what are the roots of the equation
[tex] {x}^{2} - 16x + 89 = 0[/tex]
in simplest a+bi form?

Answer:

The correct answer is option A 43°

Step-by-step explanation:

From the figure we can see a triangle and two exterior angles are given.

To find the value of p

Here we consider two angles be <1 and < 2, where <1 is the linear pair of angle measures 90° and <2 be the linear pair of angle measures 133°

m<1 = 180 - 90 = 90° and

<2 = 180 - 133 = 47

By using angle sum property

m<1 + m<2 + p = 180

p = 180 - (m<1 + m<2)

 = 180 - (47 + 90)

 = 180 - 137

 = 43°

Therefore the correct answer is option A 43°

Answer:

[tex]\large\boxed{A.\ 3\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The segments are in proportion:

[tex]\dfrac{x}{5}=\dfrac{4}{6}[/tex]               cross multiply

[tex]6x=(5)(4)[/tex]

[tex]6x=20[/tex]      divide both sides by 6

[tex]x=\dfrac{20}{6}\\\\x=\dfrac{10}{3}\\\\x=3\dfrac{1}{3}[/tex]

Answer:

First option : 0.1904

Step-by-step explanation:

Given

[tex]P(A) = 0.56\\P(B)= 0.34[/tex]

First of all, we will define independent events.

Two events are said to be independent if the occurrence of one event doesn't affect the probability of occurrence of second event.

If the events are independent then their individual probabilities are multiplied for the probability of both events.

That is:

P(A∩B) = P(A) * P(B)

= 0.56 * 0.34

=0.1904

So, the probability of A and B is 0.1904.

Hence, first option is the correct answer ..

Answer:

The answer is 0.1904

Step-by-step explanation:

The probability of event A is 0.56, and the probability of event B is 0.34. If A and B are independent events, then P(A and B) = 0.1904

.

Answer:

Step-by-step explanation:

A.

2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4              combine like terms

(2.3y + 3.1y) + 2 = (4.3y + 1.1y) + (1.6 + 0.4)

5.4y + 2 = 5.4y + 2              subtract 5.4y from both sides

2 = 2   TRUE → infinitely many solutions

B.

32x + 25 - 21x = 10x          combine like terms

(32x - 21x) + 25 = 10x

11x + 25 = 10x           subtract 11x from both sides

25 = -x       change the signs

-25 = x → x = -25   One solution

C.

1/3 + 1/7y = 3/7y              subtract 1/7y from both sides

1/3 = 2/7y             multiply both sides by 7

7/3 = 2y      divide both sides by 2

7/6 = y → y = 7/6       One solution

D. ?

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the scale factor as the ratio of the corresponding sides of the image to the original.

corresponding sides are image 0.5 and original 2.5

scale factor = [tex]\frac{0.5}{2.5}[/tex] = [tex]\frac{1}{5}[/tex] = 0.2

Answer:

It takes 1 hour to travel 90 miles.

The point (1,90) represents a specific location on the graph based on its coordinates.

The point (1,90) represents a specific location on the graph. In this case, the x-coordinate is 1, which means it is 1 unit to the right from the origin on the horizontal axis. The y-coordinate is 90, which means it is 90 units above the origin on the vertical axis. So, the point (1,90) is plotted on the graph at the intersection of the x-coordinate 1 and the y-coordinate 90.

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Answer:  The required percentage is 33.02%.

Step-by-step explanation:  Given that a bookstore owner is having a sale. The book Bart wants was originally priced at $14.99 the book is now $10.04.

We are to find the percentage by which the price was reduced.

The price by which the price of the book reduced is given by

R.P. = $(14.99 - 10.04) = $4.95.

Therefore, the percentage by which the price of the book reduced is given by

[tex]P=\dfrac{4.95}{14.99}\times 100\%\\\\=33.02\%[/tex]

Thus, the required percentage is 33.02%.

The price of the book was reduced by approximately 33.02% from its original price of $14.99 to the sale price of $10.04.

The student asked by what percentage the price of a book was reduced from its original price of $14.99 to its sale price of $10.04.

To calculate the percentage decrease, we subtract the sale price from the original price and then divide by the original price. We then multiply the result by 100 to get the percentage.

Here's the step-by-step calculation:

Therefore, the price of the book was reduced by approximately 33.02%.

Answer: The Answer Is 9

Step-by-step explanation:

If 4x - 12 = 24, add 12 to 24, and divide 36 by 4.

Answer: B.9

Step-by-step explanation:

You know that [tex]\angle A[/tex]≅[tex]\angle B[/tex], this means that the measure of the angle A and the measure of the angle B are equal. Then:

[tex]m\angle A=m\angle B[/tex]

You know that:

[tex]m\angle A=4x-12[/tex] and [tex]m\angle B=24[/tex]

Therefore, you can substitute them into [tex]m\angle A=m\angle B[/tex] :

[tex]4x-12=24[/tex]

Now you can solve for the variable "x":

[tex]4x=24+12\\\\4x=36\\\\x=\frac{36}{4}\\\\x=9[/tex]

You can observe that this value of "x" matches with the option B.

Answer:

try the third table

Step-by-step explanation:

try the third table because the others would end up nonlinear

Answer:

No, because it does not have a constant rate of change.

Step-by-step explanation:

On the x side of the table, there is a constant rate of change (+1). However, on the y side, it is not. The first change is +7, the next +5, and the last +6. The rate of change has to be constant on both sides for the table to be considered linear.

Answer:

the answer is 200

Step-by-step explanation:

217.33 - 19.19 = 198.14 rounded to the nearest ten is 200

because the nearest ten is 198.14

Answer:

200

Step-by-step explanation:

[tex] -19.19 + 217.33 = 198.14[/tex]

198,14 ≈ 200

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

n²+2n+1 = (n+1)(n+1)

n²-8n-9 = (n+1)(n-9)

the least common denominator for these two rational expressions is :

(n+1)(n-9)

Answer:

15

Step-by-step explanation:

f(x)=5x+40

f(x)=5(-5)+40

f(x)=-25+40

f(x)=15

You must replace x with -5 and solve using the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction) REMEMBER: IF NOT APPLICABLE TO THE EQUATION YOU MAY SKIP THAT STEP IN PEMDAS .

5(-5) + 40

Multiplication...

5 * -5 = -25

-25 + 40

Addition...

When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then take the sign of the largest number. In this case the largest number is 40 and its sign is positive. Your answer will  have a posititve sign.

-25 + 40 ----> 40 - 25 = 15

-25 + 40 = 15

15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

c: g(x) is shifted 3 units to the right and reflected over the x-axis

Answer: Option D

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

If we have a function f(x) and make a transformation of the form:

[tex]g (x) = f (x + h)[/tex]

Then it is true that:

If [tex]h> 0[/tex] the graph of g(x) is equal to the graph of f(x) displaced h units to the left

If [tex]h<0[/tex] the graph of g(x) is equal to the graph of f(x) displaced h units to the right

Also if we have a function f(x) and perform a transformation of the form:

[tex]g (x) = -f (x)[/tex]

Then it is true that:

The graph of g(x) is equal to the graph of f(x) reflected on the x axis.

In this case [tex]f (x) = x ^ 4[/tex] and [tex]g (x) = -(x + 3) ^ 4[/tex]

So

[tex]g(x) = -f(x+3)[/tex]

Then [tex]h = 3> 0[/tex]. Therefore the graph of g(x) is equal to the graph of f(x) displaced 3 units to the left and reflected on the x axis

The answer is the option D

i would say around 42 or so

Answer:

42

Step-by-step explanation:

-14 1/9 is close to -14

-2 9/10 is close to -3

-14 * -3 = 42

The best estimate is 42

Answer:

(-2,  3).

Step-by-step explanation:

x + 3y = 7

2x + 4y = 8

1 .   x = 7 - 3y.

2.  2(7 - 3y) + 4y = 8

3.  14 - 6y + 4y = 8

   -2y = -6

    y = 3

4.  Substitute y in the second equation:

    2x + 4(3) = 8

    2x = -14

      x = -2..

The solution to the system of equations is: (-2, 3).

Given the system of equations:

x + 3y = 7 --> eqn. 1

2x + 4y = 8 --> eqn. 2

First, isolate x in equation 1:

x = 7 - 3y

Plug in the value of x into eqn. 2 to solve for y.

2(7 - 3y) + 4y = 8

14 - 6y + 4y = 8

14 - 2y = 8

14 - 8 = 2y

6 = 2y

3 = y

y = 3

Find the value of x by substituting y = 3 into eqn. 1.

x + 3(3) = 7

x + 9 = 7

x = 7 - 9

x = -2

Therefore, the solution to the system of equations is: (-2, 3).

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Answer:

D=(-infinity, +infinity)

R=(-infinity,  4]

Step-by-step explanation:

I think that 2 is an exponent so you function is f(x)=-3(x-5)^2+4

So if this is the case this is a parabola open down when a vertex of (5,4).

Visualize or draw a rough picture of that because that is all you need to answer this question.

The domain for a parabola function is always all real numbers (do notice I said parabola function).

The range for this parabola is (-infinity, 4]  since open down and the highest point has y value 4.

Answer:

D.

Step-by-step explanation:

Domain: (-infinity, +infinity)

Range: (-infinity, 4)

Answer:

[tex]\large\boxed{x=-1\pm3\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^2+2x=17\\\\x^2+2(x)(1)=17\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\x^2+2(x)(1)+1^2=17+1\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=18\Rightarrow x+1=\pm\sqrt{18}\\\\x+1=\pm\sqrt{9\cdot2}\\\\x+1=\pm\sqrt9\cdot\sqrt2\\\\x+1=\pm3\sqrt2\qquad\text{subtract 1 from both sides}\\\\x=-1\pm3\sqrt2[/tex]

Let's say that the coordinates of the squirrel are: (x, y)

Since the coordinates of the acorn is halfway, between the tree and the squirrel, that means the acorn is the midpoint.

To work out the midpoint you do:

(sum of x-coordinates) divided by 2,  (sum of y coordinates) divided by 2.

We can use this to form an equation .

So the sum of the x coordinates of the tree and the squirrel = -1   :

x-coordinates of the squirrel:

[tex]\frac{-3+x}{2}=-1[/tex]                   (now solve for x)

[tex]-3+x = -2[/tex]

[tex]x=1[/tex]

y-coordinates:

[tex]\frac{8+y}{2}=5[/tex]                   (now solve for y)

[tex]8+y=10[/tex]

[tex]y = 2[/tex]

So the coordinates of the squirrel are: (1, 2)

____________________

Answer:

(1, 2)

Answer:

(1,2)

Step-by-step explanation:

By the information given in the problem, we know that the midpoint of the squirrel's coordinates and the tree's coordinates are the coordinates of the acorn on the tree.

Let the squirrel's coordinates be $(x,y)$ so we have $$\left(\frac{-3+x}{2},\frac{8+y}{2}\right)=(-1,5).$$Solving $\frac{-3+x}{2}=-1$ and $\frac{8+y}{2} = 5$, we find that the squirrel's coordinates are $\boxed{(1,2)}$.

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x-2y-7=0\\5x+y-3=0&\text{multiply both sides by 2}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad13x-13=0\qquad\text{add 13 to both sides}\\.\qquad\qquad 13x=13\qquad\text{divide both sides by 13}\\.\qquad\qquad x=1\\\\\text{put the value of x to the second equation:}\\\\5(1)+y-3=0\\(5-3)+y=0\\2+y=0\qquad\text{subtract 2 from both sides}\\y=-2\\\\\boxed{x=1,\ y=-2}[/tex]

Answer:

C) 33%

Step-by-step explanation:

To solve for the percentage of success, we first need to find out how many numbers we are working with. In this case, there are 9 numbers (0,1,2,3,4,5,6,7,8).

Since there are 3 "successful" numbers, (0,1,2), we can write the probability as a fraction

3/9 (represents number of successes over number of possible outcomes)

This simplifies to be 33%

Answer:

C

Step-by-step explanation:

Since you include zero as a number, then it would be 9 numbers in all. 3 if the nine numbers are success, so it would be 3/9. 3/9 as a percent would be around 33 percent.

Answer:

The measure of the angles are

m∠1=128°

m∠2=52°

m∠3=52°

m∠4=128°

m∠5=128°

m∠6=128°

m∠7=52°

m∠8=52°

Step-by-step explanation:

see the attached figure with numbers to better understand the problem

step 1

Find the measure of angle 5  

we know that

m∠5+52°=180° ----> by consecutive interior angles

m∠5=180°-52°=128°

step 2

Find the measure of angle 8

we know that

m∠8=52° ----> by vertical angles

step 3  

Find the measure of angle 7

we know that

m∠7=m∠8 ----> by corresponding angles

we have

m∠8=52°

therefore

m∠7=52°

step 4

Find the measure of angle 6

we know that

m∠6+m∠7=180° ----> by supplementary angles

we have

m∠7=52°

therefore

m∠6+52°=180°

m∠6=180°-52°=128°

step 5

Find the measure of angle 3

we know that

m∠3+m∠6=180° ----> by consecutive interior angles

we have

m∠6=128°

m∠3=180°-128°=52°

step 6

Find the measure of angle 2

we know that

m∠2=m∠3 ----> by vertical angles

we have

m∠3=52°

therefore

m∠2=52°

step 7

Find the measure of angle 1

we know that

m∠1+m∠3=180° ----> by supplementary angles

we have

m∠3=52°

therefore

m∠1+52°=180°

m∠1=180°-52°=128°

step 8

Find the measure of angle 4

we know that

m∠4=m∠1 ----> by vertical angles

we have

m∠1=128°

therefore

m∠4=128°

[tex](x-8)^2(x+7)>0 \\x\in(-7,8)[/tex]

Answer:

Commutative property

Answer:

The variance is 8732.24 and the standard deviation is 93.45

Step-by-step explanation:

* Lets explain how to find variance and the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 3832 , 3779 , 3655 , 3642 , 3579

∵ Their sum = 3832 + 3779 + 3655 + 3642 + 3579 = 18487

∵ They are five numbers

∴ The mean = 18487 ÷ 5 = 3697.4

# Step 2: subtract the mean from each data and square the answer

∴ (3832 - 3697.4)² = 18117.16

∴ (3779 - 3697.4)² = 6658.56

∴ (3655 - 3697.4)² = 1797.76

∴ (3642 - 3697.4)² = 3069.16

∴ (3579 - 3697.4)² = 14018.56

# Step 3: calculate the Variance (σ²) , by adding the square difference,

  and divide it by the number of the data

∵ Variance = sum of the square difference ÷ number of the data

∵ The sum = 18117.16 + 6658.56 + 1797.76 + 3069.16 + 14018.56  

∴ The sum = 43661.2

∴ σ² = 43661.2 ÷ 5 = 8732.24

# Step 4: the standard deviation (σ) is the square root of variance

∴ The standard deviation = √(8732.24) = 93.446455 ≅ 93.45

* The variance is 8732.24 and the standard deviation is 93.45

Answer:

The variance of the data is 49.

The median is 64.

The data point 50 is tow standard deviations away for the mean.

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

[tex]\rm \sigma ^2=7^2\\ \\ \sigma ^2=49[/tex]

The variance of the data set is 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

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1.

[tex]

2\sqrt{4}\cdot3\sqrt{8} \\

2\cdot3\sqrt{4\cdot8} \\

6\sqrt{32} \\

6\sqrt{4^2\cdot2} \\

6\cdot4\sqrt{2} \\

\boxed{24\sqrt{4}} \\

[/tex]

2.

[tex]

2\sqrt{4}+3\sqrt{8} \\

\boxed{4+3\sqrt{8}}

[/tex]

Hope this helps.

r3t40

[tex]\sqrt{27}-\sqrt{48}=\sqrt{9\cdot3}-\sqrt{16\cdot3}=3\sqrt3-4\sqrt3=-\sqrt3[/tex]

Answer:

yes

Step-by-step explanation:

connect dc to <abc and you have a triangle

connect bc to <ebc and you have the same triangle just reflected over the y axis

Congruent triangles are the exact same triangles, but they might be placed at different positions. The correct option is B.

Congruent triangles are the exact same triangles, but they might be placed at different positions.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

In the two of the given triangle, therefore, ΔADC and ΔEBC,

∠CAD = ∠CEB {Already given in the triangle}

∠ACD = ∠ ECB {It is the common angle between two triangles}

CD = CB {Already given in the triangle}

Since in the two triangles, two angles are equal and a side is equal as well, therefore, the two triangles are congruent using the AAS (Angle-Angle-Side) postulate.

Hence, the correct option is B.

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Answer:

Find the attached

Step-by-step explanation:

The inequality;

x ≤ 18

represents values of x that are at most 18. That is values that are less than or equal to 18. We can first graph the vertical line x = 18 and then shade the region to the left of this line. This shaded region will be our solution set for the inequality x ≤ 18.

Find the attached;