Answer: Area of triangle=30 cm²
Step-by-step explanation:
Let's name the triangle ABC.
Assuming these are the 3 sides of the triangle, and naming them a,b,c.
a=5 cm
b=13 cm
c=12 cm
Semi perimeter of the triangle ABC= s = (a+b+c)/2
s=(5+13+12)/2 =30/2=15.
Area of triangle ABC= √(s * (s-a)*(s-b)*(s-c)
= √(15*(15-5)*(15-13)*(15-12)
= √15*10*2*3
= √150*6
=√900
=30 cm²
Area of triangle ABC = 30 cm².
HELP PLEASE! 66pts!
Solve for x. SHOW WORK!
2^(3x+1)=1/4
The solution of the exponential equation is x = -1
How to find the value of x?
We want to solve the exponential equation:
2^(3x + 1) = 1/4
If we apply the natural logarithm in both sides of that equation, we will get:
ln( 2^(3x + 1) ) = ln( 1/4)
(3x + 1)*ln(2) = ln(1/4)
3x*ln(2) = ln(1/4) - ln(2)
x = (ln(1/4) - ln(2))/(3*ln(2)) = -1
The value of x is -1
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In ΔJKL, m∠J = 67° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
23°
113°
157°
78.5°
Answer:
[tex]157^{\circ}[/tex]
Step-by-step explanation:
Using the exterior angle theorem,
[tex]m\angle K=m\angle J+m\angle L=157^{\circ}[/tex]
Find the value of each variable 5x-7
Answer:
-35
Step-by-step explanation:
How to convert lot into units
Answer: divide the area value by 1e+6
Step-by-step explanation:
The following angles are supplementary to each other.
mzA= (4x + 30) and mzB = (2x - 30)°
Determine x.
15
20
30
60
Answer:
30
Step-by-step explanation:
Supplementary angles add to 180°.
[tex]4x+30+2x-30=180 \\ \\ 6x=180 \\ \\ x=30[/tex]
Tricia made a 72% on her science test. if she got 18 problem correct, how many questions were on the test?
Answer: 25 questions
Step-by-step explanation:
Two angles whose sum is 180° are supplementary angles. find the measure of the supplementary angle shown in the figure
Step-by-step explanation:
together they are 180°.
so,
(11x + 2) + (8x + 7) = 180
11x + 2 + 8x + 7 = 180
19x + 9 = 180
19x = 171
x = 171/19 = 9
and the angles are
(11x + 2) = 11×9 + 2 = 99 + 2 = 101°
(8x + 7) = 8×9 + 7 = 72 + 7 = 79°
A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
The total price of the toaster oven, including tax is $51.36.
How to calculate the value?Given that the toaster oven usually sells for $60 and the toaster oven is 20% off, the new price will be;
= Normal price - Discount
= $60 - (20% × $60)
= $60 - $12
= $48
Also, sales tax is 7%, therefore the new price will be:
= $48 + (7% × $48)
= $48 + $3.36
= $51.36
The price is $51.36.
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A square root function has a domain of x≥15 and a range of y≤10.
What is the range of its inverse?
y≤10
x≤15
x≥10
y≥15
Answer:
[tex] y \geq 15[/tex]
Step-by-step explanation:
The range of the inverse is the same as the domain of the original function.
Answer:y>15
Step-by-step explanation:
Find slope of line please no links
Answer:
Step-by-step explanation:
Using
Point A: x= 1 and y=3
And point B: x=-2 and y=-6
use equation of slope and substitute the values
Slope= YB-YA/Xb-Xa
= -6-3/-2-1
=3
ACTIVITY 7
In a pack of cards, there are 52 cards. There are 4 suits diamonds, hearts, spades and
clubs. Each suit has a King, a Queen, a Jack and an Ace. It also has cards for 2. 3. 4.
5, 6, 7, 8, 9 and 10 If the pack has been shuffled so that the cards are in no particular
order, and you select one card from the pack without looking, what is the probability of
selecting
a) a Queen
b) a red Queen
c) a Jack of Hearts
d) a Jack of Hearts or Diamonds
e) any club
f) a six or a seven
g) a black six
h) a picture card (Jack, Queen or King)
Answer:
Step-by-step explanation:
abcdefgh
Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded continuously.
The interest earned on a [tex]$\$ 50,000$[/tex] deposited for 6 years at [tex]$4\frac{1}{8 }\%$[/tex] in compounded continuously is [tex]$\$ 14040.97$[/tex].
Continuous compounding is the mathematical limit of the number of periods across which compound interest can be calculated and reinvested into the account balance. Although it is impractical, the concept of endlessly compounded interest is important in finance. This is an extreme example of compounding because most interest is compounded on a monthly, quarterly, or semiannual basis.
The given amount is [tex]$\$ 50,000$[/tex].
It will be deposited for 6 years.
With [tex]$4\frac{1}{8 }\%$[/tex] interest,
The formula for compounded continuously is
[tex]$$\begin{aligned}&A=P e^{r t} \\&P=50000 \\&r=4 \frac{1}{8}=\frac{33}{8}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}r &=0.04125 \\t &=6\end{aligned}$$[/tex]
Substitute all the values
[tex]$$\begin{aligned}&A=50000 e^{0.04125 \times6} \\&A=50000 e^{0.2475} \\&A=50000\times 1.28081\\&A=64040.96811\end{aligned}$$[/tex]
[tex]$\mathrm{I}=\mathrm{A}-\mathrm{P}$[/tex]
Interest [tex]$=64040.96811-50000=14040.9681$[/tex]
Hence, Interest [tex]$=\$ 14040.97$[/tex]
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On December 13,2007 one U.S. dollar was worth 0.69 euro
On that date, how many dollars was 110.66 euro worth?
Round your answer to the nearest hundredth of a dollar.
-----need a response back ASAP!----------
On that date, how many euro was 77.65 dollars worth?
Round your answer to the nearest hundredth of a euro.
On that date, 110.66 euro was worth 160.38 dollars.
On that date, 77.65 dollars was worth 53.58 euro.
How to calculate the value?Given that one U.S. dollar was worth 0.69 euro, the dollar that was 110.66 euro worth will be:
= Amount of euro / Rate
= 110.66 / 0.69
= 160.38 dollars
The euro that 77.65 dollars was worth will be:
= 77.65 × 0.69
= 53.58 euro
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A cookie recipe uses 0.75 cups of sugar for every 1.25 cups of flour
How many cups of sugar will the recipe need if it uses 5 cups of
flour?
How do I solve this problem step-by-step? 5(7+6)x9+2
Answer:587
Step-by-step explanation: multiply 5 by 7 and 6,thatll give you 30+35=65
then 65 multiplied by 9 is 585 then add2 is 587
Select all of the following that are quadratic equations. 2 x2+ 12 x = 0, x2 - 2 x = 4, x + 1 x3 - 6 x2 + 8 = 0, 5 x - 3 = 0, 5 x - 1 = 3x + 8, 9 x2 + 6 x - 3 = 0
2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are Quadratic equation
Quadratic equations are polynomial equations whose degree is of 2 in one of the variable.
The standard form of quadratic equation is ax²+bx+c = d where a, b and c are real numbers and a ≠ 0.
In general form of quadratic equation , "a" is known as leading coefficient and "c" is known as absolute term of function.
In the given question,
Equation whose max. degree will be 2 will be quadratic .
2x²+12x=0 , equation is quadratic as degree of equation is 2
x²-2x=4 , equation is quadratic as degree of equation is 2
x³-6x²+8=0 , Degree of equation is 3
Therefore , equation is not quadratic
5x-3=0 , Degree of equation is 1
Therefore , equation is not quadratic
5x-1=3x+8 , Degree of equation is 1
Therefore , equation is not quadratic
9x²+6x-3=0 , Degree of equation is 2
It is quadratic equation.
Hence , 2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are quadratic equation
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Consider the function f, where f(x) = 2x2 - x+ 3. Part A Complete the equation to represent f(x + 1). X+Y Select and drag numbers into the empty boxes to correctly complete the equation.
The numeric value of the function f(x) = 2x² - x + 3 at x = x + 1 is given as follows:
f(x + 1) = 2x² + 3x + 4.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 2x² - x + 3.
The point at which the numeric value is calculated as given by:
x = x + 1.
Hence the numeric value is obtaining replacing the two instances of x in the function by x + 1, as follows:
f(x + 1) = 2(x + 1)² - (x + 1) + 3
f(x + 1) = 2(x² + 2x + 1) - x - 1 + 3
f(x + 1) = 2x² + 4x + 2 - x - 1 + 3
f(x + 1) = 2x² + 3x + 4.
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Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
The solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
In the given question we have to solve the system using the Cramer's rule.
The given equations are
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
From the Cramer's rule
[tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Here,
A = [tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right][/tex]
X= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Now D=|A|
D= [tex]\left|\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right|[/tex]
D= [tex]-4\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
D= -4[6×(-3)-(-2)×9]+5[(-3)×(-3)-(-2)×5]+6[(-3)×9-5×6]
D= -4[-18+18]+5[9+10]+6[-27-30]
D= -4×0+5×19+6×(-57)
D= 0+95-342
D= -247
[tex]D_{x}=\left[\begin{array}{ccc}5&-5&6\\4&6&-2\\1&9&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{x}=5\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|+6\left|\begin{array}{ccc}4&6\\1&9\end{array}\right|[/tex]
[tex]D_{x}[/tex] = 5[6×(-3)-(-2)×9]+5[4×(-3)-(-2)×1]+6[4×9-1×6]
[tex]D_{x}[/tex] = 5[-18+18]+5[-12+2]+6[36-6]
[tex]D_{x}[/tex] = 5×0+5×(-10)+6×30
[tex]D_{x}[/tex] = 0-50+180
[tex]D_{x}[/tex] = 130
[tex]D_{y}=\left[\begin{array}{ccc}-4&5&6\\-3&4&-2\\5&1&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{y}= -4\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|-5\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|[/tex]
[tex]D_{y}[/tex] = -4[4×(-3)-(-2)×1]-5[(-3)×(-3)-(-2)×5]+6[(-3)×1-4×5]
[tex]D_{y}[/tex] = -4[-12+2]-5[9+10]+6[-3-20]
[tex]D_{y}[/tex] = (-4)×(-10)-5×19+6×(-23)
[tex]D_{y}[/tex] = 40-95-138
[tex]D_{y}[/tex] = -193
[tex]D_{z}=\left[\begin{array}{ccc}-4&-5&5\\-3&6&4\\5&9&1\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{z}=-4\left|\begin{array}{ccc}6&4\\9&1\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|+5\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
[tex]D_{z}[/tex] = -4[6×1-4×9]+5[1×(-3)-4×5]+5[(-3)×9-5×6]
[tex]D_{z}[/tex] = -4[6-36]+5[-3-20]+5[-27-30]
[tex]D_{z}[/tex] = (-4)×(-30)+5×(-23)+5×(-57)
[tex]D_{z}[/tex] = 120-115-285
[tex]D_{z}[/tex] = -280
As we know that; x=Dx/D, y=Dy/D, z=Dz/D
x=130/(-247)
x= -0.53
y=(-193)/(-247)
y=0.78
z=(-280)/(-247)
z=1.13
Hence, the solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
The end behavior of the given graph is as x → -∞, f(x) → ∞ and as x → ∞ f(x) = ∞.
End behavior of graph
End behavior of the graph refers the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. And the degree and the leading coefficient of a polynomial function will determine the end behavior of the graph.
Given,
Here we have the graph with some function as y = f(x).
Here we have to find the end behavior of the graph.
Here we can see that the value of x goes to the positive side (the right side of the graph), the graph increases upwards, and this is shown with the arrow pointing up.
So, which means that the value of x goes to ∞, then the value of y will also go to ∞.
Similarly, we can see the exact same behavior for the negative side of x (the left side of the graph), then as x goes to -∞, y will go to ∞.
Therefore, the correct option will be the second option, counting from the top.
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If 2 is added to a number and the sum is tripled, the result is 16 more than the number. Find the number.
Using simplification, the number is −1.
Given that, If 2 is added to a number and this sum is tripled, the result is 4 more than the number.
Let the number is x.
Therefore from given information we get
2 is added to a number.
Then it is x+2.
Sum is tripled.
So 3(x+2)
4 more than number means x+4.
So according to the given statement equation should be
3(x+2)=x+4
Simplifying the expression
3x+6=x+4
Subtract 6 on both side
3x+6−6=x+4−6
3x=x−2
Subtract x on both sie
3x−x=x−2−x
2x=−2
Divide by 2 on both side we get
x=−1
Hence, the number is −1.
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Question
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When
she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans.
Write the linear equation, Y(n), that correctly represents this situation.
Provide your answer below:
Y(n)=
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The equation that represent the given situation is y = 15x + 70
When she plants 3 stalks, each plant yields 115 ounces of beans
The first point = (3, 115)
When she plants 8 stalks, each plant yields 190 ounces of beans
The second point = (8, 190)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (190-115) / (8-3)
= 75/5
= 15
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Choose one point and substitute the values in the equation
y - 115 = 15(x - 3)
y - 115 = 15x - 45
y = 15x - 45 + 115
y = 15x + 70
Hence, the equation that represent the given situation is y = 15x + 70
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BRO PLEASE THIS IS SO HARD
Joanna was eager to know her score on the science final exam. Ms. Filer would release the scores once she graded all exams. Ms. Filer had less than 15 exams left to grade.
Which number line represents the number of exams Ms. Filer had left to grade?
number line with a closed circle on number 15 and line shaded left
number line with an open circle on number 15 and line shaded leftt
number line with an open circle on number 15 and line shaded right
number line with a closed circle on number 15 and line shaded right
Question 2(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Rational Numbers LC)
Given the equation five eighths plus h equals eleven over eight, determine the value of h.
six eighths
sixteen over eighteen
fifty five over sixty four
eight over six
Question 3(Multiple Choice Worth 5 points)
(Translating Algebraic Inequalities MC)
Water boils at a minimum temperature of 100 degrees Celsius. Which inequality represents this scenario?
100 > b
100 < b
100 ≤ b
100 ≥ b
Question 4(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Mario set a goal to run 150 miles this month to prepare for a marathon. So far this month, he has run 75 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.
m − 75 = 150; m = 225 miles
m + 75 = 150; m = 75 miles
75m = 150; m = 2 miles
m over 75 equals 150; m = 11,250 miles
Question 5(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Integers LC)
Given the equation f + 24 = −3, solve for f.
−72
−27
−21
8
Question 6(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Max organized a community toy drive for the holidays. He asked each family to donate a total of 4 gifts. Twelve families participated in the toy drive. Write and solve an equation that represents how many gifts were donated.
4g = 12; g = 3 gifts
g + 4 = 12; g = 8 gifts
g − 4 = 12; g = 16 gifts
g divided by 12 equals 4; g = 48 gifts
Question 7(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Integers LC)
Given the equation 17 equals y over -3, solve for y.
−51
−14
20
51
Question 8(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Bella is baking 42 cookies for the holiday party tonight. She baked 29 before leaving for school and will bake the rest when she returns home.
Which equation shows how many cookies Bella will bake when she returns home?
42 = x + 29
42 = x − 29
42 = 29x
29 = x − 42
Question 9(Multiple Choice Worth 5 points)
(Evaluating Inequalities MC)
Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Question 10(Multiple Choice Worth 5 points)
(Solving One-Step Equations with Rational Numbers LC)
Given the equation 5.24w = 16.506, solve for w.
86.49
21.746
11.266
3.15
Question 11(Multiple Choice Worth 5 points)
(Writing One-Step Equations with IntegersMC)
Pete was building a doghouse for his dog, Chip. He made the door 36 inches tall. The height of the door was twice the height of the window in the doghouse.
Write an equation to determine the height of the window.
36 = 2h
36 = 2 + h
36 = h − 2
36 equals h over 2
Question 12(Multiple Choice Worth 5 points)
(Evaluating Equations MC)
Determine which integer in the solution set will make the equation true.
8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
−4
12
0
3
The number line which represents the number of exams Ms. Filer had left to grade is "number line with an open circle on number 15 and line shaded left". option B
The value of h from the equation "five eighths plus h equals eleven over eight" is "six eighths". option AThe inequality which represent "Water boils at a minimum temperature of 100 degrees Celsius is 100 ≥ b. option DThe equation which shows how many miles Mario has left to run this month to reach his goal is m + 75 = 150; m = 75 miles. option BThe value of f from the equation f + 24 = -3 is -27. option BThe equation that represents how many gifts were donated is g divided by 12 equals 4; g = 48 gifts. option DThe value of y from the equation 17 equals y over -3 is - 51. option A.The equation which shows how many cookies Bella will bake when she returns home is 42 = x + 29. option AThe integer which makes the inequality 6(n − 5) < 3(n + 4) true is S:{14}. option BHow to solve equation?five eighths plus h equals eleven over eight, determine the value of h.
5/8 + h = 11/8
substract 5/8 from both sides
h = 11/8 - 5/8
h = 6/8
h = 3/4
Water boils at a minimum temperature of 100 degrees Celsius.
The inequality:
100 ≥ b
Mario total goal for the month = Number of miles Mario has left to run this month to reach her goal + number of miles Mario has run so far
150 = m + 75
substract 75 from both sides
150 - 75 = m
75 = m
The equation f + 24 = −3, solve for f.
f + 24 = -3
substract 24 from both sides
f = -3 - 24
f = -27
Number of gifts each family donates = 4
Number of families = 12
Total gifts donated = g
The equation:
g / 12 = 4
cross product
g = 12 × 4
g = 48
The equation 17 equals y over -3, solve for y.
17 = y / -3
cross product
17 × -3 = y
-51 = y
Number of cookies Bella is baking = 42
Number of cookies she has baked = 29
Number of cookies left for Bella to bake = x
The equation:
42 = x + 29
substract 29 from both sides
42 - 29 = x
13 = x
The inequality:
6(n − 5) < 3(n + 4)
open parenthesis
6n - 30 = 3n + 12
6n - 3n = 12 + 30
3n = 42
divide both sides by 3
n = 42/3
n = 14
The equation 5.24w = 16.506, solve for w.
5.24w = 16.506
divide both sides by 5.24
w = 16.506 / 5.24
w = 3.15
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3) Karen, her brother Dan, Dana, and her sister Randi own a pizza restaurant, Karen and Dan each own 2/7 of the
restaurant. The remaining share is owned equally by Dana and Randi. Exactly what fraction of the business
does Dana own?
Dana owns [tex]\frac{3}{14}[/tex] fraction of the business
How to calculate the fractions?
*Identify a fraction: When writing fractions, one number is placed above the dividing line and one number is written underneath it.
*Find the numerator: The numerator—the number at the top—indicates the number of elements that make up the fraction.
*find the denominator: The denominator is the figure at the bottom. This number reveals how many components there are in the total number.
Let us take the fraction shared by Dana and Randi as x
So the equation becomes
[tex]\frac{2}{7} +\frac{2}{7} +x+x=1[/tex]
⇒ [tex]\frac{4}{7}+2x=1[/tex]
⇒2x=1-[tex]\frac{4}{7}[/tex]
⇒[tex]2x=\frac{7-4}{7}[/tex]
⇒[tex]2x=\frac{3}{7}[/tex]
⇒[tex]x=\frac{3}{7*2}[/tex]
⇒[tex]x=\frac{3}{14}[/tex]
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HELP!!! I am having trouble understanding how to do these problems. Can someone please help explain how to complete these problems. Thank you so much!
1. Find the measure of <6.
2. Find the measure of <4.
Answer:
1=180 2=90
Step-by-step explanation:
1=∠1 and ∠2 are supplementary, so m∠2 = 180° - x°. ∠2 and ∠6 are corresponding angles. So, m∠6 = 180° - x°.
2=Their measures are equal, so m∠4 = 90 . When two lines intersect to form one right angle, they form four right angles.
Answer:
∠4 = 55°
∠6 = 35°
Step-by-step explanation:
Finding the unknown angles:In ΔABC,
35 + 90 + ∠4 = 180° {Sum of all angles of triangle}
125 +∠4 = 180
∠4 = 180 - 125
∠4 = 55°
Linear pair: If in two adjacent angles, the non-common arms form a straight line, then the two angles are called linear pair and they add up to 180.
∠7 + ∠8 = 180° {linear pair}
90 + ∠7 = 180°
∠7 = 180 - 90
∠7 = 90°
In ΔACD,
∠6 + ∠4+ ∠7 = 180 {Sum of all angles of triangle}
∠6 + 55 + 90 = 180
∠6 + 145 = 180
∠6 = 180 - 145
∠6 = 35°
decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute
Answer:
14.5 gallons will be gone in 1 minute
Step-by-step explanation:
just divide 58 by 4 and thats how much water will be gone in 1 minute
Salespeople at a certain company have a quota to meet each month. On average, they hit the quota 68% of the
time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person
doesn't hit the quota, the probability of being promoted is 0.14.
Use the tree diagram to complete each statement.
The probability of no promotion, given that a salesperson hit the quota: A is
The probability of a promotion, given that a salesperson missed the quota: B is
The probability of no promotion, given that a salesperson missed the quota: C is
The probability that a salesperson hit the quota and got promoted: D is
V
Done
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
What is a probability?
The probability of an event in an experiment is calculated by the division of the number of desired outcomes by the number of total outcomes in the experiment.
From the tree diagram, there are two ways to obtain the promotion:
0.41 of 0.68 (hit the quota).
0.14 of 0.32 (did not hit the quota).
Hence the probability of getting a promotion is:
P(A) = 0.41 x 0.68 + 0.14 x 0.32 = 0.3236.
The probability of both getting a promotion and hitting the quota is:
P(A and B) = 0.41 x 0.68 = 0.2788.
Hence the conditional probability is:
P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.86. (approximately).
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
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Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
The relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.
We know that a line has a zero slope is when the line is parallel to the x-axis.
The slope of a line is given by;
m = (y₂ - y₁) / (x₂ - x₁)
where (x₂, y₂) and (x₁, y₁) are the coordinates of any two points on the line of slope.
For option A:
The given coordinates are;
(-3, 2), (-1, 2), (1, 2), (3, 2)
Choose any two points to calculate the slope of the line.
We will choose the first two points and put the values in the above formula, we will get;
m = (2 - 2) / (-1 (-3)) = 0 / 2 = 0
So, the slope of the line is 0.
Thus, the relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.
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NASA launches a rocket at t = 0 seconds. Its position (height), in meters above sea-level, as a function
time, t, is given by s(t): - 4.9t2 + 187t + 192. Use this position function to answer the following
questions. Round solutions to three decimal places, if necessary.
The rocket splashes down after 39.164 seconds. The rocket reach its peak height 19.081 seconds after launch. The rocket peaks at 1976.13 meters above sea level.
The function of height is given by,
h(t) = -4.9t² + 187t + 192
Once the rocket will be splashed down in sea, means the height of the rocket will be zero. Means
x h(t) = 0
-4.9t² + 187t + 192 = 0
Solving the quadratic equation with quadratic formula, we have two values of t
t = 39.164 and t = -1.001
We will consider the positive value of the time
So the answer is 39.164 seconds.
For getting the maximum value, we should differentiate the function of height and make it equal to zero.
[tex]\frac{dh(t)}{dt} = \frac{d}{dt} (-4.9t^2 + 187 t + 192)[/tex]
For maximum value of h, [tex]\frac{dh (t)}{dt} = 0[/tex]
0 = -4.9 × (2t) + 187
t = 19.081 seconds
At this time, the height of rocket will be maximum.
So putting the vaiue in the given function.
h = -4.9 × (19.081)² + 187 (19.081) + 192
h = 1976.13 meters
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The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The most appropriate interpretation for the slope of the data given is the height of water in the pool increases by 2 inches per minute. Option (1) is correct.
The slope of a line, also known as its gradient, is the value of the steepness or direction of a line in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
Given that
Time Height
2 8
4 12
6 16
8 20
10 24
The slope of the line = 2
A line's slope is also known as its gradient or rate of change.
The slope can be positive or negative; positive slope values indicate an increase in x as y increases and vice versa.
A negative slope indicates that one variable decreases as the other increases.
Because the slope value given here is positive, we can conclude that the height of the water increases over time.
As a result, the height of the water rises by 2 inches per minute.
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The given quadrilateral ABCD is an isosceles trapezoid. Which choice is NOT true about ABCD?
A) 2x + 10 = 4x - 30
B) angle A+ angle B+ angle C+ angle D=180^
C) angle A+ angle B+ angle C+ angle D=360^
D) AR = CD
Answer: B
Step-by-step explanation:
What is an isosceles trapezoid?
An isosceles trapezoid is a type of quadrilateral in which the non-parallel sides have equal length and angle measure.
Let's address each answer to see which are true:
A) True: By definition of an isosceles trapezoid, the non-parallel sides have equal length and angle measure. 2x+10 and 4x-30 are written as equations to represent the unknown measurement of the angles A and D. Because this is an isosceles trapezoid, these angles would have the same measurement, meaning they are equal to each other.
B) False: A trapezoid is a quadrilateral. Quadrilaterals are four-sided figures which angles add up to 360°. Some other shapes that are quadrilaterals are squares, rectangles rhombuses and trapezoids. Because a trapezoid is a quadrilateral, the angles do not and can not add up to 180°
C) True: A trapezoid is a quadrilateral, which is a shape which angles add up to 360°. This means that Angles A, B, C, D of this shape should also add up to 360°.
D) True: An isosceles trapezoid is a type of trapezoid whose non-parallel sides have equal side lengths and angles measurements. Due to this definition, AB and CD would have the same length.