Determining the Solution
Find the solution to the system of equations: x + 3y = 7
and 2x + 4y = 8
1. Isolate x in the first equation:
2. Substitute the value for x into the second equation:
3. Solve for y:
x = 7 - 3y
207 – 3y) + 4y = 8
14-6y + 4y = 8
14 – 2y = 8
-2y = -6
y = 3
x + 3(3) = 7
4. Substitute y into either original equation:
5. Write the solution as an ordered pair:
Intro
Done
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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]

Answer:

The division was completed in the wrong order

Step-by-step explanation:

To convert [tex]\frac{5}{8}[/tex] to a percent

The numerator is divided by the denominator, that is

    0.625

8 | 5.0

Multiply 0.625 × 100% = 62.5%

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.

~

Answer:

[2x + 1\5] + ⅜

Step-by-step explanation:

Simply combine like-terms, then evaluate.

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

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)

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

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)

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]

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

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

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]

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

Answer:

8x+16

Step-by-step explanation:

Answer:36

Step-by-step explanation:

The given parameters include;

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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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]

Answer:

Part a) The elevation of the road is [tex]6\°[/tex]

Part b) The rise is [tex]0.2\ km[/tex]

Step-by-step explanation:

Part a) What is the elevation of the road to the nearest degree?

Let

y-----> the rise of the road ( vertical distance)

x ----> the run of the road (horizontal distance)

we have

y/x=1/10

we know that

The ratio y/x is equal to the tangent of the angle of the elevation of the road

Let

[tex]\theta[/tex] ---->  angle of the elevation of the road

[tex]tan(\theta)=y/x[/tex]

[tex]tan(\theta)=1/10[/tex]

[tex]\theta=arctan(1/10)=6\°[/tex]

Part b)  If the road is two km long, how much does it rise?

using proportion

[tex]1/10=y/2[/tex]

[tex]y=2/10=0.2\ km[/tex]

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

Answer:

Option (C): 8x^4yz^4√2yz

Step-by-step explanation:

Math. Give me Brainliest please?

Answer:

No, the answer is actually a) 962

Step-by-step explanation:

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]

Answer:

Step-by-step explanation:

-5x+31+3x=3

move everthing to one side

-5+31+3x-3=0

add and subtract common terms

-2x+28=0

divide across by common denominator

-x+14=0

Solve for x

x=14

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

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]

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]

[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.

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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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

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

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

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)

Answer:

156.429

Step-by-step explanation:

52.1428571 in one year x 3