Answer:
Perimeter:12cm
Area:5cm²
Step-by-step explanation:
Perimeter is the total distance around the figure ie sum of all sides of figure
∴Perimeter of triangle equals 2cm plus 5cm plus 5cm
∴The perimeter equals 12cm
Area of triangle equals 1/2×base×height,where base is 2cm & height is 5cm
(Inserting values)
∴Area of the triangle equals 1/2×2cm×5cm which equals 5cm²
Geometry!!! Find the lengths of the 45°-45°-90° Triangle
Answer:
Step-by-step explanation:
write an equivalent expression.
4 + m
Lines DE and AB intersect at point C.
D
A
C
B
(2x+2) E
(5x + 3)*
E
What is the value of x?
O12
25
38
52
Answer:
25
Step-by-step explanation:
2x+2+5x+3=180
7x=175
x=24
A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching
The probability that the colour changes, while she is watching, is 1/7
Concept: Event probability = number of favorite results /Total number of results
It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3 seconds, and then red for 30 seconds.
This means that the traffic light passes through 63 seconds to complete one-time cycle.
It is also given that Leah chooses a random 3 second time interval to watch the light.
We should find the probability that the color changes while Leah is looking.
The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.
Now let time t=0
The light changes at three different times: t=30,t = 33 and t = 63
This means that the light will change if Leah watches at intervals [27,30]
, [30,33] or [60,63]
Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.
That makes a total of 9 seconds out of 63
⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds
=9/63=17
∴ The probability that Leah observes the color change is 1/7
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Polygon abcd has the following vertics: a( -3, 3) b (5, 5) c (5, -4 ), d (-3 -4). caculate the area of the polygon
Mark the point on the coordinate system and draw the polygon (attachment).
This is the trapezoid.
The formula of an area of a trapezoid:
[tex]A=\dfrac{a+b}{2}\cdot h[/tex]
a, b - the lengths of the parallel sides
h - the height
Substitute:
[tex]a=9,\ b=7,\ h=8\\\\A=\dfrac{9+7}{2}\cdot8=\dfrac{16}{2}\cdot8=8\cdot8=64[u^2][/tex]
[tex]\huge\boxed{A=64u^2}[/tex]
Expand. (y^2 + 6)(-2y^2 + 7) =
[tex] \: \: \: \: \: \: \: \: \: \: \: \large\underline{\bf{ANSWER}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \tt↠(y^2+6)(−2y^2+7)[/tex]
[tex]\tt↠(-2y^2+7)y^2+6(-2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2+6(−2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2-12y^2+42[/tex]
[tex]\tt↠-2y^4-5y²+42[/tex]
Answer:
-2y⁴ - 5y² + 42
Step-by-step explanation:
[tex](y^2 + 6)(-2y^2 + 7)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
Here First terms are
[tex]y^2 \textrm{ and } -2y^2\\(y^2)(-2y^2) = -2y^4[/tex]
Outer terms are y² and 7 ==> (y²)(7) = 7y²
Inner terms are 6 and -2y² ==> 6(-2y²) = -12y²
Last terms are 6 and 7 ==> 6.7 = 42
So result is obtained by adding all these terms
-2y⁴ + 7y² - 12² + 42 ==> -2y⁴ - 5y² + 42
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).
What are the coordinates of the endpoints of the segment T'V'?It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.
On this note, given that the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).
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A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer
As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.
Note that 2,3,5 and 7 are the smallest primes, then use the reasoning from
(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.
But no such integers k, l, m, and n exist such that (k + 1)(l + 1)(m + 1) (n + 1) = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors
Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents, that, when 1 is added to each and all are multiplied together, would equal 20. Put another way, we are looking for k, l and m ≥ 1 such that (k + 1)(l + 1)(m + 1) = 20
Note that the only possibility here is when we have 2 *2 *5 = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) = 2^4 * 3 * 5 = 240
Now......the only remaining possibility is that this number is composed of the two smallest primes, 2 and 3, and we are looking for some k and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities are when k = 4 and l = 5, or vice-versa
So this number would factor as either 2^3 * 3^4 = 648 or 2^4 * 3^3 = 432 and both are > 240.
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Sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved?
The equation which he have solved is [tex]10/x^{2} -1=15/3x-3[/tex] as in this 1 is the extraneous solution.
Given four equations in which first equation is [tex]10/x^{2} -1=15/3x-3[/tex],second is (x+2)/(x+3)=6x/8, third is (4x-4)/(x+6)=x-1/10, fourth is 4/x-1=x+2/10.
We have to find such a equation which have a valid solution and one extraneous solution.
We have to solve these equation:
[tex]10/x^{2} -1=15/3x-3[/tex]
The above exprssion is not defined for x=1 so 1 is an extraneous solution. Simplifying the above equation by doing cross multiplication.
10(3x-3)=15([tex]x^{2} -1[/tex])
30(x-1)=15(x-1)(x+1) [We know that [tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]
2=x+1
x=1
In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.
Hence the correct equation which Sean solves is option A which is [tex]10/x^{2} -1=15/3x-3[/tex].
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The given question is incomplete as it should include the given figure.
Answer:see photo #15
Step-by-step explanation:
evaluate
3x³ 2x² + 7y for x = -3 and y = -7.
-
Answer:
2511
Step-by-step explanation:
Mark is investing his money. he thinks that he should make $10 for every $100 he invests. how much does he expect to make on an investment of $500?
6. The difference between 2 number is 36.
The larger number is 4 times as great as the
smaller. What are the 2 numbers?
Answer: 48 and 12.
Step-by-step explanation:
Let the smaller number is x. Hence, the larger number is 4*x.
The difference between 2 number is 36.
So,
4*x-x=36
3*x=36\ |:3
x=12.
4*x=12*4
4*x=48.
Good luck an' have a nice day!
25 POINTS FOR INMEDIATE RESPONSE PLEASE
What is the algebraic expression for fifteen more than n is at least 48
n+15 ≥ 48n; n≥33
15n ≥ 48; n≥33
n+15 ≥ 48; n≥33
n-15 ≥ 48; n≥33
Inequalities help us to compare two unequal expressions. The algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given statement "fifteen more than n is at least 48" can be written in the form of an algebraic expression as,
n+15 ≥ 48
Solving the inequality,
n ≥ 48 - 15
n ≥ 33
Hence, the algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.
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Please help me asap!!!!!!!
StartLayout 1st row StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot space c greater-than-or-equal-to 0 and d greater-than-or-equal-to 0. 2nd row = StartRoot StartFraction 25 times 10 c squared times c Over 9 d Superscript 6 Baseline EndFraction EndRoot. 3rd Row = StartFraction StartRoot 25 EndRoot times StartRoot c squared EndRoot times StartRoot 10 c EndRoot Over StartRoot 9 d Superscript 6 Baseline EndRoot EndFraction EndLayout
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot ?
The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³
How to simplify algebra problems?We are given the algebra problems as;
√(250c³/9d⁶)
Now 250c³ can be broken down into 250 = 25c² × 10c
Thus, we now have;
√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶
When we breakdown the above expression, we have;
5c * (√10c)]/3d³
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Answer:
the answer is a
Step-by-step explanation:
i got it right
A rectangle has sides measuring (4x 5) units and (3x 10) units. part a: what is the expression that represents the area of the rectangle? show your work. (4 points) part b: what are the degree and classification of the expression obtained in part a? (3 points) part c: how does part a demonstrate the closure property for polynomials? (3 points)
(4x + 5)(3x + 10) or 12x² + 55x +50
b: The degree of the computed expression is 2 and it is classified as a quadratic expression.c: The polynomial expression written in part a is closed under addition multiplication.Forming the Expression for the Area of Rectangle
The formula for the area of a rectangle is given as,
Area, A = length × breadth
Here, the dimensions of the rectangle are given as,
length = (4x + 5)
breadth = (3x + 10)
∴ The equation for the area of the rectangle is,
A = (4x + 5)(3x + 10)
A = 12x² + 55x +50
Hence, 12x² + 55x +50 is the required expression.
Degree and Classification of the Expression
The highest power of a variable that is present in an expression is known as its degree.
Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.
Closure Property For Polynomials
When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.
Hence the expression formed in part a indicates at the closure property for polynomials.
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A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.
Group of answer choices
27
664
544
385
The sample size suggested by this statement is 664 option second is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
At 99% confidence Z = 2.576
By using the MOE formula:
0.05 = 2.376×√(0.5(0.5)/n)
After calculating
n = 663.57 ≈ 664
Thus, the sample size suggested by this statement is 664 option second is correct.
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Myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. The vapor trails from two other jets flying from another direction crossed over the parallel trails. She printed her picture and labeled the angles and lines.
Parallel lines c and d are cut by transversals a and b. All angles are described clockwise, from uppercase left. The intersection of lines c and b form angles: 2, 4, 3, 1. The intersection of lines d and b form angles: 6, 8, 7, 5. The intersection of lines c and a form angles: 10, 12, 11, 9. The intersection of lines a and d form angles: 14, 16, 15, 13.
Assume lines c and d are parallel and Angle2 measures 98°. Which statements are true? Select three options.
mAngle3 = mAngle6 = 98°
mAngle3 = mAngle14 = 98°
mAngle4 = mAngle8 = 82°
mAngle4 = mAngle12 = 82°
mAngle5 = mAngle8 = 82°
Options 1, 3 and 5. The true statements based on the fact that c and d are parallel are:
m<3 = m<6 = 98 degrees m<4 = m<8 = 82degreesm<5 = m<8 = 82 degrees How to solve for the anglesThe sum of the angles m<4 + m<3 = 180
m<4 + 82 = 180
m<4 = 180 - 82= 98
From the question we have the first as alternate interior angles. The second is corresponding angles and the last option is vertical angles.
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Evaluate: −5−(x+y)2, where x=3 and y=6
Answer: -23
Step-by-step explanation:
-5-2x-2y
-5-2(3)-2(6)
-5-6-12 = -23
Terrell brought 42 muffins to school for his birthday He gave one each to the 17students in his class and to the 19 student in the other third grade class
Answer:
The expression is 42-17-19 OR 42-(17+19).
Step-by-step explanation:
First, we can indicate that we can use subtraction because is giving them away for his birthday.
"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".
That represents taking away 17 and 19 means that it is subtracting them.
Hope this helps. (:
The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (0, 8) as its solution? (1 point) Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D
The pair of equations that has (0, 8) as its solution is: A. equation A and equation C.
What is the Solution to a System of equations?The solution to a system of linear equations that are graphed is the pair of x and y coordinates of the points where two lines intersect.
In the graph given, the lines representing equations A and C intersect at point (0, 8). Therefore, the pair of equation that has a solution of (0, 8) is: A. equation A and equation C.
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Which statement about the following graph is correct?
O
The graph is symmetric about the line x = -1.
The graph is symmetric about the line y = -1.
The graph is not symmetric.
The graph is symmetric about the line x-1.
Answer:
the graph is symmetric about the line y=-1
Step-by-step explanation:
A function is symmetric about y=a when the following is true for all points: f(a-x) = f(a+x). By just looking at the graph, it appears to be symmetric about y=-1, and it can be further proven, by finding the difference of two points, that have the same y-value. So for example if you look at (0, 1) and (-2, 1). The difference between 0 and -1 is 1, and the difference between -2 and -1, is also 1. And this appears to be true for all the other values as well. So the graph is symmetric about the line y=-1
Answer:
The graph is symmetric about the line x=-1
Step-by-step explanation:
Write an equation of the line that passes through a pair of points: on a coordinate plane, a line goes through (0, 2) and (2, 0). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 please select the best answer from the choices provided a b c d
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
Equation of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the coordinate points (0, 2) and (2, 0)
Slope = 0-2/2-0
Slope = -1
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
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Answer:
c
Step-by-step explanation:
Given: AC and BD bisect each other.
Prove: AB | CD and BC || AD.
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a segment bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a segment bisector splits a segment into two congruent parts)
4) [tex]\angle AEB \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle BEC \cong \angle AED[/tex] (vertical angles are congruent)
9) [tex]\triangle BEC \cong \triangle DEA[/tex] (SAS)
10) [tex]\angle ECB \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
QT=
Help me please thanks:)
The length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
By intersecting chords theorem:
QM×QL = QJ×PQ
10×8 = QJ(QJ/4)
4×80 = QJ²
QJ = 4√20 units
Thus, the length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.
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In the following diagrams calculate the
sides marked with letters x and y.
All dimensions are in cm.
Answer:
x ≈ 6.5 , y ≈ 12.1
Step-by-step explanation:
(2x)² + (10.2)² = (16.5)²
4x² = 272.25 - 104.04
x² = 168.21 ÷ 4
x = √(42.0525) ≈ 6.5
y² = 42.0525 + 104.04 = 146.0925
y = √(146.0925) ≈ 12.1
Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6 meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?
meters
The distance between points M and N according to the task content is; 9.8 meters.
What is the distance between points M and N?From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.
Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;
NM/19.6 = 7.4/(2×7.4)
NM = 19.6/2 = 9.8 meters.
This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.
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Answer: 9.8 meters
Step-by-step explanation: Trust Me!! I got the answer correct on Edge.
Q: What is the distance between points M and N?
A: 9.8 meters
How to find the size of an exterior angle of a regular polygon
Answer:
exterior angle of a polygon = 360° ÷ number of sidesStep-by-step explanation:
exterior angle of a polygon = 360° ÷ number of sides
The table represents the cost of flowers at the Tigerlily Flower Shop.
Cost of Flowers
Quantity
Price
1
$2.00
2
$3.50
3
$5.00
4
$6.50
5
$8.00
6
$9.00
Which graph is the best interpretation of this table?
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A line with positive slope goes through points (2, 4) and (4, 8).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A curved line with positive slope is on the graph.
The graph which is the best interpretation of the table given is; On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).
Which graph is the best interpretation of the table?The table given in the task content is a tabular representation of the quantity and the corresponding prices. On this note, plotting the quantity on the x-axis and the price on the y-intercept with the point descriptions above best represents the graph of the table.
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Answer:
The short answer to my well taught friend, is A
7n-(4n-3) combining like terms with negative coefficient and distribution
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation/Question:}[/tex]
[tex]\mathbf{7n - (4n - 3)}[/tex]
[tex]\huge\textbf{Convert equation/question to:}[/tex]
[tex]\mathbf{= 7n - 1(4n - 3)}[/tex]
[tex]\huge\textbf{Solving the equation/question:}[/tex]
[tex]\mathbf{= 7n - 1(4n) - 1(-3)}[/tex]
[tex]\mathbf{= 7n - 4n + 3}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{= (7n - 4n) + 3}[/tex]
[tex]\mathbf{= 7n - 4n + 3}[/tex]
[tex]\mathbf{= 3n + 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{3n + 3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]