simultaneous eqautions
3x+2y=16
2x+y=9

Answer:

-6/4

Step-by-step explanation:

equivalent, that means something that is equal to so if you break -6/4 to the lowest you get -6/4

The equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

To find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y = 3x + 2, we will first find the slope(m).

To find the slope m of the perpendicular equation;

y = 3x + 2 --------------(1)

comparing the equation above with the standard equation of a circle

y=mx + c

m=3

The slope of the perpendicular equation;

 = -1

3 = -1

Divide both-side of the equation by 3

= -1/3

so, the slope of our perpendicular equation is -1/3

Then, we go ahead to find our intercept

To find the intercept, we will plug in the points and the new slope into the formula y =mx + c

5 = -(3) + c

5 = -1 +c

Add one to both-side of the equation

5+1 = -1 + c + 1

6 =c

c=6

our intercept c is equal to 6

so we can now proceed to form our equation.

y = - x  +  6

Multiply through by 3

-3y = -x + 18

We can rearrange the equation, hence;

x -3y -18=0

Therefore the equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0

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Answer:

3.14×5(2)×6=471.24

Step-by-step explanation:

you have to take square of 5

Based on the correlation coefficient between sodium and the calories in the meal, we can say that there is a strong positive correlation, and it is not likely causal.

Correlation coefficients are used to show the strength of a correlation between two variables. They go from -1 to 1 and the closer to figure is to 1, the stronger the correlation between the two.

If the figure is close to 1 (instead of -1) as is the case here it means that there is a positive correlation.

Correlation however, does not mean causation which is why there is a strong positive correlation between Sodium and calories with a coefficient of 0.74, but its likely that this isn't causal.

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The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

From the data given in the box plot, we can conclude that the mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

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Answer: C. 20 inches

Step-by-step explanation:

perimeter= 2 x (4+6)=20 inches

Answer:

x = 5

Step-by-step explanation:

5 - 3x = - 10

Subtract 5 from both sides:

5 - 5 - 3x = -10 - 5

-3x = -15

Divide -3 by both sides:

-3x/-3 = -15/-3

x = 5

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Answer:

Step-by-step explanation:

This sounds like a Pythagoras theorem question. So what I would do is 18^2 - 10^2= Ans

Then square root the answer

Answer: the answer is 15

The rate of change is $27 per month if the change in y values is 54 and change in x values is 2.

It is defined as the change in values of a dependent variable with respect to the independent variables.

From the data given in the table, we can find the rate of change per month:

To find the rate of change:

= change in y/ change in x

= (138-84)/(4-2)

= 54/2

= 27 per month

Thus, the rate of change is $27 per month if the change in y values is 54 and change in x values is 2.

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Answer:

97%

Step-by-step explanation:

Answer:

7.4 seconds

Step-by-step explanation:

878 = 16 t^2    divide both sides of the equation by 16

54.875 = t^2    take positive sq rt

7.4 seconds

Answer:

1256 cubic inches

Step-by-step explanation:

Volume of all 200 candles = volume of one mold × 200

Finding the volume of one mold:

We are given that the molds are in the shapes of cones and have a height of 6 inches as well as a diameter of 2 inches.

The volume of a cone can be calculated using the formula

V = πr²(h/3) where r = radius and h = height

Converting the diameter to radius

The volume of a cone formula requires the radius however we are only given the diameter. However we know that the radius is equal to half of the diameter or radius = diameter / 2

So if diameter = 2 then radius = 2 / 2 = 1 so r = 1

Plugging in the given values into the formula

V = πr²(h/3)

==> plug in r = 1 and h = 6 and π = 3.14 approximately

V = (3.14)1²(6/3)

==> simplify exponent

V = 3.14(1)(6/3)

==> divide 6 by 3

V = 3.14(2)

==> multiply 3.14 by 2

V = 6.28

Finding the volume of the 200 candles.

So we have calculated that the volume of one candle is about 6.28in³ and we want to find the volume of 200 of those candles.

To do so we simply multiply the volume of one of those candles by 200

So volume of 200 candles = 200 × 6.28 = 1256 cubic inches

The correct value of z in this figure is 190⁰

The image given in this question is of a circle. To solve it, let's calculate it as an equation of the first degree.

– First, let's: add the data that are on the circle and equate the equality as 360⁰, which is the value of the degree of a circle.

145 + 24 + z = 360⁰

– Now, let's: add the natural terms to each other. And finally, we'll isolate z and subtract 360⁰ by the number that's left.

145 + 24 + z = 360⁰

170 + z = 360⁰

z = 360⁰ - 170

z = 190⁰

So, the value of z, will be 190⁰

Answer:

4 cm ×12 cm

Step-by-step explanation:

To find the dimensions of the sticker, start by forming 2 equations for its area and perimeter.

Perimeter of rectangle= 2(length +breadth)

Let the length and breadth of the rectangle be L and B cm respectively.

2(L +B)= 32

Divide both sides by 2:

L +B= 16 -----(1)

Area of rectangle= length ×breadth

LB= 48 -----(2)

From (1): L= 16 -B -----(3)

Substitute (3) into (2):

(16 -B)(B)= 48

Expand:

16B -B²= 48

B² -16B +48= 0

(B -4)(B -12)= 0

B -4= 0 or B -12= 0

B= 4 or B= 12

Substitute into (3):

L= 16 -4 or L= 16 -12

L= 12 or L= 4

Thus, the dimensions of the sticker is 4 cm ×12 cm.

The jar of nickels weighs 1.55 pounds more than the jar of pennies. The correct option is d

From the question, we are to determine the jar that weighs more

From the given information

His jar of pennies weighs 84.96 ounces

and his jar of nickels weighs 3.11 kilograms

First, we will 84.96 ounces to kilogram

From the given conversion,

There are 0.0283495 kilograms per ounce

That is, 0.0283495 kg = 1 ounce

If 1 ounce = 0.0283495 kg

Then,

84.96 ounces = 84.96 × 0.0283495 kg

∴ 84.96 ounces = 2.4086 kg

His jar of pennies weighs 2.4086 kg

Since the John's jar of nickels weighs 3.11 kg, his jar of nickels weigh more.

3.11 kg - 2.4086 kg = 0.7014 kg

Convert 0.7014 kg to pounds

1kg =  2.20462 pounds

∴ 0.7014 kg = 0.7014 × 2.20462 pounds

0.7014kg ≅ 1.55 pounds

Hence, the jar of nickels weighs 1.55 pounds more than the jar of pennies. The correct option is d.

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Answer:

the Danyang–Kunshan Grand Bridge

The world's longest bridge is the Danyang–Kunshan Grand Bridge in China, part of the Beijing-Shanghai High-Speed Railway, according to Encyclopaedia Britannica (opens in new tab). The bridge, which opened in June 2011, spans 102.4 miles (165 kilometers)

Answer:

Danyang–Kunshan Grand Bridge

Step-by-step explanation:

Answer:

I graphed it on desmos:

Answer:

20h + 10 = 15h + 5

Step-by-step explanation:

Looking at the statements we see that Joseph charges 20h +5 and kellen 15h +10

Answer:

$ 142100

Step-by-step explanation:

Profit is the difference between the revenue and the cost

        P(x) = R(x) - C(x)

                = 820x - x² - (2300 + 60x)

                = 820x - x² - 2300 - 60x

                = -x² + 820x - 60x - 2300

         P(x) = -x² + 760x - 2300

a =  -1   ; b = 760  and c = -2300

       [tex]\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}[/tex]

                  [tex]\sf = -2300 - \dfrac{760^{2}}{4*(-1)}[/tex]

                  [tex]\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100[/tex]

[tex]\sf \boxed{P_{max}= \$ 142100}[/tex]

The length side of equilateral triangle is 8.08 units

The altitude or height of an equilateral triangle is the line segment from a vertex that is perpendicular to the opposite side.

Here, let the side of the equilateral triangle be x units

given altitude of the equilateral triangle = 7 units

we know,  

Altitude = √3/2 X side

   7 = √3/2 X x

   x = 7 X 2 / √3

   x = 14/√3

   x = 8.08 units

Thus, the length side of equilateral triangle is 8.08 units.

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Answer:

The first graph.

Answer:

70 points

Step-by-step explanation:

Answer:

A 1.3

Step-by-step explanation:

probabilities lie between 0 and 1 and cannot be more or less

[tex]v = \frac{2}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{2}{3} \times \pi \times {1.5}^{3} [/tex]

[tex]v = 7.07 \: {cm}^{3} [/tex]

[tex]v = \pi {r}^{2} h[/tex]

[tex]v = \pi \times {1.5}^{2} \times 4[/tex]

[tex]v = 28.27 \: {cm}^{3} [/tex]

[tex]v = 7.07 + 28.27[/tex]

[tex]v = 35.34 \: {cm}^{3} [/tex]

Hence, the volume of the given compound shape is 35.34 cubic centimeters.

v of hemisphere:

2/3 pi r^3

v of cylinder:

pi r^2 h

total:

add both the value

apply the formula and try

Answer:

25.9

Step-by-step explanation:

So calculate volume of the mold, which is a cone: (pi) r2 (h/3) where r is radius and h is height

So diameter/2 = r which is 1.5 in

h = 2 in

V = (3.14)(1.52)(2/3) = 4.71 in3

If 1 in3 = 0.55 oz, and 1 mold = 4.71 in3, then one mold = 2.59 oz

2.59 oz * 10 cupcakes = 25.9 oz total

Step-by-step explanation:

the volume of a cone is

pi×r² × h/3

the radius is always half of the diameter, so, it is here

12/2 = 6 in.

h = 10 in.

so, we have here

pi×6²×10/3 = 3.14 × 36 × 10/3 = 3.14×120 = 376.8 in³.

2 cupcakes have then

376.8 × 2 = 753.6 in³

1 in³ = 0.55 ounces

so, the weight of 2 such cupcakes is

0.55 × 753.6 = 414.48 ounces ≈ 414.5 ounces

Answer:

39.25

Step-by-step explanation:

Area of circle is pi(3.14) times r^2.

Semi means half

So 3.14 times 5^2 = 78.5

Its a semi ciricle so its 78.5/2 which is 39.25

Answer:

It's a right triangle ..

Step-by-step explanation:

By using Pythagoras theorem , we can know that it's a right angled triangle or not ..

so , H² = P² + B²

=> 34² = 16² + 30²

=> 1,156 = 256 + 900

=> 1,156 = 1,156

Hence , it's a right triangle

Answer:

8.6 × 10-9

Step-by-step explanation:

Answer:

18.7 units

Step-by-step explanation:

Diagonal² = 1² + 1²

                 = 2

[tex]\sf diagonal = \sqrt{2} = 1.41\\[/tex]

Perimeter = 3 + 3 + 9 *1.41

                =  3 + 3 + 12.69

                = 18.7 units