Answer: [tex]\frac{12}{19}[/tex]
The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. The solution to the algebraic equation here are 6 and -4.
An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.
The algebraic equation becomes =
[tex]\frac{36}{x+3}-20 = 4x\\[/tex]
We simplify the equation to find the value of x.
[tex]=\frac{36}{x+3}+20 = 4x\\\\= \frac{36}{x+3} = 4x -20\\\\= \frac{36}{x+3} = 4(x-5)\\\\=36 = 4(x-5)(x+3)\\\\=9 = (x-5)(x+3)\\\\=x^2-5x+3x -15 = 9\\\\= x^2-2x-24=0\\\\=x^2-6x+4x-24=0\\\\=x(x-6)+4(x-6) =0\\\\=(x+4)(x-6) =0\\\\x = -4,6[/tex]
Learn more about algebraic equation here
https://brainly.com/question/29131718
#SPJ2
The sum of two numbers is 30 and their difference is 10. What are the two numbers?
Answer:
20 and 10
These are the only two possible numbers who match those descriptions.
what is the probability of tossing a coin three times and getting tails each time?
Answer:
1/8
Step-by-step explanation:
This is a compund probability problem. You need to find the probability of each event and then multiply the probabilities together.
The probability of flipping tails is 1/2. We need three of these.
1/2 x 1/2 x 1/2 = 1/8
A sequence can be generated by using a,n = a,n (-1) + 2, where a,1 = 6 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
A.) 6, 12, 24, 48, 96
B.) 2, 8, 14, 20, 26
C.) 2, 12, 72, 432, 2592
D.) 6, 8, 10, 12, 14
2x(5x-2)+(3x-0.5)*2=2x+3+10x-5+2x+3
Find X
(give step by step)
Answer:
x = 1.348331477 and 0.148331477
Step-by-step explanation:
TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac.x=2×10−(−12)±(−12)2−4×10(−2)Square −12.x=2×10−(−12)±144−4×10(−2)Multiply −4 times 10.x=2×10−(−12)±144−40(−2)Multiply −40 times −2.x=2×10−(−12)±144+80Add 144 to 80.x=2×10−(−12)±224Take the square root of 224.x=2×10−(−12)±414The opposite of −12 is 12.x=2×1012±414Multiply 2 times 10.x=2012±414Now solve the equation x=2012±414 when ± is plus. Add 12 to 414.x=20414+12Divide 12+414 by 20.x=514+3Now solve the equation x=2012±414 when ± is minus. Subtract 414from 12.x=2012−414Divide 12−414 by 20.x=53−14The equation is now solved.
x=514+3x=53−14
p.7 Central Angles and Inscribed Angles
#4 What is the measure, in degrees, of arc JKI ?
4) JKI
80°
K
mJKI =
degrees
Helppp me
Answer:
280°
Step-by-step explanation:
There are 360° in a circle. you are given an arc that is 80°.
To find the arc JKI, subtract 80 from 360.
360 - 80 = 280°
Solve for the unknown angle measure θ.
A. θ=112.5
B. θ=120
C. θ=144
D. θ=150
In the given polygon-
>>Two of the angles are of 90⁰
The sum of all angle in n-sided polygon is given by -
[tex]\green{ \underline { \boxed{ \sf{(n-2)\times180}}}}[/tex]
Here number of sides,n = 8
So ,the sum of all angle = [tex]\sf (8-2)\times 180[/tex]
[tex]\sf \implies 6 \times 180[/tex]
[tex]\sf \implies 1080 \degree[/tex]
>>Since two of the angles are of 90⁰ ,let's subtract them from total angle sum to get angles in term of [tex]\theta[/tex] only.
[tex]\implies \sf 1080- 2\times 90[/tex]
[tex]\implies \sf 1080- 180[/tex]
[tex]\implies \sf 900 \degree [/tex]
Now, Sum of remaining 6 angles = 6[tex]\theta[/tex]
Also, 6[tex]\theta[/tex] = 900⁰
[tex]\theta = \dfrac{900}{6}[/tex]
[tex]\theta = 150 \degree[/tex]
Answer:
heya ^^
let's first see what the question says -
so , we're given an octagon and the figure states that two of the angles of the octagon are of measure 90°.
while , rest of the angles have been named [tex] \bold{\theta }[/tex] and this thing clears that all the other angles are of equal measure.
now , angle sum property of octagon states that the sum of all the angles of an octagon equals 1080.
therefore ,
[tex]\bold{90 \degree + 90 \degree + \theta+ \theta+ \theta+ \theta+ \theta+ \theta = 1080 \degree }\\ \\ 180\degree + 6\theta = 1080\degree \\ \\ 6\theta = 1080\degree - 180\degree \\ \\ 6\theta = 900\degree \\ \\ \theta = \frac{900}{6} \\ \\ \underline\bold\pink{\: \theta = 150\degree}[/tex]
therefore ,
option ( D ) θ=150 is correct.
hope helpful :D
Label the missing angle on this window.
Answer:
C
Step-by-step explanation:
Since the angles in a triangle add to 180 degrees, the third angle is 180-70-45=65 degrees
Find the distance between the points.?
Help 40 points!!!
Answer:
34
Step-by-step explanation:
Distance - formula
Answer:
34
Step-by-step explanation:
best to use the formula: √(X1-X2)²+(Y1-Y2)²
(If u want to know why, it's determinated by pithagoras' theory.)
=>√(30-0)²+(16-0)²=√900+256=√1156=34
Transform the solid black function to match the dotted function.
y= Voc
I f(x+
fx- +
O
+
o
у
LO
9
00
8
N
6
5
4
3
2
1
1
-18 9 8
-6 54
-3
2
1
N
-1
-
3
4
in
X
5
7
8
9 to
N
3
3
4
5
in
-6
-8
9
9
-10
Transforming the solid line to the dotted line would change the equation of the functions
The equation of the dotted line is: [tex]f(x) = -\sqrt{x - 6} + 3[/tex]
How to transform the function?The equation of the solid line is given as:
y = √x
The solid line undergoes the following transformation to match the dotted line
Reflection across the x-axisTranslate 6 units rightTranslate 3 units upThe rule of the above sequence of transformations is:
(x,y) -> (x - 6, -y + 3)
Using the above transformation rule, the equation of the dotted line is:
[tex]f(x) = -\sqrt{x - 6} + 3[/tex]
Read more about function transformation at:
https://brainly.com/question/17586310
Perform the following
mathematical operation, and
report the answer to the
correct number of significant
figures.
45.2 x 0.035 =
Answer:
4
Step-by-step explanation:
45.2 x 0.035=1.582
"Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit." -Khan Academy. org > significant figures
Answer: 1.6 is the answer
Step-by-step explanation:
45.2 x 0.035 = 1.582
After you do that step Then you'll need to round 1.582 up in the tenths, and it should be 1.6!
Hope this helps
The swiss mathematician leonhard euler and the french mathematician rene descartes both discovered a pattern in the numbers of edges, vertices, and faces of polyhedrons. solve problems 810.
Answer:
I am stuck on this two
Step-by-step explanation:
rectangle, 6 8 14 12
What does the value 40 in the equation y=7.5+40 represent in the context of this situation?
Answer:
40 is an addend in an addition
40 is the y-intercept if the question really is y = 7.5x + 40.
Step-by-step explanation:
40 is just a number in a sum of 2 numbers.
Perhaps you meant
y = 7.5x + 40
If that is the case, then 40 is the y-intercept.
A figure was flipped over the y-axis and then
enlarged three times the original size. Which
transformations were use
a.) reflection over y-axis b.) translation
C.) dilation
d. rotation
Answer:
Below.
Step-by-step explanation:
a) reflection over y-axis.
b) dilation.
solve for the variables x and y
Answer:
Step-by-step explanation:
What's the area for ABC?
Answer:
14
Step-by-step explanation:
7(length) times 4(height) equals 28
28/2= 14
Five 1/4-2 5/7 needed by 3:30
PLEASE ANSWER - BRAINLIEST IF 2 ANSWERS - 5 STAR RATING - THANKS (PROFILE TOO)
Each month, Alex’s cellphone plan costs
$15, plus $0.10 per minute of use.
Which graph could represent Alex’s total
monthly cost?
Answer:
Graph-d
Step-by-step explanation:
We are given that,Each month, Alex’s cellphone plan costs $15 and additional 0.10 per minute of use. The equation that would represent Alex's total monthly costs would be linear equation (equation of a line). Linear equation has the following form:
[tex]y = mx + b[/tex]
in this case,
m represents the cost of Alex's per minute of useb represents the initial costs of Alex's cellphone planm represents the number of minutesy represents the amount of total monthly costSince Alex’s cellphone plan initially costs $15, b would be 15 . Again he has to pay an additional cost of $0.10 per minute of use. hence, m would be 0.10 or ⅒ . Therefore our equation of line is
⇒[tex]y=\dfrac{1}{10}x+15[/tex]In conclusion
Graph d represents Alex’s total monthly cost
The original price of a computer is $579. which coupon is a better deal?
Save 25% on any computer is the better deal. Then the correct option is A.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A) Save 25% on any computer. Then the better deal will be
→ 579 × 0.25 = $ 144.75
B) Save $150 on any computer. Then the better deal will be
→ $ 150
C) Save $75 plus 5% off on any computer. Then the better deal will be
→ 579 × 0.05 + 75 = $ 103.95
D) Save $50 plus 10% off on any computer. Then the better deal will be
→ 579 × 0.10 + 50 = $ 107.9
More about the percentage link is given below.
https://brainly.com/question/8011401
If K is the midpoint of ER, EK = z+5,and ER=4x+2,What is the length of K R?
Answer:
KR = 9
Step-by-step explanation:
If K is the midpoint of ER, then EK = KR and ER = 2(EK).
Given:
ER = 4x + 2EK = x + 5ER = 2(EK)
⇒ 4x + 2 = 2(x + 5)
⇒ 4x + 2 = 2x + 10
⇒ 2x + 2 = 10
⇒ 2x = 8
⇒ x = 4
As EK = KR and EK = x + 5 and x = 4:
⇒ KR = 4 + 5
⇒ KR = 9
KR:-
x+54+5933 markers cost $5.79
Which equation would help determine the cost of 13 markers
Answer:
3/$5.79 = 13/x
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable x. Divide $5.79 by three to get the cost of one marker, $1.93. Then multiply the cost of one marker by 13 on the left. This will get the total value which is $25.09.
how to compare 10.5 to 11 and 19
Answer:
Line up the decimal points. **Answer is Least to greatest: 10.5 , 11, 19**
Step-by-step explanation:
You need to line each number up.
10.5
11.0
19.0
The reason why 11 and 19 have a decimal point and zero at the end is because you need to do that in order to compare the numbers.
This problem is also a little common sense because 10.5 is the smallest, 19 is the largest while 11 is in the middle.
Times New Roman has tiny lines at the tips of letters, creating an appearance of old-style writing with a fountain pen. Those tiny lines are called _____.
The volume of the right circular cylinder is 144 pi cubic yards. of h, the height of the cylinder is 4 yards, what is r, the radius of the base?
A solid box with height 60cm, width 10cm and length 10cm needs to be painted.
The paint costs £0.17 per cm2.
How much will it cost to paint the outside of the box?
Answer:
£442
Step-by-step explanation:
see vid on how to calculate cm² of a box here
Answer:
17cm²
Step-by-step explanation:
area of box =l×w
10cm×10cm=100cm²
0.17×100cm²=17cm²
any help would be appreciated.
Answer:
10.4
Step-by-step explanation:
cosine rule=[tex]a^{2}=b^{2} +c^{2} -2bc*cosa[/tex]
[tex](2\sqrt{3}) ^{2}=(x+2)^{2} +x^{2} -2(x+2)x*cos60\\12=x^{2} +4x+4+x^{2} -2x^{2} -4x*\frac{1}{2}\\2x-8=0\\x=4\\Area=\frac{1}{2}absinc\\ = \frac{1}{2}*6*4*sin60\\\\ =6\sqrt{3}\\=10.4(3 sig.fig)[/tex]
What is the slope ( it has a slope of -2) (it has a slope of -1) (it has a slope of 2)
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 ) = (0, 0 ) and (x₂, y₂ ) = ( - 1, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2
Answer:
[tex]slope = -2[/tex]
Step-by-step explanation:
Step 1: Determine two points
We need to take two points off of the equation that is used in thsi graph and we can see that we have (0, 0) and (-1, 2)
Step 2: Determine the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - 0}{-1 - 0}[/tex]
[tex]m = \frac{2}{-1}[/tex]
[tex]m = -2[/tex]
Answer: [tex]slope = -2[/tex]
The science club is selling homemade cookies to raise money for a field trip. The club members know that 12 dozen cookies
uses 3 pounds of flour. Use that information solve each part below. Homework Help
a. How much flour is needed for 18 dozen cookies?
b. How many cookies can be made with 10 pounds of flour?
The flour needed for 18 dozen cookies is 4.5 pounds.
The number of cookies that can be made with 10 pounds of flour is 40 cookies.
How much flour is needed?The first step is to determine the flour needed for 1 dozen cookies.
Flour needed = 3/12
Flour neeeded for 18 dozens = 3/12 x 18 = 4.5 pounds
How much cookies can be made?
The first step is to determine the number of cookies that can be made with one pound of flour:
12/3 = 4
Number of cookies that can be made iwth 10 pounds of flour = 4 x 10= 40 cookies
To learn more about multiplication, please check: https://brainly.com/question/13814687
Which is the equation of a line that has a slope of -5 and a y-intercept of -3? Show me how you arrived at your answer.
a) 2y = -5x - 3
b) -2y = 10x - 6
c) -2y = 10x + 6
d) 2y = 10x - 6
Answer:
c) -2y = 10x + 6
Step-by-step explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]
The variables stand for:
[tex]y:$ y-coordinate of any point on the line\\$x:$ x-coordinate of any point on the lien\\$m: $ Slope of the line\\$b: $ y-intercept of the line; where the line meets the y-axis[/tex]
Plugging in the given information into the equation:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
Go through the answer choices:
a) 2y = -5x - 3
Divide both sides of the equation by 2
[tex]y=-\frac{5}{2}x-\frac{3}{2}\rightarrow\text{Incorrect!}[/tex]
b) -2y = 10x - 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x-\frac{6}{-2}\\y=-5x-(-3)\\y=-5x+3\rightarrow\text{Incorrect!}[/tex]
c) -2y = 10x + 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x+\frac{6}{-2}\\y=-5x+(-3)\\y=-5x-3\rightarrow\text{Correct!}[/tex]
d) 2y = 10x - 6
Divide both sides of the equation by 2
[tex]y=\frac{10}{2}x-\frac{6}{2}\\y=5x-3\rightarrow\text{Incorrect!}[/tex]
Therefore the answer is c) -2y = 10x + 6
Additional Comments:
We can only divide both sides of the equation by 2 and/or -2 because of the Division Property of Equality. This property states that if we divide one side of the equation by a certain quantity, we must divide the other side by the same quantity so that the equation remains equal.
Solve by factorisation
2x²+3x-20=0
Answer:
x=5/2 x=-4
Step-by-step explanation:
2x^2+3x-20 = (2x-5)*(x+4)
2x-5 = 0 x=5/2
x+4 = 0 x=-4
Answer: X= -4
Step-by-step explanation:
Find the measure of each exterior angle of the polygon.