There is a mountain with 30 bat caves in a row that contain 340 bats in all. Any 7 caves in a row contain exactly 77 bats. Suppose the first cave has 7 times more bats than the last caves. How many bats in the 29th cave?

The planes are 618.75 miles from starting point

Solution:

Let t is the travel time of the jet

Then  (t + 3) is the travel time of the propellar

When the jet overtakes the propellar, they will traveled the same distance

Distance is given as:

[tex]Distance = speed \times time[/tex]

A jet plane traveling at 550 mph

[tex]Distance\ by\ jet = 550 \times t\\\\Distance\ by\ jet = 550t[/tex]

propeller plane traveling at 150 mph

[tex]Distance\ by\ propellar = 150 \times (t+3)[/tex]

Equate both distance

[tex]550t = 150(t+3)\\\\550t = 150t + 450\\\\550t - 150t = 450\\\\400t = 450\\\\t = \frac{450}{400}\\\\t = 1.125[/tex]

[tex]Distance = 550 \times t = 550 \times 1.125\\\\Distance = 618.75[/tex]

Thus they are 618.75 miles from starting point

The distance both planes are from the starting point when the jet overtakes the propeller is 451.125 miles.

This question is a math problem involving relative speed and distance traveled. In this case, we are solving for the distance each plane has flown from their respective starting points once the jet plane overtakes the propeller plane.

To start, let's think of the problem in terms of a timeframe. We know the propeller plane had a 3-hour head start. Now, we need to determine how long it took for the jet plane to catch up to the propeller plane. To calculate this, we must find the difference in speed between the two planes (550 mph - 150 mph = 400 mph), and then divide the time difference (3 hours) by the relative speed (400 mph) which equals 0.0075 hours.

Next, we compute the distance covered by the propeller plane in 3.0075 hours (150 mpg * 3.0075 hours = 451.125 miles). Both planes are at this same distance from the starting point when the jet plane overtakes the propeller plane.

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Answer:

B (-2, 0)

Step-by-step explanation:

put the first equation in for y in the second equation - watch the negative

2x - (x +2) = -4

2x - x -2 = -4

x = -2

plug this x back in to find y

y = -2 + 2 = 0

Answer:

B

Step-by-step explanation:

plug in the answers given into both equations to see if the statements true

y=x+2

0=(-2)+2

0=0

2x-y=-4

y=2x+4

0=2(-2)+4

0=0

Answer:

D.

the addition property of equality

Step-by-step explanation:

Given the expression in

Step 2: 9d - 5 = -15

The addition property of equality was used to get step 3.

That is

9d - 5 = -15

Move -5 over the equality sign and it becomes +5

9d = -15 + 5

9d = -10

OR add 5 to both sides of the equation as shown below

9d - 5 +5 = -15 + 5

9d = -10 which we have in step 3

The justification for step 3 is the subtraction property of equality, which allows us to subtract the same number from both sides of an equation to maintain its balance.

The correct answer is A: the subtraction property of equality.

Here is why: In the step before (step 2), we have 9d - 5 = -15. When we move to step 3, we're solving 9d = -10 which means we added 5 to both sides of the equation. By doing so, we subtract 5 from the left side to get 9d and add 5 to -15 on the right side to get -10. This action is consistent with the subtraction property of equality, which states that you can subtract the same number from both sides of an equation and the equation will still hold true.

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Answer:

b.

Step-by-step explanation:

Answer:

3(2s + 6t + w)

Step-by-step explanation:

Since the highest GCF is 3, I divided 6s, 18t, and 3w. This equals to 3(2s + 6t + w)

Answer:

3(2s+6t+w)

Step-by-step explanation:

Answer:

5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.                                          

Step-by-step explanation:

We are given the following in the question:

Bobby buys 10 pounds seafood for $30.

Let x pounds of shrimp be purchased and y pounds of crawfish.

Thus, we can write,

[tex]x + y =10[/tex]

Cost of shrimp = $5 per pound

Cost of crawfish = $1 per pound

Total money spent = $30

Thus, we can write the equation,

[tex]5x + y = 30[/tex]

Solving the two equation by elimination method,

[tex]5x + y-(x+y) = 30-10\\4x = 20\\x = 5\\y = 10 - x = 10 - 5 = 5[/tex]

Thus, 5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.

Answer:

C. x-intercepts: (-4,0), (-2,0)

E. Vertex: (-3,-1)

Step-by-step explanation:

Part 1) Find the x-intercepts

we have

[tex]y=(x+4)(x+2)[/tex]

This is a vertical parabola written in factored form

[tex]y=(x-x_1)(x-x_2)[/tex]

where

x_1 and X_2 are the roots or x-intercepts

so

[tex]x_1=-4\\x_2=-2[/tex]

Remember that the x-intercepts are the values of x when the value of y is equal to zero

therefore

The x-intercepts are

(-4,0) and (-2,0)

Part 2) Find the vertex

we have

[tex]y=(x+4)(x+2)[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

Applying distributive property

[tex]y=x^2+2x+4x+8\\y=x^2+6x+8[/tex]

Convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y=(x^2+6x+3^2)+8-3^2[/tex]

[tex]y=(x^2+6x+9)-1[/tex]

Rewrite as perfect squares

[tex]y=(x+3)^2-1[/tex] ----> equation in vertex form

[tex]y=(x-h))^2+k[/tex]

where

(h,k) is the vertex

therefore

The vertex is the point (-3,-1)

Answer:

Vertex: (-3,-1) X intercepts: (-4,0), (-2,0)

Step-by-step explanation:

A P E X ;)

Step-by-step explanation:

[tex]C = 2\pi \: r \\ = 2 \times 3.14 \times 4.5 \\ = 3.14 \times 9 \\ =28.26 \: units[/tex]

Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Solution:

Volume of the mega moving truck = length × width × height

                                                          [tex]$=22 \frac{1}{4}\times7 \frac{7}{12}\times 8 \frac{5}{12}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{22\times4+1}{4}\times \frac{7\times12+7}{12}\times \frac{8\times12+5}{12}[/tex]

                                                          [tex]$= \frac{89}{4}\times \frac{91}{12}\times \frac{101}{12}[/tex]

Volume of the mega moving truck = 1420.137 cubic ft

Volume of the 2-bedroom  moving truck = length × width × height

                                                          [tex]$=14 \frac{1}{2}\times7 \frac{7}{12}\times 7\frac{1}{6}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{14\times2+1}{2}\times \frac{7\times12+7}{12}\times \frac{7\times6+1}{6}[/tex]

                                                          [tex]$= \frac{29}{2}\times \frac{91}{12}\times \frac{43}{6}[/tex]

Volume of the 2-bedroom  moving truck = 788.035 cubic ft

Difference between them = 1420.137 – 788.035

                                           = 632.102 cubic ft

Hence Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Answer:

False

True

False

False

Step-by-step explanation:

1. We have to get the sum as follows :

[tex]3\frac{4}{9} + 4\frac{6}{9}[/tex]

= [tex]\frac{31}{9} + \frac{42}{9}[/tex]

= [tex]\frac{31 + 42}{9}[/tex]

= [tex]\frac{73}{9}[/tex]

= [tex]8\frac{1}{9} \neq 7\frac{1}{9}[/tex]

So, this is false.

2. We have to get the sum as follows :

[tex]4\frac{5}{6} + 1\frac{3}{6}[/tex]

= [tex]\frac{29}{6} + \frac{9}{6}[/tex]

= [tex]\frac{29 + 9}{6}[/tex]

= [tex]\frac{38}{6}[/tex]

= [tex]6\frac{2}{6}[/tex]

So, this is true.

3. We have to get the difference as follows :

[tex]4\frac{5}{8} - 2\frac{4}{8}[/tex]

= [tex]\frac{37}{8} - \frac{20}{8}[/tex]

= [tex]\frac{37 - 20}{8}[/tex]

= [tex]\frac{17}{8}[/tex]

= [tex]2\frac{1}{8} \neq 2\frac{3}{8}[/tex]

So, this is false.

4. We have to get the difference as follows :

[tex]7\frac{5}{8} - 4\frac{2}{8}[/tex]

= [tex]\frac{61}{8} - \frac{34}{8}[/tex]

= [tex]\frac{61 - 34}{8}[/tex]

= [tex]\frac{27}{8}[/tex]

= [tex]3\frac{3}{8} \neq 3[/tex]

So, this is also false. (Answer)

Answer:

B = (x + 7)^2 + (y +3)^2 = 4

Step-by-step explanation:

The equation of a circle with center (-7, -3) and radius 2 is (x + 7)² + (y + 3)² = 4.

The equation of a circle with a center at point (-7, -3) and a radius of 2 can be written based on the standard form of the circle equation (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

Plugging in the values given in the question, the equation simplifies to: (x + 7)² + (y + 3)² = 4.

Answer:

43.7 ft

Step-by-step explanation:

Radius of the semicircular garden is 8.5 ft .

Diameter = 8.5 × 2 = 17 ft

Circumference of the garden = [tex]\frac{1}{2}[/tex] × π × diameter = [tex]\frac{1}{2}[/tex] × π × 17 = 26.7 ft (rounded up to the nearest tenth of a foot)

Distance around the gardent = Circumference + diameter = 26.7 ft + 17 ft =  43.7 ft

Answer:

d ≥ 13.46

Step-by-step explanation:

Chris has to pay low balance fee if her bank balance falls below $10.

Her balance was -$3.46 before the statement date.

Now, Chris has to deposit a minimum amount of $(3.46 + 10) = $13.46 to her bank account and then only she does not need to pay a fee.

If the deposit amount is d, then the inequality to represent the situation is

d ≥ 13.46 (Answer)

Final answer:

Chris needs to deposit at least $13.46 to prevent a bank fee because her balance was -$3.46. By adding $3.46 to the minimum required balance of $10, we determine the least deposit amount through the inequality d ≥ 13.46.

Explanation:

To solve the situation where Chris avoids a fee by making a deposit, d, we must write an inequality that reflects her balance being above $10 after the deposit. Originally, her balance was -$3.46. Therefore, after deposit d, her new balance must be equal to or greater than $10 to prevent the fee. The inequality representing this situation is:

d - 3.46 ≥ 10

When you add $3.46 to both sides to isolate d, the inequality becomes:

d ≥ 13.46

This inequality indicates that Chris's deposit must be at least $13.46 to avoid the bank fee.

Final answer:

The expression equal to [tex]-x^2[/tex] - 4 is formed by multiplying two complex conjugates. Option C: (x+2i)(x-2i) correctly expands to [tex]-x^2[/tex] - 4, since the product of the imaginary parts (2i × -2i) equals -4. The correct option is C: (x+2i)(x-2i).

Explanation:

The expression [tex]-x^2[/tex] - 4 can be created by multiplying two complex numbers that, when multiplied, give a negative real part and a positive imaginary part squared. Using the fact that (i)(i) = -1, we can deduce that the product of complex conjugates will give us the desired expression because the imaginary parts will cancel each other out leaving us with a purely real number.

When we multiply two complex conjugates, the general form is (a+bi)(a-bi) = [tex]a^2 - (bi)^2 = a^2 + b^2[/tex], since [tex](bi)^2[/tex] equates to [tex]-b^2[/tex] because [tex]i^2[/tex] = -1. Applying this to our problem, we are looking for 2 numbers whose square equals 4. Since 2i × -2i = -4, we can construct the two factors as (x+2i) and (x-2i), which corresponds to option C: (x+2i)(x-2i).

3 67/100

3 will stay a whole number so you put that as the whole number. 67 is 67 percent of a whole. so you put it over 100.

Answer:

Option D. y=4x+35

Step-by-step explanation:

From the graph take the points (5,50) and (50,250)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{250-50}{50-5}[/tex]

[tex]m=\frac{200}{45}=4.4[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=4.4\\point\ (5,50)[/tex]

substitute

[tex]50=4.4(5)+b[/tex]

solve for b

[tex]b=50-22\\b=28[/tex]

substitute

[tex]y=4.4x+28[/tex]

therefore

The equation that BEST models the data is

[tex]y=4x+35[/tex]

Answer:

Step-by-step explanation:

6x ≤ -18.....divide both sides by 6

x ≤ -18 / 6

x ≤ -3

ok...so ur gonna have a closed circle because the inequality contains an equal sign......ur gonna put that closed circle on -3 and shading will go to the left because it is less then

closed circle on -3, shaded to the left <==

Answer:

closed circle on -3 and shaded to the left

Hope it Helped <3

Answer:

answer is a

Step-by-step explanation:

look at picture

Answer:

12x^2-15x

Step-by-step explanation:

PLATO

The expression 12x²-15x has the same GCF as 15x² - 21x.

An expression is combination of variables, numbers and operators.

The given expression is 15x²-21x

Let us find GCF of the given expression.

The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial

15x²-21x

3x(5x-7)

The GCF of 15x²-21x is 3x.

Now GCF of 18x²-24x,  6x(3x-4) is 6x

GCF of 12x²-15x, 3x(4x-4) is 3x

GCF of 15x²-21, 3(5x²-7) is 3

GCF of 12x²-18x, 6x(2x-3) is 6x

Hence, the expression 12x²-15x has the same GCF as 15x² - 21x.

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Answer:

1

Step-by-step explanation:

(12 - 4) - (6 / 2) - (2 * 2)

(8) - (3) - (4)

1

Answer:

1

Step-by-step explanation:

go to google calculator

Answer:

2121.6 cubic inch

Step-by-step explanation:

Length of the box = 17 inches

Width of the box = 1.3 feet = 1.3 * 12 inches = 15.6 inches

Height of the box = 8 inches

Volume of the box is given by the product of its length , width and height.

Hence, Volume = {tex]\[length * width * height\][/tex]

= [tex]\[17 * 15.6 * 8\][/tex]

= 2121.6

Hence the volume of the box is 2121.6 cubic inch

This can also be expressed in cubic feet by dividing it by 1728.

In cubic feet the volume will be 1.23 cubic ft.

To calculate the remaining blueberries after using 1/5 for muffins, subtract 1/5 from the total, leaving you with 4/5 of the original amount in pounds.

To determine how many pounds of blueberries are left after using 1/5 of them to make muffins, we need to perform a subtraction based on the fraction used. Let's assume we start with a certain quantity 'X' pounds of blueberries. After using 1/5 of them, we have 4/5 of 'X' pounds left because we subtract the 1/5 that was used for muffins from the original amount. It's important to convert any measurement units if they are not consistent, as seen when comparing pounds and ounces for other items like yogurt or apples.

The remaining amount of blueberries in the container is [tex]\( \frac{4}{5} \)[/tex] of the initial amount.

To determine how many pounds of blueberries are left in the container, we need to set up the problem and solve it step-by-step.

Let's denote the initial amount of blueberries as [tex]\( x \)[/tex] pounds.

1. Define the amount used for muffins:

If [tex]\( \frac{1}{5} \)[/tex] of the remaining blueberries is used to make muffins, it means that [tex]\( \frac{1}{5} \)[/tex] of the total blueberries is used.

Therefore, the amount of blueberries used for muffins is [tex]\( \frac{1}{5} x \)[/tex].

2. Calculate the remaining blueberries:

The remaining blueberries will be the total amount minus the amount used for muffins.

Thus, the remaining blueberries are:

[tex]\[ x - \frac{1}{5} x \][/tex]

3. Simplify the expression:

[tex]\[ x - \frac{1}{5} x = \frac{5}{5} x - \frac{1}{5} x = \frac{4}{5} x \][/tex]

Answer:

X=4 Hope it helps Lol

Step-by-step explanation:

  5*x-3-(21-x)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  6x - 24  =   6 • (x - 4)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    6   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    x-4 = 0

Add  4  to both sides of the equation :

                     x = 4

One solution was found :

                  x = 4

Answer:

X=4

Step-by-step explanation:

Answer:

The sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and  [tex]g(x)[/tex], meaning it is a reflection through the y-axis.

Therefore, [tex]g(x)[/tex]  will be the reflection of [tex]f(x)[/tex] through the y-axis.

Step-by-step explanation:

Considering the functions

We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.

Here, the sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and  [tex]g(x)[/tex], meaning it is a reflection through the y-axis.

Therefore, [tex]g(x)[/tex]  will be the reflection of [tex]f(x)[/tex] through the y-axis.

Answer:

The sign of  in  is opposite or negated. This is the only difference between  and  , meaning it is a reflection through the y-axis.

Therefore,   will be the reflection of  through the y-axis.

Step-by-step explanation:

Considering the functions

f(x) = 0.7(6)x

g(x) = 0.7(6)–x

We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.

Here, the sign of  in  is opposite or negated. This is the only difference between  and  , meaning it is a reflection through the y-axis.

Therefore,   will be the reflection of  through the y-axis.

Answer:

8x + 5

Step-by-step explanation:

By adding

2x + 6 + 6x -1

8x + 5

Answer:

-60

Step-by-step explanation:

1/4w + 5 = w/3 + 10

Collect like terms

1/4 w - 1/3 w = 10 - 5

Find lcm of 4 &3 = 12 and subtract

-1/12 w = 5

Multiply both sides by 12

-w = 5 x 12

-.w = 60

Divide both sides by -1

w = -60

I hope this was helpful, Please mark as brainliest

Answer:

It certainly doesn't make sense. Her equation means

5 times some number is 25.

hope it helps!

Answer:

  linear inequality (not a function)

Step-by-step explanation:

The given inequality is linear in the variables x and y. It maps x to an infinite number of possible values for y, so the relation is not a function.