Answers
You would set this up as a proportion with 8 being a geometric mean giving you an equation that looks like this (x/8=8/20)
The correct answer is C) 3.0. The value of [tex]x[/tex] is 3.0.
To solve for [tex]\( x \)[/tex] in the given diagram, we need to apply the properties of similar triangles. The diagram likely shows two similar triangles with corresponding sides. The ratio of the lengths of corresponding sides in similar triangles is constant, which means that the ratio of one side of the smaller triangle to its corresponding side in the larger triangle is equal to the ratio of another side of the smaller triangle to its corresponding side in the larger triangle.
Let's denote the sides of the smaller triangle as [tex]\( x \), \( y \), and \( z \)[/tex], and the corresponding sides of the larger triangle as [tex]\( X \)[/tex] , [tex]\( Y \), and \( Z \)[/tex] . Given that the triangles are similar, we have the following proportion:
[tex]\[ \frac{x}{X} = \frac{y}{Y} = \frac{z}{Z} \][/tex]
From the question, we are given the lengths of some of these sides. Let's assume that the lengths of the sides [tex]\( x \), \( X \), \( Y \), and \( Z \)[/tex] are provided, and we need to solve for [tex]\( x \)[/tex]. We can use the proportion involving [tex]\( x \)[/tex] and [tex]\( X \)[/tex] as well as [tex]\( Y \) and \( Z \)[/tex] to set up an equation:
[tex]\[ \frac{x}{X} = \frac{Y}{Z} \][/tex]
To solve for [tex]\( x \)[/tex], we multiply both sides of the equation by [tex]X[/tex]:
[tex]\[ x = \frac{Y}{Z} \cdot X \][/tex]
Now, we need to plug in the values for [tex]\( Y \), \( Z \),[/tex] and that [tex]\( X \)[/tex]are given in the diagram. Since the actual values are not provided in the conversation, we will assume that the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as a ratio, and [tex]\( X \)[/tex] is a single value. By multiplying this ratio by [tex]\( X \)[/tex] , we can find [tex]\( x \)[/tex].
Let's assume the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as [tex]\( \frac{3}{4} \)[/tex] and [tex]\( X \)[/tex] is given as 4. Then we have:
[tex]\[ x = \frac{3}{4} \cdot 4 \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, [tex]\( x \)[/tex] is 3.0, which corresponds to option C.
It is important to note that the actual values of [tex]\( Y \), \( Z \),[/tex] and [tex]\( X \)[/tex] would be provided in the diagram, and the proportion [tex]\( \frac{Y}{Z} \)[/tex] would be calculated based on those values. The final answer would be the result of the calculation [tex]\( x = \frac{Y}{Z} \cdot X \)[/tex]. In this case, the calculation led to the answer 3.0, which matches option C.
Related Questions
What is the value of "c" in the quadratic equation 3x2 + 5x + 7 = 0?
Answers
Answer:
Last option: 7
Step-by-step explanation:
The Standard form of a quadratic equation is the following:
[tex]ax^{2}+bx+c=0[/tex]
Where "a" is the quadratic coefficient (This coefficient cannot be 0), "b" is the linear coefficient, "c" is the constant and "x" is the variable.
In this case you have the quadratic equation [tex]3x^2 + 5x + 7 = 0[/tex] which is written is Standarf form. Then, you can identify that:
[tex]a=3\\b=5\\c=7[/tex]
Therefore the value of "c" is 7.
What is the approximate value of x in the equation below.
Answers
Answer: First Option
[tex]x= -3.396[/tex]
Step-by-step explanation:
We have the following expression
[tex]log_{\frac{3}{4}}25 = 3x -1[/tex]
To solve the equation add 1 to both sides of the equality
[tex]log_{\frac{3}{4}}25 +1= 3x -1+1[/tex]
[tex]log_{\frac{3}{4}}25 +1= 3x[/tex]
Divide between 3 to both sides of the equation
[tex]\frac{log_{\frac{3}{4}}25 +1}{3}= x[/tex]
[tex]x= \frac{-11.19 +1}{3}[/tex]
[tex]x= -3.396[/tex]
The answer is the first option
How many solutions can be found for the equation 3x − 2 = 3x + 5?
a)zero
b)one
c)two
d)infinitely manyHow many solutions can be found for the equation 3x − 2 = 3x + 5?
Answers
Answer:
Zero
Step-by-step explanation:
there is no solution the sides are uneven. if you solve for it 3x and 3x cancels out each other leaving you with -2=5
Answer:
Zero
Step-by-step explanation:
Periodt
Solve for x 10x+5=6x+25
Answers
Hello
Good Luck
Goodbye ♥
Answer:
x=5
Step-by-step explanation:
10x+5=6x+25
10x=6x+25-5
10x-6x=25-5
4x=20
x=5
GOOD LUCK ! ;)
cos40°+sin40°/cos40°-sin40°
Answers
Step-by-step explanation:
0.76+0.64/0.76-0.64
1.40/0.12
11.66
is the answer
Answer:
11.4300523
Step-by-step explanation:
cos 40° = 0.7660444431
sin 40° = 0.6427876097
cos 40° + sin 40° = 1.408832053
cos 40° - sin 40° = 0.1232568334
1.408832053 ÷ 0.1232568334 = 11.4300523
What is the ordered pair of M after point M (5,6) is rotated 90 clockwise
Answers
(5,6) -> (6,-5)
Hope this helps!
Final answer:
The ordered pair of M after rotating 90 degrees clockwise is (-6,5).
Explanation:
When a point undergoes a 90-degree clockwise rotation around the origin, a distinct transformation occurs. Specifically, the x-coordinate of the original point becomes the negative value of its original y-coordinate, and the y-coordinate takes on the positive value of the original x-coordinate. This geometric operation is fundamental in transforming coordinates.
Taking point M(5,6) as an example, after the 90-degree clockwise rotation, the new coordinates manifest as (-6,5). This rotation plays a crucial role in various mathematical and geometric applications, contributing to the understanding of spatial transformations and coordinate systems.
What is the factored form of x^12y^18+1?
Answers
Answer:
[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].
Step-by-step explanation:
We want to expand: [tex]x^{12}y^{18}+1[/tex].
We can rewrite this as the sum of two cubes.
[tex](x^{4})^3(y^{6})^3+1=(x^{4}y^{6})^3+1^3[/tex].
Recall and use the sum of cubes identity: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
By comparing our newly rewritten expression to this identity, we have [tex]a=x^4y^6[/tex] and [tex]b=1[/tex].
We substitute into the identity to get:
[tex](x^{4}y^{6})^3+1^3=[x^{4}y^{6}+1][(x^{4}y^{6})^2-(x^{4}y^{6})(1)+1^2][/tex].
We now use this rule of exponents :[tex](a^m)^n=a^{mn}[/tex] to get;
[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].
A company makes glass lawn ornaments with a radius of 9 inches. The glass to make the balls costs the company $0.03 per square inch. To the nearest cent, how much does the company pay for the glass to create one ornament?
Answers
Answer:
$7.63
Step-by-step explanation:
We are given:
r=9 icnhes
We have to find the area of the circular ornament first. The formula for area of circle is:
Area= πr^2
Putting the value of r
Area=3.14*(9)^2
=3.14*81
=254.34 Square inches
As the company pays $0.03 for 1 square inch, for 254.34 square inch the company will have to pay:
=254.34*0.03
=$7.6302
Rounding off to the nearest cent
The cost for one ornament = $7.63
Answer:
$30.52
Step-by-step explanation:
4 x 9^2 x 3.14 x 0.03 = around 30.52
what is the slope of the line shown below (-3,1) (5,1)
Answers
Answer:
A. 1/4
Step-by-step explanation:
The line is upwards so slope will be positive. (either A or C will be the answer)
Now to solve for slope to find out
Two coordinate points on graph (-3,-1) ad (5,1)
Slope = (y2 - y1)/(x2 - x1)
Slope = (1 + 1)/(5 + 3) = 2/8 = 1/4
Answer:
[tex]A.\frac{1}{4}[/tex]
Step-by-step explanation:
Hello, I think I can help you with this
The slope is the inclination of the line with respect to the abscissa axis, if you know two points it can be calculated using
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\[/tex]
where
[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})[/tex]
Step 1
put the values into the equation
Let
[tex]P1(-3,-1) \\P2(5,1)\\\\m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\m=\frac{1-(-1)}{5-(-3) } \\m=\frac{1+1}{5+3} \\m=\frac{2}{8} \\m=\frac{1}{4}[/tex]
Have a great day
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answers
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{5}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{5}{4}\implies \cfrac{5}{4}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-0}{2-(-2)}\implies \cfrac{5}{2+2}\implies \cfrac{5}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-1)}{10-2}\implies \cfrac{9+1}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]
Answer: Im pretty sure it answer options 1 and 5
Step-by-step explanation: 1) (-2,0) and (2,5) 5) (2,-1) and (10,9)
its on edg.
What is 726,034 rounded to the nearest ten thousand
Answers
Answer:730000
Step-by-step explanation:
Follow below steps;
To round the number 726,034 to the nearest ten thousand, we must look at the thousands digit, which is 2. Since 2 is less than 5, we do not round up, and thus, leave the ten thousands place as it is.
The number 726,034 rounded to the nearest ten thousand is 720,000. We can see that the thousand's digit is less than 5, so we round down. This process aligns with the rounding rule stating that if the number you are rounding is followed by 0, 1, 2, 3, or 4, you round the number down.
A sphere has a surface area of 12 π square inches. What is it’s exact radius?
Answers
Answer:
sqrt(3)
Step-by-step explanation:
Surface area of a sphere = 4pi(r)^2
Solve for r
Which set of side lengths forms a right triangle 2,3,13 4,6,10 9,12,18 15,36,39
Answers
Answer:
15,36,39
Step-by-step explanation:
primitive pythag: 5, 12, 13 *3
Answer:
The Answer is D
Step-by-step explanation:
Do you think that there is a rule you could use to predict the number of times your heart would beat in 15 seconds after you did 100 jumping jacks? Explain your answer.
Answers
Answer:
Yes
Step-by-step explanation:
The more you jump, the higher your blood flow becomes, since your heart needs to pump more blood to the working areas. This really doesn't belong in math though.
Answer: yes
Step-by-step explanation: but i am not that sure how i can explain it, here look at the guys answer above. Also thank the guy above, not me.
the burj khalifa a building in dubai united arab emirates is about 828 meters tall
Answers
Answer:
true
Step-by-step explanation:
Historians generally begin forming historical arguments in order to:
Answers
This is because they want to make sure their possible answers are correct, reliable and accurate.
Answer:
D. offer possible answers to historical questions.
Step-by-step explanation:
An argument is a statement which a historian proposes. In order to back up the statement the historian provides proof. The argument is then read by other historians and the proof is analyzed. After the analysis if other historians come to the same conclusion which the statement points to then the argument is accepted.
So, this is the way to offer possible answers to historical questions.
Please refer to
This kind of transformation can change the
the lengths of some or all of the sides
the area of the shape
both a and b
Answers
Answer:
Both a and b
Step-by-step explanation:
Which of the following best describes a ratio?
A. An expression that contains a radical sign
B. The cross product of two fractions
C. A comparison of two numbers
D. The inverse operation for multiplication
Answers
The best way to describe a ratio is option c, which is 'A comparison of two numbers'.
What is Ratio?A ratio shows us the number of times a number contains another number. therefore, it helps us to compare two numbers.
Which of the following best describes a ratio?As we have already discussed the ratio is the comparison of two numbers for a particular.
Hence, the best way to describe a ratio is option c, which is 'A comparison of two numbers'.
Learn more about Ratio:
https://brainly.com/question/1504221
for f(x) equal 3x+1 and g(x) equal x-6 find (f - g) (x)
Answers
Answer:
2x + 7
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x) = 3x + 1 - (x - 6) = 3x + 1 - x + 6 = 2x + 7
Where does the graph of y = –3x – 18 intersect the x-axis?
Question 16 options:
a)
(6,0)
b)
(-6,0)
c)
(0,-6)
d)
(0,6)
Answers
Answer:
b) (-6, 0)
Step-by-step explanation:
The quickest method to use is to put "0" in for y, then figure out which term for x would make the equation authentic, or genuine.
This photo 2 of This question read it and find out what is The difference in feet between The Minimum and Maximum heights of a car on The ferris wheel
Answers
Answer:
From the looks of things, it seems to be 140 ft, the maximum height being 150 ft and the minimum height being 10 ft. Find the difference, and that should be your answer :)
Answer:C 140
Step-by-step explanation:
Find three consecutive even integers whose sum is −24
Answers
For this case we have that the sum of 3 consecutive integers is 24, if we represent by means of an equation we have:
[tex]x + (x + 2) + (x + 4) = - 24\\x + x + 2 + x + 4 = -24\\3x + 6 = -24\\3x = -24-6\\x = \frac {-30} {3}\\x = -10[/tex]
Thus, the three consecutive numbers are:
[tex]x = -10\\x = -10 + 2= -8\\x = -10 + 4 = -6[/tex]
Answer:
-10,-8,-6
Answer: [tex]-10,-8,-6[/tex]
Step-by-step explanation:
Let be:
[tex]x[/tex], [tex]x+2[/tex] and [tex]x+4[/tex] the three consecutive even integers whose sum is -24
Then, we can write this expression:
[tex]x+(x+2)+(x+4)=-24[/tex]
Now, we must solve for "x":
[tex]3x+6=-24\\\\3x=-24-6\\\\3x=-30\\\\x=\frac{-30}{3}\\\\x=-10[/tex]
Then you get that the others integers are:
[tex]x+2=-10+2=-8[/tex]
[tex]x+4=-10+4=-6[/tex]
Therefore, the three consecutive even integers whose sum is -24 are:
[tex]-10,-8,-6[/tex]
choose all of the perfect squares 196 256 390 484 564
Answers
Answer:
{196, 256, 484}
Step-by-step explanation:
14² = 196;
16² = 256;
19² = 361; 390 lies between 361 and 400, and is thus NOT a perfect square;
20² = 400;
22² = 484
564 lies between the two perfect squares 23² and 24², but is itself NOT a perfect square.
Thus, the perfect squares are {196, 256, 484}
The perfect squares out of the numbers 196, 256, 390, 484, 564 are 196, 256, and 484. A perfect square is a number that can be expressed as an integer multiplied by itself.
Explanation:The perfect squares from the list you provided are: 196, 256, and 484. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 256 is a perfect square because it can be expressed as 16 times 16, or 16^2. Similarly, 196 and 484 are perfect squares as they can be expressed as 14^2 and 22^2, respectively. On the other hand, numbers 390 and 564 are not perfect squares as they cannot be expressed as the product of an integer with itself.
Learn more about Perfect Squares here:https://brainly.com/question/13521012
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State the various transformations applied to the base function ƒ(x) = x^2 to obtain a graph of the function g(x) = −2[(x − 1)^2 + 3].
(A) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.
(B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
(C) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
(D) A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.
Answers
Answer: Option B
A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
Step-by-step explanation:
If the graph of the function [tex]g(x)=cf(h-h) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] the graph moves vertically upwards b units.
If [tex]b <0[/tex] the graph moves vertically down b units
If [tex]h> 0[/tex] then the graph of f(x) moves horizontally h units to the left
If [tex]h <0[/tex] then the graph of f(x) moves horizontally h units to the right
In this problem we have the function [tex]g(x) = -2((x - 1)^2 + 3)[/tex] and our parent function is [tex]f(x) = x^2[/tex]
therefore it is true that [tex]c =-2<0[/tex] and [tex]b =-6 <0[/tex] and [tex]h=-1<0[/tex]
Therefore the graph is reflected on the x axis, stretched vertically by a factor 2. The graph of f(x) moves horizontally 1 units to the right and shift downward of 6 units.
The answer is (B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.
Final answer:
The correct transformations from f(x) = x² to g(x) = −2[(x − 1)² + 3] are a reflection about the x-axis, a vertical stretch by 2, a horizontal shift 1 unit to the right, and a vertical shift 3 units upwards, which is option (B) in the list provided.
Explanation:
The function g(x) = −2[(x − 1)² + 3] has undergone several transformations from the base function f(x) = x^2. These transformations include a reflection about the x-axis due to the negative sign in front of the equation, indicating that a flip has happened vertically. A vertical stretch by a factor of 2 is also evident from the coefficient 2 before the parenthesis.
The term (x - 1) inside the parenthesis indicates a horizontal shift of 1 unit to the right since we subtract from x to move the graph to the right. Lastly, the +3 at the end of the equation signifies a vertical shift of 3 units upwards, which is a change in the y-value of every point on the graph.
Therefore, the correct sequence of transformations to obtain g(x) from f(x) is: a reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift of 3 units upwards, which corresponds to option (B) provided by the student.
What is the value of x in the equation −x = 4 − 3x + 6?
5
10
−5
−10
Answers
−x = 4 − 3x + 6
Move the -3x to the other side and simplify 4+6.
2x= 10
Divide both sides by 2
x=5.
Answer: First option.
Step-by-step explanation:
Given the equation [tex]-x = 4- 3x + 6[/tex], you need to solve for the variable "x" to find its value.
Add the like terms on the right side of the equation:
[tex]-x = 10-3x [/tex]
Now you need to subtract 10 from both sides of the equation:
[tex]-x-10 = 10- 3x -10[/tex]
[tex]-x-10 =- 3x[/tex]
The next step is to add "x" to both sides of the equation:
[tex]-x-10+x = - 3x +x[/tex]
[tex]-10 = - 2x[/tex]
And finally, divide both side by -2:
[tex]\frac{-10}{-2}=\frac{-2x}{-2}\\\\x=5[/tex]
what is the inverse of f(x) = -5x-4
Answers
Answer:
[tex]\displaystyle f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}[/tex].
Step-by-step explanation:
The question has provided an expression for the function [tex]f(x)[/tex] and is asking for its inverse, [tex]f^{-1}(x)[/tex].
Based on the definition of inverse functions,
[tex]f(f^{-1}(x)) = x[/tex].
Let [tex]y = f^{-1}(x)[/tex].
[tex]f(y) = x[/tex].
[tex]-5 y - 4= x[/tex].
Solve this equation for [tex]f^{-1}(x) = y[/tex]:
[tex]-5y = x +4[/tex].
[tex]\displaystyle y = (-\frac{1}{5})\cdot (x + 4) = -\frac{x}{5} -\frac{4}{5}[/tex].
However, [tex]f^{-1}(x)=y[/tex] As a result,
[tex]\displaystyle f^{-1}(x) = -\frac{x}{5} -\frac{4}{5}[/tex].
Answer:
[tex]\large\boxed{f^{-1}(x)=-\dfrac{x+4}{5}}[/tex]
Step-by-step explanation:
[tex]f(x)=-5x-4\to y=-5x-4\\\\\text{Exchange x to y and vice versa:}\\\\x=-5y-4\\\\\text{Solve for}\ y:\\\\-5y-4=x\qquad\text{add 4 to both sides}\\\\-5y=x+4\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5y}{-5}=\dfrac{x+4}{-5}\\\\y=-\dfrac{x+4}{5}[/tex]
3004 wk how many years rounded to the nearest thousandth
Answers
Answer:
1 year = 52 weeks.
Divide total weeks by 52 to get total years.
Nearest Thousandth would be 3 decimal places.
3004 weeks / 52 weeks per year = 57.769 years.
Answer:
57.769
Step-by-step explanation:
There are 52 weekends in one year
3004 divided by 52 = 57.7692
Round to the nearest thousandth 57.769
Find the area of the shaded region of the trapezoid.
Answers
Answer:
36
Step-by-step explanation:
area of trapezium is (1/2)×(6+9)×8=60
area of triangle is (1/2)×6×8=24
area of shaded =60 - 24 =36
The area of the shaded region of the trapezoid is 36.
area of trapezium is (1/2)×(6+9)×8=60
area of triangle is (1/2)×6×8=24
area of shaded =60 - 24 =36
Which makes the statement true?
Answers
Answer:
3/11 + 5 5/8 > 5 6/8
Step-by-step explanation:
find the LCD's for both sides of the comparison. After this, add fractions from the same side of the comparison. Then, you must compare the two and check your answer. Have a nice day!
which statement is true