Answer:26.9 feet
Step-by-step explanation:
SOH-CAH-TOA
\tan M = \frac{\text{opposite}}{\text{adjacent}}=\frac{74}{x}
tanM=
adjacent
opposite
=
x
74
\tan 70=\frac{74}{x}
tan70=
x
74
x\tan 70=74
xtan70=74
Cross multiply.
\frac{x\tan 70}{\tan 70}=\frac{74}{\tan 70}
tan70
xtan70
=
tan70
74
Divide each side by tan 70.
x=\frac{74}{\tan 70}=26.9338\approx 26.9\text{ feet}
x=
tan70
74
=26.9338≈26.9 feet
Type into calculator and roundto the nearest tenth of a foot.
L
M
N
74
26.9
(opposite of ∠M)
(adj. to ∠M)
(hypotenuse)
70°
A bookcase is to have 5 shelves including the top. The height of the bookcase is to be 3 feet more than the width and only 20 feet of lumber is available. Use an equation to determine the width and height of the bookcase?
Answer:
The width and height is 1.375 and 4.375 respectively
Step-by-step explanation:
The computation of the width and height of the book case is shown below:
Let the width be w
And, the height be h
So, the following equations should be made
5w+3h=20 ......(i)
h = w + 3......(2)
Now
put the value of h in equation (1)
5w + 3(w + 3) = 20
5w + 3w + 9 = 20
8w = 20-9
8w = 11
w = 11 ÷ 8
= 1.375
And, the height would be
= 1.375 + 3
= 4.375
Can someone please help????
Answer:
your answer is the third one
Step-by-step explanation:
Answer:
its 4
Step-by-step explanation:
What is the slope of the equation: y = - 5x -6
Answer:
-5
Step-by-step explanation:
The slope is always the coefficient of x, and the coefficient of x here is negative 5.
Please help!
(Vieta's Formulas) Let [tex]r[/tex], [tex]s[/tex], and [tex]t[/tex] be solutions to the equation [tex]$2x^3 - 3x^2 + 4x - 1 = 0$[/tex]. Find [tex]$r^2+s^2+t^2$[/tex].
Please include an explanation as well :)
We are given the polynomial:
2x³ - 3x² + 4x - 1 = 0
We need to find the value of r² + s² + t² where r,s,t are the solutions.
Simplifying r² + s² + t²:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
[since a²+b²+c² = (a+b+c)² - 2(ab + bc + ca)]
Using the Vieta's formulae:
Above, we can see that in order to find the value of r² + s² + t², we need to find the value of the sum of solutions and sum of solutions taken 2 at a time.
Sum of roots:
We know that the Vieta's formula to find the sum of roots is:
Sum of roots = [tex]-\frac{b}{a}[/tex]
Where b and a are the coefficients from the general form: ax³ + bx² + cx - d
We notice that for the given equation, b = -3 ; a = 2
Sum of roots = [tex]-(\frac{-3}{2})[/tex]
Sum of roots = [tex]\frac{3}{2}[/tex]
Hence, the sum of roots (r + s + t) = 3/2
Sum of roots taken two at a time:
We know that the Vieta's formula to find the sum of roots taken 2 at a time is: Sum of roots taken 2 at a time = [tex]\frac{c}{a}[/tex]
Where c and a are the coefficients from the general form: ax³ + bx² + cx - d
for the given equation, c = 4 ; a = 2
Sum of roots taken 2 at a time = [tex]\frac{4}{2}[/tex]
Sum of roots taken 2 at a time = 2
Hence, the sum of roots taken 2 at a time (rs + st + rt) = 2
Finding the value of r² + s² + t²:
We proved before that:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
now that we know the values of (r + s + t) and (rs + st + rt), we can plug those values to get our answer
r² + s² + t² = ([tex]\frac{3}{2}[/tex])² - 2(2)
r² + s² + t² = ([tex]\frac{9}{4\\}[/tex]) - 4
r² + s² + t² = [tex]\frac{9 - 16}{4\\}[/tex]
r² + s² + t² = [tex]\frac{-7}{4}[/tex] = -1.75
Hence, the value of r² + s² + t² is -1.75
Can someone plz help me with this one problem plz!!!
Answer:
alam nyo BA ANG sagot dito?
Step-by-step explanation:
haha sino may alam?
If x=−5, what is the value of 7−x(2x+1)?
Answjnweijfbiqwerf
Step-by-step explanation:
help is due tomorrow morning
Answer:
5) vertical angles: FGH, KGJ
adjacent angles: FGH, FGK
6) vertical angles: LMS, PMQ
adjacent angles: NML, NMR
-5p + 3.5 = 8.5 solve for p
Answer:
p= -1
Step-by-step explanation:
Does the rule y = −2 · 2x represent a linear or an exponential function?
Exponential
Please help and show your work!!
Factor the following
[tex]3x^{2} -4x-7[/tex]
Answer:
[tex] \sf \huge \boxed{ \boxed{(3x - 7)(x + 1)}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:factoringPEMDASlet's solve:[tex] \sf \: rewrite \: - 4x \: as \: 3x - 7 x: \\ \sf {3x}^{2} + 3x - 7x - 7[/tex][tex] \sf factor \: out \: 3x: \\ \sf3x( x + 1) - 7x - 7[/tex][tex] \sf factor \: out \: - 7: \\ \sf3x( x + 1) - 7(x + 1)[/tex][tex] \sf \: group : \\ (3x - 7)(x + 1)[/tex]and we are done!
Explanation:
1.) Use the sum-pruduct pattern
3x^2-4x-7
3x^2+3x-7x -7
Common factor from two pairs
3x^2 +3x-7x-7
3x(x+1) - 7(x+1
Rewrite in factored form
3x(x+1) - 7(x+1)
(3x-7) (x+1)
Answer:
(3x-7)(x+1) I know we both have the same answerWhat is 190% of 69.70?
Answer:
[tex]\huge\boxed{132.43}[/tex]
Step-by-step explanation:
= 190 % of 69.70
[% means out of 100 and "of" means to "multiply]
= [tex]\displaystyle \frac{190}{100} * 69.70[/tex]
= 1.9 * 69.70
= 132.43
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
132.43
Step-by-step explanation:
Calculate the percentage of a number.
For example: 190% of 69.70 = 132.43
3a²b3(-4b3 + 2b2a - 7) =
Answer:
the answer is =6a^3b^5−12a^2b^6−21a^2b^3
Step-by-step explanation:
hoped I helped:)
A farmer is creating a budget for planting soybeans and wheat. Planting soybeans costs $200 per acre and planting wheat costs $500 per acre. He wants to spend no more than $100,000 planting soybeans and wheat. Name ONE SOLUTION to the inequality you wrote above.
inequality is (300,900)
Answer:
200? if not right ill delete my answer
Step-by-step explanation:
Evaluate using P E M D A S 2 x 3 + 4
Step-by-step explanation:
We would do multiplication first, because of order of operations.
2x3=6
Now we add.
6+4=10
hope it helps! :3
PLS HELP I WILL DO ANYTHING
Answer:
the solution for x is x=40
Solve each equation.
d(d+3)-d(d-4)=9d-16
Answer:
2d+3d-2d+4d= 9d-16
2d is cancelled
3d+4d=9d-16
7d=9d-16
16=9d-7d
16=2
16/2
d=8
An ice cube tray has 12 sections. Each section has the shape of a 3 m cube. What is the volume of water used to fill the tray?
Answer:
324 m³
Step-by-step explanation:
each cube = 3x3x3 = 27 m³
27 m³ 12 = 324 m³
Kareem received $50 during his birthday. In addition, he saves $10 each week. Which equation can help find w, the number of weeks it will take Kareem to save a total of $200?
Answer: 50+10w=200 w=15
Step-by-step explanation:
So we know that Kareem starts off with $50 and every week he gains an additional $10 so as many weeks it takes to get $150 in addition to the $50 he already has to get $200. so $50+$10w=$200 where w represents the number of weeks it takes until the sum is 200
Consuelo won the lottery. He can receive $100,000 or $3 on day 1, $9 on day 2, $27 on day 3... etc for 30 days. Which option will give Consuelo the most money?
how would I solve this? I'm not sure what to do on this question, don't give me the answer, just kinda tell me what to do
Answer:
ordü use uuuuuv bûsh!!!!!!!!!!
-2.5 x 3 = with shown work pls
Answer:
7.5
Step-by-step explanation:
-2.5 x 3 = 7.5
Answer:-7.5
Step-by-step explanation:
(−2.5)(3)
=−7.5
I need this answer ASAP! Please help!
A ladder is leaning against a building. The ladder forms an angle of 77° with the ground. The distance from the base of the ladder to the base of the building is 8 feet.
Answer:
Step-by-step explanation:
sin77=h/8
h=8sin77
h=8(0.9744)
h=7.7952ft
Joey earns a weekly salary of $325 plus a commission on his total sales. Last week his sales were $2950, and he earned a total of $915. What was his commission rate?
Answer:
Commission rate is 20%.
Step-by-step explanation:
Joey's weekly salary is $325
Plus a commission on his total sales.
Let commission is x% on his total sales.
So, we can set up equation for the given information as
325+x%(2950)= 915
Solve this equation for x%.
Subtract both sides 325
x%(2950) =590
Divide both sides by 2950
x%=0.2
We know x% means it is [tex]\frac{x}{100}[/tex]
So, [tex]\frac{x}{100} =0.2[/tex]
Multiply both sides by 100
x=20%.
So, commission rate is 20%
x
4
4x + 10x+4
a (2n+1)
Answer:
1st =14x+4
2nd =2an+a
Step-by-step explanation:
1st Let's simplify step-by-step.
4x+10x+4
Combine Like Terms:
=4x+10x+4
=(4x+10x)+(4)
=14x+4
2nd
a(2n+1)
=(a)(2n+1)
=(a)(2n)+(a)(1)
=2an+a
Hope this helps :)
PLS BRAINLIEST
An advertising company is curious about the impact the lengths of their television advertisements have on viewers' feelings about a product. They showed advertisements of different lengths to a group of volunteers and asked the volunteers to rate how positive they felt about the product on a scale of 111 to 101010. Their data is shown in the table below.
Avg. product rating/ 6.0/ 7.0/ 5.0/ 3.0/ 2.5
Ad length (seconds) 30/ 45/ 60/ 75/ 90
Answer:
Graph C
Step-by-step explanation:
Khan Academy
The correct graph that represents the given data effectively would be:
Graph C
The given data offers the average ratings of the product and the length of their advertisements in seconds.The third graph most effectively shows the data as it contains provided variables on the appropriate axis i.e. ad length on the x-axis and the average rating on the y-axis. The other graphs fail to represent the explanatory variable and the other variable effectively.Thus, 'graph C' in the scatter plot format is the correct answer.
Learn more about "Data" here:
brainly.com/question/16348111
If m = (3x-1) and n = (3x+1),sjow that x² = mn+1 by 9
Step-by-step explanation:
[tex] {x}^{2} = \frac{mn + 1}{9} [/tex]
[tex](3x - 1)(3x + 1)[/tex]
[tex]9 {x}^{2} - 1[/tex]
[tex] {x}^{2} = \frac{9 {x}^{2 } - 1 + 1 } {9} [/tex]
[tex] {x}^{2} = \frac{9 {x}^{2} }{9} [/tex]
[tex] {x}^{2} = {x}^{2} [/tex]
So this identity is true.
someone please help me ASAP!!!!!!!
Answer:
the change in x is 1, the change in y is 4, the slope is 1/4
Step-by-step explanation:
the time increases by one minutes as the temperature increases by 4 degrees. therefore, every one minutes the temperature increases by four degrees. 1/4
Answer:
1, 4 and 4
Step-by-step explanation:
x = 10-9 = 1
y = 64-60 = 4
Rate of change = temperture / time
= 4/1
= 4.
How do you solve for x in the equation (2x - 3)/5 = (x + 1)/6?
Answer:
x= 23 /7
Step-by-step explanation:
The point (17,−9) is translated to the point (6,2). Select the description of the translation.
A
9 down, 7 right.
B
11 left, 11 up
C
9 right, 11 up
D
11 left, 9 down plzzz answer..
Answer:
11 up , 11 left
Step-by-step explanation:
Given
[tex](17, -9)[/tex] to [tex](6,2)[/tex]
Required
Determine the translation rule
Considering the x coordinates.
From 17 to 6
6 is to the left of 17.
Using the translation rule:
[tex]x = x' + b[/tex]
[tex]17 = 6 + b[/tex]
[tex]17 - 6 = b[/tex]
[tex]11 = b[/tex]
[tex]b = 11[/tex]
Hence: From 17 to 6 is 11 units left translation
Considering the y coordinates.
From -9 to 2
2 is at the top -9.
Using the translation rule:
[tex]y = y' + b[/tex]
[tex]-9 = 2 + b[/tex]
[tex]-9 - 2 = b[/tex]
[tex]-11= b[/tex]
[tex]b = -11[/tex]
The negative value impies a upward translation.
Hence: From -9 to 2 is 11 units up translation
A polygon on a coordinate grid was transformed using the rule (x,y) -> (x-4,y-3). Which of these describes this transformation?
A: a translation 4 units to the left and 3 units down
B: a translation 4 units to the right and 3 units down
C: a translation 4 units to the left and 3 units up
D: a translation 4 units to the right and 3 units up
18x^2-8=0 I have to factor it but I’m not sure how to! Please help!
Answer:
hope it helps...........
Answer:
[tex]x=-2/3, 2/3[/tex]
Step-by-step explanation: