please help to find the value of x and explain how to get it in simple terms.
Answers
SOLUTION
From the image above
[tex]\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}[/tex]Considering the bigger right angle triangle,
[tex](3+x)^2=y^2+45[/tex]We can obtain the expression of y from the smaller right angle triangle,
Using pythagora's rule, we have
[tex]y^2=6^2+x^2[/tex]Then, recall
[tex](3+x)^2=y^2+45[/tex]Substite the expression for y², we have
[tex](3+x)^2=6^2+x^2+45[/tex]Expand the paranthesis, we have
[tex]\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}[/tex]subtract 9 from both sides, we have
[tex]\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}[/tex]Divide both sides by 6, we obtain
[tex]\begin{gathered} \frac{6x}{6}=\frac{72}{6} \\ \text{Then} \\ x=12 \end{gathered}[/tex]Therefore
Answer: x= 12
Related Questions
What coordinates point can I plot in the graph? It can't be a decimals point, It has to be whole numbers because the graph doesn't let me put for example 4.86 or a fraction
Answers
First, we can start input small whole numbers in the function to see if we get a whole number. Let's try with 0, 1 and 2:
[tex]\begin{gathered} y=(\frac{1}{2})^{0+1}-9=\frac{1}{2}-9=-8.5 \\ . \\ y=(\frac{1}{2})^{1+1}-9=\frac{1}{4}-9=-8.75 \\ . \\ y=(\frac{1}{2})^{2+1}-9=\frac{1}{8}-9=-8.875 \end{gathered}[/tex]None of those values worked. Let's try negative integers, such as -1 and -2:
[tex]\begin{gathered} y=(\frac{1}{2})^{-1+1}-9=(\frac{1}{2})^0-9=1-9=-8 \\ . \\ y=(\frac{1}{2})^{-2+1}-9=(\frac{1}{2})^{-1}-9=2-9=-7 \end{gathered}[/tex]We get integer coordinates if we use negative integers. Then, we need at least 5 points. Let's use x = -1, -2, -3, -4, -5
[tex]\begin{gathered} y=(\frac{1}{2})^{-3+1}-9=(\frac{1}{2})^{-2}-9=2^2-9=4-9=-5 \\ . \\ y=(\frac{1}{2})^{-4+1}-9=(\frac{1}{2})^{-3}-9=2^3-9=8-9=-1 \\ . \\ y=(\frac{1}{2})^{-5+1}-9=(\frac{1}{2})^{-4}-9=2^4-9=16-9=7 \end{gathered}[/tex]We have the points:
(-1, -8), (-2, -7), (-3, -5), (-4, -1) and (-5, 7)
If we locate them in the cartesian plane:
And now, we can estimate the graph. An exponential function where the base is smaller than 1, describes an exponential decay, and the term "-9" is applying a shift 9 units down, and also y = -9 is a horizontal asymptote. With all this and the points we just found:
Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
Answers
In linear equation, R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like
R = mc + b
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
Slope(m) = 88 - 60/22 - 15 = 28/7 = 4
To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b
60 = 4(15) + b
60 = 60 + b
b = 0
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
R = 4c + 0
R = 4c
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PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
Answers
Step-by-step explanation:
This should be the right solution.
Which linear inequality is represented by the graph?1. y>2/3x-22. y<2/3x+23. y
Answers
To identify the inequality of the given graph:
1. Identify the equation of the borderline in slope-intercept form (y=mx+b)
- Find the slope (m): Use two points in the line in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=\frac{1-(-3)}{3-(-3)}=\frac{1+3}{3+3}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)
b= -1
Equation of the border line:
[tex]y=\frac{2}{3}x-1[/tex]2, Identifify the inequality sing:
-When the inequality is < or > the borderline is a dotted line
-When the inequality is ≥ or ≤ the border line is a full line
-When the inequality is < or ≤ the shaded area is under the borderline
-When the inequality is > or ≥ the shaded are is over the borderline
In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:
[tex]y<\frac{2}{3}x-1[/tex]Solve each equation.
4/7 v = -8 2/3
Answers
[tex] \frac{4}{7} v = - \frac{26}{3} \\ - 26(7) = 4v(3) \\ - 182 = 12v \\ \frac{ - 182}{12} = \frac{12v}{12} \\ v = - 15 \frac{2}{12} \\ v = - 15 \frac{1}{6} [/tex]
BE AWARE I USED CROSS MULTIPLICATION.
Select the two values of x that are roots of this equation.3x² + 1 = 5xA. x =5+√13x = 5+√136☐ B. x =5-√136□ C. x=-1-√59X6D. X =-1+√596
Answers
3x^2 + 1 = 5x
3x^2 - 5x + 1 = 0
quadratic formula
[tex]x=-\frac{b\pm\sqrt{b^2-4ac}}{2a}[/tex]where ax^2 + bx + c = 0
so
[tex]x=\frac{5\pm\sqrt{-5^2-4(3)(1)}}{2(3)}[/tex][tex]x=\frac{5\pm\sqrt{25-12}}{6}[/tex]You can see that the 25 - 12 = 13 so the answers are A and B
study questions from digital text book page 2.03 : Picture's down below
Question #1 : What is m∠SVT?
Question #2: What is the m∡BEC?
Disclaimer!! these are not from a Test, Quiz, or Assignment. these are from a practice page and i wanted to know how do these questions for a Future assignment with questions like these. I am just informing you guys because i didn't know the guidelines until now and i will no longer put test questions up because I am now aware its not ok to do so. So This Is not from a Test, Quiz, or Assignment. Thank you
Answers
The angle measures in this problem are given as follows:
1. Angle SVT: 79º.
2. Angle BEC: 65º.
Angle SVTAngles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:
8y - 33 = 5y + 9
3y = 42
y = 42/3
y = 14.
Hence the measure of the angle SVT is of:
m<SVT = 5y + 9 = 5(14) + 9 = 79º.
Angle BECThe two angles given in this problem are also vertical, meaning that we can solve for x as follows:
5x - 10 = 3x + 40
2x = 50
x = 50/2
x = 25º.
Then the bottom angle is:
3 x 25 + 40 = 115º.
The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:
115 + m<BEC = 180
m<BEC = 180 - 115
m<BEC = 65º.
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composite functions 65 points helpppppp
Answers
Answer:
[tex]4\sqrt{x+2} - 6[/tex]
Step-by-step explanation:
f(g(7)) = f(sqrt(x+2))
=4(sqrtx+2) - 6)
= [tex]4\sqrt{x+2} - 6[/tex]
Answer:
[tex](f \circ g)(7)=6[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=4x-6\\g(x)=\sqrt{x+2}\end{cases}[/tex]
(f o g)(x) is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (f o g)(7) means to substitute the function g(x) when x=7 in place of the x in function f(x).
[tex]\begin{aligned}\implies (f \circ g)(7)&=f[g(7)]\\& = f(\sqrt{7+2})\\&=f(\sqrt{9})\\&=f(3)\\&=4(3)-6\\&=12-6\\&=6\end{aligned}[/tex]
Marcus runs triathlons (races that involve running, biking, and swimming). To prepare for these triathlons, he follows a strategy of running twice as far as he swims and biking fours times as far as he runs. If he swims for 3 miles this week, what is the total distanch of his swimming, running and biking this week?
Answers
1) Gathering the data
Strategy:
Running : 2x As he swims
Biking: 4x Runs
Runs = 3 miles
Then
2) Runs = 3 miles Swims = 6 miles Biking = 12 miles
The Total distance will be the sum of those activities:
3+6+12=21 miles
how many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
Answers
The number of ways to plan her schedule of menus for the 20 school days is 10^20.
How to many number of ways to plan her schedule?To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.
For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.
The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.
How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
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Which polynomial represents the difference below?2x^2 + 7x+6(3x^2 - x)O A. 2x^2 + 5x + 6B. 2x^2 + 4x + 6c. - x^2 + 6x + 6D. - x^2 + 8x+ 6
Answers
The given polynomials are as ,
[tex]\begin{gathered} 2x^2+7x+6\text{ and} \\ 3x^2-x \end{gathered}[/tex]We have to subtracrt these given polynomials,
[tex]\begin{gathered} =2x^2+7x+6-3x^2-(-x) \\ =2x^2+7x+6-3x^2+x \\ =-3x^2+2x^2+7x+x+6 \\ =-x^2+8x+6 \end{gathered}[/tex]Option D is correct.
nancy had 209 dollars to spend on 6 of the most mundane books.after buying them she had 17 dollars. on average, how much did each book cost
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The average cost of each book that Nancy got is $32
What is cost?Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice
In the question, the commodity is mundane books
How to solve how much each book costgiven that
Nancy had 209 dollars to spend
number of books = 6
amount remaining after buying = $17
The question can be represented mathematically as
6x + 17 = 209
where x is the cost of the each book
6x + 17 = 209
6x = 209 - 17
6x = 192
dividing through by 6
6x / 6 = 192 / 6
x = 32
hence each book costs $32
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Question 7 013 points Redo Which theorem is depicted by the figure and information shown below? R S Theorem? ZRAZT 2Qazs A) Opposite sides of parallelograms are congruent (Tm 16-A) B) Opposte angles in a parallelogram are congruent. (Tm 16-B) C) The sum of any consecutive angles within a parallelogram equals 180 (Tm 16-C) D) The diagonals of a parallelogram bisect each other (Tm 16-D) E) The diagonal of a parallelogram separates it into two congruent triangles (Tm 16-E)
Answers
Answer:
B. Opposite angles in a parallelogram are congruent.
Explanation:
The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.
Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.
So, the answer is B. Opposite angles in a parallelogram are congruent.
The latest crime statistics in the united states suggest that eighteen-to-twenty-four-year-olds make up about – percent of the population but account for – percent of criminal arrests, while people sixty-five and older make up more than – percent of the population but account for less than – percent of arrests
Answers
Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.
The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic requires division into further sub-categories. One common way to do this is by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.
Hence, percentage of people whose age is in between 18-24 is 7%,
people from age 18-24 engaged in illegal work=15%,
percentage of people whose age is 65 or more than =13%,
people involved in crime having age more than or equal to 65=1%
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Please help *100 POINTS*
New Orleans is 2 feet under seas level.
Salton City has a elevation lower than New Orleans.
What is a possible elevation, in feet of Salton City
With explanation please
Answers
The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.
What is a number line?A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.
The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level
The elevation of Salton City = Lower than the elevation of New Orleans
Required; The possible elevation of Salton City
The elevation of Salton City can be found by presenting the given information on a number line as follows;
Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;
<___|-3______|-2____|0______>
' S. N. SL
A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet
The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet
-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level
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A construction crew has just built a new road. They built the road at a rate of 18.75 kilometers per week. They worked for 3 weeks. How many kilometers of road did they build?
Answers
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.
Find the slope of the line that passes through (64, 94) and (48, -3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
The slope of the points has a value of 97/16
How to determine the slope of the points?From the question, the line passes through the following points
(64, 94) and (48, -3).
The slope of the line that passes through the points is then calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are the coordinates above
Substitute the known values in the above equation
So, we have the following equation
Slope = (94 + 3)/(64 - 48)
Evaluate the difference and the sum
Slope = 97/16
Hence, the slope is 97/16
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Which of the following is NOT a misuse of statistics?Choose the correct answer below.A. Utilizing valid statistical methods and correct sampling techniquesB. Making conclusions about a population based on a voluntary response sampleC. Concluding that a variable causes another variable because they have some correlationD. Misleading graphs
Answers
Required:
We need to find the statement which is NOT a misuse of statistics.
Explanation:
Recall that misuse of statistics occurs when a statistical argument asserts a falsehood.
Utilizing valid statistical methods and correct sampling techniques is not a misuse of statistics.
Final answer:
A. Utilizing valid statistical methods and correct sampling techniques
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. tan 26° = ___
Answers
Answer:
0.49
Explanation:
Given the expression:
tan 26°
Evaluating using calculator
tan 26° = 0.4877
Hence the decimal rounded to the nearest hundredth is 0.49
Answer:
0.49 to nearest hundredth
Step-by-step explanation:
tan 26⁰ = 0.48773
For the rhombus below, find the measures
Answers
For f(x) = 2x + 1 and g(x) = 2
7, find (f- g)(x)
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The value of (f- g)(x) is 2x - 26.
This is a question of subtraction of functions.
Subtraction of functions
The subtraction of function involves the creation of a new function through the addition of two other functions.
Subtraction of one real-valued function from another.
Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.
Given that:-
f(x) = 2x + 1
g(x) = 27
We have to find the value of (f- g)(x)
We know that,
(f- g)(x) = f(x) - g(x)
Hence, we can write,
(f- g)(x) = 2x + 1 - 27 = 2x - 26
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Which lines are perpendicular to 3x – y = 10? Select all that apply. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
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The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
3x – y = 10
y = 3x – 10
Then the equation of the perpendicular line is given as,
y = –(1/3)x + d
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
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A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.
Answers
Answer:
Step-by-step explanation:
30 students 15 have brown eyes 5 of the 15 are boys
1/3 chance a boy with brown eyes will be chosen.
1/2 a chance a student with brown eyes will be chosen
a grocery store wonders if their sales will be better if they play ambient music or no music at all. each day for 222 months, the manager flips a coin to determine whether or not the store will play music that day. at the end of the 222 months, the manager finds that, on average, sales were significantly better on days where music was playing. what conclusion can they draw from this study?
Answers
Answer:
They should play music
Step-by-step explanation:
They should play music obviously because the sales were higher
∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(6x+2)^{\circ}m∠A=(6x+2)
∘
and \text{m}\angle B=(4x+18)^{\circ}m∠B=(4x+18)
∘
, then find the measure of \angle A∠A.
Answers
The measure of ∠ A is 44 degrees.
Given that:-
∠ A and ∠ B are complementary angles.
∠ A = (6x +2) degrees
∠ B = (4x + 18) degrees
We have to find the measure of ∠ A.
We know that the sum of two complementary angles is 90 degrees.
Hence, we can write,
(6x + 2) + (4x + 18) = 90
(6x + 4x) + (2 + 18) = 90
10x + 20 = 90
10x = 90 - 20
10x = 70
x = 70/10
x = 7 degrees
Hence,
∠ A = 6*7 + 2 = 42 +2 = 44 degrees.
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Factor completely.x^2−10x−24 Enter your answer in the box.
Answers
Given:
[tex]x^2-10x-24[/tex]To factorize:
It can be written as,
[tex]\begin{gathered} x^2-10x-24=x^2-12x+2x-24 \\ =x(x-12)+2(x-12) \\ =(x-12)(x+2) \end{gathered}[/tex]Therefore, the factorized form is,
[tex](x-12)(x+2)[/tex]Use the given endpoint R and midpoint M of RS¯ to find the coordinates of the other endpoint S.
R(3, 0), M(0, 5)
Answers
Step-by-step explanation:
the midpoint coordinates between 2 points A and B are
((xa + xb)/2, (ya + yb)/2)
xa = 3
ya = 0
and so we get
(3 + xb)/2 = 0
3 + xb = 0
xb = -3
(0 + yb)/2 = 5
yb = 10
therefore, S = (-3, 10)
Which one is it because i thought it was 32g+26
Answers
The equivalent expression of 4(8g + 5) + 6 is 4(5 + 8g) + 6
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of 4(8g + 5) + 6.
Hence,
4(8g + 5) + 6
32g + 20 + 6
32g + 26
Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6
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A state agency recorded the number of each type of flood that occurred in the state from 2016–2020. The results are as follows. If similar proportions of flood types are predicted for the following year, what is the estimated probability that a flood in 2021 in that state will be a river flood? Round your answer to the nearest percent. A. 7%B. 60%C. 20%
Answers
The table shows different flood types and their frequencies.
Total frequency of all flood types = 18 + 6 + 4 + 2 = 30
frequency of river flood = 6
Recall, probability is expressed as
number of favorable outcomes/number of total outcomes
Thus, the estimated probability that a flood in 2021 in that state will be a river flood is
6/30 = 0.2
By changing 0.2 to percentage, we have
0.2 x 100 = 20%
The correct option is C. 20%
ABCD is a rectangle. Find angles a and b to the nearest degree
Answers
Solution
Given, ABCD is a rectangle AC is diagonal
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90
0
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle )
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90
0
..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90
0
⇒∠ACD=45
0