Explanation:
let the longer leg = x
The shorter leg = 9cm shorter than the longer leg
The shorter leg = x - 9
hypotenuse = 9cm longer than the longer leg
hypotenuse = x + 9
Using pythagoras theorem:
hypotenuse² = shorter leg² + longer leg²
(x + 9)² = x² + (x - 9)²
Expanding:
x² + 9x + 9x + 81 = x² + x ² - 9x -9x + 81
x² + 18x + 81 = 2x² -18x + 81
collect like terms:
18x + 18x + 81 - 81 = 2x² - x²
36x + 0 = x²
x² - 36x = 0
x(x - 36) = 0
x = 0 or (x - 36) = 0
x = 0 or x = 36
if x = 0
shorter side = x - 9 = 0 - 9 = -9
Since the length cannot be negative, x = 36
The longer leg = x = 36 cm
The shorter leg = x - 9 = 36 - 9
The shorter leg = 27cm
The hypotenuse = x + 9 = 36 + 9
The hypotenuse = 45 cm
Hi, the area of a circle is 100 sq. mm. The radius is 5.64 mm. What is the circumference?
11.28π mm
1) Since the area is 100 mm² we can plug into the Circumference formula to find out the perimeter of that circle
2)
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot\pi\cdot(5.64)^{} \\ C=11.28\pi \end{gathered}[/tex]3) Hence, the circumference of that circle is 11.28π mm
which of the following circles have their centers in the second quadrant
The circles in option B and D has their centers in the second quadrant
Here, we want to know which of the circles have their centers in the second quadrant
Generally, the equation of a circle can be represented as;
[tex](x-h)^2\text{ + (y-}k)^2=r^2[/tex]where (h,k) represents the center of the circle
Now, let us get the center of each of the circles;
A. (4,-3)
b. (-1,7)
C.(5,6)
D. (-2,5)
The second quadrant has its coordinates in the form (-x,y)
Out of all the options, the option that fits these quadrant is the second and fourth
So the circles in option B and D has its center in the second
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]Alicia borrow 15000 to buy a car she borrowed the money at 8% for 6 years how much will she have to pay the bank at the end of 6 years
Answer:
Explanation:
First, we identify the main components:
• Principal = $15,000
,• Rate = 8% =0.08
,• Time = 6 years
[tex]undefined[/tex]Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes.SportsPlus, a rival shoe manufacturer, then came up with a design that it claims performs even better than Fastex's design. A sports magazinedecided to test the claims. It created two groups of 15 randomly selected athletes each. Members of both groups were pretested anddetermined to have equal athletic ability. Additionally, they followed the same nutrition plan and training program during the study.The athletes did a 1-mile run to test the shoes. The magazine found that the athletes who used Fastex shoes had reduced their 1-mile run timeby an average of 396, and athletes who used Sports Plus shoes had reduced their 1-mile run time by an average of 2%.Given the magazine's data collection method and findings, what conclusion can be made?OA. The data collection method used was fair since both shoe designs were tested on identical parameters.OB. The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.OC. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than theathletes given SportsPlus shoes.OD. The data collection method used was random since the athletes in the two groups used two different shoe designs.
B: The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.
This is false because they followed the same nutrition plan and training program during the study.
C. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes.
This is also false because members of both groups were pretested and determined to have equal athletic ability
D. Each group used one shoe design.
So, the correct option is A
Solve the inequality: -1 <= x - 3 > 7
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
i need help in this please
The isosceles right is given in the diagram below
We are to rotate clockwise about point B as the origin
Rotating ABC 180° Clockwisely, we have
Rotating ABC 270° clockwise about B, we have
We now combine the four triangles together in the diagram below
concetta had a 2kg bag of flour. she used 180g of flour to make biscotti. how many kilograms of flour are left in the bag?
Answer
The amount of flour left in the bag = 1.82 kg
Explanation
Concetta had 2 kg of flour.
She uses 180 g of the flour to make biscotti.
We are then asked to calculate how much flour is left in kilograms.
Amount of flour left = (Initial Amount of flour) - (Amount of flour used)
Initial amount of flour = 2 kg
Amount of flour used = 180 g = 0.18 kg
Amount of flour left = (Initial Amount of flour) - (Amount of flour used)
Amount of flour left = 2 - 0.18 = 1.82 kg
Hope this Helps!!!
Classify the following conic section from its standard equation: 4y2 - 6x +16y - 21 = 0.My
it is a parabolla because only variable is quadratic and the other is linear.
a normal distribution has mean 62 and a standard deviation 20. find and interpret the z-score for x=46
The z - score of the normal deviation will be 0.8.
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
A normal distribution has the mean = 62
Standard deviation = 20
Since, The formula for the z - score will be;
z = (x - μ) / σ
Where, σ is the standard deviation and μ is the mean of normal distribution.
Substitute all the values in above equation, we get;
z = (x - μ) / σ
z = (46 - 62) / 20
z = - 16 / 20
z = - 0.8
Therefore,
The z - score of the normal deviation will be 0.8.
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Prove that if 3/5 x = 9 then x = -15
Given: 3/5 x = 9
Prove: x = -15
There is no proof because X ≠ -15 when 3/5 x = 9
What is multiplication?Multiplication is defined as one of the basic arithmetic operations that is used for the repeated addition of similar figures together.
From the given expression,
3/5x = 9
But X= -15
Substitute X = -15 into the given expression;
That is,
3/5 * -15 = 9
-45/5= 9
-9 = 9
Therefore, there is no proof that in the expression 3/5 x = 9, X ≠ -15 because the final answer is -9 and not ,9.
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hi, can you please explain mistake made on one side the other side the correct work with the answer thanks
Notice that:
[tex]3x-3x\ne x,[/tex]therefore the mistake is the last step.
Now, all the work of the student is correct up to:
[tex]undefined[/tex]Ali took 3 1/4 hours to clean the bathroom. Then he took 1/8 hours to clean the kitchen. How much total time did Ali take to clean the two rooms?Write your answer as a mixed number in the simplest form.
He took 3 1/4 hours to clean the bathroom and then he took 1/8 hours to clean the kitchen.
First, we can convert the mixed number 3 1/4 into a fraction:
3 1/4 = 3/1 + 1/4 = 13/4
Now, we can sum both times:
13/4 + 1/8 = ((13*8)+(4*1)) / (4*8) = (104 +4)/ 32 = 108/32 = 27/8
Finally, we need to convert the total of hours 27/8 as a mixed number:
If 27/8 = 3.375
We take the whole number and then convert the decimal remaining into a fraction:
3 - whole number
0.375* (1000/1000) = 3/8
Hence, the mixed number for the total time that Ali spent cleaning both rooms is 3 3/8
Lloyd is standing near a telephone pole. When his head touches the support wire, he is 25 feet from where the wire meets the ground. Lloydis 5 ft tall. Hon tallis the pole?1-8f feetO A 20 ft.B. 15 ftC. 80 ft.D. 17 ft
We will use the pythagorean theorem to figure the answer out.
Applying the Pythagorean Theorem, we have (let unknown side be x):
[tex]\begin{gathered} 6^2+x^2=10^2 \\ 36+x^2=100 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}[/tex]Answer 8 feet (B)You want to hang a picture on your wall the wall is 20 feet long you want to have at least 3 feet on both sides of the painting for plans to be placed right a quality showing the possible lanes of you being mean
We can consider
x = length of the painting
20 ft wall long
we want at least 3 ft per side so the total available length is 20-6= 14
x must be shorter than 14
inequality
x< 20-2(3)
x<14
Find the volume of the top of the prism, volume of the bottom prism, and total volume of figure.
Volume of the top of the prism: 460 cm^3
Volume of the bottom of the prism: 1 768 cm^3
Total volume of the figure: 2 228 cm^3
Explanation:
Volume of the top of the prism:
. Since it is a prism from trapezoid
. . Volume = Area of the trapezium base * heights between trapezium ends
[tex]\begin{gathered} Area\text{ of a trapezium base}=\frac{top\text{ base+bottom base}}{2}*height \\ ...\text{ =}\frac{6+17}{2}*(22-17) \\ ...=\frac{23}{2}*5 \\ Area\text{ = 57.5 cm}^2 \end{gathered}[/tex][tex]Volume=57.5*8=460\text{ }cm^3[/tex]Volume of the bottom prism:
. Since the price has a rectangular base:
Volume = Area of one base * height between reactangular bases
Area of one base :
[tex]17*13=221\text{ }cm^2[/tex]Volume:
[tex]221*8=1\text{ }768\text{ }cm^3[/tex]Total volume of the figure:
Volume of the top + Volume of the bottom = Total volume
[tex]221+1\text{ }768=2\text{ }228\text{ }cm^3[/tex]NB:
To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)
Find an expression equivalent to the one shown below.913 x 9-6OA. 79OB.919OC. 97OD. 9-78
Answer:
C. 9⁷
Explanation:
We will use the following property of the exponents:
[tex]x^a\times x^b=x^{a+b}[/tex]It means that when we have the same base, we can simplify the expression by adding the exponents. So, in this case, the equivalent expression is:
[tex]9^{13}\times9^{-6}=9^{13-6}=9^7[/tex]Therefore, the answer is C. 9⁷
Draw a graph, and label and scale both axes. Plot the points (-2, 3) and (1, -5), clearly labeling them.
Answer:
Explanation:
First, we draw the graph, label the x and y-axis. Then we plot the points given.
To plot the point (-2, 3), we first move to units to the left from the origin and the 3 units up as sketched below
Similarly for (1, -5), we have
We moved one unit to the right and 5 units down.
To find the slope, we take the vertical distance and the horizontal distance and then the slope will be
slope vertical distance / horizontal distance
Therefore the slope is
[tex]Slope=-\frac{8}{3}[/tex]
Form a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
in a game a player starts with 100 points each question has two parts and a incorrect answer for both parts result in a loss of one point the student loses one half of a point for getting only one part of the question correct at the end of 25 question round the player has 82.5 points what to equations and solutions represent X Missed points
Answer:
10 questions with an incorrect answer for both parts
15 questions with a correct answer in only one part
Explanation:
Let's call x the number of questions with an incorrect answer for both parts and y the number of questions with only one part of the question correct.
So, the equation that gives us the number of points after 25 rounds is:
100 - x - 0.5y = 82.5
Where: x + y = 25
So, solving for y, we get:
y = 25 - x
Replacing this on the initial equation and solving for x, we get:
[tex]\begin{gathered} 100-x-0.5y=82.5 \\ 100-x-0.5(25-x)=82.5 \\ 100-x-12.5+0.5x=82.5 \\ 87.5-0.5x=82.5 \\ 87.5-82.5=0.5x \\ 5=0.5x \\ \frac{5}{0.5}=x \\ 10=x \end{gathered}[/tex]Then, the value of y is:
[tex]\begin{gathered} y=25-x \\ y=25-10 \\ y=15 \end{gathered}[/tex]Therefore, the player gets 10 questions with an incorrect answer for both parts and 15 questions with a correct answer in only one part.
what kind of triangle congruence would i put for the last reason?
Looking at the diagram, The last statement means that trangle PQS is congruent to triangle RSQ. This means that
line PQ is equal to line RS
line QS is equal to line SQ
angle Q is equal to angle S
Thus, the reason would be
Side Angle Side(SAS)
Two sides and one angle are equal or congruent
A box is filled with shoe boxes. Each shoe box has a volume of 1 cubic foot. Six shoe boxes can fit in each layer and the height of the box is 4 feet. What is the volume of the box?
shoe box = 1 cubic foot = 1 * 1 * 1
1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot
Box height = 4 feet
Box volume = 6*4*1 = 24 feet
in the figure below, when the sun angle of elevation is 50°, the tree casts a shadow 80 feet long which can be used to find the height of the tree?
We can use the tangent of 50º. The height is approximately 95.34 ft
1) We can trace a right triangle over that mark and calculate that height, using a trigonometric ratio.
2) As we have the adjacent leg to that 50º angle and the opposite leg, we can use the tangent of 50º to find that height out.
[tex]\begin{gathered} \tan (50)=\frac{x}{80} \\ x=80\cdot\tan (50) \\ x\approx\text{ 95.34} \end{gathered}[/tex]3) Hence the answer is
We can use the tangent of 50º. The height is approximately 95.34 ft
Identify the slope and y-intercept of the line y=−2x−1.
Given the equation of the line:
[tex]y=-2x-1[/tex]The given equation as the slope-intercept form: y = m * x + b
where m is the slope and b is the y-intercept
the y-intercept is the value of y when x = 0
By comparing the given equation with the slope-intercept form
So,
The slope = m = -2
The y-intercept = b = -1
the point of y-intercept = ( 0, -1 )
a line passes through the points (2,5) and (-6,4). What is it's equation in point-slope form?
Answer:
y-5=⅛(x-2)
Explanation:
Given the points (2,5) and (-6,4).
To find the equation of the line joining these points in point-slope form, we begin by finding its slope.
[tex]\begin{gathered} \text{Slope,m}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{5-4}{2-(-6)} \\ =\frac{1}{2+6} \\ m=\frac{1}{8} \end{gathered}[/tex]Next, we substitute the slope and any of the given points into the point-slope form below:
[tex]y-y_1=m(x-x_1)[/tex]We use the point (2,5).
• x1=2, y1=5
[tex]y-5=\frac{1}{8}(x-2)[/tex]The equation in point-slope form is y-5=⅛(x-2).
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answer:
skill issue
Step-by-step explanation:
skill issue
Please help ASAP!! 31 points and brainliest!
I really need help! Please show your work so I can understand how to get the answers too!
A relation is a function if it has only One y-value for each x-value. Functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is
f(x)=2x²-4x+2
Put x=2/3
f(2/3)=2(2/3)²-4(2/3)+2
=2(4/9)-8/3+2
=8/9-8/3+2
=(8-24+18)/9
f(2/3)=2/9
Now f(x)=4x²+2x-6
Put x=1/4
f(1/4)=4(1/4)²+2(1/4)-6
=4/16+2/4-6
=1/4+1/2-6
= 1+2-24/4
f(1/4)==-21/4
Hence functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
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PLEASE help I'll send a picture in later.
Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
