Section #1: Solvi
1) Find the solution to each equation.
A) 4(2x - 1) = -3x + 32
Section​

The factorization of the expression 2b + 8 is 2 ( b + 4 ).

Given data:

The expression is represented as 2b + 8.

To factor out the coefficient of the variable in the expression 2b + 8, determine the greatest common factor (GCF) of the terms.

The GCF of 2b and 8 is 2.

So, divide each term by 2 to factor out the coefficient:

2b + 8 = 2(b) + 2(4)

Now, rewrite the expression factored out:

2b + 8 = 2(b + 4)

Hence, the expression 2b + 8 factored is 2(b + 4).

To learn more about factorization, refer:

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The point located 3/5 of the way from point A(4, 5) to point B(-6, 0) on line segment BA is at (0, 3). This is found using the formula for division of a line segment at given ratio.

The subject of this question is Geometry, specifically finding the coordinates of a point along a line segment. Line segment BA has coordinates B(-6, 0) and A(4, 5). To find the point located 3/5 of the way from point A to point B, we will need to use the formula for the division of a line segment which is: X = x1 + r(x2 - x1) and Y = y1 + r(y2 – y1), where r is the ratio, in this case 3/5.

Using the formula, the x coordinate of the point can be calculated as: X = (-6) + 3/5 [(4) - (-6)] = -6 + 3/5 * 10 = -6+6 = 0. The y coordinate of the point can be calculated as: Y = 0 + 3/5 [(5) - 0] = 0 + 3 = 3. Therefore, the point is at (0,3) which is located 3/5 of the way from point A to point B on the line segment.

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Final answer:

The coordinates of the point located 3/5 of the way from point A to point B are (0, 3), calculated by finding the weighted average of the x and y coordinates of the endpoints.

Explanation:

To find the coordinates of the point located 3/5 of the way from point A to point B, we need to calculate the weighted average of the endpoints. The coordinates of point B are (-6, 0) and the coordinates of point A are (4, 5).

The x-coordinate of the point is calculated as follows:
(-6) + ((4 - (-6)) × (3/5)) = (-6) + (10 × (3/5)) = (-6) + 6 = 0.

The y-coordinate of the point is calculated as follows:
0 + ((5 - 0) × (3/5)) = 0 + (5 × (3/5)) = 3.

Therefore, the coordinates of the point located 3/5 of the way from point A to point B are (0, 3).

Answer:

Teo is 5 and Richard is 12

Step-by-step explanation:

r+t=17

2t+2=r

2t+2+t=17

3t+2=17

3t=15

t=5

r+5=17

r=12

Answer:

i believe it would be 36

Answer:36

Step-by-step explanation:

There were 9 cats on the shelter on thursday

Solution:

Let "a" denote number of cats

Let "b" denote number of dogs

Cost per day for each cat = $ 4.50

Cost per day for each dog = $ 8.50

Given that Violet found a record showing that there were a total of 30 cats and dogs on Thursday

Thus, number of cats + number of dogs = 30

a + b = 30  ------ eqn 1

Also given that Violet noticed that the shelter spent $219.00 caring for cats and dogs on Thursday

Number of cats x cost per day for each cat + Number of dogs x cost per day for each dogs = $ 219

[tex]a \times 4.50 + b \times 8.50 = 219[/tex]

4.5a + 8.50b = 219  ----- eqn 2

Multiply first equation by 4.5

4.5a + 4.5b = 135  ---- eqn 3

Subtract eqn 2 from eqn 3

4.5a + 4.5b = 135

(-)4.5a + 8.50b = 219

---------------------------------

-4b = -84

b = 21

Substitute this y value into the first equation

a + b = 30

a + 21 = 30

a = 9

Thus "a" denotes number of cats, so number of cats on thursday = 9

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.03}{2}\right)^{2\cdot 5}\implies A=4000(1.015)^{10}\implies A\approx 4642.16[/tex]

Answer:

x = 20

Step-by-step explanation:

-7 (2) = -14 so...

10 (2) = 20

None of the given expressions (0.375 x 0.5, 0.625 x 0.5, 0.5 x 0.5, 4/5 x 1/2, 3/8 x 1/2) have the same product as 3 x 0.5, which equals 1.5.

To find out which expressions have the same product as 3 x 0.5, we first need to determine the product of 3 x 0.5. This is easy to do: 3 x 0.5 equals 1.5.

Now, let's check the given expressions:

As we can see, none of these expressions equals 1.5. Thus, none of them have the same product as 3 x 0.5.

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Answer:

12.45 pm

7.30 pm

00 00

20 15

Answer:

96/5

Hope this helps!

Answer:

The second method gives the greater heart rate.

Step-by-step explanation:

In the second method, the age and heart rate(bpm) are in a linear relationship.

Therefore, the maximum heart rate for a 90-year-old person in the second method is = 194 - (194 - 187)7 = 145 bpm.

{Since, the maximum heart rate in the second method decreases in an A.P. having value at the age of 20 is 194 and it decreases by 7 bpm per 10 years}

Now, in the first method, the maximum heart rate for 90-year-old person is y = 220 - 90 = 130 bpm.

Therefore, the second method gives a greater heart rate. (Answer)

Answer:

Step-by-step explanation:

The given expression is

[tex]y=220-x[/tex]

Where [tex]x[/tex] is age.

Now, for [tex]x=90[/tex], we have

[tex]y=220-90=130[/tex]

The equation gives 130 bpm for a 90-year-old patient.

Now, if we observe the given table, we would find a pattern there. The heart rate decreases by 7 while ages decreases by 10, so

For 60 y/o we have 166 bpm.

For 70 y/o we have 159 bpm.

For 80 y/o we have 152 bpm.

For 90 y/o we have 145 bpm.

If we compare, the second method (table) gives the greater heart rate.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{4(3x^2y^4)^3}{(2x^3y^5)^4}\implies \cfrac{4(3^3x^{2\cdot 3}y^{4\cdot 3})}{(2^4x^{3\cdot 4}y^{5\cdot 4})}\implies \cfrac{4(27)x^6y^{12}}{16x^{12}y^{20}}\implies \cfrac{108x^6y^{12}}{16x^{12}y^{20}} \\\\\\ \cfrac{108}{16x^{12}x^{-6}y^{20}y^{-12}}\implies \cfrac{108}{16x^{12-6}y^{20-12}}\implies \cfrac{27}{4x^6 y^8}[/tex]

Expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]

Need to use distributive property to write the expanded form of 3(6 + 7)

Let’s understand what is distributive property.

The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

According to distributive property, for numbers a , b and c

[tex]a(b+c)=a \times b+b \times c[/tex]  ----- eqn 1

3(6 + 7) can be rewritten as 3 ( 6 + 4 + 3 ) = 3 ( 10 + 3 )

Now in our case a = 3 , b = 10 and  c = 3  

On substituting the values of a , b and c in equation 1 we get

[tex]3(10+3)=3 \times 10+3 \times 3=3 \times 10+9 \times 1[/tex]

So expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]

Answer:

Temperature of the ice for ice-skating = -5 °C

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Temperature of the ice for an ice hockey match = - 7 °C

Temperature for ice- skating is 2 degrees warmer.

2. What is the temperature of the ice for ice-skating?

For the correct calculation, we use this formula:

Temperature for ice-skating = Temperature of the ice for a hockey match + 2

Temperature for ice-skating = -7 + 2

Temperature of the ice for ice-skating = -5 °C

We add 2 to the temperature of the ice for a hockey match because the temperature for ice-skating is described as warmer. If it were described as colder, we should subtract.

Answer:

-5c

Step-by-step explanation:

because basically  you subtract because it is below normal

Answer:

Step-by-step explanation:

20y - 60 = 5x

add 60 to both sides:

20y = 5x + 60

divide through by 20:

y = (1/4)x + 3

slope = 1/4

y-intercept = (0, 3)

Answer:

The average speed of the first plane is 315 mph and that of the second plane is 105 mph.

Step-by-step explanation:

Let us assume that the first plane has speed x mph and that of the second plane is y mph.

So, as per given condition x = 3y ......... (1)

Now, given that after traveling in the same direction for 7.5 hours, they are 1575 miles apart.

So, we write the equation as  

7.5x - 7.5y = 1575

⇒ x - y = 210 ........ (2)

Now, solving equation (1) and (2) we get, 3y - y = 210

⇒ 2y = 210

⇒ y = 105 mph

So, from equation (1) we get, x = 3y = 315 mph.

So, the average speed of the first plane is 315 mph and that of the second plane is 105 mph. (Answer)

Answer:

5

Step-by-step explanation:

(-3)(2)-7(-3)-10

-6+21-10

15-10

5

Answer:

then he would made an 85 bc he wouldve got 5 points added on to his quiz

So this is the answer...

Hope this can help :)

Answer:

0.2 Newtons

Step-by-step explanation:

Newton's Second Law of Motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Newton's Second Law formula:

F = m * a

Where:

F: the magnitude of the net force, in N

m: the mass of the object, in Kilogram

a: the acceleration of the object, in m/s2

Answer:

Step-by-step explanation:

Givens

[tex]m=100 gr[/tex]

[tex]a= 2m/s^{2}[/tex]

First, we need to transform the mass to kilograms, we know that 1 kilogram equals 1000 grams.

[tex]100gr\frac{1kg}{1000gr} =0.1 kg[/tex]

Then, by Newton's Second Law, we have

[tex]F=ma[/tex]

Replacing each variable

[tex]F=0.1kg(2m/s^{2} )\\F=0.2 N[/tex]

Therefore, the force on this wagon is 0.2 Netwons.

Answer:

-1/2 = n

Step-by-step explanation:

2/3(1+n) = -1/2n

2/3 + 2/3n = -1/2n

2/3 + 2/3n - 2/3n = -1/2n

2/3 = -1/2n -2/3n

2/3 = -.5n -.66n

2/3 = -1.16n

2/3/-1.16 = n

.66 - 1.16 =n

-0.5=n

- 1/2 = n

Answer:

x = -1

Step-by-step explanation:

Let's solve your equation step-by-step.

7x + 12 = 2(1 − x) − x

Step 1: Simplify both sides of the equation.

7x + 12 = 2(1 − x) − x

7x + 12 = (2) (1) + (2) (− x) + − x (Distribute)

7x + 12 = 2 + − 2x + − x

7x + 12 = (− 2x + − x) + (2) (Combine Like Terms)

7x + 12 = − 3x + 2

7x + 12 = − 3x + 2

Step 2: Add 3x to both sides.

7x + 12 + 3x = − 3x + 2 + 3x

10x + 12 = 2

Step 3: Subtract 12 from both sides.

10x + 12 − 12 = 2 − 12

10x = − 10

Step 4: Divide both sides by 10.

10x/10 = - 10/10

x = - 1

Hope this helps! Sorry if it is confusing!

Answer:

- 2 < x < 4

Step-by-step explanation:

We have to write in interval notation of the following interval.

The interval is given by (-2,4) which means the values of the variable, say x, vary from -2 (but not including -2) to 4 (but not including 4).

So, in interval notation this can be written as - 2 < x < 4 (Answer)

Therefore, the values -2 and 4 are the limiting end values of the variable x.

Answer:

r(x) = -7

Step-by-step explanation:

r(x) = -x - 7

+ 7 + 7

7 = -x

÷ -x ÷ -x

7/-1 = x

-7 = x

Answer: 4 and 5/18

Step-by-step explanation: In this problem, we have 7/6 divided by 3/11. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction.

So here, 7/6 ÷ 3/11 can be rewritten as 7/6 × 11/3.

Now we are simply multiplying fractions so we multiply across the numerators and multiply across the denominators.

So we have 7 × 11 which is 77 and 6 × 3 which is 18.

Now we have the fraction 77/18.

We can write 77/18 as a mixed number by dividing the denominator of the fraction into the numerator.

18 divides into 77 4 times with a remainder of 5.

So we can write 77/18 as 4 and 5/18.

Notice that the 18 stays which is the denominator of our original answer.

This means that 7/6 ÷ 3/11 = 4 and 5/18.

Answer:

C(-4,-2), D(3,-7)

[tex]Ar=35unit^{2}[/tex]

Step-by-step explanation:

we procced to identify points:

A(-4,-7), B(3,-2)

for being the sides of a rectangle parallel to the axes, we find the other two vertices (VIEW GRAPH)

C(-4,-2), D(3,-7);  Area of the rectangle Ar=b*h, where

[tex]b=(X_{D}-X_{A}); h=(Y_{B}-Y_{D})[/tex]

So Ar=(3-(-4))*(-2-(-7)) = (3+4)*(-2+7)=7*5=[tex]35unit^{2}[/tex]

Final answer:

The other two vertices of the rectangle are (3, -7) and (-4, -2), and the area of the rectangle is 35 square units.

Explanation:

To find the coordinates of the other two vertices of a rectangle given two vertices on the coordinate plane, use the fact that the sides of the rectangle are parallel to the axes.

The two given vertices are (3, -2) and (-4, -7). A rectangle has opposite sides of equal length, so the x-coordinates of the opposite vertices must be the same for one pair, and the y-coordinates must be the same for the other pair. Therefore, the other two vertices will have coordinates (3, -7) and (-4, -2).

To find the area of the rectangle, calculate the difference in the x-coordinates (length) and the difference in the y-coordinates (width), then multiply these together.

The length is |3 - (-4)| = 7 and the width is |-2 - (-7)| = 5,

so the area is 7 × 5 = 35 square units.

Answer:

y=-3x-3

Step-by-step explanation:

The equation of the line written in the form y=mx+b that passes through G and has y-intercept of -3 is y=-3x-3

The slope-intercept form is y = m x + b, where

m is the slope

b is the y-intercept

Given that the line passes through G and has y-intercept of -3

Now Substitute it in the form of the equation

∴ y = mx - 3

From the given graph we can see that the slope is -3.

Then substitute it in the equation

y = -3x - 3

The new equation is y=-3x-3

Learn more about slope-intercept form;

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Answer:The value of f is;

Step-by-step explanation:

f=1/t

Answer:

- y + 8(0) = -2              -y + 8(1)=-2                 -y + 8(2) = -2

-y + 0 =-2                    -y + 8 - 8 = -2 -8         -y +16 - 16 = -2 -16

-y= -2                           -y = -10                        -y = -18

Step-by-step explanation:

- y + 8(0) = -2              -y + 8(1)=-2                 -y + 8(2) = -2

-y + 0 =-2                    -y + 8 - 8 = -2 -8         -y +16 - 16 = -2 -16

-y= -2                           -y = -10                        -y = -18

for x = 0, 1, 2

The corresponding y values for the given x values (0, 1, 2) into the linear equation y + 8x = -2 is equal to -2, -10, and -18, respectively, it illustrates how the y value changes with different x values in a linear equation.

The linear equation y + 8x = -2 for given values of x (0, 1, 2).

Let's solve it step-by-step for each x value:

For x = 0: Substitute x with 0 in the equation, y + 8(0) = -2, which simplifies to y = -2.

For x = 1: Substitute x with 1 in the equation, y + 8(1) = -2, resulting in y = -10.

For x = 2: Substitute x with 2 in the equation, y + 8(2) = -2, simplifying to y = -18.

This exercise demonstrates how changing the value of x affects the corresponding value of y in a linear equation.

It highlights the importance of substitution in solving equations and understanding linear relationships.