Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?

10 hours
5.5 hours
8.5 hours
55 hours

Answer:

y=72

x=0

Step-by-step explanation:

In the given question, Stuart is not correct.

The sum of all internal angles of a triangle is always equal to 180°.

Value of ∠1 = 65°(given)

Value of ∠7 = 55°(given)

Now let's look into Stuart's reasoning:

Step 1 : It is correct because according to angle sum property of triangle, ∠1 + ∠7 + ∠8 = 180°.

Step 2 : This step is wrong, because ∠4 and ∠8 are corresponding angles and not ∠12 and ∠8, so ∠4 = 60°.

Step 3 : This step is also wrong , ∠4 + ∠12 = 180°

             So ∠12 = 180 - 60 = 120°

Hence, Stuart's value of ∠12 is not correct.

Learn more about angles on:

https://brainly.com/question/25716982

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Answer:

(x - 6)(x+4)

Step-by-step explanation:

Final answer:

The quadratic expression x^2 - 2x - 24 can be factored into two binomials as (x - 6)(x + 4).

Explanation:

To factor the quadratic expression x^2 - 2x - 24 completely, we start by looking for two numbers that multiply to give -24 (the constant term) and add to give -2 (the coefficient of x). These two numbers are -6 and +4 because (-6) * (+4) = -24 and (-6) + (+4) = -2.

We can now rewrite the quadratic expression as:

(x - 6)(x + 4) = 0

Therefore, the factored form of the expression x^2 - 2x - 24 is (x - 6)(x + 4).

Let's translate the sentences into equations:

One number is 20 more than another: [tex]x=20+y[/tex]

If the greater number is increased by 4: [tex]x+4\ldots[/tex]

The result is five times the smaller [/tex]\ldots=5y[/tex]

So, we have the following system:

[tex]\begin{cases}x=20y\\x+4=5y\end{cases}[/tex]

Use the expression for x given by the first equation to solve the second:

[tex]x+4=5y \iff 20+y+4 = 5y \iff 24= 4y \iff y = 6[/tex]

which easily implies

[tex]x=y+20 = 26[/tex]

Answer:

[tex]-16t^2 + 1,000>300[/tex]

[tex]t<6.61\ s[/tex]

Step-by-step explanation:

We know that the distance of the object while falling is given by the equation:

[tex]d = -16t^2 + 1,000[/tex]

To find the time interval in which the object is at a height greater than 300 ft, we must do

[tex]d> 300[/tex]

So

[tex]-16t^2 + 1,000>300[/tex]

[tex]-16t^2>-700[/tex]

[tex]16t^2<700[/tex]

[tex]t^2<\frac{700}{16}[/tex]

[tex]t<\sqrt{\frac{700}{16}}[/tex]

[tex]t<6.61\ s[/tex]

The interval is

t ∈ (0, 6.61)

And the inequality used  is: [tex]-16t^2 + 1,000>300[/tex]

Answer:

He bought 3 steaks and 4 watermelons

Step-by-step explanation:

Let

x -----> the number of steaks bought

y ----> the number of watermelons bought

we know that

[tex]x+y=7[/tex]

[tex]x=7-y[/tex] ----> equation A

[tex]3x+2.50y=19[/tex] ----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for y

[tex]3(7-y)+2.50y=19[/tex]

[tex]21-3y+2.50y=19[/tex]

[tex]3y-2.50y=21-19[/tex]

[tex]0.50y=2[/tex]

[tex]y=4\ watermelons[/tex]

Find the value of x

[tex]x=7-4=3\ steaks[/tex]

therefore

He bought 3 steaks and 4 watermelons

Answer: [tex]\angle G=23\°[/tex]

Step-by-step explanation:

Remember that an inscribed angle is defined as an angle formed by two chords and whose vertex lies on the circle.

By definition, the measure of an inscribed angle is:

[tex]Inscribed\ Angle=\frac{Intercepted\ Arc}{2}[/tex]

You know that:

[tex]Intercepted\ Arc=AD = (6x -80)\\\\Inscribed\ Angle=\angle G=(x + 2)[/tex]

Then, you need to substitute values and solve for "x":

[tex](x+2)=\frac{(6x -80)}{2}\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=\frac{84}{4}\\\\x=21[/tex]

Substituting the value of "x" into [tex]\angle G=(x + 2)\°[/tex] you get:

 [tex]\angle G=(21 + 2)\°=23\°[/tex]

Answer:

The measure of <G =  23°

Step-by-step explanation:

From the figure we can write,

The measure of <G is half the  the measure of arc AD

To find the value of x

We have  AD = (6x - 80)° and <G = (x + 2)°

6x - 80 = 2(x + 2)

6x - 80 = 2x + 4

6x - 2x = 4 + 80

4x = 84

x = 84/4 = 21

To find the measure of <g

m<G = x + 2

 = 21 + 2 = 23°

Therefore the measure of <G =  23°

3.542 is the answer; you just need to move the decimal 2 places to the left.

ANSWER

6

EXPLANATION

The given equation is:

[tex] \frac{1}{3} (12x - 24) = 16[/tex]

Multiply through by 3.

12x-24=16×3

12x-24=48

Group similar terms:

12x=48+24

12x=72

Divide both sides by 12

x=6

The answer is 6.hope this helps. please add brainlist

Answer:

Yes.

Step-by-step explanation:

Yes they are because that is the definition of congruency.

Answer:

E, F and G have determinants.

Step-by-step explanation:

Only square matrices have determinants so D which is not square does not have a determinant.

Determinant of F (2*3) - (1 * -1)

= 6 +1

= 7.

The determinant of G is obtained in the same way.,

THe determinant of E is worked out as follows

I 0  -1   1 |        0 *  | -1  -3 | - ( -1) *  | 3 -3| + 1 * | 3 -1|

I 3  -1  -3 |  =           |  0  5 !            |2  5|         |2 0|

I 2   0 5  |

= 0 *  -5 + 1 * 21 + 1 * 2

= 23.

ANSWER

Option D

EXPLANATION

The given function is

[tex]f(x) = (x - 1)(x + 4)[/tex]

The graph of this function, will touch the x-axis at x=1 and x=-4.

This graph is a minimum graph.

This parabola will open up.

The correct choice is D.

Answer:

4th Graph is correct option.

Step-by-step explanation:

Given Function is ,

f(x) = ( x - 1 )( x + 4 )

f(x) = x² + 3x - 4

Since, we are given a quadratic function.

So, Graph is a parabola.

Now we find the vertex of the parabola by expressing given function in standard form of parabola.

Consider,

y = x² + 3x - 4

x² + 3x = y + 4

[tex]x^2+3x+(\frac{3}{2})^2=y+4+(\frac{3}{2})^2[/tex]

[tex](x+\frac{3}{2})^2=y+4+\frac{9}{4}[/tex]

[tex](x+\frac{3}{2})^2=y+\frac{25}{4}[/tex]

By comparing this equation with ( x - h )² = 4a( y - k )

where, ( h , k ) is vertex of the parabola.

⇒ Vertex of the given function = [tex](\frac{-3}{2},\frac{-25}{4})[/tex]

These coordinates of the vertex lie in 3rd Quadrant.

Now looking at all given graphs. Only 4th Graph has vertex in 3rd quadrant.

Therefore, 4th Graph is correct option.

Answer:

c.) 18cm²

d.) 609m²

Step-by-step explanation:

I assumed that the question is the area of the grey fields.

c.) The white triangle is proportional to the big triangle whose side are known, (6,8). Thus the white trianlge's sides are (3,4). The area of a triangle is base*height / 2. Calculating the big triangle area subtracting the white triangle area gives the area of the grey. (6*8)/2-(3*4)/2 = 24 - 6 = 18.

d.) Area of a square is multiply the two sides. Adding together the greys, subtracting the whites will give the area of the grey. Small grey (11*14) Big grey (36*17) Big white (6*18) small white (7*7) -> 154+612-108-49=609.

The missing sides of the squares can be calculated by the given sides. Small grey 36-22=14. Big grey 28-11=17. Small white 13-6=7.

Any number (except zero) raised to the power of zero is one:

[tex]11^0=1[/tex]

On the other hand, by definition, the square of a number is that number multiplied by itself:

[tex]11^2=11\cdot 11 = 121[/tex]

So, the two answer are not the same:

[tex]11^0\neq 11^2[/tex]

After all, the exponential function

[tex]y=11^x[/tex]

is injective, which means that, given [tex]x_1\neq x_2[/tex], we have

[tex]11^{x_1}\neq 11^{x_2}[/tex]

ANSWER

The correct answer is B

EXPLANATION

The given expression is:

[tex] \sqrt[3]{ {x}^{5}y } [/tex]

We split the radical sign to obtain;

[tex] \sqrt[3]{ {x}^{5} } \times \sqrt[3]{ y } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We rewrite each radical expression in exponential form to obtain:

[tex] {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } [/tex]

The correct answer is B.

let's notice something, angles α and β are both in the I Quadrant, and on the first quadrant the x-coordinate/cosine and y-coordinate/sine are both positive.

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{5^2-3^2}=b\implies \pm\sqrt{16}=b\implies \pm 4=b\implies \stackrel{\textit{I~Quadrant}}{\boxed{+4=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill[/tex]

Answer:

c(h) = 40*h + 50

Step-by-step explanation:

Let h be the variable that represents the number of hours

As the cable operator charges $40.00 for an hour so for h hours, the expression will be 40*h

And  

Lastly, he has to charge $50.00 must as service charge,

As the number of hours is variable here so the function will be in terms of hours.

So the resulting function will be:

c(h) = 40*h + 50

Answer:

= -3x2 - 11x + 13

Step-by-step explanation:

=( +9) + (-3x2 - 11x + 4)

= -3x2 - 11x + 4 + 9

= -3x2 - 11x + 13

Answer:

The original number is 4 1 5 3 OR 4 5 8 3

Step-by-step explanation:

* Lets find a way to solve this problem

- The end of the 4-digit number is 3

∴ The number is # # # 3

- The number decrease by 738 if the 3 becomes the first number

∴ The new number is 3 # # #

- Make it as a subtraction problem

∵ # # # 3 - 3 # # # = 0 7 3 8

- Lets subtract

∵ 3 - # = 8

∵ 8 > 3 we must borrow 1 from the number before 3

∴ 13 - 8 = 5

∴ # # # 3 - 3 # # 5 = 0 7 3 8

- Put the 5 in the first number, we can not pot it as a first number

 bwcause when we subtract it from 3 the answer will be 2 but we

 need answer zero

∴ Lets put it before the 3

∴ # # 5 3 - 3 # # 5 = 0 7 3 8

∵ we borrowed 1 from the 5 before

∴ 4 - # = 3

∴ # = 4 - 3 = 1

∴ # # 5 3 - 3 # 1 5 = 0 7 3 8

- Now we must use the 1 in the first number we can not put it as a

 number because it is smaller than 3, we must put it in the 2nd

 missing place

∴ # 1 5 3 - 3 # 1 5 = 0 7 3 8

∵ 1 - # = 7

∵ 1 < 7 so we must borrow 1 from the number before it

∴ 11 - # = 7

∴ # = 11 - 7 = 4

∴ # 1 5 3 - 3 4 1 5 = 0 7 3 8

- We must use the 4 in the first number and we have only one

 missing place (the first place)

∴ 4 1 5 3 - 3 4 1 5 = 0 7 3 8

∴ The original number is 4 1 5 3

* You can find another answer if you put the 5 in the 2nd place in the

 first number the answer will be 4 5 8 3 try to do it

Answer:

what ratio man??

Step-by-step explanation:

Answer: A

Step-by-step explanation:

'A' can't be reduced anymore because 17 is a prime number.

Prime number: a number with only two factors- 1 & itself

Answer:

x = 21

Step-by-step explanation:

the answer is 8 hoped this helped !!!

Answer:

8

Step-by-step explanation:

This is because the slope of a line in an equation is m. In the equation given m=8, so that makes the slope 8.

ANSWER

[tex] {f}^{ - 1} =\pm \sqrt{x + 1} [/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 1[/tex]

Let

[tex]y = {x}^{2} - 1[/tex]

Interchange x and y to get:

[tex]x= {y}^{2} - 1[/tex]

Solve for y,

[tex]x + 1 = {y}^{2} [/tex]

Take square root of both sides to get,

[tex] \pm \sqrt{x + 1} = y[/tex]

This is the same as:

[tex]y = \pm \sqrt{x + 1} [/tex]

Therefore the inverse is

[tex] {f}^{ - 1} =\pm \sqrt{x + 1} [/tex]

Answer:

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=3x+1;\ g(x)=x^2-6\\\\(f+g)(x)=(3x+1)+(x^2-6)=x^2+3x+1-6=x^2+3x-5[/tex]

100.014. I think this is it

Answer:

Y=3

Step-by-step explanation:

The Answer is y=3-2x

Answer: its 300

aka D

Step-by-step explanation:

I did the quiz

Answer:

$7.50

Step-by-step explanation:

Since the price of the picnic cooler 7.95 with 6% sales tax, we can write:

X*1.06 = 7.95

Dividing both sides by 1.06,

X= 7.50

So Anton paid $7.50 alone without tax

Answer: Cost of cooler alone = $7.47

Step-by-step explanation:

Anton's bill including tax = $7.95

6% of his bill accounts for sales tax.

Sales tax = 6/100 × 7.95 ≈ $0.48

So cost of cooler alone =  Total bill - tax

= 7.95 − 0.48

= $7.47

There is another way of doing this problem as well, but which ever one is easier for you could it.

Anton's bill including tax = $7.95, out of this 6% is sales tax. This implies 94% (100 − 6) of total bill accounts for cooler alone.

Cost of cooler alone:

=94/100 ×7.95

= 0.94 ×7.95

= $7.47

* Hopefully this helps:) Mark me the brainliest:)!!!

~234483279c20~

Answer:

113.1

Step-by-step explanation:

Volume of sphere = [tex]\frac{4}{3}[/tex] × π × r²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 3²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 9

Volume of sphere =  [tex]\frac{4}{3}[/tex] × 9 π

Volume of sphere = 113.1

Answer:

[tex]V=113.1cm^3[/tex]

Step-by-step explanation:

The formula to calculate the volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere.

In this case we do not know the radius of the sphere, but we know the diameter.

By definition the diameter of a sphere is equal to twice the radius. This is:

[tex]d = 2r[/tex]

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

In this case d=6 cm

So

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

[tex]r = 3\ cm[/tex]

Finally

[tex]V=\frac{4}{3}\pi 3^3[/tex]

[tex]V=36\pi\ cm^3[/tex]

[tex]V=113.1cm^3[/tex]

Answer:

See below

Step-by-step explanation:

Step 1.

P = $400

r = 0.04

t = 10 years

n = 12  ( as there are 12 months in a year).

Step 2.

A(10) = 400(1 + 0.04/12)^12^10

= 400 * 1.00333333^120

= $596.33 to the nearest hundredth (answer).

Answer and Explanation:

Given : The value of $400 invested at 4% interest compounded monthly for 10 years.    

To find : The value of each of the following for this problem ?

Solution :

The interest formula is [tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

Step 1 -

P is the amount invested, P=$400

r is the interest rate, r=4%=0.04

t is the time , t=10 years

n is the number of compounding periods per year, n=12

Step 2 - To find A(10),

Substitute all the values in the formula,

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A(10)=400(1+\frac{0.04}{12})^{12\times 10}[/tex]

[tex]A(10)=400(1+0.0033)^{120}[/tex]

[tex]A(10)=400(1.0033)^{120}[/tex]

[tex]A(10)=400(1.490)[/tex]

[tex]A(10)=596.33[/tex]

Therefore, The amount after 10 year is $596.33.

Below is an image of the table cloth with its measurements

The formula for Area is:

A = length x height

The length of this shape is 8 feet

The height of this shape is 4 feet

so...

A = 8 x 4

A = 32

Hope this helped!