Answer:
Step-by-step explanation:
Part A
Eq of line passing through C and A
[tex]y-y_o=m(x-x_o)\\y-6=\frac{6-1}{1-2}(x-1)~=>y=-5x+11\\\\PERPEDICULAR~ LINE\\\\m_2=-\frac{1}{m_1}=-\frac{1}{-5}=\frac{1}{5}\\y-3=\frac{1}{5}(x-3)~=>y=\frac{1}{5}x+\frac{12}{5}[/tex]
Part B
Coordinates of point D
[tex]-5x+11=\frac{1}{5}x+\frac{12}{5}=>11-\frac{12}{5}=x(\frac{1}{5}+5)=>x=\frac{43}{26}\\y=-5(\frac{43}{26})+11=\frac{71}{26}\\D(\frac{43}{26}, \frac{71}{26})[/tex]
Part C
Distance DB
[tex]h=\sqrt{(\frac{43}{26}-3)^2+(\frac{71}{26}-3)^2}=\frac{7}{\sqrt{26}}[/tex]
Part D
Length of base
[tex]base=\sqrt{(2-1)^2+(1-6)^2}=\sqrt{26}[/tex]
[tex]area=\frac{1}{2}base*h=\frac{1}{2}\sqrt{26}*\frac{7}{\sqrt{26}}=\frac{7}{2}[/tex]
A culture started with 5,000 bacteria. After 4
hours, it grew to 5,500 bacteria. Predict how
many bacteria will be present after 13 hours.
Round your answer to the nearest whole
number.
P = Aekt
Answer:
5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47
Step-by-step explanation:
For a process, the average range for all samples was 5 and the process average was 25. If the sample size was 10, calculate UCL for the R-chart.
Answer:
8.885
Step-by-step explanation:
Given that :
Sample size, n = 10
The average range, Rbar for all samples = 5
The upper control limit, UCL for the R-chart is :
UCL L= D4Rbar
From the control chart constant table, D4 = 1.777
Hence,
UCL = 1.777 * 5
UCL = 8.885
The UCL for the R-chart is 8.885
SOLVE ASAP! PLS HELP ME!!!
9514 1404 393
Answer:
A. 2.1
Step-by-step explanation:
Put the numbers in the equation and do the arithmetic.
1/R = 1/(3 1/2) +1/(5 1/4)
1/R = 1/(7/2) +1/(21/4) = 2/7 +4/21 = (6 +4)/21
R = 1/(10/21) = 21/10
R = 2.1
find the unknown side lengths
Step-by-step explanation:
h = x
p = 10
b = 24
using pythagorean theorem
h² = p² + b²
h² = 10² + 24²
h² = 676
h = 26
thus , x = 26
Answer:
x = 26
Step-by-step explanation:
use the Pythagorean theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {10}^{2} + {24}^{2} = {c}^{2} [/tex]
[tex] = 676 = {c}^{2} [/tex]
[tex]c = \sqrt{676} [/tex]
c = 26
Joseph earns $10,000 a month working at a law firm. His monthly living expenses like food and gasoline amount to $3,500. He pays $2,700 for his mortgage. He also has $900 in credit card debt and pays $1,200 toward his auto loan each month. What is Joseph's debt-to-income ratio
mathematics question
Answer:
1+1
Step-by-step explanation:
Hello,
There is no question being asked and no attachments. I am unable to help if there is nothing to help with =)
This graph represents a quadratic function. What is the function's equation written in factored form and in vertex form?
(graph in picture)
Step-by-step explanation:
f(x) = a(x-x1) (x-x2)
from the vertex, we get a:
0 = a(4-2)²- 8
4a = 8
a = 2
so, the equation:
f(x) = 2(x-0) (x-4)
f(x) = 2x(x-4)
f(x) = 2x² -8x
In a given triangle, side "a" is 7 inches long and side "b" is 24 inches long. The length of side "c" is
Answer:
25
Step-by-step explanation:
the formula for the hypotenuse of a triangle is
a^2+b^2=c^2
plug in what we know
7^2+24^2=c^2
49+576=c^2
625=c^2
c=25
hope this helps
A basketball player made 85 out of 100 attempted free throws. What percent of free throws was
made?
Answer:
85%
Step-by-step explanation:
to find percent of the throws made put (throws made/total free throws)*100
so (85/100)*100= 85%
Arrange the steps to solve this system of linear equations in the correct sequence x+y=-2 2x-3y=-9
there you go the correct ans
Which equation is a linear function?
y=-5
y= 22 +7
y=22 - 1
y= ? +3
Answer:
let ? be x
every linear equation is y=mx+c
so the answer would be y=?+3
A machine can package 5950 boxes of cereal in 7 hours. how many boxes is the machine packing per hour?
Answer:
850 boxes per hour hope that helps
Answer: 250 boxes of cereal per hour
Work: All i did was divide the 5950 boxes by the 7 hours. After that, I got the quotient 250.
For the following right triangle, find the side length x . Round your answer to the nearest hundredth.
[tex]\huge\bold{Given:}[/tex]
Length of the base = 9
Length of the hypotenuse = 16 [tex]\huge\bold{To\:find:}[/tex]
✎ The length of the perpendicular ''[tex]x[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The length of the perpendicular [tex]x[/tex] is[tex]\boxed{±13.229}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ ⇢ {x}^{2} + {(9})^{2} = ({16})^{2} \\ ⇢ {x}^{2} + 81 = 256 \\ ⇢ {x}^{2} = 256 - 81 \\ ⇢x = \sqrt{175} \\ ⇢x = ±13.229[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:perpendicular \:"x"\:is\:±13.229.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {13.229})^{2} + ({9})^{2} = ({16})^{2} \\ ⇢ 175 + 81 = 256 \\ ⇢ 256 = 256 \\⇢ L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
A book that is 13 inches tall is leaning against the edge of a wall. If the bottom of the book is 5 inches from the wall, how far up the wall is the top of the book?
[tex]\huge\bold{Given:}[/tex]
Length of the book (hypotenuse) = 13 inches
Distance of the book from the foot of the wall (base) = 5 inches
[tex]\huge\bold{To\:find:}[/tex]
Length of the book on the wall (perpendicular ''[tex]x[/tex]").
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\purple{x\:=\:12\:inches}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
By Pythagoras theorem, we have
(Perpendicular)² + (Base)² = (Hypotenuse)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (5 in) ² = (13 in)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 25 in² = 169 in²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 169 in² - 25 in²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 144 in²
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{144 \: {in}^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{12 \times 12 \: {in}^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{ ({12 \: in})^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = 12 in
Therefore, the height of the book on the wall [tex]x[/tex] is 12 inches.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{☂}}}}}[/tex]
Plzzzzz help! I need answers quickly!!!! I’ll give best answer!
Sketch the graph of each function
8) y=x: +47 +6
Answer:
A
Step-by-step explanation:
Consider this linear function:
y= 1/2x+1.
Plot all ordered pairs for the values in the domain.
D: {-8, -4, 0, 2, 6}
Answer:
(-8,-3)
(-4,-1)
(0,1)
(2,2)
(6,4)
Step-by-step explanation:
One by one, substitue the x values and solve for y
Answer:
negative 4
Step-by-step explanation:
go
PLEASE HELP ME!! Kevin earns a base salary of $350.00 every week with an additional 12%
commission on everything he sells. If Kevin sold $4950.00 worth of items
last week, what was his total pay?
============================================================
Explanation:
He sold $4950 worth of items. Take 12% of this amount to get
12% of 4950 = 0.12*4950 = 594
So he earns $594 in commission on top of the $350 base salary paid every week. In total, he earns 594+350 = 944 dollars for that week
This isn't the per week pay because he would need to sell exactly $4950 worth of goods each week to keep this same weekly pay.
The monthly family income of a family is $15,000. They spend 28% of their monthly income on food. How much do they spend on food each month?
Answer - $
(fill in the value)
Answer:
$1000 each month.
Step-by-step explanation:
$1000 because 12 month and 1 month=$1000 the family have $3000.
Andrew wants to buy a pair of jeans costing $60. Sales tax on his
purchase is 13%.
a)
How much tax will Andrew be charged?
Answer:
$67.80
Step-by-step explanation:
$60.00*13%=$7.80
$60.00+$7.80
=$67.80
What is the volume of the sphere m? Round your answer to the nearest hundredth
Answer:
below
Step-by-step explanation:
x = 8 *sin45
x =5.657
r = x = 5.657 in
v = 4/3πr³
v = 4/3 * 3.142*(5.657)³
v= 758.41 in
Answer:
758.25 in.^3
Step-by-step explanation:
a^2 + b^2 = c^2
2a^2 = 64
a^2 = 32
a = sqrt(32)
V = (4/3)(pi)r^3
V = (4/3)(3.141592654)(5.6568542459)^3
V = 758.25 in.^3
Of the 85 learners that packed a lunch for the field trip, 60 have an apple in their lunch and 75 have an orange. All of the learners have at least one apple or orange in their lunch.
What is the probability that a learner chosen at random from the field trip has an orange but not an apple?
Using it's concept, it is found that there is a 0.1765 = 17.65% probability that a learner chosen at random from the field trip has an orange but not an apple.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, of the 85 learners, 75 - 60 = 15 have an orange but not an apple, hence the probability is given by:
p = 15/85 = 0.1765.
0.1765 = 17.65% probability that a learner chosen at random from the field trip has an orange but not an apple.
More can be learned about probabilities at https://brainly.com/question/14398287
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What is photosynthesis?
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓[tex]\pmb{\qquad{\qquad{\underline{\green{\underline{\sf{Photosynthesis}}}}}}}[/tex]
Photosynthesis is the process by which green plants take in carbon dioxide and water, in the presence of chlorophyll by using sunlight to make their own food. Oxygen is released as a by product.
Chemical Reaction for PHOTOSYNTHESIS:
[tex]\sf 12H_2O + 6CO_2 \underset{chlorophyll}{\xrightarrow{Sunlight}} C_6H_{12}O_6 + 6H_2O + 6O_2 \uparrow[/tex]▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Find the length of X (IN THE PICUTRE GIVING BRAINLEST TO BEST answer)
Answer:
x=3
Step-by-step explanation:
Since they are similar triangles, we can use ratios to solve
x 3.5
----- = -------
6 7
Using cross products
7x = 21
Divide each side by 7
7x/7 = 21/7
x = 3
Triangle ABC is a right triangle.
The lengths of one leg is 60 feet, and the hypotenuse is 61 feet.
What is the length, in feet, of the other leg?
Answer:
Hello! answer: 11
Step-by-step explanation:
60 × 60 = 3600
11 × 11 = 121
3600 + 121 = 3721
√3721 = 61
therefore 11 is the missing leg Hope that helps!
please help me !!!!
9514 1404 393
Answer:
(a) 260 square centimeters
Step-by-step explanation:
The figure consists of a 10 cm square and four congruent triangles with base 10 cm and height 8 cm. Using the formulas for the area of a square and a triangle, the total area is ...
area = square area + 4 × triangle area
area = s² + 4×(1/2bh) = (10 cm)²+ 2(10 cm)(8 cm) = (100 +160) cm²
area = 260 cm²
for an art prohect, a cirlce made of construction paper is cut into thirteen equal slices, six of the slices are removed. write the remaining portion of the circle as a fraction. do not reduce the fraction
Answer:
7/13 slices
Step-by-step explanation:
13-7
Can y’all help me solve this question it’s due by the end of the day and I’m failing math?explain it plz
Answer:
x=4 and y=−4
Step-by-step explanation:
Let's solve your system by elimination.
−x−2y=4;3x+2y=4
−x−2y=4
3x+2y=4
Add these equations to eliminate y:
2x=8
Then solve 2x=8 for x:
2x=8
2x
2
=
8
2
(Divide both sides by 2)
x=4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
−x−2y=4
Substitute 4 for x in−x−2y=4:
−4−2y=4
−2y−4=4(Simplify both sides of the equation)
−2y−4+4=4+4(Add 4 to both sides)
−2y=8
−2y
−2
=
8
−2
(Divide both sides by -2)
y=−4
I have a large money box, about 10 inches wide and 5 inches tall. Roughly, how many coins can I place in my empty money box?"
Answer:
Overall, it depends what type of coin you are using because each ones size is different. Or, if you are referring to the riddle it will be just one coin.
The correct answer is approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate a volume calculation that place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.
To estimate the number of coins that can fit in your money box, we need to consider the volume of the box and the volume of a single coin.
Calculate the volume of the money box:
Volume = Length * Width * Height
Volume = 10 inches * 10 inches * 5 inches
Volume = 500 cubic inches
Estimate the volume of a single coin. Let's assume a common coin, such as a quarter:
Diameter of a quarter ≈ 0.96 inches
Thickness of a quarter ≈ 0.07 inches
Volume of a coin ≈ π * ([tex]radius^2[/tex]) * thickness
Volume of a quarter ≈[tex]3.14 * (0.48) ^2 * 0.07[/tex]inches
Volume of a quarter ≈ 0.063 cubic inches
Calculate the number of coins that can fit in the money box:
Number of coins ≈ Volume of the money box / Volume of a coin
Number of coins ≈ 500 cubic inches / 0.063 cubic inches
Number of coins ≈ 7936 coins (approximately)
Therefore, approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate a volume calculation that place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.
Learn more about volume and estimations here:
https://brainly.com/question/20664459
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PLEASE HELP QUICK
Factor out the GCF of 14x4 + 21x2 + 28x
Answer:
14×4+21×2+28=126
Step-by-step explanation:
correct me if I'm wrong
Find the inverse of function f. f(x)=1/3 - 1/21x
Answer:
A. [tex]\displaystyle f^{-1}(x) = 7 - 21x[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsFunctionsFunction NotationInverse FunctionsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{1}{3} - \frac{1}{21}x[/tex]
Step 2: Find inverse
Rewrite: [tex]\displaystyle y = \frac{1}{3} - \frac{1}{21}x[/tex]Swap: [tex]\displaystyle x = \frac{1}{3} - \frac{1}{21}y[/tex][Subtraction Property of Equality] Isolate y term: [tex]\displaystyle x - \frac{1}{3} = -\frac{1}{21}y[/tex][Multiplication Property of Equality] Isolate y: [tex]\displaystyle -21(x - \frac{1}{3}) = y[/tex][Distributive Property] Distribute -21: [tex]\displaystyle 7 - 21x = y[/tex]Rewrite: [tex]\displaystyle f^{-1}(x) = 7 - 21x[/tex]