i would like to have an answer for this thanks!

Answer:

12cm

Step-by-step explanation:

where:

c

is the hypotenuse, and

a

and

b

are the other two sides (legs).

Let

a

=

9 cm

Rearrange the equation to isolate

b

2

. Plug in the values for

a

and

c

, and solve.

b

2

=

c

2

−

a

2

b

2

=

(

15 cm

)

2

−

(

9 cm

)

2

Simplify.

b

2

=

225 cm

2

−

81

cm

2

b

2

=

144 cm

2

Take the square root of both sides.

b

=

√

144 cm

2

Simplify.

b

=

12 cm

The equation of the quadratic function that models the data is y = x^2 + 3x + 4

A quadratic function is represented as:

y = ax^2  +bx + c

Next, we enter the data values on the table to a graphing calculator.

From the graphing calculator, we have:

a = 1, b = 3 and c = 4

Substitute these values in y = ax^2  +bx + c

So, we have

y  = x^2 + 3x + 4

Hence, the equation of the quadratic function that models the data is y = x^2 + 3x + 4 and the scatter plot is (a)

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Answer:

Step-by-step explanation:

So if you look at the first photo I sent you'll see I marked three points. So the first point is going to be the two lines meet and the other two are going to be at 0 degrees and 48 degrees. After that you're going to draw a line to connect 2 of the dots to the middle one or the one connecting the two. After this you're going to put the protractor back on the triangle and line it up and then draw a point at 24 degrees (half of 48 degrees) and then draw a line to it. And this will be the bisector. And then after that label all the points. Also for the congruency thing just do the same thing except without an angle bisector through it.

The inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have inequalities given:

[tex]1.5 > 2\dfrac{1}{2}[/tex]

or

1.5 > 2.5  (false)

1/2 > 0.5

0.5 > 0.5 (false)

-2.5 > -1.5 (false)

[tex]-3 \dfrac{1}{2} > -4.5[/tex]

-3.5 > -4.5  (true)

Thus, the inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.

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The volume of the spherical solid resulting of the drill is of 11,226 units³.

The volume of a sphere of radius r is given as follows:

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

In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:

[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]

[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]

The volume of the resulting solid is the difference of the volumes, hence:

V = 11494 - 268 = 11,226 units³.

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The inequality of the bridge's legal limit 100000x + 34000y ≤ 700000

The given parameters are:

Represent the 6-axle trucks with x and the y-axle trucks with y.

So, we have the following inequality

100000x + 34000y ≤ 700000

The number of 6-axle trucks at one time

Here, we assume that y = 0.

So, we have:

100000x ≤ 700000

Divide by 100000

x ≤ 7

Hence, the number of 6-axle trucks at one time is 7

The number of 2-axle trucks at one time

Here, we assume that x = 0.

So, we have:

34000x ≤ 700000

Divide by 34000

x ≤ 20.58

Round down

x ≤ 20

Hence, the number of 2-axle trucks at one time is 20

See attachment for the inequality of 100000x + 34000y ≤ 700000

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Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.

An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.

In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).

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Answer:

y=250000

Step-by-step explanation:

y=ab^x

y=25*100^2

The number 2007 is in the 63rd row

The pattern is given as

1

2  3

4  5  6

The sum of n natural numbers is:

Sum = 0.5n(n + 1)

Assume n = 62

Sum = 0.5 * 62 * (62 + 1)

Sum = 1953

Assume = 63

Sum = 0.5 * 63 * (63 + 1)

Sum = 2016

2007 is between 1953 and 2016

Since 2016 is greater than 1953, we can conclude that 2007 is in row 63

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The The square root of R² (the coefficient of determination) is not r, the correlation coefficient. Therefore, it's false.

It should be noted that the correlation coefficient is used to measure how string the relationship between two variables are.

The correlation formula tells us the linear relationship between the variables. R² is the square of the correlation coefficient.

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We know that if [tex]m\angle ABD=2(m\angle DBC)[/tex], then [tex]m\angle ABD=\frac{2n}{3}[/tex] and [tex]m\angle DBC=\frac{n}{3}[/tex].

Since BE bisects [tex]\angle DBC[/tex], we know that [tex]\angle DBE \cong \angle EBC[/tex], and thus [tex]\angle EBC=\boxed{\frac{n}{6}}[/tex]

Venn Diagram:

Neither a cat or dog: 37/100

A dog: (22+14)/100 = 36/100 = 18/50 = 9/25

A dog but not a cat: 22/100 = 11/50

Hope this helped!

This is just what I drew. I believe the answer for B could be somewhat different than what I drew.

Have a nice day!

In the case above, the side-side-angle (SSA) is no valid means for establishing triangle congruence.

Using the image attached:

m  angle A = M angle A

AB = A¹B¹

BC = B¹C¹

Looking at the image of both angles you will see that both are not congruence  because Two triangles can be regarded as congruent if and when all its three corresponding angles or sides are said to be equal and all the three corresponding angles are also said to have equal  measure.

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half the confidence interval is the answer.

The margin of error is a statistical measure that explains the difference between the actual and expected results of a random survey sample. Simply put, tolerances allow you to measure the level of unpredictability of your data and findings.

The margin of error is the amount added and subtracted in the confidence interval. The standard error is the standard deviation of the sample statistics when many samples of the same size can be obtained.

E = zs√n. The quantity E is called the margin of error. The margin of error is half the width of the confidence interval. The confidence interval may be given as ˉx ± E. For example, 9.95 ± 0.43.

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Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.

A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."

All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.

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The answer to the question is,

12 sin(∠B) = 2,           12 sin(∠C) = √3+√35

Sin rule is,

sin(A)/BC = sin(B)/AC = sin(C)/AB

sin(B) = (sin(A)×AC)/BC

sin(C) =(sin(B)×AB)/AC

To solve this question we apply sin rule,

Now we take

12 sin(∠B) =12 (sin(∠A)×AC)/BC

12 sin(∠B) =12 (sin(π/6)×(x/3x))          where ∠A =π/6 and AC=x, BC =3x

12 sin(∠B) =12 ((1/2)×(1/3))

12 sin(∠B) =12/6 = 2

12 sin(∠B) = 2

now we find the value of 12 sin(∠C)

12 sin(∠C) = 12(sin B)×(AB/BC)

now put the value of 12 sin(∠B) = 2

12 sin(∠C) = 2×(AB/BC)

12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]

12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]

cos (π/6) = √3/2 and BC/AC =3

then

12 sin(∠C) = 2×[(√3/2)+3×(cos B)]

cos B= √1-sin²B

12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]

12 sin(∠B) = 2

sin B = 1/6

12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]

12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]

12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]

12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]

12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]

12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]

12 sin(∠C) = 2×[(1/2)(√3+√35)]

12 sin(∠C) = √3+√35

Hence the answer is,

12 sin(∠B) = 2,         12 sin(∠C) = √3+√35

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Answer: Function 1 has the larger maximum at (4,1).

Step-by-step explanation:

The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].

For the graph, the maximum is obviously at (4,1).

So, Function 1 has the larger maximum at (4,1).

Answer:

They used coordinates P(a,0), A(d,c), and R(b,c) instead of the given coordinates.

Using it's concept, it is found that the graph on top right represents the inverse function.

The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.

Considering the table given, the graph of the inverse function will contain these following points:

(4.4, -3), (0.6, -2), (-0.8, -1), (-1,0), (-1.2, 1), (-2.6, 2), (-6.4, 3).

Hence it is the top right graph.

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The product of the given binomial is x⁴ -y².

FOIL stands for Firsts , Outsides , Insides , Lasts and while determining product of binomials this sequence is followed.

The binomials given are

( x² +y ) (x² -y)

x²  (x² -y)             + y * x² +              y* (-y)

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

Firsts  Outsides       insides             Lasts

After simplification

x⁴ - x²y +  x²y -y²

x⁴ -y²

The product of the given binomial is x⁴ -y².

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Answer: 4x^2 + 1

Step-by-step explanation:

I am assuming g(x) = x^2

4(x^2) + 1

4x^2 + 1

Answer:

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

Step-by-step explanation:

Assume [tex]g(x)=x^2[/tex]

[tex](fog)(x)[/tex] is a composition of two functions such that [tex](fog)(x)=f(g(x))[/tex].

Consider the function:

[tex]f(x)=4x+1[/tex]

Replace [tex]x[/tex] with [tex]g(x)[/tex] into the equation:

[tex]f(g(x))=4\cdot g(x)+1[/tex]

Substitute [tex]g(x)=x^2[/tex] on the right side of the equation:

[tex]f(g(x))=4\cdot x^2+1[/tex]

Therefore, the expression for [tex](fog)(x)[/tex] is [tex]4x^2+1[/tex].

Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

[tex]18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4[/tex]

There are 4 trees, and there are [tex]18x+4[/tex] acorns or 76 acorns.

Hope you have a nice day, and also you should mark brainliest :)

Answer:

76 acorns and 4 trees

Step-by-step explanation:

Let X be the number of acorns (a) Ms. Blue Jay plans to store.

We are told that she could hide 18 acorns (a) per tree (t) which we'll write as 18a/t.  This would result in 4 leftover acorns.

We then learn that if she hides 20 acorns per tree, 20a/t, she will have space for an extra four acorns.

There are t trees in both cases.  We can write these two scenarios as:

1)  18t + 4  = X [18 acorns are in each tree, t, plus there are 4 left over.]

2)  20t -4  = X [20 acorns per tree, t, with room to store 4 more]

These two are equal to each other:

18t + 4 = 20t - 4

2t = 8

t = 4

There are 4 trees.

Since 18t+4 = X, the total number of acorns is18*4+4 = 76 acorns and 4 trees.

Check to see if 76 acorns works for the second scenario:

Will hiding 20 acorns per tree leave room for 4 acorns if there are 76 acorns?

(4 trees)*(20 acorns/tree) = 80 acorns can be stored.  If Ms. Jay only has 76 acorns, there will be room for 4 more acorns.

Answer:

y = 3x + a (a > 0) - above the original line

y = 3x + b (b < 0) - below the original line

Step-by-step explanation:

Pick any number you want for a or b, as long as the number meets the condition I wrote down.

Answer:

y=3x+1 and y=3x-1

Step-by-step explanation:

y=3x+1 is above because it has a positive slope (3) while y=3x-1 is below because it has a negative slope (-3).

Answer:

y≤-x+1

Step-by-step explanation:

Since the line is slanted down and crossing through a point every one unit the slope is negative one. The line is also crossing 1 on the y-axis. This is the y-intercept. The last thing we need to know is which sign to use, less than, greater than, less than or equal to, greater than or equal to. We can immediately cross out less than and greater than because it is a solid line. The sign used on the graph is less than or equal to because it is a solid line shaded to the left. Now, we can use the formula with the information we have found to create the linear inequality.

Formula: y≤x+b

I put the less than or equal to sign there instead of the equal sign because the line graphed is less than or equal to. Plug in the information we have.

y≤-x+1

Using function notation.

f(x)≤-x+1

I have also attached a picture for you to see it is correct.

Hope this helps!

If not, I am sorry.

Answer:

3,-3

Step-by-step explanation:

g(3)= (3)³+6(3)²-9(3)-54

= 27+54-27-54

=81-81

= 0

g(-3) = (-3)³+6(-3)²-9(-3)-54

= -27+54+27-54

= 27-27

= 0

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Answer:

  (a)  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

Wherever the function crosses the x-axis, its sign changes. This lets us make a map of the signs of the function, and identify intervals where it is positive and negative.

The x-intercepts are said to be at x ∈ {-0.7, 0.76, 2.5}.  These three crossing points divide the graph into four (4) intervals. The sign of the function is given as positive at x=0 and negative at x = 1.9. So, our sign map is ...

  < -0.7 . . . . . negative

  -0.7 to 0.76 . . . . . positive (2 at x=0, for example)

  0.76 to 2.5 . . . . . negative (-5.7 at 1.9, for example)

  > 2.5 . . . . . positive

Choosing from the descriptions, the one that matches is ...

  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)