a and b are positive integers and 7a+ 5b= 49. Find the values of a and b.
3.1 What is a?
2 What is b?

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

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The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Fractions that are between 12/13 and 19/20 such that:

The numerator(N) is one less than the denominator(D).

N =  D - 1

N = (12, 19)

D = (13, 20)

D = 14, N = 13

D = 15, N = 14

D = 16, N = 15

D = 17, N = 16

D = 18, N = 17

D = 19, N = 18

The fractions that are between 12/13 and 19/20:

N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}

Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6

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Answer:

  no

Step-by-step explanation:

In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.

__

  A = 2^14 × 3^20

  B = 2^12 × 3^22

The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.

  (3^20)(2^14) is not a factor of (3^22)(2^12)

2x + 9 = 5x - 12

2x - 5x = - 1- 9

- 3x = - 21

x = 21/3

x = 7

Y = 60°

Answer:

[tex] \boxed{f(6) =2 4}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = x² - 2x[/tex]

Solution:

ATP,it is that x = 6. So substitute 6 on the function.

[tex]f(6) = 6 {}^{2} - 2(6)[/tex]

Simplifying using PEMDAS,we obtain:

[tex]f(6) = 6 \times 6- 12[/tex]

[tex]f(6) = 36 - 12[/tex]

[tex] \boxed{f(6) =2 4}[/tex]

Hence,f(6) = 24.

The answer is -0.18

when you convert 43% to decimal, it is 0.43

And the z-score of 0.43 is closest to -0.18

Hope it helps!

Answer:

cuantos billetes de 100.son en .100000?

Answer:

x = 35 and 100°

Step-by-step explanation:

the sum of the exterior angles of a triangle = 360° , then

2x + 10 + 3x + 15 + 4x + 20 = 360 , that is

9x + 45 = 360 ( subtract 45 from both sides )

9x = 315 ( divide both sides by 9 )

x = 35

then each exterior angle is

2x + 10 = 2(35) + 10 = 70 + 10 = 80°

3x + 15 = 3(35) + 15 = 105 + 15 = 120°

4x + 20 = 4(35) + 20 = 140 + 20 = 160°

the sum of an exterior angle and corresponding interior angle = 180°

then

180° - 80° = 100°

180° - 120° = 60°

180° - 160° = 20°

the largest interior angle of the triangle is 100°

Answer:

x = 35

largest interior angle = 100°

Step-by-step explanation:

The exterior angles of a triangle sum to 360°

⇒ (2x + 10) + (3x + 15) + (4x + 20) = 360

⇒ 2x + 10 + 3x + 15 + 4x + 20 = 360

⇒ 9x + 45 = 360

⇒ 9x = 315

⇒ x = 35

Therefore, the three exterior angles are:

If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.  As angles on a straight line sum to 180°:

⇒ interior angle + exterior = 180°

So the largest interior angle will be the supplementary angle to the smallest exterior angle.

The smallest exterior angle is 80°, so:

⇒ largest interior angle + 80° = 180°

⇒ largest interior angle = 180° - 80°

⇒ largest interior angle = 100°

0.66 inches of material is needed to be cut off to make the volume maximum.

When the second derivative of a function is negative, the function has a maximum point and if the second derivative is positive, the function has a minimum point.

Analysis:

After cut and folded, length = 8-2x

Width = 3-2x

Thickness = x.

Volume of the folded shape = (8-2x)(3-2x)(x)

After expansion, V = 4[tex]x^{3}[/tex]-[tex]22x^{2}[/tex] +24x

for turning point of the function, dv/dx = 0

dv/dx = 12[tex]x^{2}[/tex] -44x + 24

lowest term = 3[tex]x^{2}[/tex] - 11x + 6

3[tex]x^{2}[/tex] - 11x + 6 = 0

3[tex]x^{2}[/tex] - 9x -2x +6 = 0

3x(x-3) -2(x-3) = 0

(3x-2)(x-3) = 0

x = 2/3 or x = 3

To test for maximum point, we differentiate dv/dx again

we have 6x - 11

for x = 3,  6(3) - 11 = 18 - 11 = 7 which is positive x= 3 is a minimum

for x = 2/3 6(2/3) - 11 = 4 - 11 = -7, x = 2/3 is a maximum.

Therefore for maximum volume, the length to be cut out is 2/3 which is 0.66 inches.

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Here....

The length is given 15 feet and the width is 12 feet...Now let's find the Perimeter..

Perimeter = 2 ( l + b )

= 2 ( 15 + 12 )

= 2 × 27

= 54 feet

[tex]...[/tex]

:)...

Answer:

the graph has a parent function of f(x) = x²

The (x - 5)² tells us that the graph is shifted to the right 5 units.

The +2 tells us that the graph is shifted up 2 units.

Answers:

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

Work Shown:

n = number of sides = 26

S = sum of the interior angles of a polygon with n sides

S = 180(n-2)

S = 180(26-2)

S = 180(24)

S = 4320 degrees is the sum of the interior angles.

i = measure of one interior angle of a regular polygon

i = S/n

i = 4320/26

i = 166.1538 approximately

i = 166.15 degrees is the approximate measure of each interior angle.

Side note: The formula to determine the interior angle i only works for regular polygons. This is because each angle is the same measure.

Answer:

See below

Step-by-step explanation:

129 500     original price

selling price =   2 ( 129 500) - 9000 = 250 000

% change   Questions worded like this are often up for debate as to exactly answer the question

250 000 / 129 500 =  193 %      Selling price was 193% of original price

(250 000 - 129500)/ 129500 =   93 % INCREASE

Answer: 7

Step-by-step explanation:

As tangents drawn from a common external point to a circle are congruent,

Answer:

Step-by-step explanation:

Answer: SAS

Step-by-step explanation:

Since [tex]\frac{BC}{CD}=\frac{AC}{CE}=\frac{1}{2}[/tex], and [tex]\angle ACB \cong \angle DCE[/tex] because they are vertical angles, the triangles are similar by SAS

Answer:

0

Step-by-step explanation:0 times anything is still 0

[tex] {x}^{2} + 5x + 6 = 0 \\ \\ {x}^{2} + 2x + 3x + 6 = 0 \\ \\ x(x + 2) + 3(x + 2) = 0 \\ \\ (x + 2)(x + 3) = 0 \\ \\ x + 2 = 0 \\ \\ x = - 2 \\ \\ x + 3 = 0 \\ \\ x = - 3.[/tex]

The value of x = -2 and -3 .

Answer:

hope it helps...

it has both co ordinate and factorization

The equation for the red graph is f(x)=-x^2.

The question is an incomplete graph of a function is missing

For a complete question refer to the graph attached below

we have [tex]g(x)=4-x^2[/tex]

The vertex of the function g(x) is the point (0,4)

The vertex of the function f(x) is the point (0,0)

This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

So, the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

The translation is 4 units down

The equation of the function f(x) is

[tex]f(x)=g(x)-4[/tex]

[tex]f(x)=(4-x^2)-4[/tex]

[tex]f(x)=-x^2[/tex]

Therefore, The answer is f(x)=-x^2

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Here, the surface area, in square units, of the triangular prism is 152 units².

We know that the area of any triangle can be calculated as

Area = 1/2 * base * height

The area of any rectangular figure can be calculated as

Area = length * width

Here, the length of the rectangular portion of the prism is 8 units.

The width of the lowermost rectangle is 5 units.

The area of the uppermost rectangle = the area of the lowermost rectangle = 8 * 5 units² = 40 units²

Again the width of the middle rectangle is 6 units.

So, the area of the middle rectangle = 6 * 8 units² = 48 units²

Now, the height and base of the triangles are 4 and 6 respectively.

So, the area of the left-hand side triangle = the area of the right-hand side triangle = 2 * (1/2) * 4 * (6/2) units² = 1 * 4 * 3 units² = 12 units²

Then the area of the triangular prism = area of rectangular portion + area of triangular portion = (2 * 40 + 48) + (2 * 12) units² = (80 + 48) + 24 units² = 128 + 24 units² = 152 units²

Therefore the surface area, in square units, of the triangular prism is 152 units². So, Option C is correct.

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The probability that the sample mean would be less than 40.6 dollars will be 0.534.

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is given as

z = (x – μ) / σ

The mean cost of a five pound bag of shrimp is 40 dollars, with a standard deviation of 7 dollars.

If a sample of 51 bags of shrimp is randomly selected.

Then the probability that the sample mean would be less than 40.6 dollars will be

z = (40.6 – 40) / 7

z = 0.0857

Then the p-value will be

P(x < 40.6) = P(z < 0.0857)

P(x < 40.6) = 0.534

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A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.

Example: The formula for finding the volume of a box is:

x = 2y - 7 Formula (relating x and y)

a2 + b2 = c2 Formula (relating a, b and c)

Answer:

50 people are working in the office

Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)

Step-by-step explanation:

Reflecting over y = x maps (x,y) onto (y,x).

[tex]DE=\sqrt{13^{2}+12^{2}-2(13)(12)(\cos 59^{\circ})} \approx \boxed{12.3}[/tex]

The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

A function is a type of relation, or rule, that maps one input to a specific single output.

Given

Base salary = $2500 per month

Commision = 3% on Sales over 48000

Determine the function s(x) for sales over $48000

Let's Represent the total sales in a month with s.

So, the function s(x) is:

s(x)  = Base Amount + Commission x Sales over $48000

s(x) = 2500  + 3% (s - 48000)

s(x) = 2500  + 0.03(s - 48000)

s(x) = 2500  + 0.03s - 1440

s(x) = 0.03s - 1060

Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

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Answer:

z = -2

Step-by-step explanation:

Answer:

[tex]\boxed{\bf z = - 2}[/tex]

Step-by-step explanation:

[tex]\bf 6z + 10 = - 2[/tex]

Subtract 10 from both sides.

Simplify.

Divide both sides by 6.

Simplify.

_________________________

Answer:

=8x+14 or

=16x²+56x+49

[tex]\bf{(4x+7)2 }[/tex]

[tex]\bf{=2(4x+7)}[/tex]

[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]

[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]

[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]

Answer:

(0, 7/12)

Step-by-step explanation:

to find the y intercept we equate x to 0.

hence,

f(0) = 7/12

the coordinate is (0, 7/12)

Answer:

[tex](0,\frac{7}{12})[/tex]

Step-by-step explanation:

In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.

[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]

Simplify:

[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]

Therefore, the y-intercept for the equation is:

[tex]\frac{7}{14}[/tex]

basically you treat y like a number and not a variable

Answer:

a is 4

b is 2y

c is -10y²+9

discriminant is 4(41y²-36)

Step-by-step explanation:

4x²+2xy-10y²+9=0

rewrite in standard form of a quadratic equation like ax² + bx + c = 0

4x²+2yx-10y²+9=0

basically you treat y like a number and not a variable

a is the number with the x²

right away we know a is 4 because of 4x²

b is the one with x so in this formula b is 2y

c is the number without the x which in this case is -10y²+9

discriminant is

b² - 4ac

(2y)²- (4)(4)(-10y²+9)

4y²-(16)(-10y²+9)

4y²-(16)(-10y²+9)

4y²+160y²-144

164y²-144 =

4(41y²-36)

The angle θ to the diameter that she should row is; θ = 56.44°

It should be noted that;

a = 90° - θ. Thus;

b = 2θ

For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .

The time required to walk this distance is given by;

t_w = 4θ/5 = 0.8θ

The distance rowed is given by: cos θ = d_r/2.4

d_r = 2.4cos θ while the time needed for it is;

t_r = 2.4cos θ/3.5

t_r = 0.6857θ

Thus, total time is;

T(θ) = t_r + t_w

T(θ) = 0.6857θ + 0.8θ

T(θ) = 1.4857θ

Now we need the critical numbers:

T'(θ) = 1 - 1.2 sin θ

At T'(θ) = 0, we have;

1 - 1.2 sin θ = 0

1/1.2 = sin θ

θ = sin⁻¹(1/1.2)

θ = 56.44°

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