Answer:
x∈{-7√2, 7√2}
Step-by-step explanation:
[tex]98-x^2=0\\\\-x^2+98=0\\\\a=-1\,,\ \ b=0\,,\ \ c=98\\\\x_1=\dfrac{-0-\sqrt{0^2-4\cdot(-1)\cdot98}}{2\cdot(-1)}=\dfrac{-\sqrt{4\cdot49\cdot2}}{-2}=\dfrac{-2\cdot7\sqrt{2}}{-2}=7\sqrt2\\\\x_2=\dfrac{-0+\sqrt{0^2-4\cdot(-1)\cdot98}}{2\cdot(-1)}=\dfrac{2\cdot7\sqrt{2}}{-2}=-7\sqrt2[/tex]
A page in an average newspaper has 8 columns of print. Each column consists of 160 lines and each line averages 6 words. What's the average number of words on a full page?
Answer:
7,680
Step-by-step explanation:
A page has 8 columnsEach column consists of 160 lines.Each line averages 6 words.The average number of words on a full page
=Number of columns X Number of Lines X Number of words per line
=8 X 160 X 6
=7680
The average number of words on a full page is 7,680.
the length of a rectangle is twice its width, the perimeter of it is 36cm. what is the are of it
Answer: 72 cm²
Step-by-step explanation: lets take the width as x and length as 2x as length is twice the width= perimeter of rectangle is 2*(l+b)=36cm
So, 2×(2x+x)=36cm
2×3x=36cm
6x=36cm
X=36/6:6cm( width, since width was taken as x)
Length= 2x: 2×6=12cm
So area of the rectangle is( l*b):
12×6= 72cm²
cube of -1/2 is equal to-----------. i need urgent please.I will mark brainest
Answer:
-1/8
Step-by-step explanation:
(-1/2)(-1/2)(-1/2)=-1/8
Answer:
[tex] \frac{ - 1}{8} [/tex]solution,
[tex] (\frac{ - 1}{2} ) ^{3} \\ = \frac{( { - 1)}^{3} }{( {2}^{3} )} \\ = \frac{ - 1 \times ( - 1) \times ( - 1)}{2 \times 2 \times 2} \\ = - \frac{ 1}{8} [/tex]
hope this helps...
Good luck on your assignment
the point P = (x, 1/2) lies on the unit curcle shown below. what is the value of x in the simplest form
Answer:
x=sqrt(3)/2 or -sqrt(3)/2
Step-by-step explanation:
(x,1/2) is on the unit circle at pi/6 and 5pi/6.
so x is either sqrt(3)/2 or -sqrt(3)/2
Answer: [tex]-\sqrt{3}/2[/tex]
Step-by-step explanation: I did the question and got it right
8. The length of a side and the corresponding height
of a triangle are (x+3) cm and (2x – 5) cm respectively.
Given that the area of the triangle is 20 cm”, find
the value of x.
Answer:
x = 5
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = x + 3 and h = 2x - 5 , thus
[tex]\frac{1}{2}[/tex] (x + 3)(2x - 5) = 20 ( multiply both sides by 2 )
(x + 3)(2x - 5) = 40 ← expand factors on left using FOIL
2x² + x - 15 = 40 ( subtract 40 from both sides )
2x² + x - 55 = 0 ← in standard form
(x - 5)(2x + 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - 5.5
But x > 0 , hence x = 5
15 POINTS!!!!! suppose f(x)=x find the graph of f(x+2) please include what the graph would look like
Answer:
The graph f(x+2) would make the graph go left by 2 units.
Step-by-step explanation:
Using graph transformations, adding two would make the graph go left 2 and subtracting would make it go right 2
I really need help with this question, it's confusing. It's geometry btw
Answer:
Two regular nonagons and nine congruent rectangle
Step-by-step explanation:
Two regular nonegon=on the surface and base..
Nine congruent rectangle=look at beside it will be look like 9 rectangle.. I hope it will be right.
Please help me!!!!!!!!!!!!!
Answer:
-3.125 < -2.95 < 2.6 < 103.5
Step-by-step explanation:
1) [tex]5\frac{6}{15}- 2\frac{4}{5}[/tex]
=> [tex]\frac{81}{15} - \frac{14}{5}[/tex]
=> [tex]\frac{81-42}{15}[/tex]
=> [tex]\frac{39}{15}[/tex]
=> 2.6
2) -4.5 * -2.3
=> 103.5
3) [tex]\frac{5}{-1.6}[/tex]
=> -3.125
4) [tex]-\frac{33}{10} + \frac{7}{20}[/tex]
=> [tex]\frac{-66+7}{20}[/tex]
=> [tex]\frac{-59}{20}[/tex]
=> -2.95
Answer:
fourth, first, third, second,
Step-by-step explanation:
The first equals 2 9/15
The second equals 10.35
The third equals 3 1/8
The fourth equals -2 19/20
This can have more than one option answer this fast in two minutes
Answer:
Just QT and UX
Step-by-step explanation:
QT and TX intersect and are not parallel.
QU and ST are not parallel or intersecting.
QT and WX are not parallel or intersecting.
QT and UX are parallel.
a line has a gradient of 4 and passes through the post (1,7). what is the equation?
Answer:
y = 4x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (1, 7) into the partial equation
7 = 4 + c ⇒ c = 7 - 4 = 3
y = 4x + 3 ← equation of line
Answer:
The equation is y = 4x+3
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x + b
Substitute the x and y value into the equation
7 = 4(1)+b
7 = 4+b
Subtract 4
7-4 =b
3=b
The equation is y = 4x+3
someone help me asap please/math 10
Answer:
Step-by-step explanation:
4. a) tan x=17/12=1.416
x=54.8≈55
b)sin b=78/132=0.59
b=36.2≈36
cos 28=x/82
x=82*cos 28=82*0.9=73.8
Anyone know this one?
Answer:
(-3, 5), (1, 4), (-2, 3), and (0, 2).
Step-by-step explanation:
When a function is inverted, the x-values become y-values, and the y-values become x-values.
The ordered pairs for the function are (5, -3), (4, 1), (3, -2), and (2, 0).
After inversion, the ordered pairs will be (-3, 5), (1, 4), (-2, 3), and (0, 2).
Hope this helps!
11. Three men can build a wall in 10 hours. How
many men would be needed to build the wall in
7 hours?
Answer:
Man-hours to build the wall: 3 * 10 = 30
:
let m = no. of men required to do it 7.5 hrs
7.5m = 30
m = [tex]\frac{30}{7.5}[/tex]
m = 4 men to build it in 7.5 hrs
Step-by-step explanation:
help help meeeee pls
Simplify the question
10x /(divide) -2y
Answer:
-5x/y is the answer
Step-by-step explanation:
10x/-2y
Dividing by 2
=5x/-y
=-5x/y
I hope this will help you :)
Answer:
(-5x)/y
Step-by-step explanation:
I'm assuming you meant:
10x
---------
-2y
-5x
This reduces to ----------
y
4.8x10^-3 as an ordinary number
Answer:
0.008.
Step-by-step explanation:
10^-3 basically tells you to move the decimal point to the left by three digits.
Right now, you have 8. If the decimal point were to move left by three digits, you can visualize 8 as 0008. Move left by three digits, and you get 0.008.
Hope this kind of helps!
Answer:
0.008.
hope this helps :)
Find the value of b. Round your answer to the nearest tenth.
The figure shows acute triangle A B C. The measure of angle B is 40 degrees. The length of side A B is 10. The length of side B C is 12. The length of side C A is b.
Answer:
Side CA = 7.8
Step-by-step explanation:
Given:
Acute angled [tex]\triangle ABC[/tex].
[tex]\angle B =40^\circ[/tex]
AB = 10
BC = 12
We can use cosine rule here to find the side AC = b
Formula for cosine rule:
[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]cos 40 = \dfrac{12^{2}+10^{2}-b^{2}}{2\times 12\times 10}\\\Rightarrow cos 40 = \dfrac{144+100-b^{2}}{240}\\\Rightarrow 0.77 = \dfrac{244-b^{2}}{240}\\\Rightarrow 244-b^{2} = 0.77 \times 240\\\Rightarrow 244-b^{2} = 183.85\\\Rightarrow 244-183.85 = b^{2}\\\Rightarrow b^2 = 60.15\\\Rightarrow b = 7.76[/tex]
To the nearest tenth b = 7.8
-3.42, 10.26, -30.78, 92.34, ___,... what is the next number
Answer:
-277.02
Step-by-step explanation:
Given series:
-3.42, 10.26, -30.78, 92.34,...We can see the series is a GP with common ratio of -3, as:
10.26/-3.42= -30.78/10.26= 92.34/-30.78= -3So the next term will be:
92.34 × (-3)= -277.02
NEED MATH HELP NOW. Need help find the vertex and y intercept. Please show work.
Answer:
Vertex: ( 1 , 9 )
Y-intercept: ( 0 , 8 )
Step-by-step explanation:
y = - (x+2) (x-4)
y = -x² + 2x + 8
Find the vertex.
x = -b/2a
x = -2/2(-1)
x = -2/-2
x = 1
y = -(1)² + 2(1) + 8
y = -1 + 2 + 8
y = 9
Find the y-intercept.
Put x as 0.
y = -(0)² + 2(0) + 8
y = 8
A herd of bison currently has 55 members. Based on the available resources,
biologists estimate that the size of the herd will increase at a rate of 6% per
year. Which of the following graphs models this relationship, if the x-axis
represents years and the y-axis represents number of bison?
The equation y is equal to 55(1.06) to power x models the relationship between the x-axis which represents years and the y-axis, which represents number of bison.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have:
A herd of bison currently has 55 members, and biologists estimate that the size of the herd will increase at a rate of 6% per year.
We can model this relationship:
[tex]\rm y = 55(1+0.06)^x\\\\\rm y = 55(1.06)^x[/tex]
Thus, the equation y is equal to 55(1.06) to power x models the relationship between the x-axis which represents years and the y-axis, which represents number of bison.
Learn more about the exponential function here:
brainly.com/question/11487261
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PLEASE HELP QUICK!!!!!!!!! Given the equation x2 + 4x + c = 0, determine a value for c that gives the equation: a) Two real solutions and find its solutions. b) Complex solution(s) and find its solution(s). c) Exactly one real solution and find its solution.
Answer:
a. two (distinct) real solutions.
c = 3, x=¨{-1,-3}
b. two complex solutions
c = 17, x={-2+sqrt(13)i, -2-sqrt(13)i}
c. two coincident roots (i.e. one real solution)
c=4, x = {-2}, or x = {-2, -2}
Step-by-step explanation:
Given:
x^2+4x+c =0
a. two (distinct) real solutions.
c = 3
(x+1)(x+3) = 0
x=¨{-1,-3}
b. two complex solutions
c = 17
x^2+4x+17=0
does not have real factors.
x={-2+sqrt(13)i, -2-sqrt(13)i}
c. two coincident roots (i.e. one real solution)
c=4
x^2+4x+4=0 => (x+2)^2 = 0 => perfect square
x = {-2}, or x = {-2, -2}
what is the solution to this equation? 4X equals 32
Answer:
x = 8
Step-by-step explanation:
4x = 32
Divide each side by 4
4x/4 = 32/4
x = 8
The solution to the equation 4x = 32 is x = 8.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
4x = 32
By dividing both sides of the equation by 4, we have:
x = 32/4
x = 8
Read more on expression here: brainly.com/question/16729936
#SPJ6
Here were 87 sunflowers at the flower shop in the morning. There were 56 sunflowers left at the end of the day. How many sunflowers were sold? Explain a way to solve the problem.
Answer:
31
Step-by-step explanation:
We just have to calculate 87 - 56 which is 31 so the answer is 31 sunflowers.
Answer:
31
Step-by-step explanation:
Since we know that we started with a higher number than we ended with, it is obvious that this is a subtraction problem. Then, we simply have to find the difference by subtracting 87 by 56 (87 - 56 = x). After the calculation, we see that the answer is 31 (87 - 56 = 31).
Please help me I will give BRAINLIST and a like :))))
Answer:
18.75%
Step-by-step explanation:
Hello,
3 students are both female and senior
the total number of students is 7+10+8+5=30
so the probability to select one female senior is 3/30=1/10=0.10
probability to select one female is 16/30=16/30
probability that the student is a senior given that it's female is
=P(female and senior)/P(female)
=1/10*30/16=3/16
hope this helps
Answer:
19%
Step-by-step explanation:
Find the number of female students
3+4+6+3 = 16
P( senior given that it is female = senior/ female
= 3/16
=.1875
18.75%
To the nearest whole percent 19%
Can someone help me I really need help please help me thank you
Answer:60 degrees
Step-by-step explanation:
60 degress
43 + 167 + 90 = 300
360 - 300 = 60
<!> Brainliest is appreciated! <!>
In this activity, you will use a variable to create expressions for various relationships. Then you will use these expressions to form a linear equation. Finally, you will find the solution to the equation. Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is inches shorter than times Theresa’s height. Steve says he is inches shorter than times Theresa’s height. If they are both right, how tall is Theresa? To solve a problem like this one, you can use a linear equation where the variable represents Theresa’s height in inches. Let represent Theresa’s height in inches. Question 1 The relationships for Paul’s and Steve’s height with respect to Theresa’s height are described above. First you will write expressions for Paul’s height and for Steve’s height. Then you will relate the expressions. Part B Write an expression to represent Steve’s height in inches.
Answer:
Step-by-step explanation:
Some information is missing. The correct question is:
Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa?
Solution:
Let p represent Paul's height
Let s represent Steve's height
Let t represent Theresa's height
Since Paul and Steve are both of the same height, it means that p = s
Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. It means that
p = 1.5t - 16
Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. It means that
s = 4t/3 - 6
Since p = s, then
p = 4t/3 - 6
Therefore, it means that
1.5t - 16 = 4t/3 - 6
Multiplying through by 3, it becomes
4.5t - 48 = 4t - 18
4.5t - 4t = - 18 + 48
0.5t = 30
t = 30/0.5 = 60 inches
Theresa's height is 60 inches
Answer:
Part A : The expression that represents Paul’s height in inches is
3/2 t - 16
Part B : The expression that represents Steve’s height in inches is
4t/3 - 6
In the diagram, the measure of angle 6 is 98°. what is the measure of angle 7?
Answer:
7∠82°
Step-by-step explanation:
Well angle 6 and 7 are complementary angles, meaning they both add up to 180°.
So we do 180 - 98 which is 82°.
Answer: The measure of angle 7 is 82 degrees.
Step-by-step explanation:
Angle 6 and 7 lies on a straight line so they will add up to 180 degrees.
So if Angle 6 is 98 degrees then an a number plus 98 has to equal 180.
so we could generate an equation as x + 98 = 180
x + 98 = 180 solve for x
-98 -98
x= 82
) We throw 9 identical balls into 7 bins. How many different ways are there to distribute these 9 balls among the 7 bins such that no bin is empty? Assume the bins are distinguishable (e.g., numbered 1 through 7).
Answer:
28 ways
Step-by-step explanation:
After placing 1 ball in each of the seven bins, there are two balls left.
If we place both balls in a single bin, there are 7 different ways to place the balls (place both on bins 1 through 7).
If we place each of the remaining balls in a different bin, the number of ways to place the balls is:
[tex]n_2=\frac{7!}{(7-2)!2!}=7*3=21[/tex]
The total number of ways to distribute those balls is 21 + 7 = 28 ways.
prove that the difference between squares of consecutive even numbers is always a multiple of 4
Answer:
Let's call the numbers n and n + 2.
(n + 2)² - n²
= n² + 4n + 4 - n²
= 4n - 4
= 4(n - 1)
What is the period of the function y= 3/2 cot(3/5x) +5?
A. Pi/5 units
B. 3pi/5 units
C. 2pi/3
D. 5pi/3
Answer:
D; 5pi/3 units
Step-by-step explanation:
Here, we want to find the period of the function;
y = 3/2 cot (3/5x) + 5
By definition, the period of a function is the interval between two matching points in the function.
Let’s say it is the distance between two peaks, crests, etc on a function.
To find the value of the period. We shall standardize the function.
What this means is that we shall be writing the function in the standard form.
The standard form is as follows;
f(x) = A trig(Bx -C) + D
Where trig refers to the accompanying trigonometric function in question.
Comparing this standard form with our question, we can see that;
A is 3/2
B is 3/5
C is 0
D is 5
Now for cot and tan functions, we shall need to divide pi by the absolute value of B
Thus we have; pi divided by 3/5 which gives 5pi/3 units
Answer:
D. 5pi/3, period is the distance between the repetition of a function.
Step-by-step explanation: