The graph below shows a system of equations:

Draw a line labeled y equals 2x minus 5 by joining the ordered pairs 0, negative 5 and 4, 3. Draw a line labeled y equals negative x minus 2 by joining the ordered pairs negative 3,1 and 3, negative 5

The x-coordinate of the solution to the system of equations is __________.

Answer:

Option A is correct

2x-9

Step-by-step explanation:

Given the functions:

f(x) = 2x + 3

g(x) = x -6

We have to find  [f o g](x).

[tex][fog](x) = f[g(x)][/tex]

Substitute the function g(x),

[tex][fog](x) = f[x-6][/tex]

Replace the value of x with x-6 in f(x) we have;

[tex][fog](x) =2(x-6)+3[/tex]

⇒[tex][fog](x) =2x-12+3[/tex]

⇒[tex][fog](x) =2x-9[/tex]

Therefore, the value of [tex][fog](x)[/tex] is, 2x-9

Answer: 16 pieces

Step-by-step explanation:

To get the number of pieces, we simply divide 12 1/3 by 3/4

12 1/3 ÷ 3/4

but 12 1/3 = 37/ 4 ( converting to improper fraction)

12 1/3 ÷ 3/4

=37/ 3 ÷ 3/4

= 37/3 × 4/3

= 148/9

= 16. 44444

= 16 approximately

Therefore we can get 16 pieces of yard from the cloth

Answer: [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]

Step-by-step explanation:

Given problem to simplify is [tex]\frac{\frac{15xy^2}{x^2-5x+6} }{\frac{5x^2y}{2x^2-7x+3} } \\\\=\frac{15xy^2}{x^2-5x+6}\cdot\ \frac{2x^2-7x+3} {5x^2y}............\text{(by fractional division property,the denominator invert and its reciprocal multiply to numerator)}\\\\=\frac{15xy^2}{(x-3)(x-2)}\cdot\frac{(x-3)(2x-1)} {5x^2y}.........\ \text{(factorizing quadratic equation)}[/tex]

[tex]=\frac{3y(2x-1)}{x(x-2)}........\text{(cancelling like terms with same degree and coefficients from numerator and denominator)}[/tex]

so the simplified form of the given problem is [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]

Answer:

the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Step-by-step explanation:

          [tex](y-y_1)=m(x_2-x_1)[/tex]

We can easily take two points from given graphs are

(2,5) and (6,7)

The slope of line is;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-5}{6-2}[/tex]

[tex]m=\frac{2}{4}[/tex]

[tex]m=\frac{1}{2}[/tex]

the slope of line is [tex]\frac{1}{2}[/tex]

Now, find the equation of line with the  slope-intercept form

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-5)=\frac{1}{2}(x-2)[/tex]

Add both the sides by 5 in above expression,

[tex]y=\frac{1}{2}(x-2)+5[/tex]

[tex]y=\frac{x}{2}-1+5[/tex]

[tex]y=\frac{x}{2}+4[/tex]

Therefore, the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Answer:

$450

Step-by-step explanation:

2x+78=978

2x=900     [subtract 78 from both sides]

x=450        [divide both sides by 2]

A.

got it right on my test, flvs

Answer:

6 and 1 over 2 ÷ 1 over 4

Step-by-step explanation:

Given,

The total cups in a recipe =  6 and 1 over 2 cups

[tex]=6\frac{1}{2}\text{ cups}[/tex]

Also, the cups in each serving =  1 over 4 cup

[tex]=\frac{1}{4}\text{ cups}[/tex]

Hence, the number of servings = [tex]\frac{\text{total cups in a recipe}}{\text{cups in each serving}}[/tex]

[tex]=\frac{6\frac{1}{2}}{\frac{1}{4}}[/tex]

= 6 and 1 over 2 ÷ 1 over 4

Second option is correct.

Final answer:

To find the area of a square, we use the formula A = s², where A represents the area and s represents the length of a side. Evaluating the options, the area that could not be Jaime's square is C. 50cm².

Explanation:

To find the area of a square, we need to multiply the length of one side by itself. So, the formula for the area of a square is A = s², where A represents the area and s represents the length of a side. We can evaluate the given options using this formula:

Therefore, the answer is C. 50cm².

We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.

Given:

51 degrees.

Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.

180 – 51 – 90 = 39 degrees

39 degrees * 2 = 78 degrees.

Angle Q is 78 degrees.

In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.

We will use the formula:

Sine theta = opposite / hypotenuse

Sin(78 deg) = opposite / 4.3

Sin(78 deg) * 4.3 = opposite

4.21 = opposite. This is also the height of the triangle.

Area of a triangle = ½ * base * height

A = ½ * 3units * 4.21units

A = 6.315 square units.

Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given trinomial is  x² - 5x - 36

Now we have to factorize the given polynomial.

x² - 9x +4x - 36

x(x-9)+4(x-9)

(x+4)(x-9)

The factorial form of the trinomial  x² - 5x - 36 is (x+4)(x-9)

So x+4 is the binomial factor of the given trinomial.

Hence, Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

To learn more on Polynomials click:

https://brainly.com/question/11536910

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A point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

An angle bisector is a straight line drawn from the vertex of a triangle to its opposite side in such a way, that it divides the angle into two equal or congruent angles.

For the given situation,

Any point that is on the angle bisector is an equal distance ("equidistant") from the two sides of the angle.

A point which is always equidistant from all the sides is the point of intersection of internal angle bisectors.

Hence we can conclude that a point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

Learn more about angle bisector theorem here

https://brainly.com/question/10433817

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Final answer:

The converse of the given conditional statement 'if x=12 then 2x-5=19' is 'if 2x-5=19, then x=12'. To verify its truth, we solve for x when 2x-5 equals 19, resulting in x equaling 12, thus showing that in this instance, the converse is true.

Explanation:

The converse of a conditional statement is formed by swapping the hypothesis and the conclusion of the original statement. For the statement 'if x=12 then 2x-5=19', its converse would be 'if 2x-5=19, then x=12'. To test the validity of the converse, we substitute the value of x back into the equation 2x-5 and check if it equals 19 when x=12.

However, we need to be cautious because the converse of a true conditional statement is not always true. To determine the truth of the converse, one must check if every instance where 2x-5 equals 19 also means that x must be equal to 12. If there is even a single case where 2x-5 is 19 and x is not 12, then the converse is not true.

For instance, let's test the converse: If we solve the equation 2x-5=19 for x, we get:

x = (19+5)/2

x = 24/2

x = 12

Therefore, for this specific case, the original statement and the converse are both true.

there are 4 quarters to 1 hour

3 1/6 x 4 =

19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour

Answer:- The average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].

Explanation:-

Given: Distance traveled by Harvey [tex]=3\frac{1}{6}\ km=\frac{19}{6}\ km[/tex]

Time taken[tex]=\frac{1}{4}\ hour[/tex]

[tex]Speed=\frac{Distance}{Time}\\\Rightarrow\ Speed=\frac{\frac{19}{6}}{\frac{1}{4}}\\\\=\frac{19\times4}{6}\\\\=\frac{38}{ 3}\\\\=12\frac{2}{3}\ km/hour[/tex]

Therefore, the average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].

8 x 12 = 96

136-96 =40

40/4 = 10

 each girl averages 10 points