Answer:
(5 1/3)/7
Step-by-step explanation:
Divide 4 by 3, then times it by four and put it over the 7
Given: ΔABC, AC = BC, AB = 3 CD ⊥ AB, CD = √3 Find: AC
Answer:
[tex]\boxed{AC = 2.3}[/tex]
Step-by-step explanation:
AD = BD (CD bisects AB means that it divides the line into two equal parts)
So,
AD = BD = AB/2
So,
AD = 3/2
AD = 1.5
Now, Finding AC using Pythagorean Theorem:
[tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)
[tex]AC^2= (1.5)^2+(\sqrt{3} )^2[/tex]
[tex]AC^2 = 2.25 + 3[/tex]
[tex]AC^2 = 5.25[/tex]
Taking sqrt on both sides
[tex]AC = 2.3[/tex]
Answer:
[tex]\boxed{2.29}[/tex]
Step-by-step explanation:
The length of AB is 3 units.
The length of CD is [tex]\sqrt{3}[/tex] units.
D is the mid-point of points A and B.
AD is half of AB.
[tex]\frac{3}{2} =1.5[/tex]
Apply Pythagorean theorem to solve for length of AC.
[tex]c=\sqrt{a^2 +b^2 }[/tex]
The hypotenuse is length AC.
[tex]c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }[/tex]
[tex]c=\sqrt{2.25+3 }[/tex]
[tex]c=\sqrt{5.25}[/tex]
[tex]c= 2.291288...[/tex]
Discussion Topic There are four basic operations: addition, subtraction, multiplication, and division. Do you think these four operations can be performed on polynomials? What would it look like to perform these operations on polynomials? Which operation do you think would be the simplest? Which do you think will be difficult?
Step-by-step explanation:
1. Yes addition, subtraction, multiplication, and division can be performed on polynomials. like our everyday arithmetic dealings with mathematical operators, polynomials are no exception when it comes to math operators, the four basic operations addition, subtraction, multiplication, and division can be performed on polynomials as well.
2. It can be less handy plus the operation can get messy if you do not have a good sense/understanding/hold of what you are doing things can get messy.
3. I personally know that the simplest is the addition of polynomials
4. I cant say which is difficult, but the operation that can get things messy for me most time is the division operation
– 4 = 5(p – 2)
plz help me if you know this.
Answer:
p = 6/5
Step-by-step explanation:
-4 = 5(p - 2)
-4 = 5p - 10
-4 + 10 = (5p - 10) + 10
6 = 5p
6/5 = (5p)/5
6/5 = p
p = 6/5
Answer:
p = 6/5
Step-by-step explanation:
-4 = 5(p - 2) (DISTRIBUTE)
-4 = 5p - 10 (ADD 10 TO BOTH SIDES)
6 = 5p (DIVIDE BY FIVE ON BOTH SIDES)
p = 6/5
y + 2 = -3 (x - 4) Complete the missing value in the solution to the equation. (____, -2)
Answer:
( 4,-2)
Step-by-step explanation:
y + 2 = -3 (x - 4)
We are given y = -2
-2+2 = -3 (x-4)
0 = -3(x-4)
Divide by -3
0 = x-4
Add 4 to each side
4 = x-4+4
4 =x
Answer:4
Step-by-step explanation:
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person’s weight, in pounds, when rounded to the nearest whole number?
Answer:
193.33333 pounds
Step-by-step explanation:
Divide 87kg by 0.45
So, it's 87 ÷ 0.45 = 193.3333333
Answer: 190
Step-by-step explanation:
11/12-1/6q+5/6q-1/3 it says its wrong
Answer:
2/3q + 7/12
Step-by-step explanation:
If you are trying to simplify your expression
4/6q + 7/12
2/3q + 7/12
The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, where h(x) is the height, in feet, and x is the horizontal distance, also in feet. The path begins and ends at the same height, covers a total horizontal distance of 100 feet, and reaches a maximum height of 250 feet. Which of the functions could be used to model this situation? A. h(x)=-0.1x^2-50x+250 B. h(x)=-0.1(x-50)^2+250 C. h(x)=-0.1(x-100)^2+250 D. h(x)=-0.1x^2+100x+250
Answer:
C
Step-by-step explanation:
0.1(x - 100)² + 250
0.1[(x - 100)(x - 100)] + 250
0.1(x² -200x + 10000) + 250
0.1x² - 20x + 1000 + 250
0.1x² - 20x + 1250
0.1x² - 25x + 5x + 1250
0.1x(x - 250) + 5(x + 250)
∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)
naledi climbed up a mountain. Her initial altitude is 40 meters above sea level, and increased by 10 meters per hour. let g(n) be naledi altitude at the beginning of nth hour of her climb. g is a sequence. what kind of sequence is it. arithmetic or geometric sequence? complete the recursive formula for g(n). g(1)= ? g(n) = g(n-1) (+ or *) ?
Answer: [tex]U_{n} =(40)+(n-1)(10)[/tex]
Step-by-step:
[tex]U_{n} =a+(n-1)d[/tex]
a = 40
d = 10
[tex]U_{n} =(40)+(n-1)(10)[/tex] is the formula for nth hour
The amount of calories you consume after eating x pieces of candy is represented by the function y=150x. Find the domain of the function and determine whether it is discrete or continuous.
Answer:
The function is:
y = 150*x
where y is the number of calories consumed, and x is the number of pieces of candy consumed.
Now, the domain of a function is the possible values of x that you can input in the function.
For this particular case you can have:
x = 0 (no pieces candy)
x = 1 (one piece of candy)
x = 2 (two pieces of candy)
Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.
So we only use x = whole numbers.
Then the domain of the function is equal to all the natural numbers plus the zero, or:
D = {x ∈ N ∪ {0}}
"x belongs to the union between the set of the natural numbers and the zero"
The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0
The domain of a function is the input values of the function for which it exists.
Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:
y = 150x
The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0
The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.
Learn more about discrete function here:
https://brainly.com/question/25050804
Please answer it now in two minutes
Answer:
[tex] f = 10.7 [/tex]
Step-by-step explanation:
Given ∆DEF,
<F = 36°
DF = e = 15
EF = d = 6
DE = f = ?
f can be found using the Law of Cosine as shown below:
[tex] f^2 = d^2 + e^2 - 2(d)(e)*cos(F) [/tex]
Plug in your values:
[tex] f^2 = 6^2 + 15^2 - 2(6)(15)*cos(36) [/tex]
Evaluate:
[tex] f^2 = 36 + 225 - 180*0.809 [/tex]
[tex] f^2 = 261 - 145.62 [/tex]
[tex] f^2 = 115.38 [/tex]
[tex] f = 10.74 [/tex]
[tex] f = 10.7 [/tex] (to nearest tenth)
A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:
4/9
Step-by-step explanation:
So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.
Answer:
4/9
Step-by-step explanation:
A particular zebra is the 10th fastest animal in its herd and also
the 10th slowest animal in its hard. If every zebra in the herd is
of a different speed, then how many zebra are there in the herd?
Answer:
19
Step-by-step explanation:
The zebra is the 10th fastest, so there are 9 zebras that are faster.
It's also the 10th slowest, so there are 9 zebras that are slower.
The total number of zebras is therefore 9 + 1 + 9 = 19.
WILL GIVE BRIANLIEST Circle O is shown. Tangents B C and B A intersect at point B outside of the circle. The measure of the first arc formed is 146 degrees. In the diagram of circle O, what is the measure of ? 34° 45° 68° 73°
Answer: 34°
Step-by-step explanation:
The Arc formed by segment AC:
Total measure of an arc = 360°
Measure of Major arc AC = (360° - measure of minor arc)
Minor arc = 146°
THEREFORE,
Major arc AC = (360° - 146°) = 214°
A° = B° = (214° - 146°) / 2 ( tangent - tangent theorem)
Angle formed by tangent AB and BC = difference between major and minor arcs divided by 2 : (Major arc - minor arc) / 2
(214 - 146)° / 2 = 68° / 2 = 34°
The measure of ∠ABC as shown in the circle is 34°.
CircleA circle is the locus of a point such that all the points are equidistant from a fixed point known as the center.
∠OCB and ∠OAB = 90° (angle between a tangent and radius)
∠OCB + ∠OAB + ∠COA + ∠CBA = 360° (angles in a quadrilateral)
90 + 90 + 146 + ∠CBA = 360
∠CBA = 34°
The measure of ∠ABC as shown in the circle is 34°.
Find out more on Circle at: https://brainly.com/question/22965557
HALLLLPPP Let g(x) = 2x and h(x) = x^2 + 4. Evaluate each expression: g(-2) - h(4)
Answer:
-24
Step-by-step explanation:
g(-2) = 2(-2)
g(-2) = -4
h(4) = 4² + 4
h(4) = 16 + 4
h(4) = 20
g(-2) - h(4)
-4 - 20
= -24
Answer:
g(-2) - h(4) = - 24Step-by-step explanation:
g(x) = 2x
To find g( -2) substitute - 2 into g(x)
That's
g( -2) = 2(-2) = - 4
h(x) = x² + 4
To find h(4) substitute 4 into h(x)
That's
h(4) = (4)² + 4 = 16 + 4 = 20
So
g(-2) - h(4) is
- 4 - 20
= - 24
Hope this helps you
The length of a rectangle is 6cm and its width is 4cm. Find the perimeter
Answer: 20cm
Step-by-step explanation:
The perimeter of a rectangle can be calculated as 2(l+w)
2(6+4)
2(10)
20
Hope it helps, and if you want more info on perimeter, just ask <3
Answer:
20 cm
Step-by-step explanation:
Use folmula P=2(l+w)
Please answer this question now
Answer:
469.4ft²
Step-by-step explanation:
We have Triangle WXY
In the question, we are given already
Angle W = 27°
Angle X = ?
Angle Y = 40°
Side w =?
Side x = ?
Side y = 38ft
Area of the triangle= ?
Step 1
We find the third angle = Angle X
Sum of angles in a triangle = 180°
Third angle = Angle X= 180° - (27 + 40)°
= 180° - 67°
Angle X = 113°
Step 2
Find the sides w and x
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle WXY
w/ sin W = x/ sin X = y/ sin Y
We have the following values
Angle W = 27°
Angle X = 113°
Angle Y = 40°
We are given side y = 38ft
Finding side w
w/ sin W= y/ sin Y
w/sin 27 = 38/sin 40
Cross Multiply
sin 27 × 38 = w × sin 40
w = sin 27 × 38/sin 40
w = 26.83879ft
w = 26.84ft
Finding side x
x / sin X= y/ sin Y
x/ sin 113 = 38/sin 40
Cross Multiply
sin 113 × 38 = x × sin 40
x = sin 113 × 38/sin 40
x = 54.41795ft
x = 54.42ft
To find the area of triangle WXY
We use heron formula
= √s(s - w) (s - x) (s - y)
Where S = w + x + y/ 2
s = (38 + 26.84 + 54.42)/2
s = 59.63
Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)
Area of the triangle = √
Area of the triangle = 469.40772706541ft²
Approximately to the nearest tenth =469.4yd²
help me Please!!!!!!!
Answer:
[tex]2\sqrt{14\\}[/tex] = q
Step-by-step explanation:
use geometric mean method
4/s = s/10
s^2 = 40
s = 2[tex]\sqrt{10}[/tex]
consider the triangle STR and using the Pythagorean theorem
[tex]s^{2} +16 = q^{2} \\[/tex]
[tex](2\sqrt{10})^{2} +16 = q^{2}[/tex]
40 + 16 = q^2
56 = q^2
[tex]2\sqrt{14\\}[/tex] = q
Which statements are true about the solution of 15 greater-than-or-equal-to 22 + x? Select three options. x greater-than-or-equal-to negative 7 x less-than-or-equal-to negative 7 The graph has a closed circle. –6 is part of the solution. –7 is part of the solution.Which statements are true about the solution of 15 greater-than-or-equal-to 22 + x? Select three options. x greater-than-or-equal-to negative 7 x less-than-or-equal-to negative 7 The graph has a closed circle. –6 is part of the solution. –7 is part of the solution.
Answer:
The correct answers are B, C ,E
Step-by-step explanation:
The correct options are a, c and e
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, the solution of 15 greater-than-or-equal-to 22 + x
1) The first one is correct because the statement is x greater-than-or-equal-to negative 7. And 22+(-7) is = to 15. This means that in order to get a number below 15 by adding 22 and 15, we need a number that is lower than -7.
2) The second one is incorrect because it is the opposite of the first one. As the first one was correct, this statement is implying the complete opposite as the first one.
3) The third one is correct because we are using greater than or equal to; this means the circle would be closed.
4) The fourth option is incorrect because we need x to be lower than -7, not higher.
5) The fifth option is also correct.
Hence, the correct options are is a, c, e.
For more references on inequality, click;
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find the area of the quadrilateral ABCD in which ab=5cm,bc=4.5cm,cd=3.5cm,da=4cm and ac=6.5cm
Answer:
A(ABCD) ≈ 17.285 cm²
Step-by-step explanation:
Heron formulaA = √s(s - a)(s - b)(s - c)
s = (a + b + c)/2
a ; b ; c = the sides of the triangle
A(ABCD) = A(ABC) + A(ACD)A(ABC) = √s(s - AB)(s - BC)(s - AC)s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm
A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)
= √8×3×3.5×1.5
= √126
≈ 11.225 cm²
2. A(ACD) = √s(s - AC)(s - CD)(s - AD)
s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm
A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)
= √7×0.5×3.5×3
= √36.75
≈ 6.060 cm²
3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²
ILL GIVE BRAINLIEST PLS HELP
A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
1/5
Step-by-step explanation:
The stick has a length of 5 units
The stick is broken at two points chosen at random
First break: the probability that you get a piece that is 1 unit or longer than 1 units= 1/5.
Second break, the probability that you get a piece that is 1 unit or longer than 1 units is 1/5.
Therefore,
The total probability =probability of first break * probability of second break * original stick unit
=1/5 * 1/5 * 5
= 1/25 *5
=5/25
=1/5
What is the approximate circumference of the circle shown below?
Answer:
[tex]\boxed{\sf 43.35 \ cm}[/tex]
Step-by-step explanation:
Apply formula for the circumference of a circle.
[tex]\sf C=\pi d[/tex]
The diameter [tex]\sf d[/tex] is 13.8 cm.
[tex]\sf C=\pi (13.8)[/tex]
[tex]\sf C= 43.3539786195...[/tex]
[tex]\sf{C} \approx \sf{43.35}[/tex]
Answer:
43.4 cm
Step-by-step explanation:
Circumference of the circle = 2πr
r = radius, π = [tex]\frac{22}{7}[/tex]
f = diameter÷2
=13.8 ÷ 2
= 6.9
circumference = [tex]2 * \frac{22}{7} * 6.9\\[/tex]
= [tex]\frac{303.6}{7}[/tex]
= 43.37 cm or 43.4 cm
According to a study conducted by the Gallup Organization, the the proportion of Americans who are afraid to fly is 0.10. A random sample of 1100 Americans results in 121 {0.11} indicating that they are afraid to fly. What is the probability that the sample proportion is more than 0.11
Answer: 0.1457
Step-by-step explanation:
Let p be the population proportion.
Given: The proportion of Americans who are afraid to fly is 0.10.
i.e. p= 0.10
Sample size : n= 1100
Sample proportion of Americans who are afraid to fly =[tex]\hat{p}=\dfrac{121}{1100}=0.11[/tex]
We assume that the population is normally distributed
Now, the probability that the sample proportion is more than 0.11:
[tex]P(\hat{p}>0.11)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.11-0.10}{\sqrt{\dfrac{0.10(0.90)}{1100}}})\\\\=P(z>\dfrac{0.01}{0.0090453})\ \ \ [\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}} ]\\\\=P(z>1.1055)\\\\=1-P(z\leq1.055)\\\\=1-0.8543=0.1457\ \ \ [\text{using z-table}][/tex]
Hence, the probability that the sample proportion is more than 0.11 = 0.1457
Polynomial
Total Number
of Roots
Maximum
Number
of Complex Roots
603 - 8.02 +53 +1 = 0
-4,3 - 2 + 5 = 404
Answer:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.
Step-by-step explanation:
might help
NEED HELP ASAP I believe the answer is C but I’m not sure
MATH HELP ASAP BRAINLIEST!!!!
Answer:
first option
Step-by-step explanation:
Given
- 3x - 2y = 1 → (1)
- x + y = 3 → (2)
Rearrange (2) by adding x to both sides, that is
y = x + 3
Substitute y = x + 3 into (1)
- 3x - 2(x + 3) = 1 ← is the equation to be solved for x
The sports car travels along a straight road such
that its acceleration is described by the graph. Construct the
v-s graph for the same interval and specify the velocity of
the car when s = 10 m and s = 15 m.
Answer:
at s = 10m, v(t_1) = 7.663 m/s
at s = 15m, v(t_2) = 10.041 m/s
Step-by-step explanation:
for the interval 0-10 seconds,
a(t) = t m/s^2
v(0) = 0
v(t) = v(0) + integral(a(t)dt)
= 0 + [t^2/2]
= (1/2) t^2
s(0) = 0 .................. arbitrary
s(t) = s(0) + integral(v(t)dt)
= 0 + integral ((1/2)t^2)
= (1/6)t^3
When s(t) = 10 m,
(1/6)t^3 = 10
t^3 = 60
t_1 = 60 ^(1/3) = 3.9149 s approx.
v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s
When s = 15 m
(1/6)t^3 = 15
t^3 = 90
t_2 = 4.4814 s approx.
v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s
Answer:
at s = 10m, v(t_1) = 7.663 m/s
at s = 15m, v(t_2) = 10.041 m/s
Step-by-step explanation:
I took the test and got it right
−2(1 − 4x) = 3x + 8
Answer: x = 2
Step-by-step explanation:
First, Distribute
-2+8x=3x+8
Then, Subtract 3x
-2 + 5x=8
Then, Add 2
5x=10
Then, Divide by 5
x=2
Hope it helps <3
Answer:
-2(1-4x)=3x+8
distributive property
-2+8x=3x+8
subtract 8 on both sides
-2-8+8x=3x=-10+8x
now subtract 8x on both sides which equal: -10=-5x
now it part of the step and divide -5 on both sides to leave x or solve for x
-10/-5=x=2=x
x=2
Step-by-step explanation:
Given here is the price list of vegetables shown at a Mother Dairy vegetable Booth.
Mrs. Khanna brought the following vegetables:
potatoes
[tex]2 \frac{1}{2} [/tex]
onions
[tex]3 \: kg[/tex]
Peas
[tex]1 \frac{1}{2} kg[/tex]
Carrots
[tex]1 \frac{1}{2} kg[/tex]
She Gave a 500 - Rupee note to the man at the counter. How Much balance did she get?
Answer:
Total amount received by Mrs Khanna will be 182.5 Rs.
Step-by-step explanation:
Cost of the potatoes = 25 Rs per kg
Cost of [tex]2\frac{1}{2}[/tex] kg potatoes = Weight of the potatoes × Per kg cost of the potatoes
= 2.5 × 25
= 62.5 Rs
Cost of onions = 30 Rs per kg
Cost of 3 kg onions = 3 × 30
= 90 Rs
Per kg cost of Peas = 70 Rs
Cost of [tex]1\frac{1}{2}[/tex] kg Peas = 1.5 × 70
= 105 Rs
Per kg cost of Carrots = 40 Rs
Cost of [tex]1\frac{1}{2}[/tex] kg Carrots = 1.5 × 40
= 60 Rs
Total amount of the vegetables = 62.5 + 90 + 105 + 60
= 317.5 Rs
Since she gave a note of 500 Rs
Balance amount she got = 500 - 317.5
= 182.5 Rs
Therefore, total amount received by Mrs Khanna will be 182.5 Rs.
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
He Brought 10 packages of AA and AAA batteries for a total of 72 batteries.
The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.
Please answer in full! Thank you
Answer:
4 packages of AA batteries
6 packages of AAA batteries.
Step-by-step explanation:
Let the number of packages of AA batteries bought be x
Let
the number of packages of AAA batteries bought be Y
He Brought 10 packages of AA and AAA
thus,
x+y = 10 equation 1
Given
The AA batteries are sold in packages of 6, it means one packet contains 6 batteries
Thus,
Total number of AA batteries in x packages = 6x
The AAA batteries are sold in packages of 8, it means one packet contains 8 batteries
Thus,
Total number of AAA batteries in y packages = 8y
Given total no. of batteries is 72
thus
6x + 8y = 72 equation 2
x+y = 10
y = 10-x ---using this in equation 2
6x + 8(10 - x) = 72
=> 6x + 80 - 8x = 72
=> -2x = 72-80 = -8
=> x = -8/-2 = 4
y = 10 -x = 10 -4 = 6
y = 6
Thus,
he bought 4 packages of AA batteries
6 packages of AAA batteries.