Answer:
Length: 7
Width: 4
Step-by-step explanation:
We can create a system of equations for this problem, where [tex]w[/tex] is the width and [tex]l[/tex] is the length.
The perimeter of a rectangle is twice its length added to twice its width.
[tex]2l+2w=22[/tex]
The length is 3 more than the width:
[tex]l = w+3[/tex]
We can now substitute in [tex]w+3[/tex] as [tex]l[/tex] in the equation [tex]2l+2w=22[/tex].
[tex]2(w+3) + 2w = 22[/tex]
Distribute the first terms:
[tex]2w+6+2w=22[/tex]
Combine like terms:
[tex]4w+6=22[/tex]
Subtract 6 from both sides:
[tex]4w=16[/tex]
Divide both sides by 4:
[tex]w = 4[/tex]
Now we know that w = 4. We can now substitute this inside an equation to find [tex]l[/tex].
[tex]l = w+3\\\\l = 4+3\\\\l=7[/tex]
Hope this helped!
Answer:
What the other guy said XDDDDDDDDDD
Step-by-step explanation:
I'm awesome =D
1. Jack is 30 years old and Alice is 35 years old. What percent of Alice's age is Jack, rounded to the nearest tenth of a percent?
QR has endpoints at Q(2,6) and R(0,2). Find the midpoint M of QR
Answer:
Step-by-step explanation:
Well, the midpoint formula is M=((x↓1 +x↓2)/2,(y↓1 +y↓2)/2 ). (not exponents, they tell you which x or y value).
If you plug in your 2 points, it becomes m=((2+0)/2,(6+2)/2).
When you add, it is m=(2/2, 8/2)
When simplified, it is m=(1,4)
Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)
Answer:
The rate of change of the function at x = 0.6 is approximately -0.72
Step-by-step explanation:
The given information from the graph are;
Points (0, 0) and (1, -0.5)
We have that the graph is that of a cubic function, therefore;
f(x) = ax³ + bx² + cx + d
At f'(x) at (0, 0) and (1, -0.5) = 0 gives;
3ax² + 2bx + c = 0
∴ c = 0
Also
ax³ + bx² + cx + d = 0
d = 0
We have
3a(1)² + 2b(1) + 0 = 0
3·a + 2·b = 0..............(1)
a(1)³ + b(1)² + c(1) + d = -0.5
a + b + 0×(1) + 0 = -0.5
a + b = -0.5..........(2)
Multiplying equation (2) by 2 and subtracting it from equation (1) gives;
2 × (a + b = -0.5) = 2·a + 2·b = -1
3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1
a = 1
From
a + b = -0.5, we have;
1 + b = -0.5 = 0
b = -0.5 - 1 = -1.5
The equation becomes
f(x) = x³ - 1.5·x²
The rate of change of the function at x = 0.6 is therefore given as follows;
f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x
At x = 0.6, we have;
f'(0.6) = 3·(0.6)² - 3·(0.6)
f'(0.6) = 3×0.6² - 3×0.6 = -0.72
The rate of change of the function at x = 0.6 ≈ -0.72
show that (x+1)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx+ d where a,b,c and d are all positive integers.
Answer:
x³ + 9x² + 23x + 15
Step-by-step explanation:
Given
(x + 1)(x + 3)(x + 5) ← expand the first pair of factors using FOIL
= (x² + 4x + 3)(x + 5)
Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is
x²(x + 5) + 4x(x + 5) + 3(x + 5) ← distribute the 3 parenthesis
= x³ + 5x² + 4x² + 20x + 3x + 15 ← collect like terms
= x³ + 9x² + 23x + 15 ← in the form ax³ + bx² + cx + d
Is 144 a perfect square?
A. The whole number 144 is a perfect square because the square root of 144 is a whole number.
B. The whole number 144 is not a perfect square because the square root of 144 is not an irrational number.
C. The whole number 144 is a perfect square because 144 is divisible by 2.
D. The whole number 144 is a perfect square because 144 is divisible by 4.
Answer:
A,
Step-by-step explanation:
because the whole number 144 is a perfect square and the square root of 144 is also a whole number
please i need help with these problems thank you!!
determine which of the following pairs of triangles are similar.
Triangles given in Options (b) and (c) are similar.
Theorems of similar triangles: If two angles of a pair of triangles are equal in measure, then the triangles will be similar by A-A property. If corresponding sides of two triangles are proportional, both the triangles will be similar.
From the picture attached,
a). In triangle ABC,
∠A + ∠B + ∠C = 180° [By triangle sum theorem]
60° + ∠B + 40° = 180°
∠B = 80°
Similarly, in ΔDEF,
∠D + ∠E + ∠F = 180°
60° + 85° + ∠F = 180°
∠F = 35°
Since, measure of angles of both the triangles are different in measures, triangles will not be similar.
b). In ΔABC,
∠A + ∠B + ∠C = 180°
45° + 50° + ∠B = 180°
∠B = 85°
In ΔDEF,
∠D + ∠E + ∠F = 180°
50° + 85° + ∠F = 180°
∠F = 45°
Hence, ∠C ≅ ∠D, ∠A≅ ∠F and ∠B ≅ ∠E
Since, measure of corresponding angles are equal, both the
triangles (ΔABC ~ ΔFED) will be similar.
c). Here, corresponding sides of both the triangles are proportional,
[tex]\frac{AB}{DE}= \frac{CA}{FD}= \frac{BC}{EF}[/tex]
[tex]\frac{14}{7}= \frac{12}{6}= \frac{16}{8}[/tex]
[tex]\frac{2}{1}= \frac{2}{1}= \frac{2}{1}[/tex]
Both the triangles ΔABC and ΔDEF will be similar.
Therefore, Option B and Option C are the correct options.
Learn more about the similarity of two triangles here,
https://brainly.com/question/2499350?referrer=searchResults
A lottery claims that 3% of tickets win a prize. what is the probability that you win a prize if you purchase twenty tickets?
Iola has $75. She buys a pair of shoes on sale for one-half off and a pair of socks for $6. She has $32 left. Which equation can be used to find x, the regular price of the shoes?
Answer:
To solve for the problem above, let x be the regular price of the shoe.
1/2x is the one-half price of the shoe then we add 6 for the pair of socks,
1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.
Step-by-step explanation:
the area of triangle LMN is 26 square units. the triangle is reflected across LM and then translated 3 units to the right and 4 units up. what is the area of the resulting triangle?
Answer:
26 square units
Step-by-step explanation:
Reflection and translation are rigid motions that do not affect the size or shape of the triangle. It has the same area as the original: 26 units².
Find the distance between the points (-6,-8) and (-2,0). The answer must be a whole number or a fully simplified radical expression do not round up
Answer:
The answer is
[tex]4 \sqrt{5} \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-6,-8) and (-2,0)
The distance between them is
[tex]d = \sqrt{ ({ - 6 + 2})^{2} + ({ - 8 - 0})^{2} } \\ = \sqrt{ ({ - 4})^{2} + ({ - 8})^{2} } \\ = \sqrt{16 + 64} \\ = \sqrt{80} [/tex]
We have the final answer as
[tex]4 \sqrt{5} \: \: \: units[/tex]
Hope this helps you
2. It takes 39,090 gallons of water to manufacture a new car. Sammy thinks that rounds up to about 40,000
gallons. Susie thinks it is about 39,000 gallons. Who rounded to the nearest thousand, Sammy or Susie?
Use pictures, numbers, or words to explain.
Answer:
Susie rounded to the nearest thousandth.
Step-by-step explanation:
since the 100th place is 0 it would round down to 39,000 when you are rounding to the nearest thousand.
what number is 10 times less than 20?
Answer:
180
Mathematically, 10 times less than 20 would be: Take 20, subtract (10 x 20). Answer: -180.
Answered
Mr.carlisle paid his utility bill last weekend.he paid $50 to the phone company,$112 to the power company,and $46 to the water company.after he paid those bills,what was the change in the total amount of money that mr carlisle had ?
Answer:-$208
Step-by-step explanation:
Combine like terms in the following equation:
18 – 5W + 7w - 4 = 28
Answer:
7
Step-by-step explanation:
Step 1:
18 - 5w + 7w - 4 = 28
Step 2:
14 + 2w = 28
Step 3:
2w = 14
Answer:
w = 7
Hope This Helps :)
Which statement is true regarding the functions on the graph?
what is the inverse of f={(1,3),(4,2),(5,1)}
Answer:
f={(3,1),(2,4),(1,5)}
(01.01)
Evaluate -40 - 5. (1 point)
8
-8
-35
-45
Answer:
Step-by-step explanation:
-40 - 5 = -45
answer is D
need help someone please
Answer:
52
Step-by-step explanation:
I'm pretty sure that it would be 52 mi because it is the same said that the angel ST is. Angels NM and ST are congruent. Therefore, the answer is 52 mi.
A pitcher contains 19.25 cups of iced tea. You drink 1.25 cups of the tea each morning and 1.5 cups of the tea each evening. When will you run out of iced tea?
Answer:
Seven days
Step-by-step explanation:
From the information given, you know that you drink in a day 1.25 cups of the tea in the morning morning and 1.5 cups of the tea in the evening which is equal to:
1.25+1.5=2.75 cups a day
Now that you know the amount of cups that you drink in a day, you can divide the amount of cups in the pitcher by the amount of cups you drink in a day:
19.25/2.75= 7
According to this, the answer is that you will run out of iced tea after seven days.
This is my algebra I have a A+ but I wanna keep it up
Answer:
45 minutes
Step-by-step explanation:
We want to know how long it takes to an airplane to fly a distance of 375 miles, if the speed of the airplane is 500 miles per hour.
For this, we should divide the distance/speed to get the time that the plane needs.
T = 375mi/(500mi/h) = 0.75 hours
The plane needs 0.75 hours or 0.75*60 = 45 minutes to fly that distance.
A blueberry recipe calls for 1\frac{3}{4} cups of sugar. How many cups of sugar would need to make the muffin recipe 3 times?
Answer:
4 3/4
Step-by-step explanation:
Just multiply 1 3/4 and 3 = 4 3/4
Find the slope “m” and the y-intercept “b”. a. y = 3x − 4 b. 4x − 5y = 15
Step-by-step explanation:
Equation of a line is y = mx + b
where
m is the slope
b is the y intercept
First question
a.)y = 3x - 4
Comparing with the general equation above
Slope / m = 3
The y intercept / b = - 4
Second question
b).4x - 5y = 15
First we must write the equation in the general equation above by making y the subject
That's
5y = 4x - 15
Divide both sides by 5
That's
[tex] \frac{5y}{5} = \frac{4}{5} x - \frac{15}{5} [/tex]
We have
[tex]y = \frac{4}{5} x - 3[/tex]
Comparing with the general equation above
Slope = 4/5
Y intercept = - 3
Hope this helps you
PLEASE HELP ME I WILL MARK YOU BRAINLIEST
Answer:
D
Step-by-step explanation:
Their are 9 in the first row and their are 5 rows all together so 9 times 5 is 45.
Dana has 2 more sweets than dhabia, dhabia has double the amount of sweets than ameera. Translate this sum into an algebraic expression.
Ammera's sweet= A
Dhabia's sweet= B
Dana's sweet= C
Ax2=B+2=C
what is (4x^2y^3)^2=
16x⁴y⁶
Step-by-step explanation:(4x²y³)² =
= 4²x²ˣ²y³ˣ²
= 16x⁴y⁶
X/5=15 Question 7 options: 20 3 75 10
Answer:
x = 75
Step-by-step explanation:
X/5=15
Multiply each side by 5
x/5 * 5 = 15*5
x = 75
Answer:
Step-by-step explanation:
15*5=75
therefore answer is x=75
Record the mass of the object based on the reading from the mass of the object is
the triple-beam balance
grams
Answer:
167
Step-by-step explanation:
Answer:
167
Step-by-step explanation:
r-85=114 what is the awnser
Answer:
[tex]r=199[/tex]
Step-by-step explanation:
hopefully that was the answer you were looking for
Answer:
1.34117647059
Step-by-step explanation:
114 divided by 85 =1.34117647059
hope this helps
The layer of the atmosphere that is least densely packed is
Answer:
mesosphere
The air in the mesosphere has extremely low density: 99.9 percent of the mass of the atmosphere is below the mesosphere. As a result, air pressure is very low.