Select the correct answer. What are the zeros of the graphed function? у -6 -5 3 -2 2 3 6 2 3 OA O and 4 OB. 4,-2, and o OC. 0, 2, and 4 OD. -4 and o Reset Next

Select The Correct Answer. What Are The Zeros Of The Graphed Function? -6 -5 3 -2 2 3 6 2 3 OA O And

Answers

Answer 1

We have that the next x-intercepts 0,2 and 4, in the graph therefore the zeros of the graph are 0,2 and 4.

The correct choice is C.


Related Questions

2) (3 pt) Write the function from the table and graph.хf(x)-10004122130.52) f(x) =

Answers

(x - h)^2 = 4p(y - k)

(-1 - 3)^2 = 4p(8 - 0.5)

(-4)^2 = 4p(7.5)

16 = 30p

p = 16/30

p = 8/15

(x - 3)^2 = 16/15(y - 0.5)

15(x^2 - 6x + 9) = 16y - 8

15x^2 - 90x + 135 = 16y - 8

16y = 15x^2 - 90x + 135 + 8

y = 15/16 x^2 - 90/16 x + 143/16

f(x) = 15/16 x^2 - 90/16x + 143/16

PartBecause his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, X? Donot combine like terms.

Answers

On the first day, he biked x miles

The next day, he will bike

A chemist is using 357 milliliters of a solution of acid and water. If 18.6%of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.

Answers

Answer:

There are 66.4 milliliters of acid in the solution

Explanation:

The amount of the solution of acid and water = 357

Percentage composition of acid in the solution = 18.6%

Amount of acid in the solution = (18.6/100) x 357

Amount of acid in the solution = 66.402 milliliters

Amount of acid in the solution = 66.4 milliliters (to the nearest tenth)

There are 66.4 milliliters of acid in the solution

Leah invested $400 in an account paying an interest rate of 1 1/2%compounded annually. Lauren invested $400 in an account paying aninterest rate of 0 7/8% compounded monthly. To the nearest hundredth of ayear, how much longer would it take for Lauren's money to triple than forLeah's money to triple?

Answers

Leah investment is:

[tex]M_{\text{Leah}}=400_{}\cdot1.5^y[/tex]

Where M is the ammount of money that she has, and y the number of years.

We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:

[tex]\begin{gathered} 3\cdot400=400\cdot(1+\frac{1.5}{100})^y \\ 3=(1.015)^y \\ \ln 3=y\cdot\ln (1.015) \\ y=\frac{\ln (3)}{\ln (1.015)}\cong73.788\cong73.79 \end{gathered}[/tex]

It will take 73.79 years to triple her investment.

Lauren investment is:

[tex]M_{\text{Lauren}}=400\cdot(1+\frac{7}{8}\cdot\frac{1}{100})^m=400\cdot(1.00875)^{\frac{y}{12}}[/tex]

Where M is the ammount of money that she has, and m the number of months, and y is the number of years.

We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:

[tex]\begin{gathered} 3\cdot400=400\cdot(1.00875)^{\frac{y}{12}} \\ 3=(1.00875)^{\frac{y}{12}} \\ \ln 3=\frac{y}{12}\ln (1.00875) \\ y=12\cdot\frac{\ln 3}{\ln (1.00875)} \\ y=1513.25 \end{gathered}[/tex]

Need help answering all these questions for the red bird.Quadratic equation of the red bird: h(x) = -x^2 + 10x - 9King Pig located at the point (11,9) Moustache Pig located at the point (10,4)

Answers

[tex]h(x)=-x^2+10x+9[/tex]

The maximum heigh is located at the vertex. The vertex is:

[tex]\begin{gathered} V=(h,k) \\ where: \\ h=-\frac{b}{2a}=-\frac{10}{2(-1)}=5 \\ k=h(h)=-(5^2)+10(5)+9=-25+50-9=16 \end{gathered}[/tex]

Therefore, the maximum height is the y-coordinate of the vertex which is 16.

The axis of symetry is located at the x-coordinate of the vertex,so:

The axis of symetry is x = 5.

The distance traveled can be found using the roots:

The roots of the equation are:

[tex]\begin{gathered} -x^2+10x-9=x^2-10x+9=(x-9)(x-1) \\ so \\ x=1 \\ or \\ x=9 \end{gathered}[/tex]

So, the distance traveld is:

[tex]\Delta x=x2-x1=9-1=8[/tex]

---

The bird will hit the ground on the second root, so:

The point where it hits the grund is (9,0).

The starting point is located at the first root, so the starting point is:

(1,0)

----------------------------------

You got 84 of 100 questions on the test correct. What percent did you get correct?Answer: 84%100%16%8.4%11/100 is equal to what percent?Answer: 110%10%89%11%3 out of 4 students in your class are girls. What percent of the class are girls?Answer: 3%4%75%25%

Answers

[tex]\begin{gathered} \text{To get the percentage of divide the number of correct items in test} \\ \text{by the number of total test items} \\ \text{correct test items}=84 \\ \text{total test items}=100 \\ 84\div100=0.84 \\ \text{after, multiply it by }100\%\text{ to get the percentage} \\ 0.84\times100\%=84\% \end{gathered}[/tex]

a digital music player is marked down from its list price of $249.99 to a sale price of $194.99. What is the discount rate?

Answers

The discount rate of the digital player is 22%

How to determine the digital player's discount rate?

From the question, we have the given parameters:

List price = $249.99

Sales price = $194.99

Start by calculating the change in the price.

This is calculated as follows

Change = List price - Sales price

So, we have

Change = $249.99 - $194.99

Evaluate the difference

Change = $55

The discount rate of the digital player is then calculated as

Discount = Change/List price x 100%

This gives

Discount = 55/249.99 x 100%

Evaluate

Discount = 22%

Hence, the discount rate is 22%

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4. -X2 + 10 5x + 3 5x+3 6r 4x2 + 2x - 7 I need the perimeter.

Answers

The perimeter is the sum of all sides, therefore:

[tex]\begin{gathered} P=(5x+3)+(4x^2+2x-7)+(-x^2+10)+(5x+3) \\ add_{\text{ }}like_{\text{ }}terms\colon \\ (5x+5x+2x)+(4x^2-x^2)+(3+3+10-7) \\ 3x^2+12x+9 \end{gathered}[/tex][tex]\begin{gathered} 3x^2+12x+9 \\ \frac{1}{3}(3x^2+12x+9)=x^2+4x+3 \end{gathered}[/tex]

The factors of 3 that sum to 4 are 3 and 1. So:

[tex]x^2+4x+3=(x+3)(x+1)[/tex]

Calculate the degree of the angles in the triangles below.

Answers

the sum of the internal angles of a triangle is equal to 180, then

[tex]\begin{gathered} 2x+7+5x+12=180 \\ 7x+19=180 \\ 7x+19-19=180-19 \\ 7x=161 \\ \frac{7x}{7}=\frac{161}{7} \\ x=23 \end{gathered}[/tex]

so

answer:

angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°

angle 2 = 5x = 5(23) = 115°

angle 3 = 12°

Please ANSWER this

The table shows the parts of gelatin and water used to make a dessert.


Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
7


At this rate, how much gelatin and water will Jeff use to make 7 boxes?
Jeff will use 14 oz of powder and 21 cups of water to make 7 boxes of gelatin.
Jeff will use 13 oz of powder and10 cups of water to make 7 boxes of gelatin.
Jeff will use 27 oz of powder and 18 cups of water to make 7 boxes of gelatin.
Jeff will use 21 oz of powder and 14 cups of water to make 7 boxes of gelatin.

Answers

Jeff needs 21 oz of gelatin and 14 cups of water to make 7 boxes

How to determine the amount of gelatin and water needed to make 7 boxes?

The table of values is given as

Boxes          Gelatin Powder (oz)        Water (cups)

3                                           9                        6


From the above table, we can see that

Gelatin Powder = 3 * Boxes

Water  = 2 * Boxes

When there are 7 boxes, the equations become

Gelatin Powder = 3 * 7

Water  = 2 * 7

Evaluate the products in the above equation

So, we have

Gelatin Powder = 21

Water  = 14

Hence, the amount of gelatin and water needed to make 7 boxes are 21 oz and 14 cups respectively

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Answer: D: jeff will use 21 oz of powder and 14 cups of water

Step-by-step explanation:

the chart says there are

3 boxes of gelatin ) 9 oz of powder ) 6 cups of water

that equals the same as

1 box of gelatin ) 3 oz of power ) 2 cups of water

so for every box of gelatin, there is 3oz of powder and 2 cups of water

if he wants to make 7 boxes.....

7x3oz=21 oz

7x2cups=14 cups

so the Answer is D

Find the measurement of each subject. Assume that each figure is not drawn to scale.

Answers

To obtain the measure of segment AD, add the measurement of segment AC and segment CD.

[tex]AD=AC+CD=2\frac{3}{8}+1\frac{1}{4}[/tex]

Rewrite the fraction part as similar fractions. Multiply the numerator and teh denominator of the second fraction by 2 to obtain 8 in the denominator.

[tex]\begin{gathered} AC+CD=2\frac{3}{8}+1\frac{1\cdot2}{4\cdot2} \\ =2\frac{3}{8}+1\frac{2}{8} \end{gathered}[/tex]

Add the whole numbers, 2 and 1. Add the numerators, 3 and 2, and then copy the common denominator, which is 8.

[tex]\begin{gathered} AD=2\frac{3}{8}+1\frac{2}{8} \\ =3\frac{5}{8}_{} \end{gathered}[/tex]

Therefore, the correct answer is the third option, 3 5/8 in.

The pro shop at the Hidden Oaks Country Club ordered two brands of golf balls. Swinger balls cost$2.10 each and the Supra balls cost $1.00 each. The total cost of Swinger balls exceeded the total costof the Supra balls by $330.00. If an equal number of each brand was ordered, how many dozens ofeach brand were ordered?AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutdozen

Answers

The Solution:

Given that equal number of each brand of golf ball was ordered.

Let the number of each brand ordered be represented with n

Each swinger ball cost $2.10

So, the total cost of the swinger ball ordered is:

[tex]2.10n[/tex]

Each Supra ball cost $1.00

So, the total cost of the supra ball ordered is:

[tex]\begin{gathered} 1.00\times n \\ \text{which becomes}\colon \\ n \end{gathered}[/tex]

Given that the total cost of the Swinger balls exceeded the total cost of the Supra balls by $330.00. We have the linear equation below:

[tex]2.1n=n+330[/tex]

We are required to find the number of dozens of each brand of golf balls that were ordered.

So, we shall solve for n and then divide the value by 12.

[tex]\begin{gathered} 2.1n=n+330 \\ \text{collecting the like terms, we get} \\ 2.1n-n=330 \\ 1.1n=330 \end{gathered}[/tex]

Dividing both sides by 1.1, we get

[tex]\begin{gathered} \frac{1.1n}{1.1}=\frac{330}{1.1} \\ \\ n=300\text{ balls} \end{gathered}[/tex]

Dividing 300 by 12 (since 1 dozen = 12 balls), we get

[tex]\frac{300}{12}=25\text{ dozens of each brand of golf balls were ordered.}[/tex]

Therefore, the correct answer is 25 dozens.

need help with this question please help

Answers

Let:

[tex]k\cdot RT=TU[/tex]

Where:

k = Constant of proportionality

[tex]\begin{gathered} k\cdot4=6 \\ solve_{\text{ }}for_{\text{ }}k \\ k=\frac{6}{4} \\ k=\frac{3}{2} \end{gathered}[/tex]

So:

[tex]\begin{gathered} k\cdot RS=UV \\ \frac{3}{2}(6)=UV \\ \frac{18}{2}=UV \\ UV=9 \end{gathered}[/tex]

(G.lla, 1 point) Use the circle shown to answer the question. ♡ If MAC = 64. and m 2 ABC 16) find the value of x. A. 12 B 36 C. 25 D. 24

Answers

12

1) In this case, we have two chords within that circle. And since the arc = 64º and the m ∠ABC = 4x -16

2) Applying one Theorem that states that

3) So we can write:

[tex]\begin{gathered} (4x-16)\text{ =}\frac{64}{2} \\ 4x-16\text{ =32} \\ 4x\text{ =32+16} \\ 4x\text{ = 48} \\ x=12 \end{gathered}[/tex]

So the value of x = 12

a) Twice the difference of a number c and forty.b) Four times the sum of a number f and fifty.

Answers

a) We have a number X that is twice the difference of a number c and 40.

We can write this as:

[tex]X=2(c-40)[/tex]

b) Four times the sum of a number f and fifty.

Then, X is:

[tex]X=4(f+50)[/tex]

write an expression for the perimeter of this pentagon. if the perimeter is 157 united find x

Answers

The perimeter of the pentagon = the sum of the lengths of the sides

There are two sides of the length (4x-1) and three sides of the length (3x+2)

so,

The perimeter =

[tex]2\cdot(4x-1)+3\cdot(3x+2)[/tex]

Given the perimeter = 157

So,

[tex]2\cdot(4x-1)+3\cdot(3x+2)=157[/tex]

Solve the equation to find the value of x

[tex]\begin{gathered} 2\cdot(4x-1)+3\cdot(3x+2)=157 \\ 8x-2+9x+6=157 \\ 17x+4=157 \\ 17x=157-4 \\ 17x=153 \\ \\ x=\frac{153}{17}=9 \end{gathered}[/tex]

So, the value of x = 9

A triangle is graphed in this coordinate plane. what is the area of this triangle in square units A.9B.12C.18D.36

Answers

Answer

Option C is correct.

The area of the triangle = 18 square units

Explanation

The area of a triangle is given as

Area of the triangle = ½ × B × H

where

B = Base of the triangle = 6 units (From -3 t

The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.

Answers

The graph of the given function is attached below.

x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.

Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.

Given equation:-

15x + 20y = 1800

Where,

x represents the number of jeans shipped and,

y represents the number of khakis shipped

We have to use the x and y-intercepts to graph the equation.

Putting x = 0 to find the y -intercept, we get,

15(0) + 20y =1800

0 + 20y = 1800

y = 1800/20

y = 90

The coordinates of the point will be (0,90).

Putting y = 0 to find the x -intercept, we get,

15x + 20(0) =1800

15x + 0 = 1800

x = 1800/15

x = 120

The coordinates of the point will be (120,0).

Using the coordinates, we have graphed the graph attached.

Here, x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.

Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.

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The area of a picture projected on a wall varies directly at the square of the distance from the projector to the wall if a 10ft distance produces a 16 feet squared (^2) picture, what is the area of the picture produced when the projection unit is moved to a distance 20 ft from the wall?

Answers

The new picture is 64 ft squared. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

We are given the relation: Area of pic = constant * d^2, where d is distance from projector to wall.

For d = 10, we have A = 16 ft sqrd

Now given d = 20

what is A?

constant = 16/10*10

new A = [16/100] * 20*20 = 16 * 4 = 64 ft sqrd.

The new picture is 64 ft squared.

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The perimeter of a living room is 68 feet.if the length of the living room is 18 feet what is the width of the living room

Answers

the perimeter of a cuadrilateral is 2L+2W=68 where L is the length of the room

since L= 18 feet

we will have that

2(18)+2W=68

then

W=(68-36)/2= 32/2=16

Therefore, the width of the living room is 16 feet.

the equation of line u is y=2x+8/9. line v includes the point (7,9) and is parallel to line u. what is the equation of.line v

Answers

The linear equation parallel to line u that passes through (7,9) is y = 2x - 5

How to find the equation of line V?

Two lines are parallel if have the same slope, we know that line V is parallel to:

y = 2x + 8/9

Then line V will be of the form:

y = 2x + c

To find the value of c, we use the fact that the line passes through (7, 9), replacing these values we get:

9 = 2*7 + c

9 = 14 + c

9 - 14 = c

-5 = c

The linear equation is y = 2x - 5

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I need help on a problem

Answers

Those are similar triangles, which means, they are related by a ratio

For example in this case,

7: 10

to find x

10 / 7 = x/3

x= 10*3 /7

x= 30/ 7

x= 4.29

____________

A trampoline park charges $2 plus an hourly rate for each hour. The sign to theright gives the prices for up to 3 hours of parking. Which linear equationrepresents the given information where C is the total cost and h is the number ofhours spent at the park?

Answers

Given the following question:

Trampoline park charges $2 plus an hourly rate for each hour (variable h)

Sign gives prices for up to three hours of parking

C = total cost

h = hours

C = total cost

The sign goes up 12 dollars for every hour

The sign goes up to 3 hours

Option A isn't the answer because the sign only goes up to 3 hours

Your answer is option B

Since c represents total cost

2h = 2 +12 which is plus 12 dollars every hour

Help 50 points (show ur work)

Answers

1. The value of 34% of 850 is 289.

3. The amount that Kepley paid for the tool is $120.

How to calculate the value?

From the information, we want to calculate 34% of 850. This will be calculated thus:

= 34% ×850

= 34/100 × 850

= 0.34 × 850

= 289

The amount paid for the tool will be:

= Price or tool - Discount

= $200 - (40% × $200)

= $200 - $80

= $120

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Mackenzie drove 68 miles in 1\tfrac{3}{5}1 5 3 ​ hours. On average, how fast did she drive, in miles per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

Answers

By taking the quotient between distance and time, we conclude that her speed is 108.8 miles per hour.

How to find her speed?

Here we will use the next relation:

speed = distance/time.

Here we know that Mackenzie drove 68 miles in (1 + 3/5) hours, then:

distance = 68 mi

time = (1 + 3/5) hours = (8/5) hours.

Then the speed will be:

speed = 68mi/(8/5) hours. = 68*(8/5) mi/h = 108.8 mi/h

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Suppose you have $14,000 to invest Which of the two rates would yield the larger amount in 2 years 6% compounded monthly or 5.88% compounded continuously?

Answers

We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.

The expression used to calculate the amount compounded monthly is shown below:

[tex]A=P(1+\frac{r}{12})^{12\cdot t}[/tex]

Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.

The expression used to calculate the amount compounded continuously is shown below:

[tex]A=P\cdot e^{t\cdot r}[/tex]

Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.

With the two expressions we can calculated the final amount on both situations, this is done below:

[tex]\begin{gathered} A_1=14000\cdot(1+\frac{0.06}{12})^{12\cdot2} \\ A_1=14000\cdot(1+0.005)^{24} \\ A_1=14000\cdot(1.005)^{24} \\ A_1=14000\cdot1.127159 \\ A_1=15780.237 \end{gathered}[/tex][tex]\begin{gathered} A_2=14000\cdot e^{0.0588\cdot2} \\ A_2=14000\cdot e^{0.1176} \\ A_2=14000\cdot1.124794 \\ A_2=15747.12 \end{gathered}[/tex]

The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.

find the measure of a triangle if the vertices of triangle EFG are E(-3,3), F(1,-1), and G(-3,-5). then classify the triangle by its sides

Answers

EFG is a triangle with vertices

E(-3,3), F(1,-1) and G(-3,-5).

First, let us evaluate the length of each side of the triangle using the distanec formula.

[tex]\begin{gathered} EF=\sqrt[]{(1+3)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \\ FG=\sqrt[]{(-3-1)^2+(-5+1)^2} \\ =\sqrt[]{16+16} \\ =4\sqrt[]{2} \\ EG=\sqrt[]{(-3+3)^2+(-5-3)^2} \\ =\sqrt[]{8^2} \\ =8 \end{gathered}[/tex]

Since two sides of the triangle are equal, therefore, EFG is an isoscele triangle.

1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an apothem SM = √15 cm. Calculate the pyramid: 1) the base elevation AM; 2) the elevation SO; 3) the area of the base; 4) the area of the side surface; 5) the total surface area; 6) volume.

Answers

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

[tex]\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}[/tex]

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

[tex]SO=\sqrt{SM^2-MO^2}[/tex]

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

[tex]\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}[/tex]

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

[tex]A=\frac{1}{2}*BC*AM[/tex]

Thus, we have:

[tex]\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}[/tex]

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

[tex]SA=\frac{1}{2}*p*h[/tex]

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

[tex]\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}[/tex]

• (5). Total surface area:

To find the total surface area, apply the formula:

[tex]TSA=base\text{ area + area of side surface}[/tex]

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

[tex]V=\frac{1}{3}*area\text{ of base *height}[/tex]

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

[tex]\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}[/tex]

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

complete by using square x^2 + 4x + 1 = 0

Answers

Given:

The eqution is given as, x^2 + 4x + 1 = 0​.

The objective is to solve the equation by compleing the square.

Consider the middle of the equation.

[tex]2\cdot a\cdot b=4x[/tex]

Here, the value of a is x. Then, the value of b can be calculated as,

[tex]\begin{gathered} 2(x)\cdot b=4x \\ b=\frac{4x}{2x} \\ b=2 \end{gathered}[/tex]

To complete the equation add +b^2 and -b^2 to the equation.

[tex]\begin{gathered} x^2+4x+2^2-2^2+1=0 \\ x^2+4x+2^2-4+1=0 \\ x^2+4x+2^2-3=0 \\ (x+2)^2-3=0 \\ (x+2)^2=3 \end{gathered}[/tex]

Take square root on both sides, to solve the value of x,

[tex]\begin{gathered} \sqrt[]{(x+2)^2}=\sqrt[]{3} \\ x+2=\pm\sqrt[]{3} \\ x=\pm\sqrt[]{3}-2 \\ x=+\sqrt[]{3}-2\text{ and -}\sqrt[]{3}-2 \end{gathered}[/tex]

Hence, the value of x are +√3-2 and -√3-2.

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Answers

Answer:

The expression is -16 when m = 6

Explanation:

Given:

[tex]m^2-9m+2[/tex]

When m = 6, we have:

[tex]\begin{gathered} 6^2-9(6)+2 \\ =36-54+2 \\ =-16 \end{gathered}[/tex]

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