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2 years ago

Directions: Match the product and quotients estimates below with the correct expression on the left

Mathematics

1 answer:

prohojiy [21]2 years ago

8 0

Answer:

Answer is in attached image.

Step-by-step explanation:

Given the expressions, for which we have to find the estimates as per the expressions on the left.

The given expressions are:

1) 35 $\times$ 23

2) 132 $\div$ 168

3) 17.3 $\times$ 18.4

4) 999 $\div$ 208

5) 998 $\times$ 211

Here, we need to find the rounded off numbers.

35 can be rounded to 40 and 23 to 20.

Therefore, equivalent to 35 $\times$ 23 is 40 $\times$ 20

132 can be rounded to 130 and 168 to 170.

Therefore, equivalent to 132 $\div$ 168 is 130 $\div$ 170.

17.3 can be rounded to 17.0 and 18.4 to 18.0.

Therefore, equivalent to 17.3 $\times$ 18.4 is 17.0 $\times$ 18.0.

999 can be rounded to 1000 and 208 to 210.

Therefore, equivalent to 999 $\div$ 208 is 1000 $\div$ 210.

998 can be rounded to 1000 and 211 to 210.

Therefore, equivalent to 998 $\times$ 211 is 1000 $\times$ 210.

The solution can be found in the attached image as well.

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Evaluate the expression below for x =4 and y = 5.

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Answer:

positive 35

Step-by-step explanation:

x2 + 3(x + y) given

4(2) + 3(4+5) problem

4(2) + 3(9)

8 + 27= 35

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If matt filled a 2 1/5 cup container, how many 1/5 cups would he need to use?

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The circle Ci, intersects the y-axis at two points, one of which is (0.4).

Anuta_ua [19.1K]

Answer:

Part 1) r=5 units (see the explanation)

Part 2) $(x-4)^2+(y-7)^2=25$

Part 3) The center of the circle is (-3,4) and the radius is 4 units

Part 4) see the explanation

Step-by-step explanation:

Part 1)

step 1

Find the center of circle C_1

we know that

The distance between the center and point (0,4) is equal to the radius

The distance between the center and point (4,2) is equal to the radius

Let

(x,y) ----> the coordinates of center of the circle

Remember that

The tangent y=2 (horizontal line) to the circle is perpendicular to the radius of the circle at point (4,2)

That means ----> The segment perpendicular to the tangent is a vertical line x=4

The x-coordinate of the center is x=4

The coordinates of center are (4,y)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Remember

The distance between the center (4,y) and point (0,4) is equal to the radius

The distance between the center (4,y) and point (4,2) is equal to the radius

substitute

$\sqrt{(y-4)^{2}+(4-0)^{2}}=\sqrt{(4-4)^{2}+(y-2)^{2}}$

$\sqrt{(y-4)^{2}+16}=\sqrt{(0)^{2}+(y-2)^{2}}$

squared both sides

$(y-4)^{2}+16=(y-2)^{2}$

solve for y

$y^2-8y+16+16=y^2-4y+4$

$y^2-8y+32=y^2-4y+4\\8y-4y=32-4\\4y=28\\y=7$

The coordinates of the center are (4,7)

step 2

Find the radius of circle C_1

$r=\sqrt{(y-4)^{2}+(4-0)^{2}}$

substitute the value of y

$r=\sqrt{(7-4)^{2}+(4-0)^{2}}$

$r=\sqrt{(3)^{2}+(4)^{2}}$

$r=\sqrt{25}$

$r=5\ units$

Part 2)

Find the equation of the circle C, in standard form.

we know that

The equation of a circle in standard form is

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

substitute the given values

$(x-4)^2+(y-7)^2=5^2$

$(x-4)^2+(y-7)^2=25$

Part 3) Another circle C2 has equation x² + y2 + 6x – 8y +9=0

Find the centre and radius of C2

we have

$x^2+y^2+6x-8y+9=0$

Convert to standard form

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$(x^2+6x)+(y^2-8y)=-9$

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

$(x^2+6x+9)+(y^2-8y+16)=-9+9+16$

$(x^2+6x+9)+(y^2-8y+16)=16$

Rewrite as perfect squares

$(x+3)^2+(y-4)^2=16$

$(x+3)^2+(y-4)^2=4^2$

therefore

The center of the circle is (-3,4) and the radius is 4 units

Part 4) Show that the circle C2 is a tangent to the x-axis

we know that

If the x-axis is tangent to the circle, then the equation of the tangent is y=0

The radius of the circle must be perpendicular to the tangent

That means ----> The segment perpendicular to the tangent is a vertical line The equation of the vertical line is equal to the x-coordinate of the center

x=-3

The circle C_2, intersects the x-axis at point (-3,0)

<em>Verify</em>

The distance between the center (-3,4) and point (-3,0) must be equal to the radius

Calculate the radius

$r=\sqrt{(0-4)^{2}+(-3+3)^{2}}$

$r=\sqrt{16}$

$r=4\ units$ ----> is correct

therefore

The circle C_2 is tangent to the x-axis

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A. Proper
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Answer:

Probability of rolling a 2 and flipping a head will be $\frac{1}{12}$

Step-by-step explanation:

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Therefore, probability to get 2 by rolling the die will be P(A) = $\frac{1}{6}$

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Or probability to get head by flipping the coin P(B) = $\frac{1}{2}$

Probability of happening both the events (rolling a 2 and flipping a head) will be denoted by

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