Answer:
7 < n < 47
Step-by-step explanation:
given 2 sides of a triangle then the third side n is in the interval
difference of 2 sides < n < sum of 2 sides , that is
27 - 20 < n < 27 + 20
7 < n < 47
Please help!! I dont know what to do
The additional information needed to that triangle ADN is congruent to triangle DCO using SAS is
AN ≅ DO and < BAN ≅ CDNWhat do we mean by congruent triangles?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent
The SAS says that the corresponding sides and the included angle must be congruent
the angles and side used here include
AN - < BAN - BA
DO - < CDN - CD
Learn more about angles here:
https://brainly.com/question/29393764
#SPJ1
2. If all of the partridges eat at this same rate, how many
pears will they eat in 1 hour and 45 minutes? (Assume the
birds eat at a constant rate.)
The total number of pears consumed by all the 6 partridges is given by the equation A = 84 pears
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of pears be represented as A
Let the number of partridges be n = 6
Now , Pete the partridge eats 4 pears in 30 minutes
So , the number of pears in 1 hour = 2 x 4
The number of pears in 1 hour = 8 pears
The number of pears in 1 hour 30 minutes = 8 + 4 pears
The number of pears in 1 hour 30 minutes = 12 pears
The number of pears in 1 hour 45 minutes = 12 + 2 pears
The number of pears in 1 hour 45 minutes = 14 pears
So ,
The total number of pears by all 6 partridges A = 6 x number of pears in 1 hour 45 minutes
Substituting the values in the equation , we get
The total number of pears by all 6 partridges A = 6 x 14
On simplifying the equation , we get
The total number of pears by all 6 partridges A = 84 partridges
Therefore , the value of A is 84 partridges
Hence , the number of partridges is 84
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.
The way that they could calculate the point that is equidistant from all three gates is; By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.
How to find the the circumcenter of the triangle?The circumcenter of a triangle is defined as the locus of point equidistant from the three vertices of a triangle.
From the image attached showing the location of the three gates, the first step to take is to join all the three entry points of the friends in order to form a triangle.
The second step to take now, will be to find the centroid of the triangle, such that all three friends must start moving in the direction of the midpoint of the opposite side.
Finally, following that procedure, the point equidistant from all the three gates can be calculated.
Read more about Circumcenter of triangle at; https://brainly.com/question/19560728
#SPJ1
The area of a national park is 9, 542 square miles. If 14% of the area of the park is reserved for animal preservation, which expression represents the best approximation of the animal preservation area? J) 10,000 • 0.10 K) 10,000 divided by 0.10 L) 10,000 • 0.20 M) 5,000 divided by 0.10 N) 5,000 divided by 0.20
1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.
What is area?The idea of area is essential to contemporary mathematics. A two-dimensional shape, figure, or planar lamina in a plane will occupy a specific amount of space, which is denoted by the area.
The area can be simply defined as the volume of cloth, or other material with the specified thickness, required to construct a model of the shape, or as the volume of paint required to completely cover the surface of the shape in a single layer, or "coat," of paint.
It is a two-dimensional illustration of the length of a curve or the volume of a solid, where length is a one-dimensional concept and volume is a closely related concept that exists in three dimensions.
Area of national park = 9,542 miles²
14% of the area of the park is reserved for animal preservation
= 9542 × 14
= 9542 × 14/100
= 9542 × 0.14
= 1335.88 miles²
Thus, 1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.
Learn more about area
https://brainly.com/question/27683633
#SPJ1
Please, i need help.
The opposite sides are parallel to each other if diagonals of the quadrilateral bisect each other.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
AC and BD bisect each other.
We know that in a quadrilateral if the diagonal of the quadrilateral bisect each other then the opposite sides are parallel to each other.
AC = BD (Equal diagonal)
Then the side AB and CD are parallel to each other. And similarly, the sides BC and AD are also parallel to each other.
AB || CD or BC || AD
More about the quadrilateral link is given below.
https://brainly.com/question/13805601
#SPJ1
26.
circle
triangle
hexagon
rectangle
pentagon
Two-dimensional cross-sections could be obtained from a right rectangular prism a Rectangles. Option D
What is a right rectangular prism?Generally, A right rectangular prism may give rise to three distinct varieties of two-dimensional cross-sections, and they are as follows:
A rectangle may be created by cutting the right rectangular prism along either of its faces to create a parallelogram, which can then be folded in half.
Obtaining a parallelogram requires cutting the correct rectangular prism at an angle that is not perpendicular to any of its faces. This will result in the formation of a parallelogram.
You may acquire a trapezoid by cutting the right rectangular prism at an angle that is not parallel to any of its faces. This will result in the formation of a trapezoid.
Read more about the right rectangular prism
https://brainly.com/question/3248292
#SPJ1
(0.95x -0.04)-(0.99x -0.13)
Answer: -0.04x + 0.09
Step-by-step explanation:
(0.95x - 0.04) - (0.99x - 0.13) = 0.95x - 0.04 - 0.99x + 0.13
= 0.95x - 0.99x + 0.13 - 0.04
= (0.95 - 0.99)x + (0.13 - 0.04)
= -0.04x + 0.09
Need help with this :'( Look at attachment below please.
The matching statements and reasons:
1. Triangle RAS is isosceles, AM is a median Given2. AR = AS Definition of isosceles3. MR = MS Definition of median4. AM = AM Reflexive property5. ΔRAM ≅ ΔSAM SSSPut these numbers in order, starting with the smallest.
437.5
437.55
437.05
437.49
437.15
Answer:fsjcc
Step-by-step explanation:
8473274+5487643=593fdj
]
Consider the following set of real numbers:
open curly brackets square root of 4 comma space short dash square root of 2 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top comma space square root of 10 close curly brackets
Which of the following lists all of the rational numbers in the set?
square root of 4 comma space short dash square root of 2 comma space square root of 9 over 4 end root comma space square root of 10
square root of 4 comma space short dash square root of 2 comma space short dash 2 over 3 comma space 9 over 8 comma space square root of 9 over 4 end root comma space square root of 10
square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top
short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top
Based on the given set of real numbers, a list of all the rational numbers in the set include the following: B. √4, -2/3, 1, 9/8, √(9/4), 2.4. Therefore, the correct answer option is: B. square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.
In this scenario, the rational numbers include all of the following:
√4-2/319/8√(9/4)2.4However, -√2 and √10 would not be classified as rational numbers because they cannot be obtained when an integer is divided by another integer.
Read more on rational number here: brainly.com/question/20400557
#SPJ1
1) Classify each triangle by its angles and sides.
2) If ΔJKL is an equilateral triangle, JK=13x+5, KL=17x-19, and JL=8x+35, find x and the measure of each side.
1) The triangle classified according to their sides is given as follows:
a) Isosceles triangle - It has two equal sides
b) Scalene Right Angled Triangle.
c) obtuse scalene triangle -Has an angle that is over 90 degrees, as well as three unequal sides
d) Equilateral Triangle - Three equal sides and three equal angles
e) Isosceles Right Angled Triangle - Right angle with two equal sides and two equal angles
f) Scalene Triangle - Three unequal sides and three unequal angles.
g) Equilateral Triangle - Three equal sides and three equal angles
h) Obtuse Isosceles Triangle - has two equal sides with an angle measuring above 90 degrees.
2) Note that the value of x is 6, JK is 83, KL is 83 and JL is 83.
What is is an Equilateral Triangle?As indicated above, an Equilateral Triangle is one whose sides are equal. Thus,
JK = KL = JL
That means 13x + 5 = 17x -19 ..............1
Simplifying 1 by collecting like terms:
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can proceed to find the sides now
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Therefore, the value of x is 6, JK is 83, KL is 83 and JL is 83.
Learn more about Triangles:
https://brainly.com/question/29083884
#SPJ1
A bank loaned out $10,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $1000, how much was loaned at 7%
The amount of money loaned at a rate of 7% will be $7,000.
What is the solution to the equation?
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A bank loaned out $10,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $1000.
Let 'x' be the amount of money loaned at a rate of 7%. Then the amount of money loaned at a rate of 17% will be ($10,000 - x). Then the equation is given as,
0.07x + 0.17($10,000 - x) = $1,000
0.07x - 0.17x + $1,700 = $1,000
0.10x = $700
x = $7,000
The amount of money loaned at a rate of 7% will be $7,000.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
PLEASE HELP ANSWER!
There are 108 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and treesIf the number of weeds is 7 less than thrice the number of grasses, and the number of trees is 3 more than thrice the number of grasses, find the number of grasses, weeds, and trees that are major pollen sources.
There are 51 trees, 41 weeds, and 16 grasses that are significant pollen producers.
In the context of beekeeping, the phrase "pollen source" refers to flowering plants that provide pollen to bees and other insects. Bees gather pollen to use as a source of protein for their young.
G, W, and T should stand for the number of grasses, weeds, and trees that serve as significant pollen sources.
According to information provided, state A is home to 80 significant sources of pollen. This data can be represented as follows in an equation:
G + W + T = 108......(1)
According to what is said, there are 7 times as many weeds as there are grasses. This data can be represented as follows in an equation:
W = 3G - 7......(2)
We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:
T = 3G + 3
We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:
G + W + T = 108
G + 3G - 7 + 3G + 3 = 108
7G - 4 = 108
7G = 112
G= 112/7
G = 16
Therefore, there are 16 grasses that are major pollen sources.
Number of weeds that are major pollen sources:
W = 3G - 7 = 3(16) - 7 = 48 - 7 = 41
Therefore, there are 41 weeds that are major pollen sources.
Number of trees that are major pollen sources:
T = 3G + 3 = 3(16) + 3 = 48 + 3 = 51
Therefore, there are 51 trees that are major pollen sources.
To know more about Pollen source visit:-
https://brainly.com/question/14636921
#SPJ1
Which expression is equivalent to 6y?
6+y
7y - 1
y x y x y x y x y x y
y+y+y+y+y+y
Answer:
y + y + y + y + y + y
Step-by-step explanation:
6y =
6 * y = ==> add y 6 times
Hence, 6 * y = y + y + y + y + y + y
Please Answer and Explain
Answer:
x = 12
Step-by-step explanation:
3/9 = 4/x
3x = 36
x = 12
Answer:
The quadrilateral ABCD was dilated with a scale factor of 1.8
Take the value of x before the dilation (4), and multiply that by 1.8
The result should be 7.2
Hope this helps.
What is the radius of a hemisphere with a volume of 839\text{ cm}^3,839 cm
3
, to the nearest tenth of a centimeter?
The radius of the hemisphere with volume 3839cm³ is 11.9cm
What's is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.
The volume of a hemisphere is given as ⅔πr³
Where r is the radius
V = ⅔×3.14r³
3839 = 2/3× 3.14r³
r³ = (3839× 3)/3.14×2
r³ = 11517/6.28
r³ = 1833.9
r = cube root of 1833.9
r = 11.9cm
Therefore the radius of the hemisphere is 11.9cm
learn more about volume of hemisphere from
https://brainly.com/question/333717
#SPJ1
Nathan is solving for the measure of ECA, in the illustration below. What is the best first step he can take for this problem? Be specific and explain your choice.
The best step to use in getting angle ECA is the exterior angle property which gives us; Angle ECA = 154°
What is the missing angle of the triangle?In a triangle geometry, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as the exterior angle property. This tells us that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.
Now, in this question, we are trying to find the measure of angle ECA which is an exterior angle given by the expression 166 - 6x.
Now, the interior opposite angles are (100x - 59) and (6x + 1). Thus;
Applying the exterior angle property, we will have the first step as;
(100x - 59) + (6x + 1) = 166 - 6x
106x - 58 = 166 - 6x
112x = 166 + 58
112x = 224
x = 224/112
x = 2
Thus;
Angle ECA = 166 - 6(2) = 154°
Read more about Triangle missing angle at; https://brainly.com/question/23327304
#SPJ1
To calculate the height of a mountain, the following method was used. From a point A on a level plain, the angle of elevation of the top of the mountain was found to be 32°. At a point B nearer the mountain, where |AB| = 400m, the angle of elevation was found to be 58°. Calculate the height of the mountain to 2 s.f
The height of the mountain is derived to be 410 m approximately to 2 significant figure using the trigonometric ratio of tangent for angles of elevation 32° and 58°.
What are 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.
We shall represent the length from point B to the foot of the mountain with x and the height of the mountain with h so that:
the distance from a to the foot of the mountain = 400m + x
tan 32° = h/(400 + x)
h = tan 32° (400 + x) {by cross multiplication}
h = 400 × tan 32° + xtan 32°
h = 249.9477 + xtan 32°
also;
tan 58° = h/x
h = tan 58° × x {by cross multiplication}
h = xtan 58°
so;
xtan 58° = 249.9477 + xtan 32°
xtan 58° - xtan 32° = 249.9477 {collect like terms}
x(tan 58° - tan 32°) = 249.9477
x(0.9755) = 249.9477 {divide through by 0.9755}
x = 249.9477/0.9755
x = 256.2252
h = 256.2252 × tan 58°
h = 410.9460.
Therefore, the height of the mountain is 410 m approximately to 2 significant figures using the trigonometric ratio of tangent for angles of elevation 32° and 58°.
Know more about trigonometric ratio here:https://brainly.com/question/23130410
#SPJ1
Which expression is equivalent to (ab3rd power)4th power?
a4th power b 12th power
ab 12th power
a 5th power b 4th power
ab 7th power
The expression that is equivalent to (ab3rd power)4th power in the question is a4th power b 12th power.
Exponential expression.Exponential expression is the power to which a given term of mathematical expression is raised to. The value of the power to which a variable is raised is not limited. Sometimes, some laws are required to solve some exponential expressions. An example is the law of indices which can be applied to solve some expressions in a given question with large numbered powers. The law of indices is one of the major law to refer to when discussing power of numbers or variables.
Thus the expression that is equivalent to (ab3rd power)4th power is:
(ab3rd power)4th power = (ab^3)^4
expand the given bracket to have;
(ab^3)^4 = a^4 * b^(3*4)
= a^4b^12
Therefore the expression is equivalent to a^4b^12 i.e a4th power b 12th power.
Learn more about the exponential expressions at https://brainly.com/question/8844911
#SPJ1
In a company's first year in operation, it made an annual profit of \$117,000$117,000. The profit of the company increased at a constant 27% per year each year. How much total profit would the company make over the course of its first 5 years of operation, to the nearest whole number?
The profit the company would make over the course of its 5 years of operation, given the starting annual profit and the constant increase in the profit, is $ 998, 329.34
How to find the profit ?To find the total profit that the company would make over the first 5 years of the operation, use the future value formula :
= First profit x Future value interest factor of annuity, 27%, 5 years
First profit = $ 117, 000
Rate of increase = 27 %
Number of years = 5 years
The profit in 5 years is:
= 117, 000 x 8.53272941
= $ 998, 329.34
Find out more on profit at https://brainly.com/question/15299433
#SPJ1
Find the value of k given that both points lie on a line passing through the orgin (k,7) and (-81,-9)
The value of k for the point on the line is 63
How to determine the value of k?We can find the value of k by using the slope formula. The slope of a line can is given by:
Slope = (y2-y1)/(x2-x1)
Since the pass through the origin (0,0), (k,7) and (-81,-9). we can write:
x1 = 0, y1 = 0 and x2 = -81, y2 = -9
Slope = (-9-0)/(-81-0) = 1/9
Also, we can write:
x1 = k, y1 = 7 and x2 = -81, y2 = -9. And the slope is still the same
1/9 = (-9-7)/(-81-k)
1/9 = -16/(-81-k)
1/9(-81-k) = -16
-9 - k/9 = -16
-k/9 = -16 + 9
-k/9 = -7
-k = -7 × 9
-k = -63
k = 63
Learn more about slope of a line on:
brainly.com/question/29044610
#SPJ1
2b+8-5b+3=13+8b-5
Answer with steps please!
Answer:
[tex]b=3/11[/tex]
Step-by-step explanation:
[tex]-3b+11=8b+8 \\ \\ 11b+8=11 \\ \\ 11b=3 \\ \\ b=3/11[/tex]
Harrison’s Loan Stars loaned Nicole $800 that she needed for an unexpected car repair. She must repay the loan in 10 days. The interest is $200. What is the APR for this loan, to the nearest percent?
Answer:
APR stands for Annual Percentage Rate, which is the interest charged on a loan expressed as a yearly rate. In this case, we are given the interest rate for a loan over 10 days.
To calculate the APR, we need to determine the annualized interest rate, which is the interest rate multiplied by the number of times the interest is compounded per year.
We know that the interest on the loan is $200. The loan amount is $800 and the loan period is 10 days.
First we need to calculate the daily interest rate:
Interest/Loan amount = 200/800 = 0.25
To find the annualized interest rate, we need to multiply the daily interest rate by the number of days in a year:
0.25* 365 = 91.25%
To the nearest percent the APR for this loan is 91%
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Carla is getting her golf bag prepared for a golf tournament and decides to do a quick experiment with the three brands of golf balls she
has stored in her bag.
She randomly draws 20 golf balls to determine the frequency of occurrence for each brand, returning the drawn ball after each trial.
The data from her experiment is displayed in the table below. Determine the correct values to complete the rest of the table, and
complete the accompanying statement. For this item, any answers that are not whole numbers should be entered as a decimal,
rounded to the hundredths place.
Brand
Best Flight
Distance King
High Loft
Frequency
3
Reset
6
11
Experimental
Probability
0.30
If Carla performed another experiment using the same set of golf balls and drew 12 Best Flight golf balls, she would draw
approximately
Distance King golf balls.
on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
equation given is 3(x+2)=7x-48
value of x
[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]
value of x from the given equation comes out to be 13.5
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
What is the answer to this question
Answer:
Do you have answer choices?
The possible answers are Plane PLN, Plane LNR, Plane NRP, and Plane RPL.
Simplify -10x - 2x + 3x. 11 x 9 x -9 x
Answer:
x=16
Step-by-step explanation:
right!!
Question 3 of 11
What is the slope of the line given by the equation y = 9x?
Answer here
SUBMIT
Answer:
the slope is 9
Step-by-step explanation:
The slope is the number before the x.
Answer:
Slope = 9
Step-by-step explanation:
Now we have to,
→ find the slope of the equation.
Formula we use,
→ y = mx + b
→ m = Slope
Then the required slope will be,
→ y = mx + b
→ y = 9x + 0
→ y = 9x
→ [ m = 9 ]
Hence, the value of slope is 9.
Given the proportional relationship in the table below, write an equation to represent the relationship.
The equation that represent the proportional relationship is y = 11k.
How to write equation to represent relationships?Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝ x
y = kx
where
k = constant of proportionalityHence,
x = 2
y = 22
Therefore,
22 = 2k
k = 22 / 2
k = 11
Therefore, the equation is y = 11k
learn more on proportional relationship here: https://brainly.com/question/19298175
#SPJ1
Devon made a small batch of cookies. He’s used 5/6 of a cup of sugar, and 3/4 of a cup of flour. Evaluate the following expression to determine how much more sugar he used then flour 5/6 - 3/4
To evaluate the expression 5/6 - 3/4, we need to first convert the fractions to a common denominator. The least common multiple of 6 and 4 is 12, so we can rewrite the fractions as follows:
5/6 - 3/4 = (5/6)(2/2) - (3/4)(3/3)
= 10/12 - 9/12
= 1/12
Therefore, Devon used 1/12 of a cup more sugar than flour.
The following dot plot shows how far peter ran in each of his tennis matches this year. find the median distancethe following dot plot shows how far peter ran in each of his tennis matches this year.
a. the following dot plot shows how far peter ran in each of his tennis matches this year.
b. find the median distance.
c. find the median distance..
The median distance is 5km.
What is median distance?The median distance, symbolized by δM, is the median value of the distance among any two node pairs. This is measured over each network's largest linked component, and takes into account pairs including of the same node.
In this case, the dots in the picture (attached) represent the number of matches.
So, if we write it all down here, the data will be:
3, 4, 4, 5, 5, 5, 5, 7, 7
Since the total of values in the data is odd number, that is 9, then the formula for the median distance will be:
Median = (n + 1) / 2
with n = 9
Thus, the median distance in this case:
= (n + 1) / 2
= (9 + 1) / 2
= 10 / 2
= 5
Hence, the median distance is 5km.
Learn more about median distance at: https://brainly.com/question/20726719
#SPJ4
