Answer:
5cm
Step-by-step explanation:
50cm x 20cm x 8cm = 8000cm^3
25cm x 64cm = 1600cm^2
1600x=8000
x=5cm
A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?
Answer:
1. EF = 65m
2. DF = 73m
Step-by-step explanation:
1. EF = height of the building = h = 33 / tan 27 = 65m
2. DF = sqrt (65² + 33²) = 73m
The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
From the triangle DEF, we find the value of EF by using tan function.
tan function is a ratio of opposite side and adjacent side.
tan(27)= 33/FE
0.5095 = 33/FE
Apply cross multiplication:
FE=33/0.5095
FE=64.76
Now DF is the hypotenuse, we find it by using pythagoras theorem.
DF²=DE²+EF²
DF²=33²+64.76²
DF²=1089+4193.85
DF²=5282.85
Take square root on both sides:
DF=72.68
In a triangle the the sum of three angles is 180 degrees.
∠D + 27 +90 =180
∠D + 117 =180
Subtract 117 from both sides:
∠D =63 degrees.
Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
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PLEASE HELP!! A 5×5×5 wooden cube was painted and then sawed into 1×1×1 cubes. How many 1×1×1 cubes have exactly two faces painted?
Answer:
36
Step-by-step explanation:
There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)
A cube has 12 edges.
12x3=36
The steepness or grade of a road is expressed as a percent. if a road rises 6feet for every 24 horizontal feet. What is the slope of the road? what percent grade is this ?
Answer:
25%
Step-by-step explanation:
The ratio of rise to run is ...
rise/run = 6 ft/24 ft = 1/4
Expressed as a percentage, this is ...
1/4 × 100% = 25%
_____
Comment on this grade
Interstate highways are limited to a 7% grade. Most local jurisdictions limit the grade of a road to somewhere between 12% and 15%.
Solve the system of equations 2x - y = 11 and x + 3y = -5
Answer:
x = 4, y = -3
Step-by-step explanation:
{2x - y = 11
{x + 3y = -5
You can use the substitution method by solving for x in the second equation:
x + 3y = -5
Subtract 3y from both sides:
x = -3y - 5
Now, substitute this value for x into the first equation:
2x - y = 11
2(-3y - 5) - y = 11
Distribute:
-6y - 10 - y = 11
Add 10 to both sides:
-6y - y = 21
Combine like terms:
-7y = 21
Divide both sides by -7:
y = -3
Next, substitute this value for x into the second equation:
x + 3y = -5
x + 3(-3) = -5
Multiply:
x - 9 = -5
Add 9 to both sides:
x = 4
Answer:
(7, 3)
Step-by-step explanation:
2x - y =11 2x-y =11
-2(x+3y)= (-5)-2 -2x-6y= 10
Then you will cross out the x, and add.
-7y =21 divide 7
y=-21/7 or y=3
Then you plug in the y where the y is and solve
2x-(3) = 11
2x = 14
x=7
Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy
Answer:
she bought 7 cards
Step-by-step explanation
7x5=35 and im sure there is tax
help me plz can i have help
Answer:
6×[tex]10^{-4}[/tex]
Step-by-step explanation:
The graph of f(x) = xx is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
Answer:C and F are correct
Step-by-step explanation:
got it right on edge
please help me.... The question no.b and would like to request you all just give me correct answer.
Answer: see proof below
Step-by-step explanation:
You will need the following identities to prove this:
[tex]\tan\ (\alpha-\beta)=\dfrac{\tan \alpha-\tan \beta}{1+\tan \alpha\cdot \tan \beta}[/tex]
[tex]\cos\ 2\alpha=\cos^2 \alpha-\sin^2\alpha[/tex]
LHS → RHS
[tex]\dfrac{2\tan\ (45^o-A)}{1+\tan^2\ (45^o-A)}\\\\\\=\dfrac{2\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)}{1+\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)}{1+\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{1+\bigg(\dfrac{1-2\tan\A+\tan^2 A}{1+2\tan A+\tan^2A}\bigg)}\\[/tex]
[tex]=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{(1+2\tan A+\tan^2A)+(1-2\tan A+\tan^2 A)}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{2+2\tan^2A}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{2\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}\\\\\\=\dfrac{\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}[/tex]
[tex]=\dfrac{1-\tan A}{1+\tan A}}\times \dfrac{(1+\tan A)^2}{1+\tan^2A}\\\\\\=\dfrac{1-\tan^2 A}{1+\tan^2 A}\\\\\\=\dfrac{1-\dfrac{\sin^2 A}{\cos^2 A}}{1+\dfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{\bigg(\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A}\bigg)}{\bigg(\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}\bigg)}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A+\sin^2 A}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{1}\\\\\\=\cos^2 A-\sin^2 A\\\\\\=\cos 2A[/tex]
cos 2A = cos 2A [tex]\checkmark[/tex]
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answer:
A. 0
Step-by-step explanation:
In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices. Since four is the smallest number, the other two must have four left as well. That means Donavan drank 1 spoiled milk and 2 flat sodas. Therefore, he drank 0 purified water.
A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━
PLS HELP ME I NEED THIS FOR HOMEWORK!!!!
Answer:
36 degrees
Step-by-step explanation:
Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.
(3x+30)+(6x-12)=90
9x+18=90
9x=72
x=8
AOB = 6x-12, so substituting
8 in for x gives us 48-12=36
Clare has 150$ in her bank account. She buys a bike for 200$. What is Clares account balance now?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount left in the bank account is -$50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the bank account = $150
Cost of the bike = $200
The amount left in the bank account.
= 150 - 200
= -$50
Thus,
The amount left in the bank account is -$50.
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Triangle ABC is dilated to form new triangle DEF. If angle A is congruent to angle D, what other information will prove that the two triangles are similar by the AA similarity postulate?
Angle B is congruent to angle E.
Side AB is congruent to side DE.
Angle C is congruent to angle D.
Side BC is congruent to side EF.
Answer:
Step-by-step explanation:
option A , angle B is congruent to angle E { SINCE IT IS AA POSTULATE
Answer:
B=E (b)
Step-by-step explanation:
help me find VW and YZ
Answer:
VW=35
YZ=50
Step-by-step explanation:
As they are similar triangles with a ratio of 1:2 and we know VW:XZ=1:2, we can make the equation:
2(4y+7)=12y-14
8y+14=12y-14
4y=28
y=7
So, VW=4(7)+7=35.
Similarly, you can find YZ through VT:
2(7x-17)=8x+2
14x-34=8x+2
6x=36
x=6
Therefore, YZ=8(6)+2=50.
-5+2(10b-2)=31 need help thanks!
Answer:
[tex]\Large \boxed{b=2}[/tex]
Step-by-step explanation:
-5+2(10b-2)=31
Expand brackets.
-5+20b-4=31
-9+20b=31
Add 9 on both sides.
20b=40
Divide both sides by 20
b=2
Answer:
b = 2Step-by-step explanation:
-5+2(10b-2)=31
Multiply the terms in the bracket
That's
- 5 + 20b - 4 = 31
Group like terms
Send the constants to the right side of the equation
That's
20b = 31 + 4 + 5
Simplify
20b = 40
Divide both sides by 20
We have the final answer as
b = 2Hope this helps you
PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. What is the volume of the glass?
Answer:
0.5 L
Step-by-step explanation:
volume of bottle: 1.5 L
amount of water = 1.5 L
volume of glass: x
3/4 full is the same as 0.75 full
vol of water in bottle + vol of water in glass = total vol of water
0.75(bottle) + 0.75(glass) = 1.5
0.75(1.5) + 0.75x = 1.5
0.75x = 0.375
x = 0.5
Name five fractions whose values are between 3/8 and 7/12
Answer:
convert them to decimasls
Step-by-step explanation:
convert thhem to decimals to make it easier
Answer:
1/2 2/4 4/8 6/12 9/18
Step-by-step explanation:
The coefficient of 8.2 N is
8
2
16
Answer:
2
Step-by-step explanation:
A coefficient is the number placed before the variable. The variable gets multiplied by the coefficient.
The format is not exactly clear with the expression in the question.
Assuming the expression is '8 * 2n', the coefficient would be 2.
'n' is getting multiplied by '2'.
'8' does not have a variable next to it, so it is just a term in the expression.
The product of 8 and 2 is 16. 16 is not in the expression.
If the expression was '8.2n', 8.2 would be the coefficient.
Brainilest Appreciated.
Find the distance between (-5,-6) and (-3,-8 WILL GIVEBRANLIEST TO FIRST PERSON WHO AWNSES WITH EXPLANATION
Answer:
d = √8
d ≈ 2.82843
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in our coordinates into the distance formula:
[tex]d = \sqrt{(-3 + 5)^2+(-8 + 6)^2}[/tex]
[tex]d = \sqrt{(2)^2+(-2)^2}[/tex]
[tex]d = \sqrt{4+4}[/tex]
[tex]d = \sqrt{8}[/tex]
To find the decimal, simply evaluate the square root:
√8 = 2.82843
Answer:
[tex] \boxed{2 \sqrt{2} \: \: units}[/tex]Step-by-step explanation:
Let the points be A and B
A ( - 5 , - 6 ) ⇒ ( x₁ , y₁ )
B ( -3 , - 8 )⇒( x₂ , y₂ )
Now, let's find the distance between these two points:
AB = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
⇒[tex] \mathsf{ \sqrt{( - 3 - ( - 5) )^{2} + {( - 8 - ( - 6))}^{2} } }[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
⇒[tex] \mathsf{ \sqrt{ {( - 3 + 5)}^{2} + {( - 8 + 6)}^{2} } }[/tex]
Calculate
⇒[tex] \mathsf{ \sqrt{ {(2)}^{2} + {( - 2)}^{2} } }[/tex]
Evaluate the power
⇒[tex] \mathsf{ \sqrt{4 + 4} }[/tex]
Add the numbers
⇒[tex] \mathsf{\sqrt{8} }[/tex]
Simplify the radical expression
⇒[tex] \mathsf{ \sqrt{2 \times 2 \times 2}} [/tex]
⇒[tex] \mathsf{2 \sqrt{2} }[/tex] units
Hope I helped!
Best regards!
Find the distance between the points P and Q shown. Question 6 options: A. 73−−√ B. 13−−√ C. 5–√ D. 65−−√
Answer:
[tex]d=\sqrt{73}[/tex]
Step-by-step explanation:
[tex]Q(5, -1)[/tex]
[tex]P(-3, 2)[/tex]
Using the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_2+y_1)^2}[/tex]
[tex]d=\sqrt{(-3-5)^2+(2-(-1))^2}[/tex]
[tex]d=\sqrt{(-8)^2+(3)^2}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{73}[/tex]
[tex]d\approx 8.5[/tex]
Explain how I would rewrite 3^5 * 3^-4 as a base an exponent
Answer:
3^1 or 3
3^5 * 3^-4 are 3^5-4
so, 3^1!
Hope it helps!
Answer:
3^1
Step-by-step explanation:
Since the bases are the same and we are multiplying we can add the exponents
a^b * a^c = a^(b+c)
3^5 * 3^-4
3^ (5+-4)
3^1
Math Question (10 Points):
Answer:
x-axis
Step-by-step explanation:
Answer:
It is the x-axis
Step-by-step explanation:
In a graph, the horizontal part of it is called the x axis.
Here is an definition: horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates
help me plz can somewon help me i am bad at math mostly
Answer:
Definitely the bottom left
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Plz help I’ll mark brainliest
Answer:
Step-by-step explanation:
Using Pythagoras Theorem, hypotenuse = 5
[tex]h = \sqrt{a^{2}+ b^{2}[/tex]
[tex]h = \sqrt{9+16 }\ = \sqrt{25}\ = 5[/tex]
sin x = height / hypotenuse = 3 / 5
cos y = base / hypotenuse = 3 / 5
sin x = cos y = 3 / 5
Help please all questions.
Answer:
A is A=25
B=10
B is 40
C is A=10
B=6.428
hope i helped you
sorry if it is incorrect
PLEASE HELP! 10 POINTS Which line would be the line of best fit for the scatter plot?
Answer:
The first one
Step-by-step explanation:
This line is the best fit for the scatter plot because it touches a lot more points than the second
Answer:
The first line
Step-by-step explanation:
Hey there!
Well the first lie is a positive slope just like the dots whereas,
the second line is a negative slope.
Therefore, the first line is the line of best fit.
Hope this helps :)
What is the solution to the inequality 3t + 9 ≥ 15 ? please answer as soon as you can!!
Answer:
T≥2
Step-by-step explanation:
3t+9≥15
3T≥15-9
3T≥6
T≥2
Answer:
t ≥ 2
t ∈ [2 ; +oo)
Step-by-step explanation:
3t + 9 ≥ 15
3t ≥ 15 - 9
3t ≥ 6
t ≥ 6 : 3
t ≥ 2
t ∈ [2 ; +oo)
In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD. (made a second one since trollers ruined my last one :/ )
Answer:
approximately 5.36
Step-by-step explanation
20 - 9.28 = 10.72
BD = EC
10.72/2 = 5.36
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: 24
Step-by-step explanation:
Colleen painted 7 windows, some of which were her mother's.
Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.
If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.
8+7+3+3+3=24
The total windows in the house are 21.
What is an algebraic expression?It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.
In our given problem, the algebraic relation between different members work output and total windows can be expressed as:
Windows painted by colleen and her mother = 7
Windows painted by father = (Windows painted by colleen and her mother + 1)
= (7 + 1) = 8
∴ Windows painted by father = 8
Now, as given,
2 Windows painted by mother = Windows painted by father
∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4
and Windows painted by colleen = 7 - 4 = 3
Colleen and her 2 brothers paint equal windows;
∴ They painted 3 windows each.
The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:
⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21
Hence the total windows in the house are 21.
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