[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{ - 21}{10} \:(or) \: - 2 \frac{1}{10} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{8}{ - 5} + ( \frac{ - 1}{2} )[/tex]
[tex] \\= \frac{ - 8}{5} - \frac{1}{2} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.
The L. C. M for 5 and 2 is 10.
Now, multiply the L.C.M. with both numerator & denominator.
[tex]\\ = \frac{ - 8 \times 2}{5 \times 2} - \frac{1 \times 5}{2 \times 5} [/tex]
[tex] \\= \frac{ - 16}{10} - \frac{5}{10} [/tex]
Now that the denominators are equal, we can subtract the numerators.
[tex] \\= \frac{ - 16 - 5}{10} [/tex]
[tex] \\= \frac{ - 21}{10} [/tex]
[tex] \\= - 2 \frac{1}{10} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♨}}}}}[/tex]
Answer:
-21/10
Step-by-step explanation:
-8/5. + -1/2
2(-8/5) + (-1/2)5
-16/10 - 5/10
-21/10
How do I Simplify V5(8+3V6) ???
Answer:
[tex]8\sqrt{5}+3\sqrt{30}[/tex]
Step-by-step explanation:
When we have any quantity being multiplied to an expression, we can use the distributive property. The distributive property says that [tex]a(b+c)=ab+ac[/tex]. In other words, we can distribute the outer number inside the parentheses.
Using the distributive property, we can then simplify the given equation as follows:
[tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}[/tex]
Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root. For instance, [tex]\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}[/tex] (note, this does not work for addition or subtraction, only multiplication or division). Therefore, we can simplify [tex]\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}[/tex].
Finally, we can combine our answer into [tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}[/tex]
A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides length of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf
Answer: The value of x is 5.970.
Step-by-step explanation:
Given: The square has sides length of X cm.
Let r be the radius of the circle.
The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.
Then diagonal of square = diameter of circle
i.e. [tex]\sqrt{2}x= 2r[/tex] [Diagonal of square = [tex]\sqrt{2}[/tex](side)]
i.e. [tex]r=\dfrac{x}{\sqrt{2}}[/tex]
area of circle =[tex]\pi r^2[/tex]
i.e. [tex]56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2[/tex]
[tex]56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970[/tex]
Hence, the value of x is 5.970.
Which equation describes the
function table?
A b = a - 1
B a = b - 1
C b = 3a + 3
D b = 2a + 1
Answer:
The answer is no.d b= 2a + 1
Explanation:
Each time b goes up by 4, 'a' goes up by 2. The rate of change or slope is 4/2 = 2. This lets us see that the answer must be choice D, as no other answer choice has 2 as a slope.
A and B contributed 2700 and 1800 respectively to start a business. They agreed to share the profit in the ratio 7:5 respectively. If the profit made was 900, Calculate A's share as a percentage of total profit.
Answer:
58.33%
Step-by-step explanation:
A's Contribution = 2700
B's Contribution= 1800
Ratio = 7:5
Profit = 900
Total Ratio = 7+5 = 12
First , Calculate both share of the profit.
A's Share= 7/12 ×900
525
B's share= 5/12 ×900
375
Now , express A's Share as a percentage
A's Share= 525/900 ×100
58.33%
Someone please help me ASAP
Answer:
(4, 0)
Step-by-step explanation:
D is clearly (1, 2).
so, for D' we have (1+3, 2-2) = (4, 0).
that's it. there is nothing more to it.
NEED AN ANSWER ASAP
a linear piecewise function is represented by the graph. use the graph to evaluate the function.
when x = -5, y = ___
a) -5
b) 3
c) 5
when x = –1, y = ___
a) -2
b) 1
c) 3
When x = 3, y = ___
a) -4
b) 1
c) 3
Step-by-step explanation:
When X is - 5 then y is 3
When X is-1 then y is - 2
When X is 3 then y is -4
From the graph we get, when x is - 5 then y is 3, when x is -1 then y is - 2, and when x is 3 then y is -4.
What is a point?A point is a dot in space used to indicate an exact location in space.
Consider the first line, which has constant y values. its x value ranges from -1 to negative infinity.
The second line is starts from (-1,-2) point and tend towards positive infinity but its y values and x values are varying.
Hence, when x = -5 y is 3 and at x = -1 the y values is -2. Similarly, when x = 3 then y = -4.
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In the afternoon, the person (who is 1.8 m tall) casts a shadow that is 10 m. The distance along the ground from the person (H) to the tree (G) is 24 m, and the distance from the tree (G) to the building (F) is 150 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
Answer:
The height of the tree is 6.12 meters and the height of the building is 33.12 meters.
Step-by-step explanation:
Since the person is 1.8 meters tall, HC = 1.8
And since their shadow is 10 meters long, HD = 10.
We are also given that GH is 24 meters and that FG is 150 meters.
Height of the Tree:
The height of the tree is given by GB.
Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.
Likewise, ∠D ≅ ∠D. So, by AA-Similarity:
[tex]\displaystyle \Delta BGD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{GB}{GD}=\frac{HC}{HD}[/tex]
Note that:
[tex]GD=GH+HD[/tex]
Find GD:
[tex]GD=(24)+(10)=34[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{GB}{34}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10GB=61.2[/tex]
Therefore:
[tex]GB=6.12\text{ meters}[/tex]
The height of the tree is 6.12 meters.
Height of the Building:
The height of the building is given by FA.
Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.
∠D ≅ ∠D. So, by AA-Similarity:
[tex]\Delta AFD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{FA}{FD}=\frac{HC}{HD}[/tex]
Note that:
[tex]FD=FG+GH+HD[/tex]
Find FD:
[tex]FD=(150)+(24)+(10)=184[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{FA}{184}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10FA=331.2[/tex]
Therefore:
[tex]FA=33.12\text{ meters}[/tex]
The height of the building is 33.12 meters.
What is the simplified value of the expression below?
3(8-4)+2x5.5
31
Оооо
47
2. Solve by finding square roots. 9x^2 = 25
A. 5/3
B. (-5/-3),(5/3)
C. 2/3
D. (-2/-3),(2/3)
the difference between 8 times a number and 3 is equal to -19 what's the number
Answer:
-2
Step-by-step explanation:
x = the number
difference refers to subtraction
(8*x) - 3 = -19
8x - 3 = -19
+ 3 + 3
8x = -16
/ 8 /8
x = -2
Hope that helps!
Answer:
- 2
Step-by-step explanation:
let the number be n , then
8n - 3 = - 19 ( add 3 to both sides )
8n = - 16 ( divide both sides by 8 )
n = - 2
The number is - 2
Please explain the answer and show your work
Answer:
6
Step-by-step explanation:
Arc length ACB = 6 pi
The arc length = fraction of a circle times the circumference
6 pi = 180/360 * 2 * pi *r
6 pi = 1/2 * 2 * pi*r
6 pi = pi r
The radius is 6
I need help here please
Answer:
Simultaneous equations
Step-by-step explanation:
4a + 7m = 17.75
2a + 5m = 10.75
Double the 2nd equation and then subtract the two equations to cancel the 4a out
Work with the 'm' terms and find the value of m
After finding the value of 'm', substitute it into one of the original equations (the ones given in the question) and solve to find the value of 'a'
Hope this helped
X: A)127
B)78
C)130
D)110
Y: A)50
B)98
C)60
D)102
Answer:
a,
Step-by-step explanation:
Figure ABCD is a rhombus.
Rhombus A B C D is shown. Angle A is (5 x + 25) degrees and angle D is (7 x minus 1) degrees.
What is the value of x?
13
14
26
28
The value of x is 13 in the rhombus ABCD
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
In figure ABCD is a rhombus
Given as Angle ∠ A = (5x + 25)
Angle ∠ D = (7x - 1)
Since adjacent angles of a rhombus add up to 180°
(5x + 25) + (7x - 1) = 180 and both equal
So, 5x + 25 = 7x - 1
Rearrange the terms in the equation,
7x - 5x = 1 +25
2x = 26
x = 13
Hence, the value of x is 13 in given figure.
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Evan has 7 less pencils than isiah. If Isaiah has triangle pencils. Written an expression to describe how many pencils Evan has
Answer:
triangle - 7
Step-by-step explanation:
Because Evan has 7 less pencils than isiah, the number of pencils evan has can be determined by subtracting 7 from the number of pencils isaish has
triangle - 7
If evan had 7 more pencils : triangle + 7
SOMEBODY PLEASE HELP
The density of a certain material is such that it weighs 4 kilograms per cubic foot of
volume. Express this density in ounces per cubic meter. Round your answer to the
nearest whole number.
Answer:
Step-by-step explanation:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
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The density of the material is approximately 123 ounces per cubic meter.
Density [tex](\(D\))[/tex] is defined as mass [tex](\(m\))[/tex] per unit volume [tex](\(V\))[/tex], and it is calculated using the formula:
[tex]\[ D = \frac{m}{V} \][/tex]
In this case, the density is given in kilograms per cubic foot. To convert this to ounces per cubic meter, we need to perform the following steps:
Step 1: Convert kilograms to ounces:
1 kilogram = 35.27396 ounces
Step 2: Convert cubic feet to cubic meters:
1 cubic foot = 0.0283168 cubic meters
Now, let's substitute the given values and perform the conversion:[tex]\[ \text{Density in ounces per cubic meter} = \frac{4 \, \text{kg} \times 35.27396 \, \text{ounces/kg}}{1 \, \text{cubic foot} \times 0.0283168 \, \text{cubic meters/cubic foot}} \][/tex]
Solving this equation gives us the density in ounces per cubic meter:
[tex]\[ \text{Density} \approx 123 \, \text{ounces/m}^3 \][/tex]
Rounded to the nearest whole number, the density of the material is approximately 123 ounces per cubic meter.
In summary, we converted the given density from kilograms per cubic foot to ounces per cubic meter using unit conversions.
This involved converting the mass units and volume units before performing the calculation to obtain the final density value in the desired units.
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Add [25+(-13)+(-17) using associative property
Answer:
[25+(-13)+(-17)
25-13-17
-5
John has 50 missing assignments in his history and science class. He only has 15 days to turn everything in. How many assignments will John have to do everyday?
Answer:
3.3333 (repeating)
Step-by-step explanation:
He has 50 missing assignments and 15 days to do them.
So you do 50 missing assignments divided by 15 days, to see how many assignments a day he would have to do.
50 / 15 = 3.33 (repeating)
Answer:
3.333333333333333
Step-by-step explanation:
You will have to divide 15 by 50 to get the answer. That will give you 3.333333333333333 which is your answer.
Plz help me out ohbsbsb
Write a quadratic equation that has the solutions: 4 and -7
Answer:
y = ( x-4)(x+7)
Step-by-step explanation:
When we know the zeros of the equation, we can write the equation in the form
y= a(x-z1) (x-z2) where a is a constant and z1 and z2 are the zeros (solutions)
y = a( x-4)(x--7)
y =a( x-4)(x+7)
Since its says write an equation, we can pick a and I will let a=1
y = ( x-4)(x+7)
a rectangle and square equal perimeter if the rectangle has width 8 cm and length 12 cm what is the area of square
Answer:
Step-by-step explanation:
100 sq cm
in the diagram below given that xy=3cm,xyz=30and yz=x solve for x
Answer:
i guess you'll get that answer
Step-by-step explanation:
if xy is 3cm then y is 3 divide by 2
where y=
then if xyz=30 to get z you divide 30 by 3
where z=
then x will surely be the same value as y
so u solve for yz=x
mindy buys 12 cupcakes nine of the cupcakes have chocolate frosting and the rest have vanilla frosting what fraction of the cupcakes have vanilla frosting
Math help due soon thanks
Answers:
SkippingSee the diagram belowx = 7No they are not similar=======================================
Explanation:
SkippingWe peel the triangles apart as shown below. There's not much to say about it. The only thing I can think is that the larger horizontal side is 8+6 = 14 m.Due to the similar triangles, we can form the proportion x/4 = 14/8. The 14 is from 8+6. Cross multiplying leads to 8x = 56 which solves to x = 7.Focus on the triangle on the left. The missing angle is 180-95-35 = 50 degrees. The missing angle for the triangle on the right is 180-35-60 = 85 degrees. The angles don't all match up, so the triangles aren't similar.A circular garden is surrounded by a rectangular grassy area. The garden takes up nearly half the grassy area. The base of the grassy area is 6 yards by 3 yards.
A rectangle with a length of 6 yards and width of 3 yards. A circle inside of the rectangle has a diameter of 3 yards.
Use the base of the grassy area to find the approximate area of the circular garden. Use Pi = 3.14. If necessary, round to the nearest tenth.?
Answer:
The area of the circular garden is approximately 7.1 square yards
Step-by-step explanation:
The given parameters are;
The area surrounding the circular garden = A rectangular grassy area
The area of the circular garden ≈ (1/2) × The base of the grassy rectangular area
The dimensions of the base of the rectangular grassy area = 6 yards by 3 yards
The diameter of the circle, D = 3 yards
The area of the rectangular grassy area = 6 yards × 3 yards = 18 yards²
∴ The approximate area of the circular garden = (1/2) × 18 yards² = 9 yards²
The area of the circular garden, A = π·D²/4
∴ A = 3.14 × (3 yards)²/4 = 7.065
The area of the circular garden, A ≈ 7.1 yd².
find the value of k if the line 2x-y+k=0 may touch the circle x^2 + y^2=5
Answer:
k = ±4
Step-by-step explanation:
Equation of the circle is:
x² + y² = 5
This means from the general form of equation of a circle;
Centre coordinates is (0, 0) and radius is; √5.
The line 2x - y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;
Thus;
|((2 - 0) - (1 × 0) + k)|/(√(2² + 1²)) = √5
|(1 + k)|/√5 = √5
Multiply both sides by √5 to get;
|1 + k| = 5
|k| = 5 - 1
k = ±4
The second one: Find the nearest 10th.
Answer:
∅ = 44.9º
Step-by-step explanation:
sin = opp/hyp
Assuming ∅ is the top angle
∅ = arcsin(353/500)
use calculator
∅ = 44.910389254710144
∅ = 44.9º
8. Find TN, MP, TQ, PT
Please and thank you!
Answer:
TN = 13 units
MP = 22 units
TQ = 6.93 units
PT = 13 units
Step-by-step explanation:
If T is a circumcenter of the given triangle MNP,
Measure of TN = Measure of TM = Measure of TN
By applying Pythagoras theorem in ΔMRT,
MT² = TR² + MR²
MT² = (12)² + 5²
MT = [tex]\sqrt{169}[/tex]
MT = 13
Measure of TN = 13 units
Since, TQ, TS and RT are the perpendicular bisectors of the sides MP, NP and MN respectively,
Measure of MP = 2(PQ)
= 2(11)
= 22 units
By applying Pythagoras theorem in ΔTQM,
MT² = TQ² + MQ²
(13)² = TQ² + (11)²
TQ = [tex]\sqrt{169-121}[/tex]
TQ = [tex]\sqrt{48}[/tex]
TQ = 6.93
Measure of PT = Measure of TN = 13 units
The box part of the box plot contains all the values between which numbers?
25
30
35
40
45
50
between 27 and 36 and between 37 and 40
between 32 and 36
оооо
between 32 and 37
O between 27 and 32 and between 37 and 40
Answer:
Between 32 and 37
Step-by-step explanation:
Here, we simply want to get the data portion represented by the box alone
we can see that the box starts from 32
It ends at the number 37
Note;
between each individual number on the plot, we have 5 small lines indicating an extra point