right isosceles
rs:34&rs=rt+st
rt:17
st:17
ab=[(x(a)-x(b))+(y(a)+y(b))]
Answer:
Isosceles.
Step-by-step explanation:
We are going to check it with the distance formula
d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]
= [tex]\sqrt[2]{(-1)^{2}+(-4)^{2}}[/tex]
= [tex]\sqrt[2]{1+16}[/tex]
= [tex]\sqrt[2]{17}[/tex].
d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]
= [tex]\sqrt[2]{(-4)^{2}+(1)^{2}}[/tex]
= [tex]\sqrt[2]{16+1}[/tex]
= [tex]\sqrt[2]{17}[/tex].
d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]
= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]
= [tex]\sqrt[2]{25+9}[/tex]
= [tex]\sqrt[2]{34}[/tex].
Then, as the triangle has two sides with the same length, the triangle is isosceles.
Which figure is not a trapezoid?
Answer:
B is your answer
Step-by-step explanation:
Why this is, is because it is parallel an all four sides while a trapezoid isn't parallel on all four sides. So that means that B is not a trapezoid.
Figure B is not a trapezoid
What is a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides.
The non-parallel sides may have different lengths, and its angles can vary.
It combines characteristics of both triangles and parallelograms in its geometric properties.
Figure A represents a trapezoid cos it has a lone pair of parallel lines.
Figure B is not a trapezoid but a parallelogram because it has 2 pairs of parallel lines.
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How would you find the diagonals for a rhombus given the side length of 7 yds and an angle measure of 60 degrees?
Answer:
Long diagonal: 12.12 yd
Short diagonal: 7 yd.
Step-by-step explanation:
As you can see, 4 righ triangles are formed.
The larger diagonal divides the angle ∠AFM=60° into two angles of 30° each.
Then, choose one the triangles that has the angles of 30°. The hypotenuse will be the side lenght of 7 yards, the long diagonal (D) will be twice the adjacent side and the short diagonal (d) will be twice the opposite side.
Then:
- Long diagonal:
[tex]\frac{D}{2}=7*cos(30\°)=6.06yd\\\\D=2(\frac{D}{2})=2(6.06yd)=12.12yd[/tex]
- Short diagonal:
[tex]\frac{d}{2}=7*sin(30\°)=3.5yd\\\\d=2(\frac{d}{2})=2(3.5yd)=7yd[/tex]
Answer:
The length of diagonals are 7 yd and 12.12 yd
Step-by-step explanation:
Let the point of intersection called as 'D'
<AFD = <MFD =60/2 = 30°
Then < AFM = <AFD + <MFD
Consider the ΔAFD
The angles are 30°, 60° and 90 then sides are in the ratio
1 : √3 : 2
The two diagonals are MA and FR
MA = MD + AD = 7/2 + 7/2 = 7 yd
FR = FD + RD = 7√3/2 + 7√3/2 = 7√3 = 12.12 yd
Therefore the length of diagonals are 7 yd and 12.12 yd
the volume of a triangular prism is 42 cubic centimeters. what is the volume of a similar prism that is twice as large as large as the first prism
Answer:
The volume of the similar prism is [tex]336\ cm^{3}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x----> the volume of the larger prism
y----> the volume of the smaller prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=2[/tex] -----> the scale factor
[tex]y=42\ cm^{3}[/tex]
substitute and solve for x
[tex]x=42(2^{3})=336\ cm^{3}[/tex]
56 less than the quotient of a number and 4 is -52. What is the value of the unknown number?
Answer:
16
Step-by-step explanation:
The quotient of a number (x) and 4 is written x/4. 56 less than that is ...
(x/4) -56
The problem statement tells us the value of this is -52, so we have ...
(x/4) -56 = -52
Add 56 to both sides of this equation, and you get ...
x/4 = 4
Multiply both sides of this equation by 4 and you get ...
x = 16
The value of the unknown number is 16.
When 2 fair dice are rolled there are 36 possible outcomes. How many possible outcomes would there be if three fair dice were rolled
Answer:
Step-by-step explanation:
There would be 216 outcomes because
6*6=36 outcomes so
6*6*6, or 36*6, = 216.
When 3 fair dice are rolled then there are 216 possible outcomes.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
When 2 fair dice are rolled there are 36 possible outcomes.
Now,
Since, When 2 fair dice are rolled then possible outcomes = 6 x 6 = 36
So, When 3 fair dice are rolled then possible outcomes = 6 x 6 x 6
= 216
Thus, When 3 fair dice are rolled then there are 216 possible outcomes.
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Which technique is most appropriate to use to solve each equation. (X+3) (x+2)=0
Set (x+3) to 0. X+3=0. X=-3
Set (x+2) to 0 X+2=0. X=-2
A basketball hoop is 10 feet high. If Steve is 5 feet tall and standing 12 feet away from the hoop, what is the distance from the top of Steve's head to the hoop?
Answer:
basketball hoop= 10 feet high
steve=5 feet tall
hes standing 12 feet away
so i would say 3 feet away
The distance from the top of Steve's head to the hoop is 13 feet.
How to calculate the distance from top of Steve's head to the hoop ?Given information in the question is the height of basketball hoop is 10 feet, height of Steve 5 feet and the distance from hoop to him is 12 feet.
Therefore the distance from the top of Steve's head to the hoop is also 12 feet.
Also the distance from the top of Steve's head and the top of Hoop is (10 - 5) feet = 5 feet.
Therefore calculating the distance from top of Steve's head to the hoop by using Pythagoras Theorem -
Let the required distance is d feet .
⇒ [tex]d = \sqrt{12^{2} + 5^{2} }[/tex]
⇒ [tex]d = \sqrt{169} = 13[/tex] feet
Therefore the distance from the top of Steve's head to the hoop is 13 feet.
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At an elementary school there are two fenced in areas on the playground. The small play area is 1 4 the area of the large play area. The total square footage of the two areas is 2000 ft2. What is the size of the small play area?
Answer:
The size of the small play area is [tex]400\ ft^{2}[/tex]
Step-by-step explanation:
Let
x-----> the small play area
y-----> the large play area
we know that
[tex]x+y=2,000[/tex] ----> equation A
[tex]x=\frac{1}{4}y[/tex]
[tex]y=4x[/tex] ----> equation B
substitute equation B in equation A and solve for x
[tex]x+(4x)=2,000[/tex]
[tex]5x=2,000[/tex]
[tex]x=2,000/5[/tex]
[tex]x=400\ ft^{2}[/tex]
The function rule of a certain function is y = -3x + 1. If the input is 7, what is the output?
The output is -20 to this question
The output of the given linear function at x = 7 is -20.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
As per the given function,
y = -3x + 1
Here x is the input and y is the output.
Put x = 7
y = -3 ×7 + 1
y = -21 + 1 = -20
Hence "The output of the given linear function at x = 7 is -20".
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John has 16 boxes of apples. Each box holds 12 apples. If 7 of the boxes are full, and 9 of the boxes are half full, how many apples does John have?
Answer:
138 apples
Step-by-step explanation:
7x12=84
9x6=54
84+54=138
Consider the sequence of steps to solve the equation:
5(x - 3) = 7x/2
Step 1 ⇒ 10(x - 3) = 7x
Step 2 ⇒ 10x - 30 = 7x
Step 3 ⇒ 3x - 30 = 0
Step 4 ⇒ 3x = 30
Step 5 ⇒ x = 10
Identify the property of equality which gets us from Step 3 to Step 4.
A) Division Property
C) Subtraction Property
B) Addition Property
D) Multiplication Property
Answer: B) Addition Property
Step-by-step explanation:
The Step 3 is: [tex]3x-30=0[/tex]
The idea is to solve the equation, which means that you have to find the value of the variable [tex]x[/tex].
As [tex]3x-30[/tex] is a subtraction, you need to add 30 to both sides of the equation to keep the equation balanced. This property is known as "Addition property of equality".
This property states that adding the same number to both sides of the equation, the equality does not change:
[tex]a=b\\a+n=b+n[/tex]
Then, the Addition property of equality applied in Step 3, get you to Step 4:
[tex]3x-30+(30)=0+(30)\\3x=30[/tex]
Answer: B. Addition Property
Step-by-step explanation:
Find the distance between the two numbers on a number line. Write your answer as a mixed number. -7, -3 2/3
Answer:
3 1/3
Step-by-step explanation:
The answer is 3 1/3 because 7 - 3 2/3 = 3 1/3
Answer:
3 1/3
Step-by-step explanation:
URGENT)
In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)^x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.
A 500
B 2004
C 2005
D 2002
Answer:
B. 2004.
Step-by-step explanation:
f(x) = 100(1.0153)^x
When f(x) = 106 million:
106 = 100(1.0153)^x
(1 .0153)^x = 106/100 = 1.06
Taking logs:
x ln 1.0153 = ln 1.06
x = ln 1.06 / ln 1.0153
= 3.837
So x = 4 years.
So the year is 2000 + 4 = 2004.
Answer:
2004
Step-by-step explanation:
what is
[tex]( \sqrt{x + 8} ) \: \: + \: \: ( \sqrt{x + 8)} [/tex]
please i need the answer. thank you
Answer:
2*sqrt(x + 8)
Step-by-step explanation:
You could use the distributive property to answer your question
[sqrt(x + 8) + sqrt(x + 8)]
=sqrt(x + 8) [1 + 1]
=2*sqrt(x + 8)
Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.
Answer:
c. Reflect across the y-axis, translate 3 right and 2 down
Step-by-step explanation:
You want a description of the transformation of g(x) = ln(x) into f(x) = ln(3 -x) -2.
TransformationReflection across the y-axis is the result of replacing x by -x in a function. That is, f(x) = g(-x) will reflect g(x) across the y-axis.
Translation right h units and up k units is the result of the transformation ...
f(x) = g(x -h) +k
ApplicationThe given function f(x) can be written as ...
f(x) = g(-(x -3)) -2
The first transformation is replacement of x by -x:
f(x) = g(-x) . . . . . . . . reflection over the x-axis
The second transformation is replacement of x by x-3, and adding -2 to the function value:
f(x) = g(-(x -3)) -2 . . . . translation of the reflected function right 3, down 2
The graph of g(x) = ln(x) is transformed to the graph of f(x) = ln(3 -x) -2 by reflection over the y axis, then translation right 3 and down 2, choice C.
A soup can has a radius of 4.3 cm and a height of 11.6 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter
Final answer:
To find the volume of the soup can, one must use the formula for the volume of a cylinder, [tex]V = (pi)r^2h[/tex]. After substituting the given measurements, the calculated volume, rounded to the nearest tenth, is approximately 673.9 cubic centimeters.
Explanation:
The student asked about the volume of a cylindrical soup can with a given radius and height. To calculate this, the formula for the volume of a cylinder, which is V = \\(pi)r^2h, is used. Here, r represents the radius of the cylinder's base, and h represents the height of the cylinder. Substituting the given values into the formula, we get [tex]V = (pi)(4.3 cm)^2(11.6 cm)[/tex]. The calculated volume will give us the amount of space inside the soup can, measured in cubic centimeters (cm^3).
Step-by-step calculation:
Start by squaring the radius: (4.3 cm)^2 = 18.49 cm^2.Next, multiply this by [tex]\\(pi) (approximately 3.14159): 18.49 cm^2 \\(times)[/tex] 3.14159 = 58.095 cm^2 (rounded to three decimal places for intermediate calculation).Finally, multiply by the height of the can: 58.095 cm^2 [tex]\\(times)[/tex] 11.6 cm = 673.902 cm^3.Round the result to the nearest tenth: The volume of the soup can is approximately 673.9 cm^3.Estimate the sum by rounding each mixed number to the nearest half or whole number. 8 2/9 + 3 11/10
50 POINTS PLEASE HELP ME!! PLEASE HURRY ASAP!!!!!
Solve for x
x = 4.8
Step-by-step explanation:With angles like this these ones, the 2 lines equal the same amount. To find the length of one of the lines, you multiply the given lengths.
So, for the first angle, the line with both angles has a 4 and 6, so the length of the line is 24.
Since the lines are equal, to find the length of x you take 24 and divide it by 5, which gives you 4.8, or 24/5.
This means x = 4.8.
To double check, you can simply multiply 4 and 6, then 5 and 4.8. If the answers are the same, it is correct.
This applies to all 3 angles shown.
Hope this helps!
Visual Explanation:
the slope of a graphed line is 5 and the y-intercept is (0,3/4), what is the slope-intercept equation of the line?
ANSWER
[tex]A. \: \: y = 5x + \frac{3}{4} [/tex]
EXPLANATION
The slope-intercept form of an equation is given by;
[tex]y = mx + c[/tex]
wherever m is the slope and c is y-value of the y-intercept.
It was given that the slope is 5.
This implies that,
[tex] m = 5[/tex]
The y-intercept is
[tex](0, \frac{3}{4})[/tex]
This means that,
[tex]c = \frac{3}{4} [/tex]
We plug in the values to obtain,
[tex]y = 5x + \frac{3}{4} [/tex]
The correct choice is A.
Simplify 12y^7/18y^-3. Assume y=0
Answer:
its the third one i got that
For this case we must simplify the following expression:
[tex]\frac {12y ^ 7} {18y ^ {- 3}}[/tex]
We have that by definition of properties of powers, it is fulfilled that:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, we can rewrite the expression:
[tex]12y ^ 7 * 18y ^ 3[/tex]
By definition of multiplication properties of powers of the same base we have:
[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]
So:
[tex]12y ^ 7 * 18y ^ 3 = (12 * 18) * y ^ {7 + 3} = 216y ^ {10}[/tex]
Answer:
[tex]216y ^ {10}[/tex]
When y = 0 the expression is 0
Solve the linear equation
[tex]4^{x+7} = 8^{2x-3}[/tex]
Answer:
x = 5.75
Step-by-step explanation:
4^(x+7) = 8^(2x-3)
But; 4^(x+7) = 2^2(x+7)
8^(2x-3) = 2^3(2x-3)
2^2(x+7) = 2^3(2x-3)
Since the bases are the same;
2(x+7) = 3(2x-3)
2x + 14 = 6x -9
14 + 9 = 6x - 2x
23 = 4x
x = 23/4
x = 5.75
Find the measure of the line segment GE. Assume that lines which appear tangent are tangent.
Answer:
The measure of the line segment GE is [tex]18\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem , states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
In this problem
[tex]GE*GF=GH^{2}[/tex]
substitute the values
[tex](8+x)(8)=12^{2}[/tex]
solve for x
[tex]8x+64=144[/tex]
[tex]8x=144-64[/tex]
[tex]8x=80[/tex]
[tex]x=10[/tex]
Find the measure of the line segment GE
[tex]GE=8+10=18\ units[/tex]
Please help!! See the attachment, please!
Answer:
[tex]946[/tex]
Step-by-step explanation:
we know that
The formula to find the sum is equal to
[tex]S=(a1+an)n/2[/tex]
where
a1 is the first term
an is the last term
n is the number of terms
In this problem we have
[tex]n=11[/tex]
[tex]a1=(98-2(1))=96[/tex]
[tex]an=(98-2(11))=76[/tex]
substitute the values in the formula
[tex]S=(96+76)(11/2)=946[/tex]
A video game console requires a 140 degree span in a room. The angles on each side are congruent. Write and solve an equation to determine the measure of each angle.
Answer:
The measure of each angle is [tex]20\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
Let
x------> the angle on each side
we know that
[tex]x\°+140\°+x\°=180\°[/tex]
solve for x
[tex]2x\°=180\°-140\°[/tex]
[tex]2x\°=40\°[/tex]
[tex]x=20\°[/tex]
An ordinary fair die is a cube with the numbers 1 through 6 on the sides. Imagine that such a die is rolled twice in succession and that the faces of the 2 rolls are added together. This sum is recorded of single trial of a random experiment. Event A: The sum is greater than 6 Event B the sum is divisible by 6
Answer:
A. 5/9 B. 1/6.
Step-by-step explanation:
Total possible events = 6*6 = 36.
A. The possible combinations for the sum being <= 6 are:
1 ,1 2,2 3,3 1,2 1,3 1,4 1,5 2,1 2,3 2,4 3,1 3,2 3,3 4,1 4,2 5,1
= 16
So Probability of Sum > 6 = (36-16) / 36
= 20/36
= 5/9.
B. Possible combinations where the sum is divisible by 6 are
3,3 2,4 4,2 1,5 5,1. 6,6 = 6.
So the required probability = 6/36
= 1/6.
This reaction is an example of what type of reaction? NH3(g) + H2O(l) ? NH4OH(aq) A. a synthesis reaction B. a hydrolysis reaction C. an electrolytic reaction D. a decomposition reaction
Which graph represents the same relation as the rule y = 2x, for all real numbers x?
Answer:
C is your answer...
Answer:
Its C
Step-by-step explanation:
Edge 2020
Find the expression you can substitute for x in 5x+y=10 to solve the system below
First you would need to move the variable causing it to change its sign
5x=10-y
Then divide both sides by 5
X=2-1/5y
Then you are left with your answer:
x=2-1/5y
Hope this helps! :3
WILL MARK BRAINLIEST In this geometric sequence, what is the common ratio? 104, -52, 26, -13, ...
Answer:
r = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The common ratio r of a geometric sequence is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = .....
Hence
r = [tex]\frac{-52}{104}[/tex] = [tex]\frac{26}{-52}[/tex] = - [tex]\frac{1}{2}[/tex]
Leon graph y=12- 0.05 x to represent the number of gallons of gas left in his car after driving x miles.
Answer:
B
Step-by-step explanation:
Range of the graph is the ALLOWED y-values. The y-axis is number of gallons left in tank. So, it cannot be NEGATIVE number of gallons, so 0 is the lower limit of the range.
As we can see from the axis of the graph, we see where the line cuts the y-axis, that is the upper limit of number of gallons he starts off with. The y-intercept (y-axis cutting point) is 12.
So we can say that the range is 0 ≤ y ≤ 12
Correct answer is B