Answer:
A. 5
Step-by-step explanation:
The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.
From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:
(√61)² = (x)² + (x + 1)²
x² + x² + 2x + 1 = 61
2x² + 2x + 1 - 61 = 0
2x² + 2x -60 = 0
Dividing through by 2 gives:
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x-5)(x+6) = 0
x-5 = 0 or x+6 = 0
x = 5 or x = -6
Since the length of a side cannot be negative, x = 5 units
Answer:
The correct answer is A.
Step-by-step explanation:
X=5
Solve the system.
2x + y = 3
−2y = 14 − 6x
Answer:
y= -2 x= 3
y= 3 x= -7
Step-by-step explanation:
2) solve for h: a = 1/2 bh
(area of triangle)
Answer:
h = 2a/b
Step-by-step explanation:
a = 1/2 bh
2*a = 2* 1/2 bh
2a = bh
2a/b = bh/b
2a/b = h
When cut into 16 equal slices, each slice is 1/16 of the pizza. Express how much of the pizza 8 of these slices would be in decimal form.
Answer:
0.5
Step-by-step explanation:
If one part = 1/17
Then, 8 parts = 1/16 x 8 = 1/2
1/2/as a decimal is 0.5
Hope this helps
Which is a stretch of an exponential decay function?
f(x) = Four-fifths (five-fourths) Superscript x
f(x) = Four-fifths (four-fifths) Superscript x
f(x) = Five-fourths (four-fifths) Superscript x
f(x) = Five-fourths (five-fourths) Superscript x
Answer:
C
Step-by-step explanation:
The function [tex]f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}[/tex] represents the stretch of an exponential decay function.
What is exponential decay function?The process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y = a(1-b)^{x}[/tex]
where,
y is the final amount,
a is the original amount,
(1 -b) is the decay factor,
and x is the amount of time that has passed.
For a exponential decay function (1-b) is always less than 1. If (1-b) < 1 it represents the exponential growth function.
And if a < 1, then it represents vertical compression and if a > 1, then it represents vertical stretch.
According to given question.
We have some functions in which we have to find the which one represents the decay function.
According to the function
[tex]f(x) = \frac{4}{5}(\frac{5}{4} )^{x} }[/tex]
For the decay function, the decay factor will always less than 1. In the above function the decay factor [tex]\frac{5}{4}[/tex] i.e. 1.25 is greater than 1.
Therefore, the above function doesn't represent decay function.
[tex]f(x) = \frac{4}{5}( \frac{4}{5} )^{x}[/tex]
Here, a < 1 i.e. [tex]\frac{4}{5}[/tex] is less than 1 so the given function is not a stretch of an exponential decay function.
[tex]f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}[/tex]
Here, b < 1 so it represents the exponential decay function. Also a > 1.
Therefore, the given function is the stretch of an exponential decay function.
[tex]f(x) = \frac{5}{4} (\frac{5}{4}) ^{x}[/tex]
Here, a > 1 but b > 1. Therefore, the above function doesn't represent the exponential decay function. It represents the exponential growth function.
Find out more information about exponential decay function here:
https://brainly.com/question/14355665
#SPJ3
Please help me with my question!!
Answer:
B,C
Step-by-step explanation:
The sum of B is 1
The sum of C is -1/2
Let's try each option.
Option A:
-3 + 5 + (-1) = 2 + (-1) = 1
FALSE
Option B:
5 + (-8) + 4 = -3 + 4 = 1
TRUE
Option C:
-19/2 + 9 = -9.5 + 9 = -0.5
TRUE
Option D:
-17 + 36/2 = -17 + 18 = -1
FALSE
So, the correct answers are B and C
Best of Luck!
share £40 in the ratio 1:4 between Tim and Sam
Answer:
[tex]\£8:\£32[/tex]
Step-by-step explanation:
[tex]\frac{40}{1+4}[/tex]
[tex]\frac{40}{5}[/tex]
[tex]=8[/tex]
[tex]1:4[/tex]
[tex]1 \times 8:4 \times 8[/tex]
[tex]8:32[/tex]
Answer:
Tim gets £8
Sam gets £32
Step-by-step explanation:
Ratio is 1:4
So, Total parts are 1+4 = 5
Dividing it by total parts
= [tex]\frac{40}{5}[/tex]
= £ 8
So, Tim gets £8
But,
Sam gets 4(£8)
= Sam gets £32
£620 is divided between Malachy, Paul & Brian so that Malachy gets twice as much as Paul, and Paul gets three times as much as Brian. How much does Paul get?
Answer:
Step-by-step explanation:
9y + 6 + 2(5 + y) = blank y + blank
Answer:
11y+16Solution,
[tex]9y + 6 + 2(5 + y) \\ = 9y + 6 + 10 + 2y \\ combine \: like \: terms \\ = 9y + 2y + 6 + 10 \\ simplify \\ = 11y + 16[/tex]
hope this helps...
Good luck on your assignment..
Answer:
11y+16
Step-by-step explanation:
9y+6+2(5+y)=
9y+6+10+2y=
Combine like terms
11y+6+10=
11y+16
A rectangle is 6 inches longer than it is wide. Write and simplify an expression for
the perimeter of the rectangle in terms of the width w.
Answer:
L+6=W
Step-by-step explanation:
Answer:
4w + 12
Step-by-step explanation:
w + (w+6) + w + (w+6) = 4w + 12
for perimeter you add all the sided together
w = width
w + 6= length
I hate math bro please help me ill mark u brainliest
16.) The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 adult tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 adult tickets and 5 student tickets. What is the price of the adult and the student ticket?
Answer:
adult tickets are $8 and student tickets are $14
Step-by-step explanation:
to find the price of adult and student tickets, first look at all the given values:
a = adult tickets
s = student tickets
so: 4a + 5s = 102
and : 7a + 5s = 126
since in both equations the number of student tickets are the same, we have to find the difference of value to determine how much adult tickets are:
126-102 = 24
there are 3 more adult tickets in the equation with a total of 126, therefore:
24 / 3 = 8
that means each adult ticket is work 8 dollars.
now substitute this value:
4(8) + 5s = 102
32 + 5s = 102
you can solve this by concluding that 102- 32 is 70
that means 5(s) has to equal 70
so 70 / 5 = s
70/5 = 14
so the value of s = 14 and the value of a = 8
What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)? (1 point) Select one: a. 0 b. 5 c. 10 d. 15
Answer: C. / 10
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given a polynomial divided by a factor (x + h) then the remainder is f(- h)
Given
f(x) = 3[tex]x^{4}[/tex] + 2x³ - x² + 2x - 19 divided by (x + 2)
To find remainder evaluate f(- 2)
f(- 2) = 3[tex](-2)^{4}[/tex] + 2(- 2)³ - (- 2)² + 2(- 2) - 19
= 3(16) + 2(- 8) - 4 - 4 - 19
= 48 - 16 - 4 - 4 - 19
= 5 → B
anyone know the answer ? :(
The smallest x value allowed is x = 0, as shown as the leftmost point on the graph at (0,0).
The largest x value allowed is x = 11 because of the right-most point (11,100).
The domain is the set of any real number between those endpoints. We can pick any fractional or decimal number in this interval since time can be subdivided however you want, so the set of integers isn't enough.
A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.
A. Find the original perimeter and area of the garden
B. Find the perimeter and area of the garden with a 20% increase in each dimension.
C. By what percent will the perimeter increase? By what percent will the area increase?
D. Explain why the area and perimeter will not increase by the same percentage.
Answer:
w=12 ft
l= 20 ft
A.
P= 2(12+20)= 64 ft
A= 12*20= 240 ft²
B.
P=2(12*1.2+20*1.2)= 76.8 ft
A= 12*1.2*20*1.2= 345.6 ft²
C.
(76.8-64)/64*100%= 20%
(345.6- 240)/240*100%= 44%
D.
perimeter increase is linear function of one dimension increase
area increase is function of 2 dimensions increase
what is the middle product of (-2x+1)(-3-5)?
Answer:
7x
Step-by-step explanation:
which best decribes how to slove the equation below 26x=74
Answer fast pleaseee, Solve the following system of equations: y= -5x +1 and y= -x-3
Answer:
x=1 y=-4
Step-by-step explanation:
Answer:
(1, - 4 )
Step-by-step explanation:
Given the 2 equations
y = - 5x + 1 → (1)
y = - x - 3 → (2)
Since both are expressed in terms of y, equate the right sides, that is
- x - 3 = - 5x + 1 ( add 5x to both sides )
4x - 3 = 1 ( add 3 to both sides )
4x = 4 ( divide both sides by 4 )
x = 1
Substitute x = 1 into either of the 2 equations and evaluate for y
Substituting into (2)
y = - 1 - 3 = - 4
Solution is (1, - 4 )
Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, they increases by a common difference of 3.
For each x increase of 1, the y increases by a common factor of 3.
For each x increase of 1, the y increases by 4 more than the previous increase.
For each x increase of 1, they increases by doubling and then adding 1.
Answer:
For each x increase of 1, the y increases by a common factor of 3. (second answer listed)
Step-by-step explanation:
Notice that you have not provided the graph that the problem involves, but from the description of what the y behavior is when x increases by one, one can deduct if an exponential pattern applies.
Out of the four examples given, only one of them represents an exponential growth. Such type of growth has to include a common multiplicative factor (the base of the exponent), since the function has to be of the form:
[tex]f(x)=a\,\,b^x[/tex]
to be called exponential.
So every time that x increases by one unit, the following happens:
[tex]f(x+1)=a\,\,b^{(x+1)}\\f(x+1)= a\,\,b^x\,\,b[/tex]
So notice that the original function ends up being just multiplied by the common factor "b".
The other options don't describe such behavior.
Answer:
For each x increase of 1, the y increases by a common factor of 3.
Step-by-step explanation: hope it helps ^w^
Share £90 in the ratio 1:5
Answer:
the answer is
Step-by-step explanation:
if we take a and b as two pupil to share the money,then a gets
$15 and b gets $75
sum of the ratio is=6
a =1/6×$90
=$15
b=5/6×$90
=$75
Here's the question. Please awnser ASAP
Answer:
the answer is A because the pair of ratios are equivalent.
What is the product (40 + (-10))((36 + (-9))(32 + (-8))...(-32 + 8)(-36 + 9)(-40 + 10) where the first number in each factor is decreasing by 4 and second number in each factor is increasing by 1?
Answer:
0
Step-by-step explanation:
The first number is 40 and decreases by 4 in each factor, and the second number is -10 and increases by 1 in each factor.
The first number is positive and decreases by 10% its value in each factor, and the second number is negative and increases by 10% its absolute value in each factor. That means we will have a factor where both numbers are 0 (in the 11th value, we will have the first number 40 - 4*10 = 0 and the second number -10 + 1*10 = 0), so the factor will be 0 + 0 = 0, and then whole product will be zero.
Can someone pls help me solved this problem plz! I really need help plz someone help me solved it! I need help ASAP!
Answer:
a) 0
b) 4.5
c) 3
d) 6
Step-by-step explanation:
Formula: 3x + 4y = 12
The questions contains the values of x. So here's an example of:
d) x = -4, y = ?
Using the formula: 3(-4) + 4y = 12
-12 + 4y = 12
4y = 24
y = 6
Do the same for the others!
find the length of each side of a square field whose area is 608 sq.m
Answer:
a=24.65 sq.m
Step-by-step explanation:
A=[tex]a^{2} or l^{2}[/tex]
608=[tex]a^{2}[/tex]
[tex]a=\sqrt{608}[/tex]
[tex]a=24.65[/tex]
To check your answer
[tex]A=a^{2} \\A=24.65^{2}\\A=24.65*24.65\\A=607.6225=608[/tex]
factorise: 2x + 6y 2x-4 t + 2t squared
The volume of a cube depends on the length of its sides. This can be written
in function notation as ws). What is the best interpretation of v(4) = 64?
Answer:
46=-76.333(6×7)-÷45%€7*÷00.0001×6÷45+2
Segment AC bisects angle BAD if the measure of angle BAC is 20 degrees what’s is the measure of angle BAD
Answer:
40°
Step-by-step explanation:
An angle bisector divides an angle into 2 equal angles. 20° x 2 = 40°.
The right trapezoid below has been decomposed into a rectangle and a right triangle.Find it's area two ways: By summing the areas of the rectangle and triangle.
Answer:
103.5 m²
Step-by-step explanation:
To find the area of a right trapezoid, you can decompose it into a rectangle and a triangle. The sum of the area of the rectangle and the triangle gives the area of the trapezoid.
For the right trapezoid attached below, the area can be gotten by:
Area of rectangle = length × breadth = 9 × 8 = 72 m²
Area of triangle = 1/2(base × height) = 0.5 × 7 × 9 = 31.5 m²
Area of trapezoid = Area of rectangle + Area of triangle = 72 m² + 31.5 m² = 103.5 m²
Which similarity postulate or theorem can be used to verified that the two triangles shown below are similar? PLEASE HELP ASAPP
Answer:
Correct option: A -> AA postulate
Step-by-step explanation:
In the figure we can see that in triangle ABC we have:
A = 53°
B = 72°
And we can see in the triangle LMN that:
L = 53°
M = 72°
We have two pairs of angles (A - L and B - M) that are congruent, and therefore we can use the case AA (angle-angle) to affirm that these triangles are similar.
So the correct option is A: AA postulate.
Sam read 20 pages, which is 2/3 of the book. How many pages are there in the book?
Answer:
30pages
Step-by-step explanation:
20 is 2/3 so 10 is 1/3 so 3/3 is one book
Answer:
30 pages
Step-by-step explanation:
Monty has a total of $290 in ten dollar and five dollar bills. This can be represented by the function 10x + 5y = 290. Interpret the x- and y-intercepts.
Answer:
The x-intercept indicates that he has 29 ten dollar bills
and no five dollar bills. The y-intercept indicates that he has 58 five
dollar bills and no ten dollar bills.
Step-by-step explanation:
