what is the word form and standard form

Use the graph to determine the solution of the inequality |x + 1| + 2 > 5.

To graph this , first we make the absolute function alone

|x + 1| + 2 > 5

to make absolute function alone we subtract 2 from both sides

|x + 1|  > 3

x+1 inside the absolute function . so x=-1

From -1, move 3 units to the right and 3 units to the left.

For x>2 , shade the graph to the right

For x< -4, shade the graph to the left

The graph is attached below

The solution to the inequality is x<-4 and x>2

Answer:

Its A on E2020

Step-by-step explanation:

Answer:

37 mph

Step-by-step explanation:

if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph

Answer:

37 mph

Step-by-step explanation:

if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph

Answer:

Density of the material is 5 grams per cubic centimeter.

Step-by-step explanation:

The answer is required to be given in grams per cubic centimeter.

So we should first convert the values to match the units.

Mass is given as 2500 grams so we don't need to change the units.

Volume is given in cubic centimeters. So we don't need to change the units.

Density      = [ Mass of the material / Volume of the Solvent]

                  =2500 grams / 500 cubic centimeters

                  =5 grams per cubic centimeter

Answer:

The answer is 15 months.

Step-by-step explanation:

p = $500

r = 6.5% or 0.065

A = $543

t = ?

The formula to be used here is :

[tex]A=pe^rt[/tex]

[tex]t=(log(A/p)/log(e))/r[/tex]

Putting the values in formula we get:

[tex]t=(log(543/500)/log(e))/0.065[/tex]

[tex]t=(log(1.086)/log(e))/0.065[/tex]

This gives t = 1.3 years

In months it will be 1 year(12 months) + 3 months = 15 months.

Hence, the answer is 15 months.

Answer:

15 months

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Let us consider an equilateral triangle ABC. Now, we will define midsegments:

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle (here triangle ABC). This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

Refer the attached image:

Now, from the definition of midsegment we can see that:

[tex]PQ=\frac{1}{2}BC[/tex]

[tex]\therefore PQ=BR[/tex]

and PQ is also parallel to BR.

Now, again from the definition of midsegment we can see that:

[tex]QR=\frac{1}{2}AB[/tex]

[tex]\therefore QR=PB[/tex]

and QR is parallel to PB.

therefore, PQBR forms a parallelogram

And a diagonal of a parallelogram divides it into two congruent triangles.

Hence, triangle 2 (triangle PBR) is congruent to triangle 4(triangle PQR).

Similarly, triangle 3 (triangle QRC) and triangle 1 (triangle APQ) are congruent to triangle 4 (triangle PQR), Therefore, there are 4 congruent triangles formed when midsegments of an equilateral triangle partition the triangle.

The midsegments of an equilateral triangle partition it into four smaller congruent triangles, due to the Triangle Midsegment Theorem and the Third theorem of congruence for triangles.

When the midsegments of an equilateral triangle are drawn, they connect the midpoints of the sides of the triangle. These segments will each be parallel to one side of the triangle and half its length, according to the Triangle Midsegment Theorem. Drawing all three midsegments partitions the equilateral triangle into four congruent smaller triangles. Each smaller triangle will be similar to the original equilateral triangle.

By the Third theorem of congruence for triangles (which is often referred to as SSS or side-side-side), if three sides of one triangle are congruent respectively to the corresponding sides of another triangle, the two triangles are congruent. In this case, each smaller triangle formed by the midsegments shares a side with the original triangle and has the other two sides equal in length to the midsegments, which are congruent to each other by construction.

Therefore, all four smaller triangles are congruent to each other.

Remark

The slope intercept graph needs a table like the one provided by the graph shown below.

A sample calculation would look like this

y = (2/3)x - 2  Let x = 6 (which is not plotted on the graph).

y = 2/3 * 6 - 2   The 3 will divide into the 6 two times

y = 4 - 2

y = 2

So you would plot this as (6,2)

$5.00 x 4 = $20.00.

$20.00 divided by 2 = $10.00

She will have $10.00 to save.

Hope I helped!

Good Luck!

This type of relationship is exponential decay

Hey there!!

Slope-intercept form :

y = mx + b

m is the slope and b is the y-intercept.

Given equation :

x - 2y = 12

We will have to isolate the y.

... x - 2y = 12

... -2y = x - 12

... y = ( x - 12 ) / -2

... y = x / - 2 + 6

Hence, the slope is -1/2

Hope my answer helps!

we can see that

For x is 0, 1, 2, 3 ,4

f(x) is  0 , 1 ,  4, 9 , 16

g(x) is -2 , -1 , 1 , 5 , 13

so, g(x) is greater than f(x) for x is 0, 1, 2, 3 ,4

It means that f(x) exceeds g(x) on [0,4]

But for x=5

f(x) is 25

g(x) is 29

Here, we can see that g(x) exceeds f(x) at x=5

so, there must be intersection point between x=4 and x=5

so, option-C.........Answer

Each option describes different behaviors and relationships between the two functions over the interval [0, 5]. Without further details, we can only conceptualize the scenarios provided.

To compare the graphs of f(x) and g(x) over the interval [0, 5], we can evaluate the options provided:

Without the exact equations or a graph to analyze, we cannot definitively determine which option is correct. However, we can conceptualize the scenarios described:

Option A suggests f(x) is consistently greater than g(x) throughout the interval. Option B suggests the opposite. Option C introduces an intersection point, where f(x) transitions from being greater to less than g(x). Option D indicates g(x) is initially greater, with a reversal after an intersection between 4 and 5.

If we had the graphs or more specific information, we could more precisely identify the correct statement.

Answer:

It would be B.

Step-by-step explanation:

Dilation is the only transformation that is NOT congruent. It is similar.

[tex]\frac{3}{4}q[/tex] - 7 = 8

     +7   +7

[tex]\frac{3}{4}q[/tex] = 15

[tex]4(\frac{3}{4}q)[/tex] = 4(15)

3q = 60

[tex]\frac{3q}{3} = \frac{60}{3}[/tex]

q = 20

Answer: q = 20

All you have to do is add 25+ 27= 52

Answer:

The slope is -7/2.

Step-by-step explanation:

Convert to slope-intercept form (y = mx + b  where m = the slope)

7x + 2y = 5

2y = -7x + 5

Divide both sides by 2:-

y = (-7/2)x + 5/2

so slope m = -7/2

The expression evaluates to -4 when x equals 4.

To evaluate the expression –0.4(3x – 2) + for [tex]\( x = 4 \)[/tex], follow these steps:

1. Substitute the value of [tex]\( x \)[/tex] into the expression.

2. Perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).

Here's the step-by-step calculation:

Given expression: [tex]\(-0.4(3x - 2) +\)[/tex]

Substitute [tex]\( x = 4 \)[/tex]:

[tex]\(-0.4(3(4) - 2) +\)[/tex]

Now, simplify inside the parentheses first:

[tex]\(-0.4(12 - 2) +\)[/tex]

[tex]\(-0.4(10) +\)[/tex]

Next, multiply [tex]\(-0.4\)[/tex] by [tex]\( 10 \)[/tex]:

[tex]\(-4 +\)[/tex]

Finally, there's no more to compute since there's no other term. So the result is:

[tex]\(-4\)[/tex]

Therefore, the value of the expression [tex]\(-0.4(3x - 2)\)[/tex] when [tex]\( x = 4 \)[/tex] is [tex]\( -4 \)[/tex].

The way I did this was made everything decimals so .75/.25 and it equals 3

12.8 * 1.35 =17.28

Therefore Marissa spent $17.28 on potatoes.

Ruben has 6 new books for his collection. This increases his collection by 12%

Let x be the number of books Ruben has before 6 new books added

x + 12% of x = x+6

x + 0.12x = x+6

1.12 x = x+6

Subtract x on both sides

0.12x = 6

Divide by 0.12

x = 50

6 new books are added for his collection

So 50 + 6 = 56

He have 56 books now.

Move the decimal until its below 10 and greater than 1:

Mercury: 3.5 x 10^7

Earth: 9.2 x 10^7

Neptune: 2.7 x 10^9

hope this helps :)

Checking Account

it should be that

The account which is not the example of the type of savings vehicle is Checking Account. Thus option 3rd is correct.

The three kinds of the saving account are regular deposit, money market, and Certificate of Deposits. There is a difference in all the three types in terms of the accessibility and amount of interest.

The Checking account is the account which carries the day to day transactions of the money. It ensures the easy access to the money. Many of the people generally uses the debit card or the checks to make the purchases.  Thus option 3rd is correct.

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The answer is choice C

On the left side we have something in the form a*b+a*c+a*d

On the right side we have something in the form a*(b+c+d)

All together, we have a*b+a*c+a*d = a*(b+c+d), where the letters a,b,c,d are to be replaced with the proper values (0.5, 0.5, 0.3, and 0.2 in that exact order).

The idea of distribution is to multiply the outer value 0.5 by each of the values inside the parenthesis (0.5, 0.3, and 0.2) and add up the products.

Equation C and D that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) and 0+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) ​applies the distributive property correctly as defined "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together".

The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive property of binary operations. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication. In order to quickly solve expressions, a number is distributed among the numbers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.

The distributive property states,

A × (B + C) = AB + AC

for equation C

(0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​

for equation D,

50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)

According to the definition of the distributive property, which states that "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together," Equations C and D, which are correctly applied that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​and 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005).

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[tex]-12\leq3x-15\leq9\qquad|+15\\\\3\leq3x\leq24\qquad|:3\\\\1\leq x\leq8[/tex]

22+5d=-8x7d=56d+ -8x-4=32

22+5d=-56d+32

22+32=54 and -56d+5d=-51d

The answer would be 51d+54

Remark

The steps are the same usually. Remove the brackets and collect like terms on each side of the equal sign.

Solution

22+5d = -8(7d - 4)          Remove the brackets.

22+5d = -56d + 32        Notice the sign change on 32. 2 minus quantities = a plus when multiplied.  Add 56d to both sides.

22 + 5d + 56d = - 56d + 56d + 32

22 + 61d = 32                  Subtract 22 from both sides.

61d = 32 - 22

61d = 10                            Divide by 51

d = 10/61

d = 0.1639  Answer

Check

LHS

22 + 5*0.1639 = 22.8197

RHS

-8(7*0.1639 - 4)

-8(1.1473 - 4)

-8(-2.8527)

22.8216    

The difference is a rounding error.

The three consecutive numbers that can be equal to 24 are 7,8,9

7+8+9=24

The two fractions with the common denominator will be 6/ 15 and 4 / 15.

The fraction is defined as the division of the whole part into an equal number of parts.

The two fractions are 2 / 5 and 4 / 15 will be converted into the same common denominator as;-

For fraction 2 / 5 multiply it by 3 in both the numerator and the denominator.

= ( 2  x 3 ) / ( 5  x  3 )

= ( 6 / 15 )

Therefore two fractions with the common denominator will be 6/ 15 and 4 / 15.

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You divide the difference in y-coordinates by the diffrence in x-coordinates. Or whatever the variables are.

Lets say the coordinates of the two points are (a,b) and (c,d). Then:

Rate of change is "rise/run" = (b - d)/(c - a) = (d - b)/(a - c)