Answer:
x = 1
AB = 9
BC = 9
AC = 18
Step-by-step explanation:
Given that B is the midpoint of AC, we can say that
AB = BC
x² + 8x = 4x + 5
subtract (4x+5) from both sides to make the equation equal to 0, enabling us to solve for x
x² + 4x - 5 = 0
Because 5 and -1 add to 4 (the coefficient to x in 4x) and 5 * (-1) = -5 ( the constant), we can factor this out into
(x+5)(x-1) = 0
Therefore, x² + 8x = 4x + 5 can be true at either x=-5. x=1, or both. Plugging these values in the equations to check, starting with x=-5, we get
-5²+8(-5) =4(-5) + 5
-15 = -15
As a line segment cannot have negative length, and x² + 8x = 4x + 5 is negative when x=-5, x=-5 is not a viable solution
Next, for x=1, we get
1²+8(1) = 4(1) + 5
9=9
Therefore, x=1 is the only solution we have.
We have plugged this in for AB and BC, and 1²+8(1) = 4(1) + 5 = x² + 8x = 4x + 5 = 9 for both AB and BC
Next, AC is simply the sum of the two line segments that make them up, AB and BC, so AC = 9 + 9 = 18
Given that (1,4) is on the graph f(x), find the corresponding points of a function 1/4f(x)
Answer:
(1,1)
Step-by-step explanation:
In the equation f(x), you are plugging in the x coordinate which in this case is one. That means in 1/4f(x), x will remain the same, because you are still plugging in the same thing. What will change is the y coordinate. 1/4f(x) is saying that the y coordinate will be a fourth of the original y coordinate(4). 4 times 1/4 is equal to one.
If the x coordinate stays the same, and the y coordinate is a fourth of 4, the corresponding points in the function f(x) will be (1,1)
Ellus
Find the range of the data.
The ages of people eating
chocolate ice cream at a park.
12, 2, 8, 5, 3, 2,5
Range: [? ]
Enter the number that belongs in the green box.
Answer:
range = 10
Step-by-step explanation:
The range is the difference between the largest and smallest values in the data set.
largest value = 12
smallest value = 2
range = 12 - 2 = 10
How do I do this ? no links please
Hey there!
ASSUMING….
-14.4 = -1.2m
-1.2m = -14.4
DIVIDE -1.2 to BOTH SIDES
-1.2m/-1.2 = -14.4/-1.2
SIMPLIFY IT!
m = -14.4/-1.2
m = 12
Therefore, the answer should be:
m = 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use the following list of balances for Paul's Guitar Shop to answer the following question. Guitar Sales 24,800, Depreciation expense 2,000, Wage expense 10,950, Rent 500, Music Lesson Revenue 3,000, Interest expense 500, Supplies expense 500, Utilities expense 400. What is the TOTAL value of EXPENSES? *
Answer:
The Total Value of Expenses is $14,350
Step-by-step explanation:
AMOUNT
Depreciation Expense $ 2,000
Wage Expense $ 10,950
Interest Expense $ 500
Supplies Expense $ 500
Utility Expense $ 400
TOTAL $ 14,350
Which pairs of angles in the figure below are vertical angles?
Check all that apply
Answer:
[see below]
Step-by-step explanation:
Vertical angles are simply opposite angles that are made from intersecting lines.
The most appropriate pairs would be vertical pairs:
∠NSI and ∠TSW
∠NST and ∠ISW
The angles are opposite of each other and formed from the two lines.
Hope this helps.
Duncan is putting icing on the top of a rectangular cake if the top of the cake is 6 inches wide by 10 inches long what is the area of the top of the cake
A. 80 square inches
B.60 square inches
C.30 square inches
D. 120 square inches
Duncan is putting icing on the top of a rectangular cake if the top of the cake is 6 inches wide by 10 inches long what is the area of the top of the cake
A. 80 square inches
B.60 square inches
C.30 square inches
D. 120 square inches
Answer:
B- 60 square inches
Lin buys a candle that is 9 inches tall and burns down x inches per minute. She wants to let the candle burn for 7 minutes until it is less than 6 inches tall. 9 − 7x < 6 Solve the inequality that represents the story. If the variable is on the left, what is the sign?
Answer:
+ or > depending on what you mean exactly
Step-by-step explanation:
-7x<6-9
-7x<-3
x>3 (remember to flip the sigh)
the sign is the > symbol , or positive, not sure what you mean really
what is a kite? what are its properties? what is its use in our daily life?
Answer:
Well, in geometry, the properties would be that the angles produced by the intersection of the diagonals are right angles. A kite is basically entertainment, made by cloth and string
A kite is a four sided shape. Like an elongated rectangle.a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other instead of being adjacent. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a bird. Kites are also known as deltoids, but the word "deltoid" may also refer to a deltoid curve, an unrelated geometric object.Kites have been used for human flight, military applications, science and meteorology, photography, lifting radio antennas, generating power, aerodynamics experiments, and much more.
Please help me with this geometry question
Answer:
2) 40
Step-by-step explanation:
the perimeter of Rhombus =
4 × (√(12/2)²+(16/2)² )
= 4× (√6²+8²)
= 4× (√100)
= 4×10
= 40
Q) 4 × (√(12/2)²+(16/2)² )
→ 4 × (√6²+8²)
→ 4 × (√100)
→ 4 × 10
→ 40 is the perimeter of rhombus.
Consider the graph of the function f(x)=2x.
Which statement describes a key feature of
function g if g(x) = 2f(x)? Answers:
A. y-intercept at (0,2)
B. y-intercept at (2,0)
C. horizontal asymptote of y = -2
D. horizontal asymptote of y = 2
Given:
The parent function is:
[tex]f(x)=2^x[/tex]
The other function is:
[tex]g(x)=2f(x)[/tex]
To find:
The statement that describes a key feature of function g.
Solution:
We have,
[tex]f(x)=2^x[/tex]
[tex]g(x)=2f(x)[/tex]
Using these two functions, we get
[tex]g(x)=2(2)^x[/tex]
Putting [tex]x=0[/tex], we get
[tex]g(x)=2(2)^{(0)}[/tex]
[tex]g(x)=2(1)[/tex]
[tex]g(x)=2[/tex]
The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.
We know that [tex]g(x)\to 0[/tex] as [tex]x\to -\infty[/tex] and it will never intersect the line [tex]y=0[/tex]. It means the horizontal asymptote of the function g is
Therefore, the correct option is A.
Answer:
A
Step-by-step explanation:
Which of the following functions best describes this graph?
A. Y = (x-3)(x + 4)
B. y = x^2-5x +6
C. y = x^2 -9x+18
D. y - (x+3)(x +6)
Answer:
(A). y = ( x - 3 ) ( x + 4 )
Step-by-step explanation:
Find k if (x+1) 2x^3+kx^2+1
Find k if (x+1) is a factor of 2x³ + kx² + 1
Answer:
k = 1
Step-by-step explanation:The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.
This is because;
i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.
ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e
=> (-3)² - 9
=> (9) - 9 = 0
Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.
From the question
Given polynomial: 2x³ + kx² + 1
Given factor: x + 1.
Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e
2(-1)³ + k(-1)² + 1 = 0
2(-1) + k(1) + 1 = 0
-2 + k + 1 = 0
k - 1 = 0
k = 1
Therefore the value of k is 1.
Jack had 3bags of golf balls with b balls in each bag; then his friend gave him 6 more golf balls. How many golf balls does Jack have now?
Answer:
3(b+2)balls
Step-by-step explanation:
Given data
number of bags of golf balls= 3
number of balls in each bag=b
total number of balls in all three bags= 3b
His friend gave him 6 more= 3b+6
Hence the total balls is = 3b+6
= 3(b+2)balls
What is the definition of exponential growth?
Any help out there
Answer:
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Answer:
The answer is probably B. If not it might be C.
Step-by-step explanation:
Exponential growth is growth that becomes more and more rapid. I hope this helps :).
What is the area of the square,in square units?
3/4 unit
Answer:
9/16
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
A = (3/4)^2
A = 9/16
The y-values that a function approaches when the x-values are extremely large or extremely small. This is called the function's
Answer:
end behavior
Step-by-step explanation:
Evaluate the expression c5 when c = 3.
Replace c with 3:
3^5 = 3 x 3 x 3 x 3 x 3 = 243
The answer is 243
Answer:
15
Step-by-step explanation:
c5
3(5)
3 x 5
15
What is the slope of the line that contains the points (-2, 5)and (3,-5)?
Answer:
slope = - 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (3, - 5)
m = [tex]\frac{-5-5}{3-(-2)}[/tex] = [tex]\frac{-10}{3+2}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2
What properties of a figure stay the same after a reflection? *
Answer:
1. The preimage and image are congruent
2. Any line segment connecting the corresponding points between the preimage and image is bisected by the line of reflection
3. Corresponding angles on the preimage and image are congruent
4. Corresponding points of the preimage and image are equidistant from the line of reflection.
Jeremy’s car travels 26 miles per gallon of gas (g). If the distance traveled (d) can be given by a function, what is the input of this function?
How do the perimeters of the triangles compare? Original: height-18, slant-30, length-24 Scaled: height-6, slant-10, length-8 A) the scaled triangles perimeter is 3x's larger than the original triangles perimeter. B) the scaled triangles perimeter is 6x's smaller than the original triangles perimeter C) the scaled triangles perimeter is 1/9 the size of the original triangles perimeter D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter
Answer:
D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter
Step-by-step explanation:
Given
Original:
[tex]Height = 18, Slant = 30, Length =24[/tex]
Scaled:
[tex]Height =6, Slant=10, Length=8[/tex]
Looking at the dimension of both triangles, The relationship between the original and the scaled copy is:
[tex]Scaled = \frac{1}{3} * Original[/tex]
Hence, the perimeter is:
[tex]Perimeter (Scaled) = \frac{1}{3} * Perimeter (Original)[/tex]
Write the equation of the line in slope-intercept form
Answer:
y = 4/1 + 0
Step-by-step explanation:
we rise 4 units up and move 1 unit to the right
and the y intercept is 0 because its exactly in the center of x and y axis
Cameron is making trail mix. The ratio of peanuts to raisins to walnuts is 3:2:1. If there are 224 raisins, how many total peanuts and walnuts are there?
Answer:
336 Peanuts
112 Walnuts
Step-by-step explanation:
So first, you can not change the order of the items in a ratio. So the 224 raisins will be in the middle.
It will look like _ : 224 : _
Next, divide 224 by 2 to get the number of walnuts, the number on the right.
So the number on the right will be 112.
Next, multiply 112 by 3 to get 336.
AABC has points located at A(1, 3) B(-2, 2) C(4, 0). AABC is rotated 180° CCW about the origin then translated (x + 0, y-5). Identify the location of A A”B”C"
Answer:
i think the new points are
A(1,-2)
B(-2,-3)
C(4,5)
Step-by-step explanation:
i plugged it in
Patty measured the elementary school and made a scale drawing. The scale she used was 7 centimeters = 1 meter
What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Write the scale of the drawing as a fraction. Put the shorter length in the numerator.
[tex] \frac{7 \: cm}{1 \: cm} \\ [/tex]
First convert the denominator to the same units as the numerator. Write an equivalent fraction with centimeters in the denominator. Since 1 meter is equal to 100 centimeters, multiply the denominator by 100 to get centimeters in the denominator.
[tex] \frac{7 \: cm}{100 \: cm} = \: \frac{7}{100} \\ [/tex]
Write the scale factor as a ratio, using a colon
7/100 → 7:100
The scale factor is 7:100.
[tex] \\ [/tex]
#CarryOnLearning!
36) In the diagram, the coordinates of endpoints A and B are (-3, 9) and (9,5). Find the length from A to E?
Step-by-step explanation:
the length of AB = √(9+3)²+(5-9)²
= √144+16=√180 = 6√5
the length from A to E = ⅜× 6√5
= 2.25 √5 or 5.03
Length of AB,
→ √(9+3)² + (5-9)²
→ √144+16
→ √180
→ 6√5
Length from A to E,
→ ⅜ × 6√5
→ 2.25 √5
→ 5.03
What is the total weight of all the fruit she bought?
Image included
Answer:
1/3 kilograms
Step-by-step explanation:
4+(-7)-(-3) What will be the answer ?
Why does that formula make sense?
Answer:
Step-by-step explanation:
Draw two lines vertically down from side "A" to "B"...you now have three objects ... to triangles, and one rectangle.... the area of the rectangle is "AH"...now you have two triangles, that have area 1/2 base*height... the height is "H" and the base .... well it is (B-A)/2... so the area of the two triangles are ..... (2)*(1/2)*((B-A)/2)* H.... The total area is .... AH + (2)*(1/2)*((B-A)/2)* H .... 2* 1/2 = 1 so now we have AH + ((B-A)/2)* H .... to help see this let us write it as AH + H(B-A)/2 .. expand the right H.... AH + BH/2 - AH/2.......
you end up with : AH - AH/2 + AB/2 ...
AH - AH/2 = AH/2
BH/2 = BH/2
final answer : AH/2 + BH/2
factor out the 1/2 and H ..... 1/2 H (A+B)
Drag the numbers to label the points plotted on the number line.
Answer:
First Box: -10/5
Second Box = -1.25
Third Box = -0.5
Fourth Box = 0.75
Fifth Box = 3/2
Step-by-step explanation:
NOTE: I AM SAYING THIS FROM LEFT TO RIGHT
Answer:
The first box should be -[tex]\frac{10}{5}[/tex] ;
The 2nd box should be -1.25 ;
The 3d box should be -0.5 ;
The 4th box should be 0.75 ;
The 5th box should be 3/2 which is the last box left.