unit 1 test algebra 2
6) The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.
7) The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.
8) The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).
9) There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.
We have,
6)
x² + 8x - 15 = 5x + 13
Rearranging the equation:
x² + 8x - 5x - 15 - 13 = 0
x² + 3x - 28 = 0
Now, factorize the quadratic equation:
(x + 7)(x - 4) = 0
Setting each factor equal to zero:
x + 7 = 0 or x - 4 = 0
Solving for x:
x = -7 or x = 4
7)
2x (x - 5) (x + 7) = 0
Setting each factor equal to zero:
2x = 0 or x - 5 = 0 or x + 7 = 0
Solving for x:
x = 0 or x = 5 or x = -7
8)
(x + 5) (x + 8 + 2x - 3)
Simplifying the expression inside the parentheses:
(x + 5) (3x + 5)
9)
x³ - 5x² + 2x + 13 = 5
Substitute each integer value from 0 to 10 into the equation and count the number of solutions.
Substituting each integer value,
x = 0,
x³ - 5x² + 2x + 13 = 5
0 - 0 + 0 + 13 = 5
13 = 5
Not true.
Similarly,
x = 2,
x³ - 5x² + 2x + 13 = 5
8 - 20 + 4 + 13 = 5
25 - 20 = 5
5 = 5
True.
x = 4,
x³ - 5x² + 2x + 13 = 5
64 - 80 + 8 + 13 = 5
85 - 80 = 5
5 = 5
True.
There are two integer solutions:
x = 2 and x = 4.
Therefore,
The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.
The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.
The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).
There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.
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PLS HELP I GIVE BRAINLIEST
uh so yeah, I don't really know how to do this but if anyone could help it would be greatly appreciated
giving max points
Answer:
Step-by-step explanat it won’t let me download the PFDPLZZ give me brainless I’ll still help you put the questions in the comment section
Find the equation of the line passing through the points (5,21) and (-5,-29)
-2 1/2 divided by 3 1/2 ?
Step-by-step explanation:
[tex] - 2 \times \frac{1}{2} \div 3 \times \frac{1}{2 } \\ - \frac{5}{2} \div \frac{7}{2} \\ - \frac{5}{2} \times \frac{2}{7} \\ = - \frac{5}{7} [/tex]
please help so I can pass
2) A television regularly costs $180, but it is on sale for 40% off. There is a
5% sales tax on the sale price. How much does the television cost after
the discount and sales tax?
A. $75.60
B. $103.00
C. $113.40
D. $145.00
Answer:
$113.40Step-by-step explanation:
180 x 0.6 = 108
108 x 0.05 = $5.40
108 + 5.4 = $113.40
The ticket sales for a concert started at 4:00P.M. The table shows
the linear relationship between the number of tickets remaining
and the number of hours since 4:00 P.M.
Ticket Sales
Hours Since
4P.M.
1
2
Number of
Tickets Remaining
12,000
9,000
6,000
3,000
0
3
4
5
Which function can be used to find y, the number of tickets
remaining x hours since 4:00 P.M.?
A y = 3,000x + 12,000
B y = 3,000x + 15,000
C y = -3,000x + 12,000
D y-3,000x + 15,000
AnswerA
Step-by-step explanation:I’m not sure
For the following quadratic equation, find the discriminant.
x^2+ 10x + 44 = 0
Answer:
padlet com /vpena20241
/sv1blyklvnvfbcdw
Step-by-step explanation:
What is the answer to 3-(-8)
Answer:
11
Step-by-step explanation:
3 - (-8) = 3 + 8 = 11
Answer: 11
Step-by-step explanation:
This is because when you subtract a negative number from a positive you get a positive (here's a lil trick if you have 2 minuses In a row they become a plus sign) so the answer is 11
Find the least common denominator of the following pair of fractions:
1/2 4/5. ASAP
a. 7 b. 20 c. 30 d. 10
Answer:
10
Step-by-step explanation:
1/2 4/5 turn into
5/10 8/10
since 10 is the denominator 2*5 =10 so take the 5 and times by the numerator or 1 to make the 5
5*2 is 10 so take 2 times the numerator (4) to make 8
PLS HELP
solve the system of equation using elimination:
3x+y=-2
5x-y=-10
Answer:
(-3/2, 5/2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
3x + y = -2
5x - y = -10
Step 2: Solve for x
Eliminate y
Add 2 equations together: 8x = -12Divide 8 on both sides: x = -12/8Simplify fraction: x = -3/2Step 3: Solve for y
Define original equation: 3x + y = -2Substitute in x: 3(-3/2) + y = -2Multiply: -9/2 + y = -2Add 9/2 on both sides: y = 5/2YOOOO HELP ME ASAP DUDED BY MIDNIGHT BRO
How do you find the value of x please help me( Look at the picture provived)
Answer:
x=5
Step-by-step explanation:
We know that a pentagon is in total 540 degrees. From this, we add all other numbers and set them equal to 540 to solve for x.
So, after adding all the angles and setting them equal to 540, we get this.
21x+435=540
21x=105
x= 5
If you want, plug 5 into x and see if it adds up to 540 to check
21(5)+435=540
An education budget went from $800,000 to $900,000. What is the approximate percent increase? The approximate percent increase is 13%. The approximate percent increase is 89%. The approximate percent increase is 98%. The approximate percent increase is 113%.
Answer:
The answer is 13%
Step-by-step explanation:
The approximate percent increase is 13%.
What is Percentage Increase?Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude, intensity, or value. If the percentage increase is a negative value, then we can say that there is a percentage decrease of the same magnitude.
Percentage Increase FormulaFollowing the concept of percentage increase, the percentage increase formula is derived and expressed as: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. It should be noted that since the percentage has to be a positive quantity, we take the absolute value of the initial value. If the percentage increase is a negative value, then it is a percentage decrease. The percentage increase is the relative change in the quantity with respect to its initial value. If the percentage change is positive, then it is the percentage increase and if the percentage change is negative, it is a percentage decrease.
Given:
initial =$900,000
Final = $900,000
% increase = $900,000- $800,000/ $800,000 * 100
% increase = 100, 000/8000
% increase = 12.5 %
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Please help will mark brainliest
Answer:
The answer is C i had it on my exam on edge
Step-by-step explanation:
Answer:
ffesfsEFesfSEfESfESfeSESEF
Step-by-step explanation:
fsefesfessfsEfaesgeaergae
The indoor climbing gym is a popular field trip destination. This year the senior class at High
School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 14 vans and 5 buses with 329 students. High School B rented and filled 11 vans and 5 buses with 281 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answer:
Step-by-step explanation:
14 x + 5y = 329
11x + 5y = 281(vans is x and busses are y)
cancel out 'y' by making the '5y' in 11x + 5y = 281 negative
-1 (11x + 5y = 281) =
-11x -5y = -281
insert second equation
-11x -5y = -281
14x + 5y = 320
3x = 48
x = 16
substitute vans in one equation
11(16) + 5y = 281
5y = 105
y = 21
Burke Middle School has an $80 budget to stock the concession stand with drinks at the spring play. Each drink costs the school 75¢, but the store will discount the full order by $100. How many drinks can the school buy for the concession stand?
Drew wrote an inequality to solve the problem.
Answer:
240 ;)
Step-by-step explanation:
Between which two consecutive integers does V185 lie?
A
12 and 13
B.
13 and 14
C
14 and 15
D.
15 and 16
Answer: B
Step-by-step explanation: desmos
Julio pald 1.2 times his normal hourly rate for each hour he works over 30 hours a week Last week he worked 43 hours and earned $574.56
Answer:
482.70
Step-by-step explanation:
First, find out how much he earned per hour last week. 576.56 divided by 43 is 13.41.
Second, multiply his hourly earnings by 1.2, 1.2*13.41=16.09 So he earns 16.09 per hour
Lastly, multiply 16.09 by 30, 16.09*30=482.7 So he earns about $482.70 each week.
An assembly was held for the 7th graders. When first entering the gym 5 out of 8 of the 7th grade boys had on hoodies. If 320 boys attend the assembly , what is a reasonable amount of them that will be wearing hoodies?
140
200
180
160
The graph shows a proportional relationship between the number of miles and the number of hours Marco bikes.
What equation relates the distance, y, and the time, x? Enter your answer in the box
Please, this is urgent!
Answer:
15
Step-by-step explanation:
Its pretty simple
The equation that relates the distance (y) and the time (x) is → y = 15x.
What is the general equation of a Straight line?The general equation of a straight line is -
y = mx + c
where -
m is slope of line
c is the y - intercept
Given is a graph that shows a proportional relationship between the number of miles and the number of hours Marco bikes.
First we will find the slope of the straight line. Take two set of coordinates from the graph. We will take → (1, 15) and (2, 30).
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m =(30 - 15)(2 - 1)
m = 15
The line passes through the origin so its y - intercept (c) will be zero. So, we can write the equation as → y = 15x.
Therefore, the equation that relates the distance (y) and the time (x) is → y = 15x.
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42 + (3 x 6 - 7
PEMDAS
Answer:
53
Step-by-step explanation:
Do what is in the parentheses first and then outside. Multiply 3 by 6 then subtract 7. Add 11 to 42 and you get 53.
Answer: 53
Step-by-step explanation:
i will give the crown
Answer:
24
Step-by-step explanation:
BAM!
To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds?
400 milligrams
480 milligrams
550 milligrams
600 milligrams
Answer:
138/92*320 = 480 milligrams. ... If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who ... If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds. 2.
Step-by-step explanation:
I hope I help :)
Leila pumped 6 gallons of water out of her pool each minute for 24 minutes what was the total change in the amount of water in her pool answer in gallons
Answer:
The answer is 144.
Step-by-step explanation:
The question said 6 gallons of water comes out every minute. So, if you multiply 6x24 you get the answer of 144.
HELP PLS BRAINLIEST FOR CORRECT ANSWER
Answer:
83
Step-by-step explanation:
Answer:
x = 59
y = 83
Step-by-step explanation:
First, you need to solve for y in order to solve for x. Using the Triangle Sum Theorem, you will find that y is 83 degrees.
Now, using the Vertical Angles Theorem, you can figure out the third angle of the triangle in which x is, 83.
Using the Triangle Sum Theorem again, you will find that x is 59.
If Mis a centroid of triangle WOR and WM = 16, what is WX?
8
24
10
32
Answer:
WX = 24
Step-by-step explanation:
Centroid of a triangle divides the medians of the triangle in the ratio 2 : 1
Therefore,
WM/ MX = 2/1
16/MX = 2/1
2MX = 16
MX = 16/2
MX = 8
WX = WM + MX
WX = 16 + 8
WX = 24
The value of the side WX is equal to 24. The correct option is B.
What is the centroid of the triangle?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together.
A line connecting a side's midpoint and the triangle's opposite vertex is called the median. Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The centroid of a triangle divides the medians of the triangle in the ratio of 2: 1.
Here, the ratio of the two sides will be given as:-
WM/ MX = 2/1
Calculate the value of MX to get the value of WX.
16/MX = 2/1
2MX = 16
MX = 16/2
MX = 8
The value of WX will be:-
WX = WM + MX
WX = 16 + 8
WX = 24
Therefore, the value of the side WX is equal to 24.
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On a coordinate grid, where is the center of this circle?
x² + y² = 2
A)
(-1, -1)
B)
(0,0)
(1.1)
D)
(2, 2)
Answer:
Option B) (0,0) is the correct answer.
Step-by-step explanation:
Given equation of circle is:
[tex]x^2+y^2 = 2[/tex]
The general form of equation of circle with center at (h,k) and radius r is given by:
[tex](x-h)^2+(y-k)^2 = r^2[/tex]
The given equation of circle can also be written as:
[tex](x-0)^2+(y-0)^2 = 2[/tex]
Comparing it with the general form of equation, we get
h = 0 , k = 0
So the center is (0,0)
Hence,
Option B) (0,0) is the correct answer.
Determine whether each graph represents a function. Select Yes or No for each graph.
Yes No
Graphl
Graph II
Graph lll
Answer:
Graph 1 yes
Graph 2 yes
Graph 3 no
Step-by-step explanation:
Graph 1 is a linear function
Graph 2 is a reciprocal function
Graph 3 is not a function
In the third figure for a single input, there is two output thus it will not function thus, l Yes, II Yes, and III No.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
A relation will be a function if for every single x there must be a single y.
As per the given graphs,
In the first and second graphs, for every x value the y has a single value thus it will be a function.
In the third graph, for x there are two y for example at x = -6,(y = 1.4 and y = -6.4 approx) thus it will not be a function.
Hence "In the third figure for a single input, there is two output thus it will not function thus, l Yes, II Yes, and III No".
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5) Use any 2 of these integers: -1, -2, -5, -3, and +4.
a) Which 2 integers make the mathematically smallest number when multiplied together?
(for example, the answer - 8 is smaller than +2)?
b) Which 2 integers make the greatest sum (when they are added together)?
Answer:
a) -5 and 4 make the mathematically smallest number when multiplied together
b) 4 and -5 make the greatest sum
Step-by-step explanation:
-5 x 4 = -20
-3 x 4 = -12
-2 x 4 = -8
-1 x 4 = -4
-1 + -5 = -6
-2 + -5 = -7
-3 + -5 = -8
4 + -5 = -1