Find the values of x,y, and z.
guys please help me. I missed a class and can't find the video to help me solve this
Answers
Answer:
x = 7.2 , y = 57 , z = 10.8
Step-by-step explanation:
the sum of the 3 angles in the outer triangle = 180° , that is
y + 88 + 35 = 180
y + 123 = 180 ( subtract 123 from both sides )
y = 57
------------
the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{12}[/tex] = [tex]\frac{9}{9+6}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15x = 108 ( divide both sides by 15 )
x = 7.2
and
[tex]\frac{z}{18}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15z = 162 ( divide both sides by 15 )
z = 10.8
Related Questions
eighteen faculty members in a college math department range in age from 32 to 68. a stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 the 1.5 × iqr rule would identify an age as a high outlier if it exceeded years. group of answer choices
Answers
The Stem plot is displayed below of eighteen faculty members in a college math department range in age from 32 to 68.
How do you make a stem plot?
On the left hand side of the page, write down the thousands, hundreds or tens (all digits but the last one). These will be your stems. Draw a line to the right of these stems. On the other side of the line, write down the ones (the last digit of a number).
A Stem Plot is a chart for demonstrating the distribution of numeric variables .
It is used to analyze the shape of the distribution.
The data provided is as follows:
S = {32,48,99,40,35,69,53,47,89,96,38}
The Stem plot is displayed as follows:
3 | 2 5 8
4 | 0 7 8
5 | 3
6 | 9
8 | 9
9 | 6 9
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Type the correct number
Cars
4
12
16
Trucks
5
10
15
25
Answers
Answer:
cars= 32 , trucks= 55
Step-by-step explanation:
add all the cars up then the trucks
1.998 x 10^27
Ordinary number
Answers
The representation of the number is 1.998 multiplied by 10^27
How to evaluate the expression?The expression is given as
1.998 x 10^27
The above mathematical representation is a number in scientific form and is already in its most simplified form
This means that the scientific form cannot be further simplified
However, the scientific number can be rewritten as a mathematical statement
Recall that, we have
1.998 x 10^27
The pronunciation of the above expression is:
1.998 multiplied by 10^27
And it is evaluated by
Moving the decimal point 27 places to the right.
This gives
1998000000000000000000000000
See that the above result does not have a proper representation compared to 1.998 x 10^27
Hence, the representation of the scientific number given as 1.998 x 10^27 is the 1.998 multiplied by 10^27
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What is the volume of the following cone?
Answers
The volume of the cone, to the nearest whole number, is: 50 cm³.
How to Find the Volume of a Cone?The volume of a cone is defined as the amount of space it contains. The volume can be calculated using the formula:
Volume of cone = 1/3 × π × r² × h, where h is the height of the cone, and r is the radius of the cone.
Given the parameters:
Height of the cone (h) = 3 cmRadius of the cone (r) = 4 cmPlug in the values:
Volume of the cone = 1/3 × π × 4² × 3
Volume of the cone = 1/3 × π × 16 × 3
Volume of the cone = 16π
Volume of the cone = 50 cm³
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fully factorise
[tex]12x^3 + 38x^2 - 14x[/tex]
Answers
Answer:
2x(2x + 7)(3x - 1).
Step-by-step explanation:
12x^3 + 38x^2 - 14x
= x(12x^2 + 38x - 14)
= 2x(6x^2 + 19x - 7)
To factor the expression in the parentheses we need 2 numbers whose product is (6 * -7) = - 42 and whose sum = +19.
These are +21 and - 2.
So, we write:
6x^2 - 2x + 21x - 7
= 2x(3x - 1) + 7(3x - 1)
= (2x + 7)(3x - 1)
So, the answer is 2x(2x + 7)(3x - 1).
Answer:
[tex]2x(3x-1)(2x+7)[/tex]
Step-by-step explanation:
[tex]12x^3+3x^2-14x\\[/tex]
Factor out common factor: (2x)
[tex]=2x(6x^2+19x-7)[/tex]
Factor [tex]6x^2+19x-7[/tex]
[tex]= 2x(3x-1)(2x+7)[/tex]
Hope this helps! :) Sorry for the late reply
I’ll mark you brainliest for a correct answer!!! I have been reeling over this question forever
Answers
489.22 divided 10 to the fourth power
Answers
David is starting a new job in sales. he can choose to earn only a 10% commission on sales each month, or earn a monthly base salary of $1,500 with a 3% commission on sales over $7,500. which pay method would earn him more money if he has an average sales of $16,000 each month?
Answers
Answer:
Method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500, will earn more money.
Step-by-step explanation:
given -
method 1 - he can choose to earn only a 10% commission on sales each month,
method 2-earn a monthly base salary of $1,500 with a 3% commission on sales over $7,500.
also, he has an average sales of $16,000 each month.
according to the question;
method 1 earning =>
10% of $16,000 =>(10/100)*$16,000=$16,00.
method 2 earning =>
$1,500+(3/100)*($16000-$7500)=$1755.
in method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500. he will earn more.
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solve y-59 equal to 80
Answers
Answer:
y=139
Step-by-step explanation:
add 59 to 80
Pls help!!!: select all the expressions that are equivalent to (1/2) to the power of negative 3. a). -(1/2) to the power of 3 b).2 to the power of 3 c).(1/1/2 to the power of 3) d).1/8 e).8
Answers
Answer:
option (e) 8
Step-by-step explanation:
using identity
==>1/(a^(-x))=a^x()
=(1/2)^(-3)
=(2)^3
=2*2*2=8
option (e)
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Montel heated a 12-cup pot filled with soup. He served bowls of soup to his family.
How can Montel find out how much soup his family ate?
Answers
He can find out by using mathematical operation - subtraction.
What are Mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as a ternary operation, is the mixed product.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
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The sum of the digits of a certain two-digit number is 11. When you reverse its digits you increase the number by 45. What is the number?
Answers
Answer:
6 and 9.
Step-by-step explanation:
Let the number be xy [note: x is a digit in tens place and y is another digit in ones place]
Learn to translate the words into formulas:
"When you reverse the digits in a certain two-digit number you increase its value by 45." means
10y + x = (10x + y) + 45 [eq1]
"the sum of its digits is 11" means x + y = 11 [eq2}
Now, solve (let's use substitution):
y = 11-x [from eq2]
Put that into eq1:
10y + x = (10x + y) + 45 [eq1]
10(11-x) + x = 10x + (11-x) + 45
110 - 10x + x = 10x + 11 - x + 45
110 - 9x = 9x + 56
-18x = -54
x = 3
Now, put that into either equation to find the value of y:
3 + y = 11 [eq2]
3 + y = 11
y = 8
The number is 38.
Check:
Is 83 = 38 + 45 ?
83 = 83 ?yes
Is 3 + 8 = 11 ?
11 = 11 ?yes
Solve for b.
-14b + 1
4
<3 or b - 15 - 15b > 1
Write your answer as a compound inequality with integers, proper fr
fractions in simplest form.
or
Answers
Answer:
Step-by-step explanation:
(15, −41) (29, 37).
What is the sum of the two vectors?
Answers
Based on the vectors given, the sum of the vectors can be found to be (44, 4)
How to add vectors?When given two vectors such as (15, −41) (29, 37) and you are required to add them, the sum of the vectors can be found by the formula:
= (a1 + b1, a2 + b2)
Where the vectors are:
(a1, a2) (b1, b2)
The sum of the vectors (15, −41) (29, 37) is therefore:
= (a1 + b1, a2 + b2)
= (15 + 29, -41 + 37)
= (44, -41 + 37)
= (44, 4)
In conclusion, the sum of the vectors are (44,4).
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vince is cutting a rectangular piece of pegboard to use in his garage for organization. the width of the pegboard is 8 inches less than half the length. the perimeterof the pegboard is 224 inches. what is the length of the pegboard?
Answers
The most appropriate choice for linear equation will be given by -
Length of the rectangle is 80 inches
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let the length of the pegboard be l inches
Width of the pegboard = [tex]\frac{1}{2}l - 8[/tex]
Perimeter =
[tex]2(l + \frac{1}{2}l - 8 )\\2(\frac{3l}{2} - 8)\\[/tex]
[tex](3l - 16)[/tex] inches
But the problem,
[tex]3l - 16 = 224\\3l = 224 +16\\3l = 240\\l = \frac{240}{3}\\[/tex]
[tex]l = 80[/tex] inches
The length of the rectangle is 80 inches.
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On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours. What was the average change in temperature per hour?
Enter your answer as a decimal.
Answers
The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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J. The Math Club found a company that will sell it t-shirts for $5.00 each, but there is a set-up fee of $50.
Answers
The t stands for how many t shirts you sell and the 50 is the set fee for the start up.
tim and his sister drove 18 miles in 27 minutes. How long will it take them to drive 24 miles
Answers
It will take them 36 minutes to drive 24 miles.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Because of this, the goal of this method is to determine values in reference to a single unit. For instance, we can use the unitary technique to determine how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Given Data
Tim and his sister drove 18 miles in 27 minutes.
They drove 1 mile in :
18 mile = 27 minutes
1 mile = [tex]\frac{27}{18}[/tex] minutes
1 mile = 1.5 minutes
For 24 miles,
1 mile = 1.5 minutes
24 miles = 1.5(24) minutes
24 miles = 36 minutes.
It will take them 36 minutes to drive 24 miles.
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Write the equation of the line that passes through the points (3,−8) and(−4,−9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
Step-by-step explanation:
Point slope form: y − y1 = m(x − x1)
First, we find the slope (m):
m = [tex]\frac{y2-y1}{x2-x12} = \frac{-8-(-9)}{3-(-4)} = \frac{1}{7}[/tex]
Now insert your points and slope into the form:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
out of 150 students appeared in an examination 60% of the students passed in math 50% in Science and 20% in both subjects how many students where failed in both subjects ?by using Venn diagram find the number of student Wawa passed in maths only .
Answers
Answer:
5000 students
Step-by-step explanation:
Let total number of students appeared in the exams is x.
20% of x have failed in both maths and science.
Here,in maths 60% of students passed.
%ag of students failed in maths= 40%
%ag of students failed in math — % of students failed in both maths and science = students passed in science but failed in maths i.e. 40–20 = 20%.
Likewise as 70% of students passed science
So 30% failed in science.
And Students failed in science only but passed in maths= %ag of students failed in science- % of students failed in both maths and science.
i.e. 30–20= 10%.
Given 2500 number of students passed in both maths and science = 100–(students failed in both maths and science+ students failed only in maths and passed in science+ students failed only in science but passed in maths)%
= 100–(20+20+10)= 50% of students passed both.
50% of x = 2500
50x/100= 2500
=> x= 5000.
So total number of students appeared in exam is 5000 in number
Help quickly please!
Answers
The equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) include C. 1 2/3x + 35 - 1 1/2x + 12
How to express the expression?It should be noted that an expression simply shows the relationship between the variables.
In this case, the value of the expression illustrated will be:
5(1/3x + 7) - 3(1/2x - 4)
= 5/3x + 35 - 3/2x + 12
= 5/3x - 3/2x + 35 + 12
= 10/6x - 9/6x + 47
= 1/6x + 47.
Therefore, the equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) will be 1 2/3x + 35 - 1 1/2x + 12. This was illustrated based on the information given as it has the final value of 1/6x + 47.
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help i don’t get it
answers pls
Answers
Answer: x=13°
Step-by-step explanation: We know total amount of degrees in a triangle is 180°. We also know two of the angles' degrees: 39° and 90°. Now, with this info, we set up an equation: (3x+12)+39+90=180. We add 39 and 90 to get 129; then we subtract 129 on both sides of the equation. Our equation should now look like this: 3x+12=51. Subtract 12 on both sides to get: 3x=39. Lastly, divide 3 on both sides to find the value of x.
In WXY, m/W = (10x + 17)°, m/X = (2x - 9)°, and m/Y = (3x + 7)°. Find m/Y.
Answers
Answer:
m∠Y = 40°
Step-by-step explanation:
The sum of the three angles of a triangle must equal 180°
Thus
m∠W + m∠X + m∠y = 180°
→ (10x + 17) + (2x - 9) + (3x + 7) = 180
→ 10X + 17 + 2X + 9 + 3X + 7 = 180
Collecting like terms
→ 10X + 2X + 3X + 17 - 9 + 7 = 180°
→ 15x + 15 = 180
Subtract constant 15 from both ssides:
→ 15x + 15 - 15 = 180 - 15
→ 15x = 165
Divide both sides by 15
→ 15x/15 = 165/15
→ x = 11
m∠Y = 3x + 7
m∠Y = 3 x 11 + 7
m∠Y = 33 + 7
m∠Y = 40°
The probability of a telesales represented making a sale on a customer call is 0.15. find the probability that more than 3 sales are made in 20 calls.
Answers
Using Binomial probability distribution,
X = 20, 0.15
P (X ≤ 3) =[tex]20 C_{0} (0.15)^{0} (1-0.15)^{20} + 20C_{1} (0.15)^{1} (1-0.15)^{19} + 20C_{2} (0.15)^{2} (1-0.15)^{18} + 20C_{3} (0.15)^{3} (1-0.15)^{17}[/tex]
P(X ≤ 3) = 0.648
P (X ≥ 3) = 1 - P(X ≤ 3) = 1 - 0.648
P ( X ≥ 3) = 0.352
Therefore, thee required probability is 0.352.
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PLS HELP!! DUE TODAY! Will give branliest to the best answer, 40 points!!
What is the slope of a line that is perpendicular to the line y = 18x + 5?
A. -8
B. -1/8
C. 1/8
D. 8
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:B. \:\: - \dfrac{1}{18} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation of a line is in its slope intercept form, that is :
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
The original equation is :
[tex]\qquad \tt \rightarrow \:y = 18x + 5[/tex]
by comparing the two equations we get slope (m) of this line equal to 18
we need to find the slope (n) of line perpendicular to this.
By the property of perpendicular lines, we know :
[tex]\qquad \tt \rightarrow \:m \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:18 \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:n = - \cfrac{1}{18} [/tex]
So, slope of required line is -1/18
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: -1/18
Step-by-step explanation:
Let y=k₁x+b1 be the line. Given the perpendicularity of lines, the equation of the line perpendicular to the given line has the form:
[tex]\displaystyle\\y=-\frac{1}{k}x+b_1[/tex]
[tex]\displaystyle\\So,\ y=18x+5\\\\\Rightarrow\ -\frac{1}{18}[/tex]
−14 = −21 +
C
11
Subract
Answers
Answer:
35
Step-by-step explanation:
a couple has narrowed down the choices of a name for their new baby to first names and middle names. how many different first- and middle-name arrangements are possible?
Answers
There are 28 ways in which a couple can choose the name of the baby for its name.
What is defined as the combination?A combination is an algebraic technique for determining the number of possible arrangements in a set of items in which the order of the selection is irrelevant. You can choose the items in just about any order in combinations. Permutations and combinations are often confused.If we need to choose objects from two groups of x and n objects so that one object from each group is chosen, we can do so by calculating the combinations possible by:
= ˣC₁ × ⁿC₁
Let 'x' be the set of first name = 7
Let 'n' be the set of second name = 4
Putting the values in formula;
= ⁷C₁ × ⁴C₁
= 7 × 4
= 28
Thus, there are 28 ways in which a couple can choose the name of the baby for its name.
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The complete question is-
A couple has narrowed down the choices of a name for their new baby to 7 first names and 4 second names.
How many different first- and second-name arrangements are possible?
answer the following questions for each set: (a) what are the limit points? (b) is the set open? closed? (c) does the set contain any isolated points?
Answers
a) limit point of a set A is 1
b) set A is neither open nor closed
c) all the element of set A are isolated point except -1 and 1
Let A={(−1)^n+2/n :n=1,2,3,.....} and B={x∈Q:0<x<1}
Answer the following questions for each set:
a) What are the limit points?
b) is the set open? closed?
c) does the set contain any isolated points?
a) the limit point of a set A are -1 and 1
-1 does not belong to set A
1 belong to set A
Therefore limit point of a set A is 1
b) A set is open if every point in is an interior point. A set is closed if it contains all of its boundary points
thus set A is neither open nor closed
c) a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S and there exists a neighborhood of x which does not contain any other points of S.
all the element of set A are isolated point except -1 and 1
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Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
Answers
Answer:
x = -3 and y = 6
Step-by-step explanation:
by plugging the function (y = 3x + 15) into the y value in the function (3x + 3y = 9), you can then solve to find that x = -3
After solving for the x-value, plug -3 into the easiest equation to solve for the y-value (y = 3x + 15) to then find that y = 6
This is method of solving is called substitution
I really need help you guys pleaseeee