The sum of two numbers is -5 and their difference is -1. Find the two
numbers.

Answer:

y = 2x - 11

Step-by-step explanation:

y = 2x + b

-1 = 2(5) + b

-1 = 10 + b

-11 = b

Step-by-step explanation:

price after discount and with vat = 9605

Answer:

r = 30°

Step-by-step explanation:

According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.

Answer:

The length of the arc is 10 pi

Step-by-step explanation:

Mathematically, the length of an arc is calculated as;

theta/360 * 2 * pi * r

theta represents the central angle subtended by the arc which is a right angle according to the question (a right angle is 90 degrees)

r is the circle radius which is 20 inches

so we have the length of the arc as;

90/360 * 2 * pi * 20 = 40 pi/4 = 10 pi

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

Hello!

(3n + 2) - 10 =

= (3 × 3 + 2) - 10 =

= (9 + 2) - 10 =

= 11 - 10 =

= 1

Good luck! :)

[tex]\displaystyle\bf (3n+2) -10 \ if \ n=3\Longrightarrow 3\cdot3+2-10=11-10=\boxed{1}[/tex]

Answer:  B) y = -x+ 5

Step-by-step explanation:

If the x-value in the solution (x, y) is 2, then the y-value is:

[tex]y=\frac{1}{2} (2)+2 = \frac{2}{2} +2=1+2=3[/tex]

So the solution coordinate is (2, 3).

Test each of the answer choices to see if whether the y-value is 3 when the x-value is 2. If it's true, then it could be the other equation in the system.

A) y = -2x + 4

[tex]y = -2x + 4\\\y = -2(2) + 4 = -4 + 4 = 0[/tex]

B) y = -x+ 5

[tex]y = -x+ 5\\y = -(2) + 5 = 5 - 2 =3[/tex]

C) y = 2x

[tex]y=2x\\y=2(2)=4[/tex]

D) y = 2x + 1

[tex]y = 2x + 1\\y=2(2)+1=4+1=5[/tex]

Answer:

188 m

Step-by-step explanation:

[tex] \tan(12) = \frac{40}{x} \\ x = \frac{40}{ \tan(12) } \\ x = 188[/tex]

Answer:

I think that the other answer is WRONG

tan(12) = [tex]\frac{x}{40}[/tex]

x = tan(12)*40 = 8.5

Step-by-step explanation:

[tex]\frac{sin\left(78\right)}{40}=\frac{sin\left(12\right)}{x}[/tex] = 8.5

Answer:

5 units!

Step-by-step explanation:

Because Rectangle Perimeter = 2(a+b)

a=2w-1, b=w

2(2w-1+w)=28

3w-1=14

3w=15

w=5

So the answer is 5! 5! 5! A!A!A!

Fighting!! o(≧o≦)o

Answer:

Nope

Step-by-step explanation:

we can graph y = 5x as y = 5 units up and one unit to the right

but for right now let me be specific on what i mean

Specifically:

y = 5x is a Slope-Intercept equation, the original Slope-Intercept equation would be y = mx + b but in this case, we don't have b so we're focusing now on y = 5x, but what are we suppose to do with 5x??? well 5x represents the slope of the line so to graph a slope, use rise over run = rise/run. so only 5 is being used so 5 = rise/run = 5/1.

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Answer: (1, 3) doesn't satisfy the equation

Answer:

No, it does not satisfy the equation

Step-by-step explanation:

Hi there!

We are given the equation y=5x and we want to know if the point (1,3) will satisfy the equation

If we substitute the values of a point into the equation, and the result is a true statement (ex. 2=2), then the point satisfies the equation

If we substitute the values of a point into the equation and the result is a false statement (ex. 0=7), then the point doesn't satisfy the equation

The reason for this is because when we plug the value of a point into an equation, we're seeing if the equation will pass through that given point.

So let's substitute 1 as x and 3 as y into y=5x

3=5(1)

multiply

3=5

The result is a false statement; therefore, the point doesn't satisfy y=5x

Hope this helps!

The three inside angles of a triangle equal 180.

Subtract the two known angles from 180.

180 - 118.6 - 42.3 = 19.1

The third angle is 19.1

Answer:

hope this will help you more

Step-by-step explanation:

hope it is helpful to you

stay safe healthy and happy

Full question attached

Answer:

1. Subjects were not aware of the purpose of the experiment.

2. Subjects were not aware of all potential risks.

Subjects were not aware of the purpose of the experiment.

3. Subjects were coerced into participating

Explanation:

Ethics are the moral principles and codes that guide our daily decisions and actions. Ethical issues in conducting experiments or research aim at protecting the dignity of subjects or participants in the research. Major ethical issues in conducting research include: Respect for anonymity and confidentiality, beneficence(should not harm participants), and informed consent(independently volunteers after clear comprehensive information on research).

1. Experiment violates informed consent as participants were not aware of the purpose of research.

2. Experiment violates informed consent and beneficence as participants weren't fully informed and faced the risk of being harmed.

3. Experiment violates beneficence and informed consent as participants faced the risk of being harmed and did not independently volunteer for the research.

Answer:

1: 16

2: 4940

3: 24

4: 25

5: 9

Step-by-step explanation:

A permutation is a method of calculating the number of possible outcomes. It follows the following general formula;

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

There (n) is the number of objects, and (r) is the number of objects selected.

1. Arranging 4 pots with different plants in a row

In order to solve this, one needs two pieces of information, the number of objects, and the number of objects selected. One is given the number of objects; (4), but when the problem states "in a row" it never specifies how many plants are in a row. Thus, let one assume that a "row" can have an infinite amount of space, but in this case, only (4) space will be used. Therefore there are (4) objects with (4) objects selected. However, the drawback is that the combination formula doesn't work when the two parameters (n) and (r) are the same. Hence, to solve this special case, one simply multiplies the two numbers to get the answers:

[tex]n*r\\\\=4*4\\\\=16[/tex]

2. Forming a four-digit ATM pin

One is given that there are (4) digits in the ATM pin, this is the number of objects selected. One is also given that number of objects, there are (10) digits including (0). Set up the permutation and solve;

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

[tex]_1_0P_4=\frac{10!}{(10-4)!}\\\\=\frac{10!}{6!}\\\\=\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}\\\\=10*9*8*7\\\\=4940[/tex]

3. Securing a motorcycle with a three-digit combination lock using the numbers (1), (2), (3), and (6).

There are (4) digits to choose from on the lock. But there are (3) numbers that can be selected.

[tex]_4P_3=\frac{4!}{(4-3)!}\\\\=\frac{4!}{1!}\\\\=\frac{4*3*2*1}{1}\\\\=4*3*2*1\\\\=24[/tex]

4. Displaying 3 identical small vases, 1 figure, and a photo frame in a row.

There are (5) objects, and (5) spaces (read problem (1) for an explanation for the objects being put in a row). Thus, this is a special case; multiply the two numbers to get the result;

[tex]n*r\\=5*5\\=25[/tex]

5. 3 girls sitting around a circular table

There are (3) subjects, and (3) spaces in this problem. Apply the same logic applies to a row in this problem. Therefore, this is another special case; multiply the two numbers to get the result;

[tex]n*r\\=3*3\\=9[/tex]

Answer:

2 i think it is

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

First you would need to subtract all the irrelevant students.

So, subtract 4 from 36, which is 34.

34 - (10 + 15) =

34 - 25 =

9

The answer is 9 pupils.

Answer:

Hope you find it helpful and usef

Answer:

345

Step-by-step explanation:

The velocity of a car over five hours is given by:

[tex]\displaystyle v(t)=60\ln(t+1),\, 0 \leq t \leq 5[/tex]

And we want to find the total distance traveled from t = 0 to t = 5.

Recall that distance is the integral of the absolute value of the velocity function. Since we want to find the total distance traveled from t = 0 to t = 5, our limits of integration are t = 0 and t = 5. Hence:

[tex]\displaystyle D=\int_0^5 |\underbrace{60\ln(t+1)}_{v(t)}|\, dt[/tex]

Since v(t) ≥ 0 for all t in the interval [1, 5], we can remove the absolute value. Use a calculator:

[tex]\displaystyle D=60\left(6\ln(6)-5)=345.0334...\approx 345[/tex]

Which value is 10,000 times larger than 1,300?

answer= 1300×10000

= 13,000,000

Answer:

Step-by-step explanation:

From the picture attached,

ΔDEF is a right triangle with two sides,

EF = 17 units

DF = 20 units

By applying Pythagoras theorem in the given triangle,

DE² = DF² + EF²

(20)² = DF² + (17)²

DF² = 400 - 289

DF = √111

Trigonometric ratios for the ∠F,

sin(F) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}F=\frac{\sqrt{111}}{20}[/tex]

[tex]\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\text{cos}F=\frac{17}{20}[/tex]

[tex]\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\text{tan}F=\frac{\sqrt{111}}{17}[/tex]

Choose the correct option.

ok so we see that TR is 17 units, so RV is the same amount

3x+2 so 3x=15 so divide both sides by 3 we get x=5

now we know x=5 4x+1=21 and 9x-4=41

*drops microphone*

Answer:

TR = 12

=> 3x + 2 =17

=> x = 5

We have QT = QV (because QTV is an isosceles triangle)

=> QT = 4x+1=4x5+1=21 units

We have TS = SV (because TSV is an isosceles triangle)

=>SV = 9x-4= 9x5-4=41 units

Answer:

as x increases, y increases

Step-by-step explanation:

Answer:

B. as x increases, y increases

Step-by-step explanation:

the answer is in the picture

Answer: (c)

Step-by-step explanation:

In the given figure, two triangles are similar namely [tex]\triangle ABC[/tex] and [tex]\triangle ADB[/tex]

For similar triangles, the ratio of the corresponding sides are equal.

For option (a), Hypotenuse to Perpendicular ratio is given, that is correct

Similarly for option (b), Perpendicular to hypotenuse ratio is given

Both option (a) and (b) gives the same value of [tex]x[/tex] that is,

[tex]\Rightarrow x=\sqrt{81\times 45}\\\Rightarrow x=60.37[/tex]

Option (c) does not give the correct value of  [tex]x[/tex]

Answer:

C

Step-by-step explanation:

In the given figure, two triangles are similar namely  and  

For similar triangles, the ratio of the corresponding sides are equal.

For option (a), Hypotenuse to Perpendicular ratio is given, that is correct

Similarly for option (b), Perpendicular to hypotenuse ratio is given

Both option (a) and (b) gives the same value of  that is,

Option (c) does not give the correct value of  

Answer:

-x²-2x+3

Step-by-step explanation:

The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)

Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it

writing this in vertex form we get

-a(x+1)²+4

Where a is some constant

solve for a by plugging in (0,3)

3= -a(0+1)²+4

3= -a+4

-1= -a

a=1

therefore the equation looks like

-(x+1)²+4

expanding this so that it's in stantard form...

-(x²+x+x+1)+4

-x²-2x+3

which is the final answer

Answer:

1

Step-by-step explanation:

Let the number be n.

We are given:

n/12=q1+(7/12) where q1 is the quotient

n/6=q2+(?/6) where q2 is the quotient and ? is the remainder value we are trying to find.

? must be a integer between 0 and 5, inclusive. A remainder cannot be bigger than or equal to the divisor.

Let's rewrite the first equations

Multiply equation 1 on both sides by 2:

n/6=2q1+7/6

Remainder cannot be 7.

Rewrite again.

6 goes into 7 1 time with remainder 1.

n/6=2q1+(1+1/6)

n/6=(2q1+1)+1/6

So q2=2q1+1 and the remainder is 1 when dividing n by 6.

For fun. What is a number n with such conditions on it?

So what number has remainder 7 when divided by 12 and a remainder 1 when divided by 6.

n=12q1+7

n=6q2+1

If q1=1, we find a number right away that works.

19/12=1+7/12

19/6=3+1/6

Step-by-step explanation:

Volume of the block

[tex] = lbh[/tex]

[tex] = \frac{3}{8} \times \frac{1}{8} \times \frac{5}{8} [/tex]

[tex] = \frac{3 \times 5}{ {8}^{3} } [/tex]

[tex] = \frac{15}{512} [/tex]

Answer:

$ 2,600

Step-by-step explanation:

It's given that 260 People donated $10 is to an organisation . We need to find the total money received by the organisation .

Here we just need to the number of people with the amount each person gave , that is ;

[tex]\implies \rm Total \ amount = \$ 10 \times 260 \\\\\rm\implies Total \ amount = \$ 2,600 [/tex]

Hence the total money received by the organisation is $ 2600 .

Answer:

3/8 feet long

Step-by-step explanation:

Find how long each piece was by dividing 6 by 16:

6/16

Simplify this by dividing each number by 2:

6/16

= 3/8

So, each piece was 3/8 feet long