It is given that the side lengths of any right triangle can be put in the equation:
[tex]a^2+b^2=c^2[/tex]For a triangle with the side lengths 3 inches, 4 inches, and 5 inches, it can be substituted in two ways that will make the equation true:
Let a=3, b=4, and c=5:
[tex]\begin{gathered} 3^2+4^2=5^2 \\ \Rightarrow9+16=25 \\ \Rightarrow25=25 \end{gathered}[/tex]Hence, the equation is true.
You can also substitute a=4, b=3, and c=5.
This will also give the same result.
Notice that variable c has to match the longest side length.
The reason for this is that equality can only hold if the longest side is the variable at the right, if not there'll be an inequality instead.
A community boating center had $12,500. It bought 3 surf skis and 1 keelboat and had $265 left over. The keelboat cost $6,455 more than a surf ski. How much did the keelboat cost?
The cost of one keelboat is $7950
Given, A community boating center had $12,500.
It bought 3 surf skis and 1 keelboat and had $265 left over.
The keelboat cost $6,455 more than a surf ski.
Let the cost of one surf ski be x,
According to question,
cost of one keelboat = x + 6455
also, 3x + (x + 6455) + 265 = 12500
4x + 6520 = 12500
4x = 5980
x = 1495
So, the cost of one surf ski is $1495
and the cost of one keelboat is 1495 + 6455
= $7950
Hence, the cost of one keelboat is $7950
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How many period s of the function are there between
The period of a tangent function y = atan(bx) is the distance between any two consecutive vertical asymptotes. And it is given by:
[tex]period=\frac{\pi}{|b|}[/tex]So, given the function y = tan x, we have that b = 1, therefore the period is:
[tex]\text{period}=\frac{\pi}{|1|}=\pi[/tex]Next, between the given points:
[tex]\begin{gathered} -\frac{5\pi}{2}=-2.5\pi \\ and \\ \frac{7\pi}{2}=3.5\pi \end{gathered}[/tex]There are:
[tex]3.5\pi-(-2.5\pi)=6\pi[/tex]Since the period is π, so:
[tex]\frac{6\pi}{\pi}=6[/tex]Answer: 6
coordinate of the vertices after a rotation 270 grades counterclockwise around the origin d (2 2) F (3 4)E(9 2)
If the point (x, y) is rotated 270 degrees counterclockwise around the origin
Then its image is (y, -x)
We change the sign of the x-coordinate and switch the two coordinates
Since point D = (2, 2), then
Its image is D' = (2, -2)
Since point E = (9, 2), then
Its image E' = (2, -9)
Since point F = (3, 4), then
Its image F' = (4, -3)
2) Tell whether each relationship is a direct variation. If it is a direct variation, find the constant of variation. (Remember, the constant of variation is the k.) Explain.
2a) it is not a direct variation
2b) it is a direct variation; k = -4
Explanantion:For the relationship to be a direct variation, it must follow the formula:
y = kx
where k = constant of variation
k = y/x
The value of k must be constant for all
for 2a:
when y = 0, x = -3
k = 0/-3 = 0
when y = 3, x = 1
k = 3/1 = 3
when y = 6, x = 3
k = 6/3 = 2
From the above, the value of k is not constant. hence, it is not a direct variation
for 2b:
when y = -10, x = 2.5
k = -10/2.5 = -4
when y = -20, x = 5
k = -20/5 = -4
when y = -30, x = 7.5
k = -30/7.5 = -4
From the above, the value of k is constant. Hence, it is a direct variation
The constant of variation, k = -4
Hello! I’m struggling badly! I need to find the x, y and z
Let O be the point where the height about point C intercepts the segment AB:
Assume that CO is perpendicular to AB, C is a right angle, the length CO is equal to 4 and the length CB is equal to 5.
Since COB is a right angle, its sides must satisfy the Pythagorean Theorem:
[tex]y^2+4^2=5^2[/tex]Solve for y:
[tex]\Rightarrow y=\sqrt[]{5^2-4^2}=\sqrt[]{25-16}=\sqrt[]{9}=3[/tex]Notice that COB, AOC and ACB are similar triangles because they are all right angles and they have the same acute angles.
Then, the quotients between corresponding parts of the triangles are the same.
The legs of AOC are x and 4, and the corresponding legs of COB are 4 and 3. Then:
[tex]\begin{gathered} \frac{x}{4}=\frac{4}{3} \\ \Rightarrow x=\frac{4}{3}\times4=\frac{16}{3} \end{gathered}[/tex]Notice that z must be equal to the sum of x and y. Then:
[tex]z=x+y=\frac{16}{3}+3=\frac{16}{3}+\frac{9}{3}=\frac{25}{3}[/tex]Therefore, the values of x, y and z are:
[tex]\begin{gathered} x=\frac{16}{3} \\ y=3 \\ z=\frac{25}{3} \end{gathered}[/tex]Warning:
We have found this solution ignoring that the length AC was set to be equal to 15. That cannot be true, since the construction of the triangle ACB and the point O already tells us the values of x, y and z if CB=5 and CO=4. Using this construction, it is possible to deduce that the length AC must be 20/3.
The length of a rectangle is 5 yd more than twice the width x. The area is 462 yd".
The given problem is about rectangle areas.
The area of a rectangle is defined as
[tex]A=w\cdot l[/tex]Where w is width and l is the length.
In this case, we know that the length is 5 yards more than twice the width, where the last one is expressed as x.
[tex]l=2x+5,w=x[/tex]We also know by given that
[tex]A=462yd^2[/tex]Using all the given information, we have
[tex]462=x(2x+5)[/tex]Where we solve for x, first, we apply the distributive property.
[tex]462=2x^2+5x[/tex]Now, we move all terms to one side only
[tex]2x^2+5x-462=0[/tex]Using a calculator, we have
[tex]x_1=14,x_2=-\frac{33}{2}[/tex]Where 14 represents the width because distances cannot be expressed by negative numbers.
[tex]l=2(14)+5=28+5=33[/tex]Therefore, the width of the rectangle is 14 yards, and its length is 33 yards.What is the total area patty can reach? What is the total grazing area?
as patty can not reach the square, we have that she can reach 3/4 parts of a circle with radius equal to 12 feet. Therefore the area she can reach is :
[tex]A_p=\frac{3}{4}\pi\cdot r^2=\frac{3}{4}\pi\cdot144=108\pi\approx339.3[/tex]and the gazzing area is the area of the square so we get:
[tex]A_g=12^2=144[/tex]Data: x y 4 1 5 2 6 3 7 4 y = x - ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
x y
4 1
5 2
6 3
7 4
y = x - ?
Step 02:
equation of the line:
y = x - ?
y = mx + b
m = slope = 1
point ( 4 , 1)
Point-slope form of the line
(y - y1) = m (x - x1)
(y - 1) = 1 (x - 4)
y - 1 = x - 4
y = x - 4 + 1
y = x - 3
The answer is:
y = x - 3
The roots of x2 - 4x = 5, in ascending order, are ? and ?
For finding the roots of the function, we have to writte the equation in this form:
[tex]ax^2+bx+c=0[/tex]So in our problem will be:
[tex]x^2+(-4)x-5=0[/tex]Now we can use the cuadratic equation that is:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]and in our problem will be:
[tex]\begin{gathered} \frac{4\pm\sqrt[]{16^{}-4(1)(-5)}}{2(1)} \\ \frac{4\pm\sqrt[]{16^{}+20}}{2} \\ \frac{4\pm\sqrt[]{36}}{2} \\ \frac{4\pm6}{2} \end{gathered}[/tex]Now we can find our two solutions or roots, one with the + and the other with the -
1)
[tex]\begin{gathered} x=\frac{4+6}{2} \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]2)
[tex]\begin{gathered} x=\frac{4-6}{2} \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}[/tex]so the roots are going to be: -1, 5
1. A ball is thrown with an initial velocity of 86 feetper second 4 feet from the ground. The functionn(t) = -16t2 + 86t + 4 represents the height, h, of theball t seconds after it was thrown. After how manyseconds will the ball hit the ground?A. 4.7 secondsB. 4.9 secondsC. 5.2 secondsD. 5.4 secondsА A
D. 5.4 seconds
1) Since the course of that ball is described by the function h(t) = -16t² +86t +4.
So we can sketch out:
When the ball hits the ground, we'll have to find out the 2nd root of that function since when t=0, h =4. So let's find out the roots:
[tex]\begin{gathered} h(t)\text{ =-16t²+86t+4} \\ \Delta=(86)^2-4(-16)(4) \\ \Delta=7396+256 \\ x=\frac{-86\pm\sqrt[]{7652}}{2(-16)} \\ x_1=5.42 \\ x_2=-0.046 \end{gathered}[/tex]3) Since just the positive answer is interesting, then we can state that the answer is D (rounded off to the nearest tenth
Rich works 140 hours in a month. if his schedule stays the same ,how many hours he work in 3/4 of a month
Let's identify first what informations were given in the scenario:
What is Given: Rich works: 140 hours in a month.
What is being asked: How many hours he work in 3/4 of a month?
To be able to determine how many hours did Rich works in 3/4 of a month, we generate this equation:
[tex]Rich^{\prime}s\text{ work hours in 3/4 month = (Work hours in a month)(3/4)}[/tex][tex]\text{ = (140)(3/4) = }\frac{140\text{ x 3}}{4}[/tex][tex]\text{ = }\frac{420}{4}[/tex][tex]\text{Rich's work hours in 3/4 month = 105 hours}[/tex]Therefore, Rich works 105 hours in 3/4 of a month.
The graph shows the number of centimeters a particular plant grows over time. What is the slope of the line? Reasoning What does the slope mean?
We have the following:
The slope is about 1
The slope is the increment per unit, in this case it would be the increment in cm per week.
[tex]undefined[/tex]12. Zea has a credit limit of $2,000 on her credit card. Each month, she charges
about $200 and makes a payment of $125.
a. Estimate the number of months that Zea can continue this pattern until
she reaches her credit limit.
9001
b. Consider that part of the $125 Zea pays each month will be for finance
charges. How will the number of months from part a be affected by these
charges?
Answer:
Step-by-step explanation:
1. It will take Zea 27 months to reach her credit card limit.
2. The number of months will be less than 27.
about 120 out of every 320 people are left-handed. if 3,360 students attended Davis High School, about how many are left handed
Using the rule of 3
120 - 320
x - 3360
120*3,360 = 320x
403,200 = 320x
403,200/320 = x
x = 1,260
About 1,260 students are left handed.
Find the volume of a cone with a base radius
Solution
Step 1:
Write the formula for the volume of a cone.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{r = radius} \\ \text{h = height} \end{gathered}[/tex]Step 2:
Given data
r = 6 in
h = 8 in
Step 3
Substitute in the formula to find the volume.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{= }\frac{1}{3}\times\pi\times6^2\times8 \\ =\text{ }\frac{1}{3}\times\pi\times36\times8 \\ =\text{ }\frac{288\pi}{3} \\ =\text{ 96}\pi\text{ in}^3 \end{gathered}[/tex]Final answer
[tex]Volume\text{ of the cone = 96}\pi\text{ in}^3[/tex]A line passes through (1, -1) and (3, 5).What is the equation of the line in slope-intercept form?
Step 1 : Let's find the points given in the cartesian plane and let's draw the line.
Step 2: Let's calculate m (slope), as follows:
m = (Y - Y1)/((X -X1)
Replacing with the values we already know, we have:
m = (5 - (-1)/ 3 - 1
m = 6 /2 = 3
Step 3: Now, we can write the equation, as follows:
y - y1 = m (x -x1)
y - (-1) = 3 (x - 1)
y + 1 = 3x - 3
y = 3x -4
This is the equation that solves the question: y = 3x - 4
change to y=mx+b form 3x-y=6
Starting with the equation:
[tex]3x-y=6[/tex]Isolate the variable y. Substract 3x from both sides of the equation:
[tex]-y=6-3x[/tex]Multiply both sides of the equation by -1:
[tex]y=-6+3x[/tex]Use the commutative property of the sum to rewrite the right hand side of the equation:
[tex]y=3x-6[/tex]This equation is written in the form y=mx+b.
Solve the inequality: 4x + 8 - 5x > 13
4x+8-5x > 13
Combine like terms
4x-5x+8> 13
-x +8 > 13
Subtract 8 from both sides:
-x+8-8 > 13-8
-x > 5
Multiply both sides by -1
x < -5
Determine if the following statements are true or false. False [481] = |-481 -21 = -21 976976 1-94 = 94
I understand that you typed by error a square bracket instead of an absolute value vertical bar, right?
|481| = 481 this is a TRUE statement
|-21| = - 21 This is a FALSE statement since |-21| = 21
|976| = - |976| This is a FALSE statement, since |976| = |976| and not equal to the negative of it.
Is the last expression
|-94| = 94?
If such is the case, the statement is TRUE, since the absolute value of a number is ALWAYS the positive of that number.
|-94| = 94 TRUE statement.
I need help with this geometry question can someone help me the first one says parallelogram with non perpendicular and non congruent adjacent sides, trapezoid with exactly one pair of parallel sides, rectangle with non congruent adjacent sides, and rhombus with non perpendicular adjacent sides
a) rhombus with no perpendicular adjacent sides.
b) kite
7. Zak buys 6 gallons of fruit punch. He hascoupons for $0.55 off the regular price ofeach gallon of fruit punch. After using thecoupons, the total cost of the fruit punch is$8.70. Find the regular price of a gallon offruit punch. (Example 2)
Zak buys 6 gallons of fruit punch.
He has coupons for $0.55 off the regular price of each gallon of fruit punch.
This means that $0.55 will be subtracted from the regular price of each gallon.
After using the coupons, the total cost of the fruit punch is $8.70.
Let x be the regular price of each gallon of fruit punch.
[tex](x-\$0.55)\times6=\$8.70[/tex]Now let us solve this equation for x.
[tex]\begin{gathered} (x-\$0.55)\times6=\$8.70 \\ 6x-\$3.3=\$8.70 \\ 6x=\$8.70+\$3.3 \\ 6x=\$12 \\ x=\frac{\$12}{6} \\ x=\$2 \end{gathered}[/tex]Therefore, the regular price of each gallon of fruit punch is $2
Right angle ABC is taken by dilation with center P and scale factor 1/2 to angle A’B’C’. What is the measure of angle A’B’C’
The measure of angle A'B'C' will be 90 degree.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Right angle ABC is taken by dilation with center P and scale factor 1/2 to angle A’B’C’.
Now,
Since, We know that;
When a figure is dilated by a scale factor then the shape of the figure is not change.
Thus, The measure of ABC is same as the measure of A'B'C'.
Here, The measure of angle ABC = 90 degree
Hence, The measure of angle A'B'C' = 90 degree.
Therefore, The measure of angle A'B'C' will be 90 degree.
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use the Pythagorean theorem to find the length of the hypotenuse in the Triangle
Answer:
10 units
Explanation:
The Pythagorean theorem says that the hypotenuse c of a triangle is equal to:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where a and b are the length of the other sides of the triangle.
So, replacing a by 6 and b by 8, we get that the hypothenuse is equal to:
[tex]\begin{gathered} c=\sqrt[]{6^2+8^2} \\ c=\sqrt[]{36+64} \\ c=\sqrt[]{100} \\ c=10 \end{gathered}[/tex]Therefore, the length of the hypothenuse is 10 units
create 3 equivalent fractions for the fraction 2/7 . Explain how all of those are equivalent
create 3 equivalent fractions for the fraction 2/7 . Explain how all of those are equivalent
we have the fraction
2/7
Remember that equivalent fractions are fractions that the quotient is the same
If you multiply a number by 1 or 1/1 the result is the same number
Example
if you have 2/7 and you multiply by (3/3)
(2/7)*(3/3)
remember that 3/3=1
so
(2/7)*(3/3)=6/21
2/7 and 6/21 are equivalent fractions
because
2/7=0.2857
6/21=0.2857
second equivalent fraction
2/7 multiply by 5/5
(2/7)(5/5)=10/35
2/7 and 10/35 are equivalent
because
2/7=0.2857
10/35=0.2857
third equivalent fraction
2/7 multiply by 4/4
(2/7)(4/4)=8/28
2/7 and 8/28 are equivalent
because
2/7=8/28
multiply in cross
2*28=7*8
56=56 ----> is true
that means
fractions are equivalent
Remember
If you multiply the numerator and denominator of a fraction, by the same number, you obtain a equivalent fraction
On his way home from school board meeting , Keith fills up his car. He like the idea of using gasoline with ethanol , but think his car only handle 40% ethanol. At the gas station , he can use regular gas with 10% ethanol or E85 fuel with 85% ethanol. How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol ?
ANSWER:
6 gallons regular gas with 10% ethanol and 4 gallons E85 fuel with 85% ethanol
STEP-BY-STEP EXPLANATION:
In this case, we must test with values for each fuel class to arrive at the correct answer.
For example, 6 gallons of 10% ethanol and 4 gallons of 85% ethanol:
[tex]\begin{gathered} 10\text{\% of 6 =}\frac{10}{100}\cdot6=0.6\text{ gallons of ethanol in it} \\ 85\text{\% of 4 =}\frac{85}{100}\cdot4=3.4\text{ gallons of ethanol in it} \\ \text{ Total ethanol in 10 gallons is 0.6 + 3.4 = 4 gallons }\rightarrow\text{ 4 gallons is 40\% of 10} \\ \text{Therefore, we have 10 gallons of fuel containing 40\% ethanol } \end{gathered}[/tex]Find XFind yThe trapezoids shown below are similar. Find the length of x and y.10x 14Solve for X4 holy/2 1014Solve for y4(4x4) 11977 (10x2) 142Х[X=1.616/10l y- 2014y = 519) X1.6520) y=21) What scale factor was used to create the image of the new trapezoid? (figure 1+figure 2)Record your answer and fill in the bubbles. Be sure to use the correct place value.
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
so
Find the value of x
applying proportion
4/x=10/4
or
x/4=4/10
x=16/10
x=1.6
Find the value of y
y/2=10/4
y=5
Find the scale factor
In this problem we have an enlargement,
that means ------> the scale factor is greater than 1
Divide 10/4=2.5
the scale factor is 2.5
The length of cell A is 3x10-5 m. The length of cell B is 0.000001 m.What is the ratio of cell A's length to cell B's length? Use pencil and paper. Is it easier to find the ratiowhen the numbers are expressed in scientific notation or in standard form? Explain your reasoning.The ratio of cell A's length to cell B's length is(Type the ratio as a simplified fraction.)
we have the following:
[tex]\begin{gathered} r=\frac{L_A}{L_B} \\ r=\frac{3\cdot10^{-5}}{0.000001}=\frac{3\cdot10^{-5}}{1\cdot10^{-6}} \\ r=30 \end{gathered}[/tex]the rario is 30
Find the x and y intercept then use them to graph the line
The x-intercept = (7, 0)
The y-intercept = (0, -3.5)
Explanation:The given equation is:
-2x + 4y = -14
Find the x-intercept by setting y = 0
-2x + 4(0) = -14
-2x + 0 = -14
-2x = -14
x = -14/-2
x = 7
Therefore, the x-intercept = (7, 0)
Find the y-intercept by setting x = 0
-2(0) + 4y = -14
0 + 4y = -14
4y = -14
y = -14/4
y = -3.5
Therefore, the y-intercept = (0, -3.5)
Considering the x and y-intercepts, the graph is plotted
the total amounts of rainfall at various points And time during a thunderstorm are shown in the table. time(hours) 0.4 | 1.1 | 2.9 | 3.2 | 3.7 | 4.4Rainfall(cm) 0.3 | 0.6 | 1.8 | 2.0 | 2.2 | 2.6According to a regression calculator, what is the equation of the line of best fit for the data?answers: a y= 0.06x+0.03 | b y= 0.06x+0.29 | c y=0.59x+0.03 | d y= 0.59x+0.29Please help!
The number of kilograms of water in a human body varies directly as the mass of the body. A 66 kg person contains 44 kg of water. How many kilograms of water are in a 144 kg person?
Given:
A 66 kg person contains 44 kg of water.
To find:
The number of kilograms in a 144kg person.
Explanation:
According to the problem, 66 kg person contains 44 kg of water.
For 1 kg person contains,
[tex]\begin{gathered} 1kg\text{ of person}=\frac{44}{66}kg\text{ of water} \\ =\frac{2}{3}kg\text{ of water} \end{gathered}[/tex]Then, for 144kg of a person contains,
[tex]\begin{gathered} 144kg\text{ of a person}=144\times\frac{2}{3}kg\text{ of water} \\ =96kg\text{ of water} \end{gathered}[/tex]Therefore, 144kg per person contains 96 kg of water.
Final answer:
144kg per person contains 96 kg of water.