The set of 3 lengths that make a right triangle is {8, 15, 17}
Which three lengths should she use?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.
So if the 3 sides are A, B, and C, such that:
A < B < C
We will have:
A² + B² = C²
Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:
8² + 15² = 17²
289 = 289
That equationis true, thus, these 3 lengths make a right triangle.
Learn more about right triangles at:
https://brainly.com/question/2217700
#SPJ1
what is 3495 x 30595
Multiplication of 3495 by 30595 is: 106,929,525.
MultiplicationMultiplication can be defined as the way of multiplying a number by another name.
Using a calculator to multiply 3495 by 30595.
Hence:
Multiplication= 3495×30595
Multiplication= 106,929,525
Therefore Multiplication of 3495 by 30595 is: 106,929,525.
Learn more about multiplication here:https://brainly.com/question/10873737
#SPJ1
Pls hellp
A small bowl of candy has a piece of chocolate, cinnamon, and butterscotch candy. Over the course of a few days, the three candies were eaten. Determine the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order.
Please show work.
Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:
[tex]\frac{1}{6}[/tex].
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, there are 3 candies, hence the number of ways they can be eaten is:
[tex]A_3 = 3! = 6[/tex]
The desired order is only one, hence the probability is:
[tex]\frac{1}{6}[/tex].
More can be learned about the arrangements formula at https://brainly.com/question/24648661
#SPJ1
find the slope of this line
Adult tickets to the fall play cost $8
and student tickets cost $4. The drama class
sold 20 more adult tickets than student tickets
to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is
Solving a system of equations we will see that they sold 80 adult tickets.
how many adult tickets were sold?
To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:
x = adult tickets sold.y = student tickets sold.They sold 20 more adult tickets than student tickets, then:
x = y + 20
And they collected a total of $880, then:
x*$8 + y*$4 = $880
The the system of equations is:
x = y + 20
x*$8 + y*$4 = $880
Isolating y on the first equation we get:
y = x - 20
Replacing that on the other equation we get:
x*$8 + (x - 20)*$4 = $880
Now let's solve that for x.
x*$12 - $80 = $880
x*$12 = $880 + $80 = $960
x = $960/$12 = 80
They sold 80 adult tickets.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?
Answer:
10.4403 or the square root of 109
Step-by-step explanation:
We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value
f(x) =4x2 + 8x -5 factor completely
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.
Answer:
19.50
Step-by-step explanation:
32m = 624
m = 19.50
need more words
An 8ft length of 4 inch wide crown molding cost $13. How much it cost to buy 88ft of crow molding
The amount it costs to buy 88ft of crow molding is; $143.
How much does it cost to buy 88ft if crow molding?It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.
On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;
88 × ($13/8)
= $143.
Therefore, the cost of 88ft of crow molding is; $143.
Read more on proportions;
https://brainly.com/question/1496357
#SPJ1
suppose that you borrowed 2000 from a friend and promise to pay back 3600 in 4 years. What simple interest rate will you pay?
The simple interest rate that the money would be paid is 20%
Simple interestFrom the question, we are to determine the interest rate that the money would be paid
Using the formula for simple interest,
S.I = PRT/100
Where S.I is the simple interest
P is the principal
R is the rate
and T is the time
From the given information,
P = 2000
S.I = Amount - Principal = 3600 - 2000 = 1600
R = ?
T = 4
Putting the parameters into the equation, we get
1600 = (2000 ×R × 4) / 100
1600 = 20 × R × 4
1600 = 80R
R = 20%
Hence, the simple interest rate that the money would be paid is 20%
Learn more on Simple interest here: https://brainly.com/question/20690803
#SPJ1
give at least five problems solving about area of a sector of a circle.
five example of arc length
fixe example or arc of a circle
See below for the examples of sectors and arcs of a circle
Area of sector of a circleThe area of a sector is calculated as:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees
[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving sector areas
Calculate the area of a sector where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the sector areas are:
1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]
2. [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]
3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]
4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]
5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]
Examples of arc lengthThe length of an arc is calculated as:
[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees
[tex]L = r\theta[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving arc lengths
Calculate the length of an arc where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the arc lengths are:
1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]
2. [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]
3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]
4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]
5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]
Examples of the arcs of a circleThe examples include:
A parabolic pathDistance in a curveCurved bridgesPizzaBowsRead more about arc and sectors at:
https://brainly.com/question/15955580
#SPJ1
A committee of 6 members is to be selected from 8 senior and 10 junior. find how many ways can this be done if there is no restriction
Answer:
18564 ways
Step-by-step explanation:
The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :
then
This can be done in [tex]C^{6}_{18}[/tex] ways.
[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]
What are the exact values of a and b?
Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.
Answer:
a = 5b = 5√3Step-by-step explanation:
A right triangle with one acute angle measuring 30° is the 30°-60°-90° "special" triangle. The ratios of its side lengths are well known to be ...
1 : √3 : 2
Side lengthsIn the given triangle, the longest side is labeled 10, so is 5 times the measure of the longest side in the ratios given above. Multiplying those ratio values by 5, we have side lengths ...
a : b : c = 5 : 5√3 : 10
That is ...
a = 5
b = 5√3
__
Additional comment
If you want to figure the side lengths using trigonometry, you have ...
a = c·sin(30°) = 10·(1/2) = 5
b = c·cos(30°) = 10·(√3/2) = 5√3
find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29
Answer:
x = 15, UV = 12, SV = 31
Step-by-step explanation:
13 + 6 + (2x - 18) = 4x - 29
2x + 1 = 4x - 29
2x = 30
x = 15
UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12
SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31
Select all the correct answers.
Exponential function fis represented by the table.
2
X
0
0
-12
B
-4
Function gis represented by the equation.
9 (2) = -12 (3)
Which statements are true about the two functions?
0
3
2
4
3
Both functions are increasing on all intervals of x.
Both functions approach the same value as x approaches ...
The functions have the same x-intercept.
Both functions approach - as x approaches -...
The functions have the same y-intercept.
The true statements are
(d) they have the same y-intercept(e) they approach negative infinity as x approaches negative infinityHow to determine true statements?The function g(x) is given as:
[tex]g(x) = -12(\frac 13)^x[/tex]
Set x = 0, to determine the y-intercept
[tex]g(0) = -12(\frac 13)^0[/tex]
g(0) = -12
From the table, we y-intercept of f(x) is
f(0) = -12
This means that they have the same y-intercept
Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity
Hence, the true statements are (d) and (e)
Read more about functions at:
https://brainly.com/question/11303370
#SPJ1
Find a Cartesian equation for the curve.
r = 3 sec(θ)
Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle
[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]
[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]
[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]
Please help me with this problem. Seriously desperate again !!
Answer: 17 inches by 7 inches
Step-by-step explanation:
119 = 1 x 119 & 7 x 17
7 x 17 is the more likely answer, so let's test it
7 x 2 + 3 = 17
Therefore, the dimensions are 17 by 7.
Which choice is equivalent to the quotient shown here for acceptable
values of X?
√25(x-1) + √5(x-1)²
OA. √25(x-1)-5(x-1)²
OB.
5
1(x-1)
OC. √125(x-1)3³
OD. √5(x-1)
The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).
What is the equivalent of the quotient?It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).
It therefore follows from the the laws of indices that the evaluation is thus;
= √{(25/5) ×(x-1)/(x-1)²}.
Ultimately, upon evaluation we have;
= √(5/(x-1))
Read more on equivalent expressions;
https://brainly.com/question/11258067
#SPJ1
need help with this!
Answer:
1.The slope intercept- form of the function is:
y = x -2
2.The predicted length of the vine after 53 days is 51 cm.
Step-by-step explanation:
The slope is the [tex]\frac{change in length}{change in days}[/tex]
In the table, every time that the length increased by 5, the days also increased by 5. 5/5 = 1
Now we have to find the y-intercept, we can use the slope and one of the points that we know to do this. Let's use the first point (5,3). This is in the form (x,y).
y = mx + b
3 = (1)(5) + b
3 = 5 + b Subtract both sides by 5
-2 = b Now we can write the equation
y = mx + b
y = x -2. Plug 53 in for x and you will find your second answer.
y = 53 - 2
y = 51
1. The function's slope intercept form is y = x -2.
2. The vine should be 51 cm long in length after 53 days.
Determining the Slope Intercept Form:
The slope is given as,
m = (Change in length) / (Change in days)
In the table, it can be seen that,
The days climbed by 5 for every 5 that the length did as well [10-5 = 8-3 = 5].
∴ Slope, m =5/5 = 1
We may use the slope and one of the points we are familiar with to help us find the y-intercept. Utilizing the first point (5,3), this is how it looks for the point (x, y),
y = mx + c ..... (1)
3 = (1)(5) + c
3 = 5 + c
Subtract 5 from both sides to get c.
c = -2
Hence, from (1), the slope intercept form is given as,
y = x - 2 ...... (2)
Predicting the Vine Length:
Since x represents the number of days, put x = 53 in equation (2) to predict the vine length after 53 days.
y = (53) -2
y = 51 cm
Thus, the length of vine after 53 days would be 51 cm.
Learn more about slope here:
https://brainly.com/question/16302642
#SPJ1
To convert grams to kilograms, you can use the ratio
OA. True
B. False
1,000 grams
1 kilogrami
Answer:
A. True
Step-by-step explanation:
The ratio 1000 grams=1kilogram is correct.
Solve for d
d+13 = 40
Answer:
d=27
Step-by-step explanation:
d+13=40
-13 -13 Subtract 13 from both sides to leave by itself
d=27
Hope it helps:)
Dan & Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?
A. Alex is 50% taller than Dan.
B. Dan is 60% taller than Alex.
C. Dan is 40% taller than Alex.
D. Alex is 40% taller than Dan.
The true statement is that Alex is 50% taller than Dan.
How to solve percentage questions?They both measured themselves against a tree in their backyard.
Therefore, the tree is 80% taller than Dan and 20% taller than Alex.
Hence,
let
Dan height = x
Tree's height = x + 0.8x
Tree's height = 1.8x
let
Alex height = y
Tree's height = y + 0.2y
Tree's height = 1.2y
Therefore, if we use Dan height as 100, the height of the tree will be 180.
Then,
180 = 1.2y
y = 150
This means Alex is 50 percent taller than Dan.
learn more on percentage here: https://brainly.com/question/14177792
#SPJ1
find the y intercept of 2x - 5y + 7 = 0
How to solve for X in the triangle
Answer:
22.6
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=24^2
b^2=512
b=22.6
Answer:
[tex]x = 16\sqrt{2}[/tex]
Step-by-step explanation:
we are given a right triangle.
then
In order to determine x we need to use
the Pythagorean theorem:
[tex]x^{2}+8^{2}=24^{2}[/tex]
⇔ x² + 64 = 576
⇔ x² = 576 - 64
⇔ x² = 512
⇔ x² = 2⁹
⇔ x² = 2 × 2⁸
[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]
[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]
[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]
Find the standard deviation for the set of data. (17,26,28,9,30, 29,6,21,23}
Using it's concept, the standard deviation for the given data-set is of 8.22.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean for this problem is:
M = (17 + 26 + 28 + 9 + 30 + 29 + 6 + 21 + 23)/9 = 21
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(17-21)^2 + (26-21)^2 + (28-21)^2 + \cdots + (21-21)^2 + (23-21)^2}{9}} = 8.22[/tex]
More can be learned about the standard deviation of a data-set at https://brainly.com/question/12180602
#SPJ1
To what power must 10 be raised to give 10
The answer is 1
10¹ = 10
i hope it was helpful
How do i convert the follwing Powers Of Ten into standard numbers?
i need help w/ this fast!
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The given numbers written in standard forms are
1.0 × 10⁷
1.0 × 10⁵
1.0 × 10⁸
1.0 × 10¹²
1.0 × 10⁶
respectively
Standard form of a numberFrom the question, we are to write the given numbers in standard form
To write the given numbers in standard form,
Multiply each of the numbers by 1.0
Then,
10⁷ in standard form is 1.0 × 10⁷
10⁵ in standard form is 1.0 × 10⁵
10⁸ in standard form is 1.0 × 10⁸
10¹² in standard form is 1.0 × 10¹²
10⁶ in standard form is 1.0 × 10⁶
Hence, the given numbers written in standard forms are
1.0 × 10⁷
1.0 × 10⁵
1.0 × 10⁸
1.0 × 10¹²
1.0 × 10⁶
respectively
Learn more on Writing numbers in standard form here: https://brainly.com/question/1708649
#SPJ1
Please help ASAP
What is the measure of YZ?
A.142
B.52
C.128
D.38
Work Shown:
(arc YZ + arc XU)/2 = angle YVZ
(arc YZ + 38)/2 = 90
arc YZ + 38 = 90*2
arc YZ + 38 = 180
arc YZ = 180 - 38
arc YZ = 142
Triangle PQR is rotated, translated, and dilated to obtain triangle P'Q'R' as shown. An Image of triangle PQR and PQR prime are displayed. The Triangle PQR intersects P at (minus 2, 0.5), R at (minus 2, minus 2.5) and Q at (0, minus 1.5). Similarly P, R, Q prime at (1.5,minus 1.5), (1.5,3), and (minus 1.5,1.5). Which statement about the two figures is correct? A. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. B. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. C. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent. D. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
How to determine the true statements?The transformations are given as:
RotationTranslationDilationRotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.
Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.
The above means that the angles of triangle PQR and triangle P'Q'R' are congruent
Hence, the true statement is (d)
Read more about transformation at:
https://brainly.com/question/11709244
#SPJ1
Evaluate each expression:
I-3|=
The value of the modulus function |-3| is 3.
What is the value of modulus?'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.
The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.
For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.
Therefore, the value of the modulus function |-3| is 3.
To learn more about the value of modulus refer to:
https://brainly.com/question/271574379
#SPJ9
Find the indicated real nth root(s) of a.
n=3, a = - 216
Answer:
-6
Step-by-step explanation:
A suitable calculator can find this for you directly.
Odd root of a negative number-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:
∛(-216) = -∛216 = -6
__
Additional comment
Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.
The second attachment shows a calculator capable of finding the complex roots as well as the real one.