Answer:
3x-8
Step-by-step explanation:
Use synthetic division:
5 | 3 -23 40
____ 15 -40_
3 -8 | 0
Hence, another factor of the polynomial is 3x-8
How many distinct subsets of the set $s=\{1,8,9,39,52,91\}$ have three-digit sums?
The number of distinct subset of the set is an illustration of combination
There are 34 distinct subset of the set that have three digit sums
How to determine the number of distinct subsets?The set is given as:
S = {1,8,9,39,52,91}
Group the elements
S = {(1,8),9,39,52,91}
So, we have:
S ={s1,s2,s3,s4,s5}
To have a three-digit sum, the sum of the selected elements must be 100 or above.
The number of ways the above set can be selected is:
[tex]n_1 = 4 * [^3C_1 + ^3C_2 + ^3C_3] + 1[/tex]
Evaluate
[tex]n_1 = 4 * [3 + 3 + 1] + 1[/tex]
[tex]n_1 = 29[/tex]
The set can be further rearranged as:
S = {(52,39),9,(8,1)}
i.e.
S = {b1,b2,b3}.
The number of ways the above set can be selected such that the sum is 100 or above is:
[tex]n_2 = 2 * [^2C_1] + 1[/tex]
Evaluate
[tex]n_2 = 2 * 2 + 1[/tex]
[tex]n_2 = 5[/tex]
So, the total number of ways is:
[tex]n = n_1 +n_2[/tex]
This gives
[tex]n = 29 +5[/tex]
[tex]n = 34[/tex]
Hence, there are 34 distinct subset of the see that have three digit sums
Read more about combination at:
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There are 34 distinct subsets of the see that have three-digit sums.
What are distinct subsets of the set?When we know that S is a subset of T, we place the circle representing S inside the circle representing T.
The set is given as:
S = {1,8,9,39,52,91}
Group the elements
S = {(1,8),9,39,52,91}
S ={s1,s2,s3,s4,s5}
To have a three-digit sum, the sum of the selected elements must be 100 or above.
The number of ways the above set can be selected is:
[tex]\rm n_1=4\times (^3C_1+^3C_2+^3C_3)+1\\\\n_1=4(3+3+1)+1\\\\n_1=4 \times 7+1\\\\n_1=28+1\\\\n_1=29[/tex]
The set can be further rearranged as:
S = {(52,39),9,(8,1)}
S = {b1,b2,b3}.
The number of ways the above set can be selected such that the sum is 100 or above is:
[tex]\rm n_2=2\times ^2C_1+1\\\\n_2= 2\times 2+1\\\\n_2=4+1\\\\n_2=5[/tex]
The distinct subsets of the set are;
[tex]\rm n_1+n_2=29+5 =34[/tex]
Hence, there are 34 distinct subsets of the see that have three-digit sums.
Read more about combination at:
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NO LINKS!!! Which term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line?
Answer: C
Step-by-step explanation:
find the area of this circle. Use 3.14 as (pie symbol) click the photo to see the circle ! Please help
Answer:
Its 452.16
Step-by-step explanation:
Because the formal is [tex]\pi[/tex]r2
Which is 3.14*12*12=452.16
Can anyone solve this correctly?
Answer:
30 cm²
Step-by-step explanation:
The shaded area is the difference between the area of the rectangle and the area of the triangle.
The area of the rectangle is ...
A = LW = (12 cm)(4 cm) = 48 cm²
The area of the triangle is ...
A = 1/2bh = 1/2(9 cm)(4 cm) = 18 cm²
__
The shaded area is the difference ...
rectangle area - triangle area = 48 cm² -18 cm² = 30 cm²
The area of the shaded region is 30 square centimeters.
Answer:
ANSWER30cm²Step-by-step explanation:
A(rectangle) - A(triangle)
L×W - ½×B×H
12×4 - ½×(9)×(4)
48 - 2×(9)
48 - 18
= 30cm²
Larry earns $5.25 per hour helping his neighbor. Last month he earned $220.50. How many
hours did Larry work?
What is the area of the given triangle?
Answer:
B 12
Step-by-step explanation:
4 x 6 = 24 divided by 2 = 12
Covert 135 degrees to radian
Answer:
2.35619
Step-by-step explanation:
Answer:
2.35619
Step-by-step explanation:
Deg to Rad = ° x pi / 180
What is the equation of the line that passes through the point (-2,-1) and has a slope of 1/2? ?
equation of line will be
y+1=1/2(x+2)
Hello!
Let's write the equation of the line in both Point-Slope Form and Slope-Intercept Form.
First, point-slope form:
y-y1=m(x-x1)
y-(-1)=1/2(x-(-2) (Point-Slope Form)
Now, convert into Slope-Intercept form:
y+1=1/2(x+2)
y+1=1/2x+1
y=1/2x+1-1
y=1/2x
Hence, the equation of the line is
[tex]\boxed{\boxed{\bold{y=\frac{1}{2}}} }[/tex] (Slope-Intercept Form)
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Solve and show the answer in simplest terms 2 over 5 + 1 over 3
Answer:
11/15
Step-by-step explanation:
2/5+1/3
Find a common denominator-15. The fractions with the common denominator are 6/15 and 5/15. They make 11/15. 11/15 is in its simplest form.
If the radius of a circle is x cm. what is the length of it's circumferences?
Answer:
44/7x
Step-by-step explanation:
circumference of circle= 2πr
=2×22/7×x
=44/7x
A 20-inch pizza has an area of 314 in? That pizza is
divided into eight equal slices. What is the area of two slices of
that pizza?
A. 3114 in2
B. 78.5 in2
C. 39.25 in2
D. 314 in2
The area of each pizza is gotten by dividing the total area by the number of slices. Therefore, the area of two slices of that pizza is 31.4 inches².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words the area is the space occupied by a flat shape or the surface of an object.
Therefore, 20 inch pizza has an area of 314 inches². The pizza is divided into 8 equal slices.
Each area of the slices = 314 / 20
Each area of the slices = 15.7 inches²
Therefore, the area of two slices of the pizza is as follows:
area of two slices = 15.7 + 15.7 = 31.4 inches²
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WILL GIVE BRAINLIEST! Calculate the length of AB
Answer:
x=6.6
Step-by-step explanation:
13:5=x:3
33=5x
33/5=x
6.6=x
Answer:
15.16047 cm
Step-by-step explanation:
notice that the smaller triangles ratio is 3 : 5
so the bigger triangle's bottom side has length 13 cm
so lets multiply 13 by (3/5)
we get 7.8
we can just use pythagorean theorem to find AB
[tex]\sqrt{x} = 7.8^{2} + 13^{2}[/tex]
15.16047 cm
x/14=7
what is x?
x/5=4.1
What is x
Answer:
x = 98 , x = 20.5
Step-by-step explanation:
[tex]\frac{x}{14}[/tex] = 7 ( multiply both sides by 14 to clear the fraction )
x = 98
[tex]\frac{x}{5}[/tex] = 4.1 ( multiply both sides by 5 to clear the fraction )
x = 20.5
Step-by-step explanation:
#1
x/14=7
x=14×7
x=98
#2
x/5=4.1
x=5×4.1
x=20.5
The expression 0.09x+(x−30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax. The tax is on the original price.
Which expression represents the amount of tax that is paid on the bicycle?
ANSWER
I believe that the amount of the instant rebate is $30. X represents the price of the bike, and 0.09 is the sales tax.
So if the bike cost $100:
0.09(100) + (100-30) = 9 + 70 = $79
Although I think I would want them to tax the bike after the instant rebate and not on the original price.
If I'm wrong about the instant rebate then it would be 1.09x-30. Hope this helps.
please can i have help answering the question in the picture
Hey there!
Answer: [tex] \Rightarrow \sf{\frac{x+3}{x -2}}[/tex]
[tex] \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }[/tex]
[tex] \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}[/tex]
Teleia bought 25 shirts for $237.50. How much would only one shirt cost?
Answer:
$9.50
Step-by-step explanation:
Divide 237.50 by 25
Lowes is having a Customer Appreciation Day Sale. Everything in the store is 25% off. The final purchase for the consumer is $2021.63. What is the cost to the consumer? Sales tax is 5%.
Answer:
$1592.03
Look at image above...
Evaluate the expression for p = 3.
2p =
Answer:
6
Step-by-step explanation:
2 x 3
Express the decimal as a percent. 1.276
60 points.
To change a decimal to a percentage, all that we have to do is multiply the decimal by 100 (or move the decimal point to the right two places).
1.276 x 100 = 127.6
Percentage: 127.6%
Hope this helps!
if raymond had 50 dogs and gets 80 how many does he have?
Answer:
50+80 = 130
Step-by-step explanation:
Answer:
50+80=130
Step-by-step explanation:
please mark me the brainiest
One of the acute angles in a right triangle measures 62°. What is the measure of the other acute angle in the triangle?
Answer: 28 degrees
Step-by-step explanation:
In a right triangle, the two acute angles are complementary, so the other acute angle measures 90-62=28 degrees.
∠C and ∠D are complementary.
Let m∠C=(8x)° and m∠D=(5x−1)°.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 7Step-by-step explanation:
Complementary angles are angles that add up to 90°.
We have C and D as complementary.
Their sum is:
m∠C + m∠D = 90Substitute values and solve for x:
8x + 5x - 1 = 9013x = 90 + 113x = 91x = 91/13x = 7Answer:
x = 7
Step-by-step explanation:
Complementary angles are two angles that sum up to 90°. In this case, we are given that ∠C and ∠D are complementary. This means that the sum of ∠C and ∠D is equivalent to 90°.
⇒ ∠C + ∠D = 90°
⇒ 8x + 5x - 1 = 90° [∠C = 8x; ∠D = 5x - 1]
⇒ 13x - 1 = 90°
⇒ 13x = 90 + 1
⇒ 13x = 91
⇒ 13x/13 = 91/13
⇒ x = 91/13 = 7
What are the x-intercepts of ? f(x)=x3+4x2-9x-36? A. (1,0),(2,0),(3,0) B. (-1,0),(2,0),(18,0) C. (-6,0)(2,0)(3,0) D.(-4,0),(-3,0)(3,0)
Answer:
D. (-4,0),(-3,0)(3,0)
Step-by-step explanation:
Please help me with this please and thank you
Answer:
12
Step-by-step explanation:
4x-3x
4*3=12
it is 12
2. Triangle ABC is rotated around the origin. If vertex A transforms from A(-8,-10) to A (8, 10), which rotation was performed on the triangle?
Answer:
A. R180 degree rotation
Step-by-step explanation:
if you think about a graph, it has four quadrants, so imagine each of the quadtrants, being an add on of 90 degrees from the one you started on, so if you started in the double negative quatrant in the bottom left, it would take two quadrants to go in a circle to get to the full positive quadrant, making this, a 180 degree rotation
The mean distance from the Earth to the Sun is c gigametres (Gm), where c = 150 and 1 Gm = 10⁹ m. The mean distance from Pluto to the Sun is d terametres (Tm), where d= 5.91 and 1 Tm = 10¹² m. Express d as a percentage of c. Give your answer in standard form.
please help, I don't understand how to get percentage
yeah help me okay thanks
Answer:
4
3
Step-by-step explanation:
154-54(79-1554)+12x24
Answer:
80092
Step-by-step explanation:
Answer:
80092.Step-by-step explanation:
Given equation:
154 - 54 * (79 - 1554) + 12 * 24Step-By-Step:
Step 1
Subtract the numbers:
154 - 54 * (79 - 1554) + 12 * 24= 154 - 54 * (-1475) + 12 * 24Step 2
Multiply the numbers:
154 - 54 * (-1475) + 12 * 24= 154 + 79650 + 288Step 3
Add the numbers:
154 + 79650 + 288= 80092.Answer is 80092.
Simon's dog jumped into a stream at a 68° angle from the corner of a bridge. simon crossed the bridge and walked downstream to meet the dog.
part a how long is the bridge, in feet?
part b how many feet did the dog swim?
The length of the bridge is 12.12 feet.
The length the dog swam is 32.36 feet.
The situation forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. Therefore, the sides and angle can be found using trigonometric ratios.
The length of the bridge is the opposite side of the triangle and the length the dog swim is the hypotenuse side of the triangle.
Therefore,
Let's find the length of the bridge as follows:
tan 68° = opposite / adjacent
tan 68° = 30 / l
cross multiply
l = 30 / tan 68
l = 12.1212121212
length of the bridge = 12.12 ft
The length the dog swim is as follows:
sin 68°= opposite / hypotenuse
sin 68° = 30 / h
h = 30 / sin 68
h = 32.3561767942
The distance the dog swimmed = 32.36 ft
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How to find the area of a half of a square?
Answer:
if u make the square half by its midpoint then we can find its area by using the area of rectangle.
if u make the square half from the diagonal we can find its area by using area of triangle.