Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 6) and (x₃, y₃ ) = (5, 5)
m = [tex]\frac{5-6}{5-9}[/tex] = [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
1. Can cross multiplication be used to solve this problem? Why or why not?
HELP
Answer:
Step-by-step explanation:
Cross multiplication can be used but not in the beginning. First x should be isolated.
[tex]3 +\frac{5}{x}=\frac{7}{x}\\\\[/tex]
Now subtract [tex]\frac{5}{x}[/tex] from both sides
[tex]3 = \frac{7}{x}-\frac{5}{x}\\\\3=\frac{7-5}{x}\\\\3=\frac{2}{x}[/tex]
In this stage, cross multiplication can be used.
[tex]\frac{3}{1}=\frac{2}{x}\\\\3*x=2*1\\\\x = \frac{2}{3}[/tex]
Answer:
x =0 and x =2/3
Step-by-step explanation:
as is no
but if you put an x under the 3 to make 3x/x
then you'd have 3x+5/x = 7/x
to make
3x^2 + 5x = 7x
this makes
3x^2 -2x =0
using the quadratic formula
answers
x =0 and x =2/3
All functions have a domain and a range.
True
False
Answer:
True
Step-by-step explanation:
The definition of the function is a relation with exactly one x for each y. x is the domain, and y is the range, so all functions have a domain and a range.
OperumONS UNTUI a) Find the greatest number that divides 36, 45 and 63 without leaving a remainder. b) c) Find the greatest number by which 90, 120 and 150 are exactly divisible. Three drums contain 501, 60 l and 70 l of oil. Find the greatest capacity of a bucket which can empty out each drum with the exact number of fillings. Three bags contain 80 kg of wheat flour, 120 kg of corn flour and 160 kg of rice. What is the greatest number of people to whom these items can be distributed equally? What is the share of each item among them? d) e) Find the greatest number of children to whom 48 oranges, 80 bananas and 144 apples can be divided equally. Also find the shares of each fruit among them. 22 There are 120 mangoes in a basket and 168 mangoes in another basket. Find the greatest number of mangoes which are to be taken out at a time from each basket so that both of them will be emptied simultaneously. A rectangular floor is 12 m long and 10 m broad. If it is to be paved with squared marbles of the same size, find the greatest length of each squared marble.
Answer:
a) The greatest number that divides 36, 45, and 63 without leaving a remainder is 9
b) The greatest number which exactly divides 90, 120, and 150 is 30
c) The greatest capacity of the bucket is 10 liters
d) The greatest number of people to whom the items can be distributed equally is 40 people
ii) 2 kg of wheat flour, 3 kg of corn and 4 kg of rice
e) The greatest number of children to whom the 48 orange, 80 bananas, and 144 apples can be distributed equally is 16
ii) 3 oranges, 5 bananas and 9 apples each
f) 5 mangoes at a time from the basket containing 120 mangoes
7 mangoes at a time from the basket containing 168 mangoes
g) The greatest length of each squared marble is 2 m
Step-by-step explanation:
a) The greatest number that divides 36, 45, and 63 without leaving a remainder = The highest common factor of 36, 45, and 63, which is given as follows;
36 = 9 × 4
45 = 9 × 5
63 = 9 × 7
Therefore, The greatest number that divides 36, 45, and 63 without leaving a remainder = The highest common factor of 36, 45, and 63 = 9
b) 90 = 30 × 3
120 = 30 × 4
150 = 30 × 5
The greatest number which exactly divides 90, 120, and 150 is 30
c) The factors of the volumes are;
50 l = 10 × 5 l
60 l = 10 × 6 l
70 l = 10 × 7 l
Therefore, the greatest capacity of the bucket = 10 liters
d) The masses of the items are
The factors of 80 = 40 × 2
120 = 40 × 3
160 = 40 × 4
Therefore the items can be distributed equally to 40 people
ii) Each person gets 2 kg of wheat flour, 3 kg of corn and 4 kg of rice
e) 48 = 16 × 3
80 = 16 × 5
144 = 16 × 9
Therefore, the greatest number of children = 16
ii) Each child gets 3 oranges, 5 bananas and 9 apples
f) The factors of 120 = 24 × 5
168 = 24 × 7
Therefore;
The greatest number of mangoes which is to be taken out of the basket with 120 mangoes = 5 mangoes each (24 times)
The greatest number of mangoes which is to be taken out of the basket with 168 mangoes = 7 mangoes each (24 times)
g) The area of the floor = 12 m × 10 m = 120 m²
The factor of 120 m² which is a perfect square is 4 therefore, we have;
The side length of each squared marble, s = √4 = 2
The side length of each squared marble, s = 2 m
What is the sum of the polynomials (-x^2 +9) + (-3x^2 - 11x + 4)
Answer:
4
−
4
+
8
2
+
8
Step-by-step explanation:
-2
Simplify the expression
4ab
Assume a = 0,6=0.
1
16a2b2
a²b²
4
-162²62
16ab2
Answer:
D
Step-by-step explanation:
(4ab)^2 = 4^2a^2b^2 = 16a^2b^2
5^4x+3 ×100^-2x+1=50000
Answer:
5^4x+3 ×100^-2x+1=50000
5^4x×100^-2x=49996
isolate the variable by dividing each side by factors that don't contain the variable. Exact Form: x = 8 √ 12499 , Decimal Form: x = 894.39141319 …
A red die is tossed and then a green die
is tossed. What is the probability that
the red die shows a six or the green die
shows a six?
Answer:
2/12
Step-by-step explanation:
The answer is 2/12 because there are two dice, each with 6 sides and the probability on each dice is one sixth
Cathy ran 10 meters in 2 seconds. How much time did she take to complete 100 meters?
Answer:
If Cathy ran at a constant speed of 10 meters in 2 seconds, it took Cathy 20 seconds to run 100 meters.
Step-by-step explanation:
Hope this helps.
Answer:
If Cathy run at constant speed of 10 meters in 2 seconds, it took Cathy 20 second to run 100 meters.
a.20
b.25
c.15
d.1
help me
HELPPP IM ALMOST DONE WITH THIS CLASS
Explanation:
Normally, cosine has a period of 2pi. This means that the curve repeats itself every 2pi units. However, this graph has a period of pi.
We can see this by noting that the distance from one peak such as x = 0 to another adjacent peak x = pi is exactly pi units across.
Since T = pi is the period, we then know that
B = (2pi)/T
B = (2pi)/(pi)
B = 2
Then recall that the general template is y = Acos(B(x-C))+D
In this case, A = 1, C = 0 and D = 0. So all of this leads to y = cos(2x)
Suppose that X1 and X2 are independent random variables each with a mean μ and a variance σ^2. Compute the mean and variance of Y = 3X1 + X2.
Mean:
E[Y] = E[3X₁ + X₂]
E[Y] = 3 E[X₁] + E[X₂]
E[Y] = 3µ + µ
E[Y] = 4µ
Variance:
Var[Y] = Var[3X₁ + X₂]
Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]
(the covariance is 0 since X₁ and X₂ are independent)
Var[Y] = 9 Var[X₁] + Var[X₂]
Var[Y] = 9σ² + σ²
Var[Y] = 10σ²
Solve for x. Round to the nearest tenth of a degree, if necessary.
From one of the trigonometric ratios, tan(x), it is possible to find that x is equal to 52.1°.
Trigonometric RatiosThe main trigonometric ratios for a right triangle are presented below.
[tex]sin(x)= \frac{opposite\; side}{hypotenuse} \\ \\ cos(x)= \frac{adjacent\; side}{hypotenuse} \\ \\tan(x)= \frac{sin(x)}{cos(x)} =\frac{opposite\; side}{hypotenuse}* \frac{adjacent\; side}{hypotenuse}=\frac{opposite\; side}{adjacent\; side}[/tex]
For solving this question, you need to apply the a trigonometric ratio . You have the dimensions of two sides and you need to find the angle x.
Thus, you can apply the tan(x).
[tex]tan(x)= \frac{opposite\; side}{adjacent\; side}=\frac{36}{28} =\frac{9}{7}[/tex]
After that, you should calculate the arctan(x).
[tex]arctan\left(\frac{9}{7}\right)=52.1^{\circ \:}[/tex]
Then x= 52.1°
Learn more about trigonometric ratios here:
brainly.com/question/11967894
Help Please if you don’t mind
Answer:
trinomial = 5x
GCF = 2x(x + 5) + 5(x + 5)
Step-by-step explanation:
2x^2 + 15x + 25
using middle term break method
2x^2 + (10 + 5)x + 25
2x^2 + 10x + 5x + 25
therefore trinomial = 2x^2 + 10x + 5x + 25
GCF(Greatest Common Factor) = 2x^2 + 10x + 5x + 25
=2x(x + 5) + 5(x + 5)
take (x + 5 ) as common
(x + 5)(2x + 5)
(x + 5)(5 + 2x)since the sign of 5 and 2x is same i.e plus sign u can change their place.
Which of the following is a radical equation
Answer:
7[tex]\sqrt{x}[/tex] = 14, D
Step-by-step explanation:
A radical equation is defined by having a variable under a radical sign. This is the only option with a variable (x) under the radical sign. Hence, 7[tex]\sqrt{x}[/tex] = 14 is the correct option.
In the diagram, the length of segment QV is 15 units. What is the length of segment TQ?
Answer:
14 units is the answer
Step-by-step explanation:
^_^^_^^_^^_^^_^
On Monday, 405 students went on a trip to the zoo. All 7 buses were filled and 6 students had to travel in cars. How many students were in each bus
Answer:
57 students
Step-by-step explanation:
Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.
Then, divide that by 7, and you get the answer. 57.
Hope it helps!
Answer:
57 students
Step-by-step explanation:
405-6=399
399÷7=57
How many pairs of intersecting line segments are shown?
A. 4
B. 8
C. 16
D. 24
Answer:
I believe the answer is 24.
Step-by-step explanation:
hope it helps.
instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: SAS
Answer:
please I don't know can u please help me out
Answer:
The answer to your question where SAS is given
∠T ≈∠ W
What is the volume of the pyramid?
Answer:
[tex]volume=1/3 ~BH[/tex]
[tex]=1/3(16)^{2} \sqrt{17^{2} -8^{2} }[/tex]
[tex]=1/3\times256\times15[/tex]
[tex]=1280 ~ft^{3}[/tex]
------------------------
hope it helps...
have a great day!!
I need help. Someone please figure it out
Answer:
[tex]\frac{1}{2^{n} }[/tex]
Step-by-step explanation:
The rules of exponents state that
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] and [tex]a^{0}[/tex] = 1
Thus
[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]
[tex]2^{-4}[/tex] = [tex]\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{16}[/tex]
[tex]2^{-3}[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]
and so on , to
[tex]2^{0}[/tex] = 1
Which property would allow you to use mental computation to simplify the problem 27 + 15 + 3 + 5?
Answer:
commutative property of addition.
a sequence of additions can be done in any order and the total remains the same.
Step-by-step explanation:
so, we can actually do
27 + 3 + 15 + 5
and now it is easy to combine 27+3 to 30 and 15+5 to 20, and to make the final calculation of 30 + 20 = 50 in our minds.
Cylinders A and B are similar. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.
The question is incomplete. The complete question is :
Cylinders A and B are similar. The length of the cylinder A is 4 mm and the length of cylinder B is 6 mm. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.
Answer:
67.5 [tex]mm^3[/tex]
Step-by-step explanation:
Given that :
Cylinder A and cylinder B are similar.
Let volume of cylinder A = 20 [tex]mm^3[/tex]
We know the volume of a cylinder is given by V = [tex]$\pi r^2 h$[/tex]
where, r is the radius of the cylinder
h is the height of the cylinder
We have to find the scale factor.
The length scale factor is = [tex]$\frac{6}{4}$[/tex]
[tex]$=\frac{3}{2}$[/tex]
Area scale factor [tex]$=\left(\frac{3}{2}\right)^2$[/tex]
[tex]$=\frac{9}{4}$[/tex]
∴ Volume scale factor [tex]$=\left(\frac{3}{2}\right)^3$[/tex]
[tex]$=\frac{27}{8}$[/tex]
Therefore, the volume of cylinder B is [tex]$=20 \times \frac{27}{8}$[/tex]
= 67.5 [tex]mm^3[/tex]
CAN SOMEBODY PLEASE HELP MEEEE
Answer:
105.
Step-by-step explanation:
.
Guys I need help!!!
Is (1, 4) a solution to the equation y = 8x − 4?
Answer:
Yes
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)FunctionsStep-by-step explanation:
Step 1: Define
Identify
Point (1, 4)
y = 8x - 4
Step 2: Find
Substitute in point [Equation]: 4 = 8(1) - 4Multiply: 4 = 8 - 4Subtract: 4 = 4yes.
you just have to check like this: 1 is x and 4 is y.
4 = 8(1) - 4
4 = 8 - 4
4 = 4
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
How would the one-step equation x/5 = 5 be solved?
Multiply both sides by 1/5
Multiply both sides by the reciprocal of 1/5
Divide 5 by both sides
Divide one side by 5
Answer:
2nd option
Step-by-step explanation:
Given
[tex]\frac{x}{5}[/tex] = 5 ( multiply both sides by 5, the reciprocal of [tex]\frac{1}{5}[/tex] to clear the fraction )
x = 25
Diego deposited \$ 10,000$10,000 for 44 years at a rate of 6\%6% simple interest. Find the amount of interest Diego earned after four years.
Answer:
$2,400
Step-by-step explanation:
Note: The correct years is 4 not 44
The Principal = $10,000
Time period = 4 years
Rate = 6 % p.a.
Simple Interest = Principal * Rate * Time
Simple Interest = $10,000 * 6% * 44
Simple Interest = $2,400
So, the amount of interest Diego earned after four years is $2,400
I need help on my math!!!!!!!
Answer:
(b) 30.25 feet
Step-by-step explanation:
Given
[tex]v = \sqrt{64h[/tex]
Required
Find [tex]h[/tex] when [tex]v = 44[/tex]
Substitute [tex]v = 44[/tex] in [tex]v = \sqrt{64h[/tex]
[tex]44 = \sqrt{64h[/tex]
Take square of both sides
[tex]44^2 = 64h[/tex]
[tex]1936 = 64h[/tex]
Divide both sides by 64
[tex]30.25 = h[/tex]
Rewrite as:
[tex]h = 30.25[/tex]
I need help
Please
I hate math
The ratio of two side lengths for the triangle is given. What is the value of “q” AB:BC is 3:4
Answer:
[tex]q=8.5[/tex]
Step-by-step explanation:
The ratio of the side lengths (AB) and (BC) is given. One is also given an expression for the side lengths of each of these sides. Set up a proportion to describe this scenario, then solve using cross products;
[tex]\frac{AB}{BC}=\frac{3}{4}[/tex]
Substitute,
[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]
Cross products,
[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]
[tex](60)(4)=(10q+15)(3)\\\\240=30q+45[/tex]
Inverse operations,
[tex]240=30q+45\\\\195=30q\\\\8.5=q[/tex]
Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 +
8 = 20. Add the length of KL to the diagram.
J
12 K
20
L
X
M
12
00
8
N
Answer:
Step-by-step explanation:
Step 3:
Let LM = x
OK = KP = 12 units [Radii of circle K]
LN = LP = 8 units [Radii of circle L]
Therefore, KL = KP + PL
KL = 12 + 8
= 20 units
Step 4:
Since, ΔKOM and ΔLNM are the similar triangles,
By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.
[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]
[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]
12x = 8(x + 20) [By cross multiplication]
12x = 8x + 160
12x - 8x = 160
4x = 160
x = 40