Answer:
Step-by-step explanation:
2/4=0.5
BC gradient is 2
AB (3,2)
AC (1,1)
DE gradient is 1/2=0.5
same gradients
parallel line have the same gradients
DE=0.5
BC=0.5
D has coordinate (3,2) and E has coordinate (1,1)
Gradient of DE = (2 - 1)/(3 - 1) = 0.5
Gradient of BC = (-2 - -4)/(3 - 1) = 0.5
BC and DE have the same gradient so they are parallel.
To prove that DE is parallel to BC, we need to show that their slopes are equal. Let's start with finding the midpoints D and E:
Midpoint D: The coordinates of D are the averages of the coordinates of A and B.A = (4, 6)B = (2, -2)D = ((4+2)/2 , (6+(-2))/2) => (3, 2)Midpoint E: The coordinates of E are the averages of the coordinates of A and C.A = (4, 6)C = (-2, -4)E = ( ( 4 + (-2) )/2 = ( 6 + (-4) ) /2) = (1, 1)Step-by-step explanation:Slope of BC: The slope of line BC is calculated as follows:(y2 - y1) / (x2 - x1) = (-4 - (-2)) / (-2 - 2) = (-4 + 2) / (-4) = -2 / -4 = 1/2Slope of DE: The slope of line DE is calculated as follows:(y2 - y1) / (x2 - x1) = (1 - 2) / (1 - 3) = (-1) / (-2) = 1/2Since the slope of DE is equal to the slope of BC (both are 1/2), we can conclude that DE is parallel to BC.A quadratic equation is shown below:
3x2 − 11x + 10= 0
Part A: Find the vertex. Show your work.
Part B: Solve for x using an appropriate method. Show the steps of your work.
Answer:
Part A:
( 1.8333, -0.08333)
Part B:
x = 2 or x = 5/3
Step-by-step explanation:
The quadratic equation
[tex]3x^{2}-11x+10=0[/tex] has been given.
Part A:
We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.
[tex]\frac{d}{dx}(3x^{2}-11x+10)=6x-11[/tex]
Setting the derivative to 0;
6x - 11 = 0
6x = 11
x = 11/6
The corresponding y value is determined by substituting x = 11/6 into the original equation;
y = 3(11/6)^2 - 11(11/6) + 10
y = -0.08333
The vertex is thus located at the point;
( 1.8333, -0.08333)
Find the attached
Part B:
We can use the quadratic formula to solve for x as follows;
The quadratic formula is given as,
[tex]x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
From the quadratic equation given;
a = 3, b = -11, c = 10
We substitute these values into the above formula and simplify to determine the value of x;
[tex]x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}[/tex]
Please help ASAP!!!!!!
Answer:
8
Step-by-step explanation:
Find the point on the x-axis where x = 3 and look at the height of the line there.
Find the value of x. Round to the nearest tenth. (Will give brainliest)
Answer:
x = 51.1 degrees
Step-by-step explanation:
As this is a right triangle, we may use Sin, Cos, and Tan in order to find this answer. Sin is defined as the opposite over the hypotenuse, so that is what we can use. 7 is the opposite value and 9 is the hypotenuse of the triangle.
So we can set up an equation like this
[tex]sinx = \frac{7}{9}[/tex]
Then we can use the inverse of sin in order to solve for x
[tex]x = sin^{-1} (\frac{7}{9})[/tex]
When this is plugged into a calculator you get:
[tex]x= 51.057[/tex] degrees
This rounds to 51.1 degrees
Plz help me with this
Answer:
You don't even have to graph it.
A) X + Y -6 = 0
B) X - Y = 0
We add the equations and get:
2x -6 = 0
x = 3 and therefore, y = 3
The correct answer is the third answer (3, 3)
Step-by-step explanation:
Answer: (3, 3)
Step-by-step explanation:
Add the equations to eliminate y:
x + y = 6
x - y = 0
2x = 6
÷2 ÷2
x = 3
Substitute x = 3 into either of the equations to solve for y:
x - y = 0
3 - y = 0
3 = y
Which net represent the solid?
Answer: Figure one
Step-by-step explanation: this is a very very easy question and i will explaing it for you :) So basically all your doing is folding a peice of paper. If you look closley at figure two you can see that if you fold that it wont even turn into a shape. And if you look at figure three it has uneven sides when a square has all even sides. So your only valid option would be figure one because that would fold in to a square
I hope i helped you figure this out A thanks and a brainlist would be greatly appreciated :)
NEED HELP.. FAST!!
Rewrite with only sin x and cos x.
cos 2x + sin x
The answer is:
The rewritten expression is:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Why?To solve this problem we need to use the trigonometric identity of the double angle for the cosine which states that:
[tex]cos(2\alpha)=cos^{2}(\alpha)-sin^{2}(\alpha)[/tex]
Also, if we want to rewrite only with terms of cos(x) and sin(x), we can apply the following property:
[tex](a^{2} -b^{2})=(a+b)(a-b)[/tex]
So, rewriting the trigonometric equation, we have:
[tex]cos^{2}(\alpha)-sin^{2}(\alpha)=(cos(x)+sin(x))*(cos(x)-sin(x))[/tex]
Then, we are given the expression:
[tex]cos(2x)+sin(x)[/tex]
Now, rewriting the given expression with only sin(x) and cos(x), we have:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Hence, the answer is:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Have a nice day!
Find the area of the figure.
A) 114 cm2
B) 350 cm2
C) 418 cm2
D) 447 cm2
Answer:
C.) 418 cm²
I hope this helped you : )
Step-by-step explanation:
First, you find the area of the square:
19 cm x 19 cm = 361 cm
Next, you find the area of the triangle:
(19 cm x 6 cm) ÷2 =57 cm
Last, you add the two:
361 cm + 57 cm = 418 cm²
Answer:
it is C i took a quiz on it
Step-by-step explanation:
14 = 14
14 + 3 + c = 14 + 8
Answer:
[tex]14+3+c=14+8\quad :\quad c=5[/tex]
Hope this helps!!!
"The subject of this question is Mathematics." The student asked to solve two equations, one of which is already true and the other involves finding the value of a variable. By simplifying the equation, we can find that c is equal to 5.
Explanation:The subject of this question is Mathematics.
In the equation 14 = 14, both sides are equal to each other, so the equation is true by the reflexive property of equality.
In the equation 14 + 3 + c = 14 + 8, we can simplify both sides of the equation. Starting with the left side, 14 + 3 + c becomes 17 + c. On the right side, 14 + 8 becomes 22. So, the equation can be rewritten as 17 + c = 22.
To solve for c, we subtract 17 from both sides of the equation. This gives us c = 22 - 17, which simplifies to c = 5.
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Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)
Answer:
The total area of the five rooms = 3 × 13² + 2 × 15² ⇒ answer A
Step-by-step explanation:
* lets revise the area of the square
- The area of any square is (the length of its side)²
- We have five room
- Three of them have side length 13 feet each
- Two of them have side length 15 feet each
* lets find the total area of the five room
- The area of the three rooms of side length 13 feet
∵ The length of the side of each square is 13 feet
∴ The area of each room of the three = 13²
∴ The total area of the three rooms = 3 × 13² feet² ⇒ (1)
- The area of the two rooms of side length 15 feet
∵ The length of the side of each square is 15 feet
∴ The area of each room of the two = 15²
∴ The total area of the three rooms = 2 × 15² feet² ⇒ (2)
- To find the area of the five rooms and (1) and (2)
∴ The total area of the five rooms = 3 × 13² + 2 × 15²
Answer:
A. [tex](3*13^2)+(2*15^2)[/tex]
Step-by-step explanation:
The area of a square can be calculated with this formula:
[tex]A=s^2[/tex]
Where "s" is the lenght of any side of the square.
You know that any side of three square rooms measure 13 feet each and any side of two square rooms measure 15 feet each.
Let be [tex]s_1[/tex] the lenght of any side that measures 13 feet and and [tex]s_2[/tex] the lenght of any side that measures 15 feet.
Then, the total area will be:
[tex]A_{total}=3(s_1)^2+2(s_2)^2\\\\A_{total}=(3*13^2)+(2*15^2)[/tex]
Therefore, the expression that shows the total area of these five rooms is the expression shown in the option A.
last one thank you to all the people that helped me out today
Answer:
B
Step-by-step explanation:
It is a straight line that goes through the origin
Answer:
B
Step-by-step explanation:
Estimate the rate of change of the graphed function over the interval -4 ≤ x ≤ 0
A) 1/4
B) 0
C) 1
D) 4
We need the graph to answer.
Answer: equal 1/4
A). 1/4
What’s the distance formula
Answer:
The distance formula is really just the Pythagorean Theorem in disguise.
Step-by-step explanation:
AB=√(x2−x1)2+(y2−y1)2
Step-by-step explanation:
[tex]\text{Let}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2).\ \text{Then the distance between}\ A\ \text{and}\ B\ \text{is:}\\\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y1)^2}\\\\Example:\\\\A(2,\ 5),\ B(-1,\ 1)\\\\|AB|=\sqrt{(-1-2)^2+(1-5)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
Write a story problem where the answer is 7?
Answer: I have 4 cookies, I but 3 more cookies, how many cookies do I have now? I have 7 cookies
Step-by-step explanation:
A story problem where the answer is 7 is given above.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have number 7.
The question problem is as follows -
There are 77 chocolates and 11 childrens. How many chocolates should be given to each child such that each one gets equal number of chocolates.
Solution -
Assume each child gets [x] chocolates. Then -
11x = 77
x = 7
Therefore, a story problem where the answer is 7 is given above.
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Can somebody please help me with his pleaseee ASAP!!
Answer:
Step-by-step explanation:
1.
x= 18 y= 3
2.
x= -5 y=1
Math help please,,, thank u uwu!
Answer:
AC=BD
CAD=CBD
ACB=ADB
Step-by-step explanation:
You're essentially looking for anything of equal proportions. Obviously, your circle is split by several lines, and each side is symmetric. Since you know this, it's simply a matter of identifying one element then finding its symmetric match.
Follow the lines and trace the path with your finger for each question. If you do this, you'll see that AC=BD is an answer that involves a symmetric pair, because these two are equal distances and equal (but opposite) in placement.
Continuing with this method, keep track of the parts of the triangles you trace. With CAD=CBD, you trace across a hypotenuse, a leg, and a base in BOTH, making this true.
Continuing further with ACB=ADB, you trace across a hypotenuse, a leg, and a base with both AGAIN, making this true.
With AB=CD, this is obviously incorrect. You can't jump between points.
Answer:
only letter c is incorrect A, B, and D are correct
Step-by-step explanation:
lyn invested $7,000 into a investment paying 3% interest, compounded semi-annually, twice a year. After five years, how much would the investment be worth? A=P(1+r/n)^nt
A.) $8,050.00
B.) $8,123.79
C.) $1,123.79
D.) $8,114.92
E.) $1,050.00
Answer:
Option B.) $8,123.79
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$7,000\\ r=0.03\\n=2[/tex]
substitute in the formula above
[tex]A=\$7,000(1+\frac{0.03}{2})^{2*5}[/tex]
[tex]A=\$7,000(1.015)^{10}=\$8,123.79[/tex]
The worth of the investment after 5 years at an interest of 3% is $8,123.79.
How much would the investment be worth?As the function for interest is already given to us, also,
The principal amount, P = $7,000
The rate of Interest, r = 3%
Time period, t = 5 years
Compounded semiannually, n = 2
Substitute the values,
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
[tex]=7000(1+\dfrac{0.03}{2})^{2 \times 5}\\\\=\$ 8,123.79[/tex]
Hence, the worth of the investment after 5 years at an interest of 3% is $8,123.79.
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A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side. What is the expression for the volume of the pyramid?
A) V = 2s^2
B) V = 2s^3
C) V = 2/3s^2
D) V = 2/9s^3
E) V = 1/3s^3
Random answers will be reported!
Answer:
The correct option is option D
Step-by-step explanation:
The volume of a pyramid is:
V=1/3(B)(H)
Where
B:Base = s^2
H:Height = 2/3s
Then:
V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3
The correct option is option D
Answer:
answer is V= 2/9 s3 is correct
what is the equation of the line that passes through (-3,-1) and has a slope of 3/5
Answer:
y+1 = 3/5(x+3) (point slope form)
y = 3/5x +4/5 slope intercept form
Step-by-step explanation:
Since we have a point and a slope, we can use the point slope form of the equation
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y--1 = 3/5(x--3)
y+1 = 3/5(x+3) (point slope form)
We can distribute
y+1 = 3/5x +9/5
Subtract 1 from each side
y+1-1 = 3/5x +9/5 -1
y = 3/5x +9/5 -5/5
y = 3/5x +4/5 slope intercept form
Answer:
Equation: y = 3/5 x + 4/5
Step-by-step explanation:
y = mx + b
so
b = y - mx
passes through (-3,-1) and has a slope of 3/5
So
b = -1 - (3/5) (-3)
b = -1 + 9/5
b = - 5/5 + 9/5
b = 4/5
So equation
y = 3/5 x + 4/5
F(x) = x^2. What is g(x)?
Answer:
Option B. g(x)=(1/4 x)^2
Step-by-step explanation:
A rectangular section of wilderness will be set aside as a new wildlife refuge. Its dimensions are 5 x 105meters by 4 x104 meters. Find the area of the land in square meters. Make sure your answer is in correct scientific notation form
Answer: [tex]A=2*10^{10}m^2[/tex]
Step-by-step explanation:
The area of a rectangle can be calculated with this formula:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
You know that the dimensions of this rectangle are 5*10⁵meters and 4*10⁴ meters, then you need to multiply them to get the area:
[tex]A=(5*10^5m)(4*10^4m)[/tex]
Since 10⁵ and 10⁴ have equal base, you must add the exponents:
[tex]A=20*10^{(5+4)}m^2[/tex]
[tex]A=20*10^9m^2[/tex]
Scientific notation has the form:
[tex]a*10^n[/tex]
Where "a" is any number between 1 and 10 but less than 10, and "n" is an integer.
Since 20 is greater than 10, you must move the decimal point to the left:
[tex]A=2.0*10^{10}m^2[/tex]
Rewriting the result, you get:
[tex]A=2*10^{10}m^2[/tex]
The area of the rectangular section of wilderness that will be set aside as a new wildlife refuge is [tex]2 * 10^{10[/tex] square meters
The dimensions of the rectangular section of wilderness that will be set aside as a new wildlife refuge are given as:
5 x 10^5 meters by 4 x10^4 meters
The area is the product of the dimensions.
So, we have:
[tex]Area = 5 * 10^5 * 4 * 10^4[/tex]
Evaluate the product
[tex]Area = 20 * 10^9[/tex]
Rewrite as:
[tex]Area = 2 * 10^{10[/tex]
Hence, the area of the rectangular section of wilderness that will be set aside as a new wildlife refuge is [tex]2 * 10^{10[/tex] square meters
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The solution to 2 × 27 will be what kind of number? A. Odd B. Perfect square C. Even D. Prime
Answer:
C. Even
Step-by-step explanation:
Any multiple of 2 is an even number.
27 is 3³, so the result cannot be a perfect square.
The product of two numbers, neither of which is 1, cannot be prime.
the answer would be C. An even number
You are given odds of 7 to 8 in favor of winning a bet, what is the probability of winning the bet?
The probability of winning a bet with odds of 7 to 8 in favor is 7/15, or approximately 46.67%.
If you are given odds of 7 to 8 in favor of winning a bet, to find the probability of winning, you need to understand the relationship between odds and probability.
Odds of 7 to 8 means that for every 8 losses, there are 7 wins.
The total number of possibilities is 7 wins + 8 losses = 15 possible outcomes.
To convert odds to probability, you divide the number of ways to win by the total number of possible outcomes:
Probability of winning = 7 wins / 15 total outcomes = 7/15.
Therefore, the probability of winning the bet is 7/15, which can be approximated as 0.4667 or 46.67%.
12km 5km pythagorean theorem
Answer:
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":[1]
Step-by-step explanation:
What are the ratios for sin a and cos a?
the answer is the last one because sin =opposite/hypo.
while cosine= adjacent/hypo.Check the picture below.
Which of these triangle pairs can be mapped to each other using a reflection and a translation?
Answer:
second option
Step-by-step explanation:
The triangle pairs that can be mapped to each other using a reflection and a translation are option (b).
The following statement will clarify how that triangle pair is mapped to each other using a reflection and a translation:A translation moves a shape left or right and/or up or down.The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have shifted in one or more directions. There is no change in the shape.In Geometry, a reflection is known as a flip.A reflection is a mirror image of any given shape.Reflection is flipping an object across a line without changing its size or shape whereas Translation is sliding a figure in any direction without changing its size, shape, or orienattion.To graph a translation, perform the same change for each point. We can identify a reflection by the changes in its coordinates.Hence, the correct answer is option (b).
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look at the picture and plzzz help
Answer:
option B
option D
Step-by-step explanation:
1)
First we will remove radical sign as[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex] and then multiply the powers.
[tex]\sqrt[3]{4^{5}}=(4^{5})^{\frac{1}{3}}=4^{\frac{5}{3} }[/tex]
2)
The "power rule" tells us that to raise a power to a power, just multiply the exponents.
([tex]4^{15}[/tex])[tex]^{\frac{1}{3}}=4^{15.\frac{1}{3}}=4^{5}[/tex]
Which correctly solves the inequality t+18<43 Select one: a. t<25 b. t>61 c. t>25 d. t<61
For this case we must solve the following inequality, finding the values for the variable "t":
[tex]t + 18 <43[/tex]
We subtract 18 from both sides of the inequality:
[tex]t + 18-18 <43-18\\t <25[/tex]
Thus, the variable "t" is defined for all strict lower values than 25.
Answer:
[tex]t <25[/tex]
Option A
Translate ∆ABC by moving it 5 units to the right and 2 units up.
To translate a triangle by moving it 5 units to the right and 2 units up, you add 5 to the x-coordinates and 2 to the y-coordinates of all its vertices.
Explanation:To translate riangle ABC by moving it 5 units to the right and 2 units up, you would perform the following steps:
Select riangle ABC.Move each point of riangle ABC 5 units to the right. This is done by adding 5 to the x-coordinate of each vertex of the triangle.Then, move each point of riangle ABC 2 units up. This is done by adding 2 to the y-coordinate of each vertex of the triangle.The new position of riangle ABC is the result of this translation.This transformation doesn't change the shape or size of riangle ABC; it merely repositions it on the coordinate plane.
What is the equation of the line passing through the point (-4, -5) and having a slope of 4?
A. Y= 4x + 21
B. Y= 4x - 21
C. Y= 4x + 11
D. Y= 4x - 11
Answer:
C. is the answer
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 4, - 5) into the partial equation
- 5 = - 16 + c ⇒ c = - 5 + 16 = 11
y = 4x + 11 → C
Which of the following is a binomial?
A) 8x^5
B) 11x+18
C) 14x^2+5x+12
D) 4/x
If I am correct the best option would be answer B