[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=sides\\[-0.5em] \hrulefill\\ s=2 \end{cases}\implies h=\cfrac{2\sqrt{3}}{2}\implies h=\sqrt{3}\implies h\approx 1.7[/tex]
Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the
right. Each pair on the right will be used once.
(x-9)(3x + 4) = 0
(x-4) (9x + 1) = 0
(x+9)(3x-4)= 0
(x+4)(9x-1)=0
x = -4 or x =
x = -9 or x =
x = 9 or x = -
x = 4 or x=-1
Each correct pair using Principle of Zero Products are-
Part a: (x-9)(3x + 4) = 0: x = 9 or x = -4/3
Part b: (x-4) (9x + 1) = 0: x = 4 or x= -1/9
Part c: (x+9)(3x-4)= 0: x = -9 or x = 4/3
Part d: (x+4)(9x-1)=0; x = -4 or x = 1/9
Explain the term zeros of the equation?The values of x that fulfill the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case.The degree of a equation f(x) = 0 determines how many zeros a polynomial has.For the stated equation-
Part a: (x-9)(3x + 4) = 0
Equating each term to zero;
(x-9) = 0
x = -9
And, (3x + 4) = 0
x = -4/3
Option: x = 9 or x = -4/3
Part b: (x-4) (9x + 1) = 0
Equating each term to zero;
(x-4) = 0
x = 4
And, (9x + 1) = 0
x = -1/9
Option; x = 4 or x= -1/9
Part c: (x+9)(3x-4)= 0
Equating each term to zero;
(x+9) = 0
x = -9
And, (3x-4) = 0
x = 4/3
Option: x = -9 or x = 4/3
Part d: (x+4)(9x-1)=0
Equating each term to zero;
(x+4) = 0
x = -4
(9x-1)
x = 1/9
Option: x = -4 or x = 1/9
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The complete question is-
Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the
right.
Each pair on the right will be used once.
(x-9)(3x + 4) = 0
(x-4) (9x + 1) = 0
(x+9)(3x-4)= 0
(x+4)(9x-1)=0
x = -4 or x = 1/9
x = -9 or x = 4/3
x = 9 or x = -4/3
x = 4 or x= -1/9
Solve for X.
(Please I need help on this problem.)
Answer:
sum of angles in a triangle is 180
it is an equilateral triangle so each angle gets 60 degrees.
6x +6 is 60
6x is 60 - 6
6x is 54
divide both sides by 2
6x/6 is 54/2
x is 9
Simplify the expression: -3(2x+4)-8x
Answer:
- 14x - 12
Step-by-step explanation:
- 3(2x + 4) - 8x ← distribute terms in parenthesis by - 3
= - 6x - 12 - 8x ← collect like terms
= - 14x - 12
Answer:
-14x-12
Step-by-step explanation:
1) Expand by distributing terms.
-(6x+12)-8x
2) Remove parentheses.
-6x-12-8x
3) Collect like terms.
(-6x-8x)-12
4 Simplify.
−14x−12
√(2) rational or irrational
Answer:
√2 is irrational.
Step-by-step explanation:
√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1). Thus, p and q have a common factor 2. This statement contradicts that 'p' and 'q' have no common factors (except 1). We can say that √2 is not a rational number.
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can some help me understand this?
Function A is represented by the equation y=2 x+5
Function B is a linear function that goes through the points shown in the table.
Which statement correctly compares the rates of change of the two functions?
Answer:
The rate of change is the same for both A and B (2)
Step-by-step explanation:
In the equation, the rate of change is shown as the coefficient of the variable x. That is the number before the x which is 2.
In the table you find the rate of change as the change in y over the change in x. In the table the y's are increasing by 4 (3- -1), 2 (5-3) and 4 (9-5). The x's are increasing by 2 (3-1), 1 (4-3) and 2 (6-4).
If I take the change in y over the change in x, I will get 4/2 = 2, 2/1 = 2 or 4/2 = 2
From the table the rate of change is also 2.
The woods behind Wendy’s house were 8 miles wide and have an area of 24 mi.² what is the length of the woods 
Answer:
48 miles
Step-by-step explanation:
i think thats it.
Answer: 4.
Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.
Hope this helps!
A recipe calls for 2 cups of flour for every 1/4 cup of raisins. If 1 1/2 cups of raisins were used, how many cups of flour would be added?
The quantity of the cups of flour that would be added would be = 12 cups.
What is flour?Flour is the product of wheat grains that is commonly used for baking of dough and it measured with measuring cups or weighting scales.
According to the recipe from the given question above;
2 cups of flour = 1/4 of raisin
X cups of flour = 1½ of raisin
Make X cups of flour the subject of formula:
X cups = 2×1½ /¼
X cups = 3/¼
X cups = 3×4 = 12 cups.
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The sum of two numbers is always greater than the larger of the two numbers?
False
Step-by-step explanation:The sum is the total of an addition problem.
Addition of Positive Numbers
Most commonly, people add together positive numbers. Positive numbers are numbers greater than 0. The sum of 2 positive numbers is always greater than the addends. For example:
2 + 3 = 5The sum of these positive numbers, 5, is greater than the larger number, 3. However, the addition of positive numbers is not the only way to add.
Addition of Negative Numbers
Negative numbers are numbers less than 0. If you add negative numbers, then the sum will be less than the addends. So, the statement above is not true. For example:
-2 + 3 = 1In this case, the sum, 1, is less than the larger number, 3. This disproves the statement given.
there were 7,000 raffle tickets sold at the school carnival. Each ticket cost $0.25. How much money did the school raise by selling raffle tickets
Answer: $1750
Step-by-step explanation:
7000x$0.25 = $1750
The line x - y = 5 passes through
O (0,5)
O (-5, 0)
O (0,-5)
Answer:
(0,-5)
Step-by-step explanation:
PLEASE HELP !!!!! David is standing 500 feet away from the base of a cell phone tower. the angle of elevation from his eyes to the top of the tower is 78°. if David’s eyes are 6 feet above the ground how tall is the tower (EXPLAIN PLEASE)
The height of the tower is 2358 feets.
How to find the height of the tower?David is standing 500 feet away from the base of a cell phone tower.
The angle of elevation from his eyes to the top of the tower is 78°. David eyes are 6 feet above the ground . The height of the tower can be found as follows:
This situation forms a right angle triangle. Therefore,
using trigonometric ratios,
tan 78° = opposite / adjacent
tan 78° = x / 500
cross multiply
x = 500 tan 78°
x = 500 × 4.70463010948
x = 2352.31505474
Therefore,
height of the tower = 2352 + 6
height of the tower = 2358 ft.
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Given m || n, find the value of x.
Answer:
x = 11
Step-by-step explanation:
Since it's given n || m, we can write the following equation to find the value of x:
9x - 3 = 7x + 19 because these two are alternate exterior angles and have equal angle measurement.
transfer like terms to the same side of the equation9x - 7x = 19 + 3
add/subtract terms2x = 22
Divide both sides by 2x = 11
You’re planning to visit with 7 clients today and you estimate that at most each client will require 3/4 hours of your time. At most, how long does your estimate say it will take you to visit with all of these clients?
Mathematically, it will take you 315 minutes (5 hours, 15 minutes) at most to visit with all 7 clients.
How is the time determined?We can employ mathematical operations, including addition, subtraction, division, and multiplication to determine the total time required to visit the seven clients.
Since we know that a client requires 3/4 hours or 45 minutes of your visiting time, we can multiply 45 minutes by 7.
The product of the multiplication operation gives 315 minutes, which we can convert into hours and minutes by a division operation.
The number of clients visiting today = 7
The time it a client requires of your visit time = 3/4 hours
3/4 hours = 45 minutes (0.75 x 60)
For the 7 clients, it will take you 315 minutes (45 x 7)
315 minutes equal 5 hours and 15 minutes.
Thus, using basic mathematical operations, we can conclude that, at most, you require 5 hours and 15 minutes to attend to all seven clients today.
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Simplify.
(-√7) (-√7)
O A. √7
B. -7
OC.
C. 7
о
O
D. 49
E. -49
K
x + 2 = - 19..............
Answer: -21
Step-by-step explanation:
[tex]x+2=-19\\\\What\ value\ of\ x\ will\ make\ the\ left\ side\ equal\ to\ -19?\\\\Well,\ if\ we\ subtract\ 2\ from\ both\ sides,\ we\ get\ our\ answer...\\\\x+2-2=-19-2\\\\The\ 2\ and-2\ on\ the\ left\ cancel\ out\ leaving\ us\ with\\\\\boxed{x=-21}[/tex]
We can check our work by plugging back in -21 for x and getting -19 = -19
HELP ME OUUTT THANKS
Answer:
3/4n = 5/8
Step-by-step explanation:
your…. welcome……
I don’t trust meself so I might be wrong
The diagram shows the graphs of y=x²-3x - 2 and
y = x + 3.
Use the diagram to solve the equation x² – 3x − 2 = x + 3
=
graphically.
Y
11+
10
9
8-
7-
6543
6-
5-
4-
2-
1
-8-7-6-5-4-3-2-1, 1-2-3/4-5_6_7_8
23456
-2-
-3-
-4-
-5-
-6-
-7-
-8-
-9-
--10-
-11+
x
The solution of the expression is,
⇒ x = - 1 and x = 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Solve the expression,
x² – 3x − 2 = x + 3
Now, We can simplify as;
x² – 3x − 2 = x + 3
x² – 3x − 2 - x - 3 = 0
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x (x - 5) + 1(x - 5) = 0
(x + 1) (x - 5) = 0
x = - 1
x = 5
Thus, The solution of the expression is,
⇒ x = - 1 and x = 5
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Find the greatest common factor of 10b³ and 4b.
Solution:
2b would be the greatest common factor (GCF) between both 10b^3 and 4b.
Hope this helps!
Given the table below, write a linear equation that defines the
dependent variable, c, in terms of the independent variable, a.
No need for steps only answer someone help please brainliest
Answer:
c = -(7/5)a + 15
Step-by-step explanation:
c= (8-15)/(4-0)×a+15
c= -(7/5)a + 15
The product of 8 and b, taken from 10
Step-by-step explanation:
10-8b
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The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answer:172 cm²
when we put this in the pentagon formula, and it will get 172.03, and we round it and will be 172
formula of pentagon is 1/2 × p × a
drew checks his pulse while exercising. he counts 25 beats in 10 seconds. at this rate how many times will his heart beat in one minute?
Answer:
Step-by-step explanation:
There are 60 Seconds in a Minute.
60/10 = 6
25 x 6 = 150 beats in one minute
Answer: 150
The graph shows the speed of a car while it is
slowing down to a stop.
a) Using an appropriate triangle with two of its
vertices on the curve, estimate the distance
travelled by the car during this time.
b) Is your answer an underestimate or an
overestimate?
6. A chemist needs to create 100mL of 38% acid solution. On hand she has a 20% acid solution and
a 50% acid solution. How many mL of each solution should she use?
Answer:
Step-by-step explanation:
:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer
A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
What is percentage?The percentage is the ratio of number expressed as a fraction of 100.
Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.
A total of 100mL solution is to be created.
x+y=100
x=100-y
The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).
0.2x+0.5y=0.38(100)
0.2x+0.5y=38
Substitute x=100-y into the obtained equation.
0.2(100-y)+0.5y=38
20-0.2y+0.5y=38
20+0.3y=38
0.3y=18
y=18/0.3
y=60
Substitute y=60 into x=100-y.
x=100-60
=40
So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
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The population of a town has been decreasing since 1991. The population of the town was 26,700 people in the year 1995. In the year 2003, the population of the town had decreased to 20,300 people.
i. Find the linear function P=m- t+b that models the town's population P as a function of the number of years, t, since 1991
ii. Find a reasonable domain for the function P
Domain:
iii. Find a reasonable range for the function P
Range:
iv. Interpret the slope of the function P
The population is Select an answer at a rate of
v. In what year will the population of the town be 14,700?
Year:
Answer:
i. P = -800t + 29900
ii. as an inequality: 0≤t≤37.375; interval notation: [0,37.375]
iii. as an inequality: 0≥P≥29900; interval notation: [0,29900]
iv. the population decreases at a rate of 1600 people every 3 years
v. 2010
Step-by-step explanation:
i. a) use the points *(4,26700) and **(12,20300) to find the slope (m)
*: the year 1995(4 years after 1991) and the population that year
**: the year 2003(12 years after 1991) and the population that year
m = (20300-26700)/(12-4) = -6400/8 = -800
b) use one of the points and m in (a) to find b
26700 = -800(4) + b
26700 = -3200 + b
29900 = b
ii. starting value for domain will be 0 since 1991 is year 0. Find the ending domain value by using P=0 and solving the equation for t:
0 = -800t + 29900
800t = 29900
t = 37.375
iii. population starts at a high of 29900 people and can't go lower than 0 people.
iv. the slope is given in (population change) / (number of years)
v. make P=14700 and solve the equation for t
14700 = -800t + 29900
800t = 15200
t = 19 (19 years after 1991)
Find the value of x.
The 7x side is half the length of the 28 side.
7x = 14
x = 2
What is 3x +(-1) = -10 + 2x PLS HELP!!!
Answer:
x= -9
brainliest plssAnswer:
[tex]\boxed{\boxed{\tt x=-9}}[/tex]
Step-by-step explanation:
[tex]\tt 3x+\left(-1\right)=-10+2x[/tex]
[tex]\tt 3x-1=-10+2x[/tex]
Subtract 2x from both sides:-
[tex]\tt 3x-1-2x=-10[/tex]
Combine 3x and -2x to get x:-
[tex]\tt x-1=-10[/tex]
Add 1 to both sides:-
[tex]\tt x=-10+1[/tex]
Add -10 and 1 to get -9:-
[tex]\tt x=-9[/tex]
____________________
Hope this helps you!
Have a great day!
A $300 suit is marked down by 20%. Find the sales price to the nearest dollar.
Fill in the blanks
markdown = _% x $_
markdown = $_
$_ - $_
sale price = $_
markdown = 20% x $300
markdown = $60
$300 - $60
sale price = $240
2,239 ÷ 7
Division compatible numbers
Answer:the answer is 319.857 and round to 320
Step-by-step explanation: