Answer: 1280 Kg
Step-by-step explanation:
The weight of the object given = 128 Kg
Time 1 = 10 hr
Time 2 = 1 hr
Cancel the hours,
128×10 = 1280 Kg
On a coordinate grid, line j passes through points (8, 2) and (-2,-2). On the same grid, line k
passes through points (-4, 3) and (-6, 8). Are lines j and k parallel, perpendicular, or neither?
Answer: lines j and k are perpendicular
Step-by-step explanation:
Let's find the equations of lines j and k
[tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
Line j: (8,2) (-2,-2)
x₁= 8 x₂=-2 y₁=2 y₂=-2
[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]
Multiply both parts of the equation by -4:
[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]
Line k: (-4,3) (-6,8)
x₁=-4 x₂=-6 y₁=3 y₂=8
[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]
Multiply both parts of the equation by 5:
[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]
Hence, lines j and k are perpendicular
1. Find the equation of the straight line that passes through the points (0, -1) and (-1,0).
2. For this problem, please use the point-gradient form of the equation that passes through
the points (2, -4) and has gradient/slope 3.
3. Find the equation of the straight line that is parallel to the line y = x-2 and goes through
the point (0,1). Use Desmos Graphing Calculator to check your answer.
Answer:
1) y = -x -1
2) y + 4 = 3( x -2)
3) y = x + 1
Step-by-step explanation:
1)
The slope is the change in y over the change in x. The y values from the points given is 0 and -1. The x values from the points given is -1 and o
Slope: [tex]\frac{o - -1}{-1 - o}[/tex] = [tex]\frac{1}{-1}[/tex] = -1
y -intercept
y = mx + b Use the point (0,-1) and the slope to solve for b
y = -1
m = -1
x = 0
y = mx + b
-1 = -1(0) + b
-1 = 0 + b
-1 = b This is the y intercept.
y = mx + b
y = =x -1
2)
point-gradient form is
y -y = m (x-x)
y - -4 = 3 (x -2)
y + 4 = 3( x - 2)
3)
Parallel lines have the same slope.
slope is 1. Use this and the point (0,1) to solve for b
y = mx + b
1 = 1(0) + b
1 = 0 + b
1 = b
y = x + 1
Amir spent a total of $53.75 on breakfast sandwiches and bagels for his friends who are visiting from out of town. Each breakfast sandwich costs $4.25, and each bagel costs $2.00. He bought 5 more bagels than breakfast sandwiches.
Write a system of equations that could be used to solve for the number of breakfast sandwiches and bagels he bought.
And solve the system of equations to determine how many bagels and sandwiches Amir bought.
The system of equations is:
2b + 4.25s = 53.75
b - s = 5
The number of bagels bought is 12 and the number of sandwiches bought is 7.
How many bagels and sandwiches were bought?2b + 4.25s = 53.75 equation 1
b - s = 5 equation 2
Where:
n = number of bagels bought s = number of sandwiches boughtThe elimination method would be used to determine the required values.
Multiply equation 2 by 2
2b - 2s = 10 equation 3
Subtract equation 3 from equation 1 :
6.25s = 43.75
Divide both sides of the equation by 2.25
s = 43.75 / 6.25
s = 7
Substitute for s in equation 1:
2b + 4.25(7) = 53.75
2b + 29.75 = 53.75
2b = 53.75 - 29.75
2b = 24
b = 24 / 2
b = 12
To learn more about system of equations, please check: https://brainly.com/question/25875552
#SPJ1
allen and ben are painting a fence. the ratio of the amount of work allen does to the amount of work ben does is $3:5$. if the fence requires a total of $240$ square feet to be painted, how many square feet does ben paint?
The fence Ben paints is 150 square feet.
Given:
ratio of the amount of work allen does to the amount of work ben does is 3:5
allen : ben = 3:5
total work done in ratio = 3 + 5 = 8
Count the fence Ben paints
Since , fence requires a total of 240 square feet to be painted
Thus, ben = ratio of ben/ total ratio × total of works
ben = 5/8 × 240
ben = 1,200/8
ben = 150
Hence , The fence Ben paints is 150 square feet .
Learn more about Ratios at:
https://brainly.com/question/2328454
#SPJ4
The number of avocadoes used by restaurant in a day varies directly with the number of orders of guacamole that day. It takes 7 avocadoes to make 4 orders of guacamole. How many avocadoes would it take to make 14 orders of guacamole?
14 orders of guacamole need 24.5 avocadoes
What are equivalent ratios?
The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.
4 orders of guacamole need 7 avocadoes
14 orders of guacamole need x avocadoes
Equivalent ratios:
4/7 = 14/x
Solve for x.
=> 4x = 7*14 = 98
=> x = 98/4 = 24.5
So, 14 orders of guacamole need 24.5 avocadoes
To learn more about equivalent ratios from the link
https://brainly.com/question/2914376
#SPJ1
Suppose a triangle has two sides of length 7 and 8 and the included angle has a measure of theta degrees. What is the maximum area of the triangle?
28sinθ is the maximum area of the triangle
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The two sides of triangle are of length 7 and 8.
Triangle has an included angle has a measure of θ degrees.
We need to find the maximum area
A=1/2×7×8×sinθ
A equal to one by two time of seven times of eight times sin theta.
A=7×4×sinθ
A=28sinθ
Hence, 28sinθ is the maximum area of the triangle
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
Please help,100 points will give the brainiest.
Given the equation, 3x2 + 4x – 2 = 0, calculate the discriminant and determine the number and nature of the solutions.
1.d = 40; 2 irrational
2.d = 40; 2 rational
3.d = −8; 2 complex
Answer:
1. d = 40; 2 irrational
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}[/tex]
Given quadratic equation:
[tex]3x^2+4x-2=0[/tex]
Therefore:
a = 3b = 4c = -2Substitute the values of a, b and c into the discriminant formula:
[tex]\begin{aligned}\implies b^2-4ac&=(4)^2-4(3)(-2)\\&=16-12(-2)\\&=16+24\\&=40\end{aligned}[/tex]
Therefore, as d = 40 and 40 > 0:
[tex]\implies b^2 - 4ac > 0 \implies \text{two real solutions}.[/tex]
To determine if the solutions are irrational or rational, simply square root the discriminant.
[tex]\implies \sqrt{d}=\sqrt{40}=2 \sqrt{10}[/tex]
As the discriminant is not a perfect square, then its square root is irrational and so the solutions of the quadratic equation are irrational.
A dealer bought some 9-volt batteries for $2,400. She sold them for $5,600, making a profit of $1.60 on each
battery. How many batteries were involved in the deal? a.3,500 b.1,500 c.5,000 d.2,000 e.2,500
A dealer bought some 9-volt batteries for $2,400. She sold them for $5,600, making a profit of $1.60 on each battery. 2,500 batteries were involved in the deal.
The dealer bought some 9-volt batteries for $2,400 and she sold them for $5,600. To find out how many batteries were involved, we need to calculate how much she made from each battery. We can do this by subtracting the cost of the batteries from the selling price and then dividing it by the number of batteries. Profit per battery = $5,600 - $2,400 = $3,200. Number of batteries = $3,200/$1.60 = 2,500. Therefore, the dealer bought 2,500 batteries.
Learn more about profit here
https://brainly.com/question/28856941
#SPJ4
How do you simplify 16^(2/3)?
Answer:
4(2)^(2/3) or 4∛(4)
Step-by-step explanation:
Rules of Exponents..
16^(2/3)
= (2^4)^(2/3)
= 2^(8/3)
= 2^(2 + 2/3)
= 2^2 · 2^(2/3)
= 4(2)^(2/3) or 4∛(4)
These cones are similar. Find the volume
of the smaller cone. Round to the
nearest tenth.
2 cm
Volume = [?] cm³
3 cm
Volume = 66 cm³
The volume of the smaller cone is 19.6cm³
How to determine the volume of the smaller coneFrom the question, we have the following parameters that can be used in our computation:
Side length = 2 cmVolume = [?] cm³Side length = 3 cmVolume = 66 cm³The above parameter mean that
Smaller cone
Side length = 2 cm
Volume = [?] cm³
Large cone
Side length = 3 cm
Volume = 66 cm³
The ratio of the cones can be represented as
Ratio = Side length³ : Volume
So, we have
2³ : Volume of smaller cone = 3³ : 66
Evaluate the exponents
8 : Volume of smaller cone = 27 : 66
Express as fraction
Volume of smaller cone/8 = 66/27
So, we have
Volume of smaller cone = 8 * 66/27
Evaluate
Volume of smaller cone = 19.6
Hence, the volume is 19.6cm³
Read more about volume at
https://brainly.com/question/463363
#SPJ1
Which proportion could be used to prove that HJ is parallels to KL? multiple choice
Answer:
fourth option
Step-by-step explanation:
to prove that HJ is parallel to KL , then KL divides the sides HG and JG proportionally , that is
[tex]\frac{GK}{HK}[/tex] = [tex]\frac{GL}{LJ}[/tex]
How do I find 2/3 of a whole number?
To find [tex]\frac{2}{3}[/tex] of a whole number, you can divide the number by 3 and then multiply the result by 2.
For example, if you want to find [tex]\frac{2}{3}[/tex] of the number 15, you can perform the following calculation:
[tex]\frac{2}{3}[/tex] × 15 = 10
This means that [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
You can also find [tex]\frac{2}{3}[/tex] of a whole number by dividing the number by 3 and then multiplying the result by 2.
For example:
[tex]\frac{15}{3}[/tex] = 5
2 × 5 = 10
So, [tex]\frac{2}{3}[/tex] of the number 15 is also equal to 10.
Alternatively, you can find [tex]\frac{2}{3}[/tex] of a number by expressing it as a decimal. [tex]\frac{2}{3}[/tex] can be expressed as 0.6666666667, so you can multiply the whole number by 0.6666666667 to find [tex]\frac{2}{3}[/tex] of it. For example:
0.6666666667 × 15 = 10
So [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
A whole number is a positive integer that is greater than 0, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. Whole numbers do not include fractions, decimals, or negatives.
To learn more about whole numbers, visit:
brainly.com/question/29766862
#SPJ4
A used car bought for $10,230 was sold for $800 after 5 years of use. What was the car's rate of depreciation, to the nearest tenth percent? PLEASE SHOW WORK
Answer:
$9430 / $10,230 * 100% = 92.4%
Step-by-step explanation:
To find the car's rate of depreciation, we need to first calculate the total amount of depreciation that occurred over the 5 years of use. This can be done by subtracting the sale price of the car from its original price:
$10,230 - $800 = $<<10230-800=9430>>9430
Next, we need to divide the total amount of depreciation by the original price of the car and multiply by 100% to express the result as a percentage:
Therefore, the car's rate of depreciation was 92.4%, to the nearest tenth percent. This means that the value of the car declined by 92.4% over the 5 years of use.
34% of all college students major in stem (science, technology, engineering, and math). if 40 college students are randomly selected, find the probability that
If the 34% of the college students major in STEM than the probability that exactly 15 of them major in STEM is 0.1162 .
In the question ,
it is given that ,
percent of students that major in STEM is = 34% ;
that means , p = 0.34 ; so , q = 0.6
number of students randomly selected (n) = 40 ,
By the Binomial Probability Distribution ,
we get ;
p(x = 15) = ⁴⁰C₅*(0.34)¹⁵*(0.66)²⁵
Simplifying the above value further ,
we get ;
p(x = 15) = 0.1162 .
Therefore , the required probability is 0.1162 .
The given question is incomplete , the complete question is
The 34% of all college students major in stem (science, technology, engineering, and math). if 40 college students are randomly selected, find the probability that exactly 15 of them major in stem .
Learn more about Probability here
https://brainly.com/question/18722217
#SPJ4
What is the area of the figure?
Answer:
252 in.²
Step-by-step explanation:
12 in. by 21 in. rectangle
The 6 in. by 3 in. rectangle missing on the left bottom corner is made up by the same-sized rectangle on the right side.
A = LW
A = 21 in. × 12 in.
A = 252 in.²
If a line on the coordinate plane increases as you read it from left to right, what do you know about the slope of that line??
The slope has a value of 1.
The slope has a value of 0.
The slope is positive.
The slope is negative.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
What is slope ?
Slope is a ratio and can have a value that is positive, negative, equal to zero, or undefined. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run".
What is positive slope ?
A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
Learn more about Slope at:
https://brainly.com/question/3493733
#SPJ1
What number is 25% of 275?
Answer: 68.75
Step-by-step explanation:
25 percent equals 0.25
Multiply the decimal by the number to find the percent
0.25*275= 68.75
Answer: 68.75
Step-by-step explanation:
25%/100% = 0.25
275 times 0.25 = 68.75
The store's rectangular floor is 38 meters long and 26 meters wide. How many square meters of flooring do
they need?
Answer:
988 m^2
Step-by-step explanation:
A=wl
A=38*26 = 988 m^2
Answer:
The store needs [tex]988m^2[/tex] of flooring.
Step-by-step explanation:
To find how many square meters of flooring the store needs, we need to find the area of the floor.
⭐ What does the area of a shape mean?
the area of a shape is the measure of the inside of the shapearea = length * widthWe are given that the length is 38 meters and the width is 26 meters.
Substitute these values into the area formula.
area = length*width
area = 38*26
∴ area = 988[tex]m^2[/tex]
⭐if this response helped you, please mark it the "brainliest"!⭐
jordan ran 78 mile on monday and 56 mile on tuesday. how much farther did jordan run on monday than on tuesday? enter your answer as a fraction in simplest form by filling in the boxes. $$ mile
After subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, we know that:
Jordan runs on Monday: 7/8 miles
Jordan runs on Tuesday: 5/6 miles
Jordan runs more on Monday:
7/8 - 5/6
3*7 - 4*5/24
21 - 20/24
1/21 miles
Therefore, after subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.
Know more about fractions here:
https://brainly.com/question/28933207
#SPJ4
Correct question:
Jordan ran 7/8 miles on Monday and 5/6 miles on Tuesday.
How much farther did Jordan run on Monday than on Tuesday?
Enter your answer as a fraction in simplest form.
) what is the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher?
The probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher is 0.2937.
In the given question,
Suppose computing speed of processors are normally distributed with mean 3.5GHz with standard deviation 0.26GHz
We have to find the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher.
Probability that 3 out of 7 randomly chosen processors clocks a speeds of 3.55 or higher is given
p = 0.4247
Now the probability follows a Binomial Distribution with the parameters, n=7 ad p=0.4247
P(X=x) = [tex]^nC_{k}(p)^k(1-p)^{n-k}[/tex]
Now putting the values
P(X=x) = [tex]^7C_{3}(0.4247)^3(1-0.4247)^{7-3}[/tex]
After solving;
P(X=x) = 0.2937
Hence, the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher is 0.2937.
To learn more about probability link is here
bbrainly.com/question/29657444
#SPJ4
The write question is:
Suppose computing speed of processors are normally distributed with mean 3.5GHz with standard deviation 0.26GHz. The probability that a randomly selected processor clocks a speed of 3.55 or higher is 0.4247.
What is the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher?
Find the indicated critical value. z 0.03
The indicated critical value for significance level of 0.03 should be approximately 1.88.
In standard normal distribution, the critical value is the mark or point that seperates region of acceptance and rejection. In one-tailed test having significance level of 0.03, it will indicate the probability of getting a value that will be more than or equal to 0.03.
The calculation of critical value can be done in many ways. Either look through the standard table or use calculator for the same. The latter is done by using inverse function on standard normal cumulative distribution function. It should be around 1.88.
Learn more about critical value -
https://brainly.com/question/14040224
#SPJ4
Which graph shows a decreasing function in interval (1), an increasing function in interval (2), a constant function in interval (3), and a decreasing function in interval (4)?
The graph that shows the function with the determined behavior is the last graph, circled on the image given at the end of the answer.
How to determine the behavior of the function?The graph of a function is classified as either increasing, decreasing or constant, as follows:
Increasing: as x increases the function increases, that is, the graph moves up.Decreasing: as x increases the function decreases, that is, the graph moves down.Constant: as x increases the function remains constant, that is, the graph stays at the same position.Hence the fourth graph on the image given at the end of the answer is the one with the desired behavior on each interval.
Missing InformationThe graphs are given by the image shown at the end of the answer.
More can be learned about increasing and decreasing functions at https://brainly.com/question/1503051
#SPJ1
PLEASE PLEASE PLSSS HELP
Step-by-step explanation:
This is the answer for 1., but the steps are the same for the rest of the questions, so I am sure you will be able to get the rest!
Slope is the value in front of the X and basically tells us how far up or down the line moves in 1 square across the line. It goes up if it is positive, and down if it is negative.
Y-intercepts can be found by plugging in 0 for x.
For question 1:
y=[tex]\frac{3}{5}[/tex](0)+3=3 so the y-intercept is 3 up from 0.
Then, we can use our slope which is a fraction, the top can be thought of as rise and the bottom is run. This means each point will be 3 up and 5 to the right.
Answer:
2/ Points at (0,-5), ( 1,-4), (2,-3)
Step-by-step explanation:
The slope is rise/run
The slope is x, which mean = 1
If you can please give me a Brainliest, thank you!
A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.how much kinetic energy would a ball with a mass of 3kg and a velocity of 5m/s create
The value of kinetic energy will be 37.5 Jules.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.
Now,
Since, A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.
Hence, The value of kinetic energy with a mass of 3kg and a velocity of 5m/s create will be;
⇒ Kinetic energy = 1/2 mv²
⇒ Kinetic energy = 1/2 × 3 × 5²
= 1/2 × 3 × 25
= 37.5 Jules
Thus, The value of kinetic energy will be 37.5 Jules.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Two groups of runners leave the same locker room heading in opposite directions. Group A runs 4.6 miles due
east, then turns 40° toward north and runs 2.1 miles. Group B runs 4.6 miles due west, then turns 50° toward
south and runs 2.1 miles. Which group is farther from the locker room?
Using law of cosines, the group that is farther from the locker room is; Group B
How to use Law of Cosines?The law of cosines gives that;
c² = a² + b² - 2ab cos C
Now, for group A, we can use law of cosine to find their current distance from the locker room as;
a² = 4.6² + 2.1² - 2(4.6*2.1)*cos 40°
a² = 21.16 + 4.41 - 14.8
a = √10.77
a = 3.28 miles
Similarly, for Group B, we have;
b² = 4.6² + 2.1² - 2(4.6*2.1)*cos 50°
b² = 21.16 + 4.41 - 12.42
b = √13.15
b = 3.63 miles
This means that group B is farther from the locker room
Read more about Law of cosines at; https://brainly.com/question/4372174
#SPJ1
7.A city department of transportation studied traffic congestion on a certain highway: To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway i5 less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table: Number ol people Probability 0.56 0.28 lo.o8 10.06 0.02 Let} = 'The number of people in passenger cars in the highway". Let Y the transformation of X by the rule Y = 75X + 5.Based on the new probability distribution, wtat is theimen number of people in passengers cars on the highway? (4)7.04 (B) 6 56 I(C) 4.7 (D) 12.10 (E) 6128
The mean number of number of people in passengers cars on the highway is given as follows:
E. 6.28.
How to calculate the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each value multiplied by it's respective probability.
The distribution in this problem is given as follows:
P(X = 1) = 0.56.P(X = 2) = 0.28.P(X = 3) = 0.08.P(X = 4) = 0.06.P(X = 5) = 0.02.Then the expected value before the transformation is given as follows:
E(X) = 0.56 x 1 + 0.28 x 2 + 0.08 x 3 + 0.06 x 4 + 0.02 x 5 = 1.7.
The transformation is given as follows:
Y = 0.75x + 5.
Thus the expected value after the transformation is of:
E(X) = 0.75(1.7) + 5 = 6.28.
Meaning that option E is correct.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
#SPJ1
HELP HURRY ITS TIMED
The length of the side AB represented by x in the triangle ABC is equal to 16 using the trigonometric ratio of sine.
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
The triangles ABC and ADB are right-angled triangles, we shall be considering the trigonometric ratio of the sine of angle A which is common to both triangles.
For triangle ABC;
sinA = adjacent/hypotenuse
sinA = x/32
for triangle ADB;
sinA = 8/x
thus we can say that;
x/32 = 8/x {cross multiplication}
x² = 3 × 32
x² = 256
x =√256 {take square root for both sides}
x = 16.
Therefore, 16 is the length of the side AB labelled x, using the trigonometric ratio of sine of the common angle A to the triangles ABC and ADB.
Learn more about trigonometric ratios here: https://brainly.com/question/23130410
#SPJ1
ASAP HELP FIND ∠DCE !! !!
Angle DCE = 91°
Hope it helps
An electrician needs to buy 7 1/2 feet of electrical wire. There are 1 1/2 feet of wire on each spool. How many spools of wire should the electrician buy?
Answer:
5
Step-by-step explanation:
[tex]\frac{7.5}{1.5}[/tex] = 5
In the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 30%.
How to calculate the percentage?From the information given, in the the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week
The total number of people at the end of the week will be:
= 1060 - 100 + 130 - 348
= 742
The percentage decrease will be:
Decrease / Original value × 100
= (1060 - 742) / 1060 × 100
= 30%
Learn more about percentages on:
brainly.com/question/13797493
#SPJ1
