Answer:
x = - 6 , x = 1
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x² + 5x - 6 = 0
consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)
the factors are + 6 and - 1 , since
6 × - 1 = - 6 and 6 - 1 = + 5 , then
(x + 6)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 1 = 0 ⇒ x = 1
3p + 4 ≥ −14 and 1 – 5p ≥ 39
Answer:
1) p ≥ -6
2) p ≤ -38/5
Step-by-step explanation:
3p + 4 ≥ -14
Subtract 4 to both sides
3p ≥ -14 - 4
3p ≥ -18
Divide 3 to both sides
p ≥ -18/3
p ≥ -6
[tex]\rule[225]{225}{2}[/tex]
1 - 5p ≥ 39
Subtract 1 to both sides
-5p ≥ 39 - 1
-5p ≥ 38
Divide -5 to both sides
p ≤ -38/5
[tex]\rule[225]{225}{2}[/tex]
Please solve with explanation (high points)
Step-by-step explanation:
so, we have a large triangle made of the 2 cables as legs and the ground distance AB as baseline.
the tower is the height to the baseline of that large triangle.
let's call the top of the tower T.
and remember, the sum of all angles in a triangle is always 180°.
we know the angle A = 62°, and angle B = 72°.
assuming that AB is a truly horizontal line that means that the 2 legs (cables) have different lengths, the triangle is not isoceles, and the tower is not in the middle of the baseline.
so, the height (tower) splits the baseline into 2 parts. let's call them p and q.
p + q = 12 m
p = 12 - q
let's simply define that p is the part of the baseline on the A side, and q is the part of the baseline on the B side.
we have now 2 small right-angled triangles the large height (tower) splits the large triangle into.
one has the sides
AT, height (tower), p
angle A = 62°
angle T = 180 - 90 - 62 = 28°
the other has the sides
BT, height (tower), q
angle B = 72°
angle T = 180 - 90 - 72 = 18°
now remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and the associated angles being opposite.
p/sin(28) = height/sin(62)
q/sin(18) = height/sin(72)
we know from above that
p = 12 - q
so,
(12 - q)/sin(28) = height/sin(62)
height = (12 - q)×sin(62)/sin(28)
q/sin(18) = height/sin(72)
height = q×sin(72)/sin(18)
and therefore, as height = height we get
(12 - q)×sin(62)/sin(28) = q×sin(72)/sin(18)
(12 - q)×sin(62)×sin(18) = q×sin(72)×sin(28)
12×sin(62)×sin(18) - q×sin(62)×sin(18) =
= q×sin(72)×sin(28)
12×sin(62)×sin(18) = q×sin(72)×sin(28) + q×sin(62)×sin(18) =
= q×(sin(72)×sin(28) + sin(62)×sin(18))
q = 12×sin(62)×sin(18) / (sin(72)×sin(28) + sin(62)×sin(18))
q = 4.551603755... m
p = 12 - q = 7.448396245... m
height = q×sin(72)/sin(18) = 14.00839594... m ≈ 14 m
the cell tower is about 14 m tall.
PLEASE HELP!!!
Which point is tangent to the circle?
A
D
M
Q
Answer:
M is target to the circle
9. Marianna is making a piñata that has a ball-like shape. The piñata has a surface area of 60 square feet. Use
the formula for the surface area of a sphere (S = 4m2) to find the radius of the piñata.
a
About 22.80 ft
C.
About 3.87 ft
D
la
b. About 4.78 ft
d.
About 2.19 ft
-2 6-2
1
Answer:
D. 2.19
Step-by-step explanation:
ok so the formula for the surface area of a sphere is 4[tex]\pi[/tex][tex]r^2[/tex]
We see that 4[tex]\pi[/tex][tex]r^2[/tex]=60.
To find the radius we must isolate r on one side of the equations.
[tex]r^2[/tex]=60/4[tex]\pi[/tex]
[tex]r^2[/tex] = 4.77464829276
r = [tex]\sqrt{4.77464829276}[/tex]
That is approximately equal to 2.19
Question 2 Write the following paragraph proof as a two-column proof. Given: AB = CD and BC = DE Prove: AC = CE A B C D E We're given that AB = CD. By the addition property of equality, we add BC to both sides of the equation to get AB + BC = CD + BC. Since we're also given that BC = DE, we use the substitution property of equality to replace BC with DE on the right side of the equation. So, AB+ BC = CD + DE. Next, by segment addition, we get that AB + BC is equal to AC and that CD + DE is equal to CE. Finally, we use the substitution property of equality on the equation AB + BC = CD + DE to replace AB + BC with AC and CD + DE with CE to get that AC = CE. Type the correct answer in the box. BIUX² X₂ 14pt === Statements Reasons B.
Answer: See below
Step-by-step explanation:
Given:
AB = CD and BC = DE
To prove:
AC = CE
Statements Reasons
AB = CD GivenAB + CB = CD + BC Addition property of equalityAB + BC = CD + DE Given: BC = DEAC = CE By segment addition: AB + BC = AC and CD + DE = CETherefore, AC = CE has been proved
Write 3 + 2 log z - log(x² + 2x + 1) +1/2 log y as a single logarithm with coefficient 1.
Answer:
[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Choose the more appropriate answer
Step-by-step explanation:
I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:
[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Find the area of this irregular figure. Please explain in steps how you did it so I know how to do it for the next question please its not needed but would be appreciated
Work Shown:
A = area of the rectangle
A = length*width
A = 26*15
A = 390 square feet
B = area of the triangle
B = base*height/2
B = 8*9/2
B = 72/2
B = 36 square feet
C = total area
C = A+B
C = 390+36
C = 426 square feet
What is the range of this exponential function?
f(x) = 2.7x
The range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The exponential function is given below.
f(x) = 2.7ˣ
We know the value of the exponential function is always positive.
Then the range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
More about the domain and range link is given below.
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evaluate 10 + 8÷4 - 12
Answer:
zero
Step-by-step explanation:
pemdas
This means that 0.3 is a (n)
number. Rational or irrational
0.3 is a Rational Number written in Decimal Form
0.3 is neither an Integer nor a Whole number.
At their last practice, the basketball team shot free throws for 17 minutes, ran for 12 minutes, and then passed the ball for 16 minutes.
For how many minutes was the team practicing? Explain how you got your answer.
Answer:
45 minutes
Step-by-step explanation:
If you're trying to find the total number of minutes, they practiced you'd have to add.
So, if they did free throws for 17 minutes
Ran for 12 minutes
And passed the ball for 16
You'd add those up
17+16+12 = 45
In conclusion they practiced for a total of 45 minutes.
The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms. About 21,000 cubic feet of road salt is used during a typical snow storm.
a. What is the total volume of the storage shed?
b. How many snow storms can the town expect to handle before the storage shed needs to be refilled with additional road salt?
Answer:
a. 40000pi ft^3
b. 5 times
Step-by-step explanation:
a. the volume of a cylinder is pi * h * r^2
r = 20ft, h = 100ft
so V = pi * 100 * 20^2 = 40,000pi or around 125663.7 ft^3
b. to find the number of times, divide the volume by the amount of salt needed per storm then round down:
40000pi/21000 = 5.98 so 5 times. notes: depending on the teacher you might just round to the nearest integer
(x+y)2-2(x+y)(a+x)+(a+x)2
Answer:
2ax−2ay−2x2−2xy+2a+4x+2y
Step-by-step explanation:
Let's simplify step-by-step.
(x+y)(2)−2(x+y)(a+x)+(a+x)(2)
Distribute:
=(x)(2)+(y)(2)+−2ax+−2ay+−2x2+−2xy+(a)(2)+(x)(2)
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
Combine Like Terms:
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
=(−2ax)+(−2ay)+(−2x2)+(−2xy)+(2a)+(2x+2x)+(2y)
=−2ax+−2ay+−2x2+−2xy+2a+4x+2y
Answer:
=−2ax−2ay−2x2−2xy+2a+4x+2y
x²-3x+1=0
O A. 3±√15
OB. 3+√5
3± √5
o c. 2121224
OD. 5±10
3
Answer:
X=3+-√5/3
Step-by-step explanation:
x=-b+-√b^2-4ac/2
=3+-√(-3)^2-4(1)(1)/2
The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
Answer:
Width = 2
Length = 5
Step-by-step explanation:
let A be the area of the rectangle
L be the length of the rectangle
w be the width of the rectangle
Formula: ‘area of a rectangle’
A = L × w
…………………………………………………
A = L × w
⇔ 10 = (w + 3) × w
⇔ 10 = w² + 3w
⇔ w² + 3w - 10 = 0
Solving the quadratic equation w² + 3w - 10 = 0 :
Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49
then √Δ = 7
[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]
[tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]
-5 is not valid ,because w represents the width
which must be a positive number
Then w = 2
Conclusion:
Width = 2
Length = 2 + 3 = 5
can anyone help me with this with easy tricks
We also have to find volume
I have exams tommorow
Answer:
1,120 cm³
Step-by-step explanation:
Hello!
Think about it this way: There is a rectangular prism, with lengths of 20cm, 12cm, and 10cm, and another rectangular prism cut out of it with lengths, of 8cm, 8cm, and 20cm.
Larger rectangular prismVolume = L * W * H
V = 20cm * 12cm * 10cmV = 2,400cm³Cut-Out Rectangular PrismV = L * W * H
V = 8cm * 8cm * 20cmV = 1,280cm³Subtract:
2,400cm³ - 1,280cm³1,120cm³The total volume is 1,120cm³
Using the graph of the function g(x) = log5 (x – 3), what are the x-intercept and asymptote of g(x)? The x-intercept is 4, and the asymptote is located at x = 3. The x-intercept is 3, and the asymptote is located at x = 4. The x-intercept is 4, and the asymptote is located at y = 3. The x-intercept is 3, and the asymptote is located at y = 4.
The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
What is an Asymptote ?An asymptote is a line that a curve approaches but it never reach.
The given equation
y = log₅(x-3)
To find the asymptote
Set the argument of the logarithm equal to zero.
x - 3 = 0
The vertical asymptote occurs at
x = 3
The equation can also be written as
[tex]\rm 5^y = x-3[/tex]
To find the x intercept we will put the value of y = 0 ;
therefore
5⁰ = x -3
1=x-3
x = 4
Therefore ,The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
To know more about Asymptote
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Answer:
The x-intercept is 4, and the asymptote is located at x = 3.
Step-by-step explanation:
I got it right on the test.
Triangle Sum Theorem: The 3 angles inside a triangle add up to 180. Example: 1 + 2 + 3 = 180 Exterior Sum Theorem: The 3 exterior angles of a triangle add up to 360. Example: 4 + 5 + 6 = 360 Remote Exterior Angle Theorem: The 2 remote interior angles of a triangle add up to be the same size as the exterior angle. Example: 1+2 = 4 someone please answer this quickly
Answer:
What exactly is the question here?
Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C.
What is the measure of arc BEC in circle D?
134°
150°
209°
210°
Answer: 134°
Step-by-step explanation:
Since angle ABC is equal to 75, we know that the arc in front of it (arc AC) is 150. We then start to add all the know arc angle measures together. So, our equation to finding arc BEC 360-150+76= BEC arc.
Answer:
134
Step-by-step explanation:
cause yeah
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
This function shows a horizontal translation of the parent function to the left and 2 units up.
Square root functionThe parent function of a square root function is expressed as:
f(x) = √x
According to the question, we are to plot the expression f(x) = √x+ 3 - 2
This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;
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Answer:
It should be the first one.
Find the total selling price.
Alonzo and Catalyn Diaz paid a total of $23,289.26 for their new automobile. If the sales tax rate in their community is 6.5%, what was the total selling price of the Diaz's new automobile?
the assumption being that the tax is added to the amount advertised for the vehicle, namely 23289.26 + 6.5% of that.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 23289.26}}{\left( \cfrac{6.5}{100} \right)23289.26}\implies 1513.8~\hfill \underset{\textit{total selling price}}{\stackrel{23289.26~~ + ~~1513.8}{24803.06}}[/tex]
Which
Which of the following are characteristics of the graph of the linear parent
function?
Check all that apply
A. It is a parabola.
B. It has a slope of 2.
C. It goes through the origin.
O
D. It is a straight line.
Answer:
All of the following are answers:
B) It has a slope of 2
C) It goes through the origin
D) It is a straight line
Step-by-step explanation:
trust me
You attend a baseball game with friends and visit the snack stand between innings. Soda costs $2 a can, and a box of popcorn costs $1.50. You have $15 with you, and you wish to buy more cans of soda than boxes of popcorn. If x represents the number of cans of soda and y the number of boxes of popcorn, which graph represents the inequalities in this scenario? A. graph A B. graph B C. You attend a baseball game with friends and visit the snack stand between innings. Soda costs $2 a can, and a box of popcorn costs $1.50. You have $15 with you, and you wish to buy more cans of soda than boxes of popcorn. If x represents the number of cans of soda and y the number of boxes of popcorn, which graph represents the inequalities in this scenario? A. graph A B. graph B C. graph C D. graph D C D. graph D
Answer:
I feel that is would be D
Step-by-step explanation:
This is the most reasonable awnser.
help please!!! i need to turn this in tomorrow
Answer:
$10955.6157151671
Step-by-step explanation:
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal (which is $5000)
r = rate of interest in decimal form(which is 0.04)
t = time in years (which is 20)
Substituting,
[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671
The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
The pie chart for the expenditure of a housewife for a particular day is shown below.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
More about the pie chart link is given below.
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Solving two-step equations 3x-2=16
Hey there!
Solve for x :
Answer:x = 6 ✅
Explanation:3x - 2 = 16
>> Add 2 to both sides :
3x - 2 + 2 = 16 + 2
3x = 18
>> Divide each side by 3 :
3x / 3 = 18 / 3
x = 6
▪️Let's verify :
3(6) - 2 ⇔18 - 2 ⇔ 16
Therefore, your answer is x = 6
Learn more about first-degree equations :
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3x−2=16
Add 2 to both sides.
3x=16+2
Add 16 and 2 to get 18.
3x=18
Divide both sides by 3.
x = 18 /3
Divide 18 by 3 to get 6.
x = 6 ===> Answer
Verification
Let x = 6
3×6−2=16
18-2= 16
16 = 16
Checked ✅
{ Pisces04 }
Suppose that y varies inversely with the square of x and y = 50 when x = 4. Find y when x = 5
Answer:
y = 32.
Step-by-step explanation:
y = k/x^2 where k is the constant of variation
When y = 50 x = 4, so
50 = k / (4)^2
f = 50 * 4^2 = 800.
So the relation is
y = 800/x^2
When x = 5
y = 800/5^2
= 32.
Solve the following factorize and the en- equation of quadrate equation X² + 5x + 7 x = 0
Answer:
{-12,0}
Step-by-step explanation:
first to solve this can collect like terms and add
X² +12x=0
and solve it by factorization method
X² +12x=0
x(x+12)=0
it means x multiplied by x = X² then x multiplied by 12 = 12x
so this means x or (x+12) equals to zero
x=0 and (x+12)=0
x+12=0
x=-12
so the solution set is {-12,0}
but can also be done by formula method
What are all of the prime numbers between 30 and 40?
Answer:
the prime numbers between 30 and 40 are 31 and 37 come on its so easy