The measure of each angle is 23 degrees, 67 degrees, and 90 degrees.
What is Acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle.
What is a Right triangle ?Right triangle is also known as right angled triangle. If a triangle has atleast one 90° angle then the triangle is said to be a right angled triangle. A right angle triangle always follows the Pythagoras theorem.
Now, According to statement given :
Let smaller acute angle = x,
and measure of larger acute angle = 3x-2
Since, it is right triangle the acute angles must be complementary
x + (3x-2) = 90
4x - 2 = 90
4x = 92
x = 23
i.e. smaller acute angle is 23
now second angle = 3x-2 = 3(23) - 2 = 67
and third angle is 90 , as this is a right angled triangle.
Thus, The measurement of each angle is 23 degrees, 67 degrees, and 90 degrees.
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Which equation is neither perpendicular nor parallel to line k?
According to the question, the two equations are neither parallel nor perpendicular is 4x + 2y = 10 and x+2y =6.
When the slope of the two lines are same, then the lines are parallel to each other. And when the multiplication of the two slope is negative one, then the lines are perpendicular with each other.
Now, the slope of the first equation that is 4x + 2y = 10
slope([tex]m_{1}[/tex]) = (10 - 4x)/2 = 5
Comparing the above equation with y = mx + c
Similarly,
slope([tex]m_{2}[/tex]) = (6 - x)/2 = 3
Therefore, the calculated slopes are neither parallel nor perpendicular.
What is slope?
The slope of the line is the ratio of the horizontal axis and the vertical axis. And to calculate the slope of the lines which are parallel or perpendicular by comparing it with the standard equation. When the slopes of two or more equations are same then the lines are parallel. When the multiplication of the slope between the lines is negative one, then it is perpendicular.
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Isaac deposits $2,500 into an account that pays 4.75% interest
compounding continuously. How long will it take to double his
initial investment? Show all work for full credit and round your
answer to two decimal places.
Answer:0.02
Step-by-step explanation:
The key words in this problem is that you are compounding continuously, so that would be a equals p e to the r t power to show you that formula, and so when it says you have 2500 in the account e to the .4 excuse me, 0.0475 t Power is equal to, it says, doubling the investment, and so you just have to think about your doubling the investment you're going to take 2500 times to do it. The first thing i would do, then, is to divide the 2500 over which actually cancels out this 2500 point so you're. Looking at e to the .0475 t, power is equal to 2 right, 4.75 percent, so to solve for t want to natural log, both sides- i forgot my t in there so to solve for t natural log of 2 divided by 0475, so it takes about 14.593 Years or, however, you're supposed around it says: 2 decimals soul be 14.59 years all right, so on number 2, this time they give you the formula for ph is equal to negative log of the hydrogen plus atoms ions. So, basically, what they want you to do is take 1.7 plugging them, for the ph is equal to negative log of let's just call it h, and we have to solve for h now. So the first thing you want to do is to divide that negative 1.7. Over to undo log base 10, this would take 10 to that power and that's your answer not sure exactly where they want you to round says the nearest one hundredth would be .02, so the h plus items is equal to 0.02.
Identify the hypothesis and conclusion of conditional statement.
If you are a teenager, then you are at least 13 years old.
The hypothesis is the phrase following the word if = "you are a teenager"
The conclusion is the phrase following the word then = "you are at least 13 years old."
What is hypothesis?A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.
Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).
The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.
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Cars enter a car wash according to a poisson process at a mean rate of 2 cars per half an hour. what is the probability that, in an hour, at least 4 cars will enter the car wash?
The probability that, in an hour, at least 4 cars will enter the car wash is 0.94.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
Cars enter a car wash according to a Poisson process at a mean rate of 2 cars per half an hour.
Here the value of λ is:
λ = 2 cars/half an hour
λ = 4 cars/hour
The probability that, in an hour, at least 4 cars will enter the car wash:
P(x = 4) = 4⁴e⁻⁴/5
After solving:
P(x = 5) = 0.937 ≈ 0.94
Thus, the probability that, in an hour, at least 4 cars will enter the car wash is 0.94.
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1. Estimate the average rate of change of y over the interval -10≤x≤-8. Show your work
below.
Answer:
average rate of change = 4
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 10, - 8 ] , then
f(b) = f(- 8) = 8 ← point on graph (- 8, 8 )
f(a) = f(- 10) = 0 ← point on the graph (- 10, 0 )
average rate of change = [tex]\frac{8-0}{-8-(-10)}[/tex] = [tex]\frac{8}{-8+10}[/tex] = [tex]\frac{8}{2}[/tex] = 4
A welder gets paid $12 per hour for the first 40 hours worked, and then $20 for each overtime
hour. The welder wants to make at least $600 a week. Which inequality can be used to find
the number of overtime hours, x, that the welder needs to work each week?
To find the number of overtime hours, x, that the welder needs to work each week can be found by the inequality 20x if x>40.
What is an inequality?
Inequality, A mathematical declaration expressing an order connection between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Let x be the number of overtime hours.
A welder gets paid $12 per hour for the first 40 hours worked
⇒ 12x if x≤40
A welder gets paid $20 per hour for each overtime.
⇒ 20x if x>40
Now the welder wants to make $600 per hour,
So, the inequality used for finding the value of x is -
⇒ 20x if x>40
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Find the least common multiple of each pair of polynomials.
5 y² - 80 and y + 4
The least common multiple of each pair of the polynomial (5y² - 80) and
(y + 4) is equal to 5(y-4)(y+4).
As given in the question,
Given pair of the polynomial is (5y² - 80) and (y + 4)
Simplify the given polynomial using (a² -b²) = (a-b)(a +b)
(5y² - 80) = 5(y² -16)
⇒(5y² - 80) = 5(y² - 4²)
⇒(5y² - 80) = 5(y -4)(y + 4)
And (y + 4) = (1) (y+4)
Least common multiple = 5(y-4)(y+ 4)
Therefore, the least common multiple of the given pair of the polynomial is 5(y -4)(y+ 4).
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20x+25x=180 finding the number for X WITH STEPS pls
Answer:
x=4
Step-by-step explanation:
20x+25x=180
45x = 180
x = 4
Recognize the Error Miguel found the quotient
5
.
78
×
10
5
0
.
000002
as 0.289. Which of the following correctly identifies his mistake?
Multiple choice question.
cross out
A)
Miguel multiplied
5
.
78
×
10
5
by 0.000002, when he should have divided.
cross out
B)
Miguel found 5.78 ÷ 0.00002 and then left his answer as is. He needed to also find the correct power of 10.
cross out
C)
Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10. The numerator is
10
5
and the denominator is
10
−
6
.
When dividing, the resulting power is
10
11
.
cross out
D)
Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10. The numerator is
10
5
and the denominator is
10
−
5
.
When dividing, the resulting power is
10
10
.
The option that identifies the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.
How to calculate the values?It should be noted that the number given is illustrated as:
5.78 × 10^5× 0.000002
= 2.89 × 10^5
Therefore, the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.
In conclusion, the correct option is D
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Please find the slope of line ST
The slope of line ST is 4
How to determine the slope of the line
The formula for determining the slope of a line is expressed as;
Slope = y2 - y1/x2 - x1
It is mostly represented with 'm' and it also known as the gradient of a line.
From the points given , we have that;
y2 = -4y1 = 0x2 = -1x1 = 0Substitute the values into the formula
Slope, m = -4 - 0/ -1 - 0
Slope, m = -4/ -1
Slope, m = 4
Thus, the slope of line ST is 4
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Which equation does NOT represent a direct variation? A. y-3 x=0 B. y+2= (1/2)x C. y/x = 2/3 D. y = x/17
A. y-3 x=0 and B. y+2= (1/2)x are the equation that does not represent a direct variation.
Direct variation is a sort of proportionality in which one quantity fluctuates directly in response to a change in another number.
it is denoted as y = kx (where is the constant)
it is not directly varied if y has two x solution.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Look at the picture uploaded.
The lengths of each line segment are listed below:
AB ≈ 5.385 CD ≈ 5.099 EF ≈ 6.083How long is each line segment?
In this problem we find three line segments, of which the coordinates of all ends are known, and we must determine the lengths of each segment, task to be done by applying Pythagorean theorem.
If we know that A(x, y) = (0, 2), B(x, y) = (5, 4), C(x, y) = (- 6, 0), D(x, y) = (- 7, 5), E(x, y) = (- 5, - 8), F(x, y) = (- 6, - 2), then the length of each segment is:
AB = √[(5 - 0)² + (4 - 2)²]
AB = √(5² + 2²)
AB = √(25 + 4)
AB = √29
AB ≈ 5.385
CD = √[[- 7 - (- 6)]² + (5 - 0)²]
CD = √[(- 1)² + 5²]
CD = √(1 + 25)
CD = √26
CD ≈ 5.099
EF = √[[- 6 - (- 5)]² + [- 2 - (- 8)]²]
EF = √[(- 1)² + 6²]
EF = √(1 + 36)
EF = √37
EF ≈ 6.083
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Find the percent of the given number. 65 % of 360
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 65 % of 360 is 234.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 65 % of 360
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
65 % of 360 = 65/100 of 360
65/100 × 360 = 234
Therefore, the percent of the given number 65 % of 360 is 234.
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What is the value of z in the solution of the system? y = -2x + 10 , -x + y - 2z=-2 , 3x - 2y + 4z = 7.
For the following system of equations: y = -2x + 10 , -x + y - 2z = -2 , and 3x - 2y + 4z = 7, the value of z in the solution is 3/2.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using the substitution method, given three equation of three variables,
y = -2x + 10 (equation 1)
-x + y - 2z = -2 (equation 2)
3x - 2y + 4z = 7 (equation 3)
Using equation 1, substitute the value of y to equation 2 and 3.
-x + y - 2z = -2 (equation 2)
-x + (-2x + 10) - 2z = -2
-3x - 2z = -12
3x + 2z = 12 (equation 4)
3x - 2y + 4z = 7 (equation 3)
3x -2(-2x + 10) + 4z = 7
7x + 4z = 27 (equation 5)
Rewrite equation 4 as an equation of x in terms of z.
3x + 2z = 12 (equation 4)
3x = 12 - 2z
x = 4 - 2/3z (equation 4)
Substitute the new equation 4 to equation 5 and solve for z.
7x + 4z = 27 (equation 5)
7(4 - 2/3z) + 4z = 27
28 - 14/3z + 4z = 27
-2/3 z = -1
z = 3/2
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Why is there no horizontal-line test for functions?
This is due to the fact that each y-value has a single x-value. It is not a one-to-one function if the horizontal line crosses the graph more than once since there is more than one x-value for some y-values.
A horizontal line is not a function, so why not?
The horizontal line has one y value for every x, whereas a function cannot have two y values for the same x.
Do functions pass the horizontal line test?
It is possible to establish whether a function is surjective or bijective using variations of the horizontal line test. If and only if the graph of the function f meets any horizontal line at least once, then the function is surjective (i.e., onto).Learn more about horizontal-line test
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what 10982 to the nearest hunder
Dominic is working two summer jobs, making $10 per hour babysitting and making $6 per hour walking dogs. In a given week, he can work no more than 16 total hours and must earn at least $120. If x represents the number of hours babysitting and y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities for this problem is given by:
x + y ≤ 16.10x + 6y ≥ 120.The graphical solution is given at the end of the answer, and one possible solution is 12 hours babysitting and 3 hours walking the dog.
What is a system of inequalities?A system of equations is when two or more variables are related, and inequalities are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of hours babysitting.Variably y: number of hours walking dogs.He can work no more than 16 total hours, hence:
x + y ≤ 16.
He must earn at least $120, hence, considering the earnings with each activity:
10x + 6y ≥ 120.
These two inequalities compose the system. The graphical solution is composed by points that:
Are to the left of line y = 16 - x.Are to the right of line -1.67x + 20.Above y = 0, as there are no negative times.The graphical solution is given by the region shaded in blue at the end of the answer.
One possible solution inside the region is:
(12,3).
Meaning that he can work 12 hours babysitting and 3 hours walking the dog.
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State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
The distance from point X to line q is the length of the segment perpendicular to line q from X .
The statement " The distance from point X to line q is the length of the segment perpendicular to line q from X" is true
Given,
The statement "The distance from point X to line q is the length of the segment perpendicular to line q from X "
From the figure we can say that the distance from point X to line q is the length of the segment perpendicular to line q from X.
So the given statement is true
Hence, the statement " The distance from point X to line q is the length of the segment perpendicular to line q from X" is true
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
The distance from point X to line q is the length of the segment perpendicular to line q from X .
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ONLY, ONLY, ONLY, ONLY, ONLY, ONLY, ONLY, ONLY, ONLY, answer if you are
% because if it turns out your answer is , . You have been warned. sorry if I came off as rude or something, I have had an AWFUL day and I feel so stressed and burnt- out but I still have work to do
- ᘔᗩY
Answer:
A or -0.02. I know how you feel man
Step-by-step explanation:
-5/25 = -2/10
-2/10 = -0.2
...
-0.02 > -0.2
-0.25 < -0.2
-0.2 = -0.2
-0.268 < -0.2
Answer:
I say A, all the way!
Step-by-step explanation:
All my work is provided in the screenshot that is attached! :)
Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
Find the distance between the pair of points. Round to the nearest tenth.
J(7,11) and K(-1,5)
The distance between the pair of points J( 7, 11) and K (-1, 5) is equal to 10.
As given in the question,
Given pair of points are J( 7, 11) and K (-1, 5)
Let J( x₁ ,y₁) = J( 7, 11) and K (x₂, y₂) = K (-1, 5)
Distance between pair of points ( x₁ ,y₁) , (x₂, y₂) is equal to
[tex]= \sqrt{(y_{2}-y_{1})^{2}+ (x_{2}-x_{1})^{2} } \\\\=\sqrt{(5-11)^{2}+ (-1-7)^{2} }\\\\= \sqrt{36 +64}\\ \\=\sqrt{100}[/tex]
= 10 units
Therefore, the distance between the pair of points J( 7, 11) and K (-1, 5) is equal to 10.
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Find following measure.
m RT
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.
The measure of m RT is 126.
What is meant by inscribed arc?The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
An angle's measure exists equivalent to the intercepted arc's measure divided by two when it is surrounded by a circle.
m RT = 2(m ∠S)
m RT = 2(m ∠S) = 126
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Is 1/10 greater than 0.009
Answer:
yes
Step-by-step explanation:
1/10= 0.1 0.009= something less
Answer:
Yes
Step-by-step explanation:
1/10 (or 1 divided by 10) is .01
The blueprint for Zahra’s new office measures `4` cm long and `2` cm wide.
The scale for the blueprint is `6` cm to `15` ft.
What is the actual area of her office?
Answer:
60 square feet
Step-by-step explanation:
In the blue print, 6 cm represents 15 ft
So 1 cm represents 15/6 feet = 5/2 feet
4 cm long represents 4 x 5/2 = 10'
2 cm wide represents 2 x 5/2 = 5'
Area = 10' x 5' = 60 square feet
Answer:
60 square feet
Step-by-step explanation:
In the blue print, 6 cm represents 15 ft
So 1 cm represents 15/6 feet = 5/2 feet
4 cm long represents 4 x 5/2 = 10'
2 cm wide represents 2 x 5/2 = 5'
Area = 10' x 5' = 60 square feet
2/3 + r =-4/9
What’s the value of r
Answer:
-10/9
Step-by-step explanation:
I made it so that 2/3 a -4/9 had the same denominator which turned 2/3 into 6/9
then I solved normally
Find the equation of the axis of symmetry of the following parabola algebraically.
y=2x^2-24x+86y
The equation of the axis of symmetry is x = 6
How to find the equation of the axis of symmetry?The equation of the parabola is given as:
y = 2x^2 - 24x + 86
Differentiate the equation of the parabola
So, we have
y' = 4x - 24
Set the differentiated equation of the parabola to 0
So, we have
4x - 24 = 0
Add 24 to both sides of the differentiated equation of the parabola
4x = 24
Divide both sides of the differentiated equation of the parabola by 4
x = 6
This represents the the axis of symmetry
Hence, the equation of the axis of symmetry is x = 6
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To create their special blend of coffee, the owners of The Café, use 8 pounds of dark beans
that sell for $9.20 a pound and 12 pounds of light beans that sell for $5.50 a pound. Find the price
per pound of this special blend.
Using algebraic expressions, The price per pound of this special blend will be $64.8
Let proportion of 8 pounds = x
8x + (1 - x)9.20 = 1 × 5.50
8x - 9.20x + 9.20 = 5.50
-1.20x+9.20 = 5.50
Lets get rid of the decimals for now and multiply everything by 100
= -120x+920 = 550
x = 3.08
So the proportion of the $5.54 is 1 - 37/12
Determine the weight proportion of each bean type
Price = $64.8
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Which expressions are equivalent to -6(b+2)+8−6(b+2)+8minus, 6, left parenthesis, b, plus, 2, right parenthesis, plus, 8 ?
The equivalent expression of -6(b + 2) + 8 is -6b - 4
How to determine the equivalent expression?The expression is given as
-6(b + 2) + 8
Expand
-6b - 12 + 8
Evaluate the like terms
-6b - 4
Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4
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What rationale could Judy have provided
Using the condition needed for a graph to represent a function, it is found that:
a) It can be noticed that these graphs do not represent functions.
b) The rationale is that they have vertically aligned points.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we have that each graph has vertically aligned points, that is, they have values of x mapped to multiply values of y, hence they do not represent functions.
Examples of the vertically aligned points are given by:
In graph D, the values of x inside the circle are mapped to two values of y.In graph K, values of x > 0 are also mapped to two values of y.In graph O, in the vertical line, the coordinate of x is mapped to infinite values of y.More can be learned about graphs and functions at https://brainly.com/question/12463448
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A fiber optic cable company is installing cable along a road 6 1/2 miles long. The crew takes a day to install each 1/4 mile of cable. How many days will the installation take?
Answer:
26 days
Step-by-step explanation:
you can use the formula 13/2=1/4d to find how many days the installation will take
If you divide both sides of the formula by 1/4 you will get 26
