Consider the numbers as, if we assume our first number to be x and second number being y, then from the given information we will be having the following equations :
[tex]{:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}[/tex]
Now, rewrite the second equation as ;
[tex]{:\implies \quad \sf 3(x+y)=-12}[/tex]
Divide both sides by 3 ;
[tex]{:\implies \quad \sf x+y=-4\quad ---(i)}[/tex]
Now, consider the second equation of the above cases
[tex]{:\implies \quad \sf 5x+2y=4\quad ---(ii)}[/tex]
Now, multiply (i) by 2 on both sides :
[tex]{:\implies \quad \sf 2x+2y=-8\quad ---(iii)}[/tex]
Now, subtracting (ii) from (iii) will give us :
[tex]{:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}[/tex]
[tex]{:\implies \quad \sf 2x+2y-5x-2y=-12}[/tex]
[tex]{:\implies \quad \sf -3x=-12}[/tex]
[tex]{:\implies \quad \boxed{\bf{x=4}}}[/tex]
Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield [tex]{\boxed{\bf{y=-8}}}[/tex]
Hence, we can conclude that :
[tex]{\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}[/tex]
a woman 1.65. tall stood 50m away from the foot of a tower,and observe that the angle of elevation of the top of the tower to be 50⁰ what is the height of the tower
[tex]\sf\huge\underline{\star Solution:-}[/tex]
[tex]\rightarrow[/tex]Let the women's height be AE and distance between the women and tower be AC.
Also let the height of tower be BC.
[tex]\rightarrow[/tex]Now, clearly it is forming a triangle.
So, in triangle ABC,
[tex]\rightarrow[/tex][tex]\sf{Tan50° \:= \: \frac{BC}{AC}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{1.19 \:= \: \frac{BC}{50}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{1.19 ×50\:= \: BC}[/tex]
[tex]\rightarrow[/tex][tex]\sf{59.5m\:= \: BC}[/tex]
[tex]\rightarrow[/tex]Hence, BC = 59.5m
So, BD(total height of the tower)[tex]\sf{ = \:BC+CD}[/tex]
[tex]\sf{= \:59.5+1.65}[/tex]
[tex]\sf{=\: 61.15m}[/tex]
Therefore, total height of the tower =[tex]\sf\purple{ 61.15m.}[/tex]
________________________________
Hope it helps you:)
Answer:
61.24 m to the nearest hundredth.
Step-by-step explanation:
tan 50 = H / 50
H = 50 tan 50
Height of the tower = H + height of the woman
= 50 tan 50 + 1.65
= 61.2377 m
Each model represents one whole. In which model does the shaded section represent the
product of 5/8and 3/8 ?
You would show the answer choices for this one. 5/8 x 3/8 is 15/64 or about 0.234375.
Match each action with its effect on the set of scores shown. Use each action only once.
90, 85, 35, 70, 67, 76, 90, 79, 94, 100, 87, 61, 56, 80, 67, 65
The change that will occur to the mean, median, mode of the data matched as follows:
1. e
2. b
3. d
4. a
5. c
What is the Mean fo a Data Set?To find the mean, the sum of all the values is divided by the number of values.
Given the data, 90, 85, 35, 70, 67, 76, 90, 79, 94, 100, 87, 61, 56, 80, 67, 65, therefore:
1. 35 is an extreme value, so it is an outlier. If we remove 35, the greatest change will be on the mean. (e)
2. If we remove 90, 67 will have the highest frequency. This means the mode of the data will change to 67. (b)
3. If 76 is removed from the data, the median of the data would be 79. (d)
4. If we remove 100, the range of the data would be, 94 - 35 = 59. (a)
5. If we remove 94, the mean of the data = 1108/15 = 73.87
This means the mean of the data will change to 73.87 if we remove 94. (c)
Learn more about the mean of a data on:
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Find all relative maximum and minimums of f(x) =2x^3-3x^2-12x+5 Explain your steps in detail.
Answer:
The relative minimum is (3,-4) and the relative maximum is (-2,1)
Step-by-step explanation:
The first step is to take the derivative of f(x)
By using the power rule which is d/dx x^n=nx^n-1 you will find that the derivative is 6x^2-6x-12
The next step is to set the derivative = to 0 and by doing that you will obtain x being equaled to -2 and 3
Put -2 and 3 on a sign chart and determine the behavior for both of those functions
The outcome of your sign chart should be + - + because of the odd multimplicity of (x-3) and (x+2).
The next step is to find the f(x) values or y values of your two points
By plugging in 3 into f(x), you get -4 and by plugging in -2 into f(x) you get 1
Since there was interval given, I cannot find the absolute extremas of this function.
when asked to factor the x^2 - 100, a student gives the answer (x -10) (x-10). what is wrong with this answer?
[tex]x^2-100\\\\=x^2-10^2\\\\=(x+10)(x-10)\\\\\text{The difference of two squares formula is}~ a^2 -b^2 =(a+b)(a-b),\\\\\text{So, the student did not apply it properly}[/tex]
Pls help me worth 50 points + brainliest
(i only can give brainliest if 2 PEOPLE answer)
Answer:
$19.90
Step-by-step explanation:
Cost at Best Computers
$299 x (100 - 40)%$299 x 60%$299 x 0.6$179.40Cost at Val-U-Mart
$299 x (100 - 30)% - $10$299 x 70% - $10$299 x 0.7 - $10$209.30 - $10$199.30Money saved
199.30 - 179.40$19.90Find the slope of the line graphed below.
Answer:
—7/3
Step-by-step explanation:
1) Choose two points on it.
like (1,3) and (4,—4)
2) slope is
[tex]slope = \frac{y2 - y1}{x2 - x1} = \frac{3 + 4}{1 - 4} = \frac{7}{ - 3} = - \frac{7}{3} [/tex]
Answer:
-7/3
Step-by-step explanation:
Slope formula:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
The two points on the graph are (1,3) and (4,-4).
Substitute into the formula:
[tex]\frac{-4 - 3}{4 - 1}[/tex]
Simplify:
[tex]\frac{-4 - 3}{4 - 1} = \frac{-7}{3}[/tex]
what is fhe solution of the system of these equations? (i’m giving brainliest)
Answer:
Top-left system: (3,5)
Bottom-right
system: (-1,0)
Step-by-step explanation:
One way to solve a system of equations is to graph them. The solution is the point of intersection (where the lines cross). If you need to give the x-value and y-values separately, the first number in the pair is the x and the second number is the y.
I need help please. What is the similarity statement for the triangle pair?
A. ΔXYZ~ΔNEW
B.ΔXZY~ΔNWE
C.ΔYZX~ΔNWE
D. ΔZYX~ΔENW
PLEASE HELP BEST ANSWER GETS BRAINLY
Answer:
it is the third one 1,133.54 in²
Step-by-step explanation:
38÷2=19 = R
19²×3.14 = 1,133.54 in²
The triangles below are similar. Find x.
a. 1
b. 2
c. 3
d. 4
Answer:
a. 1
Step-by-step explanation:
[tex]\frac{x+2}{x} =\frac{6}{2} =3[/tex]
The ratio is 1:3
[tex]x+2=3x[/tex]
[tex]2=3x-x\\2=2x\\[/tex]
x = 2/2 = 1
Hope this helps
Wall Drugs offered an incentive stock option plan to its employees. On January 1, 2021, options were granted for 69,000 $1 par common shares. The exercise price equals the $5 market price of the common stock on the grant date. The options cannot be exercised before January 1, 2024, and expire December 31, 2025. Each option has a fair value of $1 based on an option pricing model.
What is the total compensation cost for this plan?
What is the area of this figure?
Enter your answer in the box.
in2
8 in.
116 in.
20 in.
Answer:
8Step-by-step explanation:
I think we should add all the numbers when you multiply them by 5 then you will get 8.8
What is the value of x in this equation? 5x= 15
Answer:
x=3
Step-by-step explanation:
15 divided by 5= 3
5(3)=15
so x=3
Form a polynomial whose zeros and degree are given. Zeros: 2, multiplicity 1; 4, multiplicity 2; degree 3
Answer:
If the polynomial is degree 3, then it is of the form y = Ax3 + Bx2 +Cx + D
And if the zeros are -2 with multiplicity of 1, then the factor is (x+2)1 = x+2
The other zero is -4 with multiplicity of 2, so it's factor is (x+4)2 = x2 +8x+16
So in general, if we let A = 1, then the polynomial is y = (x+2)(x+4)2 which multiplies out to
(x+2)(x2+8x+16) = x3 + 8x2 + 16x + 2x2 + 16x + 32
Combining like terms gives the polynomial:
y = x3 +10x2 + 32x + 32
If A is not 1, then y = A(x3 +10x2 + 32
With that in mind, try to answer the question.
If the diameter of the moon is 3476 km, what is the circumference of the moon,
in kilometers? (Round your answer to the nearest thousand kilometers.)
Answer
Answer:
10920.176064km
Step-by-step explanation:
Circumfrence = 2*pi*radius
radius = diameter/2
r = 3476/2
c=2(pi)r
c=2(pi)(3476/2)
c=10920.176064
The sale tax rate is 5%. Jadon buys a shirt at $200.What will be the total cost, including tax
Madison's favorite part of pizza is the crust. Pizza sizes are determined by their
diameter. Which size pizza should Madison order to get 37.68 inches of crust?
Answer:
Step-by-step explanation:
Use the information shown in the line plot. What is the total weight of the 4 heaviest melons?
Answer:
22.5 lbs
Step-by-step explanation:
the four heaviest melons are 5 1/2, 5 1/2, 5 1/2, and 6 pounds
when you add those together
5.5 + 5.5 + 5.5 + 6
you get
22.5 lbs
Find the slope of the line passing through the points (-4, 1) and -9,5)
The slope of the line is -0.8.
The formula for distance is...
y2−y1 5−1
______= ________
x2−x1 −9− −4
And so when simplified we get
4
__
-5
Giving us -0.8.
Help i will give thanks to the first to answer
Answer:
The value of the expression is 21
Step-by-step explanation:
You need to plug 5 into z
Expression:
5z-4
5(5) - 4
Notice that 5 shall be multiplied meaning 5 x 5
25-4
= 21
It's 21 since 5 times 5 is 25 subtracted 4 is 21
thought it was something else
The following statement is a Contingency: (P and (P => Q)) => Q T True F False
The statement (p and (p => q)) => q) is not a contingency because of it evaluating to only true while a contingency statement includes both true values and some false values.
What is a contingency statement?Contingency is a statement in which there are some true and some false values for every value of its propositional variables.
The statement given is (p and (p => q)) => q), or in more symbolic way, it is: ((p ∧ (p → q)) → q)
Now, let we evaluate it for p = False, and q = False.
Then we get:
(p → q) = T (as False implied False)
Now, (p ∧ (p → q)) is F and T which is F
Then, ((p ∧ (p → q)) → q) is F → F which is True, or T.
Thus, p = F,and q = F makes ((p ∧ (p → q)) → q) = T
Similarly, the truth table for the statement (p and (p => q)) => q) or simply ((p ∧ (p → q)) → q) is:
p q ((p ∧ (p → q)) → q)
F F T
F T T
T F T
T T T
Since all the values are true, thus, this isn't a contingency.
Thus, the statement (p and (p => q)) => q) is not a contingency because of it evaluating to only true while a contingency statement includes both true values and some false values.
Learn more about contingency here:
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I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. A ramp formed the angles shown to the right. What are the values of A and B?
Answer:
A=167⁰, B=13⁰
Step-by-step explanation:
A=167⁰
B=13⁰
I HOPE IT HELPED YOU
Answer:
a° = 167°, b° = 13°
Step-by-step explanation:
since the angles in a triangle add to 180°, we can work out b°
90° (right angle) - 77° = 167°
180° - 167° = 13°
since the angle of a straight line is also 180°, a° would be 180° - 13° which is 167°.
What is the slope-intercept equation for this line?
Answer:
the slope intersection is xy
y=-3x+4
Solution:We are given 2 points: (1,1) and (0,4)We can use these points to find the slope of the line:[tex]m=\displaystyle\frac{y2-y1}{x2-x1}[/tex][tex]\displaystyle\frac{4-1}{0-1}[/tex][tex]\displaystyle\frac{3}{-1}[/tex][tex]-3[/tex]Now, let's identify the y-intercept.The y-intercept is the point where the graph touches the y-axis.Since the graph touches the y-axis at (0,4) the y-intercept is equivalent to (0, 4) or 4.Hope it helps.
Do comment if you have any query.
There are two taxi cab companies in Redwood. Their charges are listed below.
Redwood Taxi
$2.00 for the first mile
plus
$1.00 for each additional mile
Max's Taxi Service
$5.00 for the first mile
plus
$0.50 for each additional mile
According to the graph below, for how many miles will the charges from both taxi cab companies be equal?
1. 8
2. 1
3. 7
4. 4
Answer:
The answer is number 3 or 7 miles is when the charges in both the taxi cab companies will be equal.
Step-by-step explanation:
Redwood Taxi:
$2.00 + $1.00(6)
$2.00 + $6.00 = $8.00
Max's Taxi Service:
$5.00 + $0.50(6)
$5.00 + $3.00 = $8.00
Easier Solution:
Look at the image and see what coordinate both lines cross at. The X coordinate or 7 would be the answer.
Answer:The answer is number 3 or 7 miles is when the charges in both the taxi cab companies will be equal.
Step-by-step explanation:
Redwood Taxi:
$2.00 + $1.00(6)
$2.00 + $6.00 = $8.00
Max's Taxi Service:
$5.00 + $0.50(6)
$5.00 + $3.00 = $8.00
Easier Solution:
Look at the image and see what coordinate both lines cross at. The X coordinate or 7 would be the answer.
Which decimal is equivalent to 0.75?
Answer:
Fracción
3/4
Fracciones equivalentes
6/8
Decimal
0,75
Answer:
3/4.
Step-by-step explanation:
0.75 = 75/100
= 3/4
Write an inequality for the given graph.
Answer:
y ≤ -3/4x + 3Step-by-step explanation:
Calculating slope
m = Rise/Runm = -3/4Y-intercept : (0, 3)
Equation of line
y = mx + cy = -3/4x + 3Inequality
y ≤ -3/4x + 3The sum of 15 and twice a number is -31. Find the number
Answer:
-23
Step-by-step explanation:
15 + 2n = -31
15 + 2n - 15 = -31 - 15
2n = -46
n = -23
solve for x ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou ~
Answer:
x²-5x+6 =0
x²-3x-2x+6 =0
x(x-3)-2(x-3)=0
(x-2)(x-3) =0
x-2 =0, x-3 = 0
x=2 , x = 3
x = 2 or 3 answer
Julie has 30 pounds of chocolate that she is selling for a fundraiser. She is putting the chocolate into boxes that each hold 2/3 pound of chocolate. How many boxes can she fill?
Answer:
45 boxes.
Step-by-step explanation:
30 / 2/3
= 30 * 3/2
= 90/2= 45