(13 + 7 ^ 2 / 7)/(9 - 20/4 - 16)

Answer:

0.288

Step-by-step explanation:

Given that :

Correlation (R) = 0.48

Slope of linear model which predicts Lifespan from years of education (m) = 0.8

To determine the value of slope of the model which predicts years of eductauoon from lifespan:

The square of the regression Coefficient is multiplied by the inverse of the slope of linear model which predicts Lifespan from years of education

Hence,

(R² * 1/m)

0.48² * 1/0.8

0.2304 * 1.25

= 0.288

Using Quadratic formula, x = 0.18 ft.

Keep in mind that since the quadratic is downward facing, the vertex will be the highest point, the y-intercept will represent the starting height, and the positive x-intercept will represent the distance to the child.

(a) Locate the y-intercept by setting x = 0 and solving for y.

y = -116(0)2+4(0)+3 = 3 ft

(b) As the maximum height is being requested, determine the vertex's y-value.

Vertex x-value: x=-b/2a=-4/(2*-116)=1/58

Vertex's y-value is given by: y = -116(1/58)2+4(1/58)+3 = 3.03 ft (return the x-value to the equation).

Locate the positive x-intercept (y = 0) in (c).

0 = -116x2+4x+3

Using the quadratic formula because it cannot be factored

x = [-4 ± √(42-4(-116)(3))]

/(2*-116) = -0.14 or 0.18 ft

x = 0.18 ft

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Complete Question -

The height y (in feet) of a ball thrown by a child is  y=−116x2+4x+3

The height y (in feet) of a ball thrown by a child is

y=−116x2+4x+3

where x is the horizontal distance in feet from the point at which the ball is thrown.

(a) How high is the ball when it leaves the child's hand?     feet

(b) What is the maximum height of the ball?    feet

(c) How far from the child does the ball strike the ground? Round your answers to the nearest 0.01.    feet

1. The length of side AC is 21.5 units.

2. The magnitude of ∠R is 36.9°

3. The length of side ML is 7.5 units.

3. The length of side JK is 8.5 units.

In order to determine the length of side AC, we would apply sine trigonometric ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle;

sin(θ) = Opp/Hyp

Where:

By substituting the given side lengths, we have:

sin(34) = 12/x

x = 12/sin(34)

x = 21.5 units.

Question 2.

For the magnitude of ∠R, we have:

TanR = opposite side/adjacent side

TanR = 6/8

∠R = tan⁻¹(0.75)

∠R = 36.9°.

Question 3.

For side length ML, we have the following:

Tan28 = 4/ML

ML = 4/tan28

ML = 7.5 units.

Question 4.

For side length JK, we have the following:

cos(θ) = Adjacent side/Hypotenuse

cos(58) = JK/16

JK = 16cos(58)

JK = 8.5 units.

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Answer:

\({ \bf{by \: relations : }} \\ { \tt{ \frac{28}{7} = \frac{x}{8} }} \\ \\ { \tt{x = \frac{28 \times 8}{7} }} \\ x = 32 \\ \\ { \tt{y = 83 \degree}}\)

Here m = angle UST

angle UST= 90° - 32° = 58°

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Answer:

(2x - 9)(x + 6) .

Step-by-step explanation:

2x^2 + 3x - 54

Use the 'ac' method to do this.

First multiply the first number by the last:

2 * -54 = -108.

Now we want 2 numbers whose product is -108 and whose sum is + 3,

- these are +12 and -9, so we write:

2x^2 + 12x - 9x - 54        Now factor by grouping:

= 2x(x + 6) - 9(x + 6)        x +6 is common, so:

= (2x - 9)(x + 6) .

Given:

Sol:.

Answer: x²+8x+16

Step-by-step explanation:

(x+4)^2=(x+4)(x+4)

Now use distributive property to expand (x+4)(x+4):

(x+4)(x+4)=x²+4x+4x+4(4)

x²+4x+4x+4(4)=x²+8x+16

Answer:

x^2+8x+16

Step-by-step explanation:

Assuming that is to the power of two

We can use special products to do this which states that the answer to this will be a^2+2ab+b^2 where the first value is a and the second value is b. So we just plug that in and do x^2+8x+16.

We can also just do (x+4)(x+4) and do that out but that takes more time and you'll get the same answer.

Let me know if you have any questions

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer: yes because it if u plug in x values u get y values

ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

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Answer:

7lm - 21lmn

taking common 7lm

7lm(1-3n)

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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Answer:

720 degrees

Step-by-step explanation:

sum of interior angles of any polygon is given by the equation

\(sum \: = (n - 2) \times 180\)

where n is the number of sides of the polygon. in the question the polygon has 6 sides. hence n = 6 and

\(sum \: = (6 - 2) \times 180 \\ = 4 \times 180 \\ = 720 \: degrees\)

y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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The polygon shown in the figure is trapezoid and the value if x is  .

What is trapezoid?

A trapezoid may be a polygonal shape that has just one try of parallel sides. These parallel sides also are referred to as parallel bases of trapezoid. the opposite 2 sides of trapezoids area unit non-parallel and referred to as legs of trapezoids

Main body:

by using the property of trapezoid ,

1/2(sum of both bases) = mid-line passing through trapezoid

according to question:

x = 1/2(x-8+2x-12)

x = 1/2(3x -20)

2x = 3x - 20

x = 20

Hence value of x is 20.

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Answer:

B

Step-by-step explanation:

Answer:

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

Simplify in below steps:

Answer:

7/2

Step-by-step explanation:

7 x 4 / 8

= 7 x 1/2

= (7 x 1)/2

= 7/2

Note

1. When you see a fraction, first simplify the numerator and denominator.

That is,

In 4/8,

4 is the numerator

8 is the denominator

4/8 = 1/2

2. Multiply number with numerator, then divide it with the denominator

7 x 1/2

7 x 1 = 7

(7 x 1)/2 = 7/2

Answer:

16/24+21/24

Step-by-step explanation:

Hope it helped!!

Answer: turtles

Step-by-step explanation:

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer:

5b-5

Step-by-step explanation:

Replace a with a=5/6 * b

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

x=-15/2

Step-by-step explanation:

Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}

A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.

B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.

Let, \(M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right]\)  then the set in B) is just Null(M). Again, Nullspaces are always subspaces.

Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set  \(x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right]\)  for any choice of z∈R. So this

can be a set in the span of   \(x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right]\)

C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.

D) Correct. This can be a  subspace for the same reasons as part B.

E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.

F) Not a subspace. (0,0,0)  is not in there.

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Answer:

21.43

Step-by-step explanation:

Turn 7 percent to a decimal: 0.07

8800 × 0.07 = 616

13,200÷616=21.4285 etc

Round two decimal places

21.43