[tex]x + y = 7~~~.....(i)\\\\xy=-30~~~~......(ii)\\\\\\\text{From (ii):}\\\\y= -\dfrac{30}x~~~~....(iii)\\\\\\\text{Substitute equation (iii) in equation (i):}\\\\\\x- \dfrac{30}x = 7\\\\\implies x^2 -30 = 7x\\\\\implies x^2 -7x -30 =0\\\\\implies x^2 -10x +3x -30 =0\\\\\implies x(x-10) +3(x-10) =0\\\\\implies (x+3)(x-10)=0\\\\\implies x = -3 ~~\text{or}~~ x=10\\\\\text{Substitute x = 10 in equation (iii):}\\\\\\y= -\dfrac{30}{10} =-3\\\\[/tex]
[tex]\text{Substitute x = -3 in equation (iii):}\\\\y = \dfrac{-30}{-3} =10\\\\\\\text{So, (x,y) =(10,-3) and (x,y)=(-3,10)}\\\\\\\text{Hence, the two numbers are}~ 10~ \text{and}~ -3.[/tex]
divide 3/7 by 1/2 i need answers
Answer:
6/7
Step-by-step explanation:
A line passes through (-5, -3) and is parallel to -3x - 7y = 10. The equation of the line in slope-intercept form is _____.
Answer: y = -(3/7)x - (36/7)
Step-by-step explanation:
Let's convert -3x - 7y = 10 to standard slope intercept form: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
-3x - 7y = 10
-7y = 3x + 10
y = -(3/7)x - (10/7)
This line has a slope of -(3/7). Any line that is parallel will have the same slope, so we can write y = -(3/7)x + b to start our new line.
We want a value of b that forces the line to go trough point (-5,-3). Use this point in the partial equation and solve for b:
y = -(3/7)x + b
-3 = -(3/7)(-5) + b
-3 = (15/7) + b
b = -3 - (15/7)
b = -(21/7) - (15/7)
b = -(36/7), or -5 1/7
y = -(3/7)x - (36/7)
What is the volume of a rectangular prism with a length of 2x, a width of x−2, and a height of x + 2?
Therefore, 2x³ - 8x units³ is the volume of a rectangular prism.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
(2x³ - 8x) is the volume of a rectangular prism.
What is volume?
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, a rectangular prism with a length of 2x, a width of (x−2), and a height of (x + 2)
Volume: L x B x H
= (2x) × (x - 2)(x + 2)
= (2x) × (x² - 4)
= 2x(x² - 4)
= 2x³ - 8x units³
Hence, 2x³ - 8x units³ is the volume of a rectangular prism.
For more references on volume, click;
https://brainly.com/question/13338592
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What is 11k+9=42 ? and how to do the work for it
Answer:
k = 3
Step-by-step explanation:
multiply 11 and 3 and you get 33 and then add 9 which you get 42
Answer:
k = 3
Step-by-step explanation:
[tex]11k+9=42\\\\11k+9-9=42-9\\\\11k=33\\\\\frac{11k}{11}=\frac{33}{11}\\\\k=3[/tex]
A box has 30 pencils in it.the probability of picking a red pencil is 1/6.How many red pencils are in the box
Answer:
[tex]\huge\boxed{\sf 5\ red\ pencils}[/tex]
Step-by-step explanation:
Total pencils = 30
Probability of picking a red = 1/6
Red pencils in the box = probability × total pencils
= 1/6 × 30
= 5 red pencils
So, there are 5 red pencils in the box.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807The area of rhombus is 360cmsquare and one of its diagonalis 18cm. Find the other diagonal.
Answer: 40 cm
So the diagonal formula is - 1/2* (d1*d2) d1 is the first diagonal and d2 is the second diagonal.
So,
1/2 * (18*d2)= 360
18*d2= 360*2
d2= 720/18
d2= 40
Tyler's brother Works
Tyler's brother earns $12 per hour. The store offers him a raise-a 5% increase per hour.
After the raise, how much will Tyler's brother make per hour?
Answer: $12.60 per hour
Step-by-step explanation:
5% of 12 is 0.60
12 + 0.60 = 12.60
Hope you have a great day
Answer:
$12.60 per hour
Step-by-step explanation:
5% of 12 is 0.60
and 12 + 0.60 = 12.60
Hope it makes sense
half the product of two number a and b, added to thrice a third number c
Answer:
ab/2 +3c
Step-by-step explanation:
Maybe you want to translate this to an algebraic expression.
__
The product of a and b is written ab.
Half that can be 1/2ab or ab/2. The latter tends to be less ambiguous.
Thrice c is 3c.
So, your expression is ...
ab/2 +3c
Cost to cross the bridge(one-way): Truck (2 or 3 axles): $3.00 Truck (4 or 5 axles): $6.25 Truck (6 or more axles): $10.00. One morning, 3 trucks, each with 5 axles, and 1 truck with 8 axles, crossed the bridge in one direction. write a math problem and solve it to answer. HOW MUCH WAS THE TOLL FOR THE CROSSING OF THE BRIDGE.
Truck (2 or 3 axles): $3.00
Truck (4 or 5 axles): $6.25
Truck (6 or more axles): $10.00
Day1= 3 trucks with 5 axles and 1 truck with 8 axles passed the bridge
What we need to find:
Part a: an expression that represents the first passing of the 4 trucks and
a solution to the the first expression
Part b: a modification of first expression that includes the return passing of the 4 trucks and a solution for the trucks passing both times.
Part a:
3(6.25)+1(10.00)
3(6.25)+1(10.00)=$28.75
Part b:
2[3(6.25)+1(10.00)]
2[3(6.25)+1(10.00)]=2[28.75]=$57.50
Which is correct? I wanna make sure im right
it is letter C. 3.9
hope it helps
#Chloe919
#thanks for the points
#carry on learning
The quadratic function g(x)=ax^2+bx+c has the complex roots (-7+4i) and (-7-4i)
What is the value of a?
What is the value of b?
What is the value of c?
Answers:
a = 1
b = 14
c = 65
===========================================================
Explanation:
Let's focus on the root x = -7+4i
Add 7 to both sides, then square both sides. Then get everything to one side so 0 is on the other side.
x = -7+4i
x+7 = 4i
(x+7)^2 = (4i)^2
(x+7)^2 = 16i^2
(x+7)^2 = 16(-1)
(x+7)^2 = -16
(x+7)^2+16 = 0
If you were to follow those steps for the other root -7-4i, then you should get the same result. Solving (x+7)^2+16 = 0 leads to the two complex roots -7+4i and -7-4i.
Expand out that expression to get it into standard form
(x+7)^2+16
(x+7)(x+7)+16
x^2+7x+7x+49+16
x^2+14x+65
The equation is now in y = ax^2+bx+c form
a = 1
b = 14
c = 65
If you were to plug those a,b,c values into the quadratic formula, you'll find that it leads to the two given roots -7+4i and -7-4i.
Need help fast on hs geometry please
[tex]\begin{gathered}15 = 4x + 3 \\ = > 4x = 15 - 3 \\ = > 4x = 12 \\ = > x = 3\end{gathered}
15=4x+3
=>4x=15−3
=>4x=12
=>x=3[/tex]
Therefore, YZ = 4x + 3 = 4(3) + 3 = 12 + 3 = 15Answers:
3, 15
Hope you could get an idea from here.
Doubt clarification - use comment section.
I’m so confused help please
Answer:
B. 0
Step-by-step explanation:
If you subtract the right side expression and simplify, you get ...
4/5(20x +5) -(16x -2) = 0
16x +4 -16x +2 = 0
6 = 0 . . . . . . . . . . . . false
There is no value of x that will make this true. There are no solutions.
Math problem (easy)
……………………………………..
8(3x – 6) = 6(4x + 8)
Answer: 0 = 96
Step-by-step explanation:
Answer:
The Answer is 0=96
How many different types of triangles are there?
Draw and name the 4 different triangles.
Write the properties of each triangle.
Draw a circle and name the different parts of the circle.
Find the relationship between radius and diameter.
NO SPAM!
Answer:
Explanation :How many different types of triangles are there?
There are 6 types of triangles.
➝ Scalene Triangle➝ Isosceles Triangle➝ Equilateral Triangle➝ Acute Triangle➝ Obtuse Triangle➝ Right Triangle[tex]\begin{gathered}\end{gathered}[/tex]
Draw and name the 4 different triangles.
[tex]\green\implies[/tex] The diagram of 4 different triangles is in the given pic. So, please check out the attachment.
The name of four triangles are :
➝ Right angled triangle ➝ Isosceles triangle ➝ Equilateral triangle ➝ Scalene triangle[tex]\begin{gathered}\end{gathered}[/tex]
Write the properties of each triangle.
1. Acute-angled Triangle
[tex]\pink\implies[/tex] Each of the angles is below 90⁰, and the sum of those angles is always 180⁰.
2. Right-angled Triangle
[tex]\pink\implies[/tex] One side being 90⁰, the other angles have to be acute. It is because the addition of all internal angles always produce 180⁰.
3. Obtuse-angled Triangle
[tex]\pink\implies[/tex] Naturally, the other two angles have to be smaller than an obtuse angle. It is so that the internal sum of all the angles remains 180⁰.
4. Equilateral Triangle
[tex]\pink\implies[/tex] Since the internal angles add up to 180⁰, each angle has to be equal in an equilateral triangle. In this case, each angle of this triangle is 60⁰.
5. Isosceles Triangle
[tex]\pink\implies[/tex] Since two sides have the same length, the third side has to have a different length. On top of that, the angle of the other side is also dissimilar to the previous angles.
6. Scalene Triangle
[tex]\pink\implies[/tex] In this case, the lengths of the three sides are diverse. However, the sum of dissimilar internal angles also has to be 180⁰.
[tex]\begin{gathered}\end{gathered}[/tex]
Draw a circle and name the different parts of the circle.
[tex]\green\implies[/tex] The diagram of circle is in the given pic. So, please check out the attachment.
Parts of circle :
A circle can have different parts and based on the position and shape, these can be named as follows:
➝ Centre➝ Radius➝ Diameter➝ Circumference➝ Tangent➝ Secant➝ Chord ➝ Arc➝ Segment➝ Sector[tex]\begin{gathered}\end{gathered}[/tex]
Find the relationship between radius and diameter.
[tex]\pink\implies[/tex] The relationship between radius and diameter is the diameter of a circle is twice of its radius.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
8(4p + 3) please and thanks
Answer:
32p + 24
Step-by-step explanation:
Distribute the 8 to each term
8 * 4p = 32p
8 * 3 = 24
The equation of line c is y = 5* - . Line d is parallel to line c and passes through (2, 6).
What is the equation of line d?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
Step-by-step explanation:
y = 5x is the reference line (as best as I can interpret " y = 5* - .").
We want a line, y=mx+b, where m is the slope and b is the y-intercept, that is parallel to y=5x.
Parallel lines will have the same slope as the reference line, in this case m=5. Our new line will take the form of y=5x+b. An important difference is that the new line must go through (2,6). We need to find a value of b that will make that work.
Use y=5x + b with point (2,6) and solve for b:
6 = 5*(2) + b
b = -4
The line that is parallel to y=5x and goes through the point (2,6) is thus:
y = 5x - 4
See the attachment.
The equation of line [d] in the slope intercept form can be written as -
y = 5x - 4
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + b
where -
[m] is slope of line
[b] is y - intercept
Given is the equation of line [c] is y = 5x and Line [d] is parallel to line [c] and passes through (2, 6).
The equation of line [d] in the slope intercept form can be derived as follows -
Slope of line [c] = Slope of line [d] (parallel lines)
m[d] = 5
Assume the equation of line [d] as -
y = m[d]x + b
6 = 5 x 2 + b
b = 6 - 10
b = - 4
The equation will be -
y = 5x - 4
Therefore, the equation of line [d] in the slope intercept form can be written as -
y = 5x - 4
To solve more questions on straight lines, visit the link below-
https://brainly.com/question/22038782
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Help pleaseeeeieneeiejne
Answer:
Pretty sure the domain for this is all positive numbers and range is all positive numbers over 1.
Step-by-step explanation:
domain refers to x values.
range refers to y values.
Help meeeeeeeeeeeeeeee
Answer:
D.
Step-by-step explanation:
Complementary angles are two angles whose measures add to 90°.
A.
m<CFD = 150° - 100° = 50°
m<EFD = 180° - 150° = 30°
Sum = 80°
No
B.
m<AFB = 40°
m<DFE = m<EFD = 30°
Sum = 70°
No
C.
m<AFC = 100°
Sum > 100°
No
D.
m<BFC = 100° - 40° = 60°
m<DFE = 30°
Sum = 90°
Yes
Answer: D.
STUDY TIP 1
Don't do all your studying the night before. Instead spread it out, review class materials several times a week, and focus on one topic at a time.
FOLLOW FOR MORE TIPS !!!
Answer:
THANK U!
FOR THE TIP.
HAVE A GREAT DAY!
The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
x = -8, x = 7. It can also be put into coordinate form based off what the website is looking for.
But solutions to a quadratic equation is essentially where the line crosses the 'x' line.
This is a Function?
O True
O False
Answer:
true
Step-by-step explanation:
Am I right? Should I've to add more info?(only about Rectangle and Square)
Answer:
Yh its right.
Step-by-step explanation:
Have a great day!
Answer:
yeah it is correct
Step-by-step explanation:
and well hruu
I need help with this question ASAP!
Colby worked three more hours
on Tuesday than he did on Monday. On
Wednesday, he worked one hour more
than twice the number of hours that he
worked on Monday. If the total number
of hours is two more than five times the
number of hours worked on Monday,
how many hours did he work on
Mondav?
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
Please quickly do number 12 & 13 I'll give brainliest.
Answer:
y=3.7x + 120.3, 180
Step-by-step explanation:
Add them into a graphing calculator and you get y=3.7x + 120.3
Put 16 in for x:
3.7 (16) + 120.3
59.2 + 120.3 = 179.5, rounds to 180
Write an Equation in Slope Intercept form for the line described:
passes through (2.5, 0) and (0, 5)
Answer:
y=-2x+5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-0)/(0-2.5)
m=5/-2.5
m=-2
y-y1=m(x-x1)
y-0=-2(x-2.5)
y=-2(x-2.5)
y=-2x+5
Please mark me as Brainliest if you're satisfied with the answer.
ANSWER. Robert takes a roast out of the oven when the temperature of the roast is 165 F. After 15 minutes, the temperature of the roast drops to 135 F. The temperature of the room is 70 F. How long does it take for the temperature of the roast to drop to 110 F?
ANSWER IS 34
Took the test :)