Casey picked 6 pounds of strawberries. Karen picked 48 ounces of blueberries. Jude picked 2 pounds of raspberries. They are going to make berry pies. The table shows the amount of berries needed for 1 pie.Select all of the true statements below.
A.

Together, Karen and Jude picked the same weight of fruit as Casey picked.


B.

Casey picked 2 times the weight of fruit that Karen picked.


C.

There are enough berries to make 6 berry pies.


D.

If they make as many pies as they can with the berries they picked, there will be 4 pounds of strawberries left over.


E.

To make 8 berry pies, they will need 1 more pound of blueberries and 2 more pounds of raspberries.

Answer:

The factors of the given equation are:

(11x−8)(11x+2)

Step-by-step explanation:

Since both terms are perfect squares,

Factorize using the difference of squares formula,

[tex]a^{2} -b^{2}[/tex][tex]=(a+b)(a-b)[/tex]

where a=11x−3 and b=5.

=> (11x-3+5)(11x-3-5)

=> (11x+2)(11x−8)

=>[tex](11x-3)^{2}-25[/tex]

Use the binomial theorem [tex](a-b)^{2}=a^{2} +b^{2} -2ab[/tex] to expand[tex](11x-3)^{2}-25[/tex]

=> [tex](11x^{2})+(3)^{2}- 2(11x)(3)-25[/tex]

=>[tex]121x^{2} + 9 - 66x -25[/tex]

=> [tex]121x^{2} -16+ 66x[/tex]

By the splitting method,

=> (11x−8)(11x+2)

The factors of the equation are (11x−8)(11x+2).

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Step-by-step explanation:

4a.

the circumference of a circle is

2×pi×r

we know, r = 6 cm.

so the whole circumference is

2×pi×6 = 12×pi = 37.69911184... cm

4b.

the arc BC is the part of the full circumference that corresponds to 120° out of the 360° of a full circle.

the arc BC is then

12×pi × 120/360 = 12×p × 1/3 = 4×pi = 12.56637061... cm

the perimeter of the shaded area (pie slice) is the arc BC plus 2 radius lengths (from the arc points to the center of the circle)

12.56637061... + 2×6 = 12.56637061... + 12 =

= 24.56637061... cm

4c.

the area of a circle is

pi×r²

in our case

pi×6² = 36pi = 113.0973355... cm²

the area of the shaded area (pie slice) is the 120° part of the full 360° circle area :

36pi × 120/360 = 36pi × 1/3 = 12pi = 37.69911184... cm²

Answer: [tex]3 \pm \sqrt{7}[/tex]

Step-by-step explanation:

[tex]1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}[/tex]

Using translation concepts, it is found that the function [tex]f(x) = -3\sqrt{x}[/tex] is the function [tex]g(x) = \sqrt{x}[/tex] reflected over the x-axis and vertically stretched by a factor of 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, from [tex]g(x) = \sqrt{3}[/tex] to [tex]f(x) = -3\sqrt{x}[/tex], g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.

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Statement A is needed to complete this syllogism. its diagonals are perpendicular. Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.

A logical structure for a formal argument that includes a major, minor, and conclusion.

This syllogism cannot be concluded without Statement A. The diagonals of it are parallel. As a result, a quadrilateral's diagonals are perpendicular if it has four congruent sides.

If a quadrilateral has 4 congruent sides, then it is a rhombus. If it is a rhombus, then its diagonals are perpendicular.

Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.

Hence option A is correct.

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Answer:

a quadrilateral has 4 congruent sides

Step-by-step explanation:

Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.

Answer:

-2

Step-by-step explanation:

just a guess but it's right

Answer:

286+390+468÷3= answer

[tex]( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.[/tex]

Answer:

B

Step-by-step explanation:

The vertical asymptotes are the red dashed lines. They are x = -4 and x = 0. Think of them as electric fences that the graph cannot touch or cross. The curve can only get closer and closer.

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Answer:

48 and 37

Step-by-step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

answer:

48 and 37

step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.

There are five number cards on the table.

2- digit 1 card

1- digit 0 card

2- digit 2 card

There is a possibility of putting 1 or 2 in the hundredth place.

If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2

If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place

If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place

If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.

So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.

Similarly, there will be 7 possibilities that the hundredth place is filled by 2.

Hence, there are 14 possibilities as required by the problem.

So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.

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Answer:

Standard Deviation is s = 2.9

Step-by-step explanation:

Count = [tex]N[/tex] = 5

Mean = [tex]x^-[/tex] = 9

Variance = [tex]s^2[/tex] = 8.5

SD Formula = [tex]s = \sqrt \frac{1}{N - 1} (x_{i} - x^-)^2[/tex]

Variance Formula[tex]s^2 = \frac{(x_{i} - x^-)^2}{N- 1}[/tex]

Step 1: Calculate the variance

[tex]= \frac{(7-9)^2 + (5-9)^2 + (10-9)^2 + (11-9)^2 + (12 -9)^2 }{5-1}[/tex]

[tex]=\frac{34}{4} = 8.5[/tex]

Step 2: Apply square root/SD formula

[tex]=\sqrt{8.5} = 2.9[/tex]

Answer: B. One solution

Step-by-step explanation: As you see, both of these lines intersect on the point (0, 3). The point where the lines intersect is the solution. Since these lines are perpendicular, they will only intersect one time. Therefore, there is only one solution, that being (0, 3).

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Answer:

400

Step-by-step explanation:

4/5×500

=400 6s would be riled

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

so, here

2×95 + 2×72 = 190 + 144 = 334 m

so, yes, the answer 2. 334 is correct.

The solution is Option B.

The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the number of posts be = N

Fencing posts have to be fixed at 1-metre intervals

The perimeter of the rectangular field = number of posts

Now , the equation will be

The length of the rectangular field = 95 m

The width of the rectangular field = 72 m

Perimeter P of the rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

Perimeter of the rectangle P = 2 ( 95 + 72 )

On simplifying the equation , we get

Perimeter of the rectangle P = 2 ( 167 )

Perimeter of the rectangle P = 334 m

Now , the number of posts = perimeter of the rectangular

So , the number of posts N = 334 posts

Therefore , the value of N is 334

Hence , the number of posts is 334 posts

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Answer:

46. 135°

47. 225°

47. 270°

48. 3/8

49. 3/4

Step-by-step explanation:

Answer:

46) 135°

47) 225°

48) 270°

49) [tex]\frac{3}{8}[/tex]   (3/8)

50) [tex]\frac{3}{4}[/tex]  (3/4)

Step-by-step explanation:

{the following is if you do not understand my drawing}

There are 4 segments that we can imagine - north, south, east, and west

We can imagine that these lines all meet a circle

There are 360 degrees to a circle. So, if we divide that by 4, we know that each segment is 90 degrees.

(Also, you can probably see that the angles are right angles, or you know that straight lines are 180 degrees, you probably know this information intuitively)

This means that each smaller segment, two in both of our four segments, is 45 degrees.

These 8 sections are each 1/8 of the total circle.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Standard equation of circle is :

[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

Since the circle is centered at origin, h = k = 0

[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]

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Answer:

a. y = 2(x + 3)² - 17

b. y = 4(x + 6)² - 154

Step-by-step explanation:

a. y = 2x² + 12x + 1

y = 2[(x² + 6x)] + 1

y = 2[(x + 3)² - 9] + 1

y = 2(x + 3)² - 18 + 1

y = 2(x + 3)² - 17

b. y = 4x² + 48x - 10

y = 4[(x² + 12x)] - 10

y = 4[(x + 6)² - 36)] - 10

y = 4(x + 6)² - 144 - 10

y = 4(x + 6)² - 154

Answer:

B is the correct answer

Step-by-Step:

Answer:

x = 15

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , then

6x + 20 + 3x + 25 = 180 , that is

9x + 45 = 180 ( subtract 45 from both sides )

9x = 135 ( divide both sides by 9 )

x = 15

Answer:

multiply 1/2 by each element in the matrix

Step-by-step explanation:

6. 32

39 15

Answer:

5

Step-by-step explanation:

Look at one of the coordinates to find k. For this example I'll look at the y-intercepts (0, 3) (for g(x)) and (0, -2) (for f(x))

g(0) = 3

g(0) = f(0) + k

3 = -2 + k

5 = k

Answer:

1-3

2-2

3-1

Step-by-step explanation:

Answer:

558, 500

Step-by-step explanation:

round 349,001 to 349,000             subtracted 1

round 209, 499 to 209, 500          added 1

349,000 + 209, 500 = 558, 500

Now, the added and subtract 1 cancel out so that is the final answer

Answer:

There are no solutions

Step-by-step explanation:

If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.

The above Exponential function has the parent function to be F(x).

The difference between successive terms  is: 6, 18, 54, 162. These are known to be in the powers of 2 and therefore one can say that there is an exponential increase in the parent function.

The new function is said to g(x). Translating down by 4 means that the new y-values are 4 units lower and so the answer is that the f(x)/y-values will be decreased by 4.

Therefore, looking at the above, since g(x)=f(x)-4 one need to know the value of x, the new y-value is lower by 4 from the old one. This is the case only for  (1, 52) since the old function is (1, 13).

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Answer:

5. 8π 6. 18π 7. 8.6π 8. 11/4π

Step-by-step explanation:

8. 2 3/4

2*4+3 = 11/4

Answer:

x = 115

z = 27

Step-by-step explanation:

x + 65 = 180 (same side interior angles)

x = 115

x = 3z +34 (alternate interior angles)

115 = 3z + 34

3z = 81

z = 27