Spiral Review

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15. Roberto paid $35. 75 for dinner at a restaurant, plus an additional $7. 15

tip. What percent of the bill did he pay as a tip? Round to the nearest

percent, if necessary.

The area of the triangular plot of land from the vertices is 20 square units

From the question, we have the following parameters that can be used in our computation:

A(1,5), B(7,5), and C(8,0)

Represent the vertices properly

So, we have the following representation

A = (1,5)

B = (7,5)

C = (8,0)

The area of the triangle is calculated from the vertices using the following equation

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|

Evaluate the sum of products

Area = 0.5 * |40|

Remove the absolute bracket

Area = 0.5 * 40

Evaluate

Area = 20

Hence, the area of ABC with vertices is 20 square units

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Complete question

The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)

Calculate the area.

Answer:

13X

Step-by-step explanation:

if I am correct I added 6+7 then add X to it.

Answer:

∠ 1 = 37°

Step-by-step explanation:

(9x - 8) and (6x + 7) are corresponding angles and are congruent, then

9x - 8 = 6x + 7 ( subtract 6x from both sides )

3x - 8 = 7 ( add 8 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

∠ 1 = 6x + 7 = 6(5) + 7 = 30 + 7 = 37°

The class has a 45-minute, or 0.75-hour, climb to the summit planned to observe a nearby monument. The bus driver intended to travel at a steady 40 mph. Accordingly, the average speed is 0.888.

The time required to travel 20 miles at 40 mph is 30 minutes, and the time required to go 40 miles is 60 minutes. The journey of 60 miles will therefore take 90 minutes. In most cases, an hour's worth of time, this will tell you the average speed.

As a result, Ben's average speed was 50 miles per hour when he covered 150 miles in 3 hours. 40m in an hour. 12 hour to cover 20 miles. In fifteen minutes, ten miles. It is determined by dividing something's total travel distance by its total journey time. Take the earlier automobile, for instance. The average speed of the vehicle would be 70 / 2 = 35 miles per hour if it covered 70 miles in two hours.

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Complete question is: Hassan's history class is taking a field trip to the state capitol building. The capitol building is 50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to view a local monument. The bus driver plans to drive at an average speed of 40 miles per hour. Which equation can you use to find how many hours, x, the second part of the trip will take?

Answer: The value of p and q for which the system of equations represent coincident lines is p = 2 and q = 1.

Step-by-step explanation: To represent coincident lines, the two lines must be proportional. Therefore, the slope of the second line must be equal to the slope of the first line.

The slope of the first line is 3/2. The slope of the second line is p + 2q + 2/p + q + 1. Therefore, we set these two equal:

3/2 = p + 2q + 2/p + q + 1.

Cross multiplying, we get:

3(p + q + 1) = 2(p + 2q + 2).

Simplifying, we get:

3p + 3q + 3 = 2p + 4q + 4.

Combining like terms, we get:

p - q = 1.

Therefore, the value of p and q for which the system of equations represents coincident lines is p = 2 and q = 1.

Answer:

73%

Step-by-step explanation:

Answer: False

The estimated points can be found first by counting on the x-axis then the y-axis. Negative numbers are to be counted downward on the y-axis, positive numbers are to be counted upwards on the y-axis. Negative numbers are to be counted to the left of the x-axis, positive numbers are to be counted to the right of the x-axis

Answer:

7.5

Step-by-step explanation:

You didn't list the right answer choices. But I think 7.5 is the answer.

Answer:

a=15

Step-by-step explanation:

Answer:

x=42.5

Step-by-step explanation:

First, start by setting up the equation

these are both same side interior angles, so they both add up to 180

(3x+10) + x = 180

4x+10 =180

subtract both sides by 10

    -10    -10

4x=170

divide both sides by 4

x=42.5

Answer:

16-7x

Step-by-step explanation:

10x-3x+7-6-4x+5

16-7x

Note:

Ortho centre :a point of intersection of altitudes of a triangle meets the opposite angle.

Given:

For Orthocentre:.

A(1, 2), B(2, 6), C(3,-4). are vertices of a triangle:

Slope of AB[m1]=[tex] \frac{6-2}{2-1} [/tex]=4

Since it is perpendicular to CX.

slope of CX=m2

we have for slope of perpendicular

m1m2=-1

m2=-¼

It passes through the point C(3,-4)

equation of line CX becomes;

(y-y1)=m(x-x1)

y+4=-¼(x-3)

4y+16=-x+3

x+4y+16-3=0

x+4y+13=0........[1]

again:

Slope of AC[m1]=[tex] \frac{-4-2}{3-1} [/tex]=-3

Since it is perpendicular to BY

slope of BY=m2

we have for slope of perpendicular

m1m2=-1

m2=⅓

It passes through the point B(2,6)

equation of line BY becomes;

(y-y1)=m(x-x1)

y-6=⅓(x-2)

3y-18=x-2

x-3y+18-2=0

x-3y+16=0.........[2]

Subtracting equation 1&2.

x+4y+13=0

x-3y+16=0

-__________

7y-3=0

y=[tex] \frac{3}{7} [/tex]

again

Substituting value of y in equation 1.

x+4*[tex] \frac{3}{7} [/tex]+13=0

x=-13-[tex] \frac{12}{7} [/tex]

x=[tex] \frac{-103}{7} [/tex]=-14[tex] \frac{5}{7} [/tex]

So

orthocenter is (-14[tex] \frac{5}{7} [/tex],[tex] \frac{3}{7}[/tex])

Circumcentre: a point of intersection of perpendicular bisector of the triangle.

Now

X,Y and Z are the midpoint of AB,AC and BC respectively.

X(a,b)=([tex] \frac{2+1}{2} [/tex],[tex] \frac{2+6}{2} [/tex])=

([tex] \frac{3}{2} [/tex],4)

Slope of AB=4

Slope of OX=-¼

Equation of line OX passes through ([tex] \frac{3}{2} [/tex],4)is

y-4=-¼(x-[tex] \frac{3}{2} [/tex])

4y-16=-x+[tex] \frac{3}{2} [/tex]

8y-16*2=-2x+3

2x+8y=3+32

2x+8y=35

x+4y=[tex] \frac{35}{2} [/tex]........[1]

again

Y(c,d)=([tex] \frac{3+1}{2} [/tex],[tex] \frac{-4+2}{2} [/tex]=(2,-1)

Slope of AC:-3

Slope of OY=⅓

Equation of line OY passes through (2,-1) is

y+1=⅓(x-2)

3y+3=x-2

x-3y=3+2

x-3y=5......[2]

Multiplying equation 2 by 3 and

Subtracting equation 1&2.

x+4y=35/2

x-3y=5

-_______

7y=[tex] \frac{25}{2} [/tex]

y=[tex] \frac{25}{14} [/tex]

Substituting value of y in equation 2.

x-3*[tex] \frac{25}{14} [/tex]=5

x=5+[tex] \frac{75}{14} [/tex]

x=[tex] \frac{145}{14} [/tex]

x=10[tex] \frac{5}{14} [/tex]

circumcenter of a triangle: (10[tex] \frac{5}{14} [/tex],1[tex] \frac{11}{14} [/tex])

Answer:

PLEASE DONT DELETE

Step-by-step explanation:

I am sorry that I cant answer your problem. However, I am only answering so I can get answers to my own problems. Good luck on that problem!

Answer:

i'm not to sure but i think its all no

Step-by-step explanation:

The value of x of point C is 4. The coordinate of C is (4,-1).

What is the coordinate of a point?

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.

The distance between points A and B is 4 units.

The opposite sides of a parallelogram are equal and parallel.

To make parallelogram, the point C lies on the left side of point D.

The distance between point C and D must be 4 unit.

The coordinates of C is (4,-1).

The x value of point C is 4.

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If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.

In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.

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Answer:

pretty sure its 5

Step-by-step explanation:

For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3

An equation is used to show the relationship between numbers and variables.

Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division

The degree is the highest exponent of variable for the polynomial. The polynomial with degree of 2 is known as a quadratic polynomial

Given the polynomial:

9, 3x², 8x

Writing in standard form is done by rearranging from highest exponent of variable to least. This is:

3x², 8x, 9

Hence the degree is 2 and the leading coefficient is 3

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Answer:

1,792 c = 112 gal.

Step-by-step explanation:

Because their 16 cups in 1 gallon, we will divide 1,793 by 16 and we get 112.  Therefore, 112 is our answer.

Answer:

112 gallons

Step-by-step explanation:

there are 16 cups in 1 gallon

1=16

?=1792

to solve this, divide 1792 by 16 to get 112 gallons

112*16 is 1792

Domain: all the real numbers  

Range: y ≤ 9/5

i hope u can see the attached graph! :)

Answer:

a)

Step-by-step explanation:

vertex is at (-0.4, 1.8) so range must be less than or equal to 1.8

Yes, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

Congruent refers to things that are exactly the same size and shape.

For the stated question-

The following are the steps:

Thus, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

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Answer:

3x([tex]y^{4}[/tex]+2)-9

hope this helps :DDDDD

Using PEDMAS to solve the mathematical expression given, the value is 2

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is an acronym used to remember the order of operations in math problems. It is also sometimes referred to as Order of Operations.

In this problem, we will need to use and apply the rules of PEMDAS.

We will need to break this into different components and then bring them together afterwards.

[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3(1/3)] + [6(3/4) + 5(1/2)] / [(26 ÷ 3(5/7)] - 0.05

This becomes ;

[10.2 / 34] + [12.25 / 7] - 0.005

We can further resolve this into

2.05 - 0.005

And then we just subtract the values from one another

2.05 - 0.005 = 2

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Answer:

Sabemos que una función lineal es de la forma:

f(x) = m*x

Mientras que una funcion afin es de la forma:

g(x) = m*x + n

Entonces para reconocer si una función es lineal o afín, simplemente debemos ver si tenemos un término constante o no (un término constante es un término que no está siendo multiplicado por la variable x).

a) y = -5*x

No tenemos término constante, entonces es una función lineal.

b) y = -3*x - 2

Acá tenemos un término constante igual a -2, entonces esto es una función afín.

c) y = 2*x + 4

Acá tenemos un término constante igual a 4, entonces esto es una función afín.

d) y = (1/4)*x - 2

Acá tenemos un término constante igual a -2, entonces esto es una función afín.

Answer:

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.

Answer:

all negative numbers

Step-by-step explanation:

Answer: D

Step-by-step explanation:

In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.

Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.

This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.

The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.

The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.

The domain of a function refers to the interval of the x values of the function.

In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.

To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.

The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.

Thus, the correct answer is option D, {x | −3 < x < 3}.

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Answer:

Do you have a ruler?

Step-by-step explanation:

Answer:

the answer is (a) x² - 2hx + h²

Step-by-step explanation:

(x-h)² = (x-h)(x-h) = x(x-h)-h(x-h)

x² - hx -hx + h²

= x² - 2hx + h²

Answer:

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

Use the identity:

Substitute a = x, b = h to get:

This is the option A.