Use the x-intercept method to find all real solutions of the equation.
x^2-9x^2+23x+15=0

Answer:

x = [tex] 4 \sqrt { 3 } [/tex]

Step-by-step explanation:

We are given a diagram of a pyramid with a right angled triangle which has [tex]30[/tex]°, [tex]60[/tex]° and [tex]90[/tex]° angles an the hypotenuse is [tex]8cm[/tex].

Since we have a right angled triangle, we can apply sin here:

We know that [tex]sin 60 = \frac{\sqrt{3} }{2}[/tex] so we can write it as

[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]

So we get the slant height of x = [tex]4\sqrt{3}[/tex].

Answer:

The slant height of square pyramid = 4√3 m

Step-by-step explanation:

From the figure we can see a square pyramid with lateral edge 8 m

Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.

Therefore the base is 8 m

To find the slant height

slant height² = Lateral edge² - (base/2)²

    = 8² - (8/2)² = 8² - 4²

    = 64 - 16 = 48

Slant height = √48 = 4√3 m

Therefore slant height of square pyramid =  4√3 m

Answer:

5

Step-by-step explanation:

3 + 2 = 5

The expression for the total number of dice in b boxes for both a board game, which comes with 2 dice, and a card game, which comes with 3 dice, is 5b. This is calculated by adding the number of dice in each box (2b for the board game and 3b for the card game).

The question is asking for an expression that shows the total number of dice in b boxes of the board game and the card game. The board game comes with 2 dice and the card game comes with 3 dice.

To get the total number of dice, one needs to multiply the number of dice in each type of game by the number of boxes, b, and then add the results together.

The total number of dice in the board game is 2b and the total number of dice in the card game is 3b. The sum of these two amounts gives the total number of dice. So the expression for the total number of dice in b boxes of both games is 2b + 3b, which simplifies to 5b.

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Answer:

A angle V and angle Z

Step-by-step explanation:

Using the equilateral triangle's definition of all sides and angles are equal, we can determine that V, Z, and U are congruent.

Answer:

Meghan's pencil is shorter than Kim's pencil.

Step-by-step explanation:

Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K

Now, we know that

M < T

and T < K

So, by transitive property,

M < K

A 1/6% chance because there are six sides and 5 is one of them

Answer:

(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Step-by-step explanation:

I was just doing this lesson

Answer: y = 4\5*x

We can get this through slope intercept form.

Slope intercept form is y=mx +b where m is the slope and b is the y intercept.

We plug in 4.5 for the slope and 0 for the y-intercept.

Answer:

20

Step-by-step explanation:

ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!

Answer:

Step-by-step explanation:

She needs to fill the quart container

20 times.

4 quarts make a gallon, so 20 quarts = 5 gallons.

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

A(-3, 0) , B(3, 2)

[tex]AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}[/tex]

A(-3, 0), D(-2, -3)

[tex]AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]

AB = CD and AD = BC

The area of a rectangle:

[tex]A=(AB)(AD)[/tex]

Substitute:

[tex]A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20[/tex]

The perimeter of a rectangle:

[tex]P=2(AB+AD)[/tex]

Substitute:

[tex]P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}[/tex]

the answer is (a-4)^2

Answer:

Let's factor a2−8a+16

a2−8a+16

The middle number is -8 and the last number is 16.

Factoring means we want something like

(a+_)(a+_)

Which numbers go in the blanks?

We need two numbers that...

Try -4 and -4:

-4+-4 = -8

-4*-4 = 16

Fill in the blanks in

(a+_)(a+_)

with -4 and -4 to get...

(a-4)(a-4)

Answer:

(a−4)(a−4)

Answer:

1024π

Step-by-step explanation:

The formula for the surface area of a sphere is 4πr².

Since the radius is 16 cm, the surface area is:

SA = 4×π×16²= 1024π.

A=4πr^2

A = 4π(16)^2

A = 3216.99

which is the same as 1024π cm^2

Answer:

Maria gets $14 off of the original price of $40

Step-by-step explanation:

Answer:

The volume of the model is [tex]321\ m^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the sphere (model of the earth) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

In this problem we have

[tex]r=8.5/2=4.25\ m[/tex] ----> the radius is half the diameter

substitute the values

[tex]V=\frac{4}{3}(3.14)(4.25)^{3}=321\ m^{3}[/tex]

Answer:

The answer is Box B by 82.5 inches, let me know if it helped.

Step-by-step explanation

The company should choose Box B as it is larger than Box A. The volume of Box A is 1,497.75 cubic inches and the volume of Box B is 1,428 cubic inches, making Box A 69.75 cubic inches larger than Box B.

The company should choose Box B as it is larger than Box A. To calculate the size difference, we need to find the volume of each box, which is calculated by multiplying the length, width, and height of the box. For Box A, the volume is 9 inches * 13 inches * 11.5 inches = 1,497.75 cubic inches. For Box B, the volume is 14 inches * 8.5 inches * 12 inches = 1,428 cubic inches. Therefore, Box A is 69.75 cubic inches larger than Box B.

Answer:

C. [tex]\lim_{x\rightarrow f(x)=2[/tex]

Step-by-step explanation:

Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].

Now we need to evaluate the given limit.

If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]

[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]

[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]

[tex]=\frac{(\sqrt{2})^2}{1}[/tex]

[tex]=\frac{2}{1}[/tex]

=2

Hence choice C is correct.

Answer:

B

Step-by-step explanation:

Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.

Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be  1 ≤ x ≤ 4.

Answer choice B is right.

Answer:

[tex]\large\boxed{C)\ 2}[/tex]

Step-by-step explanation:

[tex]2.5(6x-4)=10+4(1.5+0.5x)\qquad\text{use the distributive property}\\\\(2.5)(6x)+(2.5)(-4)=10+(4)(1.5)+(4)(0.5x)\\\\15x-10=10+6+2x\qquad\text{subtract 2x from both sides}\\\\13x-10=16\qquad\text{add 10 to both sides}\\\\13x=26\qquad\text{divide both sides by 13}\\\\x=2[/tex]

Answer:

C)2

Step-by-step explanation:

Trust me here boyzz

1 Gallon = 4 quarts of milk

1/4 = 1 quart of milk

4 quarts of milk = 8 pints of milk

8/6 = 1.33 pints of milk

Each friend has 1.33 pints of milk

Each friend will get 1/24 of a gallon of milk.

To find out how much milk each friend will have, we need to divide 1/4 of a gallon by 6.
how much milk each friend gets,
(1/4) ÷ 6
(1/4) × (1/6)
= 1/24

Therefore, each friend gets 1/24 of a gallon of milk.

In conclusion, if 1/4 of a gallon of milk is shared equally among 6 friends, each friend will have 1/24 of a gallon of milk.

Answer:

5/6 I think

Step-by-step explanation:

Add 2/4 + 2/6 =

2*3/4*3 + 2*2/6*2 =

6/12 + 4/12 =

6+4/12 =

10/12 =

5/6

[tex] \frac{5}{6} \\ hope \: it \: helps \: \\ :)[/tex]

Answer:

The width is 51.333

Step-by-step explanation:

l * w = area of rectangle

3 * w = 154

w= 154/3

w=51.333

Answer:

11

Step-by-step explanation:

It right

Final answer:

The engineering professor's choice of new computer models over time can be modeled using a Markov chain, with specific transition probabilities for moving between models M1, M2, and M3. These probabilities are used to construct a transition matrix that allows us to analyze the selection pattern.

Explanation:

The scenario described can be represented as a Markov chain, which is a mathematical system that undergoes transitions from one state to another, with probabilities that are dependent on the current state only. Here, we have three models, M1, M2, and M3, which represent the states of the Markov chain. The transition probabilities define how likely it is to move from one state to another.

To construct this Markov chain, we set up a probability matrix P where the rows represent the current state, and the columns represent the next state. For the given model:

If the current model is M1, we have transition probabilities of 0.2 to M2 and 0.15 to M3.

If the current model is M2, we have transition probabilities of 0.6 to M1 and 0.25 to M3.

If the current model is M3, we have transition probabilities of 0.5 to M1 and 0.1 to M2.

Since the probabilities must add up to 1, the probability of remaining in the same state is 1 minus the sum of transition probabilities to other states. With these probabilities, we can fill in the transition matrix P:

P(M2|M1) = 0.2, P(M3|M1) = 0.15, P(M1|M1) = 0.65.

P(M1|M2) = 0.6, P(M3|M2) = 0.25, P(M2|M2) = 0.15.

P(M1|M3) = 0.5, P(M2|M3) = 0.1, P(M3|M3) = 0.4.

By using this transition matrix, we can analyze the professor's behavior in selecting new computer models over time.

The circumference of a circle is calculated like this:

[tex]c = 2 \times \pi \times r = \pi \times d[/tex]

If the circumference of the circle is 34π, its diameter is 34(cm), therefore its radius is 17(cm).

To find the diameter and radius of a circle when given the circumference, you can use the formulas C = 2πr or C = πd. In this case, the circumference is 34π. The circle's diameter is 34 units, and the radius is 17 units.

To find the diameter and radius of a circle when given the circumference, you can use the formula C = 2πr or C = πd, where C is the circumference, r is the radius, and d is the diameter. In this case, the circumference is given as 34π. Using the formula C = πd, we can substitute the value of the circumference and solve for the diameter:

34π = πd

Dividing both sides of the equation by π, we get:

34 = d

So, the diameter of the circle is 34 units. To find the radius, we can use the formula r = d/2:

r = 34/2

r = 17

Therefore, the circle's diameter is 34 units, and the radius is 17 units.

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Answer:

do you have a picture?

I can't tell you how I decided it because there's not a picture

Answer:

Step-by-step explanation:

Absolute minimum is where, in the infinite domain of f(x), the least value the function is the absolute minimum.

However, the local minimum is only a specific interval on the domain of f(x) where the lowest value is, but only in that interval.

So, usually, this comes up when you're dealing with 1st and 2nd derivatives. The first derivative tells you where local max and mins are, where the 2nd derivative tells you if the concavity is up or down.

An absolute minimum is the lowest point on the entire domain of a function, while a local minimum is the lowest point in a specific interval or neighborhood around a point on the graph.

An absolute minimum and a local minimum are both points on a graph where the function reaches its lowest value, but there are key differences between them.

An absolute minimum is the lowest point on the entire domain of the function. In other words, it is the smallest function value among all the points.

On the other hand, a local minimum is the lowest point in a specific interval or neighborhood around a particular point on the graph. It is possible for a function to have multiple local minima.

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The terms in the sum are given by the sequence

[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]

We have

[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]

for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.

Answer:

B. Divergent

Step-by-step explanation:

Did test

Answer:

12.2

Step-by-step explanation:

We can say that FG = FH + HG

Since EH is the median, FH and HG is equal. Thus we can find x.

[tex]FH=HG\\6x-1.1=4x+1.3\\6x-4x=1.3+1.1\\2x=2.4\\x=\frac{2.4}{2}\\x=1.2[/tex]

Now we can find FH = 6x - 1.1 = 6(1.2) - 1.1 = 6.1, and

HG = 4x + 1.3 = 4(1.2) + 1.3 = 6.1

Hence, FG = 6.1 + 6.1 = 12.2

Final answer:

The balance at the end of six years will be approximately $899.48.

Explanation:

To calculate the balance at the end of six years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the values, we have:

[tex]A = 634(1 + 0.06/1)^(1*6)[/tex]

[tex]= 634(1.06)^6[/tex]

= 634(1.418519)

= $899.48

Answer:

the answer is false

Step-by-step explanation:

False, The shapes of the horizontal cross-sections of the cone below are not all congruent.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We are given the statement,

'The shapes of the horizontal cross-sections of the cone are all congruent'.

Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.

Further, the radius of the circle vary depending on the position form where the cone is cut i.e.

If cut from the top, the circle is approximately equal to a point.

If cut from the middle, the radius of the circle is less than the radius of the cone.

If cut from the bottom, the radius of the circle is equal to the radius of the cone.

Now, 'two figures are congruent if they overlap each other'.

Since, the circles have different radius, they will not overlap each other.

Thus, all the cross-sections of the cone would not be congruent.

Hence, the given statement is false.

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➷ Multiply the total value by 1/4:

1/4 x 8 = 2

He practiced it for 2 hours.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

2 hours.

Step-by-step explanation:

The time he practiced the piano = 1/4 * 8 = 2 hours.

Final answer:

To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.

Explanation:

To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.

The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.

Answer:

Correct answer is B.) Her monthly average would have increased by $19.57.

Step-by-step explanation:

The true statement about her average monthly tip is (b) Her monthly average would have increased by $19.57.

The average of a dataset is simply the mean value or the expected value of the dataset

The table is given as:

June       July         August       September     October     November

$133.45   $235.31    $239.45     $258.87         $298.45     $115.67

For the 6 months, the average is:

Average = (133.45+235.31+239.45+258.87+298.45+115.67)/6

Average = 213.53

For the 5 months (i.e. exclusive of December), the average is:

Average = (133.45+235.31+239.45+258.87+298.45)/5

Average = 233.10

The 5 months average is greater than the 6 months average.

And the difference (d) is:

d = 233.10 - 213.53

Evaluate

d = 19.57

Hence, Her monthly average would have increased by $19.57.

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