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.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ4
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
Anyone know how to do this? pls explain how
Find the number of real-number solutions of the equation below.
x2+7x−5=0
Answer:
12
Step-by-step explanation:
Answer:
x
=
−
7
−
√
69
2
,
−
7
+
√
69
2
Step-by-step explanation:
x
=
−
7
−
√
69
2
,
−
7
+
√
69
2
6
Estimate each percent.
70% of 103
(1 Point)
Enter your answer
Will make Brainlylist
Answer:72.1
103*.7=72.1
I hope this is good enough:
Brandi earned $140 from a summer job to buy new clothes for school. She found several items she would like to buy, but is trying to decide if she has enough money to buy all the items she likes. She found two pairs of shorts for $25 each and four shirts with an average cost of $19 per shirt. She will have to pay 7.5% sales tax.
PART A: If she buys all of the items, how much sales tax will she have to pay?
The sales tax for Brandi's purchase will be $(insert answer here)
PART B: What is the total cost of her purchase including sales tax?
Brandi will spend $(insert answer here) on her purchases, including sales tax.
Answer: a. $9.45 ; b. $135.45
Step-by-step explanation:
Since two pairs of shorts for $25 each, the total amount she'll pay for the shorts is:
= $25 × 2
= $50
Since the four shirts with an average cost of $19 per shirt. The total amount she'll pay for the shirt is:
= $19 × 4
= $76
A. Her sale tax will be calculated as:
= 7.5% × ($50 + $76)
= 0.075 × $126
= $9.45
B. Her total cost will be:
= Cost of shorts + Cost of shirts + Sales tax
= $50 + $76 + $9.45
= $135.45
Answer:
Part A- 9.45 Part B- 135.45
Step-by-step explanation:
I cant seem to understand this. Please, someone help :)
Answer:
76
Step-by-step explanation:
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.
Which number line shows the graph of -2.75
-3
-2
-1
0
1
2
3
0
1
2.
3
-3 -2
-1
0
1
2 3
-3 -2
0
1
2.
3
Answer:
B.
Step-by-step Explanation:
The correct number line for -2.75 < x in the given options is the second diagram.
What is number line?
A number line is a picture of straight line that represents real numbers. These real numbers include both negative and positive numbers.
For the given expression which -2.75 < x, that is negative 2.75 is less than x or x is greater than negative 2.75.
On the number line, the arrow with unshaded circular bottom must start from -2.75 and point towards the right.
Thus, the correct number line in the given options is the second diagram or option B.
Learn more about number line here: https://brainly.com/question/24644930
please help so I can pass
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
PLS HELP I GIVE BRAINLIEST
For f(x) = 3x2 - 2, find F(x) =
f(x)dx
Answer: below
Step-by-step explanation: Given f(x) =kxn where k is a constant, then f'(x) = nkx(n - 1)
Can you apply this principle to this problem, Let me know if you have any further questions about this problem. Thanks.
Upvote
1
Downvote
Add comment
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
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 :)
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
For the following quadratic equation, find the discriminant.
x^2+ 10x + 44 = 0
Answer:
padlet com /vpena20241
/sv1blyklvnvfbcdw
Step-by-step explanation:
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.
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.
To know more about triangles follow
https://brainly.com/question/7644338
#SPJ5
if any of you guys know someone named shurmpy or molly plz tell me they real good freinds to me
Answer:
ok
Step-by-step explanation:
-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]
What is the slope,m, of the table?
What is the y-intercept,b, of the table?
What is the equation that represents the table?
Answer:
9
Step-by-step explanation:
What is the greatest common factor of 28 and 49
Answer:
7 is the greatest comman factor of 28 and 49
YOOOO 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
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
The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces.
A table titled Weight of Books showing Number of Books, Weight per book in ounces, and Total Weight in ounces. The first row shows Hard Cover, with h, 7, and 7 h. The second row shows Paperback, with 45 minus h, 5, and x. The third row shows Total, with 45, blank, and 249.
Which value could replace x in the table?
40 – h
50 – h
5(45) – h
5(45 – h)
Answer:
The Correct answer is D.) 5(45 – h)
Step-by-step explanation:
x can be replaced by 5(45 - h)
Tap the THANKS button and RATE ⭐️
Answer:
its d
Step-by-step explanation:
just took the quiz
need help finding the slope line through each apartment of points
Answer:
how are yall so smart bc im sittin over here like bruh these guys are smarter than enistain
Step-by-step explanation:
Answer:
8/-11
Step-by-step explanation:
m=y2-y1/x2-x1
16-8=8
9-20=(-11)
8/-11
hope this helps :3
if it did pls mark brainliest
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
This is about Desmos evidence, What does y equal?
Answer:
Uhm i think this is right
Step-by-step explanation:
y=mx+b
y=2
y=2x+2
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 %
Learn more about percentage increase here:
https://brainly.com/question/27992848
#SPJ6