Determine the scale factor of 5 to 10

Both equations start with y =

Set both equations equal to each other and solve for x first:

1/3x-4 = -7/3x +4

Add 7/3x to both sides:

8/3x - 4 = 4

Add 4 to each side:

8/3x = 8

Divide both sides by 8/3

x = 3

Now you have the value of x, replace x in the equation to solve for y:

y = 1/3(3) -4 = 1-4 = -3

y = -7/3(3) +4 = -7+4 = -3

y = -3

X = 3 and y = -3

Answer:

Part 41) The solution of the compound inequality is equal to the interval  [-1.5,-0.5)

Part 45) The solution of the compound inequality is equal to the interval

(-∞, -0.5] ∪ [1,∞)

Step-by-step explanation:

Part 41) we have

[tex]-4\leq 2+4x < 0[/tex]

Divide the compound inequality into two inequalities

[tex]-4\leq 2+4x [/tex] -----> inequality A

Solve for x

Subtract 2 both sides

[tex]-4-2\leq 4x [/tex]

[tex]-6\leq 4x [/tex]

Divide by 4 both sides

[tex]-1.5\leq x [/tex]

Rewrite

[tex]x\geq -1.5[/tex]

The solution of the inequality A is the interval -----> [-1.5,∞)

[tex] 2+4x < 0[/tex] -----> inequality B

Solve for x

Subtract 2 both sides

[tex]4x < -2[/tex]

Divide by 4 both sides

[tex]x < -0.5[/tex]

The solution of the inequality B is the interval ------> (-∞, -0.5)

The solution of the inequality A and the Inequality B is equal to

[-1.5,∞)∩ (-∞, -0.5)------> [-1.5,-0.5)

see the attached figure N 1

Part 45) we have

[tex]2x-3\leq -4[/tex]  or [tex]3x+1\geq 4[/tex]

Solve the inequality A

[tex]2x-3\leq -4[/tex]

Adds 3 both sides

[tex]2x\leq -4+3[/tex]

[tex]2x\leq -1[/tex]

Divide by 2 both sides

[tex]x\leq -0.5[/tex]

The solution of the inequality A is the interval ------> (-∞, -0.5]

Solve the inequality B

[tex]3x+1\geq 4[/tex]

Subtract 1 both sides

[tex]3x\geq 4-1[/tex]

[tex]3x\geq 3[/tex]

Divide by 3 both sides

[tex]x\geq 1[/tex]

The solution of the inequality B is the interval -----> [1,∞)

The solution of the compound inequality is equal to

(-∞, -0.5] ∪ [1,∞)

see the attached figure N 2

Answer:

[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]

Step-by-step explanation:

x³+216y³+8z³-36xyz

x³+(6y)³+(2z)³-3×6×2×xyz

As we know

a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

Let a=x

b=6y

c=2z

Now.

[x+6y+2z][(x²+(6y)²+(2z)²-x×6y-6y×2z-x×2z]

[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]

Answer:

have a good day

Step-by-step explanation:

you deserve it

Answer:

Any equation of a line having a slope of 1/2.

Step-by-step explanation:

It appears that the question gives answer choices and this problem could have many solutions, but parallel lines have equal slopes. The slope of this line is 1/2 since it is in y=mx+b form where m is the slope. So a few examples of equations of lines parallel to the given equation would be y = 1/2x - 5 or y = 1/2x + 10 etc.

Answer:

B and C

Step-by-step explanation:

We are going to look at each choice:

Let's look at choice A.

f(5)=1

f(5) means look at function f and then see which piece contains x=5.

5>1 so we are looking at [tex]x^2[/tex] for x=5 which gives you [tex]5^2=25[/tex], this is not 1.

The answer is not A.

Let's look at choice B.

f(2)=4

f(2) means look at function f and then see which piece contains x=2.

2>1 so we are looking at [tex]x^2[/tex] for x=2 which gives you [tex]2^2=4[/tex], so this is true that f(2)=4.

Let's look at choice C.

f(1)=5

f(1) means look at function f and then see which piece contains x=1.

1=1 which means we are using [tex]5[/tex] for x=1, so f(1)=5 which is what choice C says so choice C is true.

Let's look at choice D.

f(-2)=4

f(-2) means look at function f and then see which piece contains x=-2

-2<1 so we use [tex]2x[/tex] for x=-2, so we get 2(-2)=-4 which is not 4 so f(-2)=4 is not true.

Answer:

The expression which will result in difference of two squares is:

 (–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

(a-b)(a+b)=a²-b²

i.e. it is a difference of two square quantities. (a^2 and b^2)

since,

a= -7x , b=4

(-7x+4)(-7x-4)= (-7x)² - (4)²

=(7x)² - 4²

So the expression is a difference of two square quantities:

(7x)² and (4)²

Hence the answer is (–7x + 4)·(–7x – 4)....

Answer:

Bethany is correct because consecutive odd integers will each have a difference of two.

For example: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...] All those are odd numbers, and have a difference of two.

So every time time we make 'x' an odd number in Bethany's equation, we will get three consecutive numbers.

For example, if 'x' equals '1', then we will get the three consecutive numbers 1, 3 and 5.

If 'x' equals 7, then we will get the three consecutive numbers 7, 9 and 11.

Answer:

A.) Bethany is correct because consecutive odd integers will each have a difference of two

Step-by-step explanation:

The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4

After the information stated we can conclude that:

The 3 odd integers will be:

x  , (x+2) and (x+4)

Their sum is given to be 91. So we can write:

x + (x+2) + (x+4) = 91

Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.

Answer with explanation:

The equation of line having X intercept (-4,0) and Y intercept (0,2) is given by the formula

    [tex]\rightarrow \frac{x}{a}+\frac{y}{b}=1\\\\ \rightarrow \frac{x}{-4}+\frac{y}{2}=1\\\\ \rightarrow x -2 y= -4\\\\ x -2 y+4=0[/tex]

This takes too long to do. I will provide the steps.

For each point given, plug into the equation y = - x.

Point 1:

(-1, -3)

y = -x

y = -(-1)

y = 1

The first point reflected across the line y = - x is (-1, 1).

Do the same with the remaining points.

Answer:

x=1

Step-by-step explanation:

1) 6x-5y=5

2) 3x+5y=4

ets perform the following operation

1) +2), This leads to the following equation:

6x+3x-5y+5y=5+4

From where we obtain the solution for x

9x=9

x=1

Answer:  southeast

Step-by-step explanation:

Draw a picture showing x to the left of y and z below y:

                                   x    y

                                         z

This results in z being south and east from x

If x is in west of y and y is in north of z,  direction of x with respect to z is South-east .

Given that x is in west of y and y is in north of z.

To obtain the direction of a respective person with respect to a given person, we draw the given image as mentioned in the question.

Drawing the required direction as per given in question -

                                  x    y

                                        z

Thus, we can clearly see that z is South-east direction of x.

Therefore, if x is in west of y and y is in north of z,  direction of x with respect to z is South-east .

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Answer:

[tex]\$1,282.28[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=25\ years\\ A=\$20,000\\ r=0.11\\n=52[/tex]  

substitute in the formula above  

[tex]20,000=P(1+\frac{0.11}{52})^{52*25}[/tex]  

[tex]20,000=P(1.0021)^{1,300}[/tex]  

[tex]P=20,000/(1.0021)^{1,300}[/tex]  

[tex]P=\$1,282.28[/tex]  

Answer:

The answer is A, (3x2-x-6)

Step-by-step explanation:

f(x)=3x2 -4

g(x)=x+2

f(x)-g(x)= 3x2-4 -x-2= 3x2-x-6

Final answer:

The expression (f - g)(x) is found by subtracting g(x) from f(x) and simplifying, which results in 3x² - x - 6, corresponding to option A.

Explanation:

To find (f - g)(x) when f(x) = 3x² - 4 and g(x) = x + 2, we need to subtract the function g(x) from f(x). The operation looks like this:

(f - g)(x) = f(x) - g(x) = (3x² - 4) - (x + 2)

Let's perform the subtraction step by step:

Distribute the negative sign to both terms in g(x):

(3x²- 4) - x - 2

Combine like terms:

3x² - x - 4 - 2

Final simplification:

3x² - x - 6

Therefore, the correct answer is 3x² - x - 6, which matches option A from the provided choices.

Answer:

1575 grams

Step-by-step explanation:

If a baker has 2,000 grams of flour and uses 425 grams of it, the mass will become 1575 grams.

2000 - 425 = 1575

Answer:

1575 grams of flour

Step-by-step explanation:

If he had 2000 grams of flour and used 425 grams of it, you have to subtract 2,000 by 425, which would equal 1,575 grams of flour left.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (2, 10)

m = [tex]\frac{10-5}{2+3}[/tex] = [tex]\frac{5}{7}[/tex], hence

y = [tex]\frac{5}{7}[/tex] x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (2, 10), then

10 = [tex]\frac{10}{7}[/tex] + c ⇒ c = 10 - [tex]\frac{10}{7}[/tex] = [tex]\frac{60}{7}[/tex]

y = [tex]\frac{5}{7}[/tex] x + [tex]\frac{60}{7}[/tex] ← in slope- intercept form

Answer:

A. right 2, up 3

Step-by-step explanation:

We are asked to find the transformation that occurs from  the graph of [tex]f(x)=x^2[/tex] to [tex]f(x)=(x-2)^2+3[/tex].

Let us recall transformation rules:

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

Upon looking at our given functions, we can see that graph of [tex]f(x)=x^2[/tex] is shifted to right by 2 units as 2 is inside parenthesis. The graph is shifted upwards by 3 units as we have positive 3 outside parenthesis.

Therefore, option A is the correct choice.

Answer:

The product of 28w(w-17) is 28w^2 - 476w

Step-by-step explanation:

Given

28w(w-17)

We have to find the product of the monomial and binomial polynomials

The term 28w will be distributed to w-17

So,

= (28w)(w) - (28w)(17)

= 28w^2 - 476w

Therefore, the product of 28w(w-17) is 28w^2 - 476w ..

Final answer:

When multiplying monomials and binomials, you can follow certain rules. Multiply the numerical coefficients, add the exponents of the variables, and then combine like terms if possible.

Explanation:

When multiplying monomials and binomials, you can follow a few rules. For monomials, you simply multiply the numerical coefficients and add the exponents of the variables. For binomials, you can use the distributive property to multiply each term of one binomial by each term of the other binomial. Then, combine like terms if possible.

For example, let's say we have (2x^2)(3x^3). We would multiply the coefficients (2 * 3 = 6) and add the exponents of the variable x (2 + 3 = 5). So the resulting expression is 6x^5.

Answer:

D. 9 inches

Step-by-step explanation:

By using proportionality theorem,

Triangle BLM ~ Triangle BAC

[tex] \frac{bm}{bc} = \frac{bl}{ba} [/tex]

as ba = bl + la and as bl = la

Therefore, bl + la = 2bl

[tex] \frac{bm}{bc} = \frac{bl}{2bl} [/tex]

Now, we get,

[tex] \frac{bm}{18} = \frac{1}{2} [/tex]

as bc = 18

Hence,

[tex]bm = 9 \: inches[/tex]

Answer: D. 9 inches

Step-by-step explanation:

Given : The midsegment of Δ ABC is line segment IM.

Such that for side BC ,  BM=MC         [ Show in the picture ]     (1)

and BC= BM+MC    (2)

The length of BC = 18 inches              (3)

From (1) and (2), we have

[tex]BC=MC+MC\\\\\Rightarrow\ BC=2MC[/tex]

Using (3), we have

[tex]2MC=18\text{ inches}\\\\\Rightarrow\ MC=\dfrac{18}{2}=9\text{ inches}[/tex]

Therefore, the length of MC = 9 inches.

Hence, D is the correct option.

Answer:

-2 degrees

Step-by-step explanation:

If you work backwards you will eventually get -2

For example: -3 + 3 = 0, then 0 - 2 = -2, so on...........

Answer:

The area of triangle DEF is [tex]282\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

To find the scale factor, divide the height of triangle DEF by the height of triangle ABC

Let

z ------> the scale factor

[tex]z=\frac{13}{5}[/tex]

step 2

Find the area of triangle DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of triangle DEF

y -----> the area of triangle ABC

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{13}{5}[/tex]

[tex]y=15\ cm^{2}[/tex]

substitute and solve for x

[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]

[tex]x=(\frac{169}{25})(15)[/tex]

[tex]x=282\ cm^{2}[/tex]

Answer:

2 hours.

Step-by-step explanation:

8 hours x 25 / 100 = 2 hours

Answer:

2 hours.

Step-by-step explanation:

Let the number of hours taken doing paperwork be x.

Shift of each day=8 hours

According to question

x=25%of 8 hours

x=25×8/100

x=2 hours

Thus, answer is 2 hours.

Answer:

−2(3x+2)(x−5)

Step-by-step explanation:

−6x2+26x+20=

=−2(3x+2)(x−5)

[tex]\huge{\boxed{\text{42 ounces}}}[/tex]

25% is equal to [tex]\frac{1}{4}[/tex], so multiplying it by 4 gets 100%.  This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.

[tex]10.5*4=\boxed{42}[/tex]

Answer:

42 ounces

Step-by-step explanation:

So a koala absorbs 25% of fiber they eat.

A koala absorbed 10.5 ounces in a day.

Let x be the amount of ounces of fiber the source(s) actually contained that day.

So we have 25% of x is 10.5

As an equation that is .25x=10.5 or 1/4 *x=10.5.

.25x=10.5

To solve this equation you can divide both sides by .25 giving you

x=10.5/.25=42.

If you chose the other equation which is an equivalent equation you would multiply both sides by 4.

1/4 *x=10.5

x=4(10.5)

x=42

Answer:

d

Step-by-step explanation:

u got the answer right

ANSWER

13.5

EXPLANATION

We write 6 cubed as 6³

We write 4 squared as 4²

The quotient of 6 cubed and 4 squared is written as

[tex] \frac{ {6}^{3} }{ {4}^{2} } [/tex]

We expand to obtain:

[tex] \frac{6 \times 6 \times 6}{4 \times 4} [/tex]

Cancel out the common factors to get,

[tex] \frac{3 \times 3 \times 3}{2} [/tex]

This simplifies to

[tex] \frac{27}{2} = 13.5[/tex]

Answer:

3/7

Step-by-step explanation:

The total number of students in the play is 10.

The number of boys in the play is 7.

The remaining students in the play must be girls, so 10-7=3.

There are 3 girls in the play.

The ratio of girls in the play to boys in the play would be:

girls/boys= 3/7.

Answer:

Step-by-step explanation:

The no of girls is 3/10

Girls : boys

3/10 : 7/10

3 : 7

Answer:

Speed = 8mph

Step-by-step explanation:

Speed of wind = 4mph

Let speed of Darrin with no wind be "x" mph

then resultant speed of Darrin, travelling in direction of wind = (x + 4) mph

Using a result, Time = Distance travelled / Net speed

Time taken by Darrin to travel 6miles in direction of wind = 6 / (x + 4)

When Darrin travel in opposite direction of wind, then its net speed                                                  = (x - 4)mph

Darrin travel 2 miles against the wind in 6/(x + 4) hr

then   Distance =  speed ×  time

           2 =  ( x- 4 ) × ( 6/x + 4)

          2x + 8 = 6x - 24

            4x  =  32

              x = 8 mph

Therefore speed of Darrin skateboard with no wind = 8mph

Answer:

Speed without wind will be 8 mph

Step-by-step explanation:

Now by revising basic formula here

Velocity = Distance/Time. . . . (A)

Assume speed without wind is 'x'

When Darrin is moving against wind to cover 2 miles;

net speed will be x-4

When Darrin is moving along with the wind to cover 6 miles;

net speed will be x+4

Please note that the time for covering distance of 2 miles and 6 miles is same,

So, from equation (A)

Time = Distance/Velocity,

Time for 2 miles will be

Time = 2/(x-4)

Time for 6 miles will be

Time = 6/(x+4)

Since, the time for both distances is same, here we can equate,

2/(x-4) = 6/(x+4)

by cross multiply

2(x+4) = 6(x-4)

2x+8 = 6x-24

4x = 32

x = 8

So, 8 miles per hour is the speed of Darrin if there is no wind.

HG^2 = FG * (FG + EF)

Fill in the values:

(x+3)^2 = x * (7+x)

Simplify the right side:

(x+3)^2 = 7x +x^2

Rewrite the left side using the FOIL method

x^2 + 6x + 9 = 7x +x^2

Subtract x^2 from both sides:

6x +9 = 7x

Subtract 6x from both sides:

x = 9

Now you have x solve for HG

HG = x +3 = 9+3 = 12

The answer is A.

Answer:

(y - 7)

Step-by-step explanation:

"7 less than y" means just that.... that you have 7 fewer units then the value of y.

Expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].

" An expression is defined as the representation of the relation between variables and numbers using mathematical operation."

According to the question,

Given statement,

[tex]7[/tex] less than [tex]y[/tex]

Expression for the given statement is,

[tex]y - 7[/tex]

Hence, the expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].

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