Answers
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
Define equation.
Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.
Here,
are the definitions of each equation:
1. x^2 + y^2 - 4x + 6y - 5 = 0
The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.
2. x^2 - 6y = 0
The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.
3. 4x^2 + 9y^2 = 1
This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.
4. 7x^2 - 9y^2 = 343
A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
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Related Questions
How do I even do thissss?
Answers
Please provide your question with a math problem in the form of an image or text.
evaluate 6²-2(5+1+3)
Answers
Answer:
18
Step-by-step explanation:
36-10-2-6
26-8
18
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6^2 - 2(5 + 1 + 3)}\\\mathsf{= 6^2 - 2(5) - 2(1) - 2(3)}\\\mathsf{= 6^2 - 10 -2(1) - -2(3)}}\\\mathsf{= 6\times 6 - 10 - 2(1) - 2(3)}\\\mathsf{= 36 - 10 - 2(1) - 2(3)}\\\mathsf{= 26 - 2(1) - 2(3)}\\\mathsf{= 26 - 2 - 2(3)}\\\mathsf{= 24 - 2(3)}\\\mathsf{= 18}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{18}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
hich are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representations of the inequality are
-6x + 15 < 10 - 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Solving inequality and determining the correct representationsFrom the question, we are to determine the correct representations of the inequality
From the given information,
The given inequality is
-3(2x - 5) < 5(2 - x)
To determine the correct representations, we would proceed to solve the inequality
Solving the inequality
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x
This is one of the representations of the inequality
Then,
Collect like terms
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
Multiply through by -1
x > 5
If the solution is represented on a number line, we would have a number line from negative 3 to 3 with an increments of 1 and an open circle at 5 and a bold line starts at 5 and is pointing to the right.
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Given:m<1+m<2=90 and m<3+m<4=90,prove m<1=m<4
Answers
The proof that the angles m<1 = m<4 is shown below
How to prove the measure of the anglesFrom the question, we have the following parameters that can be used in our computation:
Measure of angles
The angle measurements are then given as
m<1 + m<2 = 90 and m<3 + m<4 = 90
The relationship to prove is also given as
m<1 = m<4
Using the above as a guide, we have the following:
Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90
This gives
m<1 + m<2 = 90
-(m<3 + m<4 = 90)
Evaluate the difference
m<1 + m<2 = m<3 + m<4
When both sides of the angle equations are compared, we have:
m<1 = m<4
m<2 = m<3
Ignoring the second equation, we have
m<1 = m<4
Hence, the measure of the angles has been proved
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For a science experiment, each student needs 5 grams of salt. If there are 26 students in the class how many milligrams of salt will they need?
Answers
Please do 1. and 2.! 25 points, please need asap!
Answers
Step-by-step explanation:
1
We can see that RS divides ∆PQS into two equal parts
So,
PR = RQ
Therefore
RQ = 5.1
Now
PQ = PR + RQ
=> PQ = 5.1 + 5.1
=> PQ = 10.2
2
Here
KM is the angle bisector
So
JM = ML
JM = 46
Please need help ASAP, 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed.
Answers
(1). ΔIJH ≅ ΔKHJ, by SSS criterion,
and (2) we need, ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove ΔTNS ≅ ΔUHS, by HL criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangle:
ΔIJH ≅ ΔKHJ.
To prove the congruent by SSS:
We have to show that three sides of the triangle are congruent to three sides of the other triangle.
Here,
IJ ≅ KH.
IH ≅ JH, Given.
And both triangles share the same side JH.
So,
JH ≅ JH
So, ΔIJH ≅ ΔKHJ, by SSS criterion.
ΔTNS ≅ ΔUHS.
To prove the congruent by HL:
We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.
So, we need;
ΔTNS and ΔUHS are right-triangles.
S is the mid-point.
So,
SN ≅ SH.
ST ≅ US
So, ΔTNS ≅ ΔUHS, by HL criterion.
Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;
ΔTNS and ΔUHS are right-triangles and S is the mid-point.
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A blue rope is 3 times as long as a red rope. A green rope is 4 times as long as the blue rope. If the total length of the three ropes is 563.84 meters, what is the length of the blue rope?
Answers
Answer:
105.72 meters
Step-by-step explanation:
We can set up a system of equations to represent the information given in the problem, and then use algebra to solve for the length of the blue rope. Let x be the length of the red rope.
According to the problem statement:
blue rope = 3 * red rope = 3x
green rope = 4 * blue rope = 4 * 3x = 12x
we know that:
red rope + blue rope + green rope = 563.84
x + 3x + 12x = 563.84
then we can solve for x:
16x = 563.84
x = 35.24
So the length of the red rope is 35.24 meters.
The length of the blue rope is 3x = 3 * 35.24 = 105.72 meters.
Determine the value of x.
A) 2√3 B) 6√3 C) 12 D) 12√3
Answers
Sin60=6/hyperbola
•hyperbola=6/sin60
•hyperbola=4 √3
Now,
We know,
Hyperbola^2= Base ^2 +Perpendicular ^2
•Base(x)= √(Hyperbola^2-Perpendicular ^2)
•Base(x)=2√3
So Value of X is 2√3 (Ans.)
Correct Option: A) 2√3
PLEASE HELP!
An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Answers
Exact Circumference = 4pi feet
Approximate Circumference = 12.56 feet (when using pi = 3.14)
======================================================
Explanation:
The larger circle has a 3 foot radius.
The inner circle has a 3-1 = 2 foot radius.
Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.
C = 2pi*r
C = 2pi*2
C = 4pi
The exact circumference is 4pi feet. This is the perimeter around the circle.
If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.
4/9 dividend by 2/3 =
Please help!!!will give brainlest
Answers
Answer:
2/3
Step-by-step explanation:
4/9 divided by 2/3 = 4/9 times 3/2
= 2/3
Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214?
Answers
Answer:
To show 1214 using place value blocks, you would need at least 4 blocks: one thousand block, two hundred blocks, one ten block, and four ones blocks. If you have fewer than 4 blocks, it is not possible to show 1214 using place value blocks.
If you have exactly 4 blocks, you can show 1214 in only 1 way: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks.
If you have exactly 5 blocks, you can show 1214 in 2 ways: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks, or using 2 thousand blocks, 1 hundred block, 2 ten blocks, and 4 ones blocks.
If you have exactly 6 blocks, you can show 1214 in 3 ways: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks, using 2 thousand blocks, 1 hundred block, 2 ten blocks, and 4 ones blocks, or using 1 thousand block, 1 hundred block, 3 ten blocks, and 4 ones blocks.
Therefore, if you have fewer than 10 place value blocks, you can show 1214 in 3 different ways.
The length of a rectangle is twice its width. The perimeter is 30. Find it’s dimensions.
Answers
Answer:
Length = 10 Width = 5Step-by-step explanation:
Let's assume that,
→ Length = 2x
→ Width = x
→ Perimeter = 30
Perimeter of rectangle formula,
→ P = 2(L + W)
Now the value of x will be,
→ P = 2(L + W)
→ 2(2x + x) = 30
→ 2 × 3x = 30
→ 6x = 30
→ x = 30/6
→ [ x = 5 ]
Then required dimensions are,
→ Length = 2x = 2 × 5 = 10
→ Width = x = 5
Hence, these are the dimensions.
Length = 10
width = 5
Given-
Perimeter =30
l=2b........................................................ i
so
P =2(l+b)
here
30 = 2(2b +b)... ... .............. as l=2b from i
30 = 2*3b
30 = 6b
b= 5
which implies l= 2*5 --->10............................................ from i
so
Length = 10
width = 5
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Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
Answers
The rate of change of surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
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Ln 4 - Ln x = 2
Solve for x showing all steps. Round to the nearest hundredth.
Please give step by step instruction
Answers
In logs, when there is a minus you have to divide so the first step is to do the following :
Ln (4/x) = 2
Then you have to convert the logarithm into exponential form using that ln (x) = b is equal to x = e^b. Therefore the next step should look like this :
4/x = e^2
Then multiply both sides by x, which becomes :
4 = (e^2)(x)
Then divide both sides by e^2. Which becomes :
4/e^2 = x
0.541341 = x
To the nearest hundredth, it becomes 0.54
any help? please make sure it's correct thank you
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
The slope will be perpendicular to equation through A and B because of the 90 degree angle at B.
Lines that are perpendicular have opposite reciprocal slopes.
The slope of the line we know is 2 (The slope is the number before the x). The opposite reciprocal is -[tex]\frac{1}{2}[/tex].
Now that we have the slope we need a point on the line. They give us that point at (0,6) We will use the y value of 6 and the x value of 0 from the point given to find the y-intercept.
slope (m) = - [tex]\frac{1}{2}[/tex]
y = 6
x = 0
We will substitute all of this information into y = mx + b to solve for b (y-intercept)
y = mx + b
6 = - [tex]\frac{1}{2}[/tex] (0) + b
6 = b
Now that we have the slope (- [tex]\frac{1}{2}[/tex]) and the y-intercept (6) we can write the equation
y = - [tex]\frac{1}{2}[/tex] x + 6
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
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 )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
BC is perpendicular to AB
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{BC}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
the line BC has point C at (0, 6 ) ⇒ c = 6
y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line BC
PLEASE HURRY I WILL GIVE BRAINLY PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.
c = 87
c = 8.5
c = 35
c = 10
Answers
Answer:c=35
Step-by-step explanation:
i just did this
.
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18
According to the above table, what was the average number of pools sold per month during this period? Round to the nearest tenth if necessary.
Answers
According to the table, the average number of pools sold per month during this period is 14 (to the nearest tenth)
What is average?It is defined as the ratio of summation of all the data to the number of units present in the list. It can also be the middle value, calculated by dividing the total of all the values by the number of values.
The average can also be defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
It is represented mathematically as;
Average = Sum of Values/Number of Values
Average = total swimming pools sold in six months / number of months
Average = (11 + 10 + 12 + 16 + 15 + 18) / 6
Average = 82/6
Average = 13.7
Average = 14 (to the nearest tenth)
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A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels down 4.2 feet.
She then travels directly up 3.4 feet.
Next, she descends a second time, 10 feet.
Answers
Answer:
Below
Step-by-step explanation:
0 ft -4.2 + 3.4 - 10 = -10.8 ft or 10.8 ft below the surface
Need Help With This
Answers
Step-by-step explanation:
a) x+20+x+90=180 [sum of 3 angel of triangle]
2x + 110 = 180
2x = 180- 110
2x = 70
x = 70÷2
x = 35
b) 2y + y + y = 180
4y = 180
y = 180÷4
y= 45
c) 4z-30 + 2z = 180
6z = 180 + 30
6z = 210
z = 35
What is the major theme and minor theme in “Arachne and the weaving contest”
Answers
The central theme of Arachne is human limitation and hubris.The center of the ellipse is located midway between the foci .
What is major axis ?The center of the ellipse is located midway between the foci. The minor axis is the line segment going through the center and perpendicular to the major axis, with both endpoints on the ellipse. The length of the ellipse's major axis is equal to the bigger of 2a or 2b, while the length of its minor axis is equal to the smaller. The major axis, which is the largest distance between any two points on the ellipse, is the line that connects both foci and runs from one end to the other. The minor axis, which is the shortest path between two points on the ellipse, is the line that passes through the center of the major axis in a perpendicular direction.
given
The central theme of Arachne is human limitation and hubris. Arachne, a young girl who is a remarkably gifted weaver, thrives on the adulation of her customers.
As a result of her youth and inexperience as well as her awareness of her exceptional talents, Arachne eventually boasts that her weaving is even greater than Athena's.
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Find x, y, mzC, and mA' given m/A = y;
m/A' = 2x + 5, mc-3x-y,
mZC' = 4
Answers
The value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
What is the triangle translation?
In mathematics, a triangle translation refers to the geometric transformation in which a triangle is moved to a new position without rotating or scaling it. The triangle is simply slid along a straight line in a certain direction, and the new position of the triangle will be parallel to the original one.
Given that ΔABC translates to ΔA'B'C', we can assume that the measures of the angles are the same in both triangles. Therefore, if we know the measure of an angle in one triangle, we can assume that the measure of the corresponding angle in the translated triangle is the same.
Given:
m∠A = y
m∠A' = 2x + 5
m∠C = 3x-y
m∠C' = 4
Since opposite angles in a rectangle are congruent, m∠A=m∠C' and m∠C = m∠A'
Therefore,
y = 4
3x-y = 2x + 5
Solving this equation gives us:
x = y + 5 = 4 + 5 = 9
y=4
m∠C = 3x - y = 3(9) - 4 = 25
m∠A' = 2x + 5 = 2(9) + 5 = 23
Hence, the value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
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elijah used 3/4 of the memory on his cell phone memory card if the memory card can hold 32 gigabytes how many gigabytes did elijah used
Answers
Elijah used 24 gigabytes memory on his cell.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Elijah used 3/4 of the memory on his cell phone memory card.
And, The memory card can hold 32 gigabytes.
Now,
Since, The memory card can hold 32 gigabytes.
And, She used 3/4 of the memory on his cell phone memory card.
Hence. The used memory = 3/4 of 32
= 3/4 × 32
= 3 × 8
= 24 gigabytes
Thus, Elijah used 24 gigabytes memory on his cell.
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What is the following sum?
Answers
Answer:
The 4th one
Step-by-step explanation:
Right on edge!
6x(2x+3)+1(2x+3)
Rewrite the expression
Answers
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(7) = -1 B. g(-4) = -11 C. g(0) = 2 D. g(-13) = 20
Answers
Answer: B
Step-by-step explanation:
If s is directly proportional to t, and s = 30 when t = 15, find t when s = 64.
Answers
Step-by-step explanation:
please refer to sketch for detail
Ed is using the recipe shown to make fruit salad. He wants to use 30 diced strawberries in his fruit salad. How many bananas, apples, and pears should Ed use in his fruit salad?
Fruit Salad Recipe - 4 bananas, diced. 3 apples, diced. 6 pears, diced. 10 strawberries, diced.
Answers
Answer:
12 bananas
9 apples
18 pears
Step-by-step explanation:
You are tripling the recipe.
10 x 3 = 3
4 x 3 = 12
3 x 3 = 9
6 x 3 = 18
can someone help me please i really have to do this right now
Answers
Answer: Angles 2 and 4 = 38, Angle 1 = 142
Step-by-step explanation:
Given that angle 3 is equal to 142, the angle between 2 and 3 has to add up to 180. 142 + 38 = 180. The same applies for angle 4 and 3. So, angle 1 + angle 2 has to add up to 180. We already know angle 2, so now we just have to subtract that from 180 to find angle 1.
-15 POINTS-
Don’t explain.
Y=[?]
Answers
Step-by-step explanation:
of course I need to explain it, since you don't know how to get it. that is the purpose of Brainly. not to be a calculator slave to you, but to enable you to solve similar problems on your own in the future.
both shapes are similar.
that means that
1. both have the same angles
2. there is one common scaling factor for all pairs of corresponding sides (and other lengths as heights, ...).
we need 2. here to solve.
AB / EF = f = 3/2
x = AD
x / EH = f = 3/2
x / 2.4 = 3/2
x = 2.4 × 3/2 = 7.2 / 2 = 3.6