Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)
step 1
Find the slope
m=(8+5)/(3-7)
m=13/-4
m=-13/4
step 2
write the equation in point slope form
so
y-y1=m(x-x1)
we take the point (7,-5)
substitute
y+5=-(13/4)(x-7)If you take the point (3,8)
we have
y-8=-(13/4)(x-3)Convert decimal to 0.147 to fraction ( the last digit 7 repeating)
Answer:
133/900
Explanation:
To convert the decimal 0.147777 to a fraction, we first identify the decimal part, so we have 147 as a decimal part.
Then, we subtract 14 because that part is not repeating. So:
147 - 14 = 133
Now, we need to divide by 9 to get the repeating part, but the repeating part starts at the third decimal place, so we will divide by 900 instead of 9.
Therefore, 0.147777... as a decimal is:
[tex]0.14777\ldots=\frac{133}{900}[/tex]So, the answer is 133/900
Use the point-slope formula to write an equation of the line that passes through (- 1, 4) and (1, 5 ) .Write the answer in slope-intercept form (if possible).The equation of the line is Hi everyone, this is very hard for me I have tried 18 times by myself before I found you folks .I need this in the simplest terms as i don't get it if it is too involved .
To solve this problem, we will compute the slope of the line and then we will use it to find the equation of the line.
To determine the slope of a line that passes through points (x₁,y₁), and (x₂,y₂), we can use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]Substituting
[tex]\begin{gathered} (x_2,y_2)=(-1,4), \\ (x_1,y_1)=(1,5), \end{gathered}[/tex]in the above formula, we get:
[tex]s=\frac{4-5}{-1-1}=\frac{-1}{-2}=\frac{1}{2}.[/tex]Now, with the above slope, we use the following formula for the equation of a line with slope m:
[tex]y-y_1=m(x-x_1).[/tex]Finally, we substitute one of the points:
[tex]y-5=\frac{1}{2}(x-1)[/tex]and take the equation to its slope-intercept form:
[tex]\begin{gathered} y-5=\frac{1}{2}(x-1), \\ y-5=\frac{1}{2}x-\frac{1}{2}, \\ y=\frac{1}{2}x+\frac{9}{2}. \end{gathered}[/tex]Answer: [tex]y=\frac{1}{2}x+\frac{9}{2}=0.5x+4.5.[/tex]a triangular lot is 130 ft on one side and has a property line of length 700 ft. Find the area of the lot in acres.
Area of the lot = 1.03 acres
Explanations:The line length of the triangular lot = 700 ft
The height of the triangular lot = 130 ft
Note:
Area of a triangle = 0.5 x base x height
Calculate the base of the triangular lot using the Pythagora's theorem
[tex]\begin{gathered} \text{Length}^2=Height^2+Base^2 \\ 700^2=130^2+Base^2 \\ \text{Base}^2=700^2-130^2 \\ \text{Base}^2\text{ = }490000\text{ - }16900 \\ \text{Base}^2\text{ = }473100 \\ \text{Base = }\sqrt[]{473100} \\ \text{Base = }687.82 \end{gathered}[/tex]The base of the triangular lot = 687.82 ft
Area of the triangular lot = 0.5 x 687.82 x 130
Area of the triangular lot = 44708.3 ft²
NB
1 ft² = 2.3 x 10^(-5) Acres
44708.3 ft² = 44708.3 x 2.3 x 10^(-5)
44708.3 ft² = 1.03 acres
Therefore:
Area of the lot = 1.03 acres
Which of the following are rational numbers?A) 42/91B) 10.27C) 8.14 D) 0
It's important to know that a rational number can be expressed as fractions, but also when they are expressed as decimals, the decimal part repeats infinitely, that is, it has a pattern or finite decimal digits.
Having said that, we can deduct that all the answer choices are rational numbers.what is the value of x of the perimeter of the following figure is 30 miles?
The Solution:
Given:
We are required to find the value of x if the perimeter is 30 miles.
[tex]Perimeter=2(3x-8)+2(6x+5)=6x-16+12x+10=30[/tex][tex]\begin{gathered} 6x+12x-6=30 \\ \\ 18x=30+6 \\ \\ 18x=36 \end{gathered}[/tex]Divide both sides by 18.
[tex]\begin{gathered} x=\frac{36}{18}=2 \\ \\ x=2 \end{gathered}[/tex]Therefore, the correct answer is 2.
PLEASE HELP I JUST NEED TO KNOW THE POINTS AND HOW THE GRAPH LOOKS LIKE
You have the following function:
[tex]g(x)=2x^2-4x-16[/tex]the x coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]in this case, a = 2 and b = -4. Replace these values into the previous expression and simplify:
[tex]x=-\frac{-4}{2(2)}=1[/tex]next, replace the previous values of x into the function g(x):
[tex]\begin{gathered} g(1)=2(1)^2-4(1)-16 \\ g(1)=-18 \end{gathered}[/tex]then, the vertex is (1,-18)
In order to graph, calculate another point for any value of x, for instance, for x = 0:
g(0) = 2(0)^2 - 4(0) - 16
What are inequality? When do we use inequalities?What type of inequalities are there? Which symbols are used for each type?Are the following expressions variable inequalities? Why?a. 13z=27b. x<0c 3x+5x>11d. y+5≤11e. 7-1>- 32
Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.
The type of inequalities and symbols are:
[tex]<,>,\leq,\ge[/tex]So, there are four types of inequalities, for example:
[tex]\begin{gathered} x<2 \\ x>2 \\ x\leq2 \\ x\ge2 \end{gathered}[/tex]Each inequality is different from the other, this means that the symbol used represents a type of inequality.
At last, among the choices, the inequalities are
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \\ 7-1>-32 \end{gathered}[/tex]However, variable inequalities mean that the inequalities must have a variable in it. So, they are:
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \end{gathered}[/tex]Therefore, the variable inequalities are b, c, and d.
PLEASE HELP!!
Write an equation of a quadratic function with the given properties: f(3)=f(-5)=0; f(-6)=-36
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
Given,
f(3) = f(-5) = 0;
f(-6) = -36
Here,
The x intercepts of the quadratic equation are;
x₁ = 3 , x₂ = -5
The quadratic equation in factored form is equal to
f(x) = a(x - x₁) (x - x₂)
Substitute x₁ = 3 , x₂ = -5 in f(x)
Then,
f(x) = a(x - 3) (x - -5)
f(x) = a(x - 3) (x + 5)
We have;
f(-6) = -36
That is, if x = -6 then f(x) = -36
So,
f(x) = a(x - 3) (x + 5)
-6 = a(-36 - 3) (-36 + 5)
-6 = a x - 39 x - 31
-6 = 1029a
a = -1029/6
a = -201.5
Here,
f(x) = -201.5(x - 3) (x + 5)
Apply distributive property;
f(x) = -201.5(x² +5x - 3x - 15)
f(x) = -201.5 (x² +2x - 15)
That is,
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
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What is the value of the expression below when w = 3?5W^2 – 5W – 8
According to the given data we have the following expression:
5W^2 – 5W – 8
In order to calculate the value of the expression above when w=3 we would need to substitute the w with 3 and then calculate the expression.
So, if w=3 then:
5(3)^2 -5(3) -8
=45 - 15 -8
=22
The value of 5W^2 – 5W – 8 when w = 3 would be 22
Find the volume of a cone. Round your answer to the nearest wholenumber.7 ft4 ft
Answer:
117 cubic feet
Explanation:
From the diagram:
• The radius of the cone, r = 4 ft
,• The perpendicular height, h = 7 ft
[tex]\text{Volume of a cone=}\frac{1}{3}\pi r^2h[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times4^2\times7 \\ =117.2ft^3 \\ \approx117\; ft^3 \end{gathered}[/tex]The volume of a cone is 117 cubic feet (to the nearest whole number).
Look at the first Model It. In the first place-value chart, why is the thousandths column for the decimal 5.67 empty?
The thousandths column for the decimal 5.67 is empty because there's no thousandth value in the decimal.
What is a place value?Place value is the value provided by a digit in a number based on its place in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. Place value is the value provided by a digit in a number based on its place in the number.
In this case, the decimal that's given is illustrated as 5.67. It should be noted that 6 is the tenths value and 7 is the hundredth value. Therefore, there is no thousandth value. This is why it's empty.
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A rock has a mass of 14 g and a volume of 2 cm3. What is the density of the rock? *
We will determine the density of the rock as follows:
[tex]\rho=\frac{14g}{2cm^3}\Rightarrow\rho=7g/cm^3[/tex]So, the density of the rock is 7 g/cm^3.
15. The new county park is one mile square. What would be the length of a road around its boundaries?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
County park:
area = 1 mile²
Step 02:
length of a road around:
area = side²
1 mile ² = s²
[tex]\begin{gathered} s^2=1 \\ s=\sqrt[]{1}=\text{ 1 } \end{gathered}[/tex]s = 1 mile
perimeter = 4 s = 4 * 1 mile = 4 miles
The answer is:
the length of a road around its boundaries is 4 miles
The coordinate pairs for triangle ABC are A(1,2), B(4,5), C(2,2). It undergoes a translation of 2 units right and 1 unit 1 up. Write down the coordinates of A'
We will have the transformation rule (x, y) -> (x+2, y+1)
Then, for A' we will have:
A'(3, 3)
B'(6, 6)
C'(4, 3)
Vincent turned his head 30° to the side. Which of the following shows the angle that he turned his head?
Given data:
Vincent turned his head 30° to the side.
The figure in the option b is the angle that he turned his head.
solve for y. 2x-y=12
Answer:
2x - 12 = y
Step-by-step explanation:
→ Add y to both sides
2x = 12 + y
→ Minus 12 from both sides
2x - 12 = y
You need a shelf for a small space in your house, so you make a measurement with your meter stick and head to the store. Once there, you find that the dimension of the shelves you want is given in cm.If your space measured 0.9 m, and the shelves at the store measure 30 cm, answer the following questions:1) How many meters wide is the shelf you want to buy?
We will have the following:
[tex]0.9m=90cm[/tex]So, the number of shelves you need is 3.
Thus, the shelves you can buy are 0.3 m long each.
A bag contains 8 red marbles, 2 blue marbles, 5 white marbles, and 7 black marbles. What is the probability of randomly selecting:A white marble:A red marble:A red marble, white or blue marble: A black marble: A green marble:
Translate to an algebraic expression Twice "a"The translation is ...
Okay, here we have this:
Considering that twice an amount generally indicates taking two of the things in question; generally this indicates multiplying by 2.
This mean that if we have "twice a" when transferring it to an algebraic expression we obtain: 2a.
NO LINKS!! Show all work where necessary to get full credit Part 2
21. Circle R
A circle is named using its center.22. RV
A radius connects the center to a point on the circle.23. ZV
A chord connects two points on the circle.24. TX
A diameter passes through the center of the circle and connects two points on the circle.25. RV
See 22 and 24.26. 4 feet
The diameter is twice the radius, 2(2)=4.Answer:
21. R
22. RU
23. VZ
24. BE
25. RU
26. 4 feet
Step-by-step explanation:
Question 21
A circle is named by its center.
Therefore the name of the given circle is R.
Question 22
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
RZ, RT, RU, RV, RW and RX.Question 23
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
WZ, TX and VZ.Question 24
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameters of the given circle are:
TX and WZ.Question 25
As the diameters are TX and WZ, they contain the radii RZ, RT, RW and RX.
Therefore, the radii that are not contained in the diameter is:
RU and RV.Question 26
The diameter is twice the length of the radius.
Therefore, if the radius of the circle is 2 feet:
⇒ Diameter = 2 × 2 = 4 feet.
There are 16 appetizers available at a restaurant. From these, Pablo is to choose 12 for his party. How many groups of 12 appetizers are possible?
EXPLANATION
This is a combinatory, as there are 12 groups, the combinatory will be as follows:
16C12 = 16!/[12!*(16-12)!] = 1820
In conclusion, there will be 1820 possible groups of 12 appetizers.
DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: An odd number on each of the last two rolls Event B: An even number on the last roll Event C: An even number on the last roll or the second roll (or both) Explanation Check 000 0 0 OOE EEE O Outcomes OEO 0 0 EOO EEO EOE OEE 0 0 Probability 0 0 0 00 음 0/5 X Nikida V Españe
Event A:
The event A occurs when an odd number is rolled in the second roll and in the third roll. We can see in the table that the outcomes that correspond with this event are:
OOO
EOO
Now to calculate the probability, we need to divide the number of favorable outcomes by the number of total outcomes. There are 8 possible outcomes, and the favorable outcomes for event A are 2. Thus:
[tex]P(A)=\frac{2}{8}=\frac{1}{4}[/tex]Event B:
In event B we want the last roll to be even. Then, the outcomes corresponding to this event are:
OOE
EEE
EOE
OEE
The number of favorable outcomes is 4, the total outcome is 4:
[tex]P(B)=\frac{4}{8}=\frac{1}{2}[/tex]Event C:
Here, we are looking for outcomes with an even number in the second or last roll (or both). Thus the outcomes that satisfy this are:
OOE
EEE
OEO
EEO
EOE
OEE
The number of favorable outcomes is 6, and the number of total outcomes is 8:
[tex]P(C)=\frac{6}{8}=\frac{3}{4}[/tex]How to solve 11 3/7 × 7/10 =
Given:
The objective is to solve the given equation.
The given equation can be solved by,
[tex]\begin{gathered} =11(\frac{3}{7})\cdot\frac{7}{10} \\ =\frac{11\cdot3}{10} \\ =\frac{33}{10} \\ =3.3 \end{gathered}[/tex]Hence, the value of the equation is 3.3
The function c = 100+.30m represents the cost c (in dollars) of renting a car afterdriving m miles.How many miles would a customer have to drive for the cost to be $149.50?
149.5 = 100 + .30m
149.5 - 100 = .30m
49.5 = .30m
Divide both sides by 0.30
m = 49.5/0.3
m =165
Option D
28 * 81.5 can you help me
so the answer is 2282
Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 12 x − 9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list of points of form (x, y) separated by commas: It is OK to round your value(s) to to two decimal places.
Answer:
it is C) find the coordinated of two x intercept is
Which is an equivalent expression for 4 times d raised
to the negative third power all over quantity 18 times d
raised to the ninth power end quantity?
Answer:
2d⁻³/9d⁻⁹
Step-by-step explanation:
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹
the equation as a quotient:
Expression = 4d⁻³/18d⁻⁹
Expression = 2d⁻³/9d⁻⁹
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
A line graph measuring time and amount of rain. The horizontal axis is labeled Time, hours, in intervals of 1 hour. The vertical axis is labeled Amount of rain, millimeters, in intervals of 1 millimeter. A line runs through coordinates 2 comma 5 and 4 comma 10.
It is to be noted that the slope of the line is 5/2. This means that 5 mm of rain falls every 2 hours. See the calculation below.
What is a slope in math?In general, the slope of a line indicates its gradient and direction. The slope of a straight line between two locations, say (x₁,y₁) and (x₂,y₂), may be simply calculated by subtracting the coordinates of the places. The slope is often denoted by the letter 'm.'
To find the slope of the line in the graph, we use the following equation:
m = [y₂ - y₁]/[x₂-x₁]
Where (x1,y1) = coordinates of the first point in the line; and
(x₂,y₂) = coordinates of the second point in the line
Given that the points (2, 5) from the graph is (x₁, y₁) and the point on graph (4, 10) are (x₂,y₂) Hence,
m = [10-5]/[4-2]
The slope (m) = 5/2
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Full Question:
This is the complete question and the described graph is attached
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement
The slope of the line is ___
This means that ___ mm of rain falls every ___
I don't understand this. Proving and applying ASA and Salad congruence
Given two triangles, we can say that they are congruent by the SAS postulate (Side Angle Side) if both triangles have two congruent sides and the angle that they form is also congruent
In this case, we have that triangle IHG and DFE have already two congruent sides, then, to make them congruent, the angle that they each form (angle IHG and angle DEF) must be congruent so we can use the SAS postulate
Type a counter example that would have to exist in order for the conclusion to be false.5>0,6> 0.12 > 0,16 > 0,20 > 0,100 > 0.Conclusion: All numbers are greater than 0.Counterexample: ?
Here, we want to give a counter example which would exist to make the conclusion wrong.
To do this, we have to get the values which are in actual terms lesser in value to zero. These values include the negative integers i.e negative whole numbers. On the number line, these values exist before zero, to the left handside of the number line.
Examples of these values include -5, -4 , -3 , -2 etc
So the counter example can be in the form;
-3 < 0 , -5 < 0 , -2 < 0
With these set of examples, we have made the conclusion false.
