Answer:
x = 60Step-by-step explanation:
I hope it helps :)
[tex]\sqrt{x+4} -7=1\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\\sqrt{x+4}-7+7=1+7\\\sqrt{x+4}=8\\\mathrm{Square\:both\:sides}\\\left(\sqrt{x+4}\right)^2=8^2\\x+4=64\\x = 64-4\\x = 60[/tex]
On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 34 m long and the shadow is 24 m, how tall is the building
Answer:
Step-by-step explanation:
h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m
The height of the building is 10 meters.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's call the height of the building "h".
We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:
h² + 24² = 34²
Simplifying and solving for h.
h² = 34² - 24²
h² = 676 - 576
h² = 100
h = 10
Therefore,
The height of the building is 10 meters.
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write as an inequality 9 is greater than or equal to w, and -7 is less than or equal to w
[tex]9 \geqslant w \\ \\ - 7 \leqslant w[/tex]
"9 is greater than or equal to w" translates to [tex]9 \ge w[/tex] which flips to [tex]w \le 9[/tex]. We swap both sides and flip the inequality sign as well.
"-7 is less than or equal to w" translates to [tex]-7 \le w[/tex]
We have [tex]-7 \le w[/tex] and [tex]w \le 9[/tex] which then ultimately combine into the compound inequality [tex]-7 \le w \le 9[/tex]
Final Answer: [tex]-7 \le w \le 9[/tex]A researcher wants to use a confidence interval to estimate the proportion of college students in his state who plan to vote in the 2020 presidential election. He plans to randomly sample 120 college students, and plans to construct a 95% or 99% confidence interval. Which of these confidence intervals will be wider, and why
Answer:
99% confidence interval will be wider because as the level of confidence increase the width increases as well and the standard error decreases
Step-by-step explanation:
The confidence interval is directly proportional to the sample size hence the 99% confidence interval will be wider than the 95% confidence interval of the sample of 120 college students
using a 99% confidence interval gives a more accurate result than a 95% confidence because the standard error decreases with increase in confidence interval
What percentage is 420 grams of 750 grams?
%
The radius of a football is 5cm.
Calculate its volume.
Refer the attached image for the answer
HOPE SO IT HELPS YOU
Answer:
523.6 to 1 decimal place
Step-by-step explanation:
→ Utilise the formula for a volume of a sphere
[tex]\frac{4}{3}[/tex] × π × r³
→ Substitute in the radius
[tex]\frac{4}{3}[/tex] × π × 5³
→ Simplify
523.6 to 1 decimal place
Bill is building a staircase for his new home. He has measured several three-foot bars to support the handrail. If Bill nails the support bars to the handrail and to the edge of the staircase (a 2-inch-by-12-inch board attached parallel to the slope of the stairs) at 12-inch intervals, will the handrail be parallel to the staircase?
Answer:
6
Step-by-step explanation:
78
Deion is saving up to buy a new phone. He already has $95 and can save an additional $7 per week using money from his after school job. How much total money would Deion have after 6 weeks of saving? Also, write an expression that represents the amount of money Deion would have saved in w weeks.
The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.
What is an expression?A statement expressing the equality of two mathematical expressions is known as an equation.
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given,
Initial fixed money = $95
Per week saving $7/week
Total money = fixed money + money in w weeks.
⇒ 95 + 7w
For 6 weeks, w = 6
⇒ 95 + 7× 6 = $137.
Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".
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We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?
Answer: 1.18 dollars
Step-by-step explanation:
Given that:
E = Euros
D = US dollars
If the equation showing the relationship between Euros and Dollar
is E = 17/20D
To find the equivalent amount of dollars for 1 euros, substitute E for 1 in the formula and make D the subject of formula
1 = 17/20 D
Cross multiply
17D = 20
D = 20/17
D = 1.18 dollars approximately
Therefore, 1.18 dollars have the same value as 1 euro.
Which function describes this graph?
A. y = (x+5)(x-3)
B. y = x^2+7x+10
C. y = x^2+5x+12
D. y=(x-2)(x-5)
Answer:
B is the answer
Step-by-step explanation:
Answer:
B. y = x^2+7x+10
Step-by-step explanation:
During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt. The variable sss models the ice sheet's thickness (in meters) ttt weeks after the beginning of spring. s=-0.25t+4s=−0.25t+4s, equals, minus, 0, point, 25, t, plus, 4 By how much does the ice sheet's thickness decrease every 666 weeks? meters
Answer: The ice sheet's thickness decrease every 6 weeks= 1.5 meters
Step-by-step explanation:
GIven: At the beginning of spring, the ice starts to melt. The variable sss models the ice sheet's thickness (in meters) t weeks after the beginning of spring. [tex]s=-0.25t+4[/tex]
At t=0, [tex]s=4[/tex]
So, Thickness of ice sheet at the beginning = 4 meters
Now at t= 6, we get
[tex]s=-0.25(6)+4=-1.5+4=2.5[/tex]
Thickness of ice sheet after 6 weeks = 2.5 meters
Decrease in thickness = 4 meters - 2.5 meters = 1.5 meters
Hence, the ice sheet's thickness decrease every 6 weeks= 1.5 meters
Answer:
1.5
Step-by-step explanation:
in a 41-49 right triangle, the hypotenuse is 28.83 centimeters. if cos 41= 0.7547, find the length of the side opposite the 49 angle. Estimate your answer to three decimal places
Answer:
21.758
Step-by-step explanation:
If you draw the triangle out, you find that cos 41 = x/28.83, when x is equal to the side opposite the 49 angle
Simplify this into 28.83 cos 41, and plug it into the calculator and you get
21.75827.
How many times more ?
Answer:
1.3
Step-by-step explanation:
bc for each time x increases by 1, it multiplies by 1.3
i cant think of any other way to explain it
but i hope this helped :D
Answer:
1.3 times
Step-by-step explanation:
f(x)= 68 (1.3) ^x
it, means each year, the expected number of squirrels is 1.3 times, the number the year before.
x=0 so, f(0)=68
New x=1, so f(1)= 68(1.3)¹
= 68 × 1.3
f (1)= f(0) × 1.3
So, 1.3 times
OAmalOHopeO
PLEASE FIND THE ANSWER FOR B.)
Answer:
f (-3)
since -3 is between-4 and -2 for every value of x y is 2
Write in point-siope form, siope-intercept form, and standard form an equation that passes
through( - 1, 2) with slope 4.
Answer:
The forms are:
y - y1 = m(x - x1)y = mx + bax + by = cGiven:
m = 4Point (-1, 2)Use point slope form:
y - 2 = 4(x - (-1))y - 2 = 4(x + 1)Convert it to slope-intercept form:
y = 4x + 4 + 2y = 4x + 6Convert it to standard form:
4x - y = - 6Find the surface area of the composite figure
Answer:
384 cm^2
Step-by-step explanation:
Start with the prism (I multiply by 2 because some of the surfaces are more of):
4×15×2=1206×15×2=1806×4=24The Triangular Prism (I divide by 2 because it is a triangle shape on the sides):
3×4/2*2=123×6=186×5=30The Last Step (adding everything):
120+180+24+12+18+30=384
Evelyn wants to buy a dictionary that costs $9, a dinosaur book that costs $18, and a children's cookbook that costs $12. She has saved $30 from her allowance. How much more money does Evelyn need to buy all three books?
Answer:
First, you have to add 9, 18, and 12. When we add this we get 39. She has 30 dollars, do we can see that she needs $9 more to get all three books.
Step-by-step explanation:
ntroduction to Functions
Assignment Active
Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Output
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
0 (-1, -3)
O (4, -2)
O (6,-1)
Answer:
To be a function, each input must only have one output. In this case, input 4 has two outputs, so (4 , -2) can be removed for it to be a function.
Let me know if you have any other questions!
The ordered pair (4,2) could be removed to make the given relation a function.
What is the relation?A relation is a function if for every input (x-value) there is exactly one output (y-value).
If there are two or more ordered pairs with the same x-value but different y-values, then the relation is not a function. In this case, one of those ordered pairs would need to be removed in order to make it a function.
As per the question, the relation was given as {(-5,0), (2, -3), (-1, -3), (4, -2), (4, -2), (6,-1)}, the ordered pair (4,-2) would need to be removed because there are two outputs (-2 and 2) for the input of 4.
Thus, removing (4,2) would result in the function.
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The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of minutes and a standard deviation of minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than minutes, (b) between and minutes, and (c) more than minutes. (a) The probability that a randomly selected athlete uses a stairclimber for less than minutes is nothing. (Round to four decimal places as needed.) (b) The probability that a randomly selected athlete uses a stairclimber between and minutes is nothing. (Round to four decimal places as needed.) (c) The probability that a randomly selected athlete uses a stairclimber for more than minutes is nothing.
Answer:
Step-by-step explanation:
Let S be the sample space, n(S) = 60
a) Let A be the event that the selected athlete uses
s less than a minute, n(A) = 59
The probability that a randomly selected athlete uses less a minute, P(A) = n(A)/n(S) = 59/60 = 0.9833
b) 1 - 0.9833 = 0.0167
c) 1 - 1 = 0
Find the value of x in the triangle shown below.(not a test just need help with khan academy)
Using angle sum property
[tex]\\ \sf\longmapsto x+44+29=180[/tex]
[tex]\\ \sf\longmapsto x+63=180[/tex]
[tex]\\ \sf\longmapsto x=180-63[/tex]
[tex]\\ \sf\longmapsto x=117°[/tex]
The angle sum property of a triangle:
The total measure of the three angles of a triangle is 180°[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 44 \degree \: + \: 29 \degree \: = \: 180 \degree[/tex]
[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 73 \degree \: = \: 180 \degree[/tex]
[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 180 \degree \: - \: 73 \degree \:[/tex]
[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 107 \degree[/tex]
⇛ Value of x is 107°please solve this please
Answer:
2/(a-4b) is the required ans
check the attachment for help
For every 5 books her students read, Mrs. Fenway gives them 4 homework passes. Juan has earned 12 homework passes. What proportion shows how many books Juan has read?
4/12 = x/5
4/5 = x/12
4/5 = 12/x
5/12 = 4/x
Okay which class.are you first thing is that .. ok tell me then fast.
A shopkeeper allows 10% discount on the marked price of a bicycle. If a costomer pays Rs 4068 with 13% VAT find the marked price of the bicycle
[tex] \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}[/tex]
We're provided - Discount % = 10 % , Cost with VAT [ SP with VAT ] = Rs 4068 & VAT % = 13%. We're asked to find out the marked price of the bicycle. Let's start :[tex] \large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}[/tex]
[tex] \large{ \tt{❃ \: SP \: with \: VAT= SP + VAT\% \: of \: SP}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = SP + \frac{13}{100} \: sp}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = \frac{100 \: \: SP + 13 \: SP}{100} }}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = \frac{113 \: SP}{100} }}[/tex]
[tex] \large{ \tt{⇢ \: 113 \: SP = 406800}}[/tex]
[tex] \large{ \tt{⇢ \: SP = \frac{406800}{113} }}[/tex]
[tex] \large{ \tt{⇢ \: SP = 3600}}[/tex]
Hence , SP = Rs 3600[tex] \large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}[/tex]
Let Marked Price [ MP ] be x.[tex] \large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = x - \frac{10}{100} } \: x}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = \frac{100x - 10x}{100} }}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = \frac{90x}{100} }}[/tex]
[tex] \large{ \tt{⇾ \: 90x = 360000}}[/tex]
[tex] \large{ \tt{⇾ \: x = \frac{360000}{90} }}[/tex]
[tex] \large{ \tt{⇾ \: x = Rs \: 4000}}[/tex]
[tex] \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \boxed {\tt {\: Rs \: 4000}}}}}}[/tex]
Hope I helped! Let me know if you have any questions regarding my answer and don't hesitate to reach out to me if you need any assistance! :)Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x. Which equation can be used to find the measure of angle LJK? sin(x) = Ten-fifteenths sin(x) = Fifteen-tenths cos(x) = Ten-fifteenths cos(x) = Fifteen-tenths
Answer:
cos(x) = Ten-fifteenths
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between the adjacent side and the hypotenuse is ...
Cos = Adjacent/Hypotenuse
cos(x) = 10/15
Answer:
c
Step-by-step explanation:
A shopkeeper sells a DVD player at a price RM 2,500. If the cost price of the DVD player was RM 3,500, find the profit/loss in which the shopkeeper is. Also, find the percent for the same.
Answer:
see explanation
Step-by-step explanation:
Since the player was sold for less than what was paid then a loss is made.
loss = 3500 - 2500 = 1000
percent loss = [tex]\frac{loss}{cost}[/tex] × 100% , thus
percent loss = [tex]\frac{1000}{3500}[/tex] × 100% ≈ 28.6% ( to 1 dec. place )
Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-2, 4, 2)
Where x = -2, y = 4, and z = 2.
Step-by-step explanation:
We are given the system of three equations:
[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]
And we want to find the value of each variable.
Note that both the second and third equations have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.
Solve the second equation for z:
[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]
Likewise, solve the third equation for y:
[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]
Substitute the above equations into the first:
[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]
Hence, x = -2.
Find z and y using their respective equations:
Second equation:
[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]
Third equation:
[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]
In conclusion, the solution is (-2, 4, -2)
Answer:
x = -2
y =4
z=-2
Step-by-step explanation:
4x−y−2z=−8
−2x+4z=−4
x+2y=6
Solve the second equation for x
x = 6 -2y
Substitute into the first two equations
4x−y−2z=−8
4(6-2y) -y -2 = 8
24 -8y-y -2z = 8
-9y -2z = -32
−2(6-2y)+4z=−4
-12 +4y +4z = -4
4y+4z = 8
Divide by 4
y+z = 2
z =2-y
Substitute this into -9y -2z = -32
-9y -2(2-y) = -32
-9y -4 +2y = -32
-7y -4 = -32
-7y =-28
y =4
Now find z
z = 2-y
z = 2-4
z = -2
Now find x
x = 6 -2y
x = 6 -2(4)
x =6-8
x = -2
Use the drawing tool(s) to form the correct answer on the provided graph. The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x). f(x) + 6
Answer:
[tex]f(x)=x+6 \\[/tex]
Step-by-step explanation:
The transformation is a translation 6 units up.
[tex]f(x)=x+6 \\[/tex]
We can use the parent function f(x)=x, which is a linear function to graph this function.
Then just translate the function 6 units up.
Answer:
on the x-axis to the left -1 and on the y-axis up 4
Step-by-step explanation:
Start from the -2 on the y-axis and go up on the y-axis 6 times and you should be at 4 on the y-axis. But to finish the problem you have to figure out the first line.
To do that start from the -2 on the y-axis then count up till its on a corner in the graph (rise 4 up on the y-axis then to the right once) so the fraction is 4/1
so rise 6 on the y-axis, you should be at 4 then use the formula rise/run 4/1
step 1 go up 6 times y-axis
step 2 use 4/1 rise from the 4 on the y-axis the run 1 to the right
It was 100% when I did it
Combine like terms to simplify the expression: -5.55-8.55c+4.35c
Answer:
-5.55 - 4.2c
Step-by-step explanation:
-5.55 - 8.55c + 4.35c
'-8.55c' and '4.35c' are like terms because of them containing the same variable of 'c'.
Combine:
-5.55 - 8.55c + 4.35c
-8.55 + 4.35 = -4.2-5.55 - 4.2c
Hope this helps.
The equation of the line in this graph.
DUE NOW PLEASE HELP!!!
Factor completely x2 − 10x + 25.
(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)
Answer:
(x - 5)(x - 5)
Step-by-step explanation:
[tex] {x}^{2} - 10x + 25 \: is \: the \: expansion \\ of \: {(x - 5)}^{2} \\ {(x - 5)}^{2} = (x - 5)(x - 5)[/tex]
The complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
How to factor a quadratic expression?A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.
How to solve the given question?In the question, we are asked to factor the quadratic expression x² - 10x + 25 completely.
Comparing x² - 10x + 25 to ax² + bx + c, we get a = 1, b = -10, and c = 25.
To factor the expression we will use the mid-term factorization method, and try to break b in such two numbers whose product = ac.
Now, ac = 1 * 25 = 25. b = -10, which can be broken as -5, and -5.
Therefore, we can write the given expression as:
x² - 10x + 25
= x² - 5x - 5x + 25, mid-term factorization
= x(x - 5) -5(x - 5), grouping
= (x - 5)(x - 5), grouping.
Therefore, the complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
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2 hours 40 minutes +11 hours 40 minutes
Answer:
14 hours 20 minutes
Step-by-step explanation:
→ Convert 2 hours and 40 minutes into minutes
2 hours + 40 minutes ⇒ 2 hours = 120 minutes + 40 minutes ⇒ 120 + 40 ⇒ 160 minutes
→ Convert 11 hours and 40 minutes into minutes
11 hours + 40 minutes ⇒ 11 hours = 660 minutes + 40 minutes ⇒ 660 + 40 ⇒ 700 minutes
→ Add the total minutes together
700 minutes + 160 minutes = 860 minutes
→ Convert 860 minutes into hours
860 minutes = 14 hours + 20 minutes