What is the factorization of the trinomial below?

x^3 - 12x^2 + 35x

A. (x - 7)(x + 5)

B. x(x - 7)(x - 5)

C. (x^2 - 7)(x + 5)

D. x(x - 7)(x + 5)

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{6}}x+\cfrac{7}{6}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we can say that

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{5}}}[/tex]

so we're really looking for the equation of a line with a slope of -6/5 and that passes through (-8 , 9)

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{9})\qquad\qquad \stackrel{slope}{m}\implies -\cfrac{6}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-8)})\implies y-9=-\cfrac{6}{5}(x+8) \\\\\\ y-9=-\cfrac{6}{5}x-\cfrac{48}{5}\implies y=-\cfrac{6}{5}x-\cfrac{48}{5}+9\implies y=-\cfrac{6}{5}x-\cfrac{3}{5}[/tex]

Answer:

C is the correct answer hope i helped

Step-by-step explanation:

Answer:

  (a)  140 sandwiches

Step-by-step explanation:

The total number sold can be found from the given relation:

  56 sandwiches = 40% × total sold

__

Dividing by the coefficient of the variable, we find ...

  total sold = (56 sandwiches)/0.40 = 140 sandwiches

The total number of sandwiches sold last week was 140.

Answer:

18 units

Step-by-step explanation:

Area = length * width (A = L * w)

So, in order to find the length when given the width and area, you have to divide the area by the width.

432 / 24 = 18

I hope this helps! Have a lovely day!! :)

Answer:

  see attached

Step-by-step explanation:

The values are plotted on the number line attached.

__

Each value is represented on the list both as a fraction and as a decimal. Equal values map to the same point on the number line.

  0.27 = 27/100

  0.49 = 49/100

  0.75 = 75/100

The location on the number line is found by effectively dividing the distance between 0 and 1 into 100 parts, then locating the point on the corresponding division. The attached number line shows the interval divided into 50 parts, so the given values will lie halfway between the grid marks on this number line.

For statictics of Out of 780 smokers, 376 have been divorced, Non-smokers: Out of 2855 non-smokers, 902 have been divorced, the 95% confidence interval for smokers and non-smokers is mathematically given as

Generally, the equation for the Confidence interval is mathematically given as

p ± Z/2[p(1-p)]/n

Where

Z1/2=1-(0.05/2)

Z1/2=0.975

Read z table we have

Z score= 1.96

Hence

0.4907 ± 1.96 (0.4907)(1-0.4907)/485

0.4907±0.0445

Therefore

95% confidence interval = (0.5352, 0.4462)

b)

Z1/2 = 1- (0.05/2)

Z1/2 = 0.975

Z score= 1.96

0.3159 ± 1.96 (0.3159)(1-0.3159)/1184

0.3159±0.0265

Thereofore

95% confidence interval = (0.3424, 0.2894)

c)

In conclusion, The 95% confidence interval helps us read that 53% increased risk of divorce for smokers.

Read more about Confidence interval

https://brainly.com/question/17097944

Answer:

$3.78

Step-by-step explanation:

30 dollars minus 7 dollars and 28 cents is twenty-two and seventy-two cents, then minus another eighteen and ninety-four cents, would end up at three dollars and seventy-eight cents.

Answer:

[tex]\boxed{\$3.78}[/tex]

Step-by-step explanation:

To find out how much money does Kaya have left, we need to subtract the total money spent from the total money brought to the mall.

In this problem, we can tell that Kaya brought $30 to the mall as stated in the question. Furthermore, the problem states that she spent $7.28 on food, and $18.94 on a necklace. This means that the sum of 7.28 and 18.94 is the money spent by Kaya.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

[tex]\$30 - (\$7.28 + \$18.94) = \text{Money remained}[/tex]

➡ [tex]\$30 - (\$26.22) = \text{Money remained}[/tex]

➡ [tex]\$30 - \$26.22 = \text{Money remained}[/tex]

➡ [tex]\bold{\underline{\$3.78} = Money \ remained}}[/tex]

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \:5 \sin(x) = 3 \sin(x) + \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:5 \sin(x) - 3 \sin(x) = \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \sin(x) = \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sin(x) = \sqrt{2} \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sin(x) = \frac{1}{ \sqrt{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 45 \degree \: \: or \: \: \frac{\pi}{4} \: rad[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

Answer:

Center and above your top lip where it dips down....

Using the Central Limit Theorem, it is found that the condition is not met, as there are less than 10 failures.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, 34 of the 40 seniors are planning to participate in graduation, hence:

Since there are less than 10 failures, the normal condition for finding a confidence interval is not met.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer:

70 cents

Step-by-step explanation:

To figure out how much 1 paper clip costs we must divide :)

5.60/800 = 70 cents

Have an amazing day!!

Please rate and mark brainliest!!

Splitting the rectangle in half creates two right triangles

The value of tan(x) is 4/3

To calculate tan(x), we make use of the following tangent ratio

tan(x) = Opposite/Adjacent

From the figure, we have:

Opposite = AD = 4

Adjacent = CD = 3

So, we have:

tan(x) = 4/3

Hence, the value of tan(x) is 4/3

Read more about tangent ratio at:

https://brainly.com/question/1592477

Answer:

4/3

Step-by-step explanation:

Answer:

For every 2 quarts of water, ¹/₂ cup of vinegar is used.

⇒ To find the amount of vinegar, divide the number of quarts by 4.

⇒ To find the number of quarts, multiply the amount of vinegar by 4.

4 qt water = 4 ÷ 4 = 1 cup vinegar

1¹/₂ cups vinegar = 1¹/₂ x 4 = 6 qt water

8 qt water = 8 ÷ 4 = 2 cup vinegar

Plot the points on the graph (see second attached image).

Draw a line through the points.

Find 3 along the x-axis and trace up to the line. Trace along to the y-axis.

Therefore, Gavin would need to use 12 quarts of water with 3 cups of vinegar.

Answer:

The reflection coordinates of JKL would be:

J (3,7)

K (2,3)

L (-1,5)

The reflection coordinates of MNP would be:

M (8,-6)
N (2,-4)
P (8,-4)

Step-by-step explanation:

Answer:

n = 20

Step-by-step explanation:

[ 180° ( n - 2 ) ] / n = 162°  

180 ( n - 2 ) = 162 n

180n - 360 = 162n

18n = 360

n = 20

9. The rational number that is equal to its negative is zero (0)

10. [tex]\sf \dfrac{1}{3} ( 6 \ * \ \dfrac{4}{3} )[/tex] can be written as [tex]\sf ( \dfrac{1}{3} *6)*\dfrac{4}{3}[/tex]   using associate property.

associative property is when numbers are changed within the parenthesis with out the change in result.

formula of associative property : a(bc) = (ab)c

Answer:

D) none of the above

Step-by-step explanation:

To find an average, you add up all of the numbers and divide by how many numbers there were. for example, in this equation, the sum of all of the numbers was 96. then I divided 96 by 4(the amount of numbers shown)

1. d    2. a     3. c     4. b

[tex]1.d\ \{The\ intersection\ of\ three\ high\ lines\}[/tex]

[tex]2.\ a[/tex]

[tex]3.\ C[/tex]

[tex]4.\ b\ \{The\ intersection\ of\ three\ angular[/tex]

       [tex]bisectors\}[/tex]

I hope this helps you

:)

Answer:

Step-by-step explanation:

Various centers are defined for a triangle, depending on how they're constructed. Here, you're asked to match the construction with the name.

__

The orthocenter is the intersection of the altitudes of the triangle. Each altitude intersects a vertex and is orthogonal to the opposite side. The orthocenter will not be inside the triangle if the triangle is obtuse. The orthocenter of a right triangle is the right-angle vertex.

Figure D depicts the intersection of altitudes.

__

The incenter is the center of an inscribed circle of a triangle. The incenter must be the same distance from each side, so will be at the point of intersection of the angle bisectors. It always lies inside the triangle.

Figure B depicts the intersection of angle bisectors.

__

The centroid is the "center of gravity" of the triangle, the point at which the triangle could be balanced. Each median divides the triangle into two equal areas, so the intersection of medians marks a spot with equal area (weight) in every pair of opposite directions.

Figure C depicts the intersection of medians.

__

The circumcenter is the center of a circle that circumscribes the triangle. It is equidistant from the three vertices, so lies on the intersection of the perpendicular bisectors of the sides. It will lie outside the triangle for obtuse triangles. It is the midpoint of the hypotenuse of a right triangle.

Figure A depicts the intersection of perpendicular bisectors of the sides.

Answer:

D. 45

Step-by-step explanation:

To find out how many games will be played with 10 people, we need to first find the pattern of the given table. To start out, we can see that for the numbers of players added, it adds one each time it goes up one number. And, we can also see that starting at 1 games played, it adds 2 for the next and gets 3 games. Then it adds 3 to get 6 games. So, we can see that for every added person added, it starts at 1 and adds 2, then adds, 3, 4, 5, 6, etc... Knowing this, we can figure out how many games will be played with 10 people.

2 people gets 1 games

+1                    +2

3 people get 3 games

+1                    +3

4 people get 6 games

So, now we can simply skip to 6 and seven players becuase we know that the pattern holds true to itself.

6 people get 15 games

+1                   +6

7 people get 21 games

+1                   +7

8 people get 28 games

+1                    +8

9 people get 36 games

+1                   +9

10 people get 45 games

Answer:

Asare is 17 and Felicia is 7.

Step-by-step explanation:

let x be felicia's current age and y be asare's age. The equation for their age is y=3x-4. If 3x-1 + x+3 = 30, that means that 4x+2=30, so 4x=28. If 4x=28, x=7. Felicia is 7 and 3*7-4=17.

Answer:

i do not understand the questions

Step-by-step explanation:

Answer: 1/5 6/24 1/3 2/4 3/4

Step-by-step explanation: bigger the denominator smaller the value.

7.5x11 = 4.85

82.5x = 4.85

*divide 82.5 on both sides*

x = 4.85 ÷ 82.5

x = 0.058788

Answer:

0.058787879

Step-by-step explanation:

(7.5)(x)(11)=4.85

82.5(x)=4.85

x=4.85÷82.5

x= 0.058787879

Answer:26 + 15i

Step-by-step explanation: 26+ 15i is the answer because i did the assignemnt

Answer:

Step-by-step explanation:

1.1 L

Given:

A rectangular container that has:

   a length of 30 cm,

   a width of 20 cm, and

   a height of 24 cm

It is filled with water to a depth of 15 cm.

When an additional 6.5 L of water are poured into the container, some water overflows.

Question:

How many liters of water overflow the container?

The Process:

Step-1: calculate the volume of rectangular container

The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.

Step-2: calculate the volume of water filled in the container to a depth of 15 cm

The volume of water filled is 9,000³ cm, then converted to 9 L.

Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.

The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.

The volume of water overflow =

Thus, the volume of water overflow of the container is 1.1 L.

Answer:

Width: 11.5 inches; Length: 16.5 inches

Step-by-step explanation:

Let l=length and w=width

l=w+5

2(w+5)+2w=56

4w=46

w=11.5, l=16.5

Answer:

⠀

Step-by-step explanation :

⠀

As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 56 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .

⠀

Now, According to the Question :

⠀

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 56 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 ( 2x + 5 )= 56 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{ 4x + 10= 56 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{ 4x = 56 - 10}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{ 4x = 46}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{46}{4} }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 11.5}} }}} }\: \: \bigstar[/tex]

⠀

Therefore,

⠀

Now, We are to find the length of the rectangle:

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 11.5 + 5 }}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{\underline{\boxed { \frak{\pmb{Length = 16.5}}}}}} \: \: \bigstar[/tex]

⠀

Therefore,

⠀

Add the two together:

15 + 17 = 32

total miles = 32

Answer:

x=6

Step-by-step explanation:

please mark me as brainlest

Answer

8

Step-by-step explanation:

Ratio: 40 : 60

Total amount - $20

40/100 x 20

= 8  (ANS)

i hope my answer is correct if not i apologize.