Solve: 2(x - 5) < -6(1 - x)








A.

x < -1

B.

x > -1

C.

x < 1

D.

x > 1

600 m

The slope between 1 minute and 2 minutes is ...

... (800 -500)/(2 -1) = 300 . . . . . . m/min

Thus in 20 seconds, 1/3 minute, Jason will fall ...

... (1/3 min)·(300 m/min) = 100 m

This distance is in addition to the 500 m he has already fallen in the first minute.

In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.

_____

Comment on the graph

We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).

Since QC and BR are parallel, triangles CDQ and BDR are similar.

This means that corresponding sides are in proportion, so we have

[tex] BD \div QD = RD \div CD [/tex]

Substituting numbers, we have

[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]

Multiply both sides by [tex] 39x [/tex]

[tex] 65x = 39(18+x) [/tex]

Expand right hand side:

[tex] 65x = 702 + 39x [/tex]

Subtract 39x from both sides:

[tex] 26x = 702 [/tex]

Divide both sides by 26

[tex] x = \dfrac{702}{26} = 27 [/tex]

Just took the test and got the the correct answer *\(♡°▽°♡)/*

Look at the image down below!!

Answer:

(A) The number of bacteria is originally 300 and increases by 30% every hour

Step-by-step explanation:

I am assuming the function should actually read:

[tex]N(t)=300\cdot 1.30^t[/tex]

(i.e., there should be a "t" in the exponent. if this is not the case please disregard my answer).

According to the above exponential function, the initial amount 300 grows as (1+0.3)*300=300+0.3*300. In other words it increases by 30% every hour (t).

Your answer choice (A) is likely a candidate, except I am missing "every hour" at the end (again, am assuming this was omitted by mistake)

Final answer:

The function N(t)=300(1.30)^t represents the bacterial growth model where the initial amount of bacteria is 300 and increases by 30% every hour.

Explanation:

Looking at the function N(t)=300(1.30)^t, this model describes the number of bacteria, N, after t hours. The base number, 300, indicates the initial quantity of bacteria, while the term (1.30)^t suggests that the population changes by a factor of 1.30 each hour, reflecting a 30% increase in the number of bacteria each hour. Therefore, the correct statement that interprets this model is:

A. The number of bacteria is originally 300 and increases by 30% each hour.

Answer:

[tex]y= \frac{1}{28} x^2[/tex]

Step-by-step explanation:

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

The pipe is located 7 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 7 inches from the vertex (0,0)

7 inches is the focus of the mirror

The distance between the vertex and the focus = 7

Since parabola is upwards and vertex is (0,0) we use formula

[tex]4py = x^2[/tex]

Where p is the distance between the vertex and focus

p = 7 we know

[tex]4*7*y = x^2[/tex]

[tex]28y = x^2[/tex]

Now isolate y by dividing 28 on both sides

[tex]y= \frac{1}{28} x^2[/tex]

Answer:

The correct answer would be A) (4, 49.6)

Step-by-step explanation:

In order to find the equation, we first have to start with the base form of direct variation.

y = kx

Now we input the k value.

y = 12.4x

Now that we have this, we can try the ordered pairs and look for which satisfies the equation.

y = 12.4x

49.4 = 12.4(4)

49.4 = 49.4

Since this is the true statement, this is the ordered pair that works.

Answer:

(4,49.6)

Step-by-step explanation:

Answer:

Each hiker gets [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

Step-by-step explanation:

First, we need to find the total amount of cups by multiplying the number of bags with the amount of cups in each bag:

8 * 3.5 = 28

Now, we divide this by 12 to find the amount of cups per hiker:

28 ÷ 12 = [tex]\frac{7}{3}[/tex] or 2.3333

So each hiker gets  [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

The equation 15x + 8y = 56 can be rewritten in slope-intercept form (y = mx + b) as y = -15/8x + 7, where -15/8 is the slope and 7 is the y-intercept.

To convert the equation 15x + 8y = 56 into slope-intercept form (y = mx + b), we want to isolate y. Here are the steps:

In this equation, -15/8 is the slope, and 7 is the y-intercept. This means the line intersects the y-axis at y = 7, and for every 8 units increase in x, there is a 15 unit decrease in y, as the slope is negative.

https://brainly.com/question/29146348

#SPJ3

-7 = 7d - 8

Add 8 to both sides.

1 = 7d

Divide both sides by 7.

Answer:

-1,81

Step-by-step explanation:

Multiplicity of a number can be written as power

for example

-1(multiplicity 3) can be written as

[tex]-1^{3}[/tex]= -1

similiarly 3(multiplicity 4) can be written as

[tex]3^{4}[/tex]=81

The eleventh-degree polynomial (x + 3)4(x – 2)7 has the same zeroes as did the quadratic, but in this case, the x = –3 solution has multiplicity 4 because the factor (x + 3) occurs four times (that is, the factor is raised to the fourth power) and the x = 2 solution has multiplicity 7 because the factor (x – 2) occurs ... Can you do the rest on your own?

The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.

Explanation:

When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.

In this case, we have a negative exponent (-4), so we move the decimal four places to the left:

9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936

Therefore, 9.36×10-4 in standard form is 0.000936.

Answer:

D) 75%

Step-by-step explanation:

75% of 24 = 0.75 x 24 = 18

E. 168 sq units

The legs of this right triangle have length 24 and 14, so the area is ...

... A = (1/2)bh = (1/2)(24)(14) = 168 . . . . sq units

Answer:

f(x)= -x²-4x-2

Step-by-step explanation (this way is not the shortest one):

1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0

for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0

for the point (-1;1): a(-1)²+b(-1)+c=1

2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':

[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]

[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]

3. the required equation is: -x²-4x-2

Answer:

Point

Step-by-step explanation:

If you are referring to geometry

Answer:

2.5 min

Step-by-step explanation:

The tortoise takes 1 min/3 m.

7.5 × 1/3  = 2.5 min

Answer:

42.5

Step-by-step explanation:

76.8% × ? = 32.64

? =

32.64 ÷ 76.8% =

32.64 ÷ (76.8 ÷ 100) =

(100 × 32.64) ÷ 76.8 =

3,264 ÷ 76.8 =

42.5

To solve for the number that 76.8% of it equals 32.64, you can write an equation and solve for x: 0.768 * x = 32.64. Dividing both sides by 0.768 gives x = 42.5.

The question asks about a percentage of a number, which is a math concept. If 76.8% of a number equals 32.64, you can use basic algebra to find that number. Let's call it 'x'. You can write it as an equation: 0.768 * x = 32.64. Solving for x, divide both sides of the equation by 0.768.

x = 32.64 /0.768

When you perform this calculation, you'll find that x is approximately 42.5. So, 76.8% of 42.5 is approximately 32.64.

https://brainly.com/question/32197511

#SPJ3

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

i think it is true and true

Step-by-step explanation:

Answer:

35. False

36. True

Step-by-step explanation:

35. [tex]-3\:<\:-2[/tex]

On the number line [tex]-3[/tex] is to the left of [tex]-2[/tex].

Therefore [tex]-3[/tex] is not greater than [tex]-2[/tex].

[tex]-3[/tex] is rather less than [tex]-2[/tex].

36. [tex]y\leq 3[/tex] includes three as a possible solution.

The reason is that, the inequality contains an equal sign in it, the boundary is also inclusive, therefore 3 is itself a possible solution.

In order words, the statement

[tex]3\leq3[/tex] is a truth statement.

Neither one

Frog A's "unit rate" is ...

... (8 flies)/(4 minutes) = 2 flies/minute

Frog B's "unit rate" is ...

... (14 flies)/(7 minutes) = 2 flies/minute

Both rates are the same. Each frog eats 2 flies per minute.

Answer:

i dont like frogs

Step-by-step explanation:

Answer:

∠ABC ≅ ∠XYZ

Step-by-step explanation:

Given: ΔABC is similar to ΔXYZ.

If two triangles are similar, then

1. the corresponding angles are congruent

2. the corresponding sides are proportional

From the options given,

AB ≅ XY is not applicable for similar triangles. Hence the option is wrong.

∠ABC ≅ ∠XYZ since  ΔABC ≅ ΔXYZ

Hence the answer is ∠ABC ≅ ∠XYZ

Answer:

c. 12x − 24 = 60

Step-by-step explanation:

x is the number of boxes Krys bought.

12x is the number of pastries in those boxes. 2·12 = 24 is the number of pastries in the boxes Krys kept for herself. Then the number of pastries Krys brought to the party is ....

... 12x -24

We are told that number is 60, so we can use this equation to find x:

... 12x -24 = 60

Answer:

Option C : 12x − 24 =60

Step-by-step explanation:

Given :

Krys bought x boxes of pastries to bring to a party.

Each box contains 12 pastries.

She decides to keep two boxes for herself.

She brings 60 pastries to the party.

To Find : Equation can be used to find the number of boxes, x, Krys bought.

Solution :

Krys bought x boxes of pastries .

Each box contains 12 pastries.

So, total pastries she bought = 12 x

She decides to keep two boxes for herself.

Since 1 box contain 12 pastries .

Thus two box contains pastries = 12*2 =24 pastries

Now total pastries she bought is 12 x . Out of which she decides to keep 24 pastries . after keeping 24 pastries from 12 x pastries she bought 60 pastries to the party i.e.

⇒ 12 x - 24 = 60

Thus,Equation can be used to find the number of boxes, x, Krys bought:

12 x - 24 = 60

Hence Option C is correct .

Answer:

Step-by-step explanation:

Numerical reasoning

If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.

There are 10 4-point questions and 30 2-point questions.

_____

With an equation

Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...

... 2(40-x) +4x = 100

... 2x +80 = 100 . . . . simplify

... 2x = 20 . . . . . . . . .subtract 80

... x = 10 . . . . . . . . . . divide by 2.

There are 10 4-point questions and 40-10=30 2-point questions.

Answer:

C. 1,-1

Step-by-step explanation:

The sum of the coefficient is 0 so x=1 is a root and (x-1) as a factor

so x^4+3x^3+3x^2-3X-4=(x-1)(x^3+4x^2+7x+4)

and the root of that is x=-1 and the factor is (x+1)

SO the answer is: x=1 and x=-1

Answer: -1, 1

Step-by-step explanation:

To solve the polynomial equation x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, do a quick test of polynomials using 1 and -1 in place of x.

This gives the sum of coefficients as zero

Testing with 1: 1 + 3 + 3 - 3 - 4 = 0

Testing with -1: 1 + (-3) + 3 - (-3) - 4

= 1 - 3 + 3 + 3 - 4 = 0

This gives that both (x + 1) and (x - 1) are roots.

(x + 1)(x - 1) = x² - 1 {difference of two squares}

Dividing the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 by (x² - 1) results in x² - 3x + 4 as quotient. Factorizing this result would give complex roots.

Therefore, x² - 1 = 0

x² = 1

Taking square of both sides of the equation gives

x = ± 1

1 and -1 are the rational roots to the polynomial.

Answer:

b. 3x - (5y -7)

Step-by-step explanation:

Let x represent "a number". Let y represent "another number."

The "3 times a number" is represented by 3x.

And "5 times another number less 7" is represented by 5y -7.

The difference between these quantities is the second subtracted from the first:

... 3x - (5y -7) . . . . matches selection b.

Answer:

X = 37

Y = 29

Step-by-step explanation:

X + Y = 66

X - Y = 8

------

Solve second equation for X

X = Y + 8

Substitute for X in first equation

Y + 8 + Y = 66

2 * Y = 58

Y = 29

___

X - 29 = 8

X = 37

X = 37

Y = 29

Good Luck,

- I.A. -

Answer:

x = 37 and y = 29

Step-by-step explanation:

x + y = 66

x - y = 8

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

x - 29 = 8

x = 37

x = 37 and y = 29

Answer:

Question 39: False

Question 43: True

Step-by-step explanation:

Question 39

|-4| is a solution of x ≤ 4

|-4| ⇒ This mean the absolute value of 4. The sign s are neglected.

So, |-4| is not a  solution of x ≤ 4.

Question 43

The point (5, -1) is a solution of the equation: y = 2x − 11.

To prove this we are to substitute the point (5, -1) in the equation y = 2x − 11.

y = -1 and x = 5

y = 2x − 11   ⇒   -1 = 2(5) -11

                         -1 = 10 - 11

                         -1 = -1

Answer:

it should be 4x^3 y-4xy^2+xy+3x^2

Step-by-step explanation:

Answer:

6 cm,12 cm,8 cm

Step-by-step explanation:

add the perimeter of the first triangle to get 65

then divide 65 by 26 to get 2.5

then divide all the side lengths by 2.5

15/2.5=6

20/2.5=8

30/2.5=12

The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm, and 12 cm and this can be determined by using the given data.

Given :

The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm.

The following steps can be used in order to determine the lengths of the sides of a similar triangle that has a perimeter of 26 cm:

Step 1 - The formula of the perimeter of the triangle is given below:

[tex]\rm P = a + b + c[/tex]

where a, b, and c are the length of the sides of the triangle.

Step 2 - Now, determine the perimeter of the triangle whose sides are 15 cm, 20 cm, 30 cm.

P' = 15 + 20 + 30

P' = 65 cm

Step 3 - Now, divide both the perimeters of the triangles, that is:

[tex]=\dfrac{65}{26}[/tex]

= 2.5

Step 4 - So, the side length of the sides of a similar triangle is given below:

[tex]\rm \dfrac{15}{2.5} = 6\;cm[/tex]

[tex]\rm \dfrac{20}{2.5}=8 \;cm[/tex]

[tex]\rm \dfrac{30}{2.5}=12\;cm[/tex]

For more information, refer to the link given below:

https://brainly.com/question/6465134