Answer:
Correct options are A and B.
Step-by-step explanation:
From the given graph it is clear that the given points lie on a parabola because they in U-shape.
We need to find the ranges of x-values such that there must be a root of the graph.
The point (-3,2) lies above the x-axis but point (-2,-2) lies below the axis. It means when these points are connected by a curve then the curve intersects the x-axis
So, one root of the graph lies in the range -3 to -2.
Similarly, point (1,-1) lies below the x-axis but point (2,3) lies above the axis. It means when these points are connected by a curve then the curve intersects the x-axis
So, one root of the graph lies in the range 1 to 2.
Therefore, the correct options are A and B.
Find the sum of the three expressions and choose the correct answer. -8a 3 b + 3a2 b 2 - 5 2 + 5a 2 b 2 3a 3 b + 7 - 9a 2 b 2
Answer:
-9ab3a3b-52
Step-by-step explanation:
-8a3b+3a2b2-52+5a2b3a3b+7-9a2b2
-8a3b-6a-52+5a2b3a3b
-14a3b-52+5a2b3a3b
-9ab3a3b-52
Determine the measure of ∠C. answers: 1) 56° 2) 49.5° 3) 77.5° 4) 63.5°
Answer:
2) 49.5°
Step-by-step explanation:
From the above diagram, we are asked to calculate the measure of ∠C.
The formula to be used for this calculation is given as:
∠C = 1/2 (Far Arc - Near Arc)
∠BAD = 127° = Far Arc
∠EAF = 28° = Near Arc
The measure of ∠C = 1/2 (BAD - EAF)
= 1/2 ( 127° - 28°)
= 1/2 × 99°
measure of ∠C = 49.5°
Answer:
49.5
Step-by-step explanation:I took the test
There are books in a library, there are 4 different kinds of books. Science books make up 3/4 of art books. Comic books are 1/4 of the total books. History books are 1/5 of the total books. History books are 80 fewer than art books. How many books are in total?
Answer:
The total number of books is 1020.
Step-by-step explanation:
Denote the books by their first letter.
From the provided information:
[tex]S=\frac{3}{4}A[/tex] [tex]C=\frac{1}{4}T[/tex] [tex]H=\frac{1}{5}T[/tex] [tex]H = A-80[/tex]Compute the expression of T as follows:
[tex]H = A-80\\\\\frac{1}{5}T=A-80\\\\T=5A-400...(i)[/tex]
Compute the value of C in terms of A:
[tex]C=\frac{1}{4}T\\\\C=\frac{1}{4}\times {5A-400}\\\\C=\frac{5}{4}A-100...(ii)[/tex]
Compute the value of A as follows:
Use expressions (i) and (ii):
[tex]T=S+C+H+A\\\\5A-400=\frac{3}{4}A+\frac{5}{4}A-100+A-80+A\\\\5A-400=4A-180\\\\A=220[/tex]
Compute the value of T as follows:
[tex]T=5A-80\\\\T=(5\times 220)-80\\\\T=1100-80\\\\T=1020[/tex]
Thus, the total number of books is 1020.
Triangle ABC is an isosceles triangle in which side AB = AC. What is the perimeter of triangle ABC? 5 + StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 10 StartRoot 10 EndRoot units 50 units
Answer:
Option (2)
Step-by-step explanation:
This question is incomplete; find the picture attached which makes this question complete.
Vertices of the given triangle are A(-2, -4), B(2, -1) and C(3, -4).
Length of AB = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
AB = [tex]\sqrt{(2+2)^2+(-1+4)^2}[/tex]
= [tex]\sqrt{16+9}[/tex]
= 5 units
Since AB = AC
AC = 5 units
Similarly, BC = [tex]\sqrt{(3-2)^2+(-4+1)^2}[/tex]
BC = [tex]\sqrt{10}[/tex] units
Therefore, perimeter of the given triangle = AB + AC + BC
= 5 + 5 + √10
= (10 + √10) units
Option (2) will be the answer.
Answer:
b
Step-by-step explanation:
Find the equivalent expression for 7-3(2x+5)
-6x-8
4(2x+5)
7-6x+5
7-3(7x)
Answer:
-6x -8
Step-by-step explanation:
7-3(2x+5)
Distribute
7 - 6x -15
Combine like terms
-6x +7-15
-6x -8
Answer:
[tex]\boxed{\sf \ \ \ -6x - 8 \ \ \ }[/tex]
Step-by-step explanation:
Hello
7 - 3(2x+5) = 7 -3*2x -3*5 = 7 - 6x - 15 = -6x - 8
hope this helps
do not hesitate if you have any question
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned $220 in interest. How much money was invested at 3%? $2,000 $3,000 $4,000
Answer:
money invested at 3% is $4000
Step-by-step explanation:
let the money invested in 3% account be x
then money invested in 5% account = 6000 - x
we know interest = p*r*t/100
p is the principle amount invested
here t = 1 year
interest on 3% money
interest= x*3*1/100 = 3x/100
interest on 5% money
interest= (6000-x)*5*1/100
Total interest earned on both the account
3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100
given that total interest earned = $220
thus
( 30000-2x)/100 = 220
=> 30000-2x = 220*100= 22,000
=> -2x = 22,000- 30,000
=> x = -8000/-2 = 4000
Thus, money invested at 3% = x = $4000
Answer:)
$4000
Step-by-step explanation:
The first four terms of a sequence are: 1/6 4/7 9/8 16/9
Find the nth term of this sequence.
Answer:
n^2/(n + 5)
Step-by-step explanation:
The numerators are 1^2, 2^2, 3^2, 4^2, etc.
The denominators are 6, 7, 8, 9, etc.
The nth numerator is n^2.
The nth denominator is n + 5.
Answer: n^2/(n + 5)
PLease heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp urgently
Answer:
12n4t6 + n6wd - 762 + h20 - y1/4z20 - s3/5c4su + v2. 4t
3. 6 + n
4. 6w
5. d - 7
6. 62 + h
7. 20 - y
8. z/4
9. 20 - s
10. 3/5
11. 4s
12. u + v
Step-by-step explanation:**essentially in all these problems you have to determine the operation that fits each scenario and identify the constant vs. the unknown value. The unknown value is represented by a variable (a, x, y, z, t, d, etc.) and the constant is the given number.**
2. if you buy four packs of pencil with an unknown but same amount in each pack, then you have 4t. 4 TIMES the unknown amount equals the total.
3. you start with 6, your constant and then you ADD the number of pens your friend gave, but you don't know so you replace with the stated variable, n. 6 + n is the answer.
4. Each bag has six apples but you don't know how many bags you bought so if we replace this with the variable w. 6w (the constant always comes before the variable even though w6 = 6w) For example if you bought 2 bags, 6 x 2 = 12, a total of 12 apples.
5. you start with chocolates, but we don't know the number. you eat seven of them, that means from the total number we are "missing" seven. therefore d - 7 accurately describes the scenario.
6. the constant is 62, and we are increasing by something, but we don't know what it is: 62 + h
7. we start with 20 balloons, then we lose an unknown number: 20 - y. We have to SUBTRACT from the total because we "lost".
8. we have an unknown number of fish in an aquarium but we are sure that 1/4 OF that number make up the angelfish population. The word "of" means multiply in mathematical terms so z • 1/4 OR z/4.
9. we have 20 marbles total. out of that number an unknown but represented value are red, "s". the rest are blue. So we will imaginarily take out all the red marbles. This action is SUBTRACTING "s" from 20 and we have only ___ amount of blue marbles left. Therefore the answer is 20 - s.
10. 2/5 OF the class are boys. The remainder are girls. What is 5/5 - 2/5? 3/5. This is the TRICK QUESTION!!
11. A car has 4 wheels each therefore 4 TIMES the total number of cars is the right equation. 4s.
12. If you start with an unknown amount of toys, "u", and you get an unknown amount more, "v", you are adding to your collection therefore the answer is u + v.
Hope these explanations help! There really isn't much more to the concept.
True or false. Intersecting chords form a pair of congruent, vertical angles.
Answer:
True
Step-by-step explanation:
A chord of a circle is a straight line segment whose endpoints both lie on the circle.
Vertical Angles are the angles opposite each other when two lines cross.
Any intersecting segments (chords or not) form a pair of congruent, vertical angles.
PLEASE HELP!!
Which of the following statements is true for the figures shown?
B
O A A ABC has been dilated using O as the center,
B. A ABC has been reflected using C as the center.
c. A ABC has been dilated using C as the center.
OD. A ABC has been reflected using as the center.
if a watch is losing 1.5 minutes for every 12 hours that go by, how many minutes will it lose in one week?
Hey there! :)
Answer:
21 minutes.
Step-by-step explanation:
Begin by calculating the number of 12 hour periods in a week.
Each day contains two 12 hour periods. (24 hours/12 = 2)
There are 7 days in a week, therefore:
2 × 7 = 14 times the watch will lose minutes.
Multiply to find the total number of minutes lost:
14 × 1.5 = 21 minutes.
Answer:
21 minutes
Step-by-step explanation:
There are 24 hours in one day, and 7 days per week. Thus there are
(24)(7), or 168, hours in one week, or 14 - 12-hour periods.
Thus, we multiply 14 - 12-hr periods to answer this question:
1.5 minutes / 14 - 12-hour periods)= 21 minutes will be lost in one week.
write the equation of a line that is perpendicular to x=3 and that passes through the point (0 -4) will mark brainliest asap!!!
Answer:
y = -4
Step-by-step explanation:
x = 3 is a vertical line.
The perpendicular line passes through (0, -4) (x, y)
y = -4
The line is perpendicular, so the line should be also horizontal.
Answer:
y = -4
Step-by-step explanation:
The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).
Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.
What is the length of AC?
3 ft
4 ft
9 ft
18 ft
Help with this question(will gove brainlist and thanks)(determine area)
Answer:
The area of a triangle is base * height / 2. In this case that is:
3 * (2x - 4) / 2 = 3 * 2(x - 2) / 2 = 3 * (x - 2) = 3x - 6 in²
Answer:
3x-6 inches^2
Step-by-step explanation:
[tex]A =\frac{ (a \times b)}{2} \\A =\frac{(3(2x-4))}{2} \\A = \frac{(6x -12)}{2} \\\\Area = (3x-6)^2 inches[/tex]
Arman, Babken, and Cecilia decided to compete in a 100m run. When Arman crossed the finish line, Babken was 10m behind him. When Babken crossed the finish line, Cecilia was 10m behind him. How far was Cecilia behind Arman when he crossed the finish line? P.S. The answer is not 20.
Answer:
The answer is 19
Step-by-step explanation:
I am not good at explainig at all and im not sure how to explain but I had this question
Cecilia is 19 m behind the Arman.
Arman, Babken, and Cecilia decided to compete in a 100m run.
When Arman crossed the finish line, Babken was 10m behind him.
When Babken crossed the finish line, Cecilia was 10m behind him.
percentage is the ratio of composition of matter to the overall composition of matter multiplied by 100.
Here,
When Babken is 10m behind the Arman, distance covered by babken is 90 m. Cecilia is 10 m behind when Babken cross the finish line implies Cecilia cover 90% of Babken covered distance.
So Cecilia covers 90% of Babken covered distance when Arman crossed finish line.
As arman crossed finish line Cecilia is at = 90% of run covered by babken,
= 90 * 90/100
= 81
Now, Cecilia behind Arman when he crossed the finish line = 100-81
=19
Thus, Cecilia is 19 m behind the Arman.
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Question 18 (5 points)
Identify the independent and dependent variables in the following situation: The
temperature of the water decreases as a diver descends to the bottom of a lake.
The independent variable is the temperature of the water, and the dependent
variable is the depth below the surface of the lake.
The independent variable is the depth below the surface of the lake, and the
dependent variable is the temperature of the water.
The independent variable is the speed at which the diver descends, and the
dependent variable is the temperature of the water.
The independent variable is the type of boat, and the dependent variable is the
temperature of the water.
Answer:
The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water
Step-by-step explanation:
Tempeture = depth x
How many 5-digit numbers can be formed using only odd digits?
Answer:
5^5
Step-by-step explanation:
#6 I need help with that.
Answer:
Answer is x= 15
Step-by-step explanation:
(3x+18)+(8x-3)=180
11x+15=180
11x=165
x=15
Answer:
x=15 degrees
Step-by-step explanation:
The given triangle is isosceles, so both base angles are both (3x+18).
We also know that angles on a line add up to 180 degrees, so
(3x+18) + (8x-3) = 180 degrees
Simplify
11x + 15 = 180 degrees
11x = 180-15 = 165
Divide by coefficient on left-hand side
x = 165/11 = 15 degrees.
Which letter comes next? F H K N Z ? Choose from: L M T Y
Answer:
t
Step-by-step explanation:
The letter that comes next in the given sequence is K.
The given sequence is F H K N Z.
We need to find which letter comes next in the given sequence.
What is the pattern followed in the given sequence?The pattern followed by the given sequence is they are letters of sounding board consonants.
Therefore, the letter that comes next in the given sequence is K.
To learn more about the sequence visit:
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What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5)?
y=34x−92
y=34x+72
y=34x−74
y=34x+174
Answer:
y = 3/4x + 17/4
Step-by-step explanation:
Step 1: Find slope m
m = (5 - 2)/(1 + 3)
m = 3/4
y = 3/4x + b
Step 2: Find b
5 = 3/4(1) + b
5 = 3/4 + b
b = 17/4
Step 3: Rewrite equation
y = 3/4x + 17/4
Answer:
y = 3/4x + 17/9
Step-by-step explanation:
Find the slope:
5 - 2/ 1 - (- 3)
3/ 1 + 4
3/4
Find the y-intercept:
2 = 3/4(-3) + b
2 = -9/4 + b
17/4 = b
Put it in an equation:
y = 3/4x + 17/9
The coordinate grid shows points A through K. What point is a solution to the system of inequalities?
y > -2x + 10
y > 1/2x - 2
Choices:
E
K
B
D
Answer:
Option C, i.e., point B.
Step-by-step explanation:
The given system of inequalities is
[tex]y>-2x+10[/tex] ...(1)
[tex]y>\dfrac{1}{2}x-2[/tex] ...(2)
If a point is a solution of given system of inequalities, then the both inequalities must be satisfy by the point.
From the given graph it is clear that coordinates of point E are (4,-2).
Put x=4 and y=-2 in (1).
[tex]-2>-2(4)+10\Rightarrow -2>2[/tex] False.
From the given graph it is clear that coordinates of point K are (2,3).
Put x=2 and y=3 in (1).
[tex]3>-2(2)+10\Rightarrow 3>6[/tex] False.
From the given graph it is clear that coordinates of point B are (4,7).
Put x=4 and y=7 in (1).
[tex]7>-2(4)+10\Rightarrow 7>2[/tex] True.
Put x=4 and y=7 in (2).
[tex]7>\dfrac{1}{2}(4)-2\Rightarrow 7>0[/tex] True.
Since both inequalities are true for B(4,7), therefore point B is the solution.
From the given graph it is clear that coordinates of point D are (-7,1).
Put x=-7 and y=1 in (1).
[tex]1>-2(-7)+10\Rightarrow 1>24[/tex] False.
Since the given inequalities are false for points E, K and D, therefore they are not the solution.
Find the range of the graphed function.
The range of the curve is from -6 to 10, i.e. -6 ≤ y ≤ 10.
Given is a graph of a curve having endpoints at (-10, -6) and (0, 10), we need to find its range.
To find the range of a curve, we need to determine the set of all possible y-values that the curve can attain.
In this case, we have the endpoints of the curve as (-10, -6) and (0, 10).
The range of the curve is the set of all possible y-values. To find it, we need to identify the minimum and maximum y-values.
The minimum y-value can be found at the lowest point of the curve. From the given endpoints, we can see that the lowest point lies at (-10, -6).
The maximum y-value can be found at the highest point of the curve. From the given endpoints, we can see that the highest point lies at (0, 10).
Therefore, the range of the curve is from -6 to 10, inclusive: [-6, 10].
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SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
L: y= -4x + 17
Step-by-step explanation:
For a line L to pass through two points, we use the slope formula to calculate the slope, m, where
m = (y2-y1) / (x2-x1)
= (9-1) / (2-4)
= 8 / -2
= -4
Next we use the point slope form to find the line equation:
L: (y-y1) = m (x-x1)
substitute (x1,y1) = (4,1)
L: y-1 = -4 (x-4)
Simplify:
L: y = -4x + 16 + 1
L: y= -4x + 17
Check: substitute (4,1)
y = -4(4)+17 = 1 checks
substitute (2,9)
y = -4(2)+17 = 9 checks
so
L: y= -4x + 17
Answer:
y is equal to 5 and x is equal to 11
PLEASE HELP For what value of the variable will the value of 2x+1 be 20 greater than 8x+5?
It will be a negative.
for an example: -20 for x would mqke 2x + 1 into -39 and 8x + 5 into -155. that's 116 apart, so maybe -2(8) + 5 = -11
-2(2) + 1 = -3
but that's only 8 apart, so it'd be higher.
-4(2) + 1 = -7
-4(8) + 5 = -27
BOOM
Tadaaaa,
You probably thought positive, but sometimes it's negative, you know what I mean?
What is the equation of the circle graphed on the coordinate plane? answers: 1) (x – 2)2 + (y + 1)2 = 4 2) (x + 1)2 + (y – 2)2 = 16 3) (x – 2)2 + (y + 1)2 = 16 4) (x + 2)2 + (y – 1)2 = 16
Answer:
3) (x – 2)^2 + (y + 1)^2 = 16
Step-by-step explanation:
Equation of circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center, and r is the radius.
From the graph, we see the center is at (2, -1), so h = 2, and h = -1.
The radius is 4, so r = 4.
The equation is
(x - 2)^2 + (h - (-1))^2 = 4^2
(x - 2)^2 + (h + 1)^2 = 16
What is the name of the shape graphed by the function r = 1 + sine ?
A. Cardioid
B. Circle
C. Limaçon
D. Line
Please help me I need it done ASAP
Answer:
B
Step-by-step explanation:
I remember when I had this question
There are three times as many fiction books as non-fiction books in a library. 122 fiction books and 24 non-fiction books are loaned out. There are now twice as many non-fiction books as fiction books. How many books were in the library?
Answer:170
Step-by-step explanation:
122+24+24=170
Use the substitution method to solve the following system of equations: 3x + 5y = 3 x + 2y = 0 (1 point) (1, 1) (6, −3) (6, 1) (1, −3)
Step-by-step explanation:
Given.
[tex]3x+5y=3[/tex]
[tex]x+2y=0[/tex]
Take the second equation and subtract 2y to both sides.
[tex](x+2y)-2y=0-2y[/tex]
[tex]x=-2y[/tex]
Substitute x into the first equation and simplify.
[tex]3x+5y=3[/tex]
[tex]3(-2y)+5y=3[/tex]
[tex]-6y+5y=3[/tex]
[tex]-y=3[/tex]
Invert.
[tex]y=-3[/tex]
Substitute Y into your second equation.
[tex]x+2y=0[/tex]
[tex]x+2(-3)=0[/tex]
[tex]x-6=0[/tex]
Add -6 to both sides.
[tex](x-6)+6=0+6[/tex]
[tex]x=6[/tex]
Answer:
(6, -3)
Answer:
(6,-3)
Step-by-step explanation:
Got it right on the test
Hope this helps :)
What are all of the real roots of the following polynomial? f(x) = x4 - x3 - 13x2 + x + 12
We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.
Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.
x - 1 = 0 gives us x = 1.
x + 1 = 0 --> x = -1.
x - 4 = 0 --> x = 4.
x + 3 = 0 --> x = -3.
our roots are x = 1, -1, 4, and -3.