Write a linear function f with the given values f(0) = 2, f(3) = -1

The area of one triangle is 28 cm².​

From the question, we have

area = 1/2*base*height

=  1/2*8*7

=28 cm².

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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We accept the null hypothesis, according to which the average amount of trash per bin is equal to 50.

acc to our question-

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Answer: $372

Step-by-step explanation:

330 + (1.5% of 330) = 334.95

334.95 + (1.5% of 334.95) = 339.97425

339.97425 + (1.5% of 339.97425) = 345.073864

345.073864 + (1.5% of 345.073864) = 350.249972

350.249972 + (1.5% of 350.249972) = 355.503772

355.503772 + (1.5% of 355.503772) = 360.836392

360.836392 + (1.5% of 360.836392) = 366.248398

366.248398 + (1.5% of 366.248398) = 371.742124

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The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.

Other expressions are not equivalent

Expressions 1

The expressions are given as

4(2a+7) and 8a +7

Open the brackets

8a+28 and 8a +7

The above expressions are not equal

Expressions 2

Here, we have

7y + 2y+y and 10y

Evaluate the like terms

10y and 10y

The above expressions are equal

Expressions 3

Here, we have

8m-4m+4m and 8m

Evaluate the like terms

8m and 8m

The above expressions are equal

Expressions 4

Here, we have

9e+2(e+5) and 11 +5

Open the brackets

9e+2e+10 and 11 +5

Evaluate the like terms

11e + 10 and 11 + 5

The above expressions are not equal

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By using the concept of law of exponents,the required answers are: 5)  [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]

According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.

Exponents are the power of numbers, which tells us how many time a number multiply by itself.

we have,

5)   [tex]\frac{ef^0}{e^2f}[/tex]

⇒  [tex]e^{1-2}f^{0-1}[/tex]

⇒  [tex]e^{-1} f^{-1}[/tex]

8)  [tex]a^{0}b^{6} b^{-3}[/tex]         ( [tex]a^{0}[/tex]=1 )

⇒  [tex]b^{6-3}[/tex]

⇒  [tex]b^{3}[/tex]

Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]

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Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

∠ B + 72° + 36° = 180°

∠ B + 108° = 180° ( subtract 108° from both sides )

∠ B = 72°

Then

∠ B = ∠ C = 72°

this means the 2 base angles in Δ ABC are congruent , then the triangle is isosceles with the 2 legs being congruent , that is

AB = AC

The distance from the top of the tree to the tip of the shadow is 12.8 ft  

According to the Pythagorean theorem, In a right-angled triangle, the sum of the squares of the side will equal the square of the hypotenuse.
Here hypotenuse is the longest side.

=> Hoptenuse² = side² + side²

Here we have

The length of the tree = 10 feet

Length of shadow = 8 feet

Here we need to find the distance from the top of the tree to the tip of the shadow  

If we join the top of the tree to the tip of the shadow we will observe a right-angled triangle as shown below

From the figure,

AC² = AB² + BC²    [ ∵ ABC is right angle triangle ]

=> AC² = 10² + 8²  

=> AC² = 100 + 64

=> AC² = 164

=> AC = 2√41

=> AC = 12.8 ft

Therefore,

The distance from the top of the tree to the tip of the shadow is 12.8 ft  

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Answer:

b) 12.8 feet

Step-by-step explanation:

Now we have to,

→ find the required distance.

Forming the equation,

→ x² = 10² + 8²

Then the distance will be,

→ x² = 10² + 8²

→ x² = 100 + 64

→ x² = 164

→ x = √164

→ [ x = 12.8 feet ]

Hence, distance is 12.8 ft.

The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

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The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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The value needs to be added to x²+10x+6 to complete the square is 19.

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².

In the presented trinomial, we can immediately find that a = x, and b² = c,

We know that a = x, and , 2ab = 2bx.

Now, 2bx and 30x are corresponding terms, 2bx = 30x.

Take the coefficient of x = 10

Divide by 2

10/2 =5

Then Square it

5 x 5=25

Add this to make a perfect square trinomial;

x² + 10x + 25

In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.

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Answer:

Let the age of brother be x and that of a sister be y.

(x+y) =16

(x) ×(y) =63

Using the substitution method, x=16-y

Substitute in equation 2

(16-y)(y)=63

16y-y^2=63

Y^2-16y+63=0

P=63

Sum= -16

Factor=(y-7),(y-9)

(y-7)(y-9)=0

Therefore y=7 or y=9

Therefore age of brother = 16-7 =9 0r 16-9=7

Therefore their ages are 9 years and 7 years

Answer:

(3, 6)

Step-by-step explanation:

I hope this helps you!

The volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

Given:

A sphere has a diameter of 24 mm.

Radius r = diameter/2

= 24/2

r = 12 mm.

volume of sphere = 4/3π[tex]r^{3}[/tex]

= 4/3 * 22/7 * [tex]12^{3}[/tex]

= 88*[tex]12^{3}[/tex]/21

= 88*1728/21

= 152064/21

= 7241.142 m[tex]m^{3}[/tex].

Therefore the volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

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Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

According to the question,

We have the following information:

Amount to be invested = $15200

Interest earned 1% a year and 4% a year

Total amount interest to be earned at the end of first year = $548

Now, let's take the amount to be invested in 1% interest a year's mutual fund to be $x.

Then, we have the amount to be invested in mutual fund that earns 4% a year:

$(15200-x)

So, we have the following expression by removing percentage sign:

x/100 + (15200-x)4/100 = 548

Taking 100 as the least common factor and using the cross multiplication method:

x+60800-4x = 548*100

-3x = 54800-60800

-3x = -6000

x = 6000/3

x = $2000

Now, the amount invested in second mutual fund:

15200-2000

$13200

Hence, Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

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Answer:

==========================

First, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.

Since - 15 is smaller than - 6, the least number is - 3:

Now compare the positives.

Therefore:

The complete order is:

Answer:

-3 < -6/5 < 1/6 < √7 < 45

Step-by-step explanation:

Now the values will be,

→ 1/6 = 0.17

→ -3 = -3

→ √7 = 2.65

→ -6/5 = -1.2

→ 45 = 45

Let's arrange in ascending order,

→ -3, -1.2, 0.17, 2.65, 45

→ -3, -6/5, 1/6, √7, 45

Hence, number -3 comes first.

Answer:

yes for helena: not sure for edwin

Step-by-step explanation:

for helena, it would be a 270 cc rotation and then scale

for edwin, again im not sure, but it could be a refection and then scale

The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.

Therefore,

I = Prt

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

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The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.

The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.

In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.

Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.

Statements                             Reasons                                      

1. ∠Z ≅ ∠C                              1. Given

AK bisects ∠ZKC

2. ∠ZKA ≅ ∠CKA                   2. Definition of bisection

3. AK ≅ AK                             3. Reflexive property

4. ΔAKZ ≅ ΔAKC                   4. AAS

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Step-by-step explanation:

the standard form is

f(x) = y = a(x - h)² + k

(h, k) are the vertex coordinates. here (-2, -9).

a is the stretch factor.

since the parabola opens upwards, a is positive.

so, we see already :

y = a(x + 2)² - 9

to get a we need an additional point on the curve. we see e.g. (1, 0) :

0 = a(1 + 2)² - 9 = a×3² - 9 = 9a - 9

9a = 9

a = 1

so, our standard form is

f(x) = (x + 2)² - 9

1/2 ef sinG is the expression that correctly represents the area of triangle EFG. Select option d.

Given: the triangle EFG as shown in the image

The formula for the Area of triangle is:

A = 1/2 × base(b) × height(h)  

Area of EFG = 1/2 × f × h

Using trigonometric ratio:

sin G = h/e     (opp. / hyp.)

h = e sin G

put h = g sin E into the Area of EFG:

Area of EFG = 1/2 × f × e sin G = 1/2 ef sin G

Therefore, the expression correctly represents the area of EFG is 1/2 ef sinG

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Given,

The probability of head ups of a firefly = 0.1 = 10%

The average flashes per minute is 6.

1 firefly 6 flashes per minute = 0.1 flash per second

Then,

1000 × 0.1 = 100 flashes per second

100 × 10 = 1000 flashes per 10 seconds

There will be 1000 flashes per 10 seconds.

Each flash = 0.1 lumen

40 lumens = 4 flash

70/100 = 0.7

0.7 x 4 = 2.8 = 3 fireflies.

There is 3 fireflies required to produce 40 lumens

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The total change in yards where the team started is 36 yards

The given parameters in the question are:

Yards per play = 4 yards

Number of plays = 9 consecutive plays

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = 4 * 9

Evaluate

Total change = 36

Hence, the total change is 36 yards

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The expressions that are not polynomials are the second and third ones:

A polynomial is a lineal combination of terms of powers of variables, such that the exponents must be positive integers or zero.

So, for example, a polynomial of degree n is:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x + a₀

Where we also can have more than one variable.

Then, for example the first one:

-4p + 7

Is a polynomial of degree 1.

The options that are not polynomials are:

p(n) = 3 + 1/n

p(q) = q^(1/2) + 5

Which are the second and third options.

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Answer:

Those are the answers

Step-by-step explanation:

3 + 1/n

q^(1/2) + 5

A. The correlation coefficient is of 0.303.

B. There are six positive and four negative.

C. The point with the largest residual is (6,2).

By choosing the points (x,y) from the scatter plot and entering them into a calculator, the correlation coefficient can be calculated.

A) The coordinates of these points are:

(1,2), (1,3), (2,4), (3,4), (3,5), (4,3), (4,5), (5,5), (5,6), (6,2).

Now, using Pearson correlation we have

X Values:

∑ = 34

Mean = 3.4

∑(X - Mx)² = SSx = 26.4

Y Values:

∑ = 39

Mean = 3.9

∑(Y - My)² = SSy = 16.9

So, when X and Y Combined

N = 10

∑(X - Mx)(Y - My) = 6.4

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 6.4 / √((26.4)(16.9))

r= 0.303

Hence, the correlation coefficient is 0.303

B) As, The difference between the observed value and the expected value, or residual, is determined as follows:

C) The largest residual using absolute value is at the point is (6,2).

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AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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Answer:

The answer is 3.

Step-by-step explanation:

The highest coefficient is 3 (5x^3), the second one is 2 (4x), and the other two without coefficient are considered 1.

The area of the model on the right is given by 96 sq cm

The correct answer option is option D.

A model represents a real object on a drawing paper.

Given that the model is triangular in shape, the model on the right is 2 times the model on the left.

Therefore, area of model on the left = area of model on the left × 2².

Area of model on the left = 24 × 4

Area of model on the left = 96 square cm.

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large samples and small variance are combination of factors is most likely to produce a significant value  in standard deviation .

What is standard deviation?

t = x - μ/s/√n

t = √n( x- μ)/s

t will be significant when its value will be higher .

so, the answer is large samples and small variance .

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