Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
can someone help with this please
Answer:
Step-by-step explanation:
does someone mind helping me with this question? Thank you!
Can anyone help me i really need it rn
Answer:
11. g
12. f
13. e (add all the frequencies)
14. d
15. c (eg. 17.5 -8.5 = 9)
16. b
17. a
Let me know if you have any questions.
Hope this helps!
2.
janine is building a box with a height of 10 inches. the rectangular base of her box will have a perimeter of 72 inches.
select the equation where v represents the volume of the box and wrepresents the width of the base of the box.
a. v= -20w^2 + 720w
b. v=-10w^2 + 360w
c. v= -100w^2 +3,600w
d. v=-10w^2 + 720w
The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let w represent the width of the box and v represents the volume, hence:
2(w + length) = 72
Length = 36 - w
Volume = w(36 - w) * 10
Volume = 360w - 10w²
The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²
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If set A contains seven distinct numbers and set B contains three distinct letters, how many elements are in (A U B)?
=======================================================
Explanation:
Let's use an example to see why this is
A = {1,2,3,4,5,6,7}
B = {x,y,z}
A U B = {1,2,3,4,5,6,7, x,y,z}
We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).
There are 7 items in set A, and 3 items in set B.
Therefore, we have 7+3 = 10 items in set A U B
The symbol U refers to the set union operator.
If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.
The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.
-----------------
If you want a formula to write down on a notecard or reference sheet, then it would be
n(A U B) = n(A)+n(B)
where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region
Find the area of the polygon with vertices of A(2, 2), B(2, 7), C(8, 7),
and D(4, 2)
Answer:
20 units²
Step-by-step explanation:
Three multiplied by the sum of 4 and a number is the same as 18 more than the number. Find the number.
If n is "the Bumber," which equation could be used to solve for the number?
Answer:
3(4 + n) = n + 18
n = 3
Step-by-step explanation:
because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.
doubling the sum of 5 and a number is equal to the same number decreased by 2. what is the equation
Answer:
2(x + 5) = x - 2
⟹ x = -12
Step-by-step explanation:
Doubling the sum of 5 and a number is equal to the same number decreased by 2. What is the equation?
This word problem can be written as:
⟹ 2(x + 5) = x - 2
1. Distribute:
2(x) + 2(5) = x - 2
⟹ 2x + 10 = x - 2
2. Subtract x from both sides:
2x - x + 10 = x - x - 2
⟹ x + 10 = -2
3. Subtract 10 from both sides:
x + 10 - 10 = -2 - 10
⟹ x = -12
4. Check your work:
2(x + 5) = x - 2
2(-12 + 5) = -12 - 2
2(-7) = -20
⟹ -14 = -14 ✔
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a prototype rocket burns 159 gallons of liquid hydrogen fuel each second during a regular launch. Make a table that shows how many gallons of fuel are burned after 2,3,5 and 10 seconds.
Answer:
Seconds: 2 || 3 || 5 || 10 ||
---------------------||-------||--------||--------||
Gallons: 312 || 486 || 780 || 1560 ||
Use technology or a z-score table to answer the question.
The weights of boxes of rice produced at a factory are normally distributed with a
mean of 20 ounces and a standard deviation of 1.5 ounces. Consider a shipment of 1500 boxes of rice.
How many of the boxes will weigh 18 ounces or less?
138 boxes
154 boxes
632 boxes
781 boxes
The number of boxes will weigh 18 ounces or less will be 138. Then the correct option is A.
What is a normal distribution?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The weights of boxes of rice produced at a factory are normally distributed with a mean of 20 ounces and a standard deviation of 1.5 ounces.
Consider a shipment of 1500 boxes of rice.
Then the number of the boxes will weigh 18 ounces or less will be
z = (18 - 20) / 1.5
z = -1.33
Then the probability will be
P(x ≤ 18) = P(z ≤ -1.33)
P(x ≤ 18) = 1 - P(z > -1.33)
P(x ≤ 18) = 1 - [1 - P(z < -1.33)]
P(x ≤ 18) = P(z < -1.33)
P(x ≤ 18) = 0.091211
Then the number of the boxes will weigh 18 ounces or less will be
⇒ 0.091211 x 1500
⇒ 136.8
approximately 138 boxes.
Then the correct option is A.
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How old are people when their voice change
For boys, it's between the ages of 12-16
And for girls, it's between the ages of 10-14
Answer:
boys between ages 12 and 16 girls between ages 10 and 14
Write a rule for the nth term of the geometric sequence for which a1=−6 and a5=−486
The geometric rule for the nth term of the geometric sequence for which a1 =−6 and a5=−486 is -6 × 3^(n - 1)
The nth term of a geometric sequenceFirst term, a1 = -6
Fifth term, a5 = -486
a5 = ar^(n - 1)
-486 = -6 × r^(5-1)
-486 = -6r⁴
r⁴ = -486 / 6
r⁴ = 81
r = 4√81
r = 3
Geometric rule:
nth term = ar^(n-1)
nth term = -6 × 3^(n - 1)
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Which of the following statements is true concerning ABC below?
10
B
с
OA. ZA is the smallest angle.
OB. ZB is the largest angle.
C. Bis the smallest angle.
OD. ZA is the largest angle.
2
Answer:
see the attachment photo!
what is the answer to a math problem I had it on khan academy but the problem I
1 2/7 divided by (-2 1/4)
hat is the answer to a math problem I had it on khan academy but the problem I
1 2/7 divided by (-2 1/4)
Answer:
-4/7
Step-by-step explanation:
1 2/7 divided by (-2 1/4)
1 2/7 = 9/7
-2 1/4 = -9/4
9/7 divided by -9/4 =
9/7 multiplied by -4/9 =
9's cancel out
1/7 multiplied by -4/1 =
-4/7
Neena just earned her bachelor’s degree. based on her qualifications and desire for the highest pay scale, which career would she be best suited for? supply chain manager survey researchers logistic analyst marketing specialist
Based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.
Who is a supply chain manager?A supply chain manager ensures the movement of goods, from manufacturers and suppliers to the ultimate customer.
A supply chain manager oversees and manages the production flow:
Raw materials acquisitionProduction logisticsDelivery logistics.A supply chain manager requires the following skills:
Business ManagementLeadershipTransportationManufacturing production and processesCustomer servicePersonal relationshipsAnalytical skills.Thus, based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.
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6. Free trade is defined as "a system of buying and selling between countries that is
carried out with no government involvement Based on what you've learned about
international trade, write a three-to five-paragraph essay about who benefits the
most from free trade: developed, developing, or underdeveloped nations. (10 points)
Free trade is defined as "a system of buying and selling between countries that is. carried out with no government involvement Based on what you've learned about international trade,
What is International trade?The term "lobby" here refers to that action which seeks to influence or affect a certain issue most specifically those that are business and politically related. And based on the scenarios above, the one that would most likely motivate an autoworker union to lobby congress would be the first option.
The World Bank is a financial institution created after World War II by developed countries to promote economic development around the world through loans to developing countries. To get a loan, a developing nation must submit a project that is evaluated by World Bank secretaries. Some focus areas of the bank finances are human development, agriculture, environmental protection, industrial projects, infrastructure, and corporate governance.
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B) State whether the given pairs are complementary, supplementary or neither.
1) 25°, 155°
2) 46°, 44°
3) 68°, 108°
4) 180, 72⁰
6) 19⁰, 161°
5) 320, 58⁰.
Answer:
1st answer supplementary angles
2nd answer complementary angles
3rd answer neither
4th ananswe complementary angles
5th answer complementary angles
6th answer supplementary angles
hope you find this helpful
Find the function of (0,6), (3,15.8) and (9.5,0)
The polynomic function that contains the points (0, 6), (3, 15.8) and (9.5, 0) is a quadratic function, whose model is y = -0.600 · x² + 5.066 · x + 6.
How to derive a polynomic function from given points
To determine the coefficients of a polynomic function we must know a set of distinct points, whose number is the same number of coefficients. In this case, we can derive a quadratic function, as quadratic functions have three coefficients:
y = a · x² + b · x + c (1)
Now we substitute x and y in (1) and solve the resulting system of linear equations:
c = 6
9 · a + 3 · b + c = 15.8
90.25 · a + 9.5 · b + c = 0
Whose solution is a ≈ -0.600, b ≈ 5.066 and c = 6.
Remark
The statement is incomplete. The complete form is shown below:
There is a polynomial function. Find the function of (0, 6), (3, 15.8) and (9.5, 0).
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Find the measure of the angle between u = 6i - 3j and
v = 2i+j to the nearest tenth of a degree.
Answer:
θ = 53.1° (to the nearest tenth)
Step-by-step explanation:
FORMULA :
Let θ be the measure of the angle between U and V :
[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]
========================
[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]
…………………………………………………
Then
[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]
[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]
A weather forecast predicts that for each day from Monday to Friday this week, there is a $40\%$ chance of sun, a $25\%$ chance of getting 4 inches of rain, and a $35\%$ chance of getting 10 inches of rain. What is the expected value of the total number of inches of rain which will fall from Monday to Friday
Step-by-step explanation:
correct u know jsjsjsjsjajajaj shahha hshshs hsgshs hshshs hshshs hzhsvs hsvzvshsvss hshshs hshshs hshsh hshs
Solve y = ax² + c for x.
Answer:
[tex]x =\pm\sqrt{\dfrac{y-c}a}[/tex]
Step-by-step explanation:
[tex]~~~~~~y= ax^2 +c\\\\\implies ax^2 = y-c\\\\\implies x^2 =\dfrac{y-c}{a}\\\\\implies x =\pm\sqrt{\dfrac{y-c}a}[/tex]
15 points, helppp please
Answer:
the value of c is 13.
Step-by-step explanation:
See the picture attached below for a step by step explanation
Paige is working on an art project. She draws two rectangles that are connected. The total area of the two rectangles is 56 centimeters. The
dimensions of the smaller rectangle are 2 centimeters by 7 centimeters.
Answer:
2 * 21
3 * 14
6 * 7
Step-by-step explanation:
7 * 2 = 14
56 - 14 = 42
Multiples of 42 = 2,3,6,7, 14, 21
The possible dimensions of the larger rectangle are:
21 centimeters by 2 centimeters
14 centimeters by 3 centimeters
7 centimeters by 6 centimeters
Let the dimensions of the larger rectangle be length L and width W.
We know that the total area of the two rectangles is 56 square centimeters.
Area of the smaller rectangle = 2 cm * 7 cm = 14 square centimeters
Area of the larger rectangle = Total area - Area of the smaller rectangle
Area of the larger rectangle = 56 square centimeters - 14 square centimeters
Area of the larger rectangle = 42 square centimeters
Now, we need to find the possible dimensions of the larger rectangle with an area of 42 square centimeters.
To find the possible dimensions, we can list all the pairs of whole numbers (L, W) whose product is 42.
7 * 2 = 14
56 - 14 = 42
Multiples of 42 = 2,3,6,7, 14, 21
Remember that the length (L) should be greater than or equal to the width (W) to avoid counting duplicates.
The possible dimensions are:
L = 42, W = 1 (42 cm * 1 cm = 42 square centimeters)
L = 21, W = 2 (21 cm * 2 cm = 42 square centimeters)
L = 14, W = 3 (14 cm * 3 cm = 42 square centimeters)
L = 7, W = 6 (7 cm * 6 cm = 42 square centimeters)
So, the possible dimensions of the larger rectangle are:
42 centimeters by 1 centimeter
21 centimeters by 2 centimeters
14 centimeters by 3 centimeters
7 centimeters by 6 centimeters
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Question 15 of 16
Which of the following is the domain of the function based on the input-
output table below?
Answer:
C
Step-by-step explanation:
it is because the hours spent by training will determine the pay at the end of the month.
therefore it's independent that's y it is the domain.
41 Buying music
LV
Dave loves music. He wants to listen to his favorite
singer's new CD. So he goes to Itunes and buys his
songs. One song costs 1,29 € and the album 9,99 €.
There are 8 songs on the album.
. What's the best choice?
Answer:
theUse the Distance and Midpoint Formulas to find the length and midpoint of the segments with indicated endpoints. Show your solution and answer inside the box.
Endpoints
Distance
Midpoint
1. (-5,8) and (9,4)
2. (6 ,- 3) and (10,11)
3. (2,1) and (-16,13)
4. (3,0) and (9 ,- 13)
5. (-3 ,- 10) & (-7 ,- 2)
Solve for x.
JKL
2x-4
8
16
7
56
you have to use intercept theorem, also known as Thales's theorem to slove this problem
The volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. What is the volume of a cube with side 4 inches?
Volume is a three-dimensional scalar quantity. The volume of the cube with side length of 4 inches is 64 inches³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. Therefore, the volume of cube with side 4 inches will be,
Volume of the cube = (4 in)³ = 64 in³
Hence, the volume of the cube with side length of 4 inches is 64 inches³.
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Kevin is running a marathon. His time comes to 26 miles in 2 2/3 hours. What is his speed in miles per hour?
What is the volume of this sphere?
Use 3.14 and round your answer to the nearest
hundredth.
18mm
cubic millimeters
Work Shown:
[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\[/tex]
what is the vertex of: y = x^2 + 8x - 10
Answer:
vertex = -4, -26
Step-by-step explanation:
The standard form of a quadratic function is : [tex]y=ax^{2} +bx+c[/tex]
The function here : y = [tex]x^{2}[/tex] + 8x - 10
is in this form with a=1, b=8 and c = -10
x-coord of vertex = [tex]\frac{-b}{2a}[/tex]
[tex]x_{vertex} =\frac{-8}{2} = -4[/tex]
To find corresponding value of y-coord of vertex , substitute
x = -4 into the function.
x=-4 : [tex]y=(-4)^{2} +(8*(-4))-10 = 16 +(-32)-10=-26[/tex]