Mason says that (12x+4)-(-3x+5) and 15x -1 are equivalent. Is he correct

Answer:

Length of DE is 25.

Step-by-step explanation:

Right, so this is something called midsegment theorem. ΔDBE is similar (but not congruent) to ΔABC because of the angles they share. Since DE is described as a midsegment, this means BE=EC and BD=DA; so ΔDBE is half the size of ΔABC, meaning its side lengths are also half that of the larger triangle.

(Sorry if this information was unnecessary. Just got an answer deleted because I wasn't detailed enough.)

Answer:

0.966053748

Step-by-step explanation:

[tex] \sin \bigg( \frac{5\pi}{12} \bigg) \\ = \sin \bigg( \frac{5 \times 180 \degree}{12} \bigg) \\ = \sin ( 5 \times 15 \degree) \\ = \sin ( 75 \degree) \\ = \sin ( 45 \degree + 30 \degree) \\ = \sin 45 \degree \times \cos 30 \degree + \cos 45 \degree \times \sin 30 \degree \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } \\ \\ = \frac{1.732 + 1}{2 \times 1.414} \\ \\ = \frac{2.732}{2.828} \\ \\ = 0.966053748[/tex]

Answer:

C y=800(1.15)^12

Step-by-step explanation:

Answer:

[tex]1538.6mm^{3}[/tex]

Step-by-step explanation:

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

[tex]V=3.14*7^{2} *10[/tex]

[tex]V=31.4*49=1538.6[/tex]

Answer:

C

Step-by-step explanation:

When you multiply -1(x+8)(x+7)

                                 (-x-8)(x+7)

                                  -x(x+7)-8(x+7)

                                   [tex]-x^{2}-15x-56[/tex]

Answer:

(3,3)

Step-by-step explanation:

Answer:

(3,3)

Step-by-step explanation:

To find the midpoint add the x coordinates together and divide by 2

(1+ xb)/2 = 2

1+ xb = 4

xb = 4-1

xb =3

To find the midpoint add the y coordinates together and divide by 2

(7+ yb)/2 = 5

7+ yb = 10

yb = 10-7

yb =3

Answer

60 apples minus how many she picked (12) or 60-12 divided by 6 baskets. The answer will be 60-12=48. 48 divided by 6 equals 8. The ANSWER IS 8

Step-by-step explanation:

The formula used to calculate how many apples should be included in each gift basket is as follows:

6x = 48

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Jack has 48 apples left after using 12 of the 60 apples he took from the tree to make applesauce.

The leftover apples will be distributed equally among six gift baskets, he said. He puts x apples in each present basket, where x is the number of apples. Then he adds six times as many apples to each of the six gift baskets.

He has to fill the gift baskets with 48 apples, thus we can create an equation:

6x = 48

We may divide both sides of the equation by 6 after finding the value of x:

x = 8

Hence, Jack needs to fill each of the six gift baskets with 8 apples.

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Answer:

A, C and E.  

Step-by-step explanation:

[tex]70 \% \times 80[/tex]

[tex]70/100 \times 80[/tex]

[tex]560/10[/tex]

[tex]=56[/tex]

[tex]0.7 \times 80[/tex]

[tex]=56[/tex]

[tex]7/10 \times 80[/tex]

[tex]=56[/tex]

Answer:

7.

Step-by-step explanation:

Follow the order of operations.

We do the operation in the bracket first. So we are left with:

2 * (2) + 3

We multiply before we add, so:

4 + 3.

Finally, we add.

7.

I hope this helps!

Answer:

The second option will cost her less than the first one.

Step-by-step explanation:

In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.

For the first option we have:

[tex]cost_1(x) = 0.5*x[/tex]

For the second option we have:

[tex]cost_2(x) = 5000 + 0.1*x[/tex]

Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:

[tex]cost_1(60000) = 0.5*60000 = 30000[/tex]

[tex]cost_2(60000) = 5000 + 60000*0.1 = 11000[/tex]

The second option will cost her less than the first one.

Answer:

The volume of the right circular cone is [tex]1005.9\ \text{inch}^2[/tex].

Step-by-step explanation:

It is given that,

Height of a right circular cone is 18.8 inches and its diameter is 14.3 inches. We need to find the volume of the cone. The volume of cone is

[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]

So,

[tex]V=\dfrac{1}{3}\times 3.14\times (\dfrac{14.3}{2})^2\times 18.8\\\\V=1005.9\ \text{inch}^2[/tex]

So, the volume of the right circular cone is [tex]1005.9\ \text{inch}^2[/tex].

Answer:1006.5

Step-by-step explanation:

Answer:

70cm2

Please mark

Step-by-step explanation:

Answer:

396 cm²

Step-by-step explanation:

The figure is composed of 2 rectangles.

The vertical rectangle on the left has area (A) calculated as

A = 27 × 10 = 270 cm²

The horizontal rectangle on the right has area (A) calculated as

A = 9 × (24 - 10) = 9 × 14 = 126 cm²

Thus area of figure = 270 + 126 = 396 cm²

Answer:

256

Step-by-step explanation:

<1=<8 -->alt exterior angles

<4=<1 --> vertical angles

= <1=<4=<8(128)

256

Answer:

6. composite figure

7. 60+432=492

Answer:

The answer is 100% B

Step-by-step explanation:

The graph of the polynomial rational function is f ( x ) = x / ( x + 2 ) ( x - 5 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the polynomial function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x / ( x + 2 ) ( x - 5 )

The rational function is of the form P ( x ) / Q ( x ) , where Q ( x ) ≠ 0

So , the value of P ( x ) = x

And , the value of Q ( x ) = ( x + 2 ) ( x - 5 )

Therefore , the graph of the rational function is plotted

Hence , the graph of the polynomial is f ( x ) = x / ( x + 2 ) ( x - 5 )

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Answer:

Range could be 205000 to 214999. Any number in this range, when rounded to two signnificant digits will yield 210000.

Answer:

smaller r = ( 6.5 , 0)

larger r = ( 21.5 , 0)

vertex = ( 14, -56.25)

Step-by-step explanation:

f(r) = (r -14)² -56.25 square (r-14)

f(r) = r² -28r +196 -56.25 simplify

f(r) =  r² -28r + 139.75

use quadratic formula

x=−b±√(b²−4ac)/ 2a

a = 1, b =-28, c = 139.75

x=−(−28)±√(−28)2−4(1)(139.75)2(1)

x=(28±√225)/2

x=43/2 or x=13/2

or 21.5 and 6.5

This parabola is given in vertex form f (r) = a(r - h)² + k, where (h, k) is the vertex of the parabola so just write the given numbers ( 14, -56.25)

Answer:

The table of data is shown below

The equation of line best fit is given in the form y=mx+b

to find the slope 'm', follow these steps:

STEP 1

Mean (X) = \frac{4+6+8+13+11}{5}=8.4

Mean(Y)= \frac{17+12+9+4+3}{5}=9

STEP 2

Refer to Picture 2 and Picture 3 for the working out of ( x_{i} -mean(X)) and ( y_{i} -mean(Y))

( x_{i}-X)( y_{i}-Y) =(-4.4)(8)+(-2.4)(3)+(-0.4)(0)+(2.6)(-5)+(4.6)(-6)

( x_{i}-X)( y_{i}-Y) =(-35.2)+(-7.2)+0+(-13)+(-27.6)=-83

STEP 3:

( x_{i}-X) ^{2}  = (-4.4)^{2}+ (-2.4)^{2}+ (-0.4)^{2}+ (2.6)^{2}+ (4.6)^{2}=53.2

STEP 4:

To find slope, divide answer in STEP 2 by the answer in STEP 3

m= \frac{-83}{53.2} =-1.56

STEP 5:

b=Mean(Y)-[slope*mean(X)]

b=9-(-1.56*8.4)=22.105

We have the slope, m=-1.56 and y-intercept of 22.105

The equation of line is

y=22.105-1.560x

Correct answer: Last statement

Step-by-step explanation:

The answer to the question what is the value of this expression when a = 7 and b = -4? | 2a | - b/3 it is D.) 6

The value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.

The absolute value of a number or variable is returned by a modulus function. It is defined as

|x| = x, x > 0

= -x, x < 0

= 0, x = 0

The given expression is (|2a| - b)/3. Here, we have to put a = 7 and b = -4 to get the value.

Now, (|2a| - b)/3 = (|2×7| - (-4))/3 = (|14| + 4)/3 = (14 + 4)/3 [Since 14 is a positive integer]

i.e. (|2a| - b)/3 = 18/3 = 6

Therefore, the value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.

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Answer:

hey. Answer is $495 as the actual price of the motor without discount.

Step-by-step explanation:

So you would multiply 450 by .10 and you get 45. So he got $45 off. Then add 450 to 45. Yoy get $495!

Answer:

bisects, equal, midpoint

Step-by-step explanation:

According to the "Angle Bisector" Theorem, an angle bisector of a triangle divides the opposite side into segments proportional to the lengths of the other two sides of the triangle.

If a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the lengths of the other two sides. An angle bisector divides an angle into two equal halves. A perpendicular bisector is the line perpendicular to a segment passing through the segment’s midpoint.

Answer:

Not even a whole day. To be exact, it is .416667 of a day

Step-by-step explanation:

Since 60 minutes are in 1 hour, than 600 minutes would be 10 hours.

24 hours in a day, so you are 14 hours short, about 840 minutes.

Answer:

~0.42 days

Step-by-step explanation:

60 minutes in one hour

60 times 24 = 1440 minutes in a day

600 minutes divided by 1440 = 0.4166666667...

Rounded up to 0.42

technically not a whole day but yeah

Answer:

x = -3        x=2

Step-by-step explanation:

x^2 + x - 6 = 0

Factor

What two numbers multiply to -6 and add to 1

3*-2 =-6

3+-2 =1

(x+3) (x-2) = 0

Using the zero product property

x+3 = 0   x-2 = 0

x = -3        x=2

Answer:

Option (B)

Step-by-step explanation:

If A = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}[/tex] and B = [tex]\begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]

Multiplication of these matrices,

A.B = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\times \begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]

      = [tex]\begin{bmatrix}(1(-2)+3(3) & 1(1)+3(4)\\ (-2)(-2)+5(3) & 1(-2)+5(4)\end{bmatrix}[/tex]

      = [tex]\begin{bmatrix}7 & 13\\ 19 & 18\end{bmatrix}[/tex]

Therefore, Option (B) will be the answer.

Answer:

m = 4

Step-by-step explanation:

m−10+6m=10+2m

7m-10=10+2m

Subtract 2m from both sides

5m-10=10

Add 10 to both sides

5m=20

Divide both sides by 5

m=4

Answer:

m=4

Step-by-step explanation:

m − 10 + 6m = 10 + 2m

7m - 10 = 10 + 2m   (subtract 2m from both sides)

7m - 10 - 2m = 10

5m - 10 = 10   (add 10 to both sides)

5m = 10 + 10

5m = 20  (divide both sides by 5)

m = 20/5

m = 4

Answer:

C

Step-by-step explanation:

Use sine rule

17/sin130=5/sinB

(5×sin130)÷17=sinB

sinB=0.2253017892

B=sin^-1ans above

=13.4

A=(130+13) subtracted from 180=37°

a/sin37=17/sin130

=13.4

Answer:

325 adults

Step-by-step explanation:

x=#adults

y=#children

x+y=937

2x+0.75y=1109

2x+2y=1874

-2x-0.75y=1109

1.25y=765

y=612

x=937-612

x=325

Answer:

Step-by-step explanation:

The graph of f(x) = + (4) is the same as that of g(x) = 4; it's a constant function defined for all x values but its range is just one number:  4.

Answer:

the

Step-by-step explanation:

sale would be $20 for every item, duh