF (13) is the hypotenuse
so...
sinF = [tex]\frac{12}{13}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Which mathematical statements are true?
1) If 3 is an odd number, then 3 times 3 is an even number.
2) If 6 is less than 7, then 4 is greater than 7.
3) Six is divisible by 3, and 10 is a multiple of 2.
4) The average of the data is greater than the largest value in the data, or it’s less than the largest value in the data.
5) The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.
6) If an equilateral triangle has equal angles, then all its angles will measure 45°.
Answer:
1) If 3 is an odd number, then 3 times 3 is an even number.
False because multiplying odd number by an odd number also gives an odd number.
2) If 6 is less than 7, then 4 is greater than 7.
False because 4 is smaller than 6. As 6 is smaller than 7 then 4 must also be smaller.
3) Six is divisible by 3, and 10 is a multiple of 2.
True. 6/3 = 2 and 2 x 5 = 10. Both the conditions are true so it is also true.
4) The average of the data is greater than the largest value in the data, or it’s less than the largest value in the data.
True.
We have two conditions in this statement and an 'or' between them. One of the conditions is true that is "average is less than the largest value in the data". So the statement as a whole is true.
5) The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.
True.
6) If an equilateral triangle has equal angles, then all its angles will measure 45°.
False.
A triangle has 3 angles whose sum = 180 degrees.
For equilateral triangle each angle will measure 180/3= 60 degrees.
Answer: 2 following statements are true
The first true statement:
Six is divisible by 3, and 10 is a multiple of 2.
We know this because 6 is divisible by 3, and again proven by when we divide 10 by 5 we get 2, so 10 is a multiple of 2.
The second true statement:
The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.
Step-by-step explanation:
WILL GIVE YOU BRAINLIEST if you answer correctly!!
which expression is equivalent to sqrt 128 x^8 y^3 z^9? assume y> 0 and z > 0
Answer:
Option (C): 8x^4yz^4√2yz
Step-by-step explanation:
Math. Give me Brainliest please?
Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.
Find the coordinates of midpoint D.
Answer:
Midpoint D (-a-b , c)
Third option
Step-by-step explanation:
Midpoint D
x = 1/2 (-2a - 2b) = -a - b
y = 1/2 (2c) = c
Midpoint D (-a-b , c)
Answer: (-a-b, c)
Step-by-step explanation:
We know that the mid point of a line having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by :-
[tex]x=\dfrac{x_1+x_2}{2}\ , \ y=\dfrac{y_1+y_2}{2}[/tex]
In the given figure it can be seen that D is the midpoint of RT :
Since R(-2b , 2c) and T(-2a, 0)
Then , the midpoint D of a line having endpoints [tex](-2b,2c)[/tex] and [tex](-2a,0)[/tex] is given by :-
[tex]x=\dfrac{-2b+(-2a)}{2}=\dfrac{2(-a-b)}{2}=-a-b\ , \ y=\dfrac{2c+0}{2}=c[/tex]
Hence , the coordinates of midpoint D = (-a-b, c)
Solve sin θ +1 = cos2 θ on the interval 0 less than or equal to θ less than 2pi
Answer:
The solution of the equation is Ф = 0 or Ф = 3π/2
Step-by-step explanation:
* Lets revise some facts in trigonometry
- The identity sin² Ф + cos² Ф = 1
- By subtracting sin² Ф from both sides then cos² Ф = sin² Ф - 1
- In the rectangular plane the point (x , y) represents (cos Ф , sin Ф)
where x = cox Ф and y = sin Ф
- The point (1 , 0) lies on the positive part of x-axis means cos Ф = 1
and sin Ф = 0, then Ф = 0 or 2π
- The point (-1 , 0) lies on the negative part of x-axis means cos Ф = -1
and sin Ф = 0, then Ф = π
- The point (0 , 1) lies on the positive part of y-axis means cos Ф = 0
and sin Ф = 1, then Ф = π/2
- The point (0 , -1) lies on the negative part of y-axis means cos Ф = 0
and sin Ф = -1, then Ф = 3π/2
* Lets solve the problem
∵ sin Ф + 1 = cos² Ф
- To solve we must change cos² Ф to sin² Ф
∵ cos² Ф = sin² Ф - 1
- substitute cos² Ф in the equation by 1 - sin² Ф
∴ sin Ф + 1 = 1 - sin² Ф ⇒ add sin² Ф to both sides
∴ sin² Ф + sin Ф + 1 = 1 ⇒ subtract 1 from both sides
∴ sin² Ф + sin Ф = 0
- Take sin Ф as a common factor from both terms
∴ sin Ф (sin Ф + 1) = 0
- Equate each factor by 0
∴ sin Ф = 0 OR sin Ф + 1 = 0
- Remember 0 ≤ Ф < π
∵ sin Ф = 0 ⇒ from the information above
∴ Ф = 0
∵ sin Ф + 1 = 0 ⇒ subtract 1 from both sides
∴ sin Ф = -1
- From the information above
∴ Ф = 3π/2
* The solution of the equation is Ф = 0 or Ф = 3π/2
A bird leaves its nest and travels 14 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour slower and has 6 miles left after x hours.
a. What is the distance of the entire trip?
miles
b. How long does the entire trip take? (In Hours Minutes and Seconds
Answer:36
Step-by-step explanation:
The given parameters include;
The speed of the bird in the forward trip = 20 m/hTime of motion = xThe speed of the bird in the backward trip in x hours = (20 - 4)m/h = 16 mi/h.Distance remaining to complete the backward trip = 6 miles.The time to complete each trip is calculated as;
distance =[tex]speed $\times$ time[/tex]
forward distance = backward distance
[tex]&20 x=16 x+6 \\[/tex]
[tex]&20 x-16 x=6 \\[/tex]
[tex]&4 x=6 \\[/tex]
[tex]&x=\frac{6}{4} \\[/tex]
[tex]&x=1.5 h r[/tex]
The total time of the motion for the entire trip exists calculated as follows;
Time = time for forward + time for backward
[tex]\text { time } &=1.5 \mathrm{hr} r_{\text {forward }}+1.5 \mathrm{hr} \text { backward }+\frac{6 \mathrm{mi}}{16 \mathrm{mi} / \mathrm{hr}} \text { backward } \\[/tex]
time [tex]&=2(1.5) \mathrm{hr}+0.375 \mathrm{hr} \\[/tex]
time[tex]&=3.375 \mathrm{hr}[/tex]
The time for the entire trip is 3.375 hours.
The total distance of the trip exists calculated as follows;
total distance = forward distance + backward distance total distance [tex]$=20 \times 1.5+16 \times 1.5+6$[/tex] miles
Total distance =60 miles
Therefore, the total distance of the trip is 60 miles.
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What is the true solution to 3ln2+ln8=2ln(4x)? a.x=1 b.x=2 c.x=4 d.x=8
Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log x + log y ⇔ log(xy)
• log [tex]x^{n}[/tex] ⇔ n log x
• log x = log y ⇔ x = y
Given
3ln2 + ln8 = 2ln(4x)
ln 2³ + ln8 = ln(4x)²
ln8 + ln8 = ln 16x²
ln(8 × 8) = ln 16x²
ln 64 = 16x², hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
y = 2x – 7
y = x – 7
Answer:
[tex]x=0[/tex]
[tex]y=-7[/tex]
Step-by-step explanation:
Let's use elimination.
We can multiply the second equation by -2 so that we can eliminate one variable from the system of equations.
[tex]-2(y=x-7)[/tex]
[tex]-2y=-2x+14[/tex]
Now we can use elimination and subtract.
[tex]y=2x-7[/tex]
[tex]-2y=-2x+14[/tex]
[tex]-y=7[/tex]
[tex]y=-7[/tex]
Now we can plug in the value of y into the first equation.
[tex]-7=2x-7[/tex]
[tex]2x=0[/tex]
[tex]x=0[/tex]
We can plug these values to check.
[tex]-7=0-7[/tex]
[tex]-7=0-7[/tex]
Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 – 3x – 20x + 4. Her work is shown below. (15x2 – 3x) + (–20x + 4) 3x(5x – 1) + 4(–5x + 1) Talia noticed that she does not have a common factor. What should she do?
Answer:
Factor out a -1 from one of the terms so they are the same
Step-by-step explanation:
15x^2 – 3x – 20x + 4
(15x2 – 3x) + (–20x + 4)
3x(5x – 1) + 4(–5x + 1)
Talia should notice that the terms in the parentheses are opposites of each other and factor out a -1 out of the second term
3x(5x-1) +4 (-1) (5x-1)
Now the terms have a common factor
(5x-1) (3x+(-1)4)
(5x-1) (3x-4)
Answer:
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Step-by-step explanation:
[tex]15x^2 - 3x - 20x + 4[/tex]
Group first two terms and last two terms to factor it
[tex](15x^2 - 3x)+(- 20x + 4)[/tex]
Now we factor out GCF
GCF of 15x^2-3x is 3x
GCF of -20x+4 is -4 because first term should be positive
[tex](15x^2 - 3x)+(- 20x + 4)[/tex]
[tex]3x(5x- 1)-4(5x-1)[/tex]
Talia needs to factor out negative so that the binomials will be same (5x-1)
What is the quotient of 4536 and 36?
Answer:
126.
Step-by-step explanation:
Using long division:
1 2 6
---------
36 ) 4536
36
---
93
72
---
216
216
----
Answer:
126
Step-by-step explanation:
you divide 4536 and 36 and you get 126 as your quotient
NEED HELP ASAP
The equation yˆ=−2.5x+222.5 models the amount of cholesterol, LDL , for a person, in mg/dl , where x is the time spent exercising per day, in minutes.
According to the regression equation, what is the amount of cholesterol for a person exercising 20 minutes a day?
A. 61.5 mg/dl
B. 81.5 mg/dl
C. 172.5 mg/dl
D. 272.5.5 mg/dl
Answer:
172.5 mg/dl
Step-by-step explanation:
Given the equation y= -2.5x + 222.5, where 'x' is the time spent exercising in minutes. If we want to know the amount of cholesteron for a person exercising 20 minutes a day, we just have to subtitute 20 into the equation for x.
So we have: y= -2x + 222.5 → y= -2.5(20 minutes) + 222.5 = 172.5 mg/dl
Answer:
172.5
Step-by-step explanation:
Confirmed on test