Answer:
x = 24, x = -16
Step-by-step explanation:
Given the function f(x) = 0.5|x – 4| – 3, we are to find the values of x for f(x) = 7
Substitute f(x) = 7 into the expression;
7 = 0.5|x – 4| – 3
For the positive function
7 = 0.5(x – 4) – 3
7 = 0.5x - 2 - 3
7 = 0.5x - 5
7+5 = 0.5x
12 = 0.5x
12 = x/2
Swap
x/2 = 12
x = 12 * 2
x = 24
For the negative function
7 = 0.5-(x – 4) – 3
7 = 0.5(-x +4) - 3
7 = -0.5x +2 - 3
7 = -0.5x - 1
7+1 = -0.5x
8 = -x/2
Swap
-x/2 = 8
-x = 8 * 2
-x = 16
x = -16
Hence the required values of x are -16 and 24
Select the correct answer. Which expression is equivalent to 8x^2^3 sqrt 375x + 2^3 sqrt 3x^7, if x=0?
Answer:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}[/tex]
Step-by-step explanation:
The question is poorly formatted. The original question is:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7[/tex]
We have:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7[/tex]
Open bracket
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^{3* \frac{2}{3}}) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
Express 8 as 2^3
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^{3* \frac{2}{3}} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^2 *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
Express 2^3 as 8
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{75x^3} + 8\sqrt{ 3x^7}[/tex]
Expand each exponent
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2 *3x} + 8\sqrt{ 3x * x^6}[/tex]
Split
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2} *\sqrt{3x} + 8\sqrt{3x} * \sqrt{x^6}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 *5x *\sqrt{3x} + 8\sqrt{3x} * x^3[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =20x^3\sqrt{3x} + 8x^3\sqrt{3x}[/tex]
Factorize
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}[/tex]
Answer:
42x^2 ^3 square root 3x
Step-by-step explanation:
i got it right
What’s the answer. Please help.
Answer:
The answer would be the third one, 3(x -2)=18
In the diagram of right triangle ABC, AB = 4 and BC = 7.
What is AC, to the nearest hundredth?
1
5.74
2
5.75
3
8.06
8.08
Answer:
5.74
Step-by-step explanation:
The value of AC in the given right triangle is 5.74 units.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) - a² + b² = c².
Given that, the right triangle ABC, AB = 4 and BC = 7.
According to Pythagoras theorem,
AC² = AB²+BC²
AC² = 7²+4²
AC = √33 = 5.74
Hence, The value of AC in the given right triangle is 5.74 units.
For more references on Pythagoras theorem, click;
https://brainly.com/question/343682
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Write the equation of the line that passes through the points:
(-4,-4) and (8,-7)
Solve by elimination
-6x+y= -2
-3x-6y= 12
Answer:
Ans: x=0
y= -2
Step-by-step explanation:
-6x+y= -2--------- (1) × 6
-3x-6y= 12--------(2) × 1
-36x+6y= -12-----(3)
-3x-6y= 12--------(2)
(3)+(2)
-36x+6y+(-3x-6y) = -12+12
⇒ -36x+6y-3x-6y = 0
⇒ -36x-3x = 0
⇒ -39x=0
⇒ x= 0/-39
∴ x = 0
Substitute x = 0 into (1)
-6x+y= -2
⇒-6(0)+y= -2
⇒0+y= -2
∴y = -2
Ans: x = 0
y = -2
Check:
-6x+y= -2--------- (1)
= -6(0)+(-2)
= 0 - 2
= -2 ✔
-3x-6y= 12--------(2)
= -3(0)-6(-2)
= 0+12
= 12 ✔
Laura has a set of 16 books. Each book in the set weighs the same. One book has a weight of 0.8 kilograms (kg). Laura wants to find the total weight, w, of the set of books.Which equation and solution shows the total weight of the set of books A.
w=16×0.8w=12.8 kg, B.w=16−0.8w=15.2 kg
c.w=16+0.8w=16.8 kg D.w=16÷0.8w=20.0 kg
HELP THIS IS DUE TODAY I WILL NAME YOU THE BRAILIEST!!!!!!!
Determine the equation of the circle graphed below.
Answer:
[tex](x-4)^2+(y+3)^2=20[/tex]
Step-by-step explanation:
The equation of a circle with center [tex](h,k)[/tex] and radius [tex]r[/tex] is given by [tex](x-h)^2+(y-k)^2=r^2[/tex].
What we know:
Center at [tex](4,-3)[/tex]To find the radius, we can use the distance formula. For points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], the distance between them is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Let
[tex](x_1,y_1)\implies (-4, -3),\\(x_2,y_2)\implies (8,-1)[/tex]
[tex]r=\sqrt{(8-4)^2+(-1-(-3))^2},\\r=\sqrt{4^2+2^2},\\r=\sqrt{20}=2\sqrt{5}[/tex]
Thus, the equation of this circle is
[tex](x-4)^2+(y-(-3))^2=\sqrt{20}^2,\\\boxed{(x-4)^2+(y+3)^2=20}[/tex]
En la fiesta de Juan repartieron el agua en jarras, cada una puede llenar 6 vasos. Si en total se utilizaron 6 jarras, ¿cuántos vasos sirvieron?
Answer:
36
Step-by-step explanation:
6 x 6
Aarion is saving $375 to buy a new gaming system. He already has $105 and can earn $30 per week cutting grass, how long will it take him to earn the rest of what he needs?
Answer:
it will take him 9 weeks to earn the rest of what he needs.
Step-by-step explanation:
if he already has $105, then he will need $270 more.
Divide 270 by 30(the amount of money he gets each week) and you will get 9.
"Darcie wants to crochet a minimum of 333 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal." pls help lol
Answer:
Ive seen this question before, its supposed to be 3 blancckets and 15 days can be skipped
Step-by-step explanation:
60-45= 15
15 times 3 is 45
Find the surface area and no links
Answer:
184 m²
Step-by-step explanation:
Surface Area = 2(10*2) + 2(10*6) + 2(2*6)
Surface Area = 2(20 + 60 + 12)
Surface Area = 2(92)
Surface Area = 184 m²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Use elimination to solve the system of equations:
3x + y = 10
- 4x - 2y = 2
Work:
Algorithm to accept the height of a building in metres and convert it into centimetres.Also draw the flowchart
Answer:
1200cm
Step-by-step explanation:
Given data
We know that 1meter is equivalent to 100cm
i,.e 1*100
so, if height is 1.2meters
Height in centimeters is 1.2*100
Hence height in centimeters is 1200cm
Amelia is taking a road trip. She drove 250 miles the first day. If 250 is 40% of her total distance, how many miles is her roadtrip in all?
Answer: 625 miles
Step-by-step explanation:
100-40=60
so she has 60% for her distance so lets munis 40 from it and add 250 to 250
250+250=500
60-40=20
20 is half of 40 so whats half of 250? its 125
so she drove 625 miles for her road trip 2 and 1/2 a day
Using the graph, determine the value of the slope.
v
CO 3
What is the slope?
4
2
What is true about the graph?
4
-2
-2
Intro
Done
Answer:
gradient of horizontal slope is 0
The ratio of coloured paper the white paper is 3:8 if there are 48 white paper how many coloured paper are there
Answer:
18
Step-by-step explanation:
Calculation to determine how many coloured paper are there
Let 3x represent the number of coloured papers
Let 8x represent the number of white papers
Given that 8x=48
Hence,
x=48/8
x=6
Now let determine how many coloured paper are there
Coloured paper=3x
Coloured paper=3(6)
Coloured paper=18
Thereffore the number of coloured paper that are there is 18
what’s the product? (3x-6) (2x^2-7+1)
Answer:
0
Step-by-step explanation:
because the carrot is wrong
Answer:
Assuming you are using the zero product property, x = 2, √(3), -√(3)
Step-by-step explanation:
first I factored the (2x^2-7+1) into 2(x^2 - 3)
I also factored the (3x-6) into 3(x - 2)
Now I have the equation 6(x - 2)(x^2 - 3) = 0
I'll start with the easiest one, which is x - 2 = 0, which gives me 2
Now I solve for x^2 - 3 = 0, and I end up with two answers:
√(3) and -√(3)
So in total, x as 3 answers
please help me and thank you.
Answer:
[tex]482.5\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.
Area of the rectangle: [tex]25\cdot 20=500\:\mathrm{in^2}[/tex]
Area of the triangle: [tex]\frac{1}{2}\cdot 5\cdot 7=17.5\:\mathrm{in^2}[/tex]
Thus, the area of the figure is [tex]500-17.5=\boxed{482.5\:\mathrm{in^2}}[/tex]
Find the value of the y-intercept of the line whose equation is 5x - 3y = -12.
A. -12/5
B. -4
C. 4
Answer:
C. 4 is the right answer!
Step-by-step explanation:
a ball is shot out of a homemade air cannon. It flies through the air such that its height, as a function of time, is given by: h= -16t^2 + 64t + 10. where h is the height of the ball in feet and t is the time since it was fired in seconds. Max estimates that it takes 4 seconds for the ball to hit the ground and Cole estimates it takes 5 second. Algebraically determine who is closer and support your answer.
Answer:
Max
Step-by-step explanation:
the function given that h = -16t³+64t+10
the general function Equation:
h = at²+bt+c
=> t at the highest point is defined by t = -b/2a
= -64/2(-16) = -64/-32 = 2 second
the total times that the ball hits the ground
= 2× 2 seconds = 4 seconds.
so, Max is right
Answer:
Solution given:
Let h=0=when the ball hit the ground,the height=0.
h= -16t^2 + 64t + 10.
0=16t²-64t-10
8t²-32t-5=0
∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]
taking positive
t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]
t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]
So
t=4.15seconds closer to 4seconds.So
Max is closer.
PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!!
Answer:
14
Step-by-step explanation:
AB = 10+( 10/15 × 6)
= 10 + 4= 14
Given: line a ∥ line b. If m∠7 = 63° , then m∠4 = __ ? __.
Answer:
<1
Step-by-step explanation:
Could someone please help me please ASAP?
Answer mah questions Pleaseeee
Answer:
c
Step-by-step explanation:
Answer: median
I say this as the mean would be too off due to the one outlier (it's best used when there are multiple outliers), and the range wouldn't make sense as a mid-measurement.
¿Cómo expresarías la siguiente cantidad 1149,8x1018, en su equivalencia a notación científica?
URGENT PLEASE HELP: Simplify
Answer:
cot (x)
Step-by-step explanation:
cot x
---------------
cos x sec x
We know that sec = 1/ cos
cot x
---------------
cos x 1/ cos x
cot x
---------------
1
cot (x)
Answer:
You're clicking on the correct answer, it's cot with that symbol, I dont have the symbol.
I don’t know how to do this can someone help out
Answer:
Third side = 4
Step-by-step explanation:
Use Pythagoras theorem :
C = longer side, a = 10, b ?
[tex]c^2 = a^2 + b^2[/tex]
[tex](2 \sqrt{29})^2 = 10^2 + b^2\\\\4 \times 29 = 100 + b^2\\\\116 - 100 = b^2\\\\b^2 = 16 \\\\b = 4[/tex]
Hey, I need help for this question, not sure what it is. Please respond quickly!
Use the diagram and given information to answer the questions and prove the statement.
Given: Angle X ≅ Angle Z
XY ≅ ZY
Prove: AZ ≅ BX
Prove AZ ≅ BX using a flow chart proof.
Answer:
my answer is in this picture. sorry about my handwriting and my presentation because i am a Asian student and cant show better presentation
Of the 25 students who take a standardized test, the minimum score is 98 and the maximum score is 312. The mean score is 216. Standard deviation is 52. What is the number of standard deviations that includes all the data values?
Answer:
5
Step-by-step explanation:
so we can say that 5 standard deviations include all the data values.
Of the statistical processes we have covered throughout this course, which would be most helpful to determine if study hours and sleep could help estimate a student's test score?
Answer:
Pearson correlation coefficient
Explanation:
The Pearson correlation coefficient, also simply called correlation coefficient measures the linear correlation between two sets of data/variables, independent variables and dependent variable. A correlation coefficient may only be between -1 and 1 where +1 denotes a perfect positive correlation between variables(both variables increase together), 0 is no correlation, and -1 is perfect negative correlation between variables(one decreases while other increases).
