Need to study for finals need help on this problem on my study guide find the measure of each angle calculate the length of each side
Answer:
[tex]\begin{gathered} m\angle B\text{ = 28}\degree \\ AB\text{ = 9.75} \\ BC\text{ = 7.7} \end{gathered}[/tex]Explanation:
Here, we want to calculate the measure of each of the missing angles and sides
We have one missing angle and 2 missing sides
a) Let us get the angle at B
Mathematically, the sum of angles in a triangle is 180 degrees
Thus:
[tex]\begin{gathered} 90\text{ + 62 + B = 180} \\ B\text{ = 180-90-62} \\ B\text{ = 28}\degree \end{gathered}[/tex]b) Let us get the measure of AB
We can use the appropriate trigonometric ratio here
The side that measures 6 is an opposite to the angle B
Since AB is the hypotenuse (the side facing the right angle and the longest side of in the triangle), we use sine
Sine is the ratio of the opposite and the hypotenuse
Mathematically:
[tex]\begin{gathered} sin\text{ 38 = }\frac{6}{AB} \\ \\ AB\text{ =}\frac{6}{sin\text{ 38}} \\ \\ AB\text{ = 9.75} \end{gathered}[/tex]c) side BC
We can use tan to get this
Tan is the ratio of the opposite to the adjacent side
The opposite side here is the side AC, while the adjacent is BC
Thus, we have it that:
[tex]\begin{gathered} Tan\text{ 38 = }\frac{6}{BC} \\ \\ BC\text{ = }\frac{6}{Tan\text{ 38}} \\ \\ BC\text{ = 7.7} \end{gathered}[/tex]How much to the nearest penny will we have if he uses this investment? Round to the nearest cent if needed
Given:
Principal P (Initial amount) =$5100
Rate(R)= 2.75
Time(t) = 16 months = 16/12 ( In years)
We can proceed to calculate the interest using the formula below:
[tex]S\mathrm{}I=\frac{P\times R\times T}{100}[/tex][tex]=\frac{5100\times2.75\times\frac{16}{12}}{100}[/tex][tex]=\frac{5100\times2.75\times16}{100\times12}[/tex][tex]=\text{ \$187}[/tex]The amount he has for the investement = 5100 + 187 = $5287
What is the correct answer
In transversal lines, All angles are equal and parallel, so TV ║ WY are parallel lines .
What are transversal lines?
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. Different sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.A line that crosses other lines is known as a transversal. When transversals intersect parallel lines, such as the two railroad tracks, we often operate with them.∠TUX ≅ ∠UXY ( Alternate angle)
∠SUV ≅ ∠TUX ( Vertically angle)
∠UXY ≅ ∠SUV ( Interior angle )
TV ║ WY ( All angles are equal and parallel, so TV ║ WY
are parallel lines .
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Rewrite y = a (2)¹/3 in the form y = a(1+r) or y = a(1-r)'. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.yoThe rate is about %.This is a rate.
we have the equation
[tex]y=a(2)^{\frac{t}{3}}[/tex]Rewrite the given equation
[tex]\begin{gathered} y=a(2^{\frac{1}{3}})^t \\ y=a(1.26)^t \\ y=a(1+0.26)^t \end{gathered}[/tex]the base of the exponential function is b=1.26
1.26 > 1
that means
is an exponential growth function
1+r=1.26
r=1.26-1
r=0.26
therefore
The rate is about 26%This is a growth rate7.) A jug of egg nog sells for $5.12One jug holds(128 ounces. What is the unit priceper ounce?
To find the unit price per ounce, we just need to divide the total price by the total amount of egg nog(in ounces). The total price is $5.12 and the amount of egg nog is 128 ounces, therefore, the unit price per ounce is
[tex]\frac{5.12}{128}=0.04[/tex]$0.04.
What is the magnitude of -5 + 121?
Question:
Solution:
For a complex number z = x + yi, we define the magnitude, |z|, as follows:
[tex]|\text{ z |=}\sqrt[]{x^2+y^2}[/tex]thus, according to this, we can conclude that the magnitude of the given complex number is:
[tex]|\text{ z |=}\sqrt[]{(-5)^2+(12)^2}\text{ = 13}[/tex]so that, the correct answer is:
[tex]13[/tex]
please help with this practice question asap
The slope of the line passing through the points (4, -5), (-4, -5) is m = 0.
What do we mean by a slope?The slope of a line can be used to gauge how steep it is.Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).Every time the equation of a line is written as y = mx + b, the slope-intercept form of the equation is used.The slope of the line is shown by M.B is the value of b at the location of the y-intercept (0, b).For instance, y = 3x - 7 has a slope and y-intercept of 3 and 0, respectively.So, the slope of (4, -5) (-4, -5):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, substitute the values in the formula and find the slope as follows:
m = y₂ - y₁/x₂ - x₁m = (-5) - (-5)/(-4) - 4m = -5 + 5/-4 - 4m = 0/-8m = 0Therefore, the slope of the line passing through the points (4, -5), (-4, -5) is
m = 0.
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Miles has 327 action figures and 4 shoeboxes to store them in.Does miles have enough shoe boxes? ,if not, how many action figures are left over?
Step 1:
Concept
To find out if Miles has enough shoeboxes to fit all 327 of his action figures, we first need to find the amount of action figures his current amount of shoeboxes can store. We can do this by multiplying the amount of shoeboxes Miles has by the amount of action figures each shoebox can hold.
Step 2:
Shoe boxes can contain 80
Total = 4 x 80 = 320
Step 3
There will be 7 left
Left over = 7
A survey asks students who walk or ride a bike to school whether they live more than onemile from school. The results are shown in the table. Based on the results, which conclusionis best?Live More Than 1 Mile from SchoolWay to Getto SchoolYesNoTotalWalk103141Bike322759Total4258100of the students who live more than one mileaway, about 76% ride a bike.of the students who ride a bike, about 27% liveless than one mile away.of the students who ride a bike, about 76% livemore than one mile away.of the students who live more than one nabeaway, about 32% ride a bike.
Answer
Step-by-step explanation
Data is collected from 100 students on whether they walk or bike to school and whether they live more than a mile from school or not is shown in a table.
1 mile or not
Ways Yes No Total
Work 10 31 41
Bike 32 27 59
Total 42 58 100
The question then asks us to examine four options, to obtain the one(s) that are correct.
First Option
Of the students who live more than one mile away, about
if you could help me with some math bc i am bad at this stuff
Answer:
57.97 cm²
Step-by-step explanation:
Use the formula for area of a trapezoid
[tex]A = \dfrac{a + b}{2} h\\\\[/tex]
where a and b are the two sides and h is the height
Here a = 7.8, b = 10.8, h = 6.2
Substituting we get
[tex]A = \dfrac{7.9 + 10.8}{2} \times 6.2\\\\A = (7.9 + 10.8) \times \dfrac{6.2}{2}\\\\\\7.9 + 10. 8 = 18.7\\\\\dfrac{6.2}{2} = 3.1\\\\\\A = 18.7 \times 3.1 = 57.97\; cm^2[/tex]
The equation of a line is x + 4y = 15.What is the y-intercept of the line? −151515/44/15
Given:
[tex]x+4y=15[/tex][tex]4y=-x+15[/tex][tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex][tex]\text{The general equation is }[/tex][tex]y=mx+c[/tex]c is the y-intercept
[tex]y-\text{intercept (c)= }\frac{15}{4}[/tex]Use intercepts to graph the line described by the equation.4y =5x +20
We have to graph the equation 4y=5x+20 using the intercepts.
First we are going to find the y-intercept of the line, to do this we have to remember that the line intercepts the y-axis when x=0. Plugging this value of x in the equation we have
[tex]\begin{gathered} 4y=5(0)+20 \\ 4y=20 \\ y=\frac{20}{4} \\ y=5 \end{gathered}[/tex]Hence the y-intercept is 5. This represents the point (0,5).
Now we draw this point on the graph:
Now we have to find the x-intercept of the line, this happens when y=0. Plugging this value of y in the equation we have that
[tex]\begin{gathered} 4(0)=5x+20 \\ 0=5x+20 \\ 5x=-20 \\ x=-\frac{20}{5} \\ x=-4 \end{gathered}[/tex]Then, the x-intercept is -4. This represents the point (-4,0).
Drawing this point on the graph we have.
Now we only connect the points with a straight line:
That's the graph of the line that we find with the intercepts.
This data shows the height of 10 trees, in metres, after 5 years’ growth.
2.1
2.5
2.2
2.4
2.2
2.7
2.4
2.3
1.9
2.6
Calculate the median, showing your answer to two decimal places and remembering to include units with your answer.
The median of the given data would be 2.35 meters.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
The given set of data as:
{2.1, 2.5, 2.2, 2.4, 2.2, 2.7, 2.4, 2.3, 1.9, 2.6}
Arrange the data in ascending order.
1.9, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.6, 2.7
Since the number of elements in the data set is 10.
Median = [(n/2)th term + ((n/2) + 1)th term]/2
Median = [(10/2)th term + ((10/2) + 1)th term]/2
Median = [5th term + 6th term]/2
Median = [2.3 + 2.4]/2
Median = 4.7/2
Median = 2.35
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Write a quadratic function in standard form whose graph has the given characteristics.
The quadratic function in standard form that passes through (-2, 0), (4, 18), and (10, 0) is y = (- 1/2) x² + 4x + 10.
Given that, (-2, 0), (4, 18) and (10, 0).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (- 2, 0)
y = ax² + bx + c
0 = 4a - 2b + c ----------------(1)
The equation passes through (4, 18)
y = ax² + bx + c
18 = 16a + 4b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = -1/2, b = 4, and c = 10
The quadratic equation will be:
y = ax² + bx + c
y = (- 1/2) x² + 4x + 10
Therefore, a quadratic function in standard form with the given characteristics is y = (- 1/2) x² + 4x + 10.
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Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Given the triangles EFG and HIJ, you can identify that:
[tex]EG=19\text{ }[/tex][tex]EF=18[/tex][tex]\begin{gathered} FG=16\text{ } \\ \\ \text{ }HI=90 \\ \\ IJ=80 \end{gathered}[/tex][tex]\begin{gathered} m\angle F=67\text{ \degree} \\ \\ m\angle I=67\text{ \degree} \end{gathered}[/tex]By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find in they are in proportion. Set up that:
[tex]\frac{EF}{HI}=\frac{FG}{IJ}[/tex]Substituting values and simplifying, you get:
[tex]\begin{gathered} \frac{18}{90}=\frac{16}{80} \\ \\ \frac{1}{5}=\frac{1}{5} \end{gathered}[/tex]Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measure.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is: Third option.
Consider the following equation. State any restrictions on the variable, if they exist.
In equation like this one, the restriction happens when there are variables in the denominator. Since the denominator can't be equal to zero, when we have a variable in the denominator, we have to find the restrictions to the variable.
However, in this case, no denominator have variables in it.
So, in this case, there is no restriction for the values of x.
Help I’m completely lost on this I have no clue what I’m doing. I’ve tried 3 times
Answer:
Explanation:
Given the equation:
[tex]undefined[/tex]Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
randomly chosing a number from the even number between 10 and 20 nclusive
For the given experiment, the sample space has 6 elements which are:
{10, 12, 14, 16, 18, 20}
How to identify the sample space?
For any experiment with different outputs (each output with a defined probability).
We define the sample space as the set of all the possible outcomes of the experiment.
Now, the experiment here is:
"randomly choosing a number from the even number between 10 and 20 inclusive"
So the possible outcomes are all the even numbers on the interval [10, 20]
Then the sample space of the experiment is:
{10, 12, 14, 16, 18, 20}
It has 6 elements.
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I need help on this question
DA bisects EB
then
DC is congruent with AC
EC is congruent with BC
and
ED is congruent with AB
What was done to the linear parent function, f(x) = x, to get the functiong(x) = ?A. Horizontally compressed by a factor of 6B. Vertically stretched by a factor of 6C. Vertically compressed by a factor of 6D. Shifted unit up
Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
12.5% of what number is 24
Let's begin by listing out the information given to us:
[tex]undefined[/tex]Rewrite x4y2 − 6x3y3 using a common factor.
x2y2(x2 − 6xy)
x2y(xy − 6xy2)
6xy(x3y − x2y)
6xy2(x2 − x2y)
The common factor of the equation [tex]x^{4}y^{2} -6x^{3}y^{3}[/tex] is [tex]x^{2}y^{2} (x^{2}-6xy)[/tex].
What is a common factor?
A whole number that is a factor of two or more numbers is referred to as a common factor.
The largest factor that will split into two or more integers is known as the highest common factor (HCF).
The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).
The LCM and HCF
when a fraction is added or subtracted.
can be discovered by listing multiple factors. It is more effective to express greater values of a number as the product of prime factors. The Venn diagram is another option.
In finding common factors, the HCF, and LCM need knowledge of how to identify factors, build factor trees, and express integers as the product of their prime factors.
How to locate common factors?
A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10.
A factor that all whole integers share is 1, or 1.
To identify commonalities:
List each number's factors.
To identify the numbers that are the same (or frequent) in both lists, compare the factors.
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what digit is in the
The decimal number is given 16.837
Convert into fractional form by removing the decimal from the given number.
[tex]16.837=\frac{16837}{1000}[/tex]Hence the fractional notation determined is
[tex]\frac{16837}{1000}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
The science club took a survey to see how many hours each member in the club worked on a science project. The table below
shows the results of the survey.
Students Hours
Greta
16
Juan
14
Mika
20
Paulo
18
Su-Lin
16
Tanika
31
Darnell
13
Wesley
24
What is the mean (average) number of hours the students worked on the science project?
OA. 21
OB. 19
OC. 20
18
Answer: 19
Step-by-step explanation:
To find an average, you take each of your values, add them, and then divide by the numbers of values you have. There were 8 students interviewed, so your total numbers of values is 8.
Addition: 16 + 14 + 20 + 18 + 16 + 31 + 13 + 24 = 152
Division: 152 ÷ 8 = 19
What type of transformation is illustrated in the picture below? A. rotationB. translation
Rotation simply means turning around a centre . From the diagram above the vehicle rotated in a clockwise fashion.
The length of a rectangle is 3 more than the width. Find the length of the rectangle if the perimeter is 98 in.A.47.5 inB.24.5 inC.26 in.D.23 in.
Answer
Length of the rectangle = 26 inches
Explanation
Let the length of a rectangle be L
Let the width of the rectangle be W
The length of the rectangle is 3 more than the width.
L = W + 3
But we are provided with the perimeter of the rectangle.
The perimeter of a figure is the sum of the dimensions of its exterior.
For a rectangle,
Perimeter = 2 (L + W)
For this question,
Perimeter = 98 inches
L = W + 3
W = ?
Perimeter = 2 (L + W)
98 = 2 (W + 3 + W)
98 = 2 (2W + 3)
98 = 4W + 6
4W + 6 = 98
4W = 98 - 6
4W = 92
Divide both sides by 4
(4W/4) = (92/4)
W = 23 inches
L = W + 3 = 23 + 3 = 26 inches
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fx) -2 x 14 11 3 5 5 4 -8 Determine the Solution utilizing the Table of Values* (1 Point)
The domain x with the value of 5 according to the table has a range value of -8.
A. -8
Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commission on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
Base salary = $200 per week
Commission = 10% of total sales for that week
In a certain week, he makes sale of = $750
So, commission for that week = 10% of $750 = 10/100 x $750 = $75
In that particular week, Marques earned = base salary + commission = $200 + $75 = $275
For a week, in which he makes x dollars in sales,
Commission = 10% of x = 10/100 x (x) = $x/10
Total earning for that week = base salary + commission = $200 + $x/10
What are Commissions?The payment for goods or services sold in the form of commissions is a type of variable pay. Salesperson motivation and reward frequently involve commissions. Incentives like commissions might be used to promote particular sales techniques. When offering substantial reductions, for instance, commissions might be cut. Alternatively, commissions could go up when a company sells a certain product it wishes to advertise. A sales incentive program's framework, which may comprise one or more commission programs, governs how commissions are normally administered.The principal-agent problem is often solved by businesses by calculating payments as a proportion of revenue in an effort to better align employee interests with those of the business.Creating incentives that take account of an agent's performance is one of the most popular ways to try and balance principal and agent interests. The different forms of compensation systems, such as fixed salaries, straight commissions, or a mix of both, have a wide range of variations.To learn more about Commissions, refer to:
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Kari spent 1 2/3 hours painting a fence. Then he spent 4/5 of an hour walking his dog. How much longer did he spend painting than walking?