Three exterior angles of a pentagon measures 60,80and 90.Find the measure of other two exterior angle, assuming them equally Thanks!
Given:
The three exterior angles of a pentagon measures 60,80 and 90.
To find:
The measure of other two exterior angle, assuming them equally.
Solution:
Let x be the measure of two other exterior angles of the pentagon.
We know that the sum of all exterior angles of a pentagon is 360 degrees.
[tex]60^\circ+80^\circ+90^\circ+x+x=360^\circ[/tex]
[tex]230^\circ+2x=360^\circ[/tex]
[tex]2x=360^\circ-230^\circ[/tex]
[tex]2x=130^\circ[/tex]
Divide both sides by 2.
[tex]\dfrac{2x}{2}=\dfrac{130^\circ}{2}[/tex]
[tex]x=65^\circ[/tex]
Therefore, the measures of both exterior angles are 65 degrees.
Describe the steps required to determine the equation of a quadratic function given its zeros and a point.
Answer:
Procedure:
1) Form a system of 3 linear equations based on the two zeroes and a point.
2) Solve the resulting system by analytical methods.
3) Substitute all coefficients.
Step-by-step explanation:
A quadratic function is a polynomial of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
A value of [tex]x[/tex] is a zero of the quadratic function if and only if [tex]y = 0[/tex]. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: [tex]A(x,y) = (r_{1}, 0)[/tex], [tex]B(x,y) = (r_{2},0)[/tex] and [tex]C(x,y) = (x,y)[/tex]
Based on such information, we form the following system of linear equations:
[tex]a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0[/tex] (2)
[tex]a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0[/tex] (3)
[tex]a\cdot x^{2} + b\cdot x + c = y[/tex] (4)
There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:
[tex]a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
And finally we obtain the equation of the quadratic function given two zeroes and a point.
Ali sold some cakes at a cake sale.
The cakes are chocolate, lemon or vanilla flavoured.
The cakes are either large or small.
complete the two way table
Answer:
vanilla small= 14
lemon large= 25
Step-by-step explanation:
total= 120
120÷3= 40
each of flavoured cake have 40
lemon= 40 - 26= 14
vanilla= 40- 15= 25
In a triangle ABC, a=4 cm, b=3 cm and angleC=30°, find the area of triangle ABC.
a. 6
b. 1.5
c. 3
d. 3 root 3
How do I complete the table?
Answer:
From left to right, fill in 3.5 and 6.5
Step-by-step explanation:
Use the given formula to calculate y for the given values of x.
When x = 0.5, y = 3(0.5) + 1/0.5
y = 1.5 + 2
y = 3.5 if x = 0.5
When x = 2, y = 3(2) + 1/2
y = 6 + 0.5
y = 6.5 if x = 2
Help me with these 3 and explain too thank you :))
Answer:
1) 25
2) 2
3) f(g(1)) = 42
Step-by-step explanation:
1) Given that f(x) = 4x^2 + 9
If x = -2
f(-2) = 4(-2)^2 + 9
f(-2) = 4(4) + 9
f(-2) = 16 + 9
f(-2) = 25
2) Given that f(x) = 4x - 6
y = 4x - 6
Replace y with x
x = 4y - 6
MAke y the subject of the forfmula
4y = x+ 6
y = (x+6)/4
SInce x = 2
f^(-1)(2) = (2+6)/4
f^(-1)(2) = 8/4 = 2
3) If f(x) = 6x and g(x) = x+6
f(g(x)) = f(x+6)
f(x+6) = 6(x+6)
Since x = 1
f(g(1)) = 6(1+6)
f(g(1)) = 6(7)
f(g(1)) = 42
A garden store pays $85 for a planter. The percent of markup is 35%. What is the selling price of the planter
Answer:
Step-by-step explanation:
To get the selling price.
Selling price=100÷ 100-x × 85
Where x is the markup.
Sp= 100 ÷ 100-35× 85
Sp= 100÷ 65×85
Sp= $130.7692
Sam has 24 ball he gives 1/3 to Rita. How many ball did he give to Rita?
Answer:
8
Step-by-step explanation:
Find 1/3 of 24, which is 8.
Answer:
Sam gave 8 balls to Rita.
Step-by-step explanation:
24 / 3 = 8
1/3 of 24 is 8, therefore Sam gave 8 balls to Rita.
−3x−8y=−8 y=2−x Is (0,1)(0,1)left parenthesis, 0, comma, 1, right parenthesis a solution of the system?
Answer:
(0,1) is not the solution to the equation
Step-by-step explanation:
Given:
−3x − 8y = −8 (1)
y = 2 − x (2)
Substitute (2) into (1)
−3x − 8y = −8 (1)
- 3x - 8(2 - x) = -8
- 3x - 16 + 8x = -8
- 3x + 8x = -8 + 16
5x = 8
x = 8/5
Substitute x = 8/5 into (2)
y = 2 − x (2)
= 2 - 8/5
= (10-8) / 5
= 2/5
y = 2/5
Solution to the equation:
(x, y) = (8/5, 2/5)
Therefore,
(0,1) is not the solution to the equation
the first 4 questions
Answer:
(3)(4)(4)(2)Step-by-step explanation:
1.
7 > 0.7 > 0.07 > 0.007
2.
5h - 15hg
taking 5h common
5h (1 - 3g)
3.
5(2x- 1) = 35
dividing both sides by 5
2x - 1 = 7
2x = 7 + 1
2x = 8
x = 4
4.
if x is an odd number x + 2 will also be odd.
for example
11 is an odd number
on adding 2 we get 13 which is also an odd number.
Which step shows the result of applying the subtraction property of equality?
(12x+8)+4-3
Answer:
Value of expression = -3 / 4
Step-by-step explanation:
Given:
(12x + 8) + 4 = 3
Find:
Value of expression
Computation:
Given expression
(12x + 8) + 4 = 3
Step 1: Use Distributive property
12x + 8 + 4 = 3.
Step 2: By adding like terms.
12x + 12 = 3
Step 3: Transfer
12x = 3 - 12
Step 4: Subtract
12x = -9
Step 4: Divide both sides by 12
12x / 12 = -9 / 12
x = -3 / 4
Value of expression = -3 / 4
Drag numbers to the table so it shows a proportional relationship between x and y.
Answer:
7.5 30
45 180
Step-by-step explanation:
The given line has x = 1.25 and y = 5.
y/x = 5/1.25 = 4
x is multiplied by 4 to get y since 1.25 * 4 = 5.
That means the equation is
y = 4x
For a proportional function, every value of x must be multiplied by 4 to get y.
x = 7.5
y = 4x = 4(7.5) = 30
7.5 30
We need to find the values for the last line.
11 * 4 = 44
There is no 44
13.75 * 4 = 55
There is no 55.
17.5 * 4 = 70
There is no 70
30 * 4 = 120
There is no 120.
45 * 4 = 180
There is a 180.
45 180
Answer:
7.5 30
45 180
___ +(-9)=-12 need help please
Answer:
_-3__ + (-9) = -12
Step-by-step explanation:
___ + (-9) = -12
-9 is being added to the blank. You want the blank alone (isolated) on the left side. The opposite operation to adding a -9 is to add a positive 9.
You must do the same operation to both sides of an equation.
Add 9 to both sides.
___ + (-9) + 9 = -12 + 9
___ + 0 = -3
___ = -3
Answer: -3
Answer:
-3
Step-by-step explanation:
Hi there!
___ + (-9) = -12
Adding a negative number is the same as subtracting
___ - 9 = -12
To isolate the blank, we can add 9 to both sides of the equal sign so there won't be a -9 on the left side
___ - 9 + 9 = -12 + 9
___ = -12 + 9
___ = -3
Therefore, the number is -3.
I hope this helps!
eeeeeeee please help!
Answer:
1) Less than
2) greater than
Step-by-step explanation:
Equation of the first line:
(y+7)/(-13+7) = x/-1
(y+7))/-6 = -x
y+7 = 6x
y= 6x - 7
Equation of the second line:
A (4/3,0) ; B (0,8)
y/8 = (x-4/3)/-4/3
y/8 = (x-4/3) * -3/4
y/8 = -3/4x + 1
y = -6x + 8
Anelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Answer:
3x + 5 = 23
Step-by-step explanation:
Let x represents the number of persons in her group.
Since she brings 3 markers for each person, then number of markers brought for persons in her group = 3x.
She brings 5 extra markers for each person to share.
Thus, total markers she brought is now;
3x + 5
She brought 23 markers in all.
Thus, equation that represents the information is;
3x + 5 = 23
I NEED ANSWERS ASAP(WORTH 20 POINTS) WILL MARK BRAINLIEST
The graph of f(x) = |x| is transformed to g(x) = |x+1|-7. On which interval is the function decreasing?
A. (negative infinity, -7)
B. (negative infinity, -1)
C. (Negative infinity, 1)
D. (Negative infinity, 7)
Answer:
B. (negative infinity, -1)
Given a line segment that contains the points A,B, & C in order,if AB = 5x + 4, BC = 4x - 8, and AC = 23, find the length of segment AB.
Select one:
a. 23
b. 9
c. 19
d. 3
Answer:
C
Step-by-step explanation:
AB + BC = AC , that is
5x + 4 + 4x - 8 = 23
9x - 4 = 23 ( add 4 to both sides )
9x = 27 ( divide both sides by 9 )
x = 3
Then
AB = 5x + 4 = 5(3) + 4 = 15 + 4 = 19 → C
divide 3 divided by 2/5
Answer:
[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]
which of the following equations describes the line
check all that apply (1,9) (-2, 3) A. y - 1 = 2(X-9) B. Y- 2 = 2(x-3) c. y - 3 = 2(x + 2) D. Y-3 = 2(x - 2) E. y + 2 = 2(x-3) F. - 9 = 2(x - 1)
The equation of the line that connects the two points (1,9) and (-2,3) is,
y = 2x+7
or, y-3=2x+4
or, y-3=2(x+2)
So, option c, is the correct option
Answered by GAUTHMATH
if A×B ={(-1,1),(-1,2),(2,1),(2,2),(3,1),(3,2)}. find A×A and B×B. i need for exam.
Answer:
hope this will help you more
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you
stay safe healthy and happy
Tom goes to the book fair where paperback books are $3 and hardback books are $5.50. Travis
buys three paperback and four hardback books. How much change will Travis receive from a $50
bill
1.Equation/Expression:
2. Solve:
Answer:
1: 50 - (3(3) + 5.5(4))=x
2: okay so we know how much books are brought and how much each cost.
In this case paper backs are 3 dollars each and cost 3 dollars each. So 3 (3) is 9 dollars. The next scenario are hardbacks which are 5.50 each and Tom brought 4 of them. So that makes it 5.5(4) which is 22 dollars. So the total would be 9+22 which is 31 dollars. The question asks for change from a 50 dollar bill which you subtract and 50-31=19
The change would be 19 dollars
Find the length of x
Answer:
x = 3
Step-by-step explanation:
Hi there!
1) Prove similarity
The two triangles are similar due to angle-angle similarity. They both have an angle measured 90 degrees and the angles of the two corners that touch are equal, because opposite angles are equal.
2) Solve for x
Now, we can set up a proportion to solve for x:
[tex]\frac{x}{4} =\frac{4.5}{6} \\x=\frac{4.5}{6} *4\\x=3[/tex]
Therefore, x is 3 units long.
I hope this helps!
The solution of the system of equations has coordinates where x is between 2 and 3 and y is between 2 and 3. What is a reasonable approximation for each value to the tenths place? x Almost-equals 2.2, y Almost-equals 2.1 x Almost-equals 2.2, y Almost-equals 2.4 x Almost-equals 2.7, y Almost-equals 2.3 x Almost-equals 2.7, y Almost-equals 2.6
x Almost-equals 2.2, y Almost-equals 2.4
Answer:
Its B
Step-by-step explanation:
correct on edge
Find a linear function f, given f(6) = - 4 and f(-3) = - 10. Then find f(0).
f(x)=0
(Type an expression using x as the variable. Simplify your answer.)
f(0) = (Simplify your answer.)
PLZ HELP
Answer:
[tex]y = \frac{2}{3} x - 8[/tex]
f(0)=-8
Step-by-step explanation:
Slope=rise/run=(-4-(-10))/(6-(-3))=6/9=2/3=m
y=m*x+q
-4=(2/3)*(6)+q
q=-8
f(0)=(2/3)*(0)-8=-8
Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than Lana. When the four sisters' ages are added together, the result is $45$. If the youngest sister is $n$ years old, what is $n$?
Find the value of y in 4y + 2x = 8 and 2x + 5y = 14.
8
- 6
6
-8
Please help SUMMER SCHOOL
Question
(what are the slope and the y-intercept of the line shown in the graph)
Antônia tem um caneca com a capacidade de 2/3Lde água. Que fração dessa caneca ela encherá com 1/2L de água?
Answer:
The fraction of cup filled with water is 3/4.
Step-by-step explanation:
Antonia has a mug with a capacity of 2/3L of water. What fraction of that mug will she fill with 1/2L of water?
Capacity = 2/3 L
Amount of water = 1/2 L
Fraction of amount of water to the capacity of mug is
[tex]\frac{1}{2}\div \frac{2}{3}\\\\\frac{3}{4}[/tex]
Complete the function for this graph.
Answer:
y = –|x - 1| + 3
Step-by-step explanation:
The "vertex" is (1 , 3)
y = –|x - 1| + 3
What is the pH of a solution with a 1.50 × 10−9 M hydroxide ion concentration? (4 points) 0.176 5.18 8.82 9.20
Answer:
5.18
Step-by-step explanation:
This is a chemistry question. However the solution to the problem is given below:
We'll begin by calculating the pOH of the solution. This can be obtained as follow:
Concentration of Hydroxide ion [OH¯] = 1.5×10¯⁹ M
pOH =?
pOH = –Log [OH¯]
pOH = –Log 1.5×10¯⁹
pOH = 8.82
Finally, we shall determine the pH of the solution. This can be obtained as follow;
pOH = 8.82
pH =?
pH + pOH = 14
pH + 8.82 = 14
Collect like terms
pH = 14 – 8.82
pH = 5.18
Therefore, the pH of the solution is 5.18
Answer:
5.18
Step-by-step explanation:
I took the test and got it right!
