Answer:
y = 12x + 18
Step-by-step explanation:
Equation of line in slope-intercept form: y =mx +b
Here, m is the slope and b is the y-intercept.
m = 12
Substitute m =12 in the above equation,
y = 12x + b
This line passes through (-2,-6). So, plugin the point in the above equation.
-6 = 12*(-2) + b
-6 = -24 + b
-6 + 24 = b
b = 18
Equation of the line:
[tex]\sf \boxed{\bf y = 12x + 18}[/tex]
The height (h), in feet, of a balloon is calculated by using the equation h= 3+ + 2 where t is time, in seconds.What is the height of the balloon after 30 seconds?A. 60 ftB. 66 ftO C. 92 ftO D. 102 ft
Given data:
The given expression for height is h=3t+2.
Substitute 30 for t in the above expression.
[tex]\begin{gathered} h=3(30)+2 \\ =92\text{ ft} \end{gathered}[/tex]Thus, the height of the balloon after 30 seconds is 92 ft, so option (C) is correct.
can you help me solve part A and B ASAP! THANKYOU
The shape comprises a semicircle, rectangle, and a trapezoid
A) The shape below will illustrate how the side length of the rectangle will be calculated
Part I is the semicircle of diameter
[tex]\begin{gathered} d=8\operatorname{cm} \\ r=\frac{d}{2} \\ r=\frac{8}{2}=4\operatorname{cm} \end{gathered}[/tex]From the diagram above
[tex]AB=r=4\operatorname{cm}[/tex]To find the missing side length of the rectangle , we will use the relation below
[tex]AB+BC+CD=12\operatorname{cm}[/tex]Where.
[tex]\begin{gathered} AB=4\operatorname{cm} \\ CD=3.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} AB+BC+CD=12\operatorname{cm} \\ 4+BC+3.5=12\operatorname{cm} \\ 7.5+BC=12\operatorname{cm} \\ BC=12-7.5 \\ BC=4.5cm \end{gathered}[/tex]The missing side length of the rectangle is = 4.5 cm
Hence,
The rectangle can be represented below as
The formula for the area of the rectangle is
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ \text{where,} \\ \text{length}=8\operatorname{cm} \\ \text{breadth}=4.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ A_{\text{rectangle}}=8\operatorname{cm}\times4.5\operatorname{cm} \\ A_{\text{rectangle}}=36\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Area of the rectangle = 36cm²
B) To calculate the area of the semicircle, we will use the formula below
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ \text{where,} \\ r=4\operatorname{cm} \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ A_{\text{semicircle}}=\frac{\pi\times4^2}{2}=\frac{16\pi}{2}=8\pi \\ A_{\text{semicircle}}=25.13\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the semicircle = 25.13 cm²
To calculate the area of the trapezoid, we will use the formula below
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ \text{where,} \\ a=8\operatorname{cm} \\ b=15\operatorname{cm} \\ h=3.5\operatorname{cm} \end{gathered}[/tex]The diagram below represents the trapezoid
By substituting the values, we will have
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ A_{\text{trapezoid}}=\frac{1}{2}(8\operatorname{cm}+15\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{1}{2}(23\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{80.5\operatorname{cm}}{2} \\ A_{\text{trapezoid}}=40.25\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the trapezoid is = 40.25cm²
To calculate the total area of the shape, we will use the formula below
[tex]\begin{gathered} \text{Total area=} \\ =A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Total area=}A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \\ \text{Total area}=25.13\operatorname{cm}+36\operatorname{cm}+40.25\operatorname{cm}^2 \\ \text{Total area}=101.38\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Total Area of the composite shape = 101.38cm²
Describe the correlation:
r = -.009
strong positive
weak negative
weak positive
moderate negative
The correlation for r = -0.009 is B. weak negative.
What is correlation?The Pearson correlation coefficient (r) is the most commonly used metric for determining a linear relationship. It is a number ranging from -1 to 1 that indicates the strength and direction of a link between two variables. When one variable shifts, the other shifts in the same way.
Positive correlation is graded on a scale of 0.1 to 1.0. Weak positive correlation would be between 0.1 and 0.3, moderate positive correlation between 0.3 and 0.5, and strong positive correlation between 0.5 and 1.0. The stronger the positive correlation, the more probable the equities will move in unison. Having a minus means it's negative correlation.
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What is the value of X in the equation 1/5x - 2/3y = 30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
a) Simplify both sides of the equation.
1/5x - 2/3(15) = 30
1/5x + -10 = 30
1/5x - 10 = 30
b) Add 10 to both sides.
1/5x - 10 + 10 = 30 + 10
1/5x = 40
c) Multiply both sides by 5.
5 * (1/5x) = (5) * (40)
x = 200
Can someone help me in this please
Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
What are supplementary angles?Two angles are considered to be supplementary if their sums total 180 degrees. If two angles in geometry add up to 180 degrees, they are said to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°. When combined, supplementary angles always make a straight angle (180 degrees).So, angles supplementary to ∠3:
∠1 is supplementary to ∠3 (Straight angle)∠2 is supplementary to ∠3 (Inversely opposite angle)∠4 is supplementary to ∠3 (Straight angle)∠5 is supplementary to ∠3 (Adjacent angles)∠6 is supplementary to ∠3 (Alternate angles)∠7 is supplementary to ∠3 (Corresponding angle)(Refer to the image attached below)
Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
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Solve three-fourths + two-sixths = ___.
five-tenths
five-twelfths
twelve-twelfths or 1
thirteen-twelfths or one and one-twelfth
The value of three-fourths + two-sixths is thirteen-twelfths or one and one-twelfth. Option D
What is a fraction?A fraction can be defined as a part of a whole set or element.
There are several types of fractions which includes;
Simple fractionsComplex fractionsMixed fractionsProper fractionsImproper fractionsExamples of simple fractions; 1/ 2, 1/6
Examples of proper fractions; 2/3, 4/7
Examples of improper fractions; 4/3, 3/2
Examples of mixed fractions; 2 1/ 4, 7 1/2
From the information given, we have that;
3/ 4 + 2/ 6
Find the lowest common multiple
9 + 4 /12
13/ 12
Hence, the value is 13/12
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HELP HELP HELP What is the x-intercept of the line with this equation −5x+15y=15 ?
<3
Answer: (-3, 0)
Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.
0 = 1+1/3x
-1 = 1/3x
-3 = x
Answer:
x = - 3
Step-by-step explanation:
To get the x intercept, y has to be equal to 0.
- 5·x + 15·y = 15
- 5·x + 15·0 = 15
- 5·x = 15
x = 15/(- 5)
x = - 3
1013 nearest thousand
Answer: The answer is 1013, it is already rounded as much as it can go.
Step-by-step explanation:
2.) The amount of sleep that elementary school children get per night follows a Normal distribution with a
mean of 9.5 hours and a standard deviation of 0.55 hours.
a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep per
night. Sketch the Normal curve and shade the area under the curve that is the answer to the
question.
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
The amount of sleep that elementary school children get per night be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.
the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to
P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)
P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)
P(9≤ X ≤ 10) = 0.6367
P(X > 12) = P(Z>(12 - 9.50)/0.55)
P(X > 12) = P(Z>4.5455
P(X> 12) = 0.000
THere is zero possibility of student to get more than 12 houtrs of sleep
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
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problem 2 select all of the equations that represent a proportional relationship. (select all that apply.) the remaining length, , of a -inch rope after inches have been cut off: . the total cost, , after an sales tax is added to an item's price, : . the number of marbles each sister gets, , when marbles are shared equally among four sisters: . the volume, , of a rectangular prism whose height is cm and base is a square with side lengths cm: .
An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.
Equation: y = mx and m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
t/p=1.08
C. Equation: x=m/4
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
m/x=4
D. Equation: V= 12s^2
This equation is NOT proportional because side length is squared, so it is not constant linearly.
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Missy rode her bicycle 16 miles in 1 1/4 hours. What was her average speed in miles per hour
Answer: 12.8 miles per hour
Step-by-step explanation:
divide 16 by 1.25 in order to get your answer
please help with this homework
Answer:
a.) x = 5
b.) x = 35/2 = 17.5
Step-by-step explanation:
In both problems, we are trying to solve for x, which means we need to isolate it on one side of the equation.
a.) 5/2 x + 1 = 11
5/2 x = 10
Now to divide by a fraction is the same as multiplying by the reciprocal.
x = 10 * 2/5 = 4
b.) 2/7 x - 3 = 2
2/7 x = 5
To divide by a fraction is the same as multiplying by the reciprocal.
x = 5 * 7/2 = 35/2 = 17.5
Evaluate express your answer in exact simplest form9P4=
The formula for Permutation is,
[tex]^nP_r=\frac{n!}{\left(n-r\right)!}[/tex]The expression given is,
[tex]^9P_4[/tex]Given:
[tex]n=9,r=4[/tex]Plug in n = 9, r = 4
[tex]\frac{9!}{\left(9-4\right)!}[/tex]Simplify
[tex]\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}=9\times8\times7\times6=3024[/tex]Hence, the answer is 3,024.
We an equivalent agression for 40+8(n-3)
Answer:
8n+16
Explanation:
Given the expressions:
[tex]40+8\left(n-3\right)[/tex]First, distribute 8 over the terms in the bracket:
[tex]\begin{gathered} =40+8(n)+8(-3) \\ =40+8n-24 \end{gathered}[/tex]Finally, collect like terms and simplify:
[tex]\begin{gathered} =40-24+8n \\ =16+8n \end{gathered}[/tex]An equivalent expression is 8n+16.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
Step-by-step explanation:
Choose two points on the graph: (-6,-7) and (6,-9)
The straight line equation is: y=mx+b
[tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=\frac{-9-(-7)}{6-(-6)} \\\\m=\frac{-9+7}{6+6} \\\\m=\frac{-2}{12} \\\\m=-\frac{1}{6}\\\\Hence,\ y=-\frac{1}{6}x+b\ \ \ \ \ (1)[/tex]
To determine the coefficient b, take any of the two points,
for example (-6,-7), that is, x=-6 y=-7
Substitute these values into formula (1):
[tex]\displaystyle\\-7=-\frac{1}{6}(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-\frac{1}{6}x-8[/tex]
PLEASE HELP URGENT!!!!
Answer:
Step-by-step explanation:
answer is the first one: square root property of equality
BTS zzz
Answer:
Reflexive property of equality
Step-by-step explanation:
look at the image
What is the solution set for -3x + 12 < 4x - 9
A) x > 21
B) x > 3
C) x < -3
D) x < -21
Answer:
C) x < -3
Step-by-step explanation:
-3x +12 < 4x - 9
-3x -4x < -12 - 9
-7x < -21
x > -3
What is the complete factorization of 6x2 + 9x - 6?
A. 3(2x - 1)(x + 2)
B. (3x + 2)(2x - 3)
C. 3(x-2)(2x + 1)
D. 3(x-2)(2x - 1)
Answer: A. 3(2x−1)(x+2)
The sum of two rational numbers is 4. If one of the numbers is 2/3, then what is the other number
Answer:
10/3
Step-by-step explanation:
Let x be the value of the second rational number. The first rational number is 2/3, and we are told that the sum of these numbers is 4:
x + 2/3 = 4
Therefore:
x + 2/3 = 4
x = 4 - 2/3
x = 12/3 - 2/3
x = (10/3)
how can i find the angle of elevation of the sun to nearest degree?
SOLUTION
From the diagram at the right of the question, a right-angle has been formed already. So we will use SOHCAHTOA to find angle A. Looking at angle A, the opposite side is 140 ft and the adjacent side is 173 ft.
Using TOA, we have
[tex]\begin{gathered} TOA,tanA=\frac{opposite}{adjacent} \\ tanA=\frac{140}{173} \\ tanA=0.80924855 \\ A=tan^{-1}0.80924855 \\ A=38.98146539 \end{gathered}[/tex]Hence the answer is 39 degrees
4. In the graph below, what is the line of reflection for triangle XYZ and triangle X'Y'Z"? (1 point)
the x-axis
Othe y-axis
Ox=2
Oy=2
In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.
Given, the coordinates of the triangle XYZ are:
X = (4,5)
Y = (6,3)
Z = (3,2)
and the coordinates of the triangle X'Y'Z' are:
X' = (0,5)
Y' = (-2,3)
Z' = (1,2)
for image of the triangle XYZ to get reflected and become X'Y'Z',
reflection of axis takes place.
But the images are not identical and symmetrical, so the reflection is not about y axis.
we check for x=2
hence reflection of axis when x=a is :
P(x,y) →x'(2a-x , y)
therefore use the above formula and check the coordinates of the reflected image.
X(4,5) when x=2X(4,5) → X'(2(2)-4 , 5)
x(4,5) → X'(0,5)
Y(6,3) when x=2Y(6,3) → Y'(2(2)-6 , 3)
Y(6,3) → Y'(-2,3)
Z(3,2) when x=2Z(3,2) → Z'(2(2)-3 , 2)
Z(3,2) → Z'(1,2)
hence x=2 is the reflection of triangle XYZ and X'Y'Z'.
Therefore we get the requires answer.
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How do to solve this problem? (The answer is 262 Hz) I don't need to know the question that it is asking. I just want to know how to solve the equation and its answer. I am a grade 10 student if this helps you.
Step-by-step explanation:
Given the formula below
[tex]undefined[/tex]A) 35° B) 55° C) 70° D) 145° In the figure above, lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, what is the measure of Z2?
If lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, the measure of ∠2? is : D) 145°.
Parallel lineBased on the given figure ∠1 and ∠3 form a parallel line.
Now let determine the measure of ∠2
Hence,
∠1+∠3=180 °
35° +∠3= 180 °
∠3 = 180 ° - 35°
∠3 = 145 °
The corresponding angles is ∠4 = ∠3 = 145 °
∠ 2 an ∠ 4 are as well a corresponding angles
So,
∠2 = ∠4 = 145 °
Therefore the we can conclude that the correct option is D.
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What are the solutions to the inequality (x-3)(x=5)greater than or equal to 0
The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals
(-∞,3] or [5,∞) that is x ≥5 or x≤3
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
Given inequality (x-3)(x-5) ≥ 0
It generates two cases either case1 is true or case 2.
Case1. (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0
⇒(x-3) ≥0 and (x-5)≥0
⇒ x ≥ 3 and x ≥ 5
⇒ x ∈ [3,∞) and x∈ [5,∞)
⇒ x ∈ [3,∞) ∩[5,∞)
⇒ x ∈ [5,∞)
∴ x is greater than or equal to 5
Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0
⇒(x-3) ≤0 and (x-5)≤0
⇒ x ≤3 and x ≤ 5
⇒ x ∈ (-∞,3] and x∈ (-∞,5]
⇒ x ∈ (-∞,3] ∩ (-∞,5]
⇒ x ∈ (-∞,3]
∴ x is less than or equal to 3
Solution of the given inequality is case 1 or case 2
⇒ x ∈ [5,∞) or x ∈ (-∞,3]
⇒ x x ∈ (-∞,3] ∪ [5,∞)
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Find the measure of B
5y/3 = 30 solve for y simplify your answer as much as possible
Answer: y= 18
Step-by-step explanation:
5y/3 = 30
First step: multiply 3 on both sides
5y/3 * 3 = 30*3
5y = 90
Second step: divide 5 on both sides (isolating variable)
5y/5 = 90/5
y = 18
Answer:
y = 18
Step-by-step explanation:
[tex]\frac{5y}{3}[/tex] = 30 ( multiply both sides by 3 to clear the fraction )
5y = 3 × 30 = 90 ( divide both sides by 5 )
y = 18
What’s 12:28 reduced
Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.
Step-by-step explanation: I hope this helps!
4z+7 what is the value of z
Answer: it could literally be anything
Step-by-step explanation: if 4*z+7=15 then z=2
Solve for b.49 = b 2b = = 1or
√49 = +/- 7
√16 = +/- 4 as you calculated
Congrats, you did it!
Solve for x. Just write the number. Triangle btw
1 + 6x
70°
55°