Find the value of x.
Answers
Answer
Option A is correct.
x = 5 units
Explanation
We can draw the triangle and divide it into two similar right angle triangles shown below
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For each of the triangles,
a = 4
b = 3
hyp = x
a² + b² = (hyp)²
4² + 3² = x²
x² = 16 + 9
x² = 25
x = √25
x = 5 units
Hope this Helps!!!
Related Questions
DONT IGNORE! PLEASE HELP ME! 50 POINTS!
Answers
Answer: The answer is C (or the third option)
Step-by-step explanation: The formula for finding the measure of interior hexagon angles is ( n − 2) × 180 °. This means that C is the correct answer
At a sale this week,a suit is being sold for $364. This is a 35% discount from the original price. What is the original price?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested original price, so we obtain the following:
So we have the following formula:
Discount Price=Original Price*(100%-Discount)
Clearing for "Original price":
Discount Price=Original Price*(100%-Discount)
Original Price=Discount Price/(100%-Discount)
Replacing with the given data:
Original Price=Discount Price/(100%-Discount)
Original Price=$364/(100%-35%)
Original Price=$364/(65%)
Original Price=$364/(0.65)
Original Price=$560
Finally we obtain that the original price is $560.
Select all sets of triangles that can be provencongruent using Side-Angle-Side(SAS).
Answers
SOLUTION
We want to select all triangles from the image that can be proven by the side angle side theorem which states that
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Now looking at the triangles
We can see that triangles in number 1, 2, 3 follows this theorem.
4 does not because the equal angles are not present
5, the triangles are congruent, but do not follow the SAS theorem
6 follows as we can see the equal sides and angle
7 shows two equal angles only, but we need one equal angles and two equal sides.
Hence the answer is 1, 2, 3 and 6 only
Find the equation of this line.(2,2) and (0,-4)
Answers
To find the equation;
x₁ = 2 y₁ = 2 x₂ = 0 y₂=-4
we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_{}-x_1)[/tex]substituting the values into the above;
[tex]y-2=\frac{-4-2}{0-2}(x-2)[/tex]Then, we will go ahead and evaluate;
[tex]y-2\text{ = }\frac{-6}{-2}(x-2)[/tex][tex]y-2\text{ =3(x-2)}[/tex]y - 2 = 3x - 6
add 2 to both-side of the equation
y = 3x -6+ 2
y = 3x -4
A man is approaching a pole 75 feet high and walking at the rate of
3 miles/hour. At what rate is he approaching the top of the pole
when he is 100 feet away from the pole?
Answers
Answer:
375!
Step-by-step explanation:
3 x 100 = 300
Now he is at the pole. Now he has to get to the top of it
which your basically doing
3 x 100 = 300 + 75 = 375
( 375 - 75 = 300 300 ÷ 100 = 3 )
it says use the table to rewrite the expression you wrote for problem 2. rewrite that expression so that both terms are written with the same exponent number 4. says use the distributive property simplify the expression you wrote for problem 3.number 5. says write your expression as the product of a decimal times a power of 10.number 6 says write your solution in scientific notation and number 7. says Evaluate (7.4 x 10^15 -- (9.9 x 10^13number 8 says Evaluate (8.9 x 10^5) + (6.5) x 10^6
Answers
7)
Given data:
The given expresson is a=7.7x10^15-(9.9x10^13)
The given expression can be written as,
a=770x10^13-9.9x10^13
=(770-9.9)x10^13
=760.1x10^13.
8)
Given data:
The given expresson is b=8.9x10^5-(6.5)x10^6
The given expression can be written as,
b=8.9x10^5-65x10^5
=(8.9-65)x10^5
=-56.1x10^5
Hello, I need help completing and showing appropriate steps for this problem. Thank you so much!
Answers
The first step is to factorise the quadratic expression on the right side of the equation. The expression is
x^2 + 9x + 20
We would find two terms such that their sum or difference is 9x and their product is 20x^2. The terms are 5x and 4x. Replacing 9x with 5x and 4x, it becomes
x^2 + 5x + 4x + 20
By factorising, it becomes
x(x + 5) + 4(x + 5)
Since x + 5 is common, it becomes
(x + 4)(x + 5)
Thus, the original expression becomes
x/(x + 4) + 3/(x + 5) = (x + 2)/(x + 4)(x + 5)
The lowest common multiple of the denominators on both sides of the equations is (x + 4)(x + 5). We would multiply each term in the equation by
(x + 4)(x + 5). It becomes
(x + 4)(x + 5)x/(x + 4) + 3(x + 4)(x + 5)/(x + 5) = (x + 2)(x + 4)(x + 5)/(x + 4)(x + 5)
By cancelling out common terms in the numerator and denominator, we have
x(x + 5) + 3(x + 4) = x + 2
We would expand the parentheses on both sides by multiplying the terms inside with the term outside. It becomes
x^2 + 5x + 3x + 12 = x + 2
By collecting like terms, we have
x^2 + 5x + 3x - x + 12 - 2 = 0
x^2 + 7x + 12 = 0
Again, We would find two terms such that their sum or difference is 7x and their product is 12x^2. The terms are 4x and 3x. Replacing 7x with 4x and 3x, it becomes
x^2 + 4x + 3x + 12 = 0
By factorising, it becomes
x(x + 4) + 3(x + 4) = 0
Since x + 4 is common, it becomes
(x + 3)(x + 4) = 0
x + 3 = 0 or x + 4 = 0
x = - 3 or x = - 4
The solutions are x = - 3 or x = - 4
Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv
Answers
ANSWERS
• x = 5
,• m∠ZVW = 46°
,• m∠ZWV = 41°
EXPLANATION
The diagonals of a parallelogram bisect each other, so
[tex]11=5x+1[/tex]To find x subtract 1 from both sides of the equation,
[tex]\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}[/tex]Hence x = 5
By the SAS property, triangle VZW and XZY are congruent:
Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,
[tex]\angle ZVW\cong\angle\text{ZXY}[/tex][tex]m\angle ZVW=46[/tex]It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,
[tex]\angle\text{ZWV}\cong\angle\text{ZYX}[/tex][tex]m\angle ZWV=41[/tex]1. How is the orientation of the triangie affected by the translation?
Answers
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
ABC High School is debating whether or not to write a policywhere all students musthave uniforms and wear them during school hours. In a survey,45% of the studentswanted uniforms, and 55% did not.Calculate the probability that a person selected at random fromABC High School will want the school to have uniforms or willnot want the school to have uniforms.
Answers
If 45% don't want uniforms, it means that 45 out of 100 students don't want them, so the probability is 45/100 = 9/20
And 55% want unifrms, so the probability = 55/100 = 11/20
What should you multiply the first equation (top equation) by in order to eliminate the variable y when the two equations are added together? {x+2y=5{3x-4y=8
Answers
2
Explanationgiven
[tex]\begin{gathered} x+2y\rightarrow equation(1) \\ 3x-4y=8\rightarrow equation(2) \end{gathered}[/tex]Step 1
a) to eliminate the y variable we have
[tex]\begin{gathered} 2y \\ -4y \end{gathered}[/tex]in order to be eliminated both terms must have the same value and different sign,in other words the addition must equla zero, so weed a number (a) that makes the term from teh first equation equals (4y)
so
[tex]\begin{gathered} (2y*a)-4y=0 \\ 2ay=4y \\ so \\ 2a=4 \\ divide\text{ both sides by 2} \\ \frac{2a}{2}=\frac{4}{2} \\ a=2 \end{gathered}[/tex]therefore, the first equation should be multiplied by 2
I hope this helps you
Enter your answer, rounded to the nearest tenth, in the box.
Answers
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
use the diagram at the right name the following three points ray
Answers
From the geometric diagram below
(1) Three diagram
[tex]\text{ Points JQE is a 3 points}[/tex](2) A ray
[tex]RP\text{ is a ray}[/tex](3) Two intersecting lines but not perpendicular
[tex]\text{ line RF and line NI are the two intersecting lines but not perpendicular}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q17
Answers
Solution:
Given the image;
Thus, there is a local maximum at;
[tex]x=-2[/tex]CORRECT OPTION: Yes
The local maximum is;
[tex]y=4[/tex]solve for tangent x= -1 in radians without a calculator
Answers
Answer:
[tex]x\text{ = }\frac{3}{4}\pi\text{ or }\frac{7}{4}\pi[/tex]Explanation:
Here, we want to calculate the value of x without using a calculator
We have to look for the quadrants where the tan is negative
These are the second and the fourth quadrant
On the second quadrant, we have the reference angles as:
[tex]180-x[/tex]Mathematically in degrees:
[tex]\begin{gathered} \text{if tan x = 1} \\ x\text{ = 45 deg} \end{gathered}[/tex]Now, on the second quadrant, we have it that:
[tex]180-45\text{ = 135 deg}[/tex]On the fourth quadrant, we have the reference angle calculated as:
[tex]\begin{gathered} 360-\theta \\ \theta\text{ = 360-45} \\ \theta\text{ = 315 deg} \end{gathered}[/tex]Lastly, we have to convert these angles to radians
Mathematically, 1 pi is 180 degrees:
[tex]\begin{gathered} 1\text{ }\pi=\text{ 180 deg} \\ x\text{ = 135 deg} \\ x\text{ = }\frac{135\pi}{180}\text{ = }\frac{3}{4}\pi \\ \\ \text{Lastly:} \\ 1\pi\text{ = 180 deg} \\ x\text{ = 315 deg } \\ \\ x\text{ = }\frac{315}{180}\pi\text{ = }\frac{7}{4}\pi \end{gathered}[/tex]the perimeter of a square box is 12x + 32 drag number to complete an equivalent expression that shows the premier has four times the side length of the box
Answers
The perimeter of the box is given as
12x + 32
To write an equivalent expression that shows the premier has four times the side length of the box , we would factorise the expression. It becomes
4(12x/4 + 32/4)
= 4(3x + 8
The ages (in years) of the 6 employees at a particular computer store are the following.31, 41, 35, 22, 38, 31Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)
Answers
The standard deviation of the population = 6.08
Explanations:The given ages of the employers are:
31, 41, 35, 22, 38, 31
Find the mean of the dataset:
[tex]\begin{gathered} \mu\text{ = }\frac{\sum ^{}_{}x_i}{N} \\ \mu\text{ = }\frac{31+41+35+22+38+31}{6} \\ \mu\text{ = }\frac{198}{6} \\ \mu\text{ = }33 \end{gathered}[/tex]Find the summation of the square of each deviation from the mean
[tex]\begin{gathered} \sum ^6_{i\mathop=0}(x_i-\mu)^2=(31-33)^2+(41-33)^2+(35-33)^2+(22-33)^2+(38-33)^2+(31-33)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=(-2)^2+(8)^2+(2)^2+(-11)^2+(5)^2+(-2)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=4+64+4+121+25+4 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=222 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{222}{6}} \\ \sigma\text{ = }\sqrt[]{37} \\ \sigma\text{ = }6.08 \end{gathered}[/tex]The standard deviation of the population = 6.08 (rounded to 2 decimal places)
change this standard form equation into slope intercept form 6x - 2y=-8
Answers
we have the equation
6x-2y=-8
Convert to slope-intercept form
y=mx+b
so
Isolate the variable y
step 1
Adds 2y both sides
6x-2y+2y=-8+2y
6x=-8+2y
step 2
Adds 8 both sides
6x+8=-8+2y+8
6x+8=2y
step 3
Divide by 2 both sides
3x+4=y
rewrite
y=3x+4its asking for the approximate depth of the river. but I don't know how to determine that
Answers
From figure, trngles VWX and VYZ are similar.
So, the ratio of corresponding sides of triangles will be equal. Hence,
[tex]\begin{gathered} \frac{VW}{VY}=\frac{WX}{YZ} \\ \frac{3}{62}=\frac{5}{d} \\ d=\frac{5\times62}{3} \\ =103.3\text{ m} \end{gathered}[/tex]Therefore, the approximate depth of the river is d=103.3 m.
The local weather report states that there is 3/5 a chance of rain today, but it is more likely to rain tommorrow than today. What is a possible probability of rain for tommorrow? A.0.4 B. 0.5 I C. 0.6 D. 0.7
Answers
D. 0.7
Explanations:Probability is the chance (likelihood) that an event will take place
The probabilty that it will rain today = 3/5 = 0.6
There is more likelihood that it will rain tomorrow that today.
This means that the probabilty that it will rain tomorro is greater than the probability that it will rain today.
Therefore, the probability of rain tomorrow is more than 0.6
Only option D (0.7) is greater than 0.6, and it is the only correct choice
3. What is the domain of the relation described by the set of ordered pairs {(-2, 8), (-1, 1), (0, 0), (3, 5), (4, -2)}?{-2, -1, 0, 4,5){-2, 0, 1, 5, 8}{-2, -1,0,3,4}{-2, -1, 0, 1,5}
Answers
The domain is related to x axis coordinates. So, you have to take the x coordinate of each point
-2,-1,0,3,4
Michael is constructing a boat ramp. He knows that the angle of elevation of the ramp is 30°. If the distance from the bottom of the boat ramp to the top of the boat ramp is 40 feet, what is the height of the boat ramp?
Answers
Let's draw a rough figure:
Here, h is the distance we are solving for.
Now,
With respect to the given angle 30 degrees, we have the hypotenuse and want to find the opposite side.
The trig ratio relating opposite side and hypotenuse is SINE.
Thus, we can write:
[tex]\sin (30)=\frac{opposite}{\text{hypotenuse}}=\frac{h}{40}[/tex]Cross multiiplying, we solve for h [remember, value of sin(30) is 1/2]:
[tex]\begin{gathered} \sin (30)=\frac{h}{40} \\ h=40\times\sin (30) \\ h=40\times\frac{1}{2} \\ h=20 \end{gathered}[/tex]The height of the boat ramp is 20 feet.
2 points Bob flips a coin. He also spins the pointer on the spinner shown below. What is the probability that Bob flips the coin so that it lands tails up and spins the pointer so it stops on the letter R? * N E Your answer
Answers
Answer: 1/16 = 0.0625
Step by step solution:
The probability (P) of an event happening is
[tex]P=\frac{Numbe\text{r of ways it can happen}}{Total\text{ number of outcomes}}[/tex]When Bob flips the coin he has two options, head or tail. The probability that it lands tails up is:
[tex]P=\frac{1}{2}[/tex]The probability that the pointer stops on the letter R is:
[tex]P=\frac{1}{8}[/tex]Now, the probability of both events happening (tails up and pointer on R) is:
[tex]P=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}=0.0625[/tex]Solve the following equation.
(√x -7) (√x -2)= -18
Answers
Answer:NO SOLUTION
Step-by-step explanation:
During a lab Jill made a solution that was 3% water. Rewrite this percent as a fraction in simplest form.
Answers
Solve the quadratic equations in questions 1 – 5 by factoring.1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 5
Answers
Given:
There are given the equation:
[tex]-x^3+22x^2-121x=0[/tex]Explanation:
According to the question:
We need to find the value of x by using the factoring:
S0,
From the equation:
[tex]-x^{3}+22x^{2}-121x=0[/tex]Tthen,
[tex]\begin{gathered} -x^{3}+22x^{2}-121x=0 \\ -x(x^2-22x+121)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} -x(x^2-22x+121)=0 \\ x(x-11)^2=0 \\ x=0; \\ x-11=0 \\ x=11 \end{gathered}[/tex]Final answer:
Hence, the value of x by using factor method is shown below:
[tex]x=0,11[/tex])Mr. Nacarrato and his family are going on a road trip that is
2457 miles long. They have already driven 128 53/100 miles
How much further do they have to drive?
Answers
They need to go further 2328.47 miles distance.
What is improper fraction and mixed fraction?
A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances.
Here the road trip is 2457 miles long .
They already drive 128 [tex]\frac{53}{100}[/tex] miles.
That is in mixed fraction , we need to convert them in improper fraction , then,
=> 128 [tex]\frac{53}{100}[/tex] = [tex]\frac{128*100+53}{100}= \frac{12853}{100}[/tex]
Now we need to subtract them from total distance then ,
=> 2457 - [tex]\frac{12853}{100}[/tex]
=> [tex]\frac{2457*100-12853}{100}[/tex]
=> [tex]\frac{245700-12853}{100}[/tex]
=> 2328.47 miles.
They need to go further 2328.47 miles.
To learn more about improper fraction and mixed fraction
https://brainly.com/question/1055953
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Harold and Harry both rented cars from Hurry Up Motors. Harold rented his car for 6 days andwas charged $194. Harry rented his car for 3 days and was charged $122. Choose theequation that represents y, the rental cost, in terms of x, the days of the rental.
Answers
Step 1:
Write the coordinates in terms of cost and number of days.
( cost , days )
Step 2
( 3 , 122 ) and ( 6, 194)
Step 3:
Find the slope
[tex]\begin{gathered} \text{Slope m = }\frac{y_2-y_1}{x_2-x_1} \\ x_1\text{ = 3} \\ y_1\text{ = 122} \\ x_2\text{ = 6} \\ y_2\text{ = 194} \\ m\text{ = }\frac{194\text{ - 122}}{6\text{ - 3}} \\ m\text{ = }\frac{72}{3} \\ m\text{ = 24} \end{gathered}[/tex]Step 4
Find the equation using the slope m and point 1
[tex]\begin{gathered} m\text{ = }\frac{y-y_1}{x-x_1} \\ 24\text{ = }\frac{y\text{ - 122}}{x\text{ - 3}} \\ \text{y - 122 = 24(x - 3)} \\ \text{y - 122 = 24x - 72} \\ y\text{ = 24x - 72 + 122} \\ y\text{ = 24x + 50} \end{gathered}[/tex]Final answer
The equation is y = 24x + 50
Use the spinner shown in the figure below to find the probability indicated.Landing on green or a consonant
Answers
Based on the spinner, there are a total of 8 possible outcomes.
2 of which are green and 4 are consonants, however, 1 outcome is both consonant and a green (F green).
Therefore, the probability of landing on a green or consonant is:
[tex]\begin{gathered} P(A\text{ or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=\frac{2}{8}+\frac{4}{8}-\frac{1}{8} \\ P(A\text{ or B)}=\frac{5}{8} \end{gathered}[/tex]The probability of landing on a green or consonant is 5/8 or 62.5%.
Answer each part. If necessary, round your answers to the nearest hundredth.(a) Abdul runs 3 miles in 17 minutes.How many miles does he run per minute?I miles per minute(b) It takes 37 pounds of seed to completely plant a 4-acre field.How many pounds of seed are needed per acre?pounds per acre
Answers
To determine the speed of Abdul, we can divide 3 miles by 17 minutes.
[tex]\frac{3mi}{17\min}=\frac{0.17647mi}{\min}\approx\frac{0.18mi}{\min }[/tex]Therefore, Abdul runs approximately 0.18 miles per minute.