Solve the equation by completing the square. X^2+10x+24=0
Answer:
x = -4
x = -6
Step-by-step explanation:
X^2+10x+24=0
(b/2)^2 = (10/2)^2 = 25
X^2+10x+25=-24+25
(x+5)^2 = 1
(x+5) = ± 1
x = +1 -5 = -4
x = -1 -5 = -6
This graph shows the amount of money Leo earns from tutoring compared with the number of hours he works. Select the correct statement about the graph.
A. For each hour he works, his earnings go up by $7.
B. For each hour he works, his earnings go up by $14.
C. For every 7 hours he works, his earnings go up by $1.
D. For each dollar he earns, the number of hours he works goes up by 14.
Answer:
B. For each hour he works, his earnings go up by $14.
Step-by-step explanation:
Given
The attached graph
Required
The true statement
The attached graph is a linear graph.
From the graph, we have:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (1,14)[/tex]
The rate (m) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{14-0}{1-0}[/tex]
[tex]m = \frac{14}{1}[/tex]
[tex]m = 14[/tex]
This implies that the hourly rate is $14/hr
Hence (b) is true
the sum of two numbers is 20 one number is four less than the other. find the number
Answer:
is it 4 and 12 ?
Step-by-step explanation:
please let me know if it is correct! but i am 96% sure for me answer!
If the Circumstance of wobble ball is 242cm what is the surface area?
Answer:
1,166 is the SA
correct me if im wrong somehow
Step-by-step explanation:
a wobble ball is a sphere
circumference=8(pi)
242=8(3.14)
so 242 divided by 25.12
this ends up with 9.633757961783439, which is the radius of the circumference
SA of a sphere= 4(pi)r²
SA=4(3.14)9.633757961783439²
SA=4(3.14)92.80929246622581
SA=1,165.684713375796
rounded to the nearest whole # = 1166
Water runs from a faucet into a bucket at a steady rate. After 4 seconds, there are 32 ounces of water in the bucket. Write an equation that shows the relationship between time and ounces of water. Use t for time in seconds and w for ounces of water.
9514 1404 393
Answer:
w = 8t
Step-by-step explanation:
If we assume that the ounces of water are proportional to the time, then the equation will look like ...
w = kt
for some constant k.
Solving for k, we find ...
k = w/t
Using the given values, we find k to be ...
k = (32 ounces)/(4 seconds) = 8 ounces/second
The units are stated in the definitions of the variables, so we can write the equation as ...
w = 8t
Which of the following is a point-slope equation of a line that passes through the points (-1, 4) and (8,-2)?
A. y-4= -3/2(x+1)
B. y-4= -2/3(x+1)
C. y-4= 2/3(x+1)
D. y-4= -2/3(x-1)
Answer:
B
Step-by-step explanation:
We want to find the point-slope equation of a line that passes through the points (-1, 4) and (8, -2).
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's find the slope of the line first. We can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{-2-4}{8-(-1)}=\frac{-6}{9}=-\frac{2}{3}[/tex]
We can choose (-1, 4) as our point. So, (x₁, y₁) = (-1, 4).
Substitute:
[tex]\displaystyle y-(4)=-\frac{2}{3}(x-(-1))[/tex]
Simplify:
[tex]\displaystyle y-4=-\frac{2}{3}(x+1)[/tex]
Therefore, our answer is B.
What is the completely factored form of this polynomial? 4x^4+12x^2+9
Answer:
(2x^2+3)^2
Step-by-step explanation:
See image below:)
Find the 7th term of the sequence
1, 4, 16, 64,...
28
16,384
4096
2401
Answer:
3rd option, 4096
Step-by-step explanation:
4⁰ = 1, 1st term
4¹ = 4, 2nd term
4² = 16, 3rd term
.
.
.
4⁶ = 4096, 7th term
Answered by GAUTHMATH
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
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
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]
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.
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
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]▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
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!
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
What is the midpoint of the segment shown below?
(-2,4) (6,-4)
A. (3, 0)
B. (1, 0)
C. (4, 0)
D. (2, 0)
a p e x :(
Answer:
answer is option D
Step-by-step explanation:
(-2 , 4) = (x1 , y1)
(6 , -4) = (x2 , y2)
midpoint = (x1 + x2/2 , y1 + y2/2)
=(-2 +6/2 , 4+(-4)/2)
=(4/2 , 0/2)
=(2 , 0)
(5x20)+(8x10) PLEASE HELP
Answer:
180
Step-by-step explanation:
5*20 is 100. 10 *8 is 80. then you add
