Answer:
That the fractions are reduced with all common factors canceled.
Step-by-step explanation:
Hello,
Before an algebraic fraction is selected I should that the fractions are reduced with all common factors cancelled so that I got the irreducible fraction.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Could someone please explain/help me to do this using Pythagoras theorem?
Answer:
[tex]\boxed{478.02}[/tex]
Step-by-step explanation:
→ First understand what Pythagoras theorem is
Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.
→ State the formula and identify the letters
a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out
→ Substitute in the values into the formula
380² + 290² = c²
⇒ Simplify
144400 + 84100 = c²
⇒ Collect the numbers together
228500 = c²
⇒ Square root both sides to find 'c'
478.0167361 = c
→ The length of the diagonal is 478.02
a businessman bought three machines at rs 5400 each and spent 4000 on rearing and sold the machines for Rs Rs 7000 each, how much profit didi he make?
Answer:
[tex] \boxed{Rs \: 800}[/tex]Step-by-step explanation:
Cost price of three machines with repairment charge ( CP ) = 5400 × 3 + 4000
= Rs 20200
Selling price of 1 machine = Rs 7000
Selling price of 3 machines ( S.P )= Rs 7000 × 3
= Rs 21000
Since , SP > CP , he made a profit
Profit = SP - CP
= Rs 21000 - Rs 20200
= Rs 800
--------------------------------------------------------------
Further more explanation
Profit and loss
In any business , owners have intension to have profit by selling articles. The price at which an article is purchased is called it's Cost price ( C.P ) and the price at which it is sold is called Selling price ( S.P ).
If the selling price is less than cost price of an article then there is a loss.
[tex] \mathrm{Loss \: = \: Cost \: Price \: (C.P) - Selling \: Price \: (S.P)}[/tex]
If the selling price is more than cost price of an article then there is a profit ( gain )
[tex] \mathrm{Profit = Selling \: Price \: (S.P) - Cost \: Price \: (C.P)}[/tex]
So, If S.P > C.P, there is profit in dealing.
If C.P > SP , there is loss in dealing.
Hope I helped!
Best regards!!
Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to the negative balance of the credit account. The play cost $3,200.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 1,007 people attend the play's opening night, what will the balance of the bank account be?
Answer:
Hey there!
If 1007 people attend, they will make a profit of 10070 dollars.
The play costed 3200 dollars to produce, so we have -3200+10070=7500 dollars as the final balance of the bank account.
Let me know if this helps :)
Answer:
Step-by-step explanation:
the correct answer is 6,870 it was d for me it might be different :)
-
Represents the solution to the inequality -9=2/3x-7<5
Answer:
-3=x <13
Step-by-step explanation:
[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]
Multiply through by 3
[tex] - 27 = 2x - 21 < 15[/tex]
Add 21 to all sides
[tex] - 6 = 2x < 36[/tex]
Divide through by 2
[tex] - 3 = x < 18[/tex]
The solutin set is
[tex]{- 3 = x < 18}[/tex]
Find the missing the side of the triangle. A. 0 yd B.√30 yd C. 2√5. yd D. √17 yd
Answer:
x = 2√5 ydStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² - c²
where a is the hypotenuse
From the question x is the hypotenuse
Substitute the values into the above formula
We have
[tex] {x}^{2} = ( { \sqrt{10} })^{2} + (\sqrt{10} )^{2} [/tex]
[tex] {x}^{2} = 10 + 10[/tex]
[tex] {x}^{2} = 20 [/tex]
Find the square root of both sides
We have the final answer as
x = 2√5 ydHope this helps you
solve for k k + (2 - 5k)(6) = k + 12
Answer:
k=0
Step-by-step explanation:
[tex]k+(2-5k)(6)=k+12\\k-30k+12=k+12\\12-12=29k+k\\0=30k\\k=0[/tex]
Answer:
k=0
Step-by-step explanation:
Rita bought 4 CDs that were each the same price. Including sales tax, she paid a total of $ 61.60. Of that total,$ 2.80 was tax. What was the price of each CD before tax
Answer:
The price of each CD is:
$14.70
Step-by-step explanation:
(61.6 - 2.8) /4
= 58.8/4
= $14.7
Answer:
$14.70
Step-by-step explanation:
We want to find the price of each CD before tax. Therefore, we must first subtract the tax from the total.
total -tax
The total cost was $61.60 and the tax was $2.80
$61.60 - $2.80
$58.80
The price for the 4 CDs (without tax) was $58.50.
We know that each CD costs the same price and Rita bought four CDs. Therefore, we can divide the cost without tax by 4.
cost without tax / 4
The cost without tax is $58.80
$58.80 /4
$14.70
Each CD before tax costs $14.70
Emma changed £500 into rand before going on holiday to South Africa.
The rate of exchange at the time was £1 = 10.4 rand.
Emma spent 4000 rand on holiday. When she got home, she changed her leftover rand into pounds.
The exchange rate was now £1 = 9.8 rand. How much money did she get back in pounds?
Answer:
I'm sorry but I can give exact numbers but I would like to help work it out so...
Step-by-step explanation:
So overall she had £500 to start with
And £1 is equal to 10.4 rand
So you would divide 100 by 10.4 and get the potential difference between the average of money which she has then because she spent 400 rand in holiday you would divide 400 by the amount of the potential difference which was given then change that back to pounds
Hope this helps
If this seems incorrect please comment and I will change my answer thanks:)
Solve for x(in picture).
Answer:
x = 1/8
Step-by-step explanation:
[tex]\log _2\left(x\right)=-3\\\\\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\\\\\log _2\left(x\right)=-3\quad \Rightarrow \quad \:x=2^{-3}\\\\Simplify\\\\x=\frac{1}{8}[/tex]
Which is greater than 4? (a) 5, (b) -5, ...
Answer:
(a) 5
Step-by-step explanation:
5 is geater than 4
4 is greater than -5
ind the missing length. The triangles are similar. similar 16 A. 27 B. 24 C. 16 D. 21
Could anyone help me with number 25 THANK YOU!!!
Answer:
ΔABC ~ ΔQPR by the Angle-Angle (AA) similarity theorem of two triangles
Step-by-step explanation:
The coordinates of the vertices are given as follows;
A = (1, 2), B =(9, 8), C = (1, 8)
P= (5, -3), Q = (-7, 6), R = (-7, -3)
The given dimensions of AB and PQ are 10, and 15 respectively
The, l lengths of the sides of triangles are found as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For segment BC, we have;
B =(9, 8), C = (1, 8)
(x₁, y₁) = (9, 8), (x₂, y₂) = (1, 8), substituting gives;
Length BC = 8
For length CA, C = (1, 8) A = (1, 2)
(x₁, y₁) = (1, 8)
(x₂, y₂) = (1, 2)
The length found by substituting the values for (x₁, y₁), (x₂, y₂) in the length equation gives; Length CA = 6
Given that length CA² + BC² = 8² + 6² = 64 + 36 = 100 = BA², we have by Pythagoras theorem, we have ΔABC is a right triangle
Similarly, for ΔQPR, we have;
Length QR, Q = (-7, 6), R = (-7, -3) = 9
Length PR, P= (5, -3), R = (-7, -3) = 12
QR² + PR² = 9² + 12² = 225 = 15² = PQ²
∴ ΔQPR is a right triangle
By comparing the ratio of the sides, we have;
cos(θ) = PR/PQ = 12/15 = 4/5, θ = cos⁻¹(4/5) = 36.9°
∠RPQ = 36.9°
sin(θ) = QR/PQ = 9/15 = 3/5
Similarly in triangle ΔABC, we have;
cos(θ) = BC/AB = 8/10 = 4/5
∠CBA = 36.9°
Therefore, ∠CBA ≅ ∠RPQ = 36.9°
Also ∠PRQ ≅ ∠BCA = 90° (Angle opposite hypotenuse side of right triangle
Therefore, ΔABC and ΔQPR are similar triangles by the Angle-Angle (AA) similarity theorem of two triangles.
Given: AB ∥ DC , m CB =62°, m∠DAB=104° Find: m∠DEA, m∠ADB
Answer: m∠DEA = _________, m∠ADB =_______
Answer:
The values of the angles are;
m∠DEA = 62°, m∠ADB = 45°
Step-by-step explanation:
Specify an arc or an angle three letters
Angle opposite an arc on the circumference
m DA ≅ m CB = 62° (Arc between parallel lines are congruent)
∠CAB = 1/2 × m CB = 1/2 × 62° = 31° (Angle at the center = 2 × Angle st the circumference)
∠DBA = 31° (Angle at the center m DA = 2 × Angle st the circumference)
m∠DAB = 104° (Given)
∠ADB = 180° - m∠DAB - ∠DBA = 180° - 104° - 31° = 45° (Interior angles of triangle ΔADB
m∠ADB = 45°
∠AEB = 180 - ∠CAB - ∠DBA = 180° - 31° - 31° = 118°
∠AEB ≅ ∠COD (Vertically opposite angles)
∠DEA ≅ ∠CEB (Vertically opposite angles)
∠AEB + ∠COD + ∠DEA + ∠CEB = 360° (Sum of angles at a point)
118° + 118° + ∠DEA + ∠CEB = 360°
∠DEA + ∠CEB = 360° - 118° - 118° = 124°
Given that ∠DEA = ∠CEB we have;
2 × ∠DEA = 124°
∠DEA = 124°/2 = 62°
m∠DEA = 62°.
I am visiting my friend Janette in Bristol. My journey takes a total time of 1 hour 26 minutes. I travel by train for 34 minutes, then walk at a rate of 1/2 mile per 10 minutes. How many miles do I walk for?
Answer:
2.6 miles
Step-by-step explanation:
1 hour 26 minutes= 86 minutes
86-34=52 total walk time
52 minutes= 5*1/2 miles
=2.5 miles walked
and 2 minutes.
so we need to find 1/5 of 1/2
(1/2)/5=0.1 mile
2.5+0.1=2.6 miles
Perform the operation. (3x^2+4)-(-5x^2+4x-1)
Answer:
8x^2-4x+5
Step-by-step explanation:
(3x^2+4)-(-5x^2+4x-1)
Let's start by removing the parentheses.
3x^2+4-(-5x^2)-4x+1
Now let's reorder the equation to make it easier to combine like terms.
3x^2+5x^2-4x+1+4
Combine like terms.
8x^2-4x+5
plz help me Which relations are linear? Nonlinear? Explain how you know. TABLE X -2,-1,0,1,2AND Y,4,1,0,1,4,
Answer:
non-linear
Step-by-step explanation:
The given points do not fall on a straight line when plotted on a graph.
__
If you realize that the x-values go up, and the y-values go down and up, then you know the relation cannot be linear. That is, its graph cannot be a straight line.
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.767, n=25
Answer:
the critical value for r at [tex]r_{0.05, 23}[/tex] = 0.396
Step-by-step explanation:
Given that:
the linear correlation coefficient r = 0.767
the sample size n = 25
the level of significance ∝ = 0.05
The degree of freedom is expressed with the formula df = n - 2
df = 25 - 2
df = 23
the critical value for r at [tex]r_{0.05, 23}[/tex] = 0.396
The linear correlation coefficient r = 0.767 is not in the region between the critical values of -0.396 and +0.396. We can therefore conclude that the linear correlation coefficient is significant.
Paul, a dentist, determined that the number of cavities that develops in his patient's mouth each year varies inversely to the number of seconds spent brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds each night. Write the equation that relates the number of cavities, c, to the time, t, spent brushing. How many cavities would Paul expect Lori to have if she had brushed her teeth for 120 seconds each night?
Answer:
Step-by-step explanation:
Inverse variation is written as
[tex]y=\frac{k}{x}[/tex] which, in words, says "y varies inversely with x". If cavities varies inversely with time brushing, then
[tex]c=\frac{k}{t}[/tex]
We are given the initial condition for which we need to solve for k:
c = 4 when t = 30:
[tex]4=\frac{k}{30}[/tex] so
k = 120.
Now we will use that value of k to solve the problem of how many cavities, c, would she have if she brushed her teeth 120 seconds, t, each night:
[tex]c=\frac{120}{120}[/tex] (the 120 on top is the k value and the 120 on the bottom is the number of seconds she brushed) to get
c = 1
Answer:
1 cavity
Step-by-step explanation:
The inverse equation is x*y=k, where x is the amount of cavities, y is the time brushed, and k is a constant number. In your scenario, x is c and y is t, but you can really use any name for the variable. In the first equation 23 have 4*30=120, which is just a constant number. now that we know our constant, we can plug is into our second equation, and we get c*120=120. By dividing both sides by 120, c=1. This means that Paul will have 1 cavity.
multiple choice
a. 12 pie cm
b. 21 pie cm
c. 35 pie cm
Answer:
The correct option is;
a. 12 pie cm
Step-by-step explanation:
Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;
Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same
The volume of the square based prism = 452 cm³
Therefore, the volume of the cylinder (of equal base area) = 452 cm³
The formula for the volume of square based prism = Area of base × Height
∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm
Which gives;
Area of the base of the square based prism = 452/4 = 113 cm²
The area of the base of the cylinder [tex]A_c[/tex] = The area of the base of the square based prism = 113 cm²
The area of the base of the cylinder,[tex]A_c[/tex] is given by the following equation;
[tex]A_c[/tex] = π×r² = 113 cm²
r = √(113/π) = √35.97 ≈ √36 = 6 cm
The circumference of the base of the cylinder,[tex]C_c[/tex] is given by the following equation
[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm
The correct option is 12 pie cm.
I forgot how to do this. I will give brainliest!
Answer:
A = 2, B = 3 and C = 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = 2 ( subtract 2x from both sides )
3y = - 2x + 2 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, thus
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (2, 0) into the partial equation
0 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{4}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form
Multiply through by 3
3y = - 2x + 4 ( add 2x to both sides )
2x + 3y = 4 ← in standard form
with A = 2, B = 3 and C = 4
What type of function is graphed in this figure?
Question 20 options:
A)
Continuous non-linear
B)
Discrete linear
C)
Discrete non-linear
D)
Continuous linear
Answer:
The correct option is;
B) Discrete linear
Step-by-step explanation:
The graph shows scatter plots of the data points and therefore the plot is a discrete plot of points. Also, we have, from the graph of the function, changes in input values are proportional with changes in output, such that the progression of the points are unidirectional.
Therefore, the graph is a discrete linear function.
What decimal number does point A on the number line below represent? A vertical number line is shown from negative 2.00 to 0 to positive 2.00.There are tick marks to show increments of 1 over 4. Only the whole numbers are labeled. Point A is plotted at the third tick mark below negative 1.00. 0.25 −0.25 1.75 −1.75
Answer: 0.25
Step-by-step explanation:
To find : decimal number represented by point A on the given number line.
Given: Vertical number line is shown from negative 2.00 to 0 to positive 2.00.There are tick marks to show increments of 1 over 4.
Point A is plotted at the third tick .
That means, Point A is marked at 1 over 4.
1 over 4 = [tex]\dfrac{1}{4}=0.25[/tex] [divide 1 by 4]
Hence, the point A represents 0.25 on the given number line.
Answer:
Step-by-step explanation:
Where is the picture
what is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?
Answer:
-16, 0 real solutions. (Complex Roots)
Step-by-step explanation:
[tex]5x^2-2x=-1\\5x^2-2x+1\\A=5\\B=-2\\C=1\\(-b±√(b^2-4ac))/2a\\=\\=-2^2-4(5)(1)\\=4-20\\=-16[/tex]
DUE NOW PLEASE HELP!!!
Factor completely x2 − 10x + 25.
(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)
Answer:
(x - 5)(x - 5)
Step-by-step explanation:
[tex] {x}^{2} - 10x + 25 \: is \: the \: expansion \\ of \: {(x - 5)}^{2} \\ {(x - 5)}^{2} = (x - 5)(x - 5)[/tex]
The complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
How to factor a quadratic expression?A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.
How to solve the given question?In the question, we are asked to factor the quadratic expression x² - 10x + 25 completely.
Comparing x² - 10x + 25 to ax² + bx + c, we get a = 1, b = -10, and c = 25.
To factor the expression we will use the mid-term factorization method, and try to break b in such two numbers whose product = ac.
Now, ac = 1 * 25 = 25. b = -10, which can be broken as -5, and -5.
Therefore, we can write the given expression as:
x² - 10x + 25
= x² - 5x - 5x + 25, mid-term factorization
= x(x - 5) -5(x - 5), grouping
= (x - 5)(x - 5), grouping.
Therefore, the complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
Learn more about mid-term factorization at
https://brainly.com/question/25829061
#SPJ2
David’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles . If a map has a scale of 1 in = 80 mi about how far will the trip be on the map ?
You can do the proportion
1 inch/ 80 miles =x inch/ 1100 miles
1100=80x
11oo divided by 80 equals 13.75
The trip would be about 13.75 inches on the map
Feel free to brainliest :)
Answer:
13.75 inches
Step-by-step explanation:
To find an estimated distance on the map, we can simply create a proportion.
Let X represent the unknown distance in inches on the map.
1100 miles / 80 miles = X inches / 1 inch
Now let's solve for X.
X inches = (1100 miles / 80 miles) * 1 inch
X inches = 13.75 inches
So the approximate travel distance on the map will be 13.75 inches.
which of the following equations correctly represents a circle centered at the origin with a radius of 5
Answer:
x² + y² = 25
Step-by-step explanation:
The standard form of a circle is (x - h)² + (y - k)² = r² where (h, k) is the center point and r is the radius. In this case, the center is the origin which has coordinates of (0, 0) so h = 0 and k = 0. We know that the radius is 5 so r = 5. Therefore, after plugging in the values of h, k, and r, we get that the answer is x² + y² = 25.
If two of the ordered pairs was removed which two data points will cause the correlation to decrease the most? Select Two points
1) Data point A
2) Data point B
3) Data point C
4) Data point D
Answer:
1. Data point A
4. Data point D
Step-by-step explanation:
In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.
If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.
Therefore, removing data point A and point D would cause the correlation to decrease the most.
A student is given three triangles and must determine which triangles are
congruent. The student is also told that B= ZE = ZY. Which of the
following statements is true?
Answer:
D.
Step-by-step explanation:
From the given triangles above, there are just 2 triangles that look the same, that is ∆ABC and ∆XYZ.
∆ABC has two sides (AB and BC), and an included angle (angle B), which are equal to the two sides (YZ and YX) and the included angle (angle Y) of ∆XYZ as ∆ABC is a reflection of ∆XYZ.
Therefore, according to the SAS Theorem of congruency, ∆ABC is congruent to ∆XYZ.
The length of one side of a rhombus is 20 m.Find its perimeter.
Answer:
80 m
Step-by-step explanation:
Given :-
One side of rhombus = 20 m.
[ as one of the property of rhombus = all sides are equal ]
So, perimeter of rhombus = sum of all sides
= 20+20+20+20 = 80 m
...........................OR............................
Perimeter of rhombus = 4 × side
= 4 × 20 = 80 m
Hence, the perimeter of the rhombus is 80m.
Answer:
The perimeter is 80 meters
Step-by-step explanation:
The geometric characteristic of a rhombus is that it has 4 equal sides, then if one side measures 20 m, then each of the other sides measure also 20 m.Then its perimeter (addition of all the sides must render: 4 * 20 m = 80 m
Last week, 17 employees exceeded their sales quota, 13 employees met their sales quota, and 3 employees didn't meet their sales quota. Express the number of employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota. Question 11 options: A) 3:13 B) 16:17 C) 17:16 D) 17:33
Answer:
17:16
Step-by-step explanation:
Number of employees exceeded their sales quota = 17
Number of employees met their sales quota = 13
Number of employees didn't exceed their sales quota = 3
Now, we need to find the ratio of the number employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota.
