The length of two sides of the right triangle ABC shown in the illustration are given. Find the length of the third side in centimeters. a=12cm and c=37cm
Answers
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
How to find the missing side of a right triangle
In this question we know the lengths of two sides of the right triangle. By Pythagorean theorem we get the length of the missing side:
a² + b² = c²
b² = c² - a²
b = √(c² - a²)
b = √(37² - 12²)
b = 35
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
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Related Questions
Use the diagonals to determine whether a parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a rectangle, rhombus, or square. Give all the names that apply.
Answers
The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square
How to solve for the shapeIn order to get the shape using the vertices that we have, we would have to find the length of the diagonals
We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)
The length of the diagonal PQ is given as:
PQ = [tex]\sqrt{(0-4)^2+(4-0)^2}[/tex]
= [tex]\sqrt{32}[/tex]
Next we have to solve for the length of the diagonal RS
RS = [tex]\sqrt{(4-(-4))^2+(0-(-4))^2[/tex]
RS = [tex]\sqrt{32}[/tex]
Since PQ = RS we would have to conclude that the shape is a square.
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A container can hold a maximum of 17.75 pounds. There are two objects in the container. The first object weighs 6.53 pounds and the second object weighs 10.1 pounds. How many more pounds can the container hold? Wrote your answer as a decimal
Answers
The maximum weight of objects which the container can hold as required is; 1.12 pounds.
What is the maximum weight of objects which the container can hold?As evident in the task content;
The maximum which the container can is able to hold is; 17.75 pounds.
However, there are two objects in the can in which case one weighs 6.53 pounds and the other weighs 10.1 pounds.
On this note, the total weight which the can can hold more is given as;
= 17.75 - 6.53 - 10.1
= 1.12 pounds.
Ultimately, the maximum weight which the container can hold more is; 1.12 pound.
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Seniors and juniors are randomly surveyed to see if they are attending the championship football game. The results are shown in the table.
D.
Answers
Let's review the information given to us to answer the question correctly this way:
Juniors Seniors Totals
Yes 28 97 125
No 56 19 75
Totals 84 116 200
2. Find the probability of each of the events.
Let's recall that the formula of probability is:
P = Number of favorable outcomes/Total number of possible outcomes
A. P (a junior who did not attend prom)
P = Juniors who did not attend prom/Total number of students surveyed
P = 56/200
P = 7/25 (Diving by 8 numerator and denominator)
B. P (did not attend prom | senior)
P = Seniors who did not attend prom/Total number of seniors surveyed
P = 19/116
C. P (junior | attended prom)
P = Juniors who attend prom/Total number of students attended prom
P = 28/125
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PLSSS help!!!!!!!!!!!!!
Answers
Answer:
y = 70°x = 40°
Step-by-step explanation:
first of all, from the drawing, we understand that it is an isosceles triangle, 110 is an adjacent angle, we find the internal angle180 - 110 = 70°
the other angle at the base (y) is therefore congruent 70°, so we have the value of Y (70°)
we know that the sum of the internal angles of a triangle is 180°, we remove the two congruent angles and we have x
180 - 70 - 70 =
40°
What’s the denominator of x-3+5
Answers
The expression denominator is 1.
What is denominator?
In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.
Here the given is x-3+5
Now simplifying them
=> x-3+5 = x+2.
We know that the whole number or Integer always has 1 as Denominator. Then,
=> [tex]\frac{x-2}{1}[/tex]
Hence the denominator of the given is 1.
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If Jen babysits for 3 hours, she earns $12; and for 5 hours she earns $20.
Graph this linear relationship with x =#hours, and y = dollars earned.
How much does she earn per hour?
Answers
Answer:
To graph this linear relationship, we can plot two points on a coordinate plane: (3,12) and (5,20). These points represent the number of hours Jen babysits (x-coordinate) and the amount of money she earns (y-coordinate).
We can connect these two points with a line to form a linear equation that represents the relationship between the number of hours babysat and the money earned.
The slope of this line can be found using the formula: (change in y) / (change in x) = (20-12) / (5-3) = 8/2 = 4
Therefore, Jen earns $4 per hour by babysitting.
It is important to note that this is a linear relationship, and the earnings are proportional to the number of hours babysat. This means that for any number of hours babysat, the earnings can be found by multiplying that number by $4.
Step-by-step explanation:
Answer: For every hour she babysits, she earns $4. ✅
Step-by-step explanation:
To graph the linear relationship, we can start by plotting two points: (3,12) and (5,20).
This represents that for 3 hours of babysitting, Jen earns $12, and for 5 hours of babysitting, she earns $20.
We can then use these points to find the slope of the line, which is the rate at which her earnings change as the number of hours increases.
The slope can be found by using the formula: (change in y) / (change in x) = (20 - 12) / (5 - 3) = 8/2 = 4
This means that for every hour she babysits, she earns $4.
So, the equation of the line is : y = 4x + b
Where b is the y-intercept, which can be found by substituting one of the points into the equation.
For example, by substituting (3,12) in the equation:
12 = 4(3) + b
b = 0
So, she earns per hour $4. ✅
Select the correct answer. A line t runs downward to the right through two parallel horizontal lines a and b, forming 8 angles numbered from 1 to 8. In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true? A. m∠1 = m∠7 B. m∠3 = m∠6 C. m∠5 + m∠8 = 90° D. m∠6 + m∠7 = 180°
Answers
Since in the diagram, transversal t cuts parallel lines a and b, an equation which is necessarily true include the following: B. m∠3 = m∠6.
What is the Alternate Interior Angles Theorem?In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the diagram representing (showing) the two parallel horizontal lines a and b, we can reasonably infer and logically conclude that angle 3 (m∠3) and angle 6 (m∠6) forms a pair of alternate interior angles because line a is parallel to line b and transversal (t) cuts parallel lines a and b.
Similarly, angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line a is parallel to line b.
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if s1 and s2 are subspaces of rn of the same dimension, then s1 = s2.
Answers
This statement is false. Two subspaces of R^n can have the same dimension but still be different.
Here are a few bullet points that elaborate on this:
A subspace is a subset of a vector space that is closed under addition and scalar multiplication.The dimension of a subspace is the number of vectors in a basis for the subspace.Two subspaces of R^n can have the same dimension if they have the same number of vectors in a basis, but the vectors themselves could be different.For example, the subspace of all multiples of the vector (1,0) and the subspace of all multiples of the vector (0,1) both have dimension 1, but they are different subspaces because they contain different sets of vectors.The subspace of all multiples of the vector (1,0) is the set of all vectors of the form (x,0) and the subspace of all multiples of the vector (0,1) is the set of all vectors of the form (0,y) and these two sets are different.Therefore, the statement "If s1 and s2 are subspaces of R^n of the same dimension, then s1 = s2" is not true in general.
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Solve: 2x-3 = 5(x + 6)
a. x=-3
b. x=-11
c. x=-9
d. x= 33/7
Answers
Answer: the answer is -11
Distribute the 5 into the parenthesis:
2x-3=5x+30
Add 3 to both sides:
2x=5x+30+3
2x=5x+33
Subtract 5x from both sides:
2x-5x=33
-3x=33
Divide both sides by -3:
-3x/-3=33/-3
x=-11
Check the answer by plugging in x=-11 into the equation to see if it is a true statement:
2(-11)-3=5(-11+6)
-22-3=5(-5)
-25=-25
Thus, x=-11 is correct
Robert is purchasing shirts for his weekend soccer team. The shirts he wants to buy are normally $12 each but are on sale for $9 off. His team has a total of 9 players. How much will he spend to buy the shirts?
Answers
Answer:
Robert will spend $27 on shirts for the team.
Step-by-step explanation:
Given InformationThe shirts typically retail for $12The shirts are now on sale for $9 off ($3 per shirt)There are 9 players on the teamCross-multiplyIf one shirt is now $3, then 9 shirts are $X.[tex]\frac{1 shirt}{9shirts} = \frac{3 dollars}{X dollars}[/tex]3 X 9 = $27.Therefore, Robert will spend $27 on shirts for the team.
Please let me know if this helped!!!
Given: AC ⊥ BD and DB bisects ∠ABC.
Prove: △ABD ~ △CBD.
Answers
By ASA (Angle side angle) theorem, triangle △ABD≅ triangle △CBD.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now
As BD is common for both triangles ABD and CBD.
and
∠ADB=∠CDB=90°
also as DB bisects ∠ABC
∠ABD=∠CBD
Hence,
By Angle Side Angle theorem, triangle △ABD≅ triangle △CBD
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A metalworker has a metal alloy that is 30% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 51% copper alloy?
Answers
Add or subtract the following polynomials, as indicated.
(−6x3+3−4x)−(14−8x+9x3)
Answers
The result of the addition of the polynomials is -15x^3 + 4x - 11.
How do we operate on the polynomials?We have to note that the polynomials have to do with those kind of functions in which the power of x in the equation may range form 1 to infinity. We have in the question that the expression can be written as;
(−6x^3 + 3 −4x) − (14 − 8x + 9x^3)
Then we have;
−6x^3 + 3 −4x - 14 + 8x - 9x^3
We can now collect the like terms as follows;
−6x^3 - 9x^3 −4x + 8x + 3 - 14
-15x^3 + 4x - 11
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Help pls its due in 30 minutes
Answers
#19
how do i solve this..
Answers
Answer:
1. 26
2. x = 1.5
Step-by-step explanation:
1. C(0.7) means to plug in 0.7 into the equation
here, C(x) = 30x + 5. replace x with 0.7 to get
C(0.7) = 30*0.7 + 5= 26
2. C(x) = 30x + 5 = 50
30x+5 = 50
subtract 5 from both sides to isolate x and its coefficient
30x = 45
divide both sides by 30 to find x
x = 1.5
Write a ratio to represent the scale used in the drawing.
Answers
The ratio of these two figures would be for every 1cm in image A, in image B there are 2cm. So the ratio would be 1:2
What is ratio?The ratio is a mathematical term that refers to the quantified relationship between two magnitudes that reflects a proportion, that is, the ratio is the way of representing the proportion between two magnitudes. In this case, the ratio refers to the length of each side of these triangles and their relationship to each other.
According to the above, the ratio could be 1:2 because the larger triangle has lengths that are twice the lengths of the sides of the smaller triangle. For example, the left side of the small triangle is 6 cm, while the left side of the large triangle is 12 cm.
It's a proportionality relationship twice as big. Therefore, the ratio would be 1:2.
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What is the sum of a °+c °?
Answers
Answer:
300 degrees.
Step-by-step explanation:
a = 180 degrees
c = 180 - 60 = 120 degrees
a°+c°+60°=360°
We know this because the sum of all three angles form a circle, which has a measure of 360.°
Now, let’s solve for a°+c°
Subtract 60° from both sides.
a°+c°=360-60
a°+c°=300
We subtracted 60 from 360° because we want to take a “piece” of the angle away to find out the sum of a°+c.° It’s like taking away a sector (section of the area) away from a circle.
Solve for x
I need 20 characters so I’m just typing this
Answers
Answer:
x = 4
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation to find the value of x based on this information:
6x + 6 + 17x + 2 = 100
Add like terms.23x + 8 = 100
Subtract 8 from both sides23x = 92
Divide both sides by 23x = 4
The bill for dinner was $41.76 . You left $8.24 for the tip. What percentage of the original bill was the tip? Round your answer to the nearest whole percent.
Answers
Answer: 20%
Step-by-step explanation:
Im SOO sorry if i got it wrong but you make a porportion, it would look like this. 8.24/41.76 = x/100, were assuming x is the percent, we then do cross multiplication which would then look like. 41.76x=824. After this we want to seperate the variable so divide 41.76 on both sides.
Tell whether a triangle can have the given angle measures.
115.1°, 47.5°, 93°
Answers
Answer:
Step-by-step explanation:
no, it cannot be a triangle
all triangles add up to 180º
115.1+47.5+93= 255.6
255.6 doesn't equal 180, so no its not a triangle
What is the area?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
1247/90 km² or 13 77/90 km²---------------------------
Given is the parallelogram.
Area of a parallelogram:
A = bhSubstitute the values and find the area:
A = 3 2/9 × 4 3/10 = Convert to fraction 29/9 × 43/10 = Multiply 29*43/90 = 1247/90 = Fraction 13 77/90 Mixed numberPlease help!
Graph y = 3x + 7
Answers
Answer:
in attached image :)
Please asap help me with this and thanks a lot Here is the question Picture will be inserted below The points on the number line are opposite numbers. The tick marks represent
intervals of 1 unit.
Label 0 at the correct spot on the number line.
Label the point plotted to the right of 0.
Label the point plotted to the left of 0.
Answers
Answer:
0 on the left side
Step-by-step explanation:
brainly has it out for me
Answers
Answer:
answer is 341
pls mark me as brainlliest
Which system of equations cannot be readily solved by the substitution method?
Answers
Answer: C
Step-by-step explanation:
4x - 12y = -10
-3x + 10y = 10
In order to solve this using substitution method, you will have to
divide one equation by the coefficient of x or y
e.g. divide 4x-12y = -10 by 4 to get x-3y = -5/2
x = 3y-5/2
and substitute x for 3y-5/2 which is pretty complicated.
Not sure what you mean by "readily solved", though.
Does someone know the average rate of change of this equation????
Answers
The average rate of change of the equation is 7
How to determine average rate of change of a quadratic equation?
The average rate of change of an equation can be determine by using the formula below:
average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]
From the given information, f(x) = 2x²-5x-2 and x₁ = 2, x₂ = 4
average rate of change = ([2(4)²-5(4)-2] - ([2(2)²-5(2)-2]) / (4- 2)
average rate of change = (10-(-4)) / 2
average rate of change = 14/2
average rate of change = 7
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can you graph the line with the slope -2 that passes through the point (3,-1) ?
Answers
Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.
The definition of slope.A line's slope determines how steep it is. A gradient-based equation is referred to as having a gradient overflow. By dividing average horizontal difference (run) between 2 places by both the vertically change (rise) between those same two points, the slope is determined. The equation of a horizontal path is expressed as y = mx + b and is known as the hill form of an equation. The y-intercept of the line is located where the grade is m, b = b, and (0, b). In the case of the equations y = 3x - 7, the slope y y-intercept are (0, 7). The y-intercept is situated where the slope of the line is m and b is
Here,
Given :
that m=2, the point (x1,y1)=(— 3, —1)
Equation for the necessary straight line:
=>(y — y1)=m(x — x1)
=>y+1=2(x+3)
X=0 on the y-axis indicates that nothing is being measured.
=>y=2+3
The y-intercept value is 5.
Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.
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8. Bonnie worked for 40 hours each week for 30
weeks. How many hours did she work
altogether? /
Answers
Answer:
1,200 40×30=. h. h= hours
Which of the following expense items should be included when determining whether a taxpayer who wishes to file as head of household paid more than half the cost of keeping up their home?
Education.
Medical expenses.
Real estate taxes.
Rental value of the home owned by the taxpayer.
Answers
Answer:
The Answer is (D)
Step-by-step explanation:
When determining when a taxpayer wants to file as head, then the answer will become clearer when checking for their position on the house
Use the drawing tool(s) to form the correct answer on the provided number line.
What is the solution set of this compound inequality?
1≤|x+3|≤4
Answers
The solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.
What is compound inequality?An inequality that combines two other inequalities by using either "and" or "or" is referred to as a compound inequality. In certain cases, "and" won't be stated explicitly, but it is still understood. For instance, 1 x 3 simply means "x > 1 and x 3". However, a compound inequality using "or" is always explained in detail using "or." Compound inequalities may be divided into two categories: conjunction and disjunction.
The given compound inequality is:
1 ≤ | x + 3 | ≤ 4
As the equation contains a mod sign, we can write the inequality as follows:
1 ≤ x + 3 ≤ 4, and
1 ≤ - x - 3 ≤ 4
Simplify the first equation:
1 ≤ x + 3 ≤ 4
Subtract 3 from both the sides of the equation:
1 - 3 ≤ x + 3 - 3 ≤ 4 -3
-2 ≤ x ≤ 1
Simplify the second equation:
1 ≤ - x - 3 ≤ 4
Add 3 on both sides of the equation:
1 + 3 ≤ - x - 3 + 3≤ 4 + 3
4 ≤ -x ≤ 7
Convert the negative term to positive:
-4 ≥ x ≥ -7
Hence, the solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.
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