1
1
Consider the polynomial function:
p(x) = 3x3 + 10x2 + ax - 6
where a is an unknown real number.
If
(x + 3)
is a factor of this polynomial what is the value of a? Show all the steps below.

Answer:

The next statements are are;

Statement                                                  [tex]{}[/tex]        Reason

Segment [tex]\overline {DC}[/tex] ≅ Segment [tex]\overline {AB}[/tex]                        [tex]{}[/tex]   CPCTC

[tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] and [tex]\overline {DC}[/tex] ≅ [tex]\overline {AB}[/tex], therefore;

ABCD is a parallelogram                    [tex]{}[/tex]               Parallelogram side theorem

Step-by-step explanation:

Statement                                                  [tex]{}[/tex]        Reason

Segment [tex]\overline {DC}[/tex] ≅ Segment [tex]\overline {AB}[/tex]  by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Given that [tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] and we have that [tex]\overline {DC}[/tex] ≅ [tex]\overline {AB}[/tex], we get;

ABCD is a parallelogram                    [tex]{}[/tex]               Parallelogram side theorem

The parallelogram side theorem states that a quadrilateral is a parallelogram if it has two pairs or sets of congruent opposite sides.

See attachment for math work and answer.

Answer:

30° ; 80°

Step-by-step explanation:

Given that :

One angle of a certain triangle = 70°

The other two angles are in the ratio 3 : 8

Recall :

Sum of angles in a triangle = 180°

Number of angles in a triangle = 3

Hence,

Sum of the other two angles + 70 = 180

Hence, sum of the other two angles = (180 - 70)°

Sum of other two angles = 110°

The angle is in the ratio 3:8

Hence,

(3 / (3 +8)) * 110

= 3/11 * 110

= 330 / 11

= 30°

(8 / (3 +8)) * 110

= 8/11 * 110

= 880 / 11

= 80°

Hence ; 30° ; 80°

Answer:

2

Step-by-step explanation:

Answer:

y > x - 2.

2*y + x < 4

The correct option is the third one.

Step-by-step explanation:

First let's find the red shaded part.

We can see that the shade is above the line, then we will have something like:

y > a*x + b

where a*x + b is the equation for the line.

a is the slope, and b is the y-intercept.

In the graph, we can see that the line intercepts the y-axis at y = -2, then we have:

b = -2

To find the slope we need two points of the line, we can use the points (0, -2) and (2, 0)

We know that for a line that passes through the points (x1, y1) and (x2, y2) the slope is:

a = (y2 - y1)/(x2 - x1)

Then for this line, the slope will be:

a = (0 - (-2))/(2 - 0) = 2/2 = 1

Then the equation for this line is:

1*x - 2

And the inequality is:

y > x - 2.

Now for the blue one, the shaded part is below the line, then we will have:

y < a*x + b

In this case, the y-intercept is y = 2.

And we can see that this line passes through the points (0, 2) and (4, 0)

Then the slope is:

a = (0 - 2)/(4 - 0) = -2/4 = -1/2

Then this inequality is:

y < (-1/2)*x + 2

If we rewrite this as the ones shown in the options, we have:

y < (-1/2)*x + 2

2*y < -x + 2*2

2*y + x < 4

Then the two inequalities are:

y > x - 2.

2*y + x < 4

Then the correct option is the third one:

The system of linear inequalities y > x - 2 and x + 2y < 4 is represented by the graph

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

Given the inequalities  y > x - 2 and x + 2y < 4, plotting the two inequalities using the geogebra online graphing tool.

The solution of the inequality on the graph is the very dark region.

Find out more on Inequality at: brainly.com/question/24372553

Answer:

The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. A recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 . The answer is a1 =-3 & a(n) =a(n-1) •y 7

Hope this helps, have a great day/night, and stay safe!

Answer:

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

11^12 is the power

12 is the exponent

So 11 is the base

Answer:

B 11

Step-by-step explanation:

the base means the base number not the exponent, so 11

Answer:

A.In Nuuk, Greenland, in January, the average high-temperature is -4.6°C (23.7°F), and the average low-temperature is -10°C (14°F).

B. the average high-temperature is 5.7 degrees celsius and average low temperature is 3.3 degrees celsius

C. 4 degrees celsius

D. 39 degrees fahrenheit

E. Isla Hoste in august

F.On the average, the average low in January for Nuuk is 10/3 or 3.333 times farther below the freezing point of water than the average low for Isla Hoste in August.

Step-by-step explanation:

Hope this helps OwO

a) The average high and low temperatures are -8°C and -27°C.  b) The average high and low temperatures are 13°C and  7°C. c) The average net change in temperature is -19°C.  d) The average net change in temperature is 6°C.  e) Nuuk in January experiences a larger absolute change.  f) The January low for Nuuk is 3.8 times farther below the freezing point of water than the August low for Isla Hoste.

Part A

The average high temperature in Nuuk in January is -8°C and the average low temperature is -27°C.

Part B

The average high temperature in Isla Hoste in August is 13°C and the average low temperature is 7°C.

Part C

The average net change in temperature in Nuuk in January is -27°C - (-8°C) = -19°C.

Part D

The average net change in temperature in Isla Hoste in August is 13°C - 7°C = 6°C.

Part E

Nuuk in January experiences a larger absolute change between the high temperature and low temperature, with a net change of -19°C, compared to Isla Hoste in August, with a net change of 6°C.

Part F

The January low for Nuuk is -27°C, which is 27°C below the freezing point of water. The August low for Isla Hoste is 7°C, which is 7°C below the freezing point of water. Therefore, the January low for Nuuk is 27 / 7 = 3.8 times farther below the freezing point of water than the August low for Isla Hoste.

To learn more about average here:

https://brainly.com/question/24057012

#SPJ2

Answer:

623

hope this helped?

Step-by-step explanation:

The equation of the line is y = 1.5x + 3.

Answer: 0.6841

Step-by-step explanation:

Given: Probability of all SMES would file for bank loans next year = 3.5% = 0.035

Sample size : n = 100

Binomial probability distribution formula :

[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]

The probability that at least 3 will file bank loans next year :

[tex]P(x\geq3)=1-P(x<3)\\\\=1-(P(x=0)+P(x=1)+P(x=2))\\\\=1-(^{100}C_0(0.035)^0(1-0.035)^{100}+\ ^{100}C_1(0.035)^1(1-0.035)^{99}+^{100}C_2(0.035)^2(1-0.035)^{98})\\\\=1-(0.3159)\\\\=0.6841[/tex]

Hence, the required probability= 0.6841

Answer:

19 floors

Step-by-step explanation:

Let us consider the ground floor as 0 and the floors above it as positive and the floors below the ground floor as negative.

So, the floor in which she parked is -4 and the floor where her office is at +15.

The number of floors she has to climb is the absolute value of the difference of the two floors.

The number of floors she has to go up is [tex]|-4-15|=19[/tex].

The fraction numbers 2/3 and 4/6 will lie on the same point on the number line.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction numbers are given below.

2/3 and 4/6

Convert the fraction into the simplest fraction, then we have

4 / 6 = 2 / 3

The fraction numbers 2/3 and 4/6 will lie on the same point on the number line.

More about the number line link is given below.

https://brainly.com/question/13189025

#SPJ5

Answer:

the difference is 6x³

Step-by-step explanation:

19x3 – 13x3

=6x³

Answer:

18

Step-by-step explanation:

use pemdas. multiplication comes first and you go left to right. then you subtract the products of 19*3 and 13*3

Answer:1.2mph

Step-by-step explanation:

3/5*2=1.2 and 1/2*2=1 so it’s 1.2 mph

Answer:

D. [tex]x\geq 0[/tex]

Step-by-step explanation:

In order to answer this question we need to know the definition of the domain. The domain of a function is the complete set of possible values of the independent variable ("x"). In our case we can look at the function and cross out option "A" because the function has no point with a negative "x" value. Option "B" can be also crossed out because it states that "x" values can not go above 3 but by looking at the function we can see multiple point with "x" values larger then 3. Option "C" can also be crossed out because their is not point on the function that would have a negative "x" value which contradicts the statement about all numbers. And finally we are left with "D" and we know it is the right answer since the function has a point with "x" value being equal to 0 and the all other points have the "x" value greater then 0, which is exactly what option "D" states.

Answer:

y=2x+3

Step-by-step explanation:

the normal charge is 3 + 2 x number of days so this equation is the correct one.

Given :

Liam owns a small business selling bagels. He knows that in the last week 60 customers paid cash, 24 customers used a debit card, and 24 customers used a credit card.

To Find :

Based on these results, express the probability that the next customer will pay with a debit card as a percent to the nearest whole number.

Solution :

Probability that next person will pay with a debit card in percentage is :

[tex]P = \dfrac{\text{Number of customer used debit card}}{\text{Total number of customers}}[/tex]

[tex]P = 100\times \dfrac{24}{60 + 24 + 24}\\\\P = 100 \times \dfrac{24}{108}\\\\P = 22 \ \%[/tex]

Hence, this is the required solution.

Answer:51

Step-by-step explanation:

Answer:

At Irtaza's Deli

Step-by-step explanation:

For this you should find the unit price and whichever is less is where you should go.

(1) Irtaza Deli:

First I would round the 5.99 to 6 then we'll do 6 divided by 7.

[tex]\frac{6}{7}=.8571428571=.86[/tex]

(2) Brianna's Food Mart:

First I would round the 8.99 to 9 then we'll do 9 divided by 10.

[tex]\frac{9}{10}=.9[/tex]

Now let's compare:

So the first store sells oranges for $.86 and the second store sells them for $.90. I don't know about you but I would go to the first store they would be much more cheaper.

Answer:

A.) 20x + 2y = 500

B.) y-intercept = 250; its meaning is how many boxes of pencils they started with.

C.) x-intercept = 25; How many T-shirts they can sell at most

Step-by-step explanation:

2y - 500 = -20x

20x + 2y - 500 = 0

20x + 2y = 500

y-intercept = 250; its meaning is how many boxes of pencils they started with.

20x + 2y = 500

20(0) + 2y = 500

2y = 500

2y/2 = 500/2

y = 250

x-intercept = 25; How many T-shirts they can sell at most

20x + 2y = 500

20x + 2(0) = 500

20x = 500

20x/20 = 500/20

x = 25

Answer:

sas

Step-by-step explanation:

Answer:

g(4) = 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = 4x + 4

g(4) is x = 4

Step 2: Evaluate

Answer:

Jorge is hiking 4 kilometers per hour.

Step-by-step explanation:

 y=4x^2+5x-6y=4x2+5x−6

:

Given points are :

  x     =    -2      0       4

y=f(x) =    0       -6      78

We have to model the parabola with the help of these points

Solution:

We consider a standard equation of parabola y= ax^2+bx+cy=ax2+bx+c

now, we put the points in the equation we get,

at (-2,0) is    4a-2b+c=0

at (0,-6) is    c=-6

at (4,78) is    78= 16a+4b+c  

now, solving these equation we get, a= 4    , b= 5    , c= -6

so the equation formed with these points is   y=4x^2+5x-6y=4x2+5x−6

we can see this in the graph attached.

Step-by-step explanation:

Hope this helps!! :D

Answer:

the answer to 14 is D

and 15 is i think x=  [tex]\frac{5+\sqrt{13} }{2}, \frac{5-\sqrt{13} }{2} \\[/tex]

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

3/80 as a fraction maybe

3 3/4 as a mixed fraction

Answer:

No

Step-by-step explanation:

20/4=5

14/3=4.67

Since they're not the same, they're not proportional.

Answer:

not proportional        

Step-by-step explanation:

First , let's find the speed of each person by dividing the distance traveled and the time.

Using B to represent Bob's speed and K to represent Kelly's speed , we have:

[tex]B=\frac{20}{4} = 5 mph\\K=\frac{14}{3}= 4.666 mph\\\\[/tex]

The speeds 5 and 4.666 are not multiples , so they are NOT proportional.

PLEASE MARK ME BRAINLIEST

Answer:

Here are the steps I think you probably will go through.

1. Draw a line that is longer than the segment but shorter than the width of the page.

1a. Make sure this line is  at least 1/2 inch from the left hand side.  

2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.

3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.

The key step either two or three.

Answer: Step Two

Draw a line that is longer than the segment but not wider than the page's width. This line should be at least 1/2 inch away from the left-hand side. After that, measure the length of the original segment with a compass. Following that step, measure the distance along the compass line. (One end is on the left edge, while the other (the pencil end) is used to mark the section so that it is the same length as the compass) Step two is the most important step in the process of copying a line segment to ensure that the new line segment is the same length as the original.

Step-by-step explanation:

I took the test

Your answer will be D.

So, you have the angles 12, 9, 6, and 3. You may see that the place that 6 is makes this a non perfect square. When you have this problem simply add the number on top of it with the number that makes this problem.

For instance...

[tex]\boxed{6+3=9}[/tex]

So, when finding area you must multiply the 2 lengths with each other.

So here our bottom length is also 12. Thus, we must multiply 9 and 12 together.

For instance...

[tex]\boxed{9*12=108}[/tex]