Answer:
Step-by-step explanation:
Let x be the length and y be the width
The length is 1 inch longer than the width
So : x-1 =y
●●●●●●●●●●●●●●●●●●
The diagonal is 5 inches
The diagonal, width and length are forming a right triangle where the diagonal is the hypotenus
The Pythagorian theorem:
x^2 + y^2 = 5^2
●●●●●●●●●●●●●●●●●●●●●●●
Let's calculate y the width
The system is :
x-1 = y => x =y+1
x^2 + y^2 = 25
Replace x in the second equation with y+1 :
(y+1)^2 + y^2 = 25
y^2 + 2y + 1 + y^2 = 25
2y^2 + 2y +1 = 25
2y^2 + 2y -24 = 0
This is a quadratic equation so we will use the discriminant
●●●●●●●●●●●●●●●●●●●●●●
the discriminat is b^2-4ac
● b =2
● a = 2
● c = -24
b^2 -4ac = 4-4*2(-24) =196 > 0
Since the dicriminant is positive this equation has two solutions y and y'
y = (-2-14)/4 = -16/4 = -4
y '= (-2+14)/4 = 12/4 = 3
The first solution is negative
A distance is always positive so the first solution can't be the width
Then the width is 3
The graph shows data from a science experiment in which the temperature of a substance was measured over time.
What is the constant of proportionality for degrees per minute?
Answer:
The answer to this question is ---> 1/4
Step-by-step explanation:
Express 510 & 3/10 % as a decimal fraction.
Answer:
5.10 and 0.3
Step-by-step explanation:
510% in decimal form is 5.10 if u move the decimal to the left twice
3/10% is 30% which in decimal from is .3 if u move the decimal over to the left twice
hope this helps
PLSSS HELPPP Simplify: (2 - i) (4 +2i)
Step-by-step explanation:
( 2 - 1)(4+2)
= (1)(6)
= 6
PLLLLLLLLLLZZZZZZZZZ
Answer:
Hey there!
Donald would have 20x+10 dollars.
20 dollars (number of 20 dollars) + 10 dollars
Answer: 20x + 10
Step-by-step explanation:
20x in this expression means 20 * the number of dollar bills he owns. Each bill is worth twenty dollars. + 10 is simply 10 * 1(the number of 10 dollar bills he owns)
Hope it helps <3
30 POINTS! Please HELP! (5.06 MC) Determine the equation for the line of best fit to represent the data
y = 1/5x + 1 y = -5/1x + 1 y = -1/5x + 1 y = - 1/5x - 1
Answer:
y=-1/5+1
Step-by-step explanation:
Answer:
y = -1/5x + 1
Step-by-step explanation:
In these types of problems you want to guesstimate the slope and draw an imaginary solid line amongst the dots. The slope you'll end up with is -1/5 because the graph is decreasing.
and just to check, i typed this into my graphing calculator and can confirm this as the answer. :)
Two terms of an arithmetic sequence are a5=23 and a20=98. find the first 60 terms of the sequence
Answer:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
Step-by-step explanation:
The nth term of an arithmetic sequence is obtained using the formula:
[tex]a_n=a+(n-1)d[/tex]
Given that: [tex]a_5=23$ and a_{20}=98.[/tex]
a_n=a+(n-1)d
[tex]a_5=23=a+(5-1)d \implies a+4d=23\\a_{20}=98=a+(20-1)d \implies a+19d=98\\$We solve simultaneously$:\\a+19d=98\\a+4d=23\\15d=75\\d=5\\Recall:a+4d=23\\a+4(15)=23\\a=23-60\\a=-37[/tex]
Therefore, the first 60 terms of the sequence are:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
First 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
Arithmetic sequence: If two consecutive terms of a sequence has a common
difference 'd', sequence will be an arithmetic sequence and the
explicit formula for the nth term of the sequence will be,
[tex]A_n=a+(n-1)d[/tex]
Here, [tex]a=[/tex] First term
[tex]n=[/tex] nth term
[tex]d=[/tex] common difference
Given in the question,
Two terms [tex]a_5=23, a_{20}=98[/tex]
If 5th term of the sequence is 23,
[tex]23=a+(5-1)d[/tex]
[tex]23=a+4d[/tex] -------(1)
If 20th term of the sequence is 98,
[tex]98=a+(20-1)d[/tex]
[tex]98=a+19d[/tex] ----------(2)
Subtract equation (1) from equation (2),
98 - 23 = a + 19d - (a + 4d)
75 = 15d
d = 5
Substitute the value of 'd' in equation (1),
23 = a + 4(5)
a = 23 - 20
a = 3
Therefore, first 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
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The number 99 is increased to 104. What is the percentage by which the number was increased, to the nearest tenth of a percent?
Answer:
5%
Step-by-step explanation:
104/99=1.05
Answer: 5%
Step-by-step explanation:
if you do the math of 99+5% you will get 103.95 and if you round that to the tenth you get 104.
simplify the expression (-h^4)^5
when a number is to a power then to another power, the answer is the number to the power TIMES the other power
it should be:
-h^20.
can you also answer these?!?
i cannot see the question for #33, but for
#34, im sure there are a bit more efficent ways to find surface area, but i just find the area of each square. area of top and bottom=240 square inches (120+120); area of shorter sides=60 square inches (30+30); area of longer sides= 72 square inches (36+36). add all of those together, so the total surface area is 372 square inches. So basically Charlene will need 372 square inches of wrapping paper
#35 the formula for volume is length*width*height. So do 60*45.5*14=38,220 cubic ft.
#36 first find the area of that triangle. (6*14)/2=42. Then find area of square which is 20*14=280. Add those (280+42) and get 322. So the area of the polygon is 322 square mm
The hypotenuse of a right triangles is 7 inches longer than the base and 14 inches longer than the height. The perimeter is 84 inches. Find its area
Answer:
294 in^2 = A
Step-by-step explanation:
Let h represent the length of the hypotenuse, b the base and h the height. Because this is a right triangle, the Pythagorean Theorem applies.
(hypotenuse)^2 = (base)^2 + (height)^2
h^2 = (h - 7)^2 + (h - 14)^2
Perimeter of the triangle is 84 inches, equal to (h) + (h - 7) + (h - 14), which in turn simplifies to 84 = h + h - 7 + h - 14, or 84 = 3h - 21, or 3h = 105. Solving this for h, we get h = 35.
Then the base is (35 - 7), or 28, and the height is (35 - 14), or 21.
The area of the triangle is found using the formula
A = (1/2)(base)(height) = (1/2)(28)(21) = 294 in^2 = A
Determine the measure of ∠F. answers: 1) 256° 2) 52° 3) 128° 4) 64°
Answer:
4) 64
Step-by-step explanation:
f = 128/2
f = 64
Answer:
4) 64°
Step-by-step explanation:
An inscribed angle has half the measure of the arc it intercepts.
m<F = (1/2)m(arc)BD
m<F = (1/2) * 128 deg
m<F = 64 deg
-3(2x +5) how to solve this problem
Answer:
Step-by-step explanation:
-3×2x)+(-3×5)
-6x+-15
Two retailers sell vanilla extract by the following price chart. When will their price be the same and how much?
Answer:
8 oz, $41
Step-by-step explanation:
For 4 oz, Chef Mate sells their's for $22 and Grocery Gourmet sells their's $25. Chef Mate sells his vanilla extract for $4.75/oz and Grocery Gourmet sells their's for $4/oz. At the 8th ounce, Chef Mate and Grocery Gourmet will charge the same amount, $41.
Chef Mate: $22 (price of 4 oz) + ($4.75 × 4) = $41
Gourmet Garden: $25 (price of 4 oz) + ($4 × 4) = $41
Question 8
Find the indefinite integral.
csc(4x) dx.
Answer:
Option C is correct.
Step-by-step explanation:
Your solution is correct. Given the integral [tex]\int \csc \left(4x\right)dx[/tex], let y = 4x, du = 4dx, respectively [tex]\frac{1}{4}[/tex]du = dx. Rewrite the given using these values of u and du.
[tex]\frac{du}{dx}[/tex] = 4 / 1 = 4,
[tex]\int csc(u)\frac{1}{4} du[/tex] - let us combine csc( u ) and 1 / 4,
[tex]\int csc(u) / 4 * du[/tex] - as 1 / 4 is a constant with respect to u, we can move it out of the integral,
[tex]\frac{1}{4} \int csc(u)du[/tex] - the integral of csc( u ) with respect to u is present in the form
" [tex]In(|csc(u) - cot(u)|)[/tex] . " Therefore,
[tex]\frac{1}{4} ( In(|csc(u) - cot(u)|) + C )[/tex] - replace all occurrences of u with 4x to receive the third solution. It can also be written as " [tex]\frac{1}{4} ( In(|csc(4x) - cot(4x)|) + C )[/tex], but only that your move the negative sign to the left of the integral.
Sign numbers, ratios & Proportion
(+10) + (+6) = ?
Answer:
16
Step-by-step explanation:
Putting a + in front of a number indicates that the number is positive. so we are just going to add it up.
10+6=16
10:6=5:3
Hope it helps:)
Find the area of the square with a side length of 8 ft.
Answer:
The area of square is 64ft².
Step-by-step explanation:
Given that all sides of a square are equal. So you have to apply the formula for area of square :
[tex]area = length \times width[/tex]
[tex]let \: length = 8 \\ let \: width = 8[/tex]
[tex]area = 8 \times 8[/tex]
[tex]area = 64 \: {ft}^{2} [/tex]
Answer:
here,
side length (l)= 8 ft.
now, area = l^2
a= 8^2
=64ft^2 is the answer..
hope i helped uh..
what is the surface ara of a sphere with a diameter of 16cm
32pi cm^2
256 pi cm^2
1,024 pi cm^2
126 pi cm^2
Answer:
1024pi cm²
Step-by-step explanation:
4pi(16)²
4pi256
1024pi
Answer:
[tex]256\pi {cm}^{2} [/tex]
Step-by-step explanation:
surface area of a sphere=4πr^2
diametre=16
[tex]radius = \frac{diametre}{2} [/tex]
radius=8
[tex]surface \: area \: of \: sphere = 4 \times \pi \times {8}^{2} [/tex]
[tex] \: \: \: \: = 4 \times \pi \times 64[/tex]
[tex] \: \: \: \: = 256\pi {cm}^{2} [/tex]
Image point B'(4, -8) was transformed using the translation (x-2, y + 3). What were the coordinates of B?
(2, -5)
(6,-5)
(2,-11)
(6.-11)
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Answer:
B(6 , -11)
Step-by-step explanation:
(x-2 , y+3) = (4 , -8)
Compare the x & y co ordinates
x - 2 = 4 ; y + 3 = -8
x = 4 +2 ; y = -8 - 3
x = 6 ; y = -11
B(6 , -11)
Make a story problem for the expression below. Then solve the problem. (n + 15) ÷ 5
Answer:
Bob buys n number of cookies. He goes again and buys 15 more. After that he splits them among 5 friends.
Step-by-step explanation:
Answer:
Sandy buys a number of slices of pizzas from Pizza Hut. She then goes to Marco's Pizza and buys 15 more slices. Sandy goes to a party and splits the pizza slices evenly between 5 friends. How many slices of pizza did she buy from Pizza Hut?
Given that 0≤β<2π, find all the solutions to the equation 2sin^2β=7sinβ+4.
Answer:
Step-by-step explanation:
2sin²β-7sinβ-4=0
2sin²β-8sin β+1 sin β-4=0
2 sin β(sin β-4)+1(sin β-4)=0
(sin β-4)(2sin β+1)=0
either sin β-4=0
sin β=4 (rejected,as |sin β|≤1)
or
2 sin β+1=0
sin β=-1/2=-sin (π/6)=sin (π+π/6),sin (2π-π/6)
β=7π/6,11π/6
5. Points A, B and C are all
the circle.O represents the centre.
Angle AOB = 2x+28 Angle ADB = 3x-70
Calculate the value for x
Answer:
Step-by-step explanation:
angle acb=1/2angle aob=1/2(2x+28)------(anble subtended by an arc at centre is double the angle subtended by it at any other parts of the circle)
angle c+angle d=180....opp angles of a cyclic quad. are supplementry
hence,
x+14+3x-70=180
=>x=64
The value of x from the given figure is 59°.
Given that, points A, B and C are all the circle. O represents the center.
What is circle theorem to relate angle at circumference and central angle?
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, Reflection of ∠AOB= 360-(2x+28)
∠ADB=1/2 (Reflection of ∠AOB)
⇒ 3x-70=1/2 (360-(2x+28))
⇒ 3x-70=1/2 (360-2x-28)
⇒ 3x-70=180-x-14
⇒ 3x-70=166-x
⇒ 3x+x=236
⇒ 4x=236
⇒ x=59
Therefore, the value of x from the given figure is 59°.
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At Jane's school there are 22 more girls than boys, b.
a) Write and expression for the number of girls in terms of the number of boys, b.
b) Using part a), write an equation involving b and solve it to find the number of boys at the school.
c) How many girls are there at the school?
ASAP no need to explain just the answer
Answer:
A) girls=boys +22 .B)Boys=girls-22
Step-by-step explanation:
Will give brainiest :)
Answer:
x= 116°
y= 127°
Step-by-step explanation:
x... The angle subtended at the centre is twice the angle subtended at the cicumfernce by the same arch
y.... Angle in a cyclic quadrilateral add up to 180°
hence 180-53=127
Fill in the blanks for me
Answer:
Statement | Reason
MNOP is a parallelogram | Given
PM ║ ON | Definition of a parallelogram
∠PMO ≅ ∠MON | Alternate interior angles theorem
MN ║ PO | Definition of a parallelogram
∠POM ≅ ∠MNO | Alternate interior angles theorem
ΔMNO ≅ ΔPOM | ASA postulate
PM ≅ ON | CPCTC
BC is tangent to circle A. Determine the length of AC . ANSWERS: 1) 3 2) 4 3) 5 4) 6
A circle is a curve sketched out by a point moving in a plane. The length of AC in the given figure is 5 units. The correct option is
3.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
In a circle, the angle between the radius and tangent is always equal to 90°. Therefore, we can write that in the given figure ΔABC, the triangle is a right angle triangle with ∠B as the right angle.
Now, for the triangle using the Pythagoras theorem we can write,
AC² = AB² + BC²
AC² = 3² + 4²
AC² = 9 + 16
AC = √25
AC = 5
Hence, the length of AC in the given figure is 5 units.
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Question 5 (1 point)
(06.02 LC)
Which statement best describes the expression 3y = 8? (1 point)
O 1) 8 divided by 3 times y
O2) 8 times y divided by 3
03) 3 divided by 8 times y
O4) 3 times y divided by 8
Answer:
Step-by-step explanation:
None of these choices is correct.
3y = 8 is an equation, not an expression. It states that "y is 8 divided by 3," which again is an equation.
Answer:
3 times y divided by 8
Step-by-step explanation:
Is 2(–2) + 6(2) equivalent to (–3)(–3) + (–1)(1)? Let negative numbers be represented with a "–" symbol and positive numbers be represented by "+" symbol. Use a pictorial model to justify your answer.
Answer:
Yes they are equivalent
Step-by-step explanation:
2(-2) = -4, plus 6(2) = 8 and
(-3)(-3) = 9, plus (-1)(1) = 8
Answer:
Yes they are equivalent
Step-by-step explanation:
the other fella right, check his reasons out, hope you guys learn from this question Stay safe everyone who sees this
QUICK 35 POINTS PLUS BRANLIEST. PLEASE ANSWER ALL THE QUESTIONS PROPERLY AND EXPLAIN HOW YOU GOT THEM. TRY TO ANSWER THEM BY TODAY.
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Hope it helps <3
(If it does, please give brainliest, only need one more for rank up :) )
Answer:
2. [tex]18\sqrt{5}[/tex]
3. [tex]52.303...[/tex]
4. [tex]11.608...[/tex]
Step-by-step explanation:
2. Using the Pythagorean Theorem, we can see that [tex]a^2+b^2=c^2[/tex]. Therefore, [tex]90^2+90^2=8100+8100=c^2[/tex]. We know that [tex]8100+8100[/tex] is [tex]16200[/tex]. The square root of [tex]16200[/tex] is [tex]90\sqrt{2}[/tex].
3. Same as before, we use the Pythagorean Theorem. This time, we're calculating [tex]b[/tex] instead of [tex]c[/tex]. This means we have to do [tex]60^2-29.4^2=b^2[/tex], which gives us [tex]3600-864.36[/tex], which equals [tex]2735.64[/tex]. We can put this in decimal form, which would give us [tex]52.303[/tex][tex]...[/tex]
4. This one, we do [tex]15^2-9.5^2[/tex], which would give us [tex]134.75[/tex]. Simplifying this would give us [tex]11.608...[/tex].
Hope this helped! Just remember the Pythagorean Theorem.
Could someone help with this?
Answer:
30t
Step-by-step explanation:
2(15)t
30t
Answer: 30t
Step-by-step explanation:
The group earned 15t, or 15$ an hour for t hours. Then it was doubled(15t * 2=30t)
several people at a local mall were surveyed about the kind of vehicle they drive and whether they own or rent their home. Use the results listed in the table to find the probability that a randomly selected person from the survey either rents their home or drives an SUV.
Answer as a fraction = 18/25
Answer in decimal form = 0.72
Answer in percent form = 72%
=========================================================
Explanation:
We have A = 6+6+1 = 13 people who rent their home (add the values along the bottom row). There are B = 5+6 = 11 people who drive an SUV (add up the values in the SUV column). There are A+B = 13+11 = 24 people who either rent their home or drive an SUV. Keep in mind that 6 people have been double counted if we just go with A+B without adjustment. These 6 people both rent their home and drive an SUV. To correct for the double-count, we subtract off 6 from A+B to get A+B-6 = 24-6 = 18.
So there are 18 people who rent their home, drive an SUV, or both.
This is out of 4+5+3+6+6+1 = 25 people surveyed total.
The probability of selecting someone who rents their home or drives an SUV is 18/25. In decimal form that is equivalent to 0.72 which converts to 72%