The length of the diagonal AC is equal to the length of the diagonal BD,
which is 8×10 - 32 = 48.
Response:
The length of AC is 48Which properties of a rectangle is used to find the length the diagonal AC?The given parameters are;
The diagonals of the rectangle are AC and BD
The point of intersection of the rectangle = Point E
AE = 2·x + 4
BD = 8·x - 32
Required:
The length of AC
Solution:
The diagonals of a rectangle bisect each other and have equal length.
Therefore;
AE = [tex]\mathbf{\frac{1}{2}}[/tex] × BD
Which gives;
[tex]2 \cdot x + 4 = \mathbf{\dfrac{1}{2} \times \left(8 \cdot x - 32\right)}[/tex]
2·x + 4 = 4·x - 16
4·x - 2·x = 4 + 16 = 20
2·x = 20
[tex]x = \dfrac{20}{2} = 10[/tex]
x = 10
AC = 2 × AE
Which gives;
AC = 2 × (2·x + 4) = 4·x + 8
The length of AC = 4 × 10 + 8 = 48
Learn more about the properties of a rectangle here:
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Decompose price effect into income effect and substitution effect.
Answer:
➢ Breaking up Price Effect into Income and Substitution Effect (with diagram) ADVERTISEMENTS: As price of a good X falls, other things remaining the same, consumer would move to a new equilibrium position at a higher indifference curve and would buy more of good X at the lower price unless it is a Giffen good.
[tex]Into \: your Arms[/tex]
#CarryOnLearning
A) Yes, at positive x-coordination or zero
B) Yes, at negative x-coordination or zero
C) Yes, at negative and positive x-coordinates
D) No, they will not intersect
I made points on the lines of the graph at (-4, -4), (-2, -2), and (2, 2), which don't intersect so I believe the answer is D.
A) Yes, at a positive x-coordination or zero.
B) Yes, at a negative x-coordination or zero.
C) Yes, at negative and positive x-coordinates.
D) No, they will not intersect.
What is the greatest common monomial factor of _________ ?
Answer:
A
Step-by-step explanation:
find the value of w and x
Please help, thank you!
Answer:
62.6
Step-by-step explanation:
A savings account earns 5% interest each year, compounded monthly. If a person invests $300 and makes no further deposits or withdrawals, what is the balance in the account after 3 years?
Sam has a party with snacks. One bowl of snacks has a mixture of fish crackers. There are 15 pretzels, 3 orange, 5 yellow, and 7 green fish crackers in the bowl.
What percent of the fish crackers are yellow?
Explanation:
Ignore the 15 pretzels. We're only focusing on the fish crackers.
3 orange + 5 yellow + 7 green = 15 total fish crackers
Of that total, 5 are yellow.
So approximately 5/15 = 1/3 = 0.333 = 33.3% of the crackers are yellow.
Anything to the right of the decimal point is ________ than 1.
Answer:
The answer is less than 1. :)
Write an expression for the area of the shaded region.
Answer:
There is no picture
Step-by-step explanation:
There are 14 red, 10 yellow, 5 green, and 3 purple candies in a bag. What is the probability that a candy chosen at random is not red?
Answer: 9/16
Work Shown:
14 red + 10 yellow + 5 green + 3 purple = 32 total
(32 total) - (14 red) = 18 that aren't red
18/32 = 9/16 is the probability of picking something that isn't red.
The probability that Hannah will be late for dinner is 1/2 what is the probability that she will be late for dinner two nights in a row?
Answer:
1/4
or 25%
or 0.25
Step-by-step explanation:
With a question like this, you have to multiply.
1/2 * 1/2 = 1/4
or
0.5 * 0.5 = 0.25
Suppose that all pizzas have the same thickness and the cost and number of servings both depend only on the surface area.
A pizza 10 inches in diameter
costs £8.99 and serves 2 people.
a) How much should a 14-inch pizza cost
b) How many people would the 14-inch pizza serve?
Answer:
a: 17.62
b: 4
Step-by-step explanation:
not entirely sure if its correct but..
Examine the diagram.
A triangle has angles 1, 2, 3. Angle 4 is an exterior angle to angle 3.
For the angles shown in the diagram, which statements are true? Select all that apply.
The sum of m∠3 and m∠4 is 180°.
The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle.
∠3 is supplementary to ∠1.
m∠4 = m∠1 + m∠2.
m∠1 + m∠2 + m∠3 = 180°
The statements that are true regarding the diagram given are:
m∠3 + m∠4 = 180° (angles on a straight line)m∠4 = m∠1 + m∠2 (external angle theorem)m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).What is the Triangle Sum Theorem?The triangle sum theorem states that all the three interior angles in a triangle have a sum of 180 degrees all together.
Thus, in the diagram given, the statements that are all true are:
m∠3 + m∠4 = 180° (angles on a straight line)
m∠4 = m∠1 + m∠2 (external angle theorem)
m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).
Learn more about triangle sum theorem on:
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Answer:
A, D, E
Step-by-step explanation:
I got it right.
how do you use quadratic functions?
and please get correct!
Use this for formula
firstly
ax²+bx+c=0
and then
b±√(b²-4ac))/(2a)
1 . step
First compare the given equation with
general form
[tex]{a{x}^{2}\:+\:bx\:+\:c\:=\:0}[/tex]
2. step
Then find the value of discriminant
by the given equation below
[tex]\mapsto{{b}^{2}\:-\:4ac}[/tex]
3. step
subsitute the value of discriminant and other given value in Quadratic formula as per the equation .
[tex]{\rightarrow{\frac{-\:b\:±\:\sqrt{{b}^{2}\:-\:4ac}}{2a}}}\\[/tex]
On Monday a shop receives $60.30 by selling bottles of water at 45 cents each
How many bottles are sold?
Answer:
134 bottles
Step-by-step explanation:
For this, I set up a proportion :
60.30/x = 0.45/1
60.30(1) = 0.45x
60.30/0.45 = 0.45x/0.45
x = 134 :)
Answer:
134 bottles
Step-by-step explanation:
conversion of dollars to cent:
$1 equals to 100 cents.
$60.30 will be (60.30*100) cents → 6030 cents
Bottles sold: total money / each bottle cost.
→ 6030 / 45
→ 134
So 134 bottles are sold for 45 cents to earn $60.30 or 6030 cents.
Given triangle ABC is similar to triangle DEF, angle A measures 30 degrees, and angle F measures 50 degrees, what is the measure of angle B?
Answer:
100 degrees
Step-by-step explanation:
Since triangle ABC is similar to triangle DEF, their angles are basically the same.
All angles of a triangle have to add up to 180.
We are already given two angles: 30 and 50
Add them together: 30 + 50 = 80
Now we subtract the number from 180
180 - 80 = 100
The remaining angle has to be 100 degrees
Once a large pink ribbon, the sign of the fight against breast cancer, was erected out of pink post-it notes on a billboard. If the area of therectangular billboard covered by the ribbon was approximately 4200 square feet, and the width of the billboard was approximately 60 feet, what
was the height of this billboard?
Answer:
The answer is 70 feet
Step-by-step explanation:
Given;The area of therectangular billboard covered by the ribbon was approximately 4200 square feetThe width of the billboard was approximately 60 feet.To Find;The height of this billboard = ?Formula;Area = Width × HeightHere, We know the area so,
Area = Width × Height
Height = Area ÷ Width
H = 4200 ÷ 60 feet
H = 70 feet
Thus, The height of the billboard is 70 feet
-TheUnknownScientist 72
what is x
1/3+3=4-x
This is too hard for me
Answer:
x = 2/3
Step-by-step explanation:
Add the numbers
[tex]\frac{1}{3}+3=4-x[/tex]
[tex]\frac{10}{3}=4-x[/tex]
Rearrange terms
[tex]\frac{10}{3}=-x+4[/tex]
Subtract 4 from both sides of the equation
[tex]\frac{10}{3}-4=-x+4-4[/tex]
Simplify
[tex]\frac{-2}{3}=-x[/tex]
Divide both sides of the equation by the same term
[tex]\frac{-2}{3}/1=\frac{-x}{1}[/tex]
Simplify
[tex]x=\frac{2}{3}[/tex]
[RevyBreeze]
Answer:
20
3. Addie visited the elephant exhibit at the zoo. If there were 7 elephants in the
exhibit, how many elephant legs did Addie see?
Show work:
Strategy:
How much material, in square inches, is needed to make the flag? square inches If the material costs $0. 15 per square inch, how much will Marta spend on materials to make the flag? $.
The amount of material needed by Marta to make the flag is;
[tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex] square inch.
The total cost of making the flag is;
[tex]\rm 0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex] dollar.
Given
Marta is making a flag with the given dimensions.
The perimeter of the flag is 100 inches.
Let us consider that the flag has a triangular shape.
Hero's formula;According to the Hero's formula;
The area of the triangle is given by;
[tex]\rm Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where, s is the semi perimeter and a, b, and c are the sides of the triangle.
Semi perimeter s = P/2,
Since the perimeter of the flag is 100 inches.
[tex]\rm S=\dfrac{100}{2}\\\\S=50[/tex]
The dimensions of triangular shape are [tex]\rm d_1, d_2 \ and \ d_3[/tex].
Then,
The area of the triangular flag becomes;
[tex]\rm Area =\sqrt{s(s-a)(s-b)(s-c)}\\\\\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex]
So the amount of material needed to make the flag is;
[tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex]
Therefore,
The cost of material = C = $0.15 per square inch
So the total cost in making the flag will be;
[tex]\rm C\times A=0.15 \times A\\\\=0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex].
Hence, The amount of material needed by Marta to make the flag is [tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex].
To know more about Hero's formula click the link given below.
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BRAINLY PLS HELP ME ON THIS QUESTIONNN
Answer:16 square feet
Step-by-step explanation:
add the length of the top and the bottom face them multiply the sum of those two by the perpendicular height between them and the product is to be divided by 2 : ((a+b)h)/2)
Answer:
16 ft²
Step-by-step explanation:
First you'll find the area of the rectangle forming in the trapezoid:
3 x 4 = 12
Next, you'll think logically and understand that if BC is 3 feet, EF is also 3 feet. So, you'll subtract 5 - 3 = 2, so AE and FD is 1 foot.
So, you'll now multiply to find the area of the whole trapezoid:
4 x 1 = 4
So:
4 + 12 = 16
What's the simplified expression of 6x2y3/2x−2?
Step-by-step explanation:
6x^2y^3/2x-2
=6x^2y^3/2 (x-1)
=3x^2y^3/(x-1)
Answer:
3x4y3 just got this on a test and it was right
Step-by-step explanation:
The sum of 2 numbers is 15 and their qoutient is 2
x + y = 15------(1)
x/y = 2------(2)
y = 15 - x
put this value in eq 2
x/(15-x) = 2
x = 2 (15 - x)
x = 30 - 2x
2x + x = 30
3x = 30
x = 10
y= 15 - x
y = 15 - 10
y = 5
Solution:
Given:
x + y = 15x/y = 2Let’s simplify the second equation to find out the value of x.
x/y = 2 x = 2yNow, let’s substitute the value of x into the first equation.
x + y = 152y + y = 153y = 15y = 5Now, let’s substitute the value of y into the simplified second equation.
x = 2yx = 2(5)x = 10Hence, the value of x and y are 5 and 10 respectively.
this is my last question please help
Answer:
71,3Step-by-step explanation:
the first nuclear every time in this topic is y and the second one is x
40 POINTS NOW HELP 5 MINS COME ON HELP
❥[tex]\Large\pmb{ \underline {\tt Answer}}[/tex]
2x + 5 = 3x - 25
5 + 25 = 3x - 2x
x = 30
Option B
reason:- Attached picture
Answer:
letter C is the right answer
Step-by-step explanation:
hope it helps!
# CARRY ON LEARNING
BRAINLIEST ME PLEASE PLEASE PLEASE PLEASE PLEASE
Reflect about the line x=5
Step-by-step explanation:
sori po kailangan ko po ng points sori po talaga
-(6e-11) (e - f) math Algebraic expressions
Answer:
-6e^2 - 6ef + 11e + 11f
Step-by-step explanation:
FOIL
(-6e+11)(e-f)
-6e x e = -6e^2
-6e x f = -6ef
11 x e = 11e
11 x f = 11f
Rewrite and you get your answer
which set of pairs represents a function? PLSS HURRY (100 POINTS)
Answer:
{(0, 0), (1, 2), (2, 4), (3, 4)}
Step-by-step explanation:
A set of ordered pairs that represent a function is one in which each different ordered pair has a unique x-coordinate (so no two different ordered pairs can have the same x -coordinate).
Therefore, {(0, 0), (1, 2), (2, 4), (3, 4)} is a function as each different ordered pair has a unique x-coordinate.
The other sets all have different ordered pairs that share the same x-coordinate and so these sets do not represent functions.
The vertical line test is also used to determine whether a graph represents a function. If the vertical line intersects the graph only once, then the curve represents a function. This test can be applied to ordered pairs, in that if two ordered pairs have the same x-coordinate but different y-coordinates, they will be on the same vertical line and therefore do not represent a function.
Find the values of x and y.
Answer:
Given, x,y and 40 are the angles of a triangle.
Therefore, x+y+40=180
x+y=140
The difference between the two angles x and y is 30.
Therefore, x−y=30 ....(2)
Add equations (1) and (2), we get
2x=170
⇒x=85
Substitute this value n equation (2), we get
85−y=30
⇒y=85-30
⇒y=55
Therefore, angles of a triangle are x=85, y=55 and 40.
Answer:
Step-by-step explanation:
for x :
180° - 40° = 140°
40° / 2 = 20°
x = 20°
for y :
20° + 90° = 110°
180° - 110° = 70°
x = 70°
solve system of equations:
-8x - 10y = 10
3x + 2y = 12
Answer:
x=10
y = -9
Step-by-step explanation:
-8x - 10y = 10
3x + 2y = 12
Multiply the second equation by 5
5(3x + 2y) = 12*5
15x+10y = 60
Add this to the first equation to eliminate y
-8x - 10y = 10
15x+10y = 60
-----------------------
7x + 0y = 70
Divide by 7
7x/7 = 70/7
x = 10
Now find y
3x+2y = 12
3(10) +2y = 12
30 +2y =12
Subtract 30 from each side
2y = 12-30
2y = -18
Divide by 2
2y/2=-18/2
y = -9