The length of a rectangle is 4 cm more than 3 times it’s width. If the area of the rectangle is 15 cm^2, find the width. Use quadratic equations.
Answers
Related Questions
Jonathan bought a new computer for $1,716, using the electronics store's finance plan. He will pay $143 a month for 12 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Answers
Answer:
y = 1716 -143x
Step-by-step explanation:
You want an equation for the amount owed after x months on a purchase of $1716 paid at the rate of $143 per month.
PaidAfter x months, the amount paid will be 143·x. The amount owed is the difference between the original purchase price and the amount paid:
owed = $1716 - paid
y = 1716 -143x . . . . . . . . . the amount Jonathan still owes after x months
Consider isosceles ΔXYZ.
What is the value of n?
What is the measure of leg XY?
ft
What is the measure of leg XZ?
ft
Answers
1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.
In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:
XY=XZ
(9n+12)ft=(15n-6)ft
From this equation we have to find n:
9n-15n=-6-12
-6n=-18
[tex]n=\frac{-18}{-6}[/tex]
n=3
2) The measure of the leg XY in ft
XY=(9n+12)ft
Substitute the value of n calculated in the first question:
XY=(9(3)+12)ft
XY=39 ft
3) The measure of the leg XZ in ft
XZ=(15n-6)ft
Substitute the value of n calculated in the first question:
XZ=(15(3)-6)ft
XZ=39ft
A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.What is isosceles triangle?A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
Given information-
The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
The measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
a) the value of n-For the isosceles triangle, the two sides and two angle of the equal in measure.
As the measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
Thus the opposite side of this angles must be equal. Thus,
[tex]XY=XZ[/tex]
Put the values as,
[tex]9n+12=15n-6\\15n-9n=12+6\\6n=18\\n=3[/tex]
Hence the value of n is 3 units.
b) the measure of leg XYThe length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
Put the value of n,
[tex]XY=9n+12\\XY=9\times3+12\\XY=27+12\\XY=39 \rm ft[/tex]
Hence the measure of leg XY is 39 feet.
c) the measure of leg XZThe length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
Put the value of n,
[tex]XZ=15n-6\\XZ=15\times3-6\\XZ=39\rm ft[/tex]
Hence the measure of leg XZ is 39 feet.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.Learn more about the isosceles triangle here;
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25 POINTS to answer question!
Answers
This is because the line would have to cross through -4 on the y-axis on the graph. "A" is the only answer that has a line through -4.
PLEASE HELP
BRAINLIEST AVAILABLE THX
PLEASE ASSIST ME N TRY TO HELP ME
Answers
hope i helped
Which of the following choices represents the expanded form of the number 38,072?
30,000+800+70+2
30,000+8,000+70+2
30,000+8,000+700+2
3,000+800+70+2
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Final answer:
The expanded form of 38,072 is 30,000 + 8,000 + 70 + 2, where each term represents the digit's value as a product of its place value.
Explanation:
The expanded form of the number 38,072 is written by separating each digit according to its place value and expressing it as the digit multiplied by the power of ten that represents its position. Therefore, the correct expanded form is:
30,000 + 8,000 + 70 + 2
To understand this, we can consider the place value of each digit in the number 38,072. The '3' is in the ten-thousands place, so it is 3 times 10,000, which is 30,000. The '8' is in the thousands place, so it is 8 times 1,000, which is 8,000. The '0' stands for no hundreds, so we skip it. The '7' is in the tens place, so it is 7 times 10, which is 70. Finally, the '2' is in the ones place, which is just 2.
HOW would I go about figuring this out? I need explanation not just answer
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3/4 = x/24
Cross multiply:
4x = 72
Divide by 4:
x = 18
There were 18 clarinets in the music room.
Hope this helps :)
Need to find the formula for:
Car problem: Julie wants to borrow her parent's car to drive to a tournament. Her parents tell her she has to pay for the gas she uses. The car gets 26 mpg. Julie wonders how much gas she will need to purchase to get to the tournament and back.
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The Thrill amusement park charges an entry fee of $40 and an additional $5 per ride, x. The Splash water park charges an entry fee of $60 and an additional $3 per ride, x. Based on this information, which system of equations could be used to determine the solution where the cost per ride of the two amusement parks, y, is the same?
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The costs per ride for Thrill and Splash amusement parks can be represented by the equations y = 40 + 5x and y = 60 + 3x respectively. Equating these will give us the number of rides where the costs at both parks will be the same.
Explanation:The cost of visiting each park can be represented as a linear equation. For Thrill amusement park it can be written as y = 40 + 5x, where y is the total cost, 40 is the entry fee and 5x represents the cumulative cost of the rides, with x being the number of rides. For Splash Water Park, the equation is y = 60 + 3x, where 60 is the entry fee and 3x is the cost of the individual rides. To find out when the costs per ride at the two parks will be the same, we solve the system of equations by setting the two equations equal to each other: 40 + 5x = 60 + 3x.
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helppppppppppppppppppppppppppppppp
Answers
-3/2
Explanation:
The given is:
(1/36)^n = 216
Take log base 6 both sides:
log base 6 of (1/36)^n = log base 6 of (216)
log base 6 of (1/6)^2n = log base 6 of (1/6)^-3
2n * log base of (1/6) = -3 * log base 6 of (1/6)
This means that:
2n = -3
n = -3/2
Hope this helps :)
(1/36) ^ n = 216
We use log function:
log ((1/36) ^ n) = log (216)
For log properties we have:
nlog ((1/36)) = log (216)
n = log (216) / log ((1/36))
n = -1.5
Rewriting we have that the value of n is:
n = -3 / 2
Answer:
n = -3 / 2
option 2
Find an ordered pair (x,y) that is a solution to the equation.
3x-y=3
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One example is (1, 0).
We can see this will work by first selecting any value for x. We'll use the 1 that I gave.
3x - y = 3.
Now sub the value in.
3(1) - y = 3.
Multiply.
3 - y = 3.
Solve for y.
y = 0.
This gives you the ordered pair (1, 0).
Answer: The required ordered pair is (1, 0).
Step-by-step explanation: We are given to find an ordered pair (x, y) that is a solution to the following equation:
[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find an ordered pair, we should either take a value of x and find the corresponding value of y,
or,
we should take a value of y and find the corresponding value of x.
Let us consider that
x = 1.
Then, from equation (i), we get
[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]
Thus, the required ordered pair is (1, 0).
what is the value of x to the nearest tenth?
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x = 2.546
rounded to nearest tenth x = 2.5
which scale factor would produce a contraction?
A.) 5/2
B.) 1.2
C.) 2.3
D.) 3/4
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the scale factor produce a contraction when its value must be less than zero
Let
SF---------------> scale factor
SF< 0------------> produce a contraction
A.) 5/2 --------> 2.5 SF>0 not produce a contraction
B.) 1.2 --------> 1.2 SF>0 not produce a contraction
C.) 2.3 --------> 2.3 SF>0 not produce a contraction
D.) 3/4--------> 0.75 SF< 0 produce a contraction
the answer is 3/4
A regression line was calculated as ŷ = 1.7x + 2.1. What is the slope of the regression line. is _____. Type a numerical answer in the space provided.
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The slope is the number to the left of the x variable. Each time x increases by 1, the value of yhat increases by 1.7
Given Sin x= 0.5, what is cos x?
Enter your answer as a decimal, round only your final answer to the nearest hundredth.
Answers
sin x = 1/2
sin x = opp/hyp
therefore the ratio of opp/hyp = 1/2, (opp = 1, hyp = 2)
Find the opp side
1² + x² = 2²
1 + x² = 4
x² = 4 -1
x² = 3
x =√3
The opp side is √3
cos x = opp/hyp = √3/2 = 0.87 (round to the nearest hundredths)
If sin x = 0.5, cos x is approximately 0.87.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
To find cos x, we can use the identity: cos² x + sin² x = 1
We are given that sin x = 0.5.
We can substitute this into the identity to solve for cos x:
cos² x + sin² x = 1
cos² x + (0.5)² = 1
cos² x + 0.25 = 1
cos² x = 0.75
cos x = ±√0.75
We take the positive square root since cosine is positive in the first and fourth quadrants.
Evaluating the square root gives:
cos x ≈ 0.87 (rounded to two decimal places)
Therefore,
cos x is approximately 0.87.
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What is the area of the polygon given below?
Answers
A = 28 + 117 + 36
A = 181
answer
D. 181 square units
ASAP What is the lateral area of this regular octagonal pyramid?? Explain your answer if you can plz thanks
Answers
The lateral area is the area of all of the lateral faces of the pyramid. There are 8 triangles making up the lateral faces. Each has a base of 6.6. The formula for the area of a triangle is
A=1/2bh,
so we still need the height of the triangle.
The height of each lateral triangle is the slant height of the pyramid. The slant height of the pyramid forms a right triangle with the height of the pyramid and the "radius" as it were of the pyramid. Thus we use the Pythagorean theorem:
8²+8²=h²
64+64=h²
128=h²
√128=√(h²)
8√2 = h
Substituting this into our area formula we have:
A=1/2(6.6)(8√2)
We will go ahead and multiply this by 8, since there are 8 lateral faces:
LA=8(1/2)(6.6)(8√2)
LA = 298.7
Answer:
Hello! The correct answer is 298.7 [tex]cm^{2}[/tex]
Step-by-step explanation:
I am just confirming!
You made 1/2 quart of lemonade. How many 1/4 quart-sized glasses will you be able to fill with lemonade?
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The solution is 2 glasses
The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of 1/4 quart-sized glasses to fill the lemonade be A
Now , the equation will be
The amount of lemonades = 1/2 quart of lemonade
The size of the glasses = 1/4 quart-sized glasses
So , the equation will be
A x 1/4 quart-sized glasses = 1/2 quart of lemonade
On simplifying the equation , we get
A / 4 = 1/2
Multiply by 4 on both sides of the equation , we get
A = ( 1/2 ) x 4
A = 2 glasses
Therefore , the value of A is 2 glasses
Hence , the number of glasses is 2
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which descriptions from the list below accurately describe the relationship between QRS and TUV
Answers
hope it helps
Answer:
A. Similar
Step-by-step explanation:
We are given the measurements of ΔQRS and ΔTUV as,
QR = RS = 4, QS = 2 with ∠Q = ∠S = 76°, ∠R = 28°
TU = UV = 12, TV = 6 with ∠T = ∠V = 76°, ∠U = 28°
Now, we see that,
These triangles have different side lengths. So, option C i.e. same sides is not correct.
Also, they are different in size. So, option D i.e. same size is not correct.
Since, they do not have same size, they cannot overlap each other. Thus, are not congruent. So, option B is also not correct.
Thus, we see that from SAS Similarity and the measurements,
QR = RS = 4 and ∠R = 28°
TU = UV = 12 and ∠U = 28°
Both the triangles are similar to each other.
Hence, option A is correct.
Kevin is 2 times as old as Gabriela. 12 years, Kevin was 6 times as old as Gabriela.How old is Gabriela now
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Final answer:
Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.
Explanation:
Finding Gabriela's Current Age:
The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:
K = 2G (Kevin is 2 times as old as Gabriela now)K - 12 = 6(G - 12) (12 years ago, Kevin was 6 times as old as Gabriela)Substituting the first equation into the second, we get:
2G - 12 = 6(G - 12)
Expanding both sides:
2G - 12 = 6G - 72
Moving all terms involving G to one side and constant terms to the other side, we get:
2G - 6G = -72 + 12
-4G = -60
Dividing both sides by -4 to solve for G:
G = 15
So, Gabriela is currently 15 years old.
The length of a rectangle is 7mm longer than its width. It’s perimeter is more than 62mm. Let W equal the width of the rectangle, write an inequality and solve it
Answers
2(l + w) = p
Since we know the perimeter (p) is greater than 62 we can say:
2(l + w) > 62
It is also given that the length is 7 mm longer than the width, so we know the value of the length in terms of w (the width).
w = w
l = w + 7
Substitute l with (w + 7) into the equation:
2[(w + 7) + w] > 62
Now combine like terms in the parentheses
2(2w + 7) >62
Distribute the 2 into the terms in the parentheses
4w + 14 > 62
Subtract both sides by 14
4w > 62 - 14
Combine like terms
4w > 48
Divide both sides by 4
w > 48
Final answer: w > 48
Hope this helps!
What’s the value of x in 46+(7x+9)
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A bakery supplier receives an order for 2 Tons of sudar from a bakery chain. The sugar is shipped in crates. Each crate holds eight 10-pound bags of sugar. How many crates does the supplier need to ship to fulfill the order?
Answers
we have 2 tons=4,000 lbs
each crate holds 10 lbs of sugar
4,000/10=400 crates
What is the definition of a circle? A circle is a plane figure with no straight sides. A circle is a point and all the points in a plane that are the same distance from it. A circle is the set of all points in a plane that are a given distance from a given line segment. A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
Answers
The first one you mentioned, a circle is a plane figure with no straight sides... I can name another shape with no straight sides... an oval.
The second one you mentioned, is a true statement
The third one you mentioned, a circle is from a point, not a line segment.
The last one mentioned is also a true statement.
Answer:
I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!
Step-by-step explanation:
You have a bag of bubble gum containing six grape, nine sour apple and five regular flavored pieces. You randomly pick one piece , give it to your friend, and then randomly pick another piece for yourself. What is the probability that both pieces are grape?
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The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).
Explanation:The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.
The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.
Therefore, the probability that both pieces are grape is 3/38.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
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[tex] {x}^{2} = {1}^{2} + {1}^{2} \\ {x}^{2} = 1 + 1 \\ {x}^{2} = 2 \\ x = \sqrt{2} = 1.41[/tex]
Answer:
The length of the hypotenuse of the isosceles right triangle with leg of length unit is:
√2 units.
Step-by-step explanation:
Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.
Now we apply the Pythagorean Theorem as:
[tex]c^2=a^2+b^2[/tex]
Now as triangle is isosceles.
Hence, a=b=1 unit
[tex]c^2=1^2+1^2\\\\c^2=2\\\\c=\sqrt{2}[/tex]
Hence, the length of the hypotenuse is:
√2 units.
Factor. 25m^100−121n^16
(5m10−11n4)(5m10+11n4)(5m50−11n8)2(5m50−11n8)(5m50+11n8)(5m10−11n4)2
Answers
this question is a difference of squares. the basic equations is when you get 2 square numbers and you have to find their difference ;
x²-y² = (x+ y)(x-y)
you have to then find the product of these factors.
the question given can be rewritten to write the numbers in their square forms
25m¹⁰⁰ - 5²m⁵⁰ˣ² - square root - 5m⁵⁰
121n¹⁶ - 11²n⁸ˣ² - square root - 11n⁸
we have to then factorise them
the answer for 25m¹⁰⁰-121n¹⁶ = (5m⁵⁰ - 11n⁸) (5m⁵⁰ + 11n⁸)
What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box. x =
Answers
∵ Δ KJL is a right triangle at ∠J
∴ KL is the hypotenuse = 8√2
∵ ∠ JKL = 30°
∴ The side which faces the angle 30° will be the half of the hypotenuse because sin 30° = JL/KL = 0.5
∴ JL = 0.5 KL = 0.5 * 8√2 = 4√2
Δ JML is a right triangle at ∠M
∴ JL is the hypotenuse = 4√2 ⇒⇒⇒ (proved)
∵ ∠LJM = 45° , ML = x
∴ sin 45° = x/JL
∴ x = JL sin 45° = 4√2 * (1/√2) = 4
The correct answer
The length of side L M is x = 4
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answer:
m < C =
m < B =
m < A =
m < D =
Answers
1. m ∠C = 88°
2. m ∠B = 100°
3. m ∠A = 92°
4. m ∠D = 80°
Explanation:
∠A and ∠C are supplementary angles; therefore:
∠A + ∠C = 180° --- (A)
Since,
∠A = (x+2)°
and
∠C = (x-2)°
Plug-in the values in equation (A):
(A) => (x+2)° + (x-2)° = 180°
=> x° + 2° + x° - 2° = 180°
=> 2x° = 180°
=> x = 90°
Since x = 90°, therefore,
∠A = (x+2)° = 92°,
and
∠C = (x-2)° = 88°
Since ∠B and ∠D are supplementary angles; therefore,
∠B + ∠D = 180°
∠B + (x-10)° = 180°
Since,
x = 90°; therefore,
∠B + 80° = 180°
∠B = 100°
And since,
∠B + ∠D = 180°
and
∠B = 100°
Therefore,
∠D = 180° - 100°
∠D= 80°
-i
When triangle ABC is rotated about side AB, what figure is formed?
cylinder
prism
pyramid
cone
Answers
Answer:
Cone
Step-by-step explanation:
We are given that a triangle ABC .
We have to find that what shape is formed when a triangle ABC is rotated about side AB.
A given triangle ABC is a right triangle.
When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.
Hence, when a triangle ABC is rotated about side AB, the cone is formed.
Answer: Cone
Find the zeros of the polynomial function.
f(x) = x^2 - 12x + 20
I THINK THE ANSWER IS A 2,10
a. 2, 10
b. - 4, -5
c. -2, -10
d. 4, 5
Answers
[tex]given \: equation \: is \: , \\ \\ {x}^{2} - 12x + 20 = 0 \\ \\ using \: quadratic \: formula \: , \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \: \: \: = \frac{ - ( - 12) + \sqrt{ { (- 12)}^{2} - 4(1)(20) } }{2(1)} \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \: \: \: = \frac{ - ( - 12) - \sqrt{ { (- 12)}^{2} - 4(1)(20) } }{2(1)} \\ \\ x = \frac{12 + 8}{2} \: \: \: \: \: or \: \: \: \: x = \frac{12 - 8}{2} \\ \\ x = 10 \: \: \: \: \: or \: \: \: \: \: x = 2 \: \: \: ans.[/tex]