Suppose an airplane climbs 15 feet for every 40 feet it moves forward. What is the slope of this airplane's ascent?

Rewrite the given equation in slope intercept form:

5 y = 10 – 2 x

y = - 0.4 x + 2

Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:

y = - 0.4 x + b

Given that x = 5, y = -4, find for b:

-4 = - 0.4 (5) + b

b = -2

So the answer is:

y = - 0.4 x – 2

or

2 x + 5 y = - 10

Answer:

Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.

Step-by-step explanation:

Whatever color the sister choses is irrelevant, eliminating answers A and B, but it does change the odds. If there are 5 red balloons and 4 blue balloons, if the sister is given a blue balloon, the odds of the brother receiving a red balloon increases (vis versa).

The value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].

Further explanation:

There are two properties.

1. The property of addition or property of sum.

2. The property of subtraction.

3. The property of division.

4. The property of multiplication.

Given:

The equation is 3ab - 9ab + 7ab.

Explanation:

Consider the equation S = 3ab - 9ab + 7ab.

The equation contains the two variables that are “a” and “b”.

In the equation we have two operations one is addition and another is subtraction.

Solve the above equation to obtain the value of the equation.

First add 3ab and 7ab.

[tex]\begin{aligned}X&=3ab+7ab\\&=10ab\\\end{aligned}[/tex]

Now subtract 9ab from 10ab.

[tex]\begin{aligned}S&=10ab-9ab\\&=1ab\\&=ab\\\end{aligned}[/tex]

The value of S is ab.

Hence, the value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Number System

Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables.

Answer:

The dog  is rather running towards the trainer to receive a treat. So it is the second answer.

The interest for each loan is $40.32, $4, $175 and $468 respectively.

The formula to find the simple interest is S.I=P×T×R/100.

Where, P=Principal, T=Time period and R=Rate of interest.

With P=$252, T=2 years and R=8%.

Now, SP=252×2×8/100=$40.32

With P=$400, T=6 months (0.5 years) and R=2%.

Now, SP=400×0.5×2/100=$4

With P=$5000, T=1 year and R=3.5%.

Now, SP=5000×1×3.5/100=$175

With P=$6,240, T=9 months (0.75 years) and R=10%.

Now, SP=6,240×0.75×10/100=$468

Therefore, the interest for each loan is $40.32, $4, $175 and $468 respectively.

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Answer:

x = 7

Step-by-step explanation:

Figure ABCD is a parallelogram

So sides AD and BC will be parallel and their length will be same.

[Since opposite sides of parallelogram are equal in length]

So mAD = mBC

(5x + 3) = 38

5x = 38 - 3 = 35

x = [tex]\frac{35}{5}[/tex]

x = 7

Therefore, x = 7 will be the answer.

The graph represents the function y = (x - 1), as per linear equation.

A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.

The given equation is:

y - 3 = x - 4

⇒ y = x - 1

Therefore, for x = 0, y = - 1

for x = 1, y = 0

for x = - 1, y = - 2

Therefore, the graph will pass through points (0, - 1), (1, 0), (- 1, - 2).

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Answer:

its A

Step-by-step explanation:

Answer:

The original price of socks was $8.

Step-by-step explanation:

James buys a shirt and a pair of socks on sale for 25% off.

The price of the shirt before the sale was $24 that means after discount the price was:

[tex]24-(0.25\times24)[/tex] = $18

And James paid a total of $24.

That means the price of socks after discount is = [tex]24-18[/tex] = $6

Let the original price of socks be x. And after 25% discount, it was for $6.

So, [tex]x-0.25x=6[/tex]

=> [tex]0.75x=6[/tex]

x = 8.

Hence, the original price of socks was $8.

There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard

The probability of an event is defined as the possibility of an event occurring against sample space.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination is the number of ways to select objects.

[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]

Let us tackle the problem.

This problem is similar to Pascal Triangle.

The Lord can move to the right or up in one way only.

We can put "1" in each box on the bottom and left to represent 1 possible movement.

To get the possibility of movement to another box, we will add the possibility of movement to the left, right, and diagonal squares as shown in Figure 1.

This process is repeated for the next box as shown in Figure 2.

Finally, after this process is repeated until the top right box, we get the results as shown in Figure 3.

There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard.

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

Answer:

the answer is 7x on edg... i just took the pretest

Step-by-step explanation:

The converse, inverse, and contrapositive of the given statement are provided. They are logically consistent with the original statement, pointing to the synonymous relationship between congruence and identical length in segments. The additional statement about angles is also factual, as one greater than an acute angle is, by definition, an obtuse.

1.) Converse: If two segments have the same length, then they are congruent.
2.) Inverse: If two segments are not congruent, then they do not have the same length.
3.) Contrapositive: If two segments do not have the same length, then they are not congruent.

The contrapositive is true because it is a logical inverse of the original statement, which is also true. In geometry, congruent means being of the same size and shape, which directly implies having the same length.

4.) The statement: 'If m∠A is greater than an acute ∠B, then ∠A must be obtuse' is true. An acute angle is one that is less than 90 degrees. If ∠A is greater than this, it must be between 91 and 180 degrees, which by definition, makes it an obtuse angle.

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Final answer:

To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.

Explanation:

Cost of Each Slice of White Chocolate Torte

To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:

Total cost for 2 tortes: $11.90

Number of slices per torte: 8

Total number of slices: 2 tortes × 8 slices/torte = 16 slices

Cost per slice: $11.90 / 16 slices = $0.74375 per slice

Therefore, each slice costs approximately 74 cents to make.

The length of each side of the tablecloth is 13 inches.

To find the length of each side of the tablecloth, we need to take the square root of the area. Since the area is given as 169 square inches, we can take the square root of 169. The square root of 169 is 13, so each side of the tablecloth is 13 inches long.

Answer:

If Veronica gave $35 to Bill, she spent $70 to buy books and she has $70 left.

Step-by-step explanation:

Final answer:

To express 112 as a product of prime numbers in index form, we perform prime factorization to get 2⁴ x 7.

Explanation:

To express 112 as a product of prime numbers in index form, we start by performing prime factorization, which is breaking down a composite number into the prime numbers that, when multiplied together, give the original number.

Let's find the prime factors of 112:

So, we can express 112 as a product of prime factors as 2⁴ × 7¹ or simply 2⁴ × 7, since any number to the power of 1 is the number itself.

Answer:

[tex]6x^2-31x+35[/tex]

Step-by-step explanation:

Given expression,

[tex](3x-5)(2x-7)[/tex]

By using distributive property,

[tex](3x-5)(2x) - (3x - 5)(7)[/tex]

Again by distributive property,

[tex]3x(2x) - 5(2x) - 3x(7) + 5(7)[/tex]

[tex]6x^2 - 10x - 21x + 35[/tex]

[tex]6x^2-31x+35[/tex]

Hence, FIRST option is correct.

Answer:

Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]

Step-by-step explanation:

Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here r is the radius of the cone and h is the height of the cone.

Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]

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

Height of the cone = radius of the cylinder = r

Now we put the values of radius and height of cone in the formula

Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]

= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]

= [tex]\frac{1}{12}\pi r^{3}[/tex]

Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]

Answer:

22 secs.

Step-by-step explanation:

h(t) = -16t^2 + 704t

The maximum will happen where the first derivative is equal to 0.

h’(t) = -32t + 704

-32t + 704 = 0 => -32t = -704 After subtracting 704 from both sides of the equation

Now divide both sides of the equation by -32

t = 22 secs.

Double Check: recalculated/reasonable ✅ ✅

Answer: 22 secs.

Just an interesting aside. After 22 secs, the projectile will be -16(22)^2 + 704(22) = -7744 + 15,488 = 7744 units up as its maximum height.

Answer:

the top tier is 64 cubic centimeters

the middle tier is 576 cubic centimeters

the bottom tier is 1728 cubic centimeters

the entire cake is 2368 cubic centimeters

The expression of the word problem can be written as M-99=299 where M is 398.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 99 subtracted from m is 299. The expression for the word problem can be written as:-

M-99=299

M = 299 + 99

M = 398

Therefore, the expression of the word problem can be written as M-99=299 where M is 398.

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