Answer:
1. The quadratic equation is 3x² +17.5x - 58.5 = 0
2. The values of x are 2.38 and -8.21, but we only take 2.38 for our problem.
3. The dimensions of the combined area are approximately 6.38 inches and 12.64 inches.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Photograph dimensions = 4 inches * 6 inches
Frame dimensions = x inches * 3x - 0.5 inches
Area of the combined area of the photograph and the frame = 80.5 inches²
2. Write a quadratic equation for the combined area. Then use the quadratic equation formula to find x.
One side of the combined area of the photograph and the frame = 4 + x inches
Second side of the combined area of the photograph and the frame = 6 + 3x - 0.5 inches
Now, we can write the quadratic equation this way:
Combined area of the photograph and the frame = One side * Second side, replacing with the values we know:
80.5 = (4 + x) * (6 + 3x - 0.5)
80.5 = (4 + x) * (5.5 + 3x)
80.5 = 22 + 5.5x + 12x + 3x²
3x² +17.5x - 58.5 = 0
Using the quadratic formula, where, a = 3, b = 17.5 and c = - 58.5, we have:
x = (-b +/- √b² - 4ac)/2a
x = (-17.5 +/- √17.5² - 4 * 3 * -58.5) 2 * 3
x = (-17.5 +/- √306.25 + 702)/6
x = (-17.5 +/- √1,008.25)/6
x = (-17.5 +/- 31.75)/6
x₁ = 14.25/6 = 2.38
x₂ = -49.25/6 = -8.21
We took the value of x₁ because x₂ is negative and we can't have a negative value for the length or the width, therefore:
80.5 = (4 + x) * (5.5 + 3x)
Replacing x, we have:
80.5 = (4 + 2.38) * (5.5 + 3 * 2.38)
80.5 = 6.38 * 12.64
80.5 ≅ 6.38 * 12.64
Divide using Long division (6x^3-26x-21+x^2) by (-7+3x)
Step-by-step explanation:
Hope it helps you in your learning process.
Write an equivalent expression for x + x + x + 2x + x
Answer:
6x
Step-by-step explanation:
x + x + x + 2x + x
Simplify the equation
4x + 2x
6x
Hope this was useful to you!
Use the quadratic formula to solve the equation
Answer:
=3
=2
Step-by-step explanation:
12−5+6=0
using the Quadratic Formula where
a = 1, b = -5, and c = 6
=−±2−4‾‾‾‾‾‾‾‾√2
=−(−5)±(−5)2−4(1)(6)‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(1)
=5±25−24‾‾‾‾‾‾‾√2
=5±1‾√2
The discriminant 2−4>0
so, there are two real roots.
Simplify the Radical:
=5±12
=62=42
which becomes
=3
=2
hope this helps :)
Suppose the diameter of a circle is \color{green}{6}6start color green, 6, end color green units. What is its circumference?
Answer:
C = 6pi units
or
C is approximately 18.84 units
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
The diameter is 6 units
C = 6*pi units
If we approximate pi by 3.14
C = 6*3.14
C = 18.84 units
Name the property shown by each statement and which is associative or commutation or simply
Answer:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.
The Commutative property states that order does not matter. Multiplication and addition are commutative.
hope this helps please mark brainliest!
Order the side lengths of the triangle from shortest to longest.
59°
56°
1659
•
If AB = 4x + 9, BC = 5x + 2, and AC = 56, find the measure of AB and BC.
Answer:
Step-by-step explanation:
Given that
AB=4x+9
BC=5x+2
Then, AC=56
From vector
AC=AB+BC
Then,
56=4x+9+5x+2
56=9x+11
Subtract 11 from both sides
56-11=9x+11-11
45=9x
Divide both sides by 9
45/9=9x/9
5=x
Then, x=5
Now,
1. AB=4x+9, x=5
AB=4(5)+9
AB=20+9
AB=29
2. Also
BC=5x+2
BC=5(5)+2
BC=25+2
BC=27
Is 4/6 is farther from 1/2
Answer: Yes
sdizjaoijf
what is 2 and 1 4th times 1 and 1 half
Answer:
3 3/8
Step-by-step explanation:
What is the 10th term 1,
1/2,1/4
Answer:
The 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
Step-by-step explanation:
Considering the sequence
[tex]1,\:\frac{1}{2},\:\frac{1}{4}...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{\frac{1}{2}}{1}=\frac{1}{2},\:\quad \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}[/tex]
[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]
[tex]r=\frac{1}{2}[/tex]
[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]
[tex]a_1=1[/tex]
[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]
[tex]a_n=\left(\frac{1}{2}\right)^{n-1}[/tex]
Putting n = 10 to determine in the nth term to determine the 10th term
[tex]a_{10}=\left(\frac{1}{2}\right)^{10-1}[/tex]
[tex]a_{10}=\left(\frac{1}{2}\right)^9[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]a_{10}=\frac{1^9}{2^9}[/tex]
[tex]a_{10}=\frac{1}{2^9}[/tex] ∵ [tex]1^9=1[/tex]
[tex]a_{10}=\frac{1}{512}[/tex] ∵ [tex]2^9=512[/tex]
Therefore, the 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
Helppppppppppppppppppp
0.1 percent as fraction in simplest form ?
Answer:
1/10
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
In its simplest form, expressing the decimal as a fraction to its simplest form will give one over ten.
Therefore if you divide 1/10, the answer will be 0.1. it is also called one-tenth.
Although there are other expressions or fractions that give 0.1, but 1/10 is the simplest of them all, and the question specified to use it in its simplest form.
Which helps to establish a negative credit history?
O Make payments on or before the due date.
O Never miss a payment.
O Pay Sif the full amount with the first monthly statement.
O Pay less than the minimum amount due.
Answer:
D: Pay less than the minimum amount due.
Step-by-step explanation:
lily can travel 60 miles in 1.5 hours. If her speed is reduced by 5 mph,how har can she travel in 3 hours
Answer:
110
Step-by-step explanation:
Answer:
105 miles
Step-by-step explanation:
first we have to find her speed before it is reduced
so
60/1.5
thats equal to 40
she can travel 40 mph
reduce that by 5 so her speed is now 35mph
35*3=105
An art supply store typically sells bottles of green paint for every 9 bottles of aqua paint. How many bottles of aqua paint does it sell when it sells 30 bottles of green paint?
Final answer:
The store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
Explanation:
To find out how many bottles of aqua paint the store sells when it sells 30 bottles of green paint, we can set up a proportion. Since the store sells 9 bottles of aqua paint for every 1 bottle of green paint, we have the ratio 9/1. We can set this equal to the unknown quantity, x, over 30 (the number of green paint bottles).
9/1 = x/30
Next, cross multiply to solve for x. Cross multiplying gives us:
9 * 30 = 1 * x
Simplifying this equation gives us:
270 = x
Therefore, the store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
The distance between two cities on a map is 4 1/2 inches. The actual distance between the two cities is 24 miles.
What is the scale used on the map?
If the scale on a different map of the same area is 1/4 inch = 1 mile, how many inches separate the same two cities?
Answer:
1 inch : 5⅓ miles
6 inches
Step-by-step explanation:
Map : Actual
4½ : 24
1 : 24/4.5
24 ÷ 9/2 = 24 × 2/9 =
1 inch on map represents an actual distance of 16/3 miles in actual
16/3 = 5⅓ miles
Map : Actual
¼ inch : 1 mile
X inch : 24
¼×24 = 6 inches
Answer: 3/16 inches : 1 mile
6 inches
Step-by-step explanation:
[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{4\frac{1}{2}\ inches}{24\ miles}\div\dfrac{24}{24}=\dfrac{\frac{3}{16}}{1}\quad \longrightarrow \quad \large\boxed{\dfrac{3}{16}\ inches:1\ mile}\\[/tex]
[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{\frac{1}{4}\ inches}{1\ mile}=\dfrac{x}{24\ miles}\\\\\\\text{Cross Multiply}:\quad \dfrac{1}{4}\bigg(24\bigg)=x\\\\.\qquad \qquad \qquad \qquad \quad \quad \large\boxed{6=x}[/tex]
The wholesale price for a pair of shoes is $8.50. A certain department store marks up the wholesale price by 90%. Find the price of the pair of shoes in the department store. Round your answer to the nearest cent, as necessary.
Answer:
$16.15
Step-by-step explanation:
The wholesale price:
$8.50Selling Price:
$8.50 + 90% = $8.50 *1.9 = $16.15Pair of shoes sold for $16.15 in the store
The department store marks up the wholesale price by 90%, equating to $7.65. Adding this to the original wholesale price of $8.50, the retail price of the shoes in the department store is $16.15.
Explanation:To calculate the retail price of the shoes in the department store, we need to add the markup value to the original wholesale price. The markup is 90% of the wholesale price. Therefore, we calculate 90% of $8.50, and then add that to the original price.
To find 90% of $8.50, we multiply $8.50 by 90/100. This gives us $7.65. This is the markup value.
We then add this markup value to the original wholesale price. So, $8.50 + $7.65 = $16.15.
The price of the pair of shoes in the department store is therefore $16.15.
Learn more about markup here:https://brainly.com/question/34159861
#SPJ3
the retail cost of a computer is 22% more than its wholesale cost. what is the whole sale cost?
Answer:5
Step-by-step explanation:
you do it
2. A boy who is 5 feet 6 inches tall casts a shadow that is 8 feet and 3 inches long. What is the measure of the
angle of elevation of the sun, A, as shown in the picture. Round to the nearest degree. Be careful with your
units in this problem.
Answer:
34°
Step-by-step explanation:
The boy is 5 feet 6 inches tall.
The boy casts a shadow that is 8 feet and 3 inches long.
We know 12 inches equal 1 foot.
Therefore the boy's height is 5.5ft and the shadow is 8.25ft.
The angle of elevation of the sun is given by the tangent of the angle A.
[tex] \tan(A) = \frac{5.5}{8.25} [/tex]
[tex]\tan(A) = 0.6667[/tex]
[tex]A= {\tan}^{ - 1} (0.6667)[/tex]
[tex]A=33.69 \degree[/tex]
To nearest degree is 34°
Answer: 34 degrees
Step-by-step explanation:
the boy is 5’6
5x12=60+6=66
The shadow is 8’3
8x12=96+3=99
You would use tan(X)= 5.5/8.25
calculate to get 33.69 round to 34.
Fill in the blank to make a true equation. (-9)(___) = 36 A. - 4 B. 4 C. 6 D. - 6
Answer:
Option A, -4
Step-by-step explanation:
Step 1: Make an equation to represent the problem
(-9)(x) = 36
Step 2: Solve for x by dividing both sides by -9
-9x / -9 = 36 / -9
x = -4
Answer: Option A, -4
The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 A cube of gold weighs 652 grams. Calculate the length of the edge of the cube in centimeters. Answer with two decimal places.
The length of the edge of the cube is 3.23 cm .
Step-by-step explanation:
We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] . A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:
[tex]y = 19.3x^3[/tex]
⇒ [tex]y = 19.3x^3[/tex]
⇒ [tex]652= 19.3x^3[/tex]
⇒ [tex]19.3x^3=652[/tex]
⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]
⇒ [tex]x^3=\frac{652}{19.3}[/tex]
⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]
⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]
⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]
⇒ [tex]x =3.23[/tex]
Therefore, the length of the edge of the cube is 3.23cm.
-4x + 26 = -2 whats x?
Answer:
The value of x is equal to 7
Step-by-step explanation:
if -4x + 26 = -2
-4x = -2 - 26
-4x = - 28
Divide both sides by -4, then we will have
x = -28/-4
x = 7
Steps to solve:
-4x + 26 = -2
~Subtract 26 to both sides
-4x + 26 - 26 = -2 - 26
~Simplify
-4x = -28
~Divide -4 to both sides
-4x/-4 = -28/-4
~Simplify
x = 7
Best of Luck!
PICTURE SHOWN
Write the equation of the given line in
slope- intercept form
Answer:
y=2x+3
Step-by-step explanation:
Answer:
y = -3x - 1
Step-by-step explanation:
Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find the slope using [tex]\frac{y2 - y1}{x2 - x1}[/tex]
(x1, y1) = (-1, 2)
(x2, y2) = (1, -4)
m = [tex]\frac{-4 - 2}{1 -(-1)}[/tex]
m = [tex]\frac{-6}{1+1}[/tex]
m = [tex]\frac{-6}{2}[/tex]
m = -3
Step 2: Plug into point slope form and solve for y
(y - y1) = m(x - x1)
(y - 2) = -3(x - (-1))
y - 2 = -3(x + 1)
y - 2 + 2 = -3x - 3 + 2
y = -3x - 1
Answer: y = -3x - 1
9 yd
12 yd
What is the length of the hypotenuse?
Answer:
Hi there!
The correct answer will be 15 yd
Step-by-step explanation:
There are two ways you can go about solving this problem
Method One: Pythagorean Theorem
a^2 + b^2 = c^2 then all you have to do is plug in the values
(12)^2 + (9)^2 = c^2 you should get c^2 = 225 then you square root both sides and you get c = 15
Method Two: Pythagorean Identities
This triangle represents a 3,4,5 triangle
All the sides just tripled so that means the hypotenuse is 5*3 which equals 15
i need help finding the area of a figure where the rectnagles area is 5 x 14 and the half circles diameter is 6
Answer:
84.14 square units, total
Step-by-step explanation:
Use the formulas for area of the figures you're interested in.
Rectangle Area
A = LW
Circle Area
A = πr^2
__
Your rectangle area will be ...
A = 5 × 14 = 70 . . . . square units
The area of a full circle with diameter 6 (radius = 6/2 = 3) will be ...
A = π × 3^2 = 9π
The area of a semicircle of that size is half that:
semicircle area = 9π/2 = 4.5π
Then the total area of the two figures is ...
70 + 4.5π ≈ 70 +14.14 = 84.14 . . . square units
Find, to the nearest degree, the angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long.
Trigonometry
Answer:
Θ = 52°
Step-by-step explanation:
Once you've set up the triangle, you can see that the adjacent side is 170 cm and the opposite side is 220 cm.
tanΘ = [tex]\frac{220}{170}[/tex]
Θ = tan-1 (220/170)
Θ = 52°
The angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long is 37.694°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
A person 170 cm tall casts of shadow 220 cm long.
Then the angle will be
[tex]\rm tan \theta = \dfrac{Perpendicular }{Base}[/tex]
We have
Perpendicular = 170 cm
Base = 220 cm
Then
[tex]\rm tan \theta = \dfrac{170}{220}\\\\\\ \theta \ \ \ \ = tan^{-1} \dfrac{170}{220}\\\\\\\theta \ \ \ \ = 37.694^o[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
What is it I really need to know please
Answer:
12
Step-by-step explanation:
Just take 35 and subtract 23.
pLeAsE hElP! HuRrY!
Solve for A:
14a < 112
A.) a < -8
B.) a > 8
C.) a > -8
D.) a < 8
−4 5/9+8/9+ 0+0+0+0+0+0+0+0=
Answer:
-3.66666666668
Step-by-step explanation:
The zero's you do not have to add because they have to content or value.
-4 5/9 into improper = 31/9 = -4.55555555556
8/9 = 0.88888888888
ADD
[tex]\left\begin{array}{ccc}-4.55555555556\\+\\0.88888888888\end{array}\right\\---------[/tex]
-3.66666666668
Hope this helps you!
Have a good night! :)
Answer:
-3.66666666668
Step-by-step explanation:
Consider the given statement. At least one gift in the bag is wrapped.
For each statement below, determine whether it is a negation of the given statement is True or False.
At least one gift in the bag is not wrapped.
Not every gift in the bag is wrapped.
Every gift in the bag is wrapped.
None of the gifts in the bag are wrapped.
Answer:
The negation to the given statement "At least one gift in the bag is wrapped - true" is " At least one gift in the bag is not wrapped" - False
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-FalseStep-by-step explanation:
Given statement is At least one gift in the bag is wrapped is true
The negation to the given statement is " At least one gift in the bag is not wrapped" - False
To determine whether the statement is a negation of the given statement is True or False :
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-False