A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?

Answer:

8 : 1

Step-by-step explanation:

Given ratio of sides = a : b, then

ratio of area = a² : b²

ratio of volumes = a³ : b³

Given

ratio of areas = 384 : 96 = 4 : 1 ← in simplest form, then

ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{1}[/tex] = 2 : 1

Hence

ratio of volumes = 2³ : 1³ = 8 : 1

to get the slope of it, we simply need two points off the table, say (-4,-114) and (2,48).  Recall that the y-intercept, where the graph intercepts the y-axis, when that happens x = 0, so is right there on the table already.

[tex]\bf \begin{array}{rrll} x&y\\ \cline{1-2} -4&-114\\ -2&-60\\ 0&-6&\leftarrow y-intercept\\ 2&48\\ 4&102 \end{array}~\hfill (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-114})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{48})[/tex]

[tex]\bf slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{48-(-114)}{2-(-4)}\implies \cfrac{48+114}{2+4}\implies \cfrac{162}{6}\implies 27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(\stackrel{slope}{27}~~,~~\stackrel{y-intercept}{-6} \right)~\hfill[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]g\left(x\right)=\left|x+4\right|+2[/tex]

The vertex of the function is the point (-4,2)

The y-intercepts is the point (0,6)

using a graphing tool

see the attached figure

Answer:

It is the second graph

Look at the picture that's attached to that is the answer

Final answer:

To convert 27 feet to inches, multiply 27 by the conversion factor of 12 inches per foot, resulting in 324 inches.

Explanation:

To convert 27 feet to inches, we use the unit equivalence that 1 foot = 12 inches. We multiply the number of feet by the conversion factor to get the measurement in inches.

27 feet × 12 inches/foot = 324 inches.

Therefore, 27 feet is equivalent to 324 inches. This is a straightforward application of unit conversion, which is a fundamental skill in mathematics, especially useful for various applications in science, engineering, and everyday calculations.

Answer:

j=2

Step-by-step explanation:

First, subtract by 5 from both sides of equation.

5-j-5=3-5

Simplify.

3-5=-2

-j=-2

Divide by -1 from both sides of equation.

-j/-1=-2/-1

Simplify, to find the answer.

-2/-1=2

It change negative to positive.

j=2 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

2

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1st step: again, reverse the equation (by flipping the equation around)

2nd step: do the equation ; 5 - 3  = 2

3rd step: (check your answer) ; 3 plus 2 equals 5

therefore, the answer 2 is correct.

Answer:

Top Right

Step-by-step explanation:

First things first, you can eliminate the bottom left option. The domain 3≤x≤6 means that the graph will only show points greater than or equal to 3 and less than or equal to 6. That option shows x = 2, which is not in this domain.

The symbols on either side of the x are known as ceiling functions. It means that y equals whatever whole number is greater than or equal to than x.

Basically, whatever y is, round it up to the nearest whole number to get x.

So, let's do a table from x = 3 to x = 6

   x ║ y               Now, see which graph best matches these

2.5 ║ 3               coordinates. Keep in mind that to be a function,

  3 ║ 3                the points cannot overlap (they have to pass the

3.5 ║ 4                vertical line test). It looks like the best answer is

  4 ║ 4                going to be the top right.

4.5 ║ 5

  5 ║ 5

5.5 ║ 6

  6 ║ 6

Answer:

Top Right Corner

Step-by-step explanation:

The swiftest way to know this is that on each end is a closed circle from 3 [open] to 6 [close]. Bottom left is close, but has an extra line signaling that x is equal to 2, and it is not included, so do not pick this one.

I am joyous to assist you anytime.

Answer:

No; 1,000 will cause him to exceed 1,800.

Step-by-step explanation:

Given,

The consumed calories = 1,600,

Burned calories = 400,

Thus, the remaining calories = 1600 - 400 = 1200

Since, 1,800 calories per day would be like to keep,

Also, 1200 < 1800

Hence, remaining calories is less than the required calories,

And, the calories left to consume for the day = Required calories - remaining calories

= 1800 - 1200

= 600

Therefore, 600 is the viable solution to this problem.

Note : If 1,000 a viable solution to this problem then the required calories will be more than 1800 or exceed 1800.

Answer:

c

Step-by-step explanation:

Divide using synthetic division, remembering to place a zero to denote the terms x³, x² and x

Since division by (x - 3) then evaluate using h = 3

3 | 1  0  0  0  7

    ↓

    1    3  9  27 81

   ----------------------

    1  3  9  27  88 ← degree 3 polynomial

quotient = x³ + 3x² + 9x + 27 , remainder = 88 → c

Follow below steps:

To divide x^4 + 7 by x - 3, we will use polynomial long division. This process is similar to the long division we use with numbers. Let's perform the division step by step:

Divide the term with the highest power in the dividend (x^4) by the highest power in the divisor (x) to get x^3.

Multiply the entire divisor by x^3 and subtract the result from the dividend.

The subtraction will give a new polynomial. Repeat the process until the degree of the remainder is less than the degree of the divisor, or until no further division can be carried out.

The correct result for the division of x^4 + 7 by x - 3 is option (a): x^3 - 3x^2 - 9x - 27 R 88.

Answer:

20 students

Step-by-step explanation:

It says 80% of 25 students got 83%+.

This means the number of students that got 83%+ is 80% of 25, or 25*0.8.

25*0.8 is 20, so 20 students got 83%+.

Answer:

20 students earned 83% or better in last maths test.

Step-by-step explanation:

We are given that on Ms. Smith's last math test, 80% of her 25 students earned an 83% or better.

We are to find the number of students who earned 83% or better on the test.

Number of students who earned 83% or more = 80% × 25 = [tex] \frac { 8 0 }{ 1 0 0 } \times 2 5[/tex] = 20

Answer:

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

Step-by-step explanation:

We need to identify the equation in point slope form.

The standard equation of point slope form is:

(y-y₁) = m (x-x₁)

where m is the slope and x₁ and y₁ are the points

We are given point(4,-1) so,

x₁=4 and y₁=-1

And a perpendicular line: y =3x+5

Which is equal to y = mx+b

where m is slope so, slope m = 3

Since the line is perpendicular, so the slope in negative inverse of actual slope that m = -1/m

i.e, m = -1/3

So, the equation in point slope form is:

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

=> y+1 = (-1/3)(x-4)

Answer:

The equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

Step-by-step explanation:

Given

Let P represent the lind

Equation of P; y = 3x + 5

Let Q represent the other point.

Coordinates of Q; Q(4,-1)

It is said that the line P is perpendicular to point Q.

So, the first thing to do is to calculate the slope of Q;

Since both lines are perpendicular, then we make use of formula for calculating the condition of perpendicularity

This is given as m1m2 = -1

Where m1 = slope of P

m2 = slope of Q

To get m1;

m1 is the coefficient of x in equation of line P.

So, m1 = 3.

Now we can solve for m2

m1.m2 = -1. ---- make m2 the subject of formula

m2 = -1/m1

Substitute 3 for m1

m2 = -1/3

m2 = -⅓

Recall that the coordinates of Q is 4 and -1.

To calculate the equation of Q; we make use of the following

m = (y - y1)/(x - x1)

Where m = m2 = -⅓

x1 = 4 and y1 = -1

By substituton, we have

-⅓ = (y - (-1))/(x - 4)

-⅓ = (y + 1)/(x - 4) --- multiply both sides by 3(x - 4)

-⅓ * 3(x - 4) = 3(x - 4) * (y + 1)/(x - 4)

-(x - 4) = 3(y + 1)

-x + 4 = 3y + 3 --- make y the subject of formula

3y = -x + 4 - 3

3y = -x + 1 --- divide through by 3

3y/3 = (-x + 1)/3

y = -x/3 + 1/3

y = -⅓x + ⅓

Hence, the equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

Answer:

$11,340

Step-by-step explanation:

1 month: 630

18 months: 18×630=11,340

Anna pays a total of $11,340 in rent over the course of 18 months by multiplying her monthly rent of $630 by 18.

To find out how much rent Anna pays over the course of 18 months, we need to multiply her monthly rent by the number of months. Anna pays $630 each month, so over 18 months, she would pay:

$630 times 18 = $11,340.

Therefore, Anna pays a total of $11,340 in rent over the course of 18 months.

Answer:

16π

Step-by-step explanation:

The surface area of a sphere is:

A = 4πr²

where r is the radius, or half the diameter.

If the diameter is 4 units, then the radius is 2 units:

A = 4π (2)²

A = 16π

The surface area is 16π square units.

Answer:

(–2.2, –3)

Step-by-step explanation:

y = – 3

y = x – 0.8

Substitute the value of y into the second equation

-3 = x-.8

Add .8 to each side

-3 +.8 = x-.8+.8

-2.2 = x

-3 =y

Answer:

The solution for the system of equations is (–2.2, –3)

Step-by-step explanation:

The solution of the system of equations can be expressed with its components in x and y in the form (x,y) where x is the value of x and y is the value of y. The values of x and y can be found solving the system of equations given.

1. Write the system of equations and name each equation:

[tex]y=-3[/tex] (Eq.1)

[tex]y=x-0.8[/tex] (Eq.2)

2. Replacing Eq. 1 in Eq. 2 and solving for x, we have:

[tex]y=x-0.8[/tex]

[tex]-3=x-0.8[/tex]

[tex]-3+0.8=x[/tex]

[tex]-2.2=x[/tex]

3. Express the answer as the solution tho the system of equations:

(x,y)=(-2.2,-3)

Answer:

16 : 25

Step-by-step explanation:

The ratio of girls : boys = 320 : 500

To simplify divide both parts by 10

320 : 500 = 32 : 50 ← now divide both parts by 2

32 : 50 = 16 : 25 ← in simplest form

Final answer:

To calculate the simplified ratio of the number of girls to the number of boys in the school, we divide the numbers 320 (girls) and 500 (boys) by their greatest common divisor, which is 80, resulting in the simplest form of 4:6.25 or 16:25.

Explanation:

The question is asking us to find the ratio of the number of girls to the number of boys in a school, and then to simplify this ratio to its simplest form. There are 320 girls and 500 boys in the school. To find the ratio, we compare the number of girls to the number of boys, which gives us 320 to 500.

To simplify the ratio, we look for the greatest common divisor (GCD) that both numbers share. Both 320 and 500 are divisible by 10 for certain, and further simplification can be found by dividing by the GCD of 80. So, if we divide both numbers by 80, we get 4 to 6.25, which simplifies further to a ratio of 4:6.25 or 16:25 when both sides are multiplied by 4. Therefore, the simplified ratio of the number of girls to the number of boys is 16:25.

Answer:

Step-by-step explanation:

From the picture we have:

4w = 3l

If w = 12 ft, then

3l = 4(12)

3l = 48             divide both sides by 3

l = 16 ft

The dimensions of rectangular floor are 4w × (l + w).

Substitute the values of w and l:

4w = 4(12) = 48 ft

l + w = 16 + 12 = 28 ft

The formula of an area of a rectangle:

A = width × length

Substitute:

A = (48)(28) = 1344 ft²

Step-by-step explanation:

problem answer in picture

The value of the expression after factorization is (x² + 2)(x² - 6)

'In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.'

According to the given problem,

[tex]x^{4} - 4x^{2} - 12\\[/tex]

⇒ [tex]x^{4} + 2x^{2} - 6x^{2} - 12\\[/tex]

⇒ [tex]x^{2} (x^{2} +2) -6(x^{2} +2)[/tex]

⇒ [tex](x^{2} +2)(x^{2} -6)[/tex]

Hence, we can conclude the value of the given expression after factorization is [tex](x^{2} +2)(x^{2} -6)[/tex].

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Answer:

[tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]

Step-by-step explanation:

Apply Distributive property:

[tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex]

Add like terms and then add 63 to both sides of the equation:

[tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex]

Pick the coefficient of the x term, divide it by 2 and square it:

[tex](\frac{2}{2})^2=1[/tex]

Add it to both sides of the equation:

[tex]x^2-2x+1=88+1[/tex]

Rewriting the left side as a squared binomial, we get:

[tex](x-1)^2=89[/tex]

Apply square root to both sides:

[tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex]

And finally we need to add 1 to both sides of the equation. Then we get:

[tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]

Answer:

[tex]56wx - 15yz - \frac{29}{3} [/tex]

Step-by-step explanation:

[tex]1. \: 56wx - 5y \times 3z - 9 - \frac{2}{3} \\ 2. \: 56wx - 15yz - 9 - \frac{2}{3} \\ 3. \: 56wx - 15yz + ( - 9 - \frac{2}{3} )[/tex]

The expression equivalent to given condition is 56wx - 15yz - 29/3.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression,

(8w.7x - 5y.3z - 9) - 2/3

since variables are in the product, so their constants are multiplied,

8w.7x  = 56wx

5y.3z  = 15yz

the equation can be written as,

56wx - 15yz - 9 - 2/3

and   - 9 - 2/3 = (-27 - 2)/3 = -29/3

=> 56wx - 15yz - 29/3

Therefore, the equivalent form of the equation is  56wx - 15yz - 29/3.

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Answer:he needs to sell 180 cookies or more

Step-by-step explanation:

90.00/.50=180

Answer:

The number is -8

Step-by-step explanation:

Let

x ---> the number

we know that

The algebraic expression is equal to

[tex]7x-x=-48[/tex]

Solve for x

[tex]6x=-48[/tex]

divide by 6 both sides

[tex]x=-48/6=-8[/tex]

-8 y e s -8 is the answer doods

Hello There!

Amount Saved = Original Price x Discount % / 100. So,

Amount Saved = 35 x 60 / 100

Amount Saved = 2100 / 100

Amount Saved = $21 (answer)

35 - 21 = 14

60% Off of $35.00 Is $14.00

Answer:  The required product is [tex]4x^5\sqrt[3]{3x}[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.[/tex]

We will be using the following property of exponents :

[tex](i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.[/tex]

The required multiplication is as follows :

[tex]P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.[/tex]

Thus, the required product is [tex]4x^5\sqrt[3]{3x}.[/tex]

Answer:

73 m is equal to 730 dm

Step-by-step explanation:

We Need to convert 73 m into dm

We know that 1 meter is equal to 10 decimeter

We are given 73 m. Multiply it with 10 and we will get value in decimeter

73*10

= 730 decimeter

So, 73 m is equal to 730 dm

Answer:

The correct answer would be 730 dm.

Step-by-step explanation:

M is the abbreviation of Meter and dm is an abbreviation of Decimeter. A meter is a unit of length as prescribed by the international system of units. This unit is used to measure the length. Decimeter is the smaller unit of meter. 10 Decimeter makes one meter, which means 1M equals 10DM. So where there are 73 meters, there would be 73 * 10 Decimeters in it. This is shown as below.

73 m = 73 * 10 = 730 DM

Answer:

x = 19°

Step-by-step explanation:

Let The angle be "a"

Now according to the question,

⇒ 3 × a = (90° - a) - 14° (Then remove the brackets)

⇒ 3a =  90° - a - 14°

⇒ 3 + a = 76°

⇒ 40° = 76°

⇒ a = 76/4

Now since you got 76/4 you have to make it into simplest form so it'll be :

19/1

Your answer is : a = 19°

Answer:

A on edg.

Step-by-step explanation:

Answer:

b. 3

Step-by-step explanation:

In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].

30°-60°-90° Triangles

x√3 → long side

x → short side

2x → hypotenuse

45°-45°-90° Triangles

x → two legs

x√2 → hypotenuse

I am joyous to assist you anytime.

Answer:

x = ±√ 24.500 = ± 4.94975

Step-by-step explanation:

:  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Step-by-step explanation:

4x² + 98 = 0

2x² + 49 = 0

2x² = -49

x² = -49/2

x = ±√(-49/2)

x = ±7i√(1/2)

x = (±7i√2) / 2

Answer:

[tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]-2x * -4x = 8x^2[/tex]

Outside terms: [tex]-2x * -3 = 6x[/tex]

Inside terms: [tex]-9y^2 * -4x = 36xy^2[/tex]

Last term in each binomial: [tex]-9y^2 * -3 = 27y^2[/tex]

Now, rearrange the terms correctly. [tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

This is our final answer, since it can not be simplified any more.

Answer:

C

Step-by-step explanation:

Edge 2020

Answer:

[tex]-439[/tex]

Step-by-step explanation:

we have

[tex]s(x)=2-x^{2}[/tex]

[tex]t(x)=3x[/tex]

we know that

[tex](sot)(x)=2-(3x)^{2}[/tex]

[tex](sot)(x)=2-9x^{2}[/tex]

For x=-7

substitute

[tex](sot)(-7)=2-9(-7)^{2}[/tex]

[tex](sot)(-7)=2-441[/tex]

[tex](sot)(-7)=-439[/tex]

[tex]\bf \begin{cases} x+2y=12\\ \cline{1-1} -x=-y-6\\ \boxed{x}=y+6 \end{cases}\qquad \qquad \stackrel{\textit{doing some substitution in the 1st equation}}{\boxed{y+6}+2y=12\implies 3y+6=12} \\\\\\ 3y=6\implies y=\cfrac{6}{3}\implies \blacktriangleright y=2 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{x=y+6\implies }x=(2)+6\implies \blacktriangleright x=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8,2)~\hfill[/tex]