All of the factors and multiples of 21 and 48

Answer:

Are you in geometry?

For question 5:

To solve for x:

Triangle to the right with the 72 degrees in one angle.

All triangles add up to 180.

Subtact 72 from 180 = 108

Now we need to find the two other angles of that triangle.

We know that the two given eqations for that triangle is 6x-2 and 11x-9 (remeber the property creating the area of intersection, two congruent angles, so the equation 11x-9 applys for both triangles.)

So for the triangle to the right;

(6x-2) + (11x-9) = 108

lets add like terms next

17x - 11 = 108

add 11 to 108

17x = 119

divide 17 from both sides

x = 7

Now we need to find y.

On triangle to the right we have 30degrees. Lets subtract 30 degrees from 180. This equals 150.

We can plug in 7 to the equation 11x-9 which give us 68.

We now know to angles of the triangle. Lets subtract 68 from 150.

We get 82.

The last angle is 82, Which means lets find y.

5y - 8 = 82

add 8 to both sides

5y = 90

divide by 5 to both sides

y = 18

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try number 6. on your own to see if you get it know. If you don't, comment to me regarding what you don't understand.

Answer:

it is irrational number

Answer: False

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Explanation:

We simply need one counterexample to disprove the original claim.

The values 5 and 11 are prime, but 11-5 = 6 is not prime.

We see that taking two primes, and subtracting them, leads to some value outside the set of primes. Therefore, the set of primes is not closed under subtraction.

Answer:

r = - 29

Step-by-step explanation:

Given

- 3r = 87 ( divide both sides by - 3 )

r = [tex]\frac{87}{-3}[/tex] = - 29

Answer:

r=87÷ -3

r= -29

Answer:

yes their size is medium

The formula that gives us the cost, in dollars, to fill up the rest of the tank is,

Cost = (g - 2) × c

Given that;

The car currently has 2 gallons of gas and can hold a maximum of g gallons,

Hence, the amount of gas needed to fill the tank is,

(g - 2) gallons.

If the cost of gas is c dollars per gallon, the total cost to fill up the rest of the tank can be calculated by multiplying the number of gallons needed by the cost per gallon:

Cost = (g - 2) × c

Thus, the formula that gives us the cost, in dollars, to fill up the rest of the tank is,

Cost = (g - 2) × c

To learn more about the equation visit:

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Answer:

$7.10

Step-by-step explanation:

Step 1: We make the assumption that 35.5 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=35.5$.

Step 4: In the same vein, $x\%=20$.

Step 5: This gives us a pair of simple equations:

$100\%=35.5(1)$.

$x\%=20(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

Step 7: Taking the inverse (or reciprocal) of both sides yields

Hope this helps <3

This value is approximate.

============================================================

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

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To sum things up so far, we have these known properties of triangle ABC

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

The weather station A is 31.2 miles from the storm

From the triangle shown:

m<B = 90° - 48°

m<B = 42°

m<A = 17° + 90°

m<A = 107°

m<A + m<B + m<C = 180° (Sum of angles in a triangle)

107° + 42° + m<C = 180°

m<C = 180° - 149°

m<C = 31°

The distance between the weather stations A and B = 24 miles

That is, AB = 24 miles

The storm is at point C

The length AC is found by using the rule of sines:

[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]

The weather station A is 31.2 miles from the storm

Learn more on sine rule here: https://brainly.com/question/4372174

Answer:

∠YDC measures 140°.

Step-by-step explanation:

We can consider using the Exterior Angle Theorem. According to the theorem, the exterior angle of a triangle is equal to the two opposite interior angles.

In other words:

[tex]\displaystyle m \angle YDC = m\angle DCB + m\angle CBD[/tex]

Substitute:

[tex]\displaystyle (15x + 5) = (80) + (6x+6)[/tex]

Solve for x. Combine like terms:

[tex]15x + 5 = 6x + 86[/tex]

Simplify:

[tex]9x = 81[/tex]

And divide. Hence, the value of x is:

[tex]x = 9[/tex]

∠YDC is given by:

[tex]\displaystyle m\angle YDC = 15x + 5[/tex]

Since we now know the value of x, substitute and evaluate:

[tex]\displaystyle \begin{aligned} m\angle YDC &= 15x + 5 \\ &= 15(9) + 5 \\ &= 135 + 5 \\ &= 140^\circ\end{aligned}[/tex]

In conclusion, ∠YDC measures 140°.

Answer:

C. 8/17

Step-by-step explanation:

PM = 16+14 = 30 cm

KP= LN = 16×tan45° = 16×1 = 16cm

by using pythagorean theorem, we find :

KM² = PM²+KP²

= 30²+16²

= 900+256

= 1156

=> KM =√1156 = 34cm

so, cos theta = KP/KM = 16/34 = 8/17

Answer:

10

Step-by-step explanation:

Only the third number is divisible by 3. So the HCF is 2 * 5 = 10

That's the most that is common between all three numbers.

The first two only have a HCF of 100. Nothing else goes into both of them.

Answer:

[tex] {10x}^{2} - 18 {x}^{3} + {14x}^{4} \\ [/tex]

factorise out x² :

[tex] = {x}^{2} (10 - 18x + 14 {x}^{2} )[/tex]

then factorise out 2:

[tex] = 2 {x}^{2} (7 {x}^{2} - 9x + 5)[/tex]

Let other be x

Using angle sum property

[tex]\\ \rm\Rrightarrow x+7+90=180[/tex]

[tex]\\ \rm\Rrightarrow x+97=180[/tex]

[tex]\\ \rm\Rrightarrow x=180-97[/tex]

[tex]\\ \rm\Rrightarrow x=83°[/tex]

Answer:

width = 12 ft

Step-by-step explanation:

A = w * l

w = a/ 1 = 204/ 17 = 12 ft

Answer:

1st option

Step-by-step explanation:

Calculate the distance using the absolute value function, that is

distance = | 4.7 - (- 11.2) | = | 4.7 + 11.2 | = | 15.9 | = 15.9

or

distance = | - 11.2 - 4.7 | = | - 15.9 | = 15.9

Answer:

The first answer

Step-by-step explanation:

I just know it was the right answer on k12

Step-by-step explanation:

8. b1 = (2×401.94)/19.8 - 14.4

= 40.6 - 14.4 = 26.2 cm

9. h = (2×205)/(20+21)

= 410/41

= 10cm

Answer:

a) Option A is correct.

b) Option B is correct.

Step-by-step explanation:

[tex]a) \: \: 5 \times a \\ = 5a[/tex]

[tex]b) \: \: b \times b \\ = {b}^{2} [/tex]

Answer:

Ah Here We Go Again :) After Five Years

Answer:

1st

Step-by-step explanation:

..............

Answer:

105 per hour = x

Step-by-step explanation:

You subtract the parts cost of 77 from the total first.

497 - 77 = 420

Then you divide the 420 by 4 to get the unit rate per hour.

420/4

= 105

Answer:

hey please saw the figure

Answer:

Step-by-step explanation:

its 24

Step-by-step explanation:

4x is the real answer of that question

Answer: hola

Step-by-step explanationno

Answer:

Given = 6 x 0 = 0

Step 2 = Substitute. Any number plus its opposite equals 0 (10 +-10)

Step 3 = Use the distributive property

Step 5 = Subtract 60 from both sides

Step 6 = Simplify to solve for 6 x -10

Distribute the figure into three rectangles, namely, A, B and C as shown in the picture.

We know that,

Area of a rectangle

= 2(l + b)

Now,

Consider rectangle A,

Length = 25in

Breadth = 15in

Hence,

Area = 2 (l + b)

= 2 (25 + 15)

= 2 (40)

= 80in²

Consider rectangle B,

Length = 25 - 7 = 18in

Breadth = 16in

Hence,

Area = 2 (l + b)

= 2 (18 + 16)

= 2 (34)

= 68in²

Consider rectangle C,

Length = 11in

Breadth = 24in

Hence,

Area = 2 (l + b)

= 2 (24 + 11)

= 2 (35)

= 70in²

Area of the figure

= Area of rectangle A + Area of rectangle B + Area of rectangle C

= 80in² + 68in² + 70in²

= 218in²

Answer:

(0,4)

Step-by-step explanation:

The line AD is a median, because D is the midpoint of BC.

The centroid is the point of intersection of three medians of triangle, we don't need to depict any another median, because we know that centroid divide each median in ratio 2:1 from the vertices of a triangle from which a median was depicted. That's obvious that the median AD was depicted from A. Let the point of centroid be M. AM:MD is 2:1. So we should find the coordinates of D

xD= (xa*1+xd*2)/ (2+1)= ((-4)*1+2*2)/3=0

yd= (ya*1+yd*2)/ (2+1)= (2*1+ 5*2)/3=12/3=4

(0,4)