Joe walked 1/3 of the journey to the library to his house to meet his cousin Lucy how far did he travel

Answer:

both angles are acute

Step-by-step explanation:

The solution is : (f + g)(x) = x² + 4x - 4 ⇒ B, is the required function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

Let us solve the question

∵ f(x) = 4x + 4

∵ g(x) = x² - 6

→ We need to find (f + g)(x) which means f(x) + g(x)

∴ (f + g)(x) = f(x) + g(x)

∵ f(x) + g(x) = (4x + 2) + (x² - 6)

∴ f(x) + g(x) = 4x + 2 + x² - 6

→ Add the like terms

∵ f(x) + g(x) = 4x + x² + (2 - 6)

∴ f(x) + g(x) = 4x + x² + (-4)

→ Remember (+)(-) = (-)

∴ f(x) + g(x) = 4x + x² - 4

→ Arrange the terms from greatest power of x

∴ f(x) + g(x) = x² + 4x - 4

∴ (f + g)(x) = x² + 4x - 4,  is the required function.

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Answer:

60%

Step-by-step explanation:

Let the total number of people polled to vote be 1000

80% said they would vote for him

That is 800

20% said they would not vote for him

That is 200

Out of the 800, 70% actually voted

That will be ;

70/100 * 80 = 560

Also, 20% of the 200 that said they would not vote actually voted

That will be ;

20/100 * 200 = 40

Total is thus;

569 + 40 = 600

% is 600/1000 = 60%

Answer:

1) x = -2.5

2) x = 21 1/3

3) x = 12

4) x = 4

5) y = 40.5

Step-by-step explanation:

Answer:

1) x = -2.5

2) x = 21 1/3

3) x = 12

4) x = 4

5) y = 40.5

Give the person above a brainliest

Answer:

It may take 20 to 30 seconds.

Step-by-step explanation: Hope this helped

brainliest?

The average time it took for a tablet to dissolve in water that was 22 °C in temperature was 28.3 seconds.

Any substance that, when consumed, alters the physiology or psychology of an organism qualifies as a drug.

The properties of the API (active pharmaceutical ingredient) such as

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Answer:

7.5m

Step-by-step explanation:

Since we are not asked what to look for we can find the maximum height reached by the ball

The ball reaches its maximum height when dh/dx = 0

dh/dx = -2.4x + 6

0 = -2.4x + 6

2.4x = 6

x = 6/2.4

x = 2.5

Get the max height

Recall:

h =-1.2x^2 + 6x ,

h(2.5) = -1.2(2.5)^2 + 6(2.5)

h(2.5) = -1.2(6.25)+15

h(2.5) = -7.5 + 15

h = 7.5

Hence the maximum height reached by the ball is 7.5m

Answer:

Cost of each ticket per person = $42

For groups of up to 8 people, the cost per ticket decreases by $3 for each person in the group.

Marco's ticket cost $30.

This means he paid 42-30=12 dollars less.

Now when there are 8 members, the cost decreases by $3.

So, $12 will decrease, when there will be  members

I hope this helps! Have an awesome day!

Answer:

The answer is there are 32 people in this group

Step-by-step explanation:

here is proof work if you need it:

Answer:

$4.69

Step-by-step explanation:

$11.96/4 (because he bought 4 candles)

$2.99

each candle was $2.99 at the sale price

Now because the question is only asking for the amount of 1 candle before the sell price all you have to do is add $1.70 to $2.99 and you have your answer. Hope this helps!

Answer:

3x²y==

Step-by-step explanation:

Multiple the number

Answer:

6.862035456*10^26 m/s^2

Step-by-step explanation:

We know that:

m=70kg

M=Mass of earth=5.98*10^24kg

R=Distance between object's and earth's center=6.38*10^6m

G=6.6726*10^-11 N/m/kg^2

Thus, we can use the equation [tex]F_g=\frac{GmM}{R^2}\\[/tex]:

[tex]F_g=\frac{(6.6726*10^-11)(70)(5.98*10^{24})}{(6.38*10^{-6})^2}\\\\F_g=6.862035456*10^{26}[/tex]

This means the force of gravitational attractions is 6.862035456*10^26 m/s^2

Answer:

x = - 3

Step-by-step explanation:

g(x) = 4x + 1...... (1)

g(x) = -11.... (2)

From equations (1) & (2)

-11 = 4x + 1

-11 - 1 = 4x

-12 = 4x

-12/4 = x

-3 = x

x = - 3

Answer:

(-10) + 3

Step-by-step explanation:

hopefully it helped

Answer:

Step-by-step explanation:

according to the question

the equation is

[tex] \tan(45 {}^{o} ) = \frac{x}{6} [/tex]

[tex]1 = \frac{x}{6} [/tex]

[tex]x = 6[/tex]

Answer:

Domain: -3<=x<4

Range:-1<=y<-3

(can I get brainliest please)

Answer:

range: [-3,-1) domain: [4,-3); idrk know the second one srry.

Step-by-step explanation:

Answer:it is 180

Step-by-step explanation:

Answer:

look below

Step-by-step explanation:

I think the answer is for A 12mm because there is a -3 in the spot and you have 15 mm and for B 17mm because you still have that 15mm but this time you have a +2  

I think this might be the answer I am kind of good at math but I don't really know this one sorry if I get it wrong

Answer:

2(5x – 1)

Step-by-step explanation:

Answer:

[tex]\sin 2A + \csc 2A = 2.122[/tex]

Step-by-step explanation:

Let [tex]f(A) = \sin A + \csc A[/tex], we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

[tex]\csc A = \frac{1}{\sin A}[/tex] (1)

[tex]\sin^{2}A +\cos^{2}A = 1[/tex] (2)

Now we perform the operations: [tex]f(A) = 3[/tex]

[tex]\sin A + \csc A = 3[/tex]

[tex]\sin A + \frac{1}{\sin A} = 3[/tex]

[tex]\sin ^{2}A + 1 = 3\cdot \sin A[/tex]

[tex]\sin^{2}A -3\cdot \sin A +1 = 0[/tex] (3)

By the quadratic formula, we find the following solutions:

[tex]\sin A_{1} \approx 2.618[/tex] and [tex]\sin A_{2} \approx 0.382[/tex]

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

[tex]\sin A \approx 0.382[/tex]

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

[tex]A \approx 22.457^{\circ}[/tex]

Then, the values of the cosine associated with that angle is:

[tex]\cos A \approx 0.924[/tex]

Now, we have that [tex]f(A) = \sin 2A +\csc2A[/tex], we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:

[tex]\sin 2A = 2\cdot \sin A\cdot \cos A[/tex] (4)

[tex]\csc 2A = \frac{1}{\sin 2A}[/tex] (5)

[tex]f(A) = \sin 2A + \csc 2A[/tex]

[tex]f(A) = \sin 2A + \frac{1}{\sin 2A}[/tex]

[tex]f(A) = \frac{\sin^{2} 2A+1}{\sin 2A}[/tex]

[tex]f(A) = \frac{4\cdot \sin^{2}A\cdot \cos^{2}A+1}{2\cdot \sin A \cdot \cos A}[/tex]

If we know that [tex]\sin A \approx 0.382[/tex] and [tex]\cos A \approx 0.924[/tex], then the value of the function is:

[tex]f(A) = \frac{4\cdot (0.382)^{2}\cdot (0.924)^{2}+1}{2\cdot (0.382)\cdot (0.924)}[/tex]

[tex]f(A) = 2.122[/tex]

Answer:

70 heartbeats per second

Step-by-step explanation:

Answer:

The hundreds place

Step-by-step explanation:

If you divide it

it would start out on the 4

Which is the hundreds Place

Answer:

-2.5 km

Step-by-step explanation:

80 - 45= 35

35 / 14 sec. = 2.5

So if your decreasing it would turn that 2.5 into a negative.

Answer:

K = ½

Equation: y = ½x

Step-by-step explanation:

✔️Constant of proportionality (k) = y/x

Using a point on the line, (2, 1),

k = ½

✔️Equation of a proportional relationship would be in the form of y = kx

To write an equation, substitute k = ½, into y = kx

Thus:

y = ½x

Given:

Cost of two donuts and three cookies = $3.30

Cost of five donuts and two cookies = $4.95

To find:

The cost of each donut.

Solution:

Let x be the cost of each donut and y be the cost of each cookie.

Cost of two donuts and three cookies = $3.30

[tex]2x+3y=3.30[/tex]          ...(i)

Cost of five donuts and two cookies = $4.95

[tex]5x+2y=4.95[/tex]          ...(ii)

Multiply equation (i) by 2.

[tex]4x+6y=6.60[/tex]          ...(iii)

Multiply equation (ii) by 3.

[tex]15x+6y=14.85[/tex]      ...(iv)

Subtracting (iii) from (iv), we get

[tex]15x+6y-4x-6y=14.85-6.60[/tex]

[tex]11x=8.25[/tex]

Divide both sides by 11.

[tex]x=\dfrac{8.25}{11}[/tex]

[tex]x=0.75[/tex]

Therefore, the cost of each donut is $0.75.

Answer:

Step-by-step explanation:

The correct option is C.

Step-by-step explanation:

The width of the rectangular pen is

The length of the rectangular pen is

The perimeter of a rectangle is

Therefore the correct option is C.

Answer:

The correct options for the solution values are:

Step-by-step explanation:

Given the expression

[tex]x^2+10x+25=8[/tex]

Subtract 25 from both sides

[tex]x^2+10x+25-25=8-25[/tex]

Simplify

[tex]x^2+10x=-17[/tex]

Add 25 or 5² to both sides

[tex]x^2+10x+5^2=8[/tex]

as

[tex]x^2+10x+5^2=\left(x+5\right)^2[/tex]

so the expression becomes

[tex]\left(x+5\right)^2=8[/tex]

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

solve

[tex]x+5=\sqrt{8}[/tex]

Subtract 5 from both sides

[tex]x+5-5=2\sqrt{2}-5[/tex]

[tex]x=2\sqrt{2}-5[/tex]

solve

[tex]x+5=-\sqrt{8}[/tex]

Subtract 5 from both sides

[tex]x+5-5=-2\sqrt{2}-5[/tex]

[tex]x=-2\sqrt{2}-5[/tex]

Therefore, the solution to the equation

[tex]x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5[/tex]

Hence, the correct options for the solution values are:

Answer:

7

Step-by-step explanation: