Answer:
-177,856 does not equal 15
-177,856=15
Saniya writes a positive integer on each edge of a square. She also writes at each vertex the product of the numbers on the two edges that meet at that vertex. The sum of the numbers at the vertices is 15. What is the sum of the numbers on the edges of the square?
To solve this problem, we first set up an equation to express the product of the numbers at the vertices of the square in terms of their sum. Then, we use this equation to find the values of the numbers on the edges of the square. The sum of all the numbers on the edges equals to 2 times the square root of 15.
Explanation:Let's denote the four numbers on the edges of the square as a, b, a, b (since it's a square, opposite sides are equal). The products at the vertices are: ab (top left), ab (top right), ab (bottom right) and ab (bottom left).
So the sum of these numbers at the vertices is 4ab = 15. From here, we can solve the equation for ab, giving us ab = 15 / 4.
The problem asks for the sum of the numbers on the edges, which equates to 2a + 2b. As due to our current setup, a = b, we can simplify this to 4a or 4b. But we don't have a or b - we have ab. Because of this, we require a bit of algebra. We know that (a + b)^2 = a^2 + 2ab + b^2. In our case, where a = b, this can simplify to 4a^2. From here, we proceed with ab = 15/4 to replace 2ab in the equation with the latter, and then solve for a^2, followed by a.
The result is a=root(15/4). To get the sum of all the edges, we would then multiply this by 4, giving us 4*root(15/4) = 2root(15).
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The sum of the numbers on the sides of the square is calculated by doubling the number on the side 'a', adding to double the number of 'b'. With 'b' equals to 15 divided by four times 'a', the sums equals to 2a plus 2 times 15 divided by four times 'a'.
Explanation:Let's denote the numbers on the sides of the square as a, b, a, b, respectively. Hence, each vertex will be the product of a and b, making each vertex to be ab. Given that the total sum of these vertex is 15, we have 4ab = 15, which simplifies to ab = 15/4.
To find the total sum of the numbers on the sides of the square (the edges), we should sum up all a and b's. Therefore the sum will be 2a + 2b. Given that b = 15 / (4a), we can substitute b into the equation, simplifying to get the total sum = 2a + 2*(15 / (4a)). This is the solution to the problem.
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The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he
purchased the car is modeled by the following equation,
V = 22,500 - 10"
How many years after purchase will Vishal's car be worth $10,000?
Give an exact answer expressed as a base-10 logarithm.
years
Answer:
t = -24*log(2/3)
Step-by-step explanation:
The expression is:
V = 22,500*10^(-t/12)
Replacing with V = 10,000 and isolating t, we get:
10,000 = 22,500*10^(-t/12)
10,000/22,500 = 10^(-t/12)
4/9 = 10^(-t/12)
(2/3)² = 10^(-t/12)
2*log(2/3) = -t/12
-12*2*log(2/3) = t
t = -24*log(2/3)
Answer:
The number of years after purchase at which Vishal's car will be worth $10,000 is [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years
Step-by-step explanation:
The relationship is given as follows
Value, V of the car = 22500×[tex]10^{-t/12}[/tex]
Therefore, when the car is $10,000 we will have
$10,000 = 22,500×[tex]10^{-t/12}[/tex]
Which will give;
[tex]\frac{10000}{22500} =\frac{4}{9} = 10^{-\frac{t}{12}}[/tex]
Hence;
[tex]Log\frac{4}{9} = Log(10^{-\frac{t}{12}} )[/tex]
Therefore;
[tex]-\frac{t}{12}\times Log_{10} 10 = Log\frac{4}{9}[/tex]
[tex]\because Log_{10} 10 = 1, \ we \ have; \ -\frac{t}{12} = Log_{10}\frac{4}{9}[/tex]
Which gives;
[tex]t = -12 \times Log_{10}\frac{4}{9} \ or \ t = Log_{10}\left (\frac{4}{9} \right )^{-12}[/tex]
[tex]\therefore t = Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years
Evaluated, the above equation becomes t = 4.226 years
Therefore, the number of years after purchase at which Vishal's car will be worth $10,000 = [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years.
Can you answer these questions? Im doing them on my own but I need to check if they're right
Answer:
Sure! But I need to see the questions to answer them.
~Lexi
Answer:
Sure I can.
Step-by-step explanation:
Just post what questions you need checking, and I'll try to the best I can.
Three coins are tossed. Each coin has a Head and a Tail. Find the probability of getting three tails. Write answers as a simplified FRACTION.
Your answer would be 1/8.
The probability for getting a tail one time would be 1/2 because there are only 2 sides of a coin. Since tossing one coin doesn't affect the outcome of tossing the other coins, the probability for getting a tail on all of the coins is 1/2 each. We want this to happen 3 times, so the answer would be 1/2 × 1/2 × 1/2 = 1/8.
I hope this helps!
Answer:
1/2 x 1/2 x 1/2 = 1/8
1/8
Step-by-step explanation:
Terrence records the number of e-mails he receives per day.
During one week, he receives 7,3, 10,5,5, 6, and 6 e-mails. What are the mean, median, and mode of the data?
What is the perimeter of this composite figure?
16.56 in.
14.28 in.
18.28 in.
10.28 in.
Answer:
D, 10.28
Step-by-step explanation:
2+2+3.14x2/2+3.14x2/2=10.28
Answer:
10.28 in
Step-by-step explanation:
r = 2in/2 = 1in
P = 2π·r + 2·l
= 2×3.14×1in + 2×2in
= 6.28in + 4in
= 10.28 in
Which value can be added to the set below without changing its mean?
{4, 10, 14, 18, 22, 22}
Answer:
4?
Step-by-step explanation:
Answer:
The mean is 15 so adding another 15 keeps the mean unchanged.
Step-by-step explanation:
A new cyclindrical swimming pool is being built at the
local rec center. It has a radius of 13 feet and a height of 6
feet. Tim determined that 1,0141 ft of water would be
needed to fill the pool, but jasmine calculated that
3,185.57 ft of water would be needed. Explain who
calculated the volume properly.
Sample Response: Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.
Solve for b.
x =ab + c/b-d
A) b = c(a - x + d)
B) b =
c
(x + d - a)
C) b =
c
(a + x - d)
D) b =
x
(a - c - d)
Answer:
its B
Step-by-step explanation:
i got it right on USA TEST PREP
Shannon bought 5 1/8 pounds of apples. Bill bought 2 7/8 pounds of apples. Which most
closely estimates how many more pounds of apples Shannon bought than Bill?
To find out how many more pounds of apples Shannon bought compared to Bill, subtract the weight of Bill's apples from the weight of Shannon's apples. The most close estimate of how many more pounds Shannon bought is 2 1/4 pounds.
Explanation:To find out how many more pounds of apples Shannon bought compared to Bill, we need to subtract the weight of Bill's apples from the weight of Shannon's apples.
Shannon bought 5 1/8 pounds of apples, which can be written as a mixed number as 5 + 1/8.
Bill bought 2 7/8 pounds of apples, which can be written as a mixed number as 2 + 7/8.
To subtract these mixed numbers, we can find a common denominator and then subtract the whole numbers and fractions separately.
Let's convert the mixed numbers into improper fractions and subtract:
Shannon's apples = 5 + 1/8 = 40/8 + 1/8 = 41/8Bill's apples = 2 + 7/8 = 16/8 + 7/8 = 23/8Shannon's apples - Bill's apples = 41/8 - 23/8 = (41 - 23)/8 = 18/8 = 9/4The most closely estimate of how many more pounds of apples Shannon bought than Bill is 9/4 pounds or 2 1/4 pounds.
Which graph represents the compound inequality?
–3 < n < 1
Answer:
the graph that represents the compound inequality –3 < n < 1 is the straight line from -3 to 1 in which there is a hollow circle in the -3 point and in the 1 point. This is because < means that the possible values of n is only greater than -3 exluding -3 and less than -1 excluding -1
Answer:
is d
Step-by-step explanation:
plz help me will give you brainliest!!!!
Answer both questions please!!!
Stay Safe!!
Answer:
10
Step-by-step explanation:
Area of a triangle is
A = [tex]\frac{1}{2}[/tex]bh
A = [tex]\frac{1}{2}[/tex] 5 x 4
A = [tex]\frac{1}{2}[/tex] 20
A = 10
For the second image you find the area of the poster
5 x 3 = 15
15 ÷ $2 = 7.5 = $7.50
Sorry if its wrong
Factorise
b2 + 5b + 6
Step-by-step explanation:
Step 1: Factor
[tex]b^2 + 5b + 6[/tex]
[tex]b^2 + 3b + 2b + 6[/tex]
[tex](b + 3)(b + 2)[/tex]
Answer: [tex](b + 3)(b + 2)[/tex]
(b + 2) (b + 3)
Step-by-step explanation:
b² + 5b + 6
Known :
a = 1
b = 5
c = 6
Asked :
Factorise b² + 5b + 6 = ...?
Answer :
p × q = c
p + q = b
So :
p × q = 6
2 × 3 = 6
p + q = 5
2 + 3 = 5
So, p = 2 & q = 3
So, factorise b² + 5b + 6 is (b + 2) (b + 3)
Hope it helpful and useful :)
Solve the equation.
3
4
(2a − 6) + 1
2
= 2
5
(3a + 20)
a =
Answer:
a = 40 if simplified :)
Answer:
Dear mate your answer is 40...
Twelve more than seven times a number is the number plus 18. What is the number?
Answer:
1
Step-by-step explanation:
Let the number be X
condition
12 more than seven times the number
it can be represented numerically by using process given belwo
seven times the number will be 7 * X = 7X
12 more than 7X will be equal to 7X + 12
______________________________
This number (7X + 12) is equal to number plus 19
number plus 18 will be X + 18
therefore according to the question
7X + 12 = X + 18
=> 7X - X = 18 - 12
=> 6X = 6
=> X = 6/6 = 1 (Answer)
The number is 1.
PLEASE HELP FAST!!!!! What is the formula for the surface area and volume of a rhombus.
Answer:
Step-by-step explanation:
Rhombus is a two dimensional shape. So it doesn't have volume.
Area of rhombus = (pq)/2
Here p & q are the diagonals
What is the solution of sqrt 1-3x =x+3
Answer:
x= -1
Step-by-step explanation:
1-3x=x²+6x+9
1-3x-x²-6x-9=0
-8-9x-x²=0
x²+9x+8=0
x²+8x+x+8=0
(x+8)(x+1)=0
x+8=0
x+1=0
sqrt 1-3(-8)=-8+3
sqrt 1-3(-1)=-1+3
5=-5
2=2
x≠8
x=-1
On a number line point M is the midpoint of PQ. Point P is -2 point M is 5. What number is located at point Q?
A) 7
B)8
C)12
D)14
Answer:
12
Step-by-step explanation:
We know 5 in the midpoint and P = -2. Point P is 7 points away (5--2=7). Then to find the point Q you add 7 to 5 which equals 12.
Does anybody know this true or false question ?????
Answer:True
Step-by-step explanation: The smaller triangle is half as small
The triangles are similar, so this is true.
The blue triangle has been enlarged by a scale of 2. It's 4 units up and 2 units to the right and the second larger triangle is 8 units up and 4 to the right, so it's 2 times bigger.
I hope this helps :)
Please help meeeeee!!!!
Answer:
B
Step-by-step explanation:
I think the answer is B as it is on the positive side.
Find lim
12+1)-(2)
if f(x) = x² + x + 1
Answer:
The answer is 11 Hope this helps ;)
Step-by-step explanation:
Triangle A B C. Line A B and C B extend past the triangle to form an angle with measure 70 degrees. Angle A C B is 58 degrees.
What is the measure of Angle CAB?
38°
52°
70°
128°
Answer:
The answer is 52°
Step-by-step explanation:
58°+70°+x=180
128°+x=180°
180°-128°
=52°
A submarine was located 800 feet below sea level. There is a drone
flying 250 feet above sea level over the submarine, how far apart are
the submarine and the drone?
Answer:
1,050
Step-by-step explanation:
Answer:
1050 feet
Step-by-step explanation:
The submarines location is 800 feet below which is -800 and the drones location is 250 feet above which is just 250. To get to -800 from 250 you subtract 1050 so the total distance is 1050.
I need help with Pythagorean theorem
Answer:
1 2/7 just multiply
Step-by-step explanation:
in an exponential function, (x) = a(b)^x, it is known that f(5)=15 and f(8)=170. which of the following is closest to the value of b?
(1)1.87
(2)2.25
(3)3.19
(4)3.72
Answer:
2.25
Step-by-step explanation:
5=15 and d8=170=which of the following is closest to the value of fb
The value of b is closest to (2) 2.25
An exponential function is represented as:
[tex]f(x) = a(b)^x[/tex]
[tex]f(5) = 15[/tex] means that:
[tex]ab^5 = 15[/tex] ---- equation (1)
[tex]f(8) = 170[/tex] means that:
[tex]ab^8 = 170[/tex] ---- equation (2)
Divide equation (2) by equation (1)
[tex]\frac{ab^8}{ab^5}= \frac{170}{15}[/tex]
Divide common factors
[tex]b^3= 11.33[/tex]
Take the cube root of both sides
[tex]b= \sqrt[3]{11.33}[/tex]
Evaluate the expression
[tex]b= 2.246[/tex]
2.246 can be approximated to 2.25
Hence, the value of b is closest to (2) 2.25
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Practice Writing Trig Ratios
Answer:
13.) tanC=40/30
14.) tanA=21/20
15.) tanC=12/35
16.) tanX=30/40
17.) sinZ=12/37
18.) sinZ=30/50
Final answer:
Trigonometry focuses on the ratios between sides and angles of right-angled triangles. Ratios are used to maintain relationships between quantities in scaled models or mathematical problems. Practicing these calculations aids in mental math and practical applications.
Explanation:
Practice Writing Trig Ratios
Trigonometry involves understanding the relationship between the angles and sides of right angled triangles. These trigonometric ratios, which include sine, cosine, and tangent, are essential in connecting angles to their respective side lengths. They are ratios and thus dimensionless, meaning they have no units. These calculations become easier with practice, allowing one to approximate and compute them mentally.
When dealing with practical problems, such as scaling distances for a model or building, it is common to write proportions to maintain the relationships between lengths and widths. For example, if you have a scale that says 1 inch on the model represents 10 feet in reality (inches/feet = 1/10), you would write a ratio that respects this scale. Similarly, if comparing areas, you would establish a ratio outlining how one area relates to the other based on their respective dimensions.
It is also valuable to familiarize oneself with the functions of a calculator by experimenting with various operations such as squaring, square roots, trigonometric functions, and logs. This helps in comprehending the interconnectedness of these mathematical concepts and their practical application.
Find the equation of the line that passes through point (7,5) and (-9,5)
Answer:
y = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (- 9, 5)
m = [tex]\frac{5-5}{-9-7}[/tex] = [tex]\frac{0}{-16}[/tex] = 0
This means the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (7, 5) and (- 9, 5) with y- coordinates 5, thus
y = 5 ← equation of line
Akemi plants a tree that is 4 feet tall. The tree is expected to grow 1/2 of a foot each month. Akemi wants to know after how many months, m, she can expect the tree to be at least 10 feet tall. Which graph best represents all possible solutions for m?
Answer:
12 months
Step-by-step explanation:
On a coordinate plane, triangle L M N has points (1, negative 1), (3, 2), and (1, 3). An altitude is drawn from point M to point P on side N L.
What is the area of triangle LMN?
3 square units
4 square units
6 square units
8 square units
The triangle LMN is a scalene triangle, and the area of the triangle LMN in the coordinate plane is 4 square units.
Below you can understand more about areas of triangle
What is a triangle?A triangle is a shape that has 3 sides and 3 angles
Check below on how to determine the triangle area
The coordinates are given as:
L = (1,-1)
M = (3,2)
N = (1,3)
Calculate the length of side NL using:
NL = √[(x2 -x1)^2 + (y2 - y1)^2]
So, we have:
NL = √[(1 -1)^2 + (3 + 1)^2]
NL = √16
NL = 4
The altitude MP is 2 units.
So, the area is:
Area = 0.5 * NL * MP
This gives
Area = 0.5 * 4 * 2
Evaluate the product
Area = 4
Hence, the area of the triangle is 4 square units
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List three levels of craftspeople you might find in a shoemaker’s shop and describe their duties
The roles of three levels of craftspeople in a shoemaker’s shop are Master Craftsman, Journeyman and Apprentice.
The three levels of craftspeople you might find in a shoemaker’s shop and their duties are:
Master Craftsman: Oversees the entire shoemaking process, creates designs, and ensures quality.
Journeyman: Skilled worker who assists the master craftsman, carries out specific tasks like cutting leather or stitching, and trains apprentices.
Apprentice: Learns the trade under the guidance of the master craftsman and journeyman, performs basic tasks to gain experience.