Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
Valery increases her speed by 4% the next time she rides her bike. Her goal is to ride faster than Manuel.
Is the 4% increase enough to ride faster than Manuel? yes or no.
As part of your explanation, identify Valery's new speed. Then explain why or why not she met her goal.

Answer:

7 and 3

Step-by-step explanation:

Using the given information, one can form an equation. Let the first number be (x) and the second (y).  For two equations based on the given information.

"the sum of two numbers is 10"

x + y = 10

" the sum of their squares is 58 determine"

[tex]x^2+y^2=58[/tex]

Solve for the equation for (x), then substitute the expression for (x) into the second equation. Simplify and solve to find the value of (y), and backsolve for the value of (x).

x + y =10

x = 10 -y

Substitute into the other equation:

[tex]x^2+y^2=58[/tex]

[tex](10-y)^2+y^2=58[/tex]

Simplify, remember the pattern for opening a binomial squared:

[tex](a - b)^2=a^2-2ab+b^2[/tex]

Apply this pattern here to simplify,

[tex](10-y)^2+y^2=58[/tex]

[tex]100-20y+y^2+y^2=58[/tex]

Simplify further,

[tex]100-20y+y^2+y^2=58[/tex]

[tex]2y^2-20y+100=58[/tex]

Inverse operations,

[tex]2y^2-20y+100=58[/tex]

[tex]2y^2-20y+42=0[/tex]

Factor, take out a common factor that all of the terms have. Then rewrite the quadratic trinomial as the product of two linear binomials. Remember the general pattern for factoring, add the inverse of the factors of the constant term to the variable, the sum of these factors must equal the coefficient of the linear term of the quadratic trinomial.

[tex]2y^2-20y+42=0[/tex]

[tex]2(y^2-10y+21)=0[/tex]

[tex]2(y-7)(y-3)=0[/tex]

Now use the zero product property to solve, the zero product property states that any number times zero equals zero.

[tex]2(y-7)(y-3)=0[/tex]

[tex]y = 7, y = 3[/tex]

Since the sum of (7) and (3) is (10), one has found the values of (y), it can be either (7) or (3), it doesn't matter which equals which.

Answer:

The lowest score could be 85

Step-by-step explanation:

Let the  lowest score = x

(x + 89 + 92 + 94)/4 = 90                     Add the 3 scores you know

(x + 275)/4 = 90                                    Multiply both sides by 4

(x + 275) = 360                                     Remove the brackets.

x + 275 = 360                                       Subtract 275

x = 360 - 275

x = 85

Answer:

10 Km/h

Step-by-step explanation:

Let the speed of the container ship be y

The speed of the aircraft = y + 5

Next, we shall determine the time taken by the aircraft to travel 450 Km. This can be obtained as follow:

Speed of aircraft (Sₐ) = y + 5

Distance travelled (dₐ) = 450 Km

Time for aircraft (tₐ) =?

Speed = distance / time

Sₐ = dₐ / tₐ

y + 5 = 450 / tₐ

Cross multiply

(y + 5) × tₐ = 450

Divide both side by (y + 5)

tₐ = 450 / (y + 5)

Finally, we shall determine the speed of the carrier. This can be obtained as follow:

Speed of container ship (S꜀) = y

Distance travelled (d꜀) = 300 Km

Time for container ship (t꜀) = Time for aircraft (tₐ)

Time for aircraft (tₐ) = 450 / (y + 5)

t꜀ = tₐ

t꜀ = 450 / (y + 5)

Speed = distance / time

S꜀ = d꜀ / t꜀

y = 300 ÷ 450 / (y + 5)

y = 300 × (y + 5) / 450

y = (300y + 1500) / 450

Cross multiply

450y = 300y + 1500

Collect like terms

450y – 300y = 1500

150y = 1500

Divide both side by 150

y = 1500 / 150

y = 10 Km/h

Thus, the speed of the container ship is 10 Km/h.

Answer:

ᴀꜱ ᴡᴀʀᴍ ᴀꜱ ꜱᴜɴ

ᴀꜱ ꜱɪʟʟʏ ᴀꜱ ꜰᴜɴ

ᴀꜱ ᴄᴏʟᴅ ❄️ ᴀꜱ ᴀ ᴛʀᴇᴇ

ᴀꜱ ꜱᴄᴀʀʏ ᴀꜱ ꜱᴇᴀ

ᴀꜱ ʜᴏᴛ ᴀꜱ ꜰɪʀᴇ

ᴀꜱ ᴄᴏʟᴅ ᴀꜱ ɪᴄᴇ

ꜱᴡᴇᴇᴛ ᴀꜱ ꜱᴜɢᴀʀ

ᴀɴᴅ ᴇᴠᴇʀʏᴛʜɪɴɢ ɴɪᴄᴇ

ᴀꜱ ᴏʟᴅ ᴀꜱ ᴛɪᴍᴇ ⌛

ᴀꜱ ꜱᴛʀᴀɪɢʜᴛ ᴀꜱ ʟɪɴᴇ ➖

ᴀꜱ ʀᴏʏᴀʟ ᴀꜱ ᴀ ᴀɴɢᴇʟ☺️

ᴀꜱ ʙᴜᴢᴢᴇᴅ ᴀꜱ ʙᴇᴇ

ᴀꜱ ꜱᴛᴇᴀʟᴛʜ ᴀꜱ ᴛɪɢᴇʀ

ꜱᴍᴏᴏᴛʜ ᴀꜱ ɢʟɪᴅᴇʀ

ᴘᴜʀᴇ ᴀꜱ ʜᴇᴀʀᴛ ❤️

ᴘᴜʀᴇ ᴀꜱ ɪ ᴡᴀɴɴᴀ ʙᴇ

Step-by-step explanation:

Answer: SP is Rs 690

Step-by-step explanation:

CP= Rs 750

loss percent = 8%

so

loss = 8% of CP

= 8/100 * 750

= Rs 60

Loss = Rs 60

so

SP = Rs 750-60

= Rs 690

Answer:

here,

CP=750

loss%=8%

now,

SP= (100-L)×cp/100

= (100-8)×750/100

= (92×750)/100

= 69000/100

= 690

hence the SP of the article is Rs 690

any problem then comment it

hope this helped you ☺️

Answer:

B

Step-by-step explanation:

x -> x and y -> y+5

-1 -> - 1 and - 3 -> 2, so b is the correct answer.

The function f(x) will be sometimes positive and sometimes negative on the interval so option (3) will be correct.

A certain kind of relationship called a function binds inputs to essentially one output.

In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.

Given function is

f(x) = (x - 5) (2x - 7) (7x - 3)

The term (x - 5) will be negative if x < 5.

The term (2x - 7) will be negative if x<3.5

Let's say if x = 4 then (x - 5) will be negative but (2x - 7) will be positive and hence overall value will be negative.

But if x = 3 then (x - 5) will be negative and (2x - 7)  will also be negative and hence overall value will be negative

Hence the function f is sometimes positive and sometimes negative on the interval.

For more about the function

brainly.com/question/23712366

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Answer:

always negative the other guy was wrong because when you wrote 2x - 7 you meant 2x + 7 I know this because it’s on Khan Academy

Step-by-step explanation:

Answer:

x = 12 , s = 41

Step-by-step explanation:

The sides of a square are equal , so

4x - 7 = 3x + 5 ( subtract 3x from both sides )

x - 7 = 5 ( add 7 to both sides )

x = 12

Then

length of side s is

s = 4x - 7 = 4(12) - 7 = 48 - 7 = 41

since in a cube length, width and height are equal,

h = 6

w = 6

l = 6

and volume is 6³ = 216cm³

hope it helps :)

Answer:

Step-by-step explanation:

Hello!

-5/8 = (-5*-3)/ (8*-3) = 15/-24

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The initial value is the y value of the first term shown ( when x=1)

y = 2 when x=1

The initial value is 2

Answer:

What is the initial value of the sequence?

Step-by-step explanation:

Edge 2021

Answer: 24(option A) is the answer

exterior angle = 360/n

so, n = 15

then, 360/15 = 24

Answer:

g = At/60

Step-by-step explanation:

A = 60(g/t)

To solve for 'g'

Open the bracket

A = 60g/t

Multiply both sides by t

At = 60g

Divide both sides by 60

At/60 = 60g/60

At/60 = g

Answer: The number = 3 /4 or 4 / 3

Concept:

Here, we need to know the idea of a reciprocal.

Reciprocal is also called the multiplicative inverse.  It is similar to turning the number upside down which is found by interchanging the numerator and denominator.

Number ⇒ Reciprocal = 1 / Number

Solve:

STEP ONE: Set up the equation

Let x = the number

Let 1 / x = the reciprocal

x + 1 / x = 25 / 12

STEP TWO: Multiply x on both sides

(x + 1 / x) · x = (25 / 12) · x

x² + 1 = 25x / 12

STEP THREE: Multiply 12 on both sides

(x² + 1) × 12 = (25x / 12) × 12

12x² + 12 = 25x

STEP FOUR: Subtract 25x on both sides

12x² + 12 - 25x = 25x - 25x

12x² - 25x + 12 = 0

STEP FIVE: Solve for the quadratic equation

(3x - 4) (4x - 3) = 0 ⇔ (Factorization of the equation)

(x - 4 / 3) (x - 3 / 4) = 0

x = 4 / 3 or x = 3 / 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

6

Step-by-step explanation:

tan 45 = 6 / x

1 = 6 / x

x = 6

Note :

Tan 45 value = 1

Answer:

x=6

Step-by-step explanation:

Since this is an isosceles triangle, the sides must be equal next to the base angles that are equal

x=6

Answer:

48

Step-by-step explanation:

using the formula 1/2 b*h

8*12=96

96/2=48

Answer:

x = 14

[tex]h^2 = p^2 + b^2\\h^2 = 7^2 + 12^2\\x^2 = 49 + 144\\x^2 = 193\\so, x = 13.89\\so, x = 14[/tex]

Answer:

~ 220.6

Step-by-step explanation:

sine rule : a/sinA =b/sinB = c/sinC

AB/sinC =BC/sinA

A = 180 - 110.2 - 13.5 = 56.3 degrees

AB/sin13.5 = 786/sin56.3

AB = 786sin13.5/sin56.3 = 220.5506

The distance across the river of AB is 220.55 m.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given a triangle ABC.

We have,

∠B = 110.2° and ∠C = 13.5°

We know that the sum of the interior angles of a triangle is 180°.

∠A = 180 - (110.2 + 13.5) = 56.3°

Using the law of sines,

BC / Sin A = AB / Sin C

Substituting the values,

786 / sin (56.3°) = AB / sin (13.5°)

AB = (786 / sin (56.3°)) sin (13.5°)

     = 220.55 m

Hence the distance is 220.55 m.

Learn more about Law of Sines here :

https://brainly.com/question/13098194

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Answer:

Step-by-step explanation:

Given circle:

Convert the equation into the standard form of (x - k)² + (y - h)² = r²:

As per above:

Correct choice is A

A.2

Answer:

Solution given:

equation of a circle is:

x²+y²+4x-2y=-1

x²+y²+4x-2y+1=0

Comparing above equation with

ax²+by²+2gx+2fy+c=0

we get

a=1

b=1

g=2

f=-1

c=1

now

radius of a circle (r)=[tex]\sqrt{g²+f²-c}[/tex]

substituting value

r=[tex]\sqrt{2²+(-1)²-1}=2[/tex]

therefore radius of a circle is 2 units

Answer:

522.5in^3

Step-by-step explanation:

4/3 ×3.14×5^3

4/3×3.14×125

1.33×3.14×125

4.18×125

522.5

Step-by-step explanation:

[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]

Answer:

The first option is the right one.

Step-by-step explanation:

7/2. Rate is rise/run

7 is your rise

and 2 is your run

therefore, the answer is 7/2

Answer:

96 darling

Step-by-step explanation:

youre gonna take all the times this was teice as mich as that

like this:blueberrybagel twice as much 2

than plain bagels 1

cinnamonbags 3 times as much than

blueberry bagels 2×3= 6+

=9

EACH portion contains144:9=16 bagels

blueberry ones16×2=32

plain ones16×1=16

cinnamon ones 3×32=96

Answer:

D. <15/√346>

Have a nice day! :)

Step-by-step explanation:

1:4 bcos u need to divide both sides by 4

Answer:

20 is the answer

Step-by-step explanation:

x+3x+10=90(right angle triangle)

4x=90-10

x=80/4

x=20°

Answer:

x = 20

Step-by-step explanation:

Based on the square indication at the corner of the angle, we can assume it's a right angle, so 90°. This means that x + 3x + 10 = 90. Solve it like any algebraic equation, isolating x. add x to 3x + 10, this would net you 4x + 10 = 90. Subtract 10 on both sides of the equation to further isolate x, meaning 4x = 80. Simplify this, dividing 4 on both sides, meaning x = 20.

Answer:

True

Step-by-step explanation:

assuming that you meant to write

cot (x-π//2) = - tan x

the identity is TRUE because,

- you can graph cot (x-π//2)  and  - tan x, and see that the graphs overlap

OR

-you solve for cot (x-π/2)

useful to know is that :

cot x=1/tan x, tan x = sin x/cos x,  

cos(x) =cos(-x), sin(-x) = -sin x,

cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x

cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1

cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x),  use facts: cos(x) =cos(-x), sin(-x) = -sin x

cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x

cot (x-π/2) = -tan x

Answer:

P.=2(2x+5)+2(x-10)=80cm

6x-10=80

x=90/6=15cm

Area= L*W= 35*5=175 squared cm= 0.0175 squared m