Answer:
∠T ≅ ∠A
Step-by-step explanation:
Since, ∆MTW ≅ ∆CAD
Therefore, ∠T ≅ ∠A (cpct)
Please help quickly!!
A truck is driving up a hill with a 24% grade, so it climbs 24 feet vertically for every 100 feet horizontally.
What is the slope of the hill?
Answer:
6/25
Step-by-step explanation:
rise / run
24/100 = 6/25
Answer:
[tex]\frac{6}{25}[/tex]
Step-by-step explanation:
The slope of any relationship is always rise over run. This means the vertical distance traveled over the horizontal distance traveled will get us our slope.
We travels 24 feet vertically for every 100 feet horizontally, so:
[tex]\frac{24}{100}[/tex].
We can simplify this fraction to find the slope in fraction form.
[tex]\frac{24\div4}{100\div4} = \frac{6}{25}[/tex]
So the slope of this equation is [tex]\frac{6}{25}[/tex].
Hope this helped!
I will give brainliest to the right answer!! Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7
Answer:
(7, 5)2Step-by-step explanation:
When the quadratic is written in vertex form:
x = a(y -k)^2 +h
the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.
For your given equation, ...
x = (1/2)(y -5)^2 +7
you have a=1/2, k = 5, h = 7, so ...
the vertex is (7, 5)
the length of the latus rectum is 1/(1/2) = 2
Describe how to solve an absolute value equation
*will give brainliest*
Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
Events A and B are mutually exclusive. Find the missing probability.
P(A) = 1/4 P(B) = 13/20 P(A or B) = ?
4/5
1/2
9/10
3/8
Answer:
Option C.
Step-by-step explanation:
It is given that,
[tex]P(A)=\dfrac{1}{4}[/tex]
[tex]P(B)=\dfrac{13}{20}[/tex]
It is given that events A and B are mutually exclusive. It means they have no common elements.
[tex]P(A\cap B)=0[/tex]
We know that,
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
On substituting the values, we get
[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]
[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]
[tex]P(A\cup B)=\dfrac{18}{20}[/tex]
[tex]P(A\cup B)=\dfrac{9}{10}[/tex]
Therefore, the correct option is C.
The P (A or B) should be [tex]\frac{9}{10}[/tex]
Given that,
P(A) = 1 by 4 P(B) = 13 by 20Based on the above information, the calculation is as follows:
[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]
Learn more: https://brainly.com/question/17429689?referrer=searchResults
In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?
Answer:
37,139
Step-by-step explanation:
Given the following :
Population in 2002 = Initial population (P0) = 22,800
Growth rate (r) = 5% = 0.05
Growth in 2012 using the exponential growth function?
Time or period (t) = 2012 - 2002 = 10years
Exponential growth function:
P(t) = P0 * (1 + r) ^t
Where P(t) = population in t years
P(10) = 22800 * (1 + 0.05)^10
P(10) = 22800 * (1.05)^10
P(10) = 22800 * 1.62889
P(10) = 37138.797
P(10) = 37,139 ( to the nearest whole number)
Raj tested his new flashlight by shining it on his bedroom wall. The beam of light can be described by the equation . How many inches wide is the beam of light on the wall?
Answer:
12 inches
Step-by-step explanation:
Raj tested his new flashlight by shinning it on his bedroom wall the beam of the light can be described by the equation (x^2-2x) + (y^2-4y) - 31=0. how many inches wide is the beam of light on the wall
Solution
Given:
(x^2-2x) + (y^2-4y) - 31=0
By completing the square
(x^2-2x) + (y^2-4y) - 31=0
(x^2-2x+1-1) + (y^2-4y+4-4)-31=0
(x-1)^2 -1 + (y-2)^2 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 1 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 36=0
(x-1)^2 + (y-2)^2=36
Writing the equation in the form: (x-h)^2+(y-k)^2=r^2
(x-1)^2+(y-2)^2=6^2
From the above, r=6
Where,
r=radius
how wide is the diameter ?
radius=6
Diameter= 2 × radius
=2×6
=12 inches
Answer:
12
Step-by-step explanation:
to graph it just scan the equation on photo math!!
Translate the following phrase into an algebraic expression using the variable m. Do not simplify,
the cost of renting a car for one day and driving m miles if the rate is $39 per day plus 45 cents per mile
Answer:
y = 0.45X + 39
Find the volume of a pyramid with a square base, where the side length of the base is 17 in 17 in and the height of the pyramid is 9 in 9 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
One type of fabric costs $31.25 for 5 square yards. Another type of fabric costs $71.50 for 11
square yards. Is the relationship between the number of square yards and the cost
proportional between the two types of fabric?
Answer:
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Step-by-step explanation:
For a relation to be proportional
a:b = c:d
in other form
a/b = c/d
______________________________________________
Ratio for first type of fabric
cost of fabric/ area of fabric = 31.25/5 = 6.25
Ratio for other type of fabric
cost of fabric/ area of fabric = 71.50/11 = 6.5
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
Manipulate the radius and height of the cone, setting different values for each. Record the radius, height, and exact volume of the cone (in terms of π). The first one has been done for you. Also calculate the decimal value of the volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= 2000π unit³
Volume= 6284 unit³
Step-by-step explanation:
The decimal value of the volume already given= 600π
The decimal value of the volume already given= 600*3.142
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= πr²h/3
Volume= 11²*12/3 *π
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume = πr²h/3
Volume= 4²*6/3(π)
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= πr²h/3
Volume= 20²*15/3(π)
Volume= 2000π unit³
Volume= 6284 unit³
Here's the right answer.
What does the law of cosines reduce to when dealing with a right angle
Answer:
It is reduced to the equation of the Theorem of Pythagoras.
Step-by-step explanation:
Any triangle can be modelled by this formula under the Law of Cosine:
[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.
[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.
Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:
[tex]\cos B = 0[/tex]
And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:
[tex]b = \sqrt{a^{2}+c^{2}}[/tex]
Astrid is in charge of building a new fleet of ships. Each ship requires 404040 tons of wood, and accommodates 300300300 sailors. She receives a delivery of 444 tons of wood each day. The deliveries can continue for 100100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 210021002100 sailors.
To build the fleet of ships, Astrid must consider each of the given rates (i.e. the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.
Given that:
Required quantities
[tex]Wood = 40\ tons[/tex]
[tex]Sailors = 300[/tex] per ship
Available quantities
[tex]Wood = 4\ tons[/tex] daily
[tex]Days = 100[/tex] at most
First, we calculate the total tons of woods Astrid can receive.
[tex]Total = Days \times Wood\ Available[/tex]
[tex]Total = 100 \times 4[/tex]
[tex]Total = 400\ tons[/tex] ---- in 100 days
Next, we calculate the number of ships that can be made from the 400 tons.
[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]
So, we have:
[tex]Ships = \frac{400}{40}[/tex]
[tex]Ships = 10[/tex]
This means that Astrid can build up to 10 ships
The number of sailors the ship can accommodate is:
[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]
So, we have:
[tex]Sailors = 10 \times 300[/tex]
[tex]Sailors = 3000[/tex]
It means the 10 ships can accommodate 3000 sailors.
3000 sailors is greater than 2100 sailors.
So, we can conclude that she can build enough ship for the 2100 sailors.
Read more about
https://brainly.com/question/17174491
Answer:
280 tons
Step-by-step explanation:
:)
(x+3)(x-5)=(x+3)(x−5)=
Answer:
All real numbers are solutions. 0=0
Step-by-step explanation:
(x+3)(x−5)=(x+3)(x−5)
Step 1: Simplify both sides of the equation.
x2−2x−15=x2−2x−15
Step 2: Subtract x^2 from both sides.
x2−2x−15−x2=x2−2x−15−x2
−2x−15=−2x−15
Step 3: Add 2x to both sides.
−2x−15+2x=−2x−15+2x
−15=−15
Step 4: Add 15 to both sides.
−15+15=−15+15
0=0
All real numbers are solutions.
ABC is an equilateral triangle, solve y
Answer:
y is 60⁰
because all sides are equal
Answer:
60 degrees
Step-by-step explanation:
In an equilateral triangle, the angles are equiangluar and the sides are equal.
180 degrees in a triangle/3 sides =
= 60 degrees per side
PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B
Answer:
Sector
Step-by-step explanation:
A sector of a circle is the portion of circle enclosed by two radii and arc
Simplify the following expression.
Answer:
3x+11y-3
Step-by-step explanation:
Hey! So here is what you do to solve the problem-
Combine like terms:
(x) 5x-2x=3x
(y) 3y+8y=11y
(#) 7-10 =-3
So....
3x+11y-3 is your answer!
Hope this helps!:)
9(p−4)=−18 p= I am not great at math, please explain just a little bit
Answer:
[tex]\large \boxed{{p=2}}[/tex]
Step-by-step explanation:
9(p-4) = -18
Expand brackets.
9p -36 = -18
Add 36 on both sides.
9p -36 + 36 = -18 + 36
9p = 18
Divide both sides by 9.
(9p)/9 = 18/9
p = 2
Answer:
p = 2
Step-by-step explanation:
9(p - 4) = -18
You are solving for the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 9 from both sides:
(9(p - 4))/9 = (-18)/9
(p - 4) = -18/9
p - 4 = -2
Isolate the variable, p. Add 4 to both sides:
p - 4 (+4) = -2 (+4)
p = -2 + 4
p = 4 - 2
p = 2
Check. Plug in 2 for p in the equation:
9(p - 4) = -18
9(2 - 4) = -18
9(-2) = - 18
-18 = -18.
~
Pick out the set of numbers that is not Pythagorean triple
9 40 46
16 30 34
10 24 26
50 120 130
Answer:
[tex]\huge\boxed{9,40,46}[/tex]
Step-by-step explanation:
Let's check it using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the longest sides, a and b are rest of the 2 sides
1) 9 , 40 , 46
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]46^2 = 9^2 + 40^2[/tex]
=> 2116 = 81 + 1600
=> 2116 ≠ 1681
So, this is not a Pythagorean Triplet
2) 16, 30 and 34
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]34^2 = 16^2 + 30^2[/tex]
=> 1156 = 256 + 900
=> 1156 = 1156
No need to check more as we've found the one which is not a Pythagorean Triplet.
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \blue{9 , \: 40 \:, 46 \: }}}}}[/tex]Option A is the correct option.
Step-by-step explanation:
1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.
From Pythagoras theorem,
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Here, we know that the hypotenuse is always greater than perpendicular and base,
h = 46 , p = 40 , b = 9
⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]
⇒[tex]2116 = 1600 + 81[/tex]
⇒[tex] \sf{2116 ≠ 1681}[/tex]
Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9
So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.
------------------------------------------------------
2. 16 , 30 , 34
h = 34 , p = 30 , b = 16
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]
⇒[tex] \sf{1156 = 900 + 256}[/tex]
⇒[tex] \sf{1156 = 1156}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16
So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.
------------------------------------------------------
3. 10, 24 , 26
h = 26 , p = 24 , b = 10
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]
⇒[tex] \sf{676 = 576 + 100}[/tex]
⇒[tex] \sf{676 = 676}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10
So, the set of numbers 10, 24 , 26 is the Pythagorean triple.
-----------------------------------------------------
4. 50 , 120 , 130
h = 130 , p = 120 , b = 50
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]
⇒[tex] \sf{16900 = 14400 + 2500}[/tex]
⇒[tex] \sf{16900 = 16900}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50
So, the set of numbers 50, 120 , 130 is the Pythagorean triple.
-----------------------------------------------------
In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.
Hope I helped!
Best regards!!
n urn contains 3 red balls, 9 green, 2 yellow, 2 orange, and 4 purple balls. Two balls aredrawn, one at a time with replacement. Find the probability of drawing a green ball and an orangeball.
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
Given:
Number of red balls, n(R) = 3
Number of green balls, n(G) = 9
Number of yellow balls, n(Y) = 2
Number of orange balls, n(O) = 2
Number of purple balls, n(P) = 4
Two balls are drawn one at a time with replacement.
To find:
Probability of drawing a green ball and an orange ball ?
Solution:
Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability that a green ball is drawn at first:
[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Green) = \dfrac{9}{20}[/tex]
Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]
[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]
ASAP PLEASE GIVE CORRECT ANSWER
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point $(-15, 8)$? Enter your answer
distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$
so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$
Answer:
Distance=17 units
Step-by-step explanation:
Coordinates of the origin: (0, 0)
Coordinates of the point in question: (-15, 8)
Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]
simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)
Answer:
[tex]\huge \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]
Distribute negative sign.
[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]
Combine like terms.
[tex]0xe^2 +0x-1[/tex]
[tex]0-1=-1[/tex]
What are the dimensions of the matrix?
The order of a matrix is m×n where m is the number of rows and n is the number of columns.
can you count and find what are m and n here?
Answer:
Step-by-step explanation:
Number of rows X Number of columns
Rows = 3
Columns = 2
answer = 3x2
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
For a ,a relationship to be a function, which values cannot repeat: the x-
values or the y-values? *
Answer:
The x - valuesThe y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)
Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49
Answer:
The expression in factored form is (3x - 7)(3x + 7)
Step-by-step explanation:
Here in this question, we are interested in using the difference of two squares to factor the given expression.
Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.
By using the difference of two squares;
a^2-b^2 can thus be written as;
(a-b)(a + b)
Now, we can apply same approach to the problem at hand.
9x^2 - 49
kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2
So applying what we have said earlier about difference of two squares;
9x^2 - 49 will be ;
(3x-7)(3x + 7)
Answer:
The answer is (3x - 7) (3x +7)
Step-by-step explanation:
Calculate JK if LJ = 14, JM = 48, and LM = 50
Answer:
JK = 6.86
Step-by-step explanation:
The parameters given are;
LJ = 14
JM = 48
LM = 50
[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]
[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]
∠JML = 16.26°
Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.
From the angle bisector theorem, we have;
LM/JM = LK/JK
50/48 = LK/JK................(1)
LK + KJ = 14.....................(2)
From equation (1), we have;
LK = 25/24×JK
25/24×KJ + JK = 14
JK×(25/24 + 1) = 14
JK × 49/24 = 14
JK = 14×24/49 = 48/7. = 6.86.
JK = 6.86
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
Solve for x and draw a number line. 3x−91>−87 AND 17x−16>18
Answer:
I hope this will help!
Step-by-step explanation:
A company makes nylon and canvas backpacks. The profit on a nylon backpack is $3 and the profit on a canvas backpack is $10. How many backpacks must the company sell to make a profit of more than $250? Write a linear inequality that describes the situation.
Answer:
3x +10y is greater than or equal to 250.
Step-by-step explanation:
The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.
Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.
Answer:
3n + 10c > 250
Step-by-step explanation:
I confirmed it in grandpoint