Hiro is creating a larger scaled replica of a triangular canvas.
triangles ABE and ACD on a coordinate plane with point A at 1 comma 0, point C at 2 comma 3 and point D at 5 comma 0, point B is between points A and C and point E is between points A and D
Which of the following expressions will help him determine the length of segment AC?
AC = AD
AC = AB
AC equals AD times AB over AE
AC equals AD times AC over AB
Answers
Answer:
C - AC equals AD times AB over AE
Step-by-step explanation:
If Hiro is creating a larger scaled replica of a triangular canvas, then Hiro will get two similar triangles ABE (the small one) and ACD (the large one). Similar triangles have proportional corresponding sides, so
[tex]\dfrac{AC}{AB}=\dfrac{AD}{AE}[/tex]
From this proportion:
[tex]AC=\dfrac{AD\cdot AB}{AE}[/tex]
So, option C (AC equals AD times AB over AE) is correct option
Related Questions
Consider the binomial 4x3 – 32. Is there a GCF > 1 for the two terms? The completely factored form of this polynomial is (x2 + 2x + 4).
Answers
Answer:
Yes there is GCF > 1 ⇒ (GCF = 4)
The completely factored form is 4(x - 2)(x² + 2x + 4)
Step-by-step explanation:
* Lets find the greatest common factor of the two terms
- The binomial is 4x³ - 32
- The terms of the binomial are 4x³ and 32
- The greatest common factor of 4 and 32 is 4 because both of them
can divided by 4
∵ 4x³ ÷ 4 = x³
∵ 32 ÷ 4 = 8
∴ The greatest common factor GCF is 4
∴ 4x³ - 32 = 4(x³ - 8)
* Yes there is GCF > 1
# x³ - 8 is the difference of two cubs, it can factorize it into two
brackets
- The first bracket has cube root of x³ and cube root of 8
- The second bracket comes from the first bracket it has three terms
# The 1st term is square the 1st term in the first bracket
# The 2nd term is the product of the 1st term and the 2nd term of the
1st bracket with opposite sign of the 2nd term in the 1st bracket
# The 3rd term is the square of the 2nd term in the 1st bracket
* Lets do these steps with x³ - 8
∵ The first bracket = (∛x³ - ∛8)
∵ ∛x³ = x and ∛8 = 2
∴ The first bracket = (∛x³ - ∛8) = (x - 2)
- Lets make the 2nd bracket from the 1st bracket
∴ The second bracket = (x² + (x)(2) + 2²)
∴ The second bracket = (x² + 2x + 4)
∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)
* The completely factored form is 4(x - 2)(x² + 2x + 4)
Answer:
....Yes it is 4 ....4(x-2)
Step-by-step explanation:
the screenshot shows proof :))
If two angles of a triangle are acute then what is the third angle
Answers
The third angle would have to be either an obtuse angle or a right angle.
The third angle can either be an acute angle or obtuse angle
The sum of an interior angle of a triangle is 180 degrees
Acute angles are angles that are less than 90 degrees. If the two angles of a triangle are acute, the two angles can be 30 and 45 degrees
If the third angle is m<C
m<C = 180 - (30 + 45)
m<C = 180 - 75
m<C = 105 degrees
Since the angle is greater than 90 and less than 180, hence it is an Obtuse angle.
Similarly, if the two angles of a triangle are acute, the two angles can be 30 and 89 degrees
If the third angle is m<D
m<D = 180 - (30 + 90)
m<D = 180 - 119
m<D = 61 degrees
Since the angle is less than 90degrees, hence it is an acute angle.
This shows that the third angle can either be an acute angle or obtuse angle
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The graph above shows Carmel's distance from home over a one-hour period, during which time he first went to the library, then went to the grocery store, and then returned home. Which of the following statements could be true?
A) The grocery store is about 5 miles from Carmel's house.
B) Carmel traveled a total of 7 miles from the time he left home until he returned.
C) The grocery store is 7 miles farther from Carmel's house than the library is.
D) Carmel spent 10 minutes at the library and 15 minutes at the grocery store.
Answers
Answer:
D
Step-by-step explanation:
From the graph we can see:
The library is 5 miles from home (upward sloping line)He spends 10 minutes at library (sraight line for 10 minutes)The grocery store is 2 miles from library , hence 7 miles from homeHe spends 15 minutes at grocery store (straight line for 15 minutes)Returns back home (7 miles)Given the information extract, we can rule out A, B, and C immediately. Answer choice D is right.
Use long division or synthetic division to find the quotient of 2x^3+x^2+1 / x+1
Answers
Answer:
The quotient is 2x^2 - x + 1.
Step-by-step explanation:
If x + 1 is the divisor in long division, then -1 is the divisor in synthetic division:
-1 / 2 1 0 1
-2 1 -1
----------------------
2 -1 1 0
The quotient is 2x^2 - x + 1. The coefficients were obtained through synthetic division.
Factor the following expression completely. 16x^5-x^3
A.
B.
C.
D.
Answers
Answer:
x^3(2x+1)(2x-1)
Step-by-step explanation:
first take common then use formula of a^2-b^2
Answer:
The factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]16x^5-x^3[/tex]
Here the Greatest common factor in the above expression is x³.
The above expression can be written as:
[tex]x^3(16x^2-1)[/tex]
[tex]x^3((4x)^2-1^2)[/tex]
Now use the difference of the square property: [tex]a^2-b^2=(a+b)(a-b)[/tex]
By using the above property we can rewrite the provided expression as shown:
[tex]x^3(4x-1)(4x+1)[/tex]
Hence, the factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]
Two angles are supplementary if their sum is 180 degrees. One angle measures three times the measure of a smaller angle. If X represents the measure of the smaller. Angle and these two angles are supplementary, find the measure of each angle.
Answers
3x + x= 180
4x = 180
X= 45
3(45) + 4(45) = 180
Hope this helps!
The value of larger and smaller angles are 135 and 45 degrees respectively.
Supplementary angle :Two angles are supplementary if their sum is 180 degrees.
Since, given that One angle measures three times the measure of a smaller angle.
Let us consider that one angle is 3x and other is x.
[tex]3x+x=180\\\\4x=180\\\\x=180/4=45[/tex]
Larger angle is, [tex]3x=3*45=135[/tex]
Smaller angle is, [tex]x=45[/tex]
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You need a 15% alcohol solution. On hand, you have a 210 mL of a 35% alcohol mixture. How much pure water will you need to add to obtain the desired solution?
Answers
Answer:
280 mL
Step-by-step explanation:
If x is the amount of 35% solution and y is the amount of pure water, then:
0.15 = (0.35x + 0y) / (x + y)
0.15 = (0.35x) / (x + y)
Given that x = 210 mL:
0.15 = (0.35×210) / (210 + y)
210 + y = 490
y = 280
A. 530 ft^2
B. 500 ft^2
C. 470 ft^2
D. 450 ft^2
Answers
Answer: OPTION A.
Step-by-step explanation:
Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:
[tex]lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}[/tex]
Then, the area scale factor is:
[tex]area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}[/tex]
To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:
[tex]A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2[/tex]
So, the option that shows an approximation of the area of the larger triangle is the option A:
[tex]A_{(larger)}[/tex]≈[tex]530ft^2[/tex]
10x®y 12
Which expression is equivalent to 7-2.. 6? Assume X+0.y* 0.
Answers
For this case we must find an expression equivalent to:
[tex]\frac {10x ^ 6y ^ {12}} {- 5x ^ {- 2} y^ {- 6}}[/tex]
We have to:
[tex]\frac {10} {- 5} = - 2[/tex]
Now, by definition of division of powers of equal base, we put the same base and subtract the exponents. Rewriting the expression we have:
[tex]-2x ^ {6 - (- 2)} y^ {12 - (- 6)} =\\-2x ^ {6 + 2} y ^ {12 + 6} =\\-2x ^ 8y ^ {18}[/tex]
Answer:
Option B
If f(x) = -x + 8 and g(x) = x4, what is (gºf)(2)?
Enter the correct answer.
Answers
Answer:
[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]
Step-by-step explanation:
[tex]f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\(g\circ f)(x)=\bigg(-x+8\bigg)^4\\\\(g\circ f)(2)\to\text{put x - 0 to the equation of the function:}\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]
if P is 30 units and I is 10 units, w is
Answers
Note that perimeter of rectangle [tex]P=2l+2w[/tex]
So we have to solve for width or w.
[tex]P=2l+2w[/tex]
[tex]30=2\times10+2w[/tex]
[tex]w=5[/tex]
Width of a rectangle is 5 units.
Hope this helps.
r3t40
what is .84 /.02?
i really need help with this question so please help me!
Answers
Answer:
42
Step-by-step explanation:
This means 0.84 divided by 0.02
which equals to 42
the points mean that there is a zero
if a number has been written in that format of "point" then "number" without any number before the point, it means there is a zero there
if you need anything else clarified please do so in the comment section i would like to help more
Hope this helps and if it does mark as branliest answer thx
A force of 60 N is used to stretch two springs that are initially the same length. Spring A has a spring constant of 4 N/m, and spring B has a spring constant of 5 N/m.
How do the lengths of the springs compare?
A:Spring B is 1 m longer than spring A because 5 – 4 = 1.
B:Spring A is the same length as spring B because 60 – 60 = 0.
C:Spring B is 60 m longer than spring A because 300 – 240 = 60.
D:Spring A is 3 m longer than spring B because 15 – 12 = 3.
Answers
Answer:
D:Spring A is 3 m longer than spring B because 15 – 12 = 3.
Step-by-step explanation:
In this question, you should remember the Hooke's Law in physics.
The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.
The mathematical expression for this law is
[tex]F=-kx[/tex]
where;
F= force applied on the spring
x = the extension on the spring
k= the spring constant which varies in spring.
The question will need you to calculate the extension on the springs A and B then compare the values obtained.
In spring A
Force, F=60N and spring constant ,k=4 N/m
To find the extension x apply the expression;
[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]
Here the spring extension is 15 m
In spring B
Force, F=60N and spring constant , k=5N/m
To find the extension x apply the same expression
[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]
Here the extension on the spring is 12 m
Compare
The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m
[tex]=15m-12m=3m[/tex]
Answer:
D)Spring A is 3 m longer than spring B because 15 – 12 = 3.
trust
Find m /_B.
A) 60°
OB) 75°
OC) 90°
OD) 100°
Answers
180(n-2). Where n is the number sides of the shape.
There are 4 sides
180(4-2) = 180(2) = 360
So this shape is 360 degrees
120 + 120 + 60 +x = 360
300 + x = 360
X= 60
But as you can see that you don’t need this form for this question the alternate interior show you that the missing angles is 60
The slope of the line containing the points (6, 4) and (-5, 3) is:
A. 1/11
B. 1
C. -1
Answers
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}[/tex]
Answer:
1/11
Step-by-step explanation:
How do you solve the questions for the probability
Answers
Final answer:
To solve probability questions, you need to understand the basic concepts and formulas.
Explanation:
To solve probability questions, you need to understand the basic concepts and formulas.
To find the probability that the student belongs to a club, divide the number of students in the club by the total number of students.To find the probability that the student works part-time, divide the number of part-time students by the total number of students.To find the probability that the student belongs to a club and works part-time, multiply the probability of belonging to a club by the probability of working part-time.To find the probability that the student belongs to a club given that the student works part-time, divide the probability of belonging to a club and working part-time by the probability of working part-time.To find the probability that the student belongs to a club or works part-time, add the probabilities of belonging to a club and working part-time, and then subtract the probability of belonging to a club and working part-time.Simplify the following expression:
18g+7-12g-3
Answers
Please mark brainliest
:)
Answer:
[tex]18g + 7 - 12g - 3 = 6g + 4[/tex]
Step-by-step explanation:
[tex]18g+7-12g-3\\=18g-12g+7-3\\=6g+7-3\\=6g+4[/tex]
How long is AC
Angle B =60°
And BC = 3√ 3
Answers
Answer:
AB or x =6sqrt(3) (which is what the pic ask for)
but you ask for AC which is 9
Step-by-step explanation:
The hypotenuse is twice the length of the short leg.
The short leg is 3sqrt(3) (because I see it is opposite the smallest angle which is 30 in this case).
So the hypotenuse is twice 3sqrt(3) which is 6sqrt(3)
You are also asking for AC though... That is the short leg times sqrt(3) so that measurement is 3sqrt(3)*sqrt(3)=3(sqrt(3*3))=3(3)=9
Which of the following is equal to the rational expression when x -2 or -1? x^2-4/(x+2)(x+1)
Answers
The value of the rational expression when x is -2 or -1 is 0 and 3, respectively.
Explanation:To find the value of the rational expression when x is -2 or -1, we substitute these values into the expression. Plugging in -2, we have (-2)^2 - 4/((-2)+2)((-2)+1) = 0.
Next, plugging in -1, we have (-1)^2 - 4/((-1)+2)((-1)+1) = 3.
Therefore, the value of the rational expression when x is -2 or -1 is 0 and 3, respectively.
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For f (x) = 3x +1 and g(x) = x2 - 6, find (f 3)(x)
Answers
Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f(3)= 3 * 3 + 1 + 10
Rita has taken out a loan for $2000 to help pay for a car. The 2-year loan has 12% simple annual interest. What is the total amount of money that she will have paid back at the end of two years
Answers
Answer:
it should be $2480Step-by-step explanation:
Answer:
The Answer IS: 2480 I just did the question
Step-by-step explanation:
8-4 2/5 ? 3 9/12
<,>, or =
Answers
[tex]8 - 4 \frac{2}{5} < 3 \frac{3}{4} \\ 3 \frac{3}{5} < 3 \frac{3}{4} [/tex]
what are the length and width of a rectangular traffic sign if the length exceeds the width by 24 inches and the perimeter by 128 inches
Answers
Answer:
length = 44 in, width = 20 inStep-by-step explanation:
[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(l+w)\\\\l-length\\w-width\\\\\text{We have}\ l=(w+24)\ in,\ P=128\ in\\\\\text{Substitute:}\\\\128=2(w+24+w)\qquad\text{divide both sides by 2}\\\\64=2w+24\qquad\text{subtract 24 from both sides}\\\\40=2w\qquad\text{divide both sides by 2}\\\\20=w\to w=20\ in\\\\l=20+24=44\ in[/tex]
The common ratio is 2
40, 20, 10, 5,...
Answers
Answer:
2.5
Step-by-step explanation:
because half of 5 is 2.5
what is the solution for 3/2 = 3/2x - 6/5x
Answers
Answer:
x=5
Step-by-step explanation:
3/2 = 3/2x - 6/5x
Get a common denominator of 10 for the fractions with x
3/2 = 3/2 *5/5 x - 6/5 *2/2 x
3/2 = 15/10x - 12/10x
3/2 = 3/10 x
Multiply each side by 10/3 to isolate x
10/3 * 3/2 = 10/3 * 3/10 x
10/2 = x
5 =x
Solve the system
{f (x) = 2x-1
{g (x) = x^2-4
Answers
Answer:
2 sets of possible solutions:
x=3, y = 5
and
x=-1, y = -3
Step-by-step explanation:
Using the graphical method, (see attached)
you can graph both equations and find their intersection points.
From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)
Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.
y = 2x + 1 ------------------- eq. (1)
y = x² - 4 ------------------- eq. (2)
Multiply or divide as indicated. x^-8/x^-7
Answers
Answer:
your answer would be just x
Step-by-step explanation:
you just subtract the exponents
The expression x^-8/x^-7 simplifies to 1/x. This is due to the rule for dividing exponential expressions with the same base, which involves subtracting the exponents.
Explanation:To solve x^-8/x^-7, we need to understand the rule for division of expressions with exponents which is: x^a / x^b = x^(a-b).
When you divide exponential expressions with the same base, you subtract the exponents.
In our case, x^-8 / x^-7 = x^(-8 - -7). This simplifies to x^-1 or x^-1 = 1/x. So, the result is 1/x.
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in a relation, the input is the number of people and the output is the number of watches
is this relation a function? why or why not
Answers
Answer:
function
Step-by-step explanation:
hoped this helped;)
Answer:
Step-by-step explanation:
Not a function. The number of people has little direct connection with the total number of watches owned.
Which of the following is true about the relationship between the slopes of the lines whose equations are 8x - 9y = 5 and 9x - 8y = 1?
They are equal.
They are reciprocals.
They are opposites.
Answers
Answer:
reciprocals
Step-by-step explanation:
Let's actually find the slopes. Then we can better compare them.
8x - 9y = 5 → - 9y = 5 - 8x → slope is m = (-8) / (-9), or 8/9.
9x - 8y = 1 → - 8y = 1 - 9x → slope is (-9) / (-8), or 9/8
These two slopes are reciprocals (but not negative reciprocals).
Answer:
reciprocals, but not negative reciprocals
Step-by-step explanation:
8x - 9y = 5
9y = 8x - 5
y = 8/9x - 5/9
m1 = 8/9
9x - 8y = 1
8y = 9x - 1
y = 9/8x - 1/8
m2 = 9/8
Which proportion could be used to find the length of side b?
Answers
Answer:
D sin 85 sin 31
---------- = ----------
b 9.3
Step-by-step explanation:
We can use the law of sins
sin B sin A sin C
---------- = ----------- = ----------
b a c
We do not know angle C, but we can calculate it
The angles of a triangle add to 180
A + B + C = 180
64+ 85 + C = 180
149 + C = 180
C = 180-149
C =31
sin B sin C
---------- = ----------
b c
We know B = 85, C = 31, b = unknown and c = 9.3
sin 85 sin 31
---------- = ----------
b 9.3
the correct answer would be D