Question is Incomplete, Complete question is given below.
Prove that a triangle with the sides (a − 1) cm, 2√a cm and (a + 1) cm is a right angled triangle.
Answer:
∆ABC is right angled triangle with right angle at B.
Step-by-step explanation:
Given : Triangle having sides (a - 1) cm, 2√a and (a + 1) cm.
We need to prove that triangle is the right angled triangle.
Let the triangle be denoted by Δ ABC with side as;
AB = (a - 1) cm
BC = (2√ a) cm
CA = (a + 1) cm
Hence,
[tex]{AB}^2 = (a -1)^2[/tex]
Now We know that
[tex](a- b)^2 = a^2+b^2 - 2ab[/tex]
So;
[tex]{AB}^2= a^2 + 1^2 -2\times a \times1[/tex]
[tex]{AB}^2 = a^2 + 1 -2a[/tex]
Now;
[tex]{BC}^2 = (2\sqrt{a})^2= 4a[/tex]
Also;
[tex]{CA}^2 = (a + 1)^2[/tex]
Now We know that
[tex](a+ b)^2 = a^2+b^2 + 2ab[/tex]
[tex]{CA}^2= a^2 + 1^2 +2\times a \times1[/tex]
[tex]{CA}^2 = a^2 + 1 +2a[/tex]
[tex]{CA}^2 = AB^2 + BC^2[/tex]
[By Pythagoras theorem]
[tex]a^2 + 1 +2a = a^2 + 1 - 2a + 4a\\\\a^2 + 1 +2a= a^2 + 1 +2a[/tex]
Hence, [tex]{CA}^2 = AB^2 + BC^2[/tex]
Now In right angled triangle the sum of square of two sides of triangle is equal to square of the third side.
This proves that ∆ABC is right angled triangle with right angle at B.
i dont get this plz help me
Answer:
1] Estimated cost for 1 semester=$22800
2] Total semester in 4 years=8
3] Estimated total cost for 4 years =$182400
Step-by-step explanation:
Given:-
Estimated cost per semester
Tuition fee(T) =$10000
Books(B) = $1200
Room and board(R)=$10030
Other expense(O)=$1570
Now,
1] To find the estimated cost to attend this college for 1 semester.
Answer:-
Estimated cost for 1 semester(E)= Tuition fee+Books+Room and Board+Other expense
[tex]E=T+B+R+O[/tex]
[tex]E=10000+1200+10030+1570[/tex]
[tex]Estimated\ cost\ for\ 1\ semester=22800[/tex]
Therefore estimated cost to attend this college for 1 semester = $22800
2]Each year has 2 semester. How many semester will Joe pay for if he attends for 4 years.
Answer:-
If 1 year has 2 semester, then
total semester in 4 years=[tex]2\times 4[/tex]
total semester in 4 years=8
Therefore Joe will pay for 8 semester if attends for 4 years.
3] What is the estimated total cost for Joe to attend this college for 4 years.
Estimated total cost for 4 years = Estimated total cost for 1 semester[tex]\times[/tex]8
Estimated total cost for 4 years=22800[tex]\times[/tex]8
Estimated total cost for 4 years =$182400
4x3+12+14+40x20-32+43/32+90-12
Answer:
40x20+4x3+
2347
32
Step-by-step explanation:
Let's simplify step-by-step.
4x3+12+14+40x20−32+
43
32
+90−12
=4x3+12+14+40x20+−32+
43
32
+90+−12
Combine Like Terms:
=4x3+12+14+40x20+−32+
43
32
+90+−12
=(40x20)+(4x3)+(12+14+−32+
43
32
+90+−12)
=40x20+4x3+
2347
32
Answer:
Step-by-step explanation:
=40x^20+4x^3+2347/32
Hope this helps mark me as brainiest pls
Mary's dog needs medication she told the veterinarian that the dog weighs 30 pounds the medicine is measured as 16 mg for each kilogram of the animals mass how much medicine should be given to Mary's dog
Answer:
217.6 mg of medicine
Step-by-step explanation:
13.6 kilograms in 30 pounds
13.6*16
Scientists determined that Antarctica’s average winter temperature was -34.44 Celsius. The difference between this temperature and Antarctica’s highest recorded temperature was 49.44 degrees. What was Antarctica’s highest recorded temperature?
Answer:
Antarctica's highest recorded temperature was 15 degrees.
Step-by-step explanation:
I am going to say that Antarctica highest recorded temperature is x.
I suppose there is a small typing mistake.
It is that the difference between Antarctica highest recorded temperature and this is 49.44.
So we have that x - (-34.44) = 49.44 instead of -34.44 - x = 49.44, which would lead to a highest temperature way lower than the one recorded in this winter.
Sooo
x - (-34.44) = 49.44
x + 34.44 = 49.44
x = 49.44 - 34.44
x = 15
Antarctica's highest recorded temperature was 15 degrees.
The function c=3x-y is minimized at the vertex point of the feasible region at (4,5). What is the minimum value
(x,y)=(4,5)
c = 3x-y = 3(4) - 5 = 7
Answer: 7
Final answer:
The minimum value of the function c=3x-y at the vertex point (4,5) of the feasible region is 7.
Explanation:
The question provided by the student involves finding the minimum value of a function of two variables, given by c=3x-y, at a certain point in the feasible region. Since the minimum is achieved at the vertex point (4,5), we can directly substitute these values into the function to find the minimum value.
To calculate the minimum value of the function c=3x-y at the point (4,5), we substitute x=4 and y=5 into the equation:
c = 3×4 - 5
c = 12 - 5
c = 7
Therefore, the minimum value of the function is 7 at the vertex point (4,5).
If f(x) = 9x – 8, which of the following is the inverse of f(x)?
A.
f –1(x) =
B.
f –1(x) =
C.
f –1(x) =
D.
f –1(x) =
Answer: [tex]f^{-1}[/tex] (x) = [tex]\frac{x+8}{9}[/tex]
Step-by-step explanation:
f(x) = 9x - 8 , to find the inverse of f(x) , replace f(x) with y , then the equation becomes
y = 9x - 8 , then make x , the subject of the formula ,
9x = y + 8
x = [tex]\frac{y+8}{9}[/tex]
Finally , replace x , with [tex]f^{-1}[/tex] (x) and y with x , so we have
[tex]f^{-1}[/tex] (x) = [tex]\frac{x+8}{9}[/tex]
A group of 3 adults and 5 children pay a total of 52$ for movie tickets
A group of 2 adults and 4 children pay a total of 38$ for tickets what is the cost of one adult ticket and what is the cost for one child ticket
Answer:
$9 adult$5 childStep-by-step explanation:
Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:
3a +5c = 52
2a +4c = 38
__
We can solve this system of equations using "elimination" as follows:
Dividing the first equation by 2 we get
a +2c = 19
Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:
3(a +2c) -(3a +4c) = 3(19) -(52)
c = 5 . . . . . . collect terms
a +2·5 = 19 . . substitute for c in the 3rd equation above
a = 9 . . . . . . subtract 10
One adult ticket costs $9; one child ticket costs $5.
What is the value of y?
Enter your answer in the box.
Answer:
y = 20
Step-by-step explanation:
Since AB and AC are congruent then the triangle is isosceles, thus
∠B = ∠C = 25°
To find ∠A subtract the sum of the 2 angles from 180°
∠A = 180° - (25 + 25)° = 180° - 50° = 130°, thus
3y + 70 = 130 ( subtract 70 from both sides )
3y = 60 ( divide both sides by 3 )
y = 20
AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.
Answer:
The required points of the given line segment are ( - 1, - 5 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] ) then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -
then by the midpoint formula M are-
( 3, - 2 ) = ( [tex]\frac{7 + x}{2}[/tex] , [tex]\frac{ - 9 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ 7 + x}{2}[/tex] = 3 , [tex]\frac{- 9 + y}{2}[/tex] = - 2)
( 7 + x = 6, - 9 + y = - 4 )
( x = 6 - 7, y = - 4 + 9 )
( x = - 1, y = -5 )
Hence the required points A are ( - 1, - 5 ).
We can also verify by putting these points into Midpoint formula.
solve the inequality 4y+3>2y+14
Step-by-step explanation:
Step 1. subtract 2Y from both sides
4y+3-2y>+14-2y 2y+3>14
step 2. subtract 3 from both sides
2y+3-3>14-3 2y>11
step 3. divide both sides by 2
2÷2y>11÷2 y>11÷2
answer is: y>11/ 2
The given inequality (4y + 3 > 2y + 14) is reduced to y > 5.5 and this can be evaluated by using the arithmetic operations.
Given :
Inequality -- 4y + 3 > 2y + 14
The following steps can be used to evaluate the given inequality:
Step 1 - Write the given inequality.
4y + 3 > 2y + 14
Step 2 - Subtract 3 from both sides in the above inequality.
4y + 3 - 3 > 2y + 14 - 3
4y > 2y + 11
Step 3 - Subtract 2y from both sides in the above inequality.
4y - 2y > 2y + 11 - 2y
Step 4 - Simplify the above inequality.
2y > 11
Step 5 - Divide by 2 on both sides in the above inequality.
y > 5.5
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building A has 7500 square feet of office space for 320 employees. building B has 9500 square feet of office space for 370 employees.which building offers more square feet per employee, and how much more
Building B offers more square feet per employee
Building B offers 2.2375 square feet more space for 1 employee than building A
Solution:
Building A has 7500 square feet of office space for 320 employee
Let us find the square feet needed for 1 employee
[tex]\text{ square feet needed for 1 employee } = \frac{7500 square feet}{320 employee}[/tex]
[tex]\text{ square feet needed for 1 employee } = \frac{7500}{320} = 23.4375[/tex]
Thus unit rate for building A is 23.4375 square feet per employee
Building B has 9500 square feet of office space for 370 employees
[tex]\text{ square feet needed for 1 employee } = \frac{9500}{370}\\\\\text{ square feet needed for 1 employee } = 25.675[/tex]
Thus unit rate for building B is 25.675 square feet per employee
On comparing the unit rate of both buildings, we can clearly see that Building B offers more square feet per employee
To find out how much more Building B offers more square feet per employee than building A, we can find difference between unit rates of both buildings
[tex]\rightarrow 25.675 - 23.4375 = 2.2375[/tex]
Thus Building B offers 2.2375 square feet more space for 1 employee than Building A
Final answer:
Building B offers 25.68 square feet per employee, which is 2.24 square feet more per employee than Building A, which offers 23.44 square feet per employee.
Explanation:
To determine which building offers more square feet per employee, we calculate the square footage per employee for each building:
Building A: «Building A has 7500 square feet of office space for 320 employees.
Building B: «Building B has 9500 square feet of office space for 370 employees.
Now we calculate the square footage per employee for both buildings:
For Building A: 7500 square feet / 320 employees = 23.44 square feet per employee.
For Building B: 9500 square feet / 370 employees = 25.68 square feet per employee.
Comparing the two, Building B offers more square footage per employee. To find out how much more:
25.68 - 23.44 = 2.24 square feet more per employee in Building B than Building A.
Find the length of the third side of each triangle
Answer:Where is the picture?
Step-by-step explanation:
I need help please and thank you
Answer:
400
Step-by-step explanation:
Movies, drinks and candies are independent events and you can choose one for each.
Movie: 10 options can be selected
drinks: 5
candy: 8
All types: 10 x 5 x 8 = 400
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels
at the zoo.
How many baby camels are at the zoo
Answer: 20
Step-by-step explanation: For every 6 adult camels there are 5 baby camels so if you add both together, you get 11 and if you multiply that times 4 you get 44. Now you multiply 4 times the 5 baby camels to go your answer, 20.
There are 20 baby camels at the zoo.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Let x be the number of groups of adult and baby camels, each consisting of 6 adult camels and 5 baby camels. Then we know that:
The total number of adult camels is 6x.
The total number of baby camels is 5x.
The total number of adult and baby camels is 44.
Therefore, we can write the equation:
6x + 5x = 44
Simplifying, we get:
11x = 44
Dividing both sides by 11, we get:
x = 4
So there are 4 groups of adult and baby camels. To find the number of baby camels, we can multiply the number of groups by the number of baby camels in each group:
5x = 5(4) = 20
Therefore, there are 20 baby camels at the zoo.
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I have way more questions than this answer them if you want pleaseee!!
The right answer is Option C.
Step-by-step explanation:
Given inequality is
6(2x-1) > 24
Solving the inequality
[tex]6*2x-1*6>24\\12x-6>24[/tex]
Adding 6 on both sides
[tex]12x-6+6>24+6\\12x>30[/tex]
Dividing both sides by 12
[tex]\frac{12x}{12}>\frac{30}{12}\\x>\frac{5}{2}[/tex]
Therefore,
[tex]x>\frac{5}{2}[/tex]
The right answer is Option C.
Keywords: inequality, division
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To see how fast the moss was growing students recorded how long it took the moss to cover a rule. After one hour, the moss had covered 1 1/8 inches of the ruler. After two hours, it had covered another 1 1/3 inches of the ruler. How much of the ruler did the moss cover altogether after two hours?
Answer:
The moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days.
Step-by-step explanation:
After one hour, the moss had covered [tex]1\frac{1}{8}[/tex] inches of the ruler.
Again, after two hours, it had covered another [tex]1\frac{1}{3}[/tex] inches of the ruler.
Therefore, after two hours the moss covers altogether ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex]) inches of the ruler.
Now, ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex])
= [tex]\frac{9}{8} + \frac{4}{3}[/tex]
= [tex]\frac{9\times 3 + 4 \times 8}{24}[/tex]
= [tex]\frac{59}{24}[/tex]
= [tex]2\frac{11}{24}[/tex] inches
Therefore, the moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days. (Answer)
A rectangle has a length of 6 and a width of y + 4. Use your area expression to find the area of the rectangle when y = 3 inches. Show your work.
Answer:
42
Step-by-step explanation:
here,
if y=3 then
width is 3+4=7
We know,
Area = l*b
6*7=42 ans
Answer:
A = 42 in²Step-by-step explanation:
[tex]\bold{METHOD\ 1:}[/tex]
[tex]\text{The formula of an area of a rectangle:}\\\\A=l\times w\\\\l-\text{length}\\w-\text{width}\\\\\text{We have:}\\\\l=6,\ w=y+4\\\\\text{Substitute:}\\\\A=6\times(y+4)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\\A=(6)(y)+(6)(4)\\\\A=6y+24[/tex]
[tex]\text{Put}\ y=3\ \text{to the expression}\\\\A=6(3)+24=18+24=42\ in^2[/tex]
[tex]\bold{METHOD\ 2:}[/tex]
[tex]\text{Put}\ y = 3\ \text{to}\ y+4:\ 3+4=7\\\\\text{Put the values of length and width to the formula of an area of a rectangle:}\\\\A=(6)(7)=42\ in^2[/tex]
If function g has the factors (x − 7) and (x + 6), what are the zeros of function g?
A.
-7 and 6
B.
-6 and 7
C.
6 and 7
D.
-7 and -6
Answer:
B)
Step-by-step explanation:
Do the zero property.
x-7=0, x+6=0
x=0+7=7,
x=0-6=-6
Answer:
b 100% true
Step-by-step explanation:
Which of the following is a quadratic function?
Answer:
First answer at the top.
Step-by-step explanation:
What is the solution to the following equation?
х+ (-21) = 8
ОА. x= 27
B. х = 29
с.
x
х = 13
х = 17
What is the solution to the following equation?
х+ (-21) = 8
О А. x= 27
B. х = 29
с. х = 13
D. х = 17
Answer:Option B
The solution to given equation is x = 29
Solution:Given that we have to find the solution of given equation
Given equation is x + (- 21 ) = 8
The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable.
The goal is to have the variable on one side of the equation and numbers on the other.
From given equation,
x + ( -21) = 8
Let us first remove the brackets around -21
We know when we multiply a positive sign number with negative sign number, we get a negative sign number
x + 1( - 21 ) = 8
x - 21 = 8
Move -21 from L.H.S to R.H.S
x = 21 + 8
x = 29
Thus solution to given equation is x = 29 Thus Option B is correct
Kinda blurry need help answer this
Answer:
(a) 24 cents.
(b) The slope is: [tex]24[/tex]
Step-by-step explanation:
(a) Notice that the x-axis is labeled as "Weight (ounces)" and the y-axis is labeled as "Cost (cents)".
You can identify that when:
[tex]x=1;y=24[/tex]
[tex]x=2;y=48[/tex]
[tex]x=3;y=72[/tex]
Then, you can determine that the cost of the cheese increases 24 cents for each ounce Dale buys.
(b) The slope can be found with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
If you choose two points on the line, for example the points (0,0) and (2,48), and you substitute the corresponding coordinates into the formula, you get that the slope of the line is:
[tex]m=\frac{0-48}{0-2}\\\\m=24[/tex]
Solve the equation for g
w=gh-2gk^2
Answer:
The Answer is in the picture above
plz Mark me brainliest answer
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What is -13r+ 20r = -14
Answer:
r = -2.
Step-by-step explanation:
-13r+ 20r = -14
7r = -14
r = -14/7
r = -2.
Answer:
-2
Step-by-step explanation:
-13r+20r=-14
7r=-14
r=-2
Hey salsa recipe uses green pepper onion and tomato and the extended ratio 1:3:8 how many cups of onion are needed to make 24cps of salsa
Answer:
onion : tomato : something = 1:3:8
onion required = 1/12 × 24 = 2 cup
Three-fourths of a number multiplied by seven
Answer:
5 1/4 or 5.25
Step-by-step explanation:
Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.
3*7 = 21
4*1 = 4
We end up with the improper fraction 21/4. We can convert this into a mixed number.
Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25
write the first five terms of the sequence by the recursive formula t1=2 and tn=tn-1+3
Answer:
T1 =2 , Tn = 1 /tn-1 For The Geometricseries 6 + 3 + 3/2 + 3/4 + .
Step-by-step explanation:
Answer:
2, 5, 8, 11, 14
Step-by-step explanation:
Find the first 5 terms by substituting n = 2, 3, 4, 5 into the recursive formula
t₂ = t₁ + 3 = 2 + 3 = 5
t₃ = t₂ + 3 = 5 + 3 = 8
t₄ = t₃ + 3 = 8 + 3 = 11
t₅ = t₄ + 3 = 11 + 3 = 14
The first 5 terms are 2, 5, 8, 11, 14
how is it possible that all proportional relationships are linear functions but not all linear functions are proportional relationships
Step-by-step explanation:
A line that passes through the origin is proportional (y = mx). But a line that doesn't pass through the origin isn't proportional (y = mx + b). So all proportional relationships are linear, but not all linear relationships are proportional.
proportional relationship is just a linear relationship where the line passes through the origin (0, 0).
which of the following is a solution of x^2+4x+6
Answer:
Option 1) [tex]x=-2+i\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +4x+6=0[/tex]
so
[tex]a=1\\b=4\\c=6[/tex]
substitute in the formula
[tex]x=\frac{-4\pm\sqrt{4^{2}-4(1)(6)}} {2(1)}[/tex]
[tex]x=\frac{-4\pm\sqrt{-8}} {2}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-4\pm i\sqrt{8}} {2}[/tex]
[tex]x=\frac{-4\pm2i\sqrt{2}} {2}[/tex]
[tex]x=-2\pm i\sqrt{2}[/tex]
The solutions are
[tex]x=-2+i\sqrt{2}[/tex]
and
[tex]x=-2-i\sqrt{2}[/tex]
The surface area of the box of cereal displayed is 2x^2+48x+88. What is the value of x if the box of cereal has a total surface area of 192 in
To find the value of x for the box of cereal, set the given expression for the surface area equal to 192 and solve for x.
Explanation:To find the value of x, we need to set the given expression for the surface area of the box equal to 192 and solve for x. So, we have:
2x^2 + 48x + 88 = 192
2x^2 + 48x - 104 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's factor it:
(2x - 4)(x + 26) = 0
Setting each factor equal to zero and solving for x, we get:
2x - 4 = 0, x = 2
x + 26 = 0, x = -26
So, the possible values of x are 2 and -26. However, since the dimensions of a box cannot be negative, the value of x for the box of cereal is 2.
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e - 2f = -10
8e + 4f = 0
Answer:
f = 4 e = -2
Step-by-step explanation:
e - 2f = -10
8e + 4f = 0
Solve by substitution
8e + 4f = 0
8e = -4f
e = -0.5f
Substitute into e - 2f = -10
-0.5f - 2f = -10
-2.5f = -10
2.5f = 10
f = 4
Substitute into 8e + 4f = 0
8e + 16 = 0
8e = -16
e = -2
Answer:
e=-2, f=4. (-2, 4).
Step-by-step explanation:
e-2f=-10
8e+4f=0
-------------
e=-10+2f
e=2f-10
8(2f-10)+4f=0
16f-80+4f=0
20f=0+80
20f=80
f=80/20
f=4
e-2(4)=-10
e-8=-10
e=-10+8
e=-2