Find the length of the hypotenuse of the triangle pictured below. Give your answer accurate to at least 2 decimal places. 8. 7 hypotenuse =
Answers
We can use the Pythagoras Theorem:
[tex]\begin{gathered} 8^2+7^2=hypotenusa^2 \\ \text{hypotenusa}=\sqrt[\square]{8^2+7^2}=\sqrt[]{64+49}=\sqrt[]{113}\approx10.63 \end{gathered}[/tex]The hypotenuse is 10.63
Related Questions
I need some help on number 4...Also, was my answer right for number 5, I believe it is..
Answers
In order to find the solution of this system of equations, we need to find the ordered pair that is a solution to both equations.
To do so, let's use the value of x from every option and calculate the corresponding value of the functions:
[tex]\begin{gathered} x=0\colon \\ f(0)=\sqrt[]{0+4}=2 \\ g(0)=0-4=-4 \\ \\ x=1.6\colon \\ f(1.6)=\sqrt[]{3.2+4}=2.68 \\ g(1.6)=1.6^3-4=0 \\ \\ x=-1.3\colon \\ f(-1.3)=\sqrt[]{-2.6+4}=1.18 \\ g(-1.3)=(-1.3)^3-4=-6.2 \\ \\ x=1.9\colon \\ f(1.9)=\sqrt[]{3.8+4}=2.8 \\ g(1.9)=(1.9)^3-4=2.8 \end{gathered}[/tex]So the correct option is the fourth one.
4 x 107 is
?
times as much as 4 x 10³.
Answers
Answer:
The answer is 10^4
Step-by-step explanation:
This is because 4 x 10^7 is 40,000,000
And 4 x 10^3 is 4,000
If you divide 40,000,000 by 4,000 you get
10,000
That answer is equivalent to 10^4.
So this is why the answer is 10^4
can i get some help on this one?
Answers
Answer:
[tex](x+9)^2=-4[/tex]Step by step explanation:
Completing the square is where we take a quadratic equation like this:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{ and turn it into this:} \\ a(x+d)^2+e=0 \end{gathered}[/tex]Where d and e can be represented by the following expressions:
[tex]\begin{gathered} d=\frac{b}{2a} \\ e=c-\frac{b^2}{4a} \end{gathered}[/tex]Since we have the following equation:
[tex]\begin{gathered} x^2+18x+74=-11 \\ x^2+18x+85=0 \end{gathered}[/tex]So, for a=1, b=18 and c=85.
Find d and e:
[tex]\begin{gathered} d=\frac{18}{2}=9 \\ e=85-\frac{18^2}{4}=4 \end{gathered}[/tex]Then, the result for completing the square would be:
[tex]\begin{gathered} (x+9)^2+4=0 \\ (x+9)^2=-4 \end{gathered}[/tex]3. Which of the following equations is equivalent to the equation shown below? x^2 + 4x + 15 = 0
Answers
We need to expand the answer choices and see which one matches the equation
[tex]x^2+4x+15=0[/tex]Remember the algebraic rules:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Now, if we expand choice D, we should get this. Let's expand:
[tex]\begin{gathered} (x+2)^2=-11 \\ x^2+2(1)(2)+(2)^2=-11 \\ x^2+4x+4=-11 \\ x^2+4x+4+11=0 \\ x^2+4x+15=0 \end{gathered}[/tex]solve each system of the equation by elimination method.3x-4y=1x-7y=23
Answers
Solve the system by elimination. This way:
Now, use the value of y to find the value of x.
[tex]\begin{gathered} 3x-4y=1 \\ 3x-4(-4)=1 \\ 3x+16=1 \\ 3x=-15 \\ x=-\frac{15}{3} \\ x=-5 \end{gathered}[/tex]The solution of the system is x=-5 and y=-4.
you have 20oz of egg noodles. You need 5oz to make one of chicken noodle soup how many service can you make
Answers
Okay. You have 20 oz of egg noodles.
You need 5 oz to make one of chicken noodle soup,
Then I can make 20 / 5 = 4 services
For 4.5 lb,
I6 ounces = 1 pound.
4. 5 x 16 ounces = 4.5 lb= 72 ounces
Then, we have 8 oz per serving.
Then we can have 72/8 = 9 services.
4.5 x 16 / 8 = 72/8 =9 servings
Okay. 2 tbsp = 1 serving
18 tbsp = (18 x 1) / 2 = 9 servings
What is the answer to this please need answers asap
Answers
SOLUTION:
Case: Geometry: Sum of angles in a triangle
Given: Three angles in a triangle in algebraic format
Required: To find angle K by first solving the resulting algeba
Method: Use sum of angles in a triangle to find x, then plug the value of x to get angle K.
Finding the value of x using sum of angles in a triangle
[tex]\begin{gathered} \measuredangle J\text{ + }\measuredangle K+\text{ }\measuredangle L\text{ = 180}\degree\text{ (Sum of angles in a triangle)} \\ (6x-11)\text{ + (8x-29) + (3x -1) =180}\degree \\ \text{Collecting like terms} \\ 6x+\text{ 8x+3x -11}\degree\text{-29}\degree\text{-1}\degree=\text{ 180}\degree \\ 17x\text{ -41}\degree=180\degree\text{ } \\ 17x=\text{ 180}\degree+41\degree \\ 17x=\text{ 221}\degree \\ \text{Dividing both sides by 17} \\ x=\text{ 13}\degree \end{gathered}[/tex]Finding the angles K
[tex]\begin{gathered} \measuredangle K=\text{ 8x -29}\degree \\ \measuredangle K=\text{ 8(13) -29}\degree \\ \measuredangle K=\text{ 104}\degree\text{ -29}\degree \\ \measuredangle K=75\degree \end{gathered}[/tex]Final answer:
The value of angle K is 75 degrees
In the Kite ABCD, AB = 52‾√52 mm AP= 5 mm, PD = 7 mm, find the area to the nearest mm2.
Answers
Step 1
the area of a kite is given by:
The area of a kite is half the product of the lengths of its diagonals
[tex]Area=x*y[/tex]Step 1
given the rigth triangle
so, we can find the x and y values
hence
a)x
[tex]\begin{gathered} \frac{x}{2}=\text{ 5} \\ to\text{ solve for x, multiply both sides by 2} \\ \frac{x}{2}*2=5*2 \\ x=10 \end{gathered}[/tex]b) y
[tex]\begin{gathered} \frac{y}{2}=7 \\ to\text{ solve for y, multiply both sides by 2} \\ \frac{y}{2}*2=7*2 \\ y=14 \end{gathered}[/tex]so
x=10
y=14
Step 2
finally, replace in the formula to find the area
[tex]\begin{gathered} Area=xy \\ area=10\text{ mm *14 mm} \\ area=140\text{ mm}^2 \end{gathered}[/tex]therefore, the answer is
[tex]\begin{equation*} 140\text{ mm}^2 \end{equation*}[/tex]I hope this helps you
Six months ago, Guillermo purchased a coffee truck as a business. To determine how his coffee
truck is doing, he plotted the net profits over each of the past six months on the scatter plot below.
Guillermo's business partner told him that the data Guillermo plotted is misleading. What is the
BEST reason why the data is misleading?
The data is misleading because the scatter plot starts at $532, so a small increase in profits looks very large.
The data is misleading because Guillermo should expect to make more profits than $500-$600 per month.
The data is misleading because the profits of a new company should not show a decrease between months 2
and 3
The data is misleading because the scatter plot only shows the first six months of profits, and it does not show
projected profits over the next six months.
Answers
In just one month, this coffee truck spent over $11,000. This month's margins were extraordinarily good, and the overhead was less than $2,000 as a result. Although not every month exceeds $10,000, I've had quite a few.
I make between $6,000 and $9,000 a month on the coffee van on average working 30 to 40 hours a week.
Because so much can depend on the revenue from coffee cater or other events, there is a wide variety.
Three significant occasions significantly increased our income.
What is the first successful coffee truck event?The first was a contract for hot chocolate I had gotten the year before. During the holidays, a nearby church gave hot coffee to its attendees during one of its services. three distinct nights for the host. We had previously catered for one of their nights, but this year they ordered three times as much. At a cost of 0.97 cents apiece, we supplied 6,988 cups of hot chocolate. The price of each cup was 0.09 cents.
∴ 6 778.36 cents per cup× 6,988 cups.
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the inequality is 0.6x>6000
The graph of the solution is open circle at 10,000; arrow right
The ages of the people on the bus are 24, 38, 47, 29, 51, 44, 40, 31, 36, and 43. If a bus passenger is selected at random, what is the probability that he or she is younger than 30?
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We want to know the probability of a passenger to be younger than 30.
There are 10 persons on the bus and out of those, just 2 are younger than 30.
Denote by E the event: "obtaining a person younger than 30 when its selected at random from the bus". Then,
[tex]P(E)=\frac{\text{number of persons younger than 30}}{\text{total persons on the bus}}=\frac{2}{10}=\frac{1}{5}=0.2[/tex]This means that the probability of a passenger to be younger than 30 is 0.2.
A car rental company charges $15 per day and $0.55 per kilometer to rent a car. What is the total bill if a car is rented for 4 days and is driven 146 kilometers?
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the total bill is $140.30
A group of hikers tracked how long it took to hike a 15-mile trail. They hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.6 miles per hour.
No, it is not proportional because 3.5 miles in 2 hours is not equivalent to 8.75 miles in 5 hours.
No, it is not proportional because 8.75 miles in 5 hours is not equivalent to 12.25 miles in 7 hours.
Answers
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
What are Ratio and Proportion?
When comparing two items of the same kind, a ratio is utilized. For two numbers, a and b, the ratio formula is written as a: b or a/b. Two or more ratios are deemed to be in proportion if they are all equal.
A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios.
A ratio is a comparison between two amounts that is calculated by dividing one amount by the other.
The equivalence of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio symbol (::) is used to express proportions, which aid in solving problems involving ambiguous quantities.
Given that,
15-mile trail covered as hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
determining the ratio for given data,
3.5/2→1.75
8.75/5→1.75
12.25/7→1.75
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
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A new road is being constructed parallelto the train tracks through point V. An equation of the line representing thetrain tracks is y = 2x.Find an equation of the linerepresenting the new road.
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the equation of the line representing the new road will be 2 x - y + 7 = 0.
The line is:
y = 2 x.
The slope of the line is:
m = 2
Now, the point V is:
V = (- 2, 3)
Since the train track is parallel to the line, its slope will be:
m' = 2 ( slope of parallel lines are equal)
So, the equation of the new road line will be:
y - y₁ = m (x - x₁)
y - 3 = 2 ( x + 2)
y - 3 = 2 x + 4
2x - y + 7 = 0
Therefore, the equation of the line representing the new road will be 2 x - y + 7 = 0.
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Alison is preparing for a math contest. Each day, she works on multiplication problems for 10 minutes anddivision problems for 50 minutes.How many minutes does Alison practice multiplication and division problems in 20 days?Alison practices multiplication and division problems forminutes in 20 days.W
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Each day she works on multiplication problems for 10 minutes and division for 50 minutes. In a day she studies a total of 60 minutes
For 20 days that means she will spend the following minutes studying
[tex]20\times60=1200\text{ minutes}[/tex]For multilication she will spend the following minutes studying
[tex]10\times20=200\text{ minutes}[/tex]For division she will spend the following minutes studying
[tex]50\times20=1000\text{ minutes}[/tex]Match each letter in the image with the correct description.Question 1Not yetansweredAPoints out of1.00Flag question- 5GBandChoose..g for27)Quadrant5cions,Quadrant IVE10/4)Quadrant IIDourseOrigin-5Y-AxisX-Axis
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we have that
y-axis ------> point A
x-axis ------> point C
origin -----> point E
I quadrant ------> point B
II quadrant -----> point G
III quadrant ----> point F
IV quadrant ----> point D
60 POINTS
Three points determine △ABC. The distance between A and B is 16.2 feet. The distance between B and C is 12.9 feet. What is the range for the distance between A and C? The range of the distance from A to C is greater than___feet and less than___feet.
Answers
The range of the distance from A to C is greater than 3.3 feet and less than 29.1 feet.
How to determine the range of distance?The given parameters are
AB = 16.2 feet
BC = 12.9 feet
To determine the range of the third length, we use the triangle inequality theorem
Using this theorem, we have the following inequalities
AB + BC > AC
AB + AC > BC
BC + AC > AB
So, we have
16.2 + 12.9 > AC
16.2 + AC > 12.9
12.9 + AC > 16.2
Solve for AC in the above inequalities
29.1 > AC
AC > -3.3
AC > 3.3
Remove the negative value
29.1 > AC
AC > 3.3
Rewrite as
AC > 29.1
AC > 3.3
This means that the values of AC are between 3.3 and 29.1 feet
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If p and q vary inversely and p is 19 when q is 16, determine q when p is equal to 8.
Answers
The value of q solving with variation method is 38
How to calculate the value of q ?Variation van be described as the relationship between a set of variable. We will be applying inverse variation to solve the question
The value of q can be calculated by using variation method
p= k/q
The first step is to calculate the constant k
19= k/16
cross multiply both sides
k= 19 × 16
k= 304
Since the value of k is 304, then the value of q can be calculated as follows
p = k/q
8= 304/q
cross multiply both sides
8q= 304
q= 304/8
q= 38
Hence the value of q when the value of p is 8 is 38
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A gardener has a bag of flower seeds. Half of the seeds are roses, one fourth are gardenias,
and one fourth are irises.
a. P(gardenias)
b. P(not gardenias)
Answers
can you help me please
Answers
Determine the sine and cosine ratios for an angle that measures pi/2
Answers
We need to determine the values of the functions sine and cosine for the angle π/2.
One way of finding those values is by observing the following unit circle:
Then, for the angle π/2, we have:
[tex]\begin{gathered} \sin\left(\frac{\pi}{2}\right)=1 \\ \\ \cos\left(\frac{\pi}{2}\right)=0 \end{gathered}[/tex]Suppose that the functions p and q are defined as follows in the attachment
Answers
1) In this question, we need to write out two composite functions.
2) So let's start with the following composite functions and then evaluate them for x=-5:
[tex]\begin{gathered} (q\circ p)(x)=\mleft(x-2\mright)^2+1 \\ (p\circ q)(x)=-(x^2+1)+2=-x^2-1+2=-x^2+1 \end{gathered}[/tex]2.2) Now, we can evaluate those two composite functions for x=-5
[tex]\begin{gathered} (q\circ p)(x)=\mleft(x-2\mright)^2+1 \\ (q\circ p)(-5)=\mleft(\mleft(-5\mright)-2\mright)^2+1=50 \\ \\ (p\circ q)(x)=-(x^2+1)+2 \\ (p\circ q)(-5)=-((-5)^2+1)+2=-(26)+2=-24 \end{gathered}[/tex]3) Hence, the answers are:
[tex]\begin{gathered} (q\circ p)(-5)=50 \\ (p\circ q)(-5)=-24 \end{gathered}[/tex]Hi, can you help me to solve this exercise, please!!
Answers
Based on the statement, we can deduce that cot(θ) must be negative as θ is in the fourth quadrant.
We have to find the ratio between the adjacent leg and the opposite leg knowing that the ratio between the hypotenuse and the opposite leg is -(√638)/22.
Using the pythagorean theorem for this purpose, we have:
[tex]\begin{gathered} (\sqrt[]{638})^2=22^2+a^2\text{ (Given that the sum of the squares of the legs must be equal to the square of } \\ \text{ the hypotenuse)} \end{gathered}[/tex][tex]\begin{gathered} 638=484+a^2\text{ (Raising the numbers to the power of 2)} \\ 154=a^2(\text{ Subtracting 484 from both sides of the equation)} \\ \sqrt[]{154}=a\text{ (Taking the square root of both sides)} \end{gathered}[/tex][tex]\begin{gathered} \text{ The ratio between the adjacent leg and the opposite leg would be: } \\ \frac{\sqrt[]{154}}{22} \end{gathered}[/tex]Given that cot(θ) must be negative the answer would be:
[tex]\cot \mleft(\theta\mright)=-\frac{\sqrt[]{154}}{22}[/tex]Gravel is being dumped from a conveyor belt at a rate of 40 ft/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 5 ft high?
(Round your answer to two decimal places.)
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm/s) when the diameter is 40 mm? (Round your answer to two decimal places.)
Answers
The formula Wh = Rs + Q, where Q stands for total energy losses experienced upon impact, can be used to represent any of the five fundamental types of dynamic pile drive formulas now in use.
Calculate dynamic pile ?
Fixed Formula
Maximum load a pile or set of piles (group pile) can support (Qu)
Depending on the soil's properties
Qu=Qp+Qs
Maximum failure load
Qp is the pile's point resistance.
Qs is the shaft resistance caused by rubbing between the pile and the dirt.
Load (Q) (Q)
Qp
QsQs.
Given diameter
height = h = ft(say)
radius = r =h/2
volume =v =1/3πr²h =1/3π(h/2)²h
=1/3π(h²/4)(h)
=1/12πh³
dv/dt = 1/12π(3h²dh/dt)
dv/dt = π/4 h² dh/dt
here dv/df =40ft³ and h =5ft
40 = π/4 (5² dh/dl
=40*4/100π
= 160/100π
=8/5π
So, the height is increasing at the rate of (8/5π) ft/min.
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What is the range of the following relation?{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
Answers
What is the range of the following relation?
{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
The range is
[tex]\lbrace3,1,-2,-4,-1\rbrace[/tex]Given the image below, identify the value of x. 9 2x - 19 M
Answers
You have the the length of segment NK is 23.
Furthermore, you have that segment NK is the sum of the following segments:
NK = NM + ML + LK
Each of the previous segments are given by the following algebraic expressions:
NM = x - 6
ML = 9
LK = 2x - 19
You sum the previous expression, by taking into account that the result is 23. Then you solve for x, just as follow:
NM + ML + LK = NK
(x - 6) + (9) + (2x - 19) = 23 eliminate parenthesis
x - 6 + 9 + 2x - 19 = 23 simplify similar terms
x + 2x - 6 - 19 + 9 = 23
3x - 16 = 23 add 16 both sides
3x = 23 + 16
3x = 39 divide by 3 both sides
x = 39/3
x = 13
Hence, the solution for x is x = 13
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a 9 and an 8
Answers
The probability to being a 9 and an 8 from a standard 52 - card deck
will be;
⇒ 2 / 13
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
The total number of cards = 52
Number of a 9 dealt = 4
Number of a 8 dealt = 4
Now,
Total number of cards = 52
And, Number of dealt a 9 and an 8 card = 4 + 4
= 8
Since, Probability = Number of dealt a 9 or 8 / Total number of cards
Thus, The probability of being dealt a 9 and an 8 will be;
= 8 / 52
= 2 / 13
Therefore, The probability to being a 9 and an 8 from a standard 52 - card deck will be;
⇒ 2 / 13
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write -6/11×3/4 in lowest terms.-6/136/139/22-9/22
Answers
In order to multiply two fractions we just multiply each side of the fraction:
Then, in this case:
[tex]-\frac{6}{11}\cdot\frac{3}{4}=\frac{-6\cdot3}{11\cdot4}=\frac{-18}{44}[/tex]Since 18 and 44 are pair numbers, but can be divided by 2, then we divide both:
[tex]-\frac{18}{44}=-\frac{9}{22}[/tex]Answer: D -9/22Please help with math problem FAST
Answers
The percent error in his calculation is 13.04%
How to find percent error?He calculated the object will take 2.3 seconds to fall on the ground.
It takes 2.5 seconds for the object to fall.
Therefore, the percent error can be calculated as follows:
percent error = | theoretical value - experimental value | / theoretical value × 100
Therefore,
percent error = |2.3 - 2.5| / 2.3 × 100
percent error = 0.3 / 2.3 × 100
percent error = 0.3 × 100 / 2.3
percent error = 30 / 2.3
percent error = 13.0434782609
Therefore,
percent error = 13.04 %
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A T-shirt company has determined that the profit it makes from a new T-shirt design can be modeled by the quadratic equation below:y = -100(x - 9)(x - 17)Where x represents the price of a T-shirt in dollars and y represents the company profit in dollars.According to this model, how much should the T-shirt company charge if they want to maximize their profit.Round your answer to the nearest penny.
Answers
Given data:
The expression for the profit function is y=-100(x-9)(x-17).
Differentiate teh above expressionn and equate to zero, in order to maimize the profit function.
[tex]\begin{gathered} \frac{dy}{dx}=0 \\ -100\frac{d}{dx}(x-9)(x-17)=0 \\ -100(x-9)\frac{d(x-17)_{}}{dx}-100(x-17)\frac{d(x-9)}{dx}=0 \\ -100(x-9)-100(x-7)=0 \\ -100(x-9+x-7)=0 \\ 2x=16 \\ x=8 \end{gathered}[/tex]Thus, 8 T-shirts must be sold in order to maximmize tthe profit.
divide 80 into two parts so that the greater part is 4 times the smaller
only answer this when u know the answer pls bcz this is important
Answers
Answer:16 and 64
Step-by-step explanation: 4x+x=80 5x=80 x=16 16*4=64
16 and 64
