What’s the correct answer?

Answer:

Value of a =3

Value of b =5

Step-by-step explanation:

[tex]If\ the\ polynomial\ p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b,\ p\left(1\right)\ =\ 3\ and\ p\left(2\right)\ =\ 19,\ find\ a\ \&\ b[/tex]

We are given p(1)=3 and p(2)=19

Putting x =1 to find p(1)

[tex]p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b\\p(1)=2(1)^3+a(1)^2-7(1)+b\\We \ know \ p(1)=3\\3=2+a-7+b\\3=-5+a+b\\a+b=3+5\\a+b=8[/tex]

Now putting x=2 as p(2)=19

[tex]p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b\\p(2)=2(2)^3+a(2)^2-7(2)+b\\We \ know \ p(2)=19\\19=2(8)+4a-14+b\\19=16+4a-14+b\\4a+b=19-16+14\\4a+b=17[/tex]

Solving these equations to find values of a and b

[tex]a+b=8---eq(1)\\4a+b=17---eq(2)[/tex]

Subtract both equations

[tex]a+b=8\\4a+b=17\\-\ \ \ - \ \ \ -\\------\\-3a=-9\\a=\frac{-9}{-3}\\a=3[/tex]

So, value of a =3

Now finding value of b bu putting value of a in equation 1

[tex]a+b=8\\3+b=8\\b=8-3\\b=5[/tex]

So, Value of b =5

Answer:

90.24 divided by 6.3

Step-by-step explanation:

For reaching to the answer, we have to test each of the options given

The first option says that the divisor and dividend is 90.24 and dividend is 6.3

Now if we rounded it

So it would be 90 and 6

So, the quotient is

= 90 ÷ 6

= 15

Hence, the first option is correct

i.e. 90.24 divided by 6.3

And, all the other options are wrong

Answer:

y=1.5x+2.5 ,

y=32x+52 ,

y=32x+2.5 ,

or

y=1.5x+52

The equation in slope-intercept form to model the cooking time in minutes, y, for x patties is y = (3/2)x + 1.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given,  On a box of chicken patties state that one patty should be cooked for 2.5 minutes in the microwave.

If more than one patty is cooked, an additional 1.5 minutes should be added per patty.

So,  The equation in slope-intercept form to model the cooking time in minutes, y, for x patties.

If we write this as y = 1.5x + 2.5 and put x = 0 , y = 2.5 which is not satisfying the given statement.

∴ y  = 1.5x + (2.5 - 1.5). (the additional patty cooking time).

y = 1.5x + 1.

y = (3/2)x + 1.

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Answer:

88 hrs

Step-by-step explanation:

1/3/4 = 7/4hr ; 7/4 = 1.75hr (the number of hours used to travel for 154km)

154/1.75 = 88 (the number of km van travels per hour)

Answer: 23.74625 miles

Answer:

8:10

Step-by-step explanation:

If Timothy has some coins in a jar. He has 6 pennies,8 nickels,10 dimes, and four quarters. Then 4:5 is the ratio of the number of nickels to the number of dimes

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Timothy has some coins in a jar.

The number of Pennies = 6

The number of Nickels = 8

The number of dimes =10

The number of quarters =4

We need to find the ratio of  the number of nickels to the number of dimes

8/10

4/5

Hence 4:5 is the  ratio of  the number of nickels to the number of dimes

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44

Step-by-step explanation:

let boys be x and girls be y

x/y=5/6

x=5y/6....(1)

if 6 boys join the club that will be x+6

Therefore:

(x+6)/y=13/12

13y=12x+72

13y-12x=72

Recall x=5y/6

Therefore:

13y-12(5y/6)=72

13y-(2*5y)=72

13y-10y=72

3y=72

y=24 people

Therefore:

x=(5*24)/6

x=20 people

Therefore people in the club before are 20+24=44

Answer:

D

Step-by-step explanation:

3 (4x + 18y) means that 3 will multiply 4x and 18y factor which results to 12x + 54y

hence dissimilar to the original expression

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

c is the answer and that's a good tung twister math problem

Answer:

The new vertices will be: A'(-1,-3), B'(-2,-2) and C'(-4,-3)

Step-by-step explanation:

Rotation about the origin depends on the degrees the point is being rotated and direction of rotation.

Let (x,y) be a point on the xy-coordinate plane,

When this point will be rotated about origin 90 degrees counter clockwise, the coordinates of the point become (-y,x) which means that the coordinates will be exchanged and y will be negated.

Given vertices of triangle are:

A(-3, 1), B(-2, 2), and C(-3, 4)

After rotation the new points will be:

A(-3, 1) => A'(-1,-3)

B(-2,2) => B'(-2,-2)

C(-3,4) => C'(-4,-3)

Hence,

The new vertices will be: A'(-1,-3), B'(-2,-2) and C'(-4,-3)

Answer:

(1,3)

Step-by-step explanation:

Answer:

42 degrees

Step-by-step explanation:

Answer:

x=42°

Step-by-step explanation:

In any triangle, when all three angles are added together, their sum will always be 180°:

∠1+∠2+∠3=180

Insert any known values:

[tex]29+109+x=180[/tex]

Simplify the addition:

[tex]138+x=180[/tex]

Use inverse operations to find angle three. Subtract 138 from both sides:

[tex]138-138+x=180-138\\\\x=42[/tex]

Therefore, the unknown angle is 42°.

:Done

Answer:

29

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Any number multiplying to a variable will be a term, but not a constant.

A constant is a term, just one without variables.

We are given 6y + 29. 6y would be a term and 29 would be another term. Since 29 has no variables, it will be the constant.

Answer:

the answer is 12

Step-by-step explanation:

Answer:

x>−3

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

73 - 11 = 62

62 / 2 = 31

Answer:

Step-by-step explanation:

They're asking for what other information is needed.

We were given triangle ABC is congruent to triangle DEF. We know for certain line AB and line DC are congruent to each other as well as lines BC and EF.

The additional information we need to know is if line AC is congruent to line DF to absolutely be sure.

Remember SSS by definition is:  Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other. If all three sides in one triangle are the same length as the corresponding sides in the other, then the triangles are congruent.

SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).

Thus, the needed answer is:

Line segment DF is congruent to line segment AC

or [tex]\overline{DF} \cong \overline{AC}[/tex]

If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)

Since it is given that the sides CB and FE are congruent,

and since it is given that sides AB and DE are congruent too,

thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.

Thus, we need the line segment DF congruent to the line segment AC.

We can write it symbolically as:

[tex]\overline{DF} \cong \overline{AC}[/tex] (remember that order doesn't matter here. You could've written [tex]\overline{AC} \cong \overline{DF}[/tex] too.)

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Answer:

i told you in the comment it equals 7

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given

- 2 (1 - 4x) = 3x + 8 ( distribute parenthesis on left side )

- 2 + 8x = 3x + 8 ( subtract 3x from both sides )

- 2 + 5x = 8 ( add 2 to both sides )

5x = 10 ( divide both sides by 5 )

x = 2

Answer:

She can cut 180 (9 - inch) pieces

Step-by-step explanation:

A dressmaker needs to cut 9-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 9-inch pieces can the dressmaker cut from 15 of these rolls of ribbon? Before you try that problem, answer the question below.

Step 1

How many inches of ribbon does the dressmaker have, in total?

1 roll of ribbon = 9 feet

15 rolls of ribbon = x feet

x = 15 roll × 9 feet

x = 135 feet

Converting from Feet to inches

1 foot = 12 inches

135 feet = x inches

Cross Multiply

x = 135 × 12 inches

x = 1620 inches

The dress maker cuts 9 inches each

How many 9-inch pieces can the dressmaker cut from 15 of these rolls of ribbon?

15 rolls of ribbon = 1620 inches of ribbons

Hence: = 1620 inches/9

= 180 pieces

She can cut 180 (9 - inch) pieces

Answer:

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.

In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector

→

A

in a plane is described by a pair of its vector coordinates. The x-coordinate of vector

→

A

is called its x-component and the y-coordinate of vector

→

A

is called its y-component. The vector x-component is a vector denoted by

→

A

x. The vector y-component is a vector denoted by

→

A

y. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:

Step-by-step explanation:

Answer:

approximately 85 m

Step-by-step explanation:

use the law of cosines

x²=120²+90²-2(120)(90)cos(45)

*120 & 90 are given values

*45 is from 25+20; bcuz of alternate interior angles, the other angle from mirror 1 is 25 degrees, making the total 45 degrees

x=√120²+90²-2(120)(90)cos(45)

x=85, the distance btwn origin point and mirror 2

Answer:

BEcause the sign is a greater than its gonna have a hollow circle. greater than or equal too would have a filled in circle. To solve, divide by -1/3 each side to find the answer

-4>-4/3s

-4/ -4/3>2

-4/-4/3=3

3>s

Therefore

3>S

So you are going to put a hollow circle at 3 and draw an arrow going to the left of 3.

Step-by-step explanation:

Answer:

s>3

Step-by-step explanation:

place it on 3, it may be an open circle. :)

You’re welcome :)

Answer:

697

Step-by-step explanation:

Answer:

698

Step-by-step explanation:

(721-24)+1= 698

Answer:

A’ (6,-2)

B’ (1,3)

Step-by-step explanation:

Here, we want to give the coordinates after a counterclockwise rotation of 90 degrees

Given a point with coordinates (x,y)

A counterclockwise rotation at 90 degrees to the origin will yield the coordinates (-y,x)

So A (-2,-6) will be A’ (6,-2) while B (3,-1) will be B’ (1,3)

Answer:

the answer would be around 1.5 to two percent

Step-by-step explanation:

Answer: 6 1/2

Step-by-step explanation:

six and 1 half of a hour

Answer:

a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Subtract x from each side so you get

2y = -x-6

Then divide them by 2 to get

y = -x-6/2