Mathematics High School
Answers
Answer 1
The measure of all the angles of triangle are 27.5° , 110° and 42.5°.
The angle sum property states that the sum of angles in a triangle is 180°. That is if the angles of a triangle are A,B and C then
angle A + angle B + angle C = 180° (1)
According to the question,
Let the smallest angle be x°
Then the second angle will be 4 times the other on which is 4x°
And the third angle will be 15° greater than the smallest one which will be = 15° + x°
Now putting all the required values in equation (1) we get,
x° + (4x°) + (15° + x°) = 180°
6x° = 180° - 15°
x° = 165°/6
x° = 27.5°
Thus the angles will be,
Smaller angle = x° = 27.5°
Other angle = 4x° = 4*27.5° = 110°
Third angle = 15° + x° = 15° + 27.5° = 42.5°
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Related Questions
When testing the differences between means, the null hypothesis suggests that any observed difference is due to?
Answers
The null hypothesis suggests that any observed difference is due to random error.
What is a null hypothesis?
This refers to the type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
While the alternative hypothesis does proposes that there is a difference, the null hypothesis does proposes that there is no difference between the characteristics.
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Pls help again for this as well algebraic proofs
Answers
Answer:
answer =0
Step-by-step explanation:
2(x+2) = -4(x-1)
2x+4 = -4x+4
4x+2x = 4-4
6x = 0
x = 0
Find (cd)(x).
c(x) = 5x + 6
d(x) = 3x
Write your answer as a polynomial in simplest form.
(cod)(x)
Answers
Answer: 15x+6
Step-by-step explanation:
c(x) = 5x + 6
d(x) = 3x
(cod)(x)=
c(d(x))=
5(3x)+6=15x+6
It cost Blake $8.00 to send 80 text messages. How much would it cost to send
130 text messages?
Answers
Answer:
13
Step-by-step explanation:
$. : text message
8. : 80
= ? : 130
? = ( 8 * 130) / 80
? = 13
Answer:
13
Step-by-step explanation:
$. : text message
8. : 80
= ? : 130
? = ( 8 * 130) / 80
? = 13
The graph shows the height of a
roller coaster in terms of its distance away from the
starting point. Describe and interpret the end behavior
in the context of the situation.
Answers
The end behavior of the function means that when the roller coaster gets farther from it's starting point, it's height approaches 0.
What is the end behavior of a function?
The end behavior of a function is the output of the function when it moves to infinity, either to the left and to the right.
For this problem, the function is defined only towards negative infinity, when it moves toward zero with waves of decaying amplitude, but we can state that:
[tex]\lim_{x \rightarrow \infty} h(x) = 0[/tex]
Distances toward infinity means that the roller coaster gets farther from it's starting point, and the result of the limit means that it's height approaches 0.
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Which ordered pairs make the open sentence true?
3x+y<14
Select all the correct answers.
(3, 6)
left parenthesis 3 comma 6 right parenthesis
(7, −7)
left parenthesis 7 comma negative 7 right parenthesis
(6, 0)
left parenthesis 6 comma 0 right parenthesis
(−1, 6)
left parenthesis negative 1 comma 6 right parenthesis
(4, −1)
Answers
The ordered pairs which make the open sentence true are:
(-1, 6).(4, -1).
What is an inequality?
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).
For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.
When ordered pairs = (3, 6), we have:
3x + y < 14
3(3) + 6 < 14
9 + 6 < 14
15 < 14 (False).
When ordered pairs = (7, -7), we have:
3x + y < 14
3(7) + (-7) < 14
21 - 7 < 14
14 < 14 (False).
When ordered pairs = (6, 0), we have:
3x + y < 14
3(6) + 0 < 14
18 - 0 < 14
18 < 14 (False).
When ordered pairs = (-1, 6), we have:
3x + y < 14
3(-1) + 6 < 14
-3 + 6 < 14
3 < 14 (True).
When ordered pairs = (4, -1), we have:
3x + y < 14
3(4) + (-1) < 14
12 - 1 < 14
11 < 14 (True).
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When an integer is subtracted from 8 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.
Answers
The value of the lesser integer is 7
What are algebraic expressions
Algebraic expressions are expressions consisting of both variables and constants and are also made up of mathematical operations such as addition, subtraction, division, multiplication, etc.
From the information given, we have;
Let the integers be (x) and ( x + 2)
8(x + 2) - (x)= 23
Expand the bracket
8x + 16 - x = 23
collect like terms
8x - x = 23 - 16
Add/subtract like terms
7x = 7
Make 'x' the subject
x = 7/7
The value for the lease integer = x
Substitute the value of x
7
Thus, the value of the lesser integer is 7
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what is the multiplicative inverse of x (if x equals 0)
Answers
The multiplicative inverse of x is 1/x
Multiplicative inverse
A multiplicative inverse or reciprocal for a number x, denoted by 1/x. It is a number which when multiplied by x yields the multiplicative identity, 1.
According to the question we are to find the multiplicative inverse of x
Let the multiplicative inverse be b
b * x = 1
Divide both sides by b
bx/x = a/x
b = 1/x
Hence the multiplicative inverse of x is 1/x
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Graph this line:
y - 3 = -(x + 9)
Click to select points on the graph.
Answers
Answer:
See picture below
Step-by-step explanation:
The box plot represents the distribution of the number of points scored by a cross country team at 12 meets. If possible, find the median. If not possible, explain why not.
Answers
The median is the value equivalent to the vertical line as shown. Hence the median point is 34
What is a median?
The median is defined as the value at the middle after rearrangement.
From the given boxplot, we have the following
The minimum value is equivalent to the lower position of the whisker = 22
The maximum value is equivalent to the upper position of the whisker = 42
The median is the value vertical line in between the box = 34
The lower quartile (Q1) = starting point of the box = 33
Upper quartile (Q3) = end point of the box = 38
For the boxplot, the median is the value equivalent to the vertical line as shown. Hence the median point is 34
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Which property of equality matches the statement AB = BC and BC = CD, the AB = CD?
Answers
Answer:transversive property
Step-by-step explanation:
what are solutions to the inequality -x-2y>3
Answers
The coordinates (-1, -2), (-2, -1), and (2, -4) are solutions to the given inequality.
How to find the solutions to an Inequality?
We are given the Inequality as;
-x - 2y > 3
Now, for us to find the points that are the solutions to the given inequality, substitute the given points into -x - 2y, and anyone that gives a result greater than 3 is a solution to the inequality
For the coordinate (-1, -2), substitute x = -1, and y = -2 into -x - 2y
-(-1) - 2(-2)
= 1 + 4
= 5
Since 5 > 3, then (-1, -2) is a solution to the inequality
For the coordinate (1, -2)
Substitute x = 1, and y = -2 into -x - 2y
-(1) - 2(-2)
= -1 + 4
= 3
Since the result is not greater than 3, then (1, -2) is not a solution to the inequality.
For the coordinate (-2, -1);
Substitute x = -2, and y = -1 into -x - 2y
-(-2) - 2(-1)
= 2 + 2
= 4
Since 4 > 3, then we say that (-2, -1) is a solution to the inequality
For the coordinate (2, -4);
Substitute x = 2, and y = -4 into -x - 2y
-(2) - 2(-4)
= -2 + 8
= 6
Since 6 > 3, then we say that (2, -4) is a solution to the inequality
Therefore, (-1, -2), (-2, -1), and (2, -4) are solutions to the inequality
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When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates that?
Answers
When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.
The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.
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Please help me. Will give brainliest.
Answers
Based on the given formula of compounding interest, and the amount that Javier invested, the value of n in this situation is 2.
What is the value of n?
In the compound interest formula given, the parts of the formula are shown to be:
n = number of times the interest compounds per year
p = principal amount
r = interest rate
t = number of years
We are told that the investment compounds every six months which means in a year, the number of times compounded is:
= 12 months in year / 6 months
= 2 times
In conclusion, n is 2.
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Write the possible range of the measurement: 220 km ± 5%.
Answers
5% of 25 km is:
0.05*25 = 1.25 km
25 - 1.25 = 23.75
25 + 1.25 = 26.25
The possible range is (23.75, 26.25). Hope it helps
Irrational numbers, like 0.0123456...., can be written as a fraction.
True; all decimals can be written as a fraction
False; any decimal that does not terminate or repeat cannot be written as a fraction
Answers
Fase; any decimal that does not terminate or repeat cannot be written as a fraction
False; any decimal that does not terminate or repeat cannot be written as a fraction.
Irrational numbers are a type of real number that cannot be expressed exactly as a fraction of two integers. Their decimal expansions neither terminate nor repeat in a predictable pattern. Classic examples of irrational numbers include the square root of 2 (√2) and the mathematical constant π (pi). While rational numbers can be represented as fractions, irrational numbers are fundamentally different, and their decimal representations go on forever without a repeating pattern.
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Ralph Chase plans to sell a piece of property for $155000. He
wants the money to be paid off in two ways - a short-term note at 10% interest and a long-term note at 8% interest. Find the amountof each note if the total annual interest paid is $14100.
Answers
Ralph chase invested $85000 at an interest of 10% and $70000 at an interest of 8%
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
Let a represent the amount invested at interest of 10% and b represent the amount invested at 8%, hence:
a + b = 155000 (1)
Also:
0.1a + 0.08b = 14100 (2)
From both equations:
a = 85000, b = 70000
Ralph chase invested $85000 at an interest of 10% and $70000 at an interest of 8%
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In your own words, why will rigid transformations always produce congruent figures? Could non-rigid transformations also produce congruent figures?
Answers
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
Dilation is a non rigid transformation and does not produce congruent figures.
What is a transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
Dilation is a non rigid transformation and does not produce congruent figures.
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Jenny has 1.5 times more tennis balls than Janis. Together they have 50 tennis balls. Jenny wrote this equation to model the number of tennis balls they have, where x represents the number of tennis balls that Janis has. How many tennis balls does each girl have?
x + 1.5x = 50
Answers
The number of tennis balls that Jenny and Janis have are 30 and 20 respectively.
How many tennis balls does Jenny and Janis have?
Given the equation that models the number of tennis balls Jenny and Janis have.
x + 1.5x = 50
We solve for the value of x
x + 1.5x = 50
2.5x = 50
x = 50/2.5
x = 20
Hence,
Janis's tennis balls = x = 20
Jenny's tennis balls = 1.5x = 1.5(20) = 30
Therefore, the number of tennis balls that Jenny and Janis have are 30 and 20 respectively.
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Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 56.
Answers
Using the hypergeometric distribution, there is a 0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.
What is the hypergeometric distribution formula?
The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.
For this problem, we want to take 6 numbers from a set of 56, hence the values of the parameters are:
N = 56, k = 6, n = 6.
The probability of selecting none of the correct six integers in a lottery is of P(X = 0), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,56,6,6) = \frac{C_{6,0}C_{50,6}}{C_{56,6}} = 0.4894[/tex]
0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.
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9 times1+9 times1\10+2 times 1\100+1 times1\1000
Answers
Answer:9.921
Step-by-step explanation:
9x1=9+9/10+2x1/100+1/1000=9.921
Simplify.
3 – (−2) + |−7|
I am dum dum
Answers
The simplified form of the expression as given in the task content is; 12.
What is the simplified form of the expression given in the task content?
The expression given in the task content can be simplified by means of PEMDAS guidelines as follows;
3 – (−2) + |−7|
= 3 +2 +7
= 12.
Hence the simplified form of the expression is 12.
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when x=-5 what does y= ?
when x=-1 y=?
when x= 3 y= ?
Answers
The value of y is x are -5, 1 and 3 are 3, -3 and -4 respectively.
What are piecewise functions?
A piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
From the given graph, we need to find the cooresponding y-values if the value of x are -5, 1 and 3
From the given graph, the value of y is x are -5, 1 and 3 are 3, -3 and -4 respectively.
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Equations & Inequalities Task Card # 9
The number of seventh graders in
choir is three times the number of
sixth graders. There are 72
seventh graders in the choir. Write
and solve an equation to find s, the
number of sixth graders that are in
the choir?
..
Answers
Answer:
72/3=S=24
Step-by-step explanation:
The question states that there are 3 time as many 7th graders as their are 6th graders in choir so to find S we would have to do the opposite equation which is division so we divide 72 by 3
Find the equation of a line passing through the given point and parallel to the given equation. Write you answer in slope-intercept form.
(-2,4) and y= -x + 3
Answers
The equation of a line passing through the given point and parallel to the given equation is y = -x + 2
Equation of a line
The equation of a line in slope-intercept form is expressed as y = mx + b
where
m is the slope
b is the intercept
The equation in point-slope form is expressed as y - y1 =m(x - x1)
Given
Slope = -1
Point = (-2, 4)
Substitute
y - 4 =-1(x - (-2))
y - 4 = -(x+2)
y - 4 = -x - 2
y = -x - 2+ 4
y = -x + 2
Hence the equation of a line passing through the given point and parallel to the given equation is y = -x + 2
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My question wouldn't go through for some reason so I've put the question on the picture
Answers
The measures of the angles are given as follows:
ABC = 46.2º.CBD = 35.8º.
What is the value of x?
Angle ABD is the sum of angles BCD and ABC, hence:
ABD = BCD + ABC.
We replace the measures to find the value of x, hence:
6x - 9 + 4x - 1 = 82.
10x - 10 = 82.
10x = 92.
x = 9.2.
What are the measures of the angles?
With x, we can find the measures of the angles, as follows:
ABC = 6(9.2) - 9 = 46.2º.CBD = 4(9.2) - 1 = 35.8º.
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I need answers to this question
Answers
Answer:
good luckkkkk...........
3x-2y=8
-2y=-3x+8
Y= (-3x+8)/2
write the number 0.9333 as a fraction
Answers
Answer:9333/10000
Step-by-step explanation:
0.9333
=
0.9333 × 10000
___________
1 × 10000
=
9333
10000
the answer is 9333/10000
Organizing Information and Activating Prior Knowledge Fill in the blanks to complete the chart
Answers
1) The equation of a line in slope intercept form is used when we know the slope and y-intercept.
2) The linear equation is in Point Slope form
What is the interpretation of equation of a line?
1) The equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
We use this equation form when we know the slope and y-intercept.
2) The equation of a line in Point Slope form is;
y - y1 = m(x - x1)
This is used when we know the slope and a point on the line.
Thus, we conclude that;
1) The equation of a line in slope intercept form is used when we know the slope and y-intercept.
2) The linear equation is in Point Slope form
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Estimate the solution to the system of equations. You can use the interactive graph below to find the solution. { y = − 2 x − 5 y = 2 x − 2 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−2x−5 y=2x−2 Choose 1 answer: Choose 1 answer: (Choice A) A x = − 3 4 , y = − 2 1 2 x=− 4 3 ,y=−2 2 1 x, equals, minus, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 2, start fraction, 1, divided by, 2, end fraction (Choice B) B x = − 1 3 4 , y = − 3 1 2 x=−1 4 3 ,y=−3 2 1 x, equals, minus, 1, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 3, start fraction, 1, divided by, 2, end fraction (Choice C) C x = − 3 4 , y = − 3 1 2 x=− 4 3 ,y=−3 2 1 x, equals, minus, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 3, start fraction, 1, divided by, 2, end fraction (Choice D) D x = − 1 3 4 , y = − 2 1 2 x=−1 4 3 ,y=−2 2 1 x, equals, minus, 1, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 2, start fraction, 1, divided by, 2, end fraction 1 1 2 2 3 3 4 4 5 5 6 6 - 2 - 2 - 3 - 3 - 4 - 4 - 5 - 5 - 6 - 6 1 1 2 2 3 3 4 4 5 5 6 6 - 2 - 2 - 3 - 3 - 4 - 4 - 5 - 5 - 6 - 6 y y x x Stuck
Answers
The solution to the system is (-3/4, -9/2)
What are linear equations?
Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?
A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y = -2x - 5
y = 2x - 2
Substitute y = 2x - 2 in y = -2x - 5
2x - 2= -2x - 5
Evaluate the like terms
4x = -3
Divide by 4
x = -3/4
Substitute x = -3/4 in y = 2x - 2
y = 2 * -3/4 - 2
This gives
y = -3/2 - 2
Evaluate
y = -9/2
Hence, the solution to the system is (-3/4, -9/2)
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