Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
A ladder is 12 ft tall, and the base is 4 ft from the house. How high up thehouse does the ladder reach? Round to the nearest tenth of a foot.
ok
t = 12
b = 4
h = ?
[tex]\begin{gathered} \text{ 12}^2=4^2+h^2 \\ \text{ h}^2\text{ = 144 - 16} \\ \text{ h}^2\text{ = 128} \\ \text{ h = }\sqrt[]{128} \\ h\text{ = 11.3 ft} \end{gathered}[/tex]height = 11.3 ft
Consider the following equation of a parabola.y? + 4y = 8r + 4Step 1 of 3: Find the focus of the parabola.
Given the equation:
[tex]y^2+4y=8x+4[/tex]Let's find the focus of the parabola.
To find the focus of the parabola, let's first rewrite the equation in vertex form:
[tex]y=a(x-h)^2+k[/tex]We have:
[tex]undefined[/tex]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]after three tests, brandon has a test average of 90. after his fourth test, his average dropped to an 85. what did he score on his fourth test?
Answer:
70
Step-by-step explanation:
Average = Sum/Number of tests
90 = Sum/3 tests
Sum = 270
85 = 270 + test/4 tests
340 = 270 + test
70
classify given equation as rational or irrational:2 root 3 + 3 root 2 - 4 root 3 + 7 root 2
Irrational
Explanation
[tex]2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2}[/tex]
Step 1
simplify
[tex]\begin{gathered} 2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2} \\ \lparen2-4)\sqrt{3}+\left(3+7\right)\sqrt{2} \\ -2\sqrt{3}+4\sqrt{2} \\ \end{gathered}[/tex]Step 2
the square root of 2 is an irrational number,because there is not number such that
[tex]\sqrt{2}=\frac{a}{b}[/tex]and
The square root of 3 is an irrational number √3 cannot be expressed in the form of p/q
hence
the sum of 2 irrational numbers gives a irrational result,Sum of two irrational numbers is always irrational.
so, the answer is
Irrational
I hope this helps you
A truck carries 4 chairs and tables. The table weighs 35 pounds. The total weight of the chairs and tables is 63 pounds. How much does each chair weigh?
The weight of each chair is 7 pounds.
What is basic arithmetic?Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
Total weight = 63 pounds
Weight of the table = 35 pounds
Weight if 4 chairs = 63 - 35
= 28 pounds
Weight of one chair = 28/4
= 7 pounds
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please determine 8/12 - 3/8 =
8/12 -3/8=16/24-9/24=7/24
You should make like numbers then subtract
If you need to simplify at the end
A person invests $9000 at 3% interest compound annually for 4 years and then invests the balance (the $9000 plus the interest earned) in an account at 7% interest for 8 years. find the final value of the investment.
Answer:
$17,404.5
Explanation:
To calculate the balance after t years, we can use the following equation:
[tex]A=P(1+r)^t[/tex]Where P is the initial investment and r is the rate.
So, we can calculate the balance after 4 years, replacing t by 4, r by 3%, and P by $9000. Therefore the balance is:
[tex]\begin{gathered} A=9000(1+0.03)^4 \\ A=9000(1.126)_{} \\ A=10129.579 \end{gathered}[/tex]Now, we can use this quantity to calculate the final value of the investment. So, replacing P by 10129.579, r by 7%, and t by 8 years, we get:
[tex]\begin{gathered} A=10129.579(1+0.07)^8 \\ A=10129.579(1.718) \\ A=17404.503 \end{gathered}[/tex]Therefore, the final value of the investment is $17,404.5
question given below slove the following equations for r4al x and y .
S={(-24,7/3)}
1) When we're dealing with Complex Numbers we can rewrite this expression:
[tex](3+4i)^2-2(x-yi)=x+yi[/tex]Considering that their real and their imaginary parts can be taken as equal, so:
[tex]\begin{gathered} (3+4i)^2-2(x-yi)=x+yi \\ (3+4i)^2-2(x-iy) \\ 9+24i+16i^2+2x+2yi \\ \end{gathered}[/tex]2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:
[tex]\begin{gathered} 9+24i-16+2x+2yi \\ (-7-2x)+i(24+2y)\text{ = x+ iy} \\ \end{gathered}[/tex]Finally writing those two expressions as a System of equations we have:
[tex]\begin{gathered} \begin{cases}-7-2x=\text{ x} \\ 24+2y=y\end{cases} \\ -7-2x=x\Rightarrow-7=2x+x\Rightarrow3x=7\Rightarrow\frac{3x}{3}=\frac{7}{3} \\ 24+2y=y\Rightarrow24=-2y+y\Rightarrow-y=24\Rightarrow y=-24 \\ S=\mleft\lbrace(\frac{7}{3},-24)\mright\rbrace \end{gathered}[/tex]3) Hence, the answer is S={(-24,7/3)}
find the value of x for which r parallels s. then find the measures of angles 1 and 2 measure angle 1= 80-2xmeasure angle 2= 93-3xthe value of x for which r parallels s is....measure of angle 1 is.....°measure of angle 2 is.....°
Since the lines r and s are parallel the angles 1 and 2 must be equal
write an equation
[tex]80-2x=93-3x[/tex]solve the equation for x
[tex]\begin{gathered} 80-2x=93-3x \\ -2x+3x=93-80 \\ x=13 \end{gathered}[/tex]the value for x in which r and s are parallel must be 14
measure of angle 1 and 2 must be 54°
Find the slope of the line through the given points . If the slope of the line is undefined state so (13,1) and (1,4)
ANSWER:
A. The slope of the line is -1/4
STEP-BY-STEP EXPLANATION:
Given:
(13,1) and (1,4)
The slope can be calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute each value and calculate the slope:
[tex]m=\frac{1-4}{13-1}=\frac{-3}{12}=-\frac{1}{4}[/tex]Therefore, the correct answer would be:
A. The slope of the line is -1/4
image
Determine the value of x.
Question 17 options:
A)
x = 20°
B)
x = 45°
C)
x = 4.5°
D)
x = 90°
The value of the x in the rectangle is 4.5°
Rectangle:
A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles
Given,
Here we have the rectangle with one angle as 90°.
Here we have to find the value of x.
We know that, we we divide the rectangle as two distinct right angled triangle.
We know that, the right triangles are triangles in which one of the interior angles is 90 degrees, a right angle.
So,
20x = 90
x = 90/20
x = 4.5°
Therefore, the value of x is 4.5°.
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What is 175% of 48? Show work.
Let 175% of 48 be y.
This implies that
[tex]\frac{175}{100}\times48=y[/tex]To evaluate y,
[tex]\begin{gathered} \frac{175}{100}\times48=y \\ \Rightarrow\frac{175\times48}{100}=y \\ \frac{8400}{100}=y \\ \Rightarrow y=84 \end{gathered}[/tex]Hence, 175% of 48 is 84.
The garden that Julian is enclosing with chicken wire is in the shape of a parallelogram, Plan The measure of angle A is two thirds less than twice the measure of angle L. Find the measure of each angle of the garden enclosure.
Solution
We can do the following:
1) The condition given is:
m L -2/3
2) We have the other properties in a parallelogram:
m
m
And we also know that:
3) m L + m
2 m 2(2m 4 m6 mm
m
m< P = 1078/9
m < N= 542/9
Simplity 9 - [x - (7+ x)]
First we resolve the part between the square brackets:
[tex]\lbrack x-(7+x)\rbrack=(x-7-x)=0x-7=-7[/tex]Then:
[tex]9-\lbrack x-(7+x)\rbrack=9-(-7)[/tex]Then you apply the opperation with the symbols knowin that:
[tex](+)(+)=+[/tex][tex](+)(-)=-[/tex][tex](-)(-)=+[/tex]And the final answer is:
[tex]9+7=16[/tex]The number of bottles a machine fills is proportional to the number of minutes the machine operates. The machine
fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, the machine fills in a minutes.
To graph a line, select the line tool. Click on a point on the coordinate plane that lies on the line. Drag your mouse to
another point on the coordinate plane and a line will be drawn through the two points
It is to be noted that the correct graph is graph A. This is because it shows the coordinates (2, 25). See the explanation below.
What is the calculation justifying the above answer?It is information given is the rate of change of the linear relationship between the stated variable variables:
Number of Bottles; andTime.The ratio given is depicted as:
r = [250 bottles]/ [20 mintures]
r = 25/2 bottles per min
By inference, we know that our starting point coordinates (0,0), because zero bottles were filled at zero minutes.
Thus, we must use the point-slope form to arrive at the equation that exhibits or represents the relationship of the linear graph.
The point-slope form is given as:
y-y₁ = m(x-x₁)
Recall that our initial coordinates are (0, 0,) where x₁ = 0 and y₁ = 0. Hence
⇒ y - 0 = 25/2(x-0)
= y = 25x/2
Hence, if x = 2, then y must = 25
Proof: y = 25(2)/2
y = 50/2
y = 25.
Hence, using the principle of linear relationships, the first graph is the right answer, because it shows the points (2,25) which are part of the relation.
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6. Point A (-16,8) is one of the verticesof a rectangle. After a dilation of 1/2, arotation of 90 degrees clockwise, and areflection over the x-axis, what are thecoordinates of A"'?
Given the coordinate: A(-16, 8), let's perform the following:
First step:
A dilation with a scale factor of 1/2.
Here, we are to multiply the coordinates by 1/2.
A(-16, 8) ==> A'(-16*½, 8*½) = A'(-8, 4)
Second step:
Perform a rotation of 90 degrees clockwise.
(x, y) will change to (y, -x)
A'(-8, 4) ==> A''(4, 8)
Third step:
A reflection over the x axis.
To perform a reflection over the x axis, (x, y) becomes (x, -y)
A''(4, -8) ==> A'''(4, -8)
Therefore, the coordinates of A''' are:
A'''(4, -8)
Point Q is shown on the number line. Which Value is best represented by point Q? 15 6
According to the given graph, the point Q is between 5 and 5.50.
Therefore, the number that best describes point Q is
[tex]\sqrt[]{29.5}\approx5.4[/tex]Since it's between 5 and 5.50 too.
The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2
metersGiven:
a.) The length of a rectangle is given by a number, x (meters).
b.) The width is two meters longer than the length.
c.) The area of the rectangle is 120 m^2.
Let's first recall the formula for getting the area of the triangle.
Area = L x W
Where,
L = Length
W = Width
The width is two meters longer than the length. Therefore, we can say that:
W = L + 2
Let's now determine the measure of the dimension of the rectangle:
Let,
x = length of the rectangle
We get,
[tex]\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}[/tex]Based on the relationships given, the Length of the rectangle has two possible measures.
L - 10 = 0
L = 10 m
L + 12 = 0
L = -12 m
Since a length must never be a negative value, the length of the rectangle must be 10 m.
For the width, we get:
W = L + 2 = 10 + 2 = 12 m
Summary:
Length = 10 m
Width = 12 m
▸ Charice created a painting with an area of 63 square inches and a length of 7 inches. They create a second painting with an area of 81 square inches. It has the same width as the first painting. What is the length of the second painting?
The length of the second painting is 9 inches.
Given,
The area of the first painting = 63 square inches
Length of the first painting = 7 inches
The area of the second painting = 81 square inches
Width of the first painting = Width of the second painting = x
We have to find the length of the second painting:
Here,
We can consider the painting as a rectangle.
Area of rectangle = length × width
Now,
First painting:
Area = length × width
63 = 7 × x
x = 63/7 = 9
That is, the width of the first painting is 9 inches.
The width of the second painting also 9 inches.
Now,
Second painting:
Area = length × width
81 = length × 9
length = 81/9 = 9
Therefore, the length of the second painting is 9 inches.
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Identify the algebraic expression for the following word phrase: 5 less than twice a number y.
Answer:
5-2y because 5 less is 5- and 2 twice a number is y number is y and twice mean 2
A water tank holds 276 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds414 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of waterin the two tanks be the same?The amount of water in the two tanks will be the same inweeks.
In order to solve the problem we will first create equations to represent the volume of water on the gallons through the weeks. The output of the functions will be the volume of each and the entry will be the number of weeks passed.
For the first one:
[tex]\text{vol(week) = 276 -3}\cdot week[/tex]While on the second one:
[tex]\text{vol(week) = 414 -5}\cdot week[/tex]In order to calculate the number of weeks it'll take until they have the same volume of water we need to find the "week" which would make them equal. So we will equate both expressions and solve for that variable.
[tex]\begin{gathered} 276\text{ - 3}\cdot week\text{ = 414 - 5}\cdot week \\ 5\cdot\text{week - 3}\cdot week\text{ = 414 - 276} \\ 2\cdot\text{week = }138 \\ \text{week = }\frac{138}{2}\text{ = }69 \end{gathered}[/tex]It'll take 69 weeks for the tanks to have the same volume.
Find the measure of the indicated angle to the nearest degreeQuestion 15
Question 15.
Given:
Length of side opposite the indicated angle = 12 units
Length of side adjacent the hypotenuse = 24 units
Let's find the measure of the indicated angle.
Here, we have a right triangle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Where:
θ is the indicated angle.
Thus, we have:
[tex]\begin{gathered} sin\theta=\frac{12}{24} \\ \\ sin\theta=\frac{1}{2} \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} \theta=sin^{-1}(\frac{1}{2}) \\ \\ \theta=30^o \end{gathered}[/tex]Therefore, the measure of the indicated angle us 30 degrees.
• ANSWER:
30°
choose which group of sets the following number belongs to. Be sure to account for ALL sets. 2/7
A. Real numbers, rational numbers
Explanations:Note:
Real numbers are numbers that can be found on the number line. They include all rational and irrational numbers
Natural numbers are counting numbers. They include 0 and all whole numbers (1, 2, 3, ....)
Rational numbers are numbers that can be expressed as fractions of two integers. eg 2/3, 5/4, etc
Irrational numbers are numbers that cannot be expressed a s fractions of two integers. eg √7, π, etc
2/7 is a real number because it can be found on the number line, and is continuous
Also, 2/7 is a rational number because it is expressed as a fraction of two integers (2 and 7)
9Use the expression 43 + 8 – to find an example of each kind of expression.уKind of expression ExampleQuotientу9SumyVariable43 + 8Stuck? Review related articles/videos or use a hint.Repc
A quotient is a division between two terms. In this expression, and example of a quotient is "9/y".
An example of a sum from this expression is"4^3+8".
NOTE: A substraction can be also expressed as a sum by changing the sign of the second term.
In this case, the only variable is "y" which can take different values.
Answer:
Quotient: 9/y
Sum: 4^3+8
Variable: y
the rotation are is a 60° rotation about O,the center of the regular hexagon State the image of B for the following rotation
You have the following rotation:
[tex]R^2\circ R^{-2}[/tex]The result of the previous rotation, by taking into account the rules for the exponents for the transformations is:
[tex]R^2\circ R^{-2}=R^0[/tex]The rotation R⁰ means a rotation of 0 degrees of a specific point.
Then, the given rotation appiled to point B does not move the point B from its place. The transformation makes B to go to B
answer: B
In which month was the average temperature closest to 0°C ?
I List two types of angle pairs: 14) 15)
Let's recall that a type of angle pairs are complementary angles. They're complementary if the sum of their degree measurements equals 90 degrees or the right angle.
Example:
[tex]\angle ABZ\text{ and }\angle ZBC\text{ are complementary angles }[/tex]Let's recall that a second type of angle pairs are suplementary angles. In this case, the angles add up to 180 degrees.
Example:
[tex]\angle ABF\text{ and }\angle FBC\text{ are suplementary angles}[/tex]Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
To find out the slope, we need two points
so
looking at the graph
we take
(-4,5) and (0,-3)
m=(-3-5)/(0+4)
m=-8/4
m=-2the y-intercept (value of y when the value of x is zero) is the point (0,-3)
the equation of the line in slope-intercept form is
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
so
m=-2
b=-3
substitute
y=-2x-3use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time
A frequency table is a table that shows how many times each number appears.
Looking at this set of numbers, we can see that each number appears only one time.
So we can create the following frequency table:
[tex]\begin{gathered} \text{value | frequency} \\ 135\text{ | 1} \\ 211\text{ | 1} \\ 220\text{ | 1} \\ 180\text{ | 1} \\ 175\text{ | 1} \\ 161\text{ | 1} \\ 246\text{ | 1} \\ 201\text{ | 1} \\ 192\text{ | 1} \\ 167\text{ | 1} \\ 235\text{ | 1} \\ 208\text{ | 1} \end{gathered}[/tex]