Answer:
1) if Line AB is parallel to line CD then value of a is: a=3
2) if Line AB is perpendicular to line CD then value of a is: a=1
Step-by-step explanation:
We are given A(3,5), B(7, 10), C(0, 2), and D(1, a) we need to find value of a for which:
We can use slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] to find value of a according to conditions given.
We are given:
[tex]x_1=3, y_1=5, x_2=7, y_2=10 \ for \ line \ AB \ and \\\x_1=0, y_1=2, x_2=1, y_2=a \ for \ line \ CD \[/tex]
a) Line AB is parallel to line CD.
When 2 lines are parallel there slope is same so, using this we can find value of a
[tex]Slope \ of \ line \ AB = Slope \ of \ line \ CD[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1}= \frac{y_2-y_1}{x_2-x_1}\\\frac{10-5}{7-3}=\frac{a-2}{1-0} \\\frac{5}{5}=\frac{a-2}{1}\\1=a-2\\a=1+2\\a=3[/tex]
So, if Line AB is parallel to line CD then value of a is: a=3
b) Line AB is perpendicular to line CD.
When 2 lines are perpendicular there slopes are opposite of each other so, using this we can find value of a
[tex]Slope \ of \ line \ AB =-\frac{1}{Slope \ of \ line \ CD}[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1}=-\frac{1}{ \frac{y_2-y_1}{x_2-x_1}} \\\frac{y_2-y_1}{x_2-x_1}=-\frac{x_2-x_1}{y_2-y_1}\\\frac{10-5}{7-3}=-\frac{1-0}{a-2} \\\frac{5}{5}=-\frac{1}{a-2}\\1=-\frac{1}{a-2}\\a-2=-1\\a=-1+2\\a=1[/tex]
So, if Line AB is perpendicular to line CD then value of a is: a=1
a shipping crate is a perfect cube with volume of 2,197 cubic feet. the ceiling of the warehouse is 14 feet high. will the crate fit in the warehouse explain why
Answer:
As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.
Step-by-step explanation:
Given that
Volume of cube = V = 2197 cubic feet
Side of cube = a =?
Height of ware house = h = 14 feet
In order for the crate to fit in the warehouse the height of crate has to be less than the height of warehouse i.e. a<h
In order to check this we have to find the side/height of crate
So,
[tex]V = a^3\\2197 = a^3[/tex]
Taking cube root on both sides
[tex]\sqrt[3]{a^3} = \sqrt[3]{2197}\\\sqrt[3]{a^3} = \sqrt[3]{13^3}\\ a = 13\ feet[/tex]
So the height of cube is 13 feet.
Comparing the height of c and height of ware house we can conclude that
Height of Warehouse > Height of crate
h>a
14>13
As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.
In a two-digit number, the units digit is six less than three times the tens digit. Four times the units digit minus five times the tens digit equals 11. Find the digits.
Answer:
The tens digit = 5
The units digit = 9
The two digit number is 59
Step-by-step explanation:
Let the tens digit be represented by x
The units digits be represented by y
In a two-digit number, the units digit is six less than three times the tens digit.
y = 3(x) - 6
y = 3x - 6
Four times the units digit minus five times the tens digit equals 11.
4(y) - 5(x) = 11
4y - 5x = 11
We substitute
4(3x - 6) - 5x = 11
12x - 24 - 5x = 11
Collect like terms
12x - 5x = 11 + 24
7x = 35
x = 35/7
x = 5
y = 3x - 6
y = 3(5) - 6
y = 15 - 6
y = 9
Hence,
The tens digit = 5
The units digit = 9
The two digit number is 59
Answer:
5=tens 9=units
Step-by-step explanation:
I think its this
q is the midpoint of segment pr. pq=2x+1 and qr= 3x-5. what is the length of segment pr
how long is a meter
you can not use google
1 km=1000 m
1 m=100 cm
please mark as brainliest
AABC is an isosceles triangle with vertex angle B, AB = 2x + 10, AC = 2x,
and BC = 4x - 16. Determine the length of the base of the triangle.
Answers are
A.117 degrees
B.26 degrees
C.15 degrees
D.22 degrees
Answer:
AC = 26 units
Step-by-step explanation:
Given that,
ABC is an isosceles triangle with vertex angle B such that,
AB = 2x + 10, AC = 2x, and BC = 4x - 16
Two sides of an isosceles triangle are equal. It means that the angles corresponding to the same sides are equal. It means AB = BC
2x + 10 = 4x - 16
2x-4x = -10-16
-2x = -26
x = 13
AC is the base of the traingle.
AC = 2x
AC = 2(13)
AC = 26 units
So, the base of the triangle is equal to 26 units.
65.1 acres divided by 3
Answer:
according to me is 87 816.7844 m2
Answer:
21.7
Step-by-step explanation:
65.1 ÷ 3 = 21.7
Hope this helps!
A circle has a diameter of 3 meters. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical value of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
Step-by-step explanation:
A circle has a diameter of 3 meters. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical value of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Using the area and the circumference of the circle, it is found that the correct statement is given by:
The numerical value of the circumference is greater than the numerical value of the area.
What is the area of a circle?The area of a circle of diameter d is given by:
[tex]A = \frac{\pi}{4}d^2[/tex]
What is the circumference of a circle?The circumference of a circle of diameter d is given by:
[tex]C = \pi d[/tex]
In this problem, we have that d = 3, hence:
[tex]A = \frac{\pi}{4} \times 3^2 = \frac{9\pi}{4} = 2.25\pi[/tex]
[tex]C = \pi \times 3 = 3\pi[/tex]
Hence the correct option is given by:
The numerical value of the circumference is greater than the numerical value of the area.
More can be learned about the area and the circumference of a circle at https://brainly.com/question/15673093
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I need help pleaseeee
Find the slope and y-intercept for the table.
slope:
y-intercept:
Answer:
Slope is 3
y-intercept is 2
If QS and TV are parallel lines and m<QRU=127, what is m<TUW? HELP ASAP
Based on the corresponding angles theorem, m<TUW = 127°.
What is the Corresponding Angles Theorem?If two angles on two parallel lines that are cut across by a transversal are corresponding to each other, the corresponding angles theorem states that they are congruent to each other.
Given:
m<QRU = 127
Angles QRU and TUW are corresponding angles. Therefore:
m<TUW = m<QRU = 127° [corresponding angles theorem]
m<TUW = 127°
Learn more about the corresponding angles theorem on:
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Which equation represents the rectangular form of 5pi/6
Answer:
D, StartRoot 3 EndRoot x + 3 y = 0
Step-by-step explanation:
The equation which represents the rectangular form of 5pi/6 is √3x-y=0.
We are given that;
The expression 5pi/6
Now,
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
The rectangular form of a polar point (r, θ) is given by (x, y) where x = r cos(θ) and y = r sin(θ).
Therefore, the rectangular form of 5π/6 is given by (x, y) where x = 5 cos(5π/6) and y = 5 sin(5π/6).
Using the unit circle, we can find that cos(5π/6) = -√3/2 and sin(5π/6) = 1/2.
Hence, the rectangular form of 5π/6 is (-5√3/2, 5/2).
Therefore, by the equation answer will be √3x-y=0.
To learn more about equations :
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UN PASTEL SE CORTA QUITANDO CADA VEZ LA TERCERA PARTE DEL PASTEL QUE HAY EN EL MOMENTO DE CORTAR ¿QUE FRACCION DEL PASTEL ORIGINAL QUEDO DESPUES DE CORTAR TRES VECES?
Answer:
No queda nada del pastel.
Step-by-step explanation:
El pastel representaria un entero, si al entero lo dividimos en tercios, son tres tercios los que los conforman, por ende si lo cortamos tres veces, en el primer corte quedarian dos tercios de pastel, en el segundo corte un tercio, y en el tercer corte el ultimo tercio , generando asi que no quede nada de este.
Los enteros se dividen en cuartos, tercios y hasta octavos, o muchas mas fracciones.
Un entero es equivalente a 4 porciones de 1/4 y a 3 porciones de 1/3
If f(x) = 2x2
+3 and g(x) = x2 - 7, find (f + g)(x).
A. x² - 4
B. X2 + 10
C. 3x2 - 4
D. 3x2 - 10
Answer:
Im stupid so dont trust me but imma guess and say c
Answer:
YEH its B X to the second power Plus 10
Step-by-step explanation:
evaluate [tex]2^{x}[/tex] for (a) x=-2 and (b) x=3. write your answer in simplest form
Can somebody help with my math gotta be serious about it tho!
Answer: ok
Step-by-step explanation:
Answer:
I can try to help
Step-by-step explanation:
It depends one the question and what math subject.
So ask the question and people should help.
I NEED THIS ANSWER I DONT UNDERSTAND PLEASE HELP
Answer:
A. 904.3 cm³
Step-by-step explanation:
Radius of the ice cream cone (r) = 6 cm
Height of the ice cream cone (h) = 12 cm
Radius of the shape of hemisphere formed by the half scope of ice cream = 6 cm
Total volume of ice cream = volume of cone + volume of hemisphere
= [tex] (\frac{1}{3} \pi r^2 h) + (\frac{2}{3} \pi r^3) [/tex]
Plug in the values
[tex] (\frac{1}{3} \times 3.14 \times 6^2 \times 12) + (\frac{2}{3} \times 3.14 \times 6^3) [/tex]
[tex] (\frac{1}{3} \times 3.14 \times 36 \times 12) + (\frac{2}{3} \times 3.14 \times 216) [/tex]
[tex] = (1 \times 3.14 \times 12 \times 12) + (2 \times 3.14 \times 72) [/tex]
[tex] = (452.16) + (452.16) [/tex]
Total volume of ice cream = 904.3 cm³ (nearest tenth)
Help. IM SO LOST ON THIS! ;(
Answer:
1. 4[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
For question 1, you need to know the ratio between the recipe and the amount in question.
So if in the recipe, it says it uses 3/4 cup of diced ham, and the question uses 1 cup of diced ham, you can divide 1 by 3/4 to get 4/3. This is how many times bigger the amount used in the question than the recipe.
Then it asks for how many cups of potatoes, to do this, you look at the recipe and how many potatoes it uses: 3.5 cups
To solve it then, you just do 3.5 x 4/3 to get 4[tex]\frac{2}{3}[/tex] cups of potatoes
There's your answer.
what does rise over run mean in math?
Answer:The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run". Rise means how many units you move up or down from point to point. Run means how far left or right you move from point to point. On the graph, that would mean a change of x values.
Step-by-step explanation:
10+10*10-100 try to do it
Answer:
the correct answer is 10 have a brilliantaa day
Step-by-step explanation:
need help with another HW assignment.
Given the exponential function [tex]f(x) = 9(3)^x[/tex], what is the value of f(x) when x =-1
Answer:
f(-1) = 3
General Formulas and Concepts;
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = 9(3)ˣ
x = -1
Step 2: Solve
Substitute: f(-1) = 9(3)⁻¹Evaluate: f(-1) = 9(1/3)Multiply: f(-1) = 9/3Divide: f(-1) = 3On a map, the distance between NY and Washington D.C. is 3.6 inches. The scale is 1 inch: 55 miles. What is the actual distance between the two cities?
Giving 100 points if someone can answer this correctly...
x³+y³+z³=42
What is x y and z multiplied by 9.08 * 10³
this question is dumb. you should be able to get it
Answer:
3813.6
Step-by-step explanation:
90.8 x 42 = 3813.6
Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35and an additional fee of $12per class taken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal.
Answer:
Step-by-step explanation:
12 x 5 = 60 + 35 = 85, and we cannot go any higher without exceeding 100. However it would be different if it was a decimal. So for now the answer would be 5 classes added with the initial one time fee of 35 dollars.
11(p-3)=5(p+3) really need an answer please hahaha
Answer:
P = 8
Step-by-step explanation:
Answer:
p=104/33
Step-by-step explanation:
Please help!!!!
Compare the slopes of the linear functions f(x) and g(x) and choose the best answer that best describes them.
Answer choices:
A- The slope of f(x) is greater than the slope of g(x)
B- The slope of f(x) is less than the slope of g(x)
C- The slope of f(x) is equal to the slope of g(x)
D- The slope of g(x) is undefined
Answer:
The answer is C. The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
Did the test
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game
Answer: answer 80%
Step-by-step explanation:
Answer:
ew teachers really out here trying to make video games about school huh
Step-by-step explanation:
write the equation of a line that has a slope of 3 and passes through the point (1,2) in slope intercept form
Answer:
The equation is y = 3x - 1
Step by Step Explanation:
Ok, so your first step in solving this would be substituting m in the equation with the slope, since m represents the slope. So then you would have y = 3x + b. Now, to find b, you would have to substitue the point (1,2) into the equation. You would replace 2 with y since that's the y coordinate, and 1 with x since that's the x coordinate. Then you have 2 = (3*1) + b. Now, you solve for this. You get 2 = 3 + b. Isolating the variable b, you have b = -1. So, the result is y = 3x - 1. That's your answer
Gavin has $50,000 with which to start a new business. He wants to maintain a cash balance of more than $26,000.
If w is the amount Gavin withdraws to pay for expenses, the inequality representing the situation is BLANK. The amount he can withdraw is given by BLANK.
Answer: the answer is $76,000 dollars.
Step-by-step explanation:
$50,000 + $26,000= $76,000
The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they prefer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in a :b form)