Knowledge Check
Question 8
The sum of two numbers is 39. The larger number is 13 more than the smaller number. What are the numbers?

Answer: 384

Step-by-step explanation: 10% also equals 0.1 so, 3840*0.1 = 384.

Answer:

$3840

Step-by-step explanation:

10%= x/10 and the x is equal to 3840. 3840/10=384 now that I know what %10 of 3840 I can take off the discount price onto the original price,                 3840-384=3456. So 3456 is the final price after including the 10% discount.

Answer:

The distance between them is 5km

Step-by-step explanation:

Given

[tex]Car\ A =4km[/tex]

[tex]Car\ B =3km[/tex]

Required

Distance between them

The scenario can be represented with the attached image

The distance between them is then calculated using Pythagoras theorem

[tex]d^2 = 4^2 +3^2[/tex]

[tex]d^2 = 16 +9[/tex]

[tex]d^2 = 25[/tex]

Take square roots of both sides

[tex]d = \sqrt{25[/tex]

[tex]d = 5[/tex]

Rule: If x is the leg of a 45-45-90 triangle, then x*sqrt(2) is the hypotenuse.

We can prove this by showing that x^2+x^2 = (x*sqrt(2))^2 is an identity. It's from the pythagorean theorem a^2+b^2 = c^2.

Put another way, if we know that a = x and b = x are the two congruent legs, then x^2+x^2 = c^2 leads to c = x*sqrt(2). This triangle is known as an isosceles right triangle.

So if 4*sqrt(2) is the hypotenuse, we match that up with the template x*sqrt(2) and see that x = 4 must be the case.

Answer:

13cm

Step-by-step explanation:

Let the given lengths be the opposte amd adjacent sides of a right triangle'

The missing side will be the hypotenuse

Using the pythagoras theorem;

hyp^2  = 5² + 12²

hyp² = 25 + 144

hyp² = 169

hyp =√169

hyp = 13cm

Hence the missing one is 13cm

Answer:

Yea you correct, you answer is right

Answer:

I believe the answer is 58.1 degrees

Step-by-step explanation:

acrsin 45/53=58.1

45/53 is the sin of P

Step-by-step explanation:

y = -4x + 17

=> (4,1)

x=4 --> y = -4(4)+17=-16+17=1

(4,1) matched

=> (2,9)

x=2 --> y=-4(2)+17=-8+17=9

(2,9) matched

Answer:

35.2 ; 4.75

Step-by-step explanation:

Given that :

Mean age, μ = 35.2 years

Standard deviation, σ = 9.5 years

The mean of the sampling distribution will be equal to the population mean, μ, this is according to the central limit theorem.

The standard deviation of the sampling distribution, is given by : σ/√n

n = sample size = 4

SD of sampling distribution = 9.5/√4 = 9.5 / 2 = 4.75

Answer:

The answer is r^10s^6/r-5s^9= r^10/r-^5 = r^15

Step-by-step explanation:

the answer is r^15

Answer:

339.29

Step-by-step explanation:

Use formula for cylinder: [tex]V=\pi r^2h[/tex].

Note: I rounded to the nearest hundreth.

Answer:

p because variables are shown by letters not numbers

Hope this helped:)

Step-by-step explanation:

Step-by-step explanation:

I=?

P= $4500

R=8%=0.08

T=1 year

8%*0.01= 0.08

I=(4500)(0.08)(1)

(4500)(0.08)=360

360*1=360

The interest after one year is $360

Answer:125

Step-by-step explanation:hope this help

Answer:

11.70

Step-by-step explanation:

d=√((16-5)^2+(14-10)^2)=11.7046999...

Answer:

( Hint)

Step-by-step explanation:

55-5= 5x>-25-5

50= 5x>-30

10=x>-6

9514 1404 393

Answer:

  5. x° = 38°; b° = 90°

  6. m∠TSU = 110°

Step-by-step explanation:

The relationship relevant to these problems is that an inscribed angle is half the measure of the arc it intercepts. That is also true of the angle formed by a chord and a tangent.

__

5. Angle x° intercepts an arc marked 76°, so is half its measure: 76°/2 = 38°

  x° = 38°

Arc b° is intercepted by an inscribed angle of 45°, so is twice that measure.

  b° = 90°

__

6. Long arc SU is the remaining portion of the circle after short arc SVU is subtracted:

  long arc SU = 360° -140° = 220°

Angle TSU is half that measure: 220°/2 = 110°.

  m∠TSU = 110°

Answer:

51 is 340% of 1500

Step-by-step explanation:

Answer:

15.

Step-by-step explanation:

have  a great day!

Answer: 303

Step-by-step explanation:

Answer:

There are 1766 chipmunks in the population

Step-by-step explanation:

Number of individuals increasing per year = 265

Rate of increase = 0.15

Rate of increase = increase in number of individuals in a given population /total population

Substituting the given values, we get -

0.15 = (265/total population)

Total population = 265/0.15 = 1766

Answer:

The answer would be 17

Step-by-step explanation:

The answer would be 17 because if you add 12 plus 5 That would be your answer

Answer:

G = 50

Step-by-step explanation:

50 is the initial after-cost, right?

answer is : The function formula will be

Since we have given that

Charges per each magical broom he makes for his customers = 125 gold pieces

Charges of one time fees = 50 gold pieces

Let the number of magical brooms he makes be 'x'.

Let the total number of gold pieces be 'G'.

According to question, it becomes

Step-by-step explanation:Since we have given that

Charges per each magical broom he makes for his customers = 125 gold pieces

Charges of one time fees = 50 gold pieces

Let the number of magical brooms he makes be 'x'.

Let the total number of gold pieces be 'G'.

According to question, it becomes

Since we have given that

Charges per each magical broom he makes for his customers = 125 gold pieces

Charges of one time fees = 50 gold pieces

Let the number of magical brooms he makes be 'x'.

Let the total number of gold pieces be 'G'.

According to question, it becomes

Answer:

X would be equal to 37 degrees

Step-by-step explanation:

Answer:

x=37

Step-by-step explanation:

118+25+x= 180

143 + x = 180

= 37

check answer by 25+118+37=180

Answer:

The scale is 1:200

Step-by-step explanation:

On the plan we have the drawing as 6 cm

In real representation, we have the distance as 12 m

Firstly we have to convert to same unit

In this case, we use the cm for convenience

Mathematically, 100 cm is 1 m

Thus, 12 m

will be 12 * 100 = 1,200 cm

So, we have the ratio as;

6 cm : 1,200 cm

and that is 1:200 (since 6/1200 = 1/200 and in ratio form, we have that as 1:200)

Answer:

Long part= 45

Short part= 25

Step-by-step explanation:

Let the short part of the stick be x

Let the long part be x+20

The total length of the stick is 70cm

x + (x+20)= 70

x+x+20= 70

2x+20= 70

2x= 70-20

2x= 50

x= 50/2

= 25

Longer part length= 20+25

= 45

The short part is 25

Answer:

<B = 40degrees

x = 9

Step-by-step explanation:

Find the diagram attached. From the diagram, <A = <B (corresponding angle)

5x - 5 = 3x+ 13

5x - 3x = 13 + 5

2x = 18

x = 18/2

x = 9

Since <B = 3x+13

<B = 3(9) + 13

<B = 27 + 13

<B = 40degrees

Answer:

It was 48

Step-by-step explanation:

Did it on khan hope this helps :)

Answer:

110

Step-by-step explanation:

5/6 of 132 is 110

Answer:

1

Step-by-step explanation:

m/8n > 4/8(1/2) ( since its 1/2 all u need to do is change the fraction to whole number which is 1/2 = 0.5)

The given will become 4/4 then simplest form is 1

Answer:

x and y =   5√2.

Step-by-step explanation:

This is a 45:45:90 triangle so length of x = length of y.

In this triangle the ratio of the sides is 1:1:√2

Finding length of x and y:

1/√2 = x/10

√2x = 10

x = 10/√2

=  10√2/2

=  5√2.

Answer:

x = 16

Step-by-step explanation:

*A triangle's interior angles always add up to 180 degrees*

1. The square on the left-hand side means 90 degrees

2. To find the degrees on the 150 degrees side we need to subtract 180 from 150  as the line it's on equals 180 degrees

180 -151 = 29

3. Now we know 3 out of the two angles, so if we add them up and subtract them from 180 degrees we will have the 3rd angle

29 +90 = 119

180 - 119 = 61

4. Now we can put that in with the equation

4x + 3 = 61

5. Solve

4x - 3 = 61

    + 3   +3

4x = 64

/4     /4

x = 16