Answer:
The coordinates of C are (8,2)
Step-by-step explanation:
We are given the segment from A(-4,-7) to B(12,5) and it's required to find a point C(x,y) that is located at 3/4 of the distance from A to B.
This means that:
[tex]d_{AC}=3/4\cdot d_{AB}[/tex]
where dAC is the distance from A to C and dAB is the distance from A to B.
The same proportion of the distances is satisfied by the coordinates of the point C, that is:
[tex]\displaystyle x-x_A=\frac{3}{4}(x_B-x_A)[/tex]
Adding xA:
[tex]\displaystyle x=\frac{3}{4}(x_B-x_A)+x_A[/tex]
[tex]\displaystyle x=\frac{3x_B+x_A}{4}[/tex]
Similarily:
[tex]\displaystyle y=\frac{3y_B+y_A}{4}[/tex]
Calculating:
[tex]\displaystyle x=\frac{3(12)-4}{4}[/tex]
x = 8
[tex]\displaystyle y=\frac{3(5)-7}{4}[/tex]
y = 2
The coordinates of C are (8,2)
7. Constructed Response: Work and answer will be scored on a 3-point
rubric. A garden is bordered on three sides by a tiled walkway. (see
diagram below). PART A: Write a polynomial that represents the total area
of the garden AND the walkway combined, in standard form. *
Fence
x ft
x ft
Garden
10 ft
-25 ft
Walkway
x ft
Answer:
the answer is -25
Step-by-step explanation:
the answer is -25
Find the length of segment JK with endpoints J(4, 8) and K(-1, -2). Leave the answer as a radical. Simplify if necessary
Answer:
The length of segment JK is 5[tex]\sqrt{5}[/tex] ⇒ C
Step-by-step explanation:
The formula of the distance between the two points (x1, y1) and (x2, y2) is
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
Let us use the formula above to solve the question
∵ Jk is a line segment
∵ J = (4, 8) and K = (-1, -2)
∴ x1 = 4 and y1 = 8
∴ x2 = -1 and y2 = -2
→ Substitute them in the formula above
∵ JK = [tex]\sqrt{(-1-4)^{2}+(-2-8)^{2}}[/tex]
∴ JK = [tex]\sqrt{(-5)^{2}+(-10)^{2}}[/tex]
∴ Jk = [tex]\sqrt{25+100}[/tex]
∴ Jk = [tex]\sqrt{125}[/tex]
→ Simplify the root
∵ 125 = 5 × 5 × 5
∴ [tex]\sqrt{125}[/tex] = 5[tex]\sqrt{5}[/tex]
∴ JK = 5[tex]\sqrt{5}[/tex]
∴ The length of segment JK is 5[tex]\sqrt{5}[/tex]
You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measures of the interior angles of the triangle.
Answer:
Step-by-step explanation:
A linear pair are two given angles whose sum is equal to [tex]180^{o}[/tex].
Let the exterior angle be represented by [tex]x^{o}[/tex], and the three interior angles of the triangle be represented by [tex]a^{o}[/tex], [tex]b^{o}[/tex] and [tex]c^{o}[/tex].
Assume that the vertex angle [tex]c^{o}[/tex] is the linear pair to the exterior angle [tex]x^{o}[/tex].
i.e [tex]x^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)
Thus,
i. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex] (sum of two opposite interior angles is equal to an exterior angle)
⇒ [tex]a^{o}[/tex] = [tex]x^{o}[/tex] - [tex]b^{o}[/tex]
Also,
[tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
But,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
⇒ [tex]c^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]a^{o}[/tex] + [tex]b^{o}[/tex])
and
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]180^{o}[/tex] - [tex]c^{o}[/tex]
ii. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]a^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]b^{o}[/tex] + [tex]c^{o}[/tex])
Also,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex]
⇒ [tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
[tex]c^{o}[/tex] = [tex]180^{o}[/tex] - [tex]x^{o}[/tex]
HELP QUICKLY!!!
what is the y intercept of the line
Answer:
-23
Step-by-step explanation:
the equation of the line is y=-2/3x-23 so the b in the equation (y=mx+b) is the y int so that is -23
y-8= 4(x-10
...............
Answer:
y=mx+b
y=4x-32
Answer:
y=23
Step-by-step explanation:
Given a slope of 3 and the point (2, 1), find the Y-intercept of the line.
Answer:
(0,-5)
Step-by-step explanation:
my work is in the picture I attached. lmk if you'd like me to explain more :)
Step-by-step explanation:
The graph shows the average speed of Car 1 which is traveling on a highway. The equation y= 55x represents the average speed of Car 2, where y is the distance in miles and x is the time in hours. Which car is traveling at the greater speed?
Answer:
Car 1 is traveling faster than Car 2. Car 1 is traveling at a speed of 64 miles per hour and Car 2 is traveling at a speed of 55 miles per hour.
what's the slope intercept form
Find the perimeter of the figure.
9 mi
5 mi
9 mi
4 mi
Janelle wants to learn to play the piano. Her friends recommended two different music schools. Make Music charges $525 for 10 hours of lessons. Piano Play offers 12 hours of lessons for $540. Which school offers the better deal?
Answer:
Piano Play
Step-by-step explanation:
Answer:
Piano Play offers the better deal.
Step-by-step explanation:
If you divide $525 by 10 you will get $52.50 every hour for Make Music but if you divide $540 by 12 you will get $45 every hour for Piano Play so Piano Play offers the better deal.
Hope this helps!!
Which system of equations represents the graph?
Answer:
B
Step-by-step explanation:
if you look at the line one going up, the y axis is at the negatives meaning it begins as -5 . Then notice how it goes up 3 times and it goes to the right once. So the slope is 3/1 or simplified 3 so we know the slope intercept form is = y is 3x-5. Now we look at the second one. None of the answers of the second one are in slope intercept form. for that you have to turn them into it. When you do that for B will be y= -1/2x + 2. When you look at the line the y axis is 2 and the slope is -1/2x.
Bob buys eggs and potatoes at the store.
• He pays a total of $25.92.
• He pays $2.57 for the eggs.
• He buys 5 bags of potatoes that each cost the same amount.
What equation can be used to determine the cost, x, of each bag of potatoes?
I have no idea how to do this, any clues?
Answer:
(2x-5)+(x+25)+x
4x+20
Step-by-step explanation:
Simplify the expression.
What is the slope of a line parallel to the line that passes through (4, -3) and (3, -1)?
Answer:
-2
Step-by-step explanation:
find rise over run with y1-y2/x1-x2 = -2/1 = -2
The slope m of the line passing through the points A ( 4 , -3 ) and B ( 3 , -1 ) is m = -2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the first point be A ( x₁ , y₁ ) = A ( 4 , -3 )
Let the second point be B ( x₂ , y₂ ) = B ( 3 , -1 )
Now , the equation for the slope of the line is given by ,
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -1 - ( -3 ) ) / ( 3 - 4 )
Slope m = 2 / -1
Slope m = -2
Hence , The slope m of the line passing through the points A ( 4 , -3 ) and B ( 3 , -1 ) is m = -2
To learn more about equation of line click :
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place the following numbers in order from least to greatest
-8.2, 0.4, NEGATIVE 2 AND 1/2, and 2.4
Answer:
-8.2,-2 1/2, 0.4,2.4
Step-by-step explanation:
hope that helps
Tristán wants to build a square garden in his backyard if the garden is going to be 64 ft2 how many feet of material will he need for the perimeter of the garden
Answer:
Tristan will need 32 feet of material for the perimeter of the garden.
Step-by-step explanation:
Given that
Area of square garden = A = 64 square feet
Perimeter = P = ?
We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.
So,
[tex]Area = A = s^2[/tex]
s is for side
Putting the value of area
[tex]64 = a^2[/tex]
Taking square root on both sides
[tex]\sqrt{s^2} = \sqrt{64}\\s = 8\ feet[/tex]
The length of side is 8 feet.
Perimeter will be:
[tex]P = 4*s\\P = 4*8\\P = 32\ feet[/tex]
Hence,
Tristan will need 32 feet of material for the perimeter of the garden.
What’s the answer
What are the slope and the y-intercept of the linear function that is represented by the graph
Which of the following statements about the congruent triangles below is true?
A.) AB=DE
B.) AC=EF
C.) AC=DE
D.) BC=DE
Answer:
AB=DE
Step-by-step explanation:
they're literally the only pair on the same sides lol
The side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
We have two triangles shown in the picture.
As we know from the definition of the congruent triangle, the same size, and shape.
The three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle
Thus, the side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.
Learn more about the congruent triangle here:
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the product of two consecutive integers is 72. find the integers
Answer:
the integers are 8 and 9
Step-by-step explanation:
consecutive means one right after the other. 9 is right after 8. and its product is 72, well 8x9 is 72.
Which expression is equal to (1.5)3? Select all that apply. A. 5.0625 B. 3.375 C. 4.5 D. 2.25 × 1.5 E. 2.5 × 1.25
Answer:
its B and D
Step-by-step explanation:
cause 1.5 times 1.5 times 1.5 is 3.375 which is (1.5) and the explanation for D is that 2.5 times 1.25 Is 3.375 which is (1.5) Hope i helped:)
The expression is equivalent to 3.375 and 2.25 × 1.5.
We have to determine
Which expression is equal to [tex](1.5)^3[/tex]?
The expression is equivalent to;
[tex]= (1.5)^3\\\\= 1.5 \times 1.5 \times 1.5\\\\= 3.375[/tex]
Therefore,
The expression is equivalent to;
[tex]= 2.25 \times 1.5\\\\= 3.375[/tex]
Hence, the expression is equivalent to 3.375 and 2.25 × 1.5.
To know more about Expression click the link given below.
https://brainly.com/question/19943359
Which of the following expressions are equivalent to 20t5⋅2−4t?
There may be more than one correct answer. Select all that apply.
Answer:mark brain list answers
mark
get 3 point
freee
Step-by-step explanation:
9 3/4 as a percent step by step
Answer:
9 3/4 in a percent is 975%.
If you change 9 3/4 into a decimal, it will be 9.75, and 9.75 converted into a percent is 975%
i need the answer to this please help
Answer:
-1/11
Step-by-step explanation:
[tex]\frac{11x}{12} -\frac{1}{6} =\frac{-1}{4}[/tex] add 1/6 to both sides
[tex]\frac{11x}{12} =\frac{1}{6} -\frac{1}{4}[/tex] make the same denominator 12 on the right side
[tex]\frac{11x}{12} =\frac{1}{6}*\frac{2}{2} -\frac{1}{4}*\frac{3}{3}[/tex] solve
[tex]\frac{11x}{12} =\frac{2}{12} -\frac{3}{12} =\frac{2-3}{12} = \frac{-1}{12}[/tex]
[tex]\frac{11x}{12}*12 =\frac{-1}{12} *12[/tex] multiply by 12 both sides
11x= -1 divide by 11
x= -1/11
Lisa puts $8,000 in an account that earns 12% simple annual interest. If she leaves her money in the account for 4 years, how much interest will she earn?
Answer:
392000
Step-by-step explanation:A=p(1+
ASAP PLS....I need this for tomorrow:(
Answer:
your answer is 2x2y
Step-by-step explanation:
that's it
If the given figure is rotated 180° around the origin, what are the new coordinates of point Z?
Answer:
im not sure if there is a picture it would help more :)
Step-by-step explanation:
ANSWER ASAP PLEASE & SHOW UR WORK!!!
Find the real or imaginary solutions. x^4 + 3x^2 - 18 = 0
Answer:
[tex]x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}[/tex]
Step-by-step explanation:
Biquadratic Equations
Solve:
[tex]x^4 + 3x^2 - 18 = 0[/tex]
The biquadratic equations are equations of degree 4 without the terms of degree 1 and 3.
Solving such equations requires to express the equation as a second-degree equation with [tex]x^2[/tex] as the variable.
Rewriting the equation:
[tex](x^2)^2 + 3(x^2) - 18 = 0[/tex]
The quadratic equation can be factored as:
[tex](x^2+6)(x^2-3)=0[/tex]
It leads to two equations:
[tex]x^2+6=0[/tex]
[tex]x^2-3=0[/tex]
The first equation has imaginary roots. Solving for x:
[tex]x^2=-6[/tex]
[tex]x=\pm\sqrt{-6}[/tex]
[tex]x_1=\mathbf{i}\sqrt{6}[/tex]
[tex]x_2=-\mathbf{i}\sqrt{6}[/tex]
Where
[tex]\mathbf{i}=\sqrt{-1}[/tex]
The second equation has two real roots:
[tex]x^2-3=0[/tex]
[tex]x^2=3[/tex]
[tex]x=\pm\sqrt{3}[/tex]
[tex]x_3=\sqrt{3}[/tex]
[tex]x_4=-\sqrt{3}[/tex]
The roots are:
[tex]\mathbf{x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}}[/tex]
Cuál es el resultado de la suma de 12/3 + 3 1/2
Answer:
el resultado es facil es: 7 1/2 espero que te ayude
Answer:
7 1/2
Step-by-step explanation:
aflati termenul necunoscut din egalitatile de mai jos
a)x-2002=41535-1003 b)20+x-30=150-20;
c) x-(284-130)=110 d)853-(x + 1)=249;
e)613-(243-11-x)=549; f)312+11-(x+4)=323-(51+93
Answer:easy thats C
Step-by-step explanation:
enjoy
Part A what is the measure of the missing angle in the triangle?
Answer:
39
Step-by-step explanation:
the interior angles of a triangle equal 180.
180-(51+90)
180- 141 = 39
hope this helps :)