factor the following expression
[tex]16x^{2} - 25[/tex]
[tex]16x^2-25\\\\=(4x)^2-5^2\\\\=(4x+5)(4x-5)[/tex]
(t divide 3) + 1= 5 + 1
Answer:
t=15
Step-by-step explanation:
t/3 + 3/3 = 6
combine fractions w/ common denominator:
t+3/3 = 6
multiply both sides by denominator (3):
note: the two threes from 3 x t+3/3 cancel each other out
t+3=3x6
t+3=18
subtract 3 from both sides and you get 15
t=15
hope this helps :)
Complete part (a) and part(b) given the following system of equations. I really need help!!!
x-y=0
2x+3y=-5
a) Solve this system graphically.
b) Write your answer
Answer:
x=−1 and y=−1
Step-by-step explanation:
Solve by substitution
x−y=0;2x+3y=−5
Step: Solve x−y=0 for x:
x−y+y=0+y(Add y to both sides)
x=y
Step: Substitute yfor x in 2x+3y=−5:
2x+3y=−5
2y+3y=−5
5y=−5(Simplify both sides of the equation)
5y/5=−5/5 (Divide both sides by 5)
y=−1
Step: Substitute−1 for y in x=y:
x=y
x=−1
Answer:
x=−1 and y=−1
The solution to the system is x = -1.8 and y = -1.8.
What is a system of equations?A group of two or more equations that must be solved simultaneously make up a system of equations. There are many unknown variables in a system of equations, and each equation in the system depicts the relationship between those variables.
A set of variable values that satisfy every equation in a system of equations is the solution to the system of equations.
To solve this system of equations graphically, we can plot the two equations on a coordinate plane and find the point where they intersect, which represents the solution to the system.
a) To plot the equation x - y = 0, we can rearrange it to y = x and plot the line passing through the origin and the point (1, 1), as shown below:
Graph of the line y = x passing through the origin and the point (1, 1).
To plot the equation 2x + 3y = -5, we can rearrange it to y = (-2/3)x - 5/3 and plot the line passing through the points (-2, 1) and (1/3, -5/3), as shown below:
Graph of the line y = (-2/3)x - 5/3 passing through the points (-2, 1) and (1/3, -5/3).
b) The point where the two lines intersect is the solution to the system. From the graph, we can see that this point is approximately (-1.8, -1.8).
Therefore, the solution to the system is x = -1.8 and y = -1.8.
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A graph has the two points (2, 110) and (4, 220). What is the rate of change?
Answer:
55
Step-by-step explanation:
220-110
110/2=55
will give brainliest, thanks in advance!!
Answer:
-3+15i
Step-by-step explanation:
Apply complex arithmetic rule: [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex]
[tex]\left(-3\cdot \:3-3\left(-2\right)\right)+\left(-3\left(-2\right)+3\cdot \:3\right)i[/tex]
-3 * 3 -3 (-2) = -3
[tex]-3+15i[/tex]
Write your answer in lowest terms.
Working pls
Answer:
4 5/6 or 29/6
Step-by-step explanation:
Conversion a mixed number 8 1/
4
to a improper fraction: 8 1/4 = 8 1/
4
= 8 · 4 + 1/
4
= 32 + 1/
4
= 33/
4
To find a new numerator:
a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/
4
= 32/
4
b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 4.
Eight and one quarter is thirty-three quarters
Conversion a mixed number 3 5/
12
to a improper fraction: 3 5/12 = 3 5/
12
= 3 · 12 + 5/
12
= 36 + 5/
12
= 41/
12
To find a new numerator:
a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/
12
= 36/
12
b) Add the answer from previous step 36 to the numerator 5. New numerator is 36 + 5 = 41
c) Write a previous answer (new numerator 41) over the denominator 12.
Three and five twelfths is forty-one twelfths
Subtract: 33/
4
- 41/
12
= 33 · 3/
4 · 3
- 41/
12
= 99/
12
- 41/
12
= 99 - 41/
12
= 58/
12
= 2 · 29/
2 · 6
= 29/
6
Find the surface area of the cylinder. Type an exact answer in terms of pi.
Answer:
~150.8
Step-by-step explanation:
surface area of a cylinder=2 pi r h + 2 pi r²
[tex]\large{\boxed{\mathfrak\pink{\fcolorbox{pink}{pink}{Answer:-}}}}[/tex]
→ POINTS TO BE NOTED
SURFACE AREA OF THE CYLINDER IS ALSO KNOWN AS TOTAL SURFACE AREA A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder.nd, to find Surface area of cylinder there is one formula
[tex] \pink{ \boxed{ \sf2 \pi \: r(h + r)}}[/tex]
[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}[/tex]
★Here
r( RADIUS) = 3cmh(HEIGHT)= 5cm★ Let's solve:-
[tex] \sf \: ↦2 \pi \times 3(5 + 3) \\ \sf \:↦ 2\pi \times 15 + 9 \\ \sf \:↦ 2\pi \times 24 \\ \sf \: ↦48\pi\:cm²[/tex]
[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}}\orange{ \rule18mm{2.5pt}}[/tex]
Hence;
The surface area of the cylinder=48πcm²Find the common ratio of the geometric sequence 20,40,80
Answer:
a = 2a(- 1)
Step-by-step explanation:
I have done the maths
For f(x)= 2x + 1 and g(x) = x^2 - 7, find (f+g)(x).
Answer:
x^2+2x-6, or C
Step-by-step explanation:
We want to combine the values of both f(x) and g(x) into one equation.
We could write this as 2x+1+x^2-7
Simplified- x^2+2x-6, or C
Please answer ASAP for 15 points pls
Answer: 125
Step-by-step explanation:
Given that f(x) = 3x + 3 and g(x)=x2- 2x-5, find (g of)(4).
(gof)(4)=0
(Simplify your answer. )
Answer:
-5=0
Step-by-step explanation:
g(4)=8-8-5=-5 you substitute 4 into x
-5=0
Determine the equation of the circle graphed below.
10
8
-10 -8
8
-6
-2
F
4
2
N
T
-6.
2
10
Answer:
[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]
Step-by-step explanation:
From the graph we can see that
Diameter = 6 units
=> Radius = 3 units and centre is at (-3,7)
=> Equation is Circle with centre (-3,7) and radius of 3 units will be
[tex] = > {(x + 3)}^{2} + {(y - 7)}^{2} = {3}^{2} [/tex]
[tex] = > ( {x}^{2} + 6x + 9) + ( {y}^{2} - 14y + 49) = 9[/tex]
[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]
I’ve been struggling with these three for awhile I got everything else on the worksheet but these please help SOH CAH TOA
The distance between Casey and the base of the lighthouse is 49 ft.
What is the angle of elevation and depression?The angle of elevation refers to the angle formed by the straight horizontal line and an object. The crosshair of an observer is usually above the horizontal.
The angle of depression is the angle formed by the horizontal and a downward angle to an object. The crosshair of an observer is usually above below the horizontal.
1.The distance between Casey and the base of the lighthouse can be determined by using the tangent of trigonometry.
(TOA)
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 58 = \dfrac{78}{x}}[/tex]
[tex]\mathbf{x= \dfrac{78}{1.6003}}[/tex]
x ≅ 49 ft
2.The height of the goal post can be determined by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan 17 = \dfrac{x}{131}}[/tex]
x = (tan 17) × 131
x = 0.3057 × 131
x ≅ 40 ft
3.The horizontal distance between Zack and the water fountain is calculated by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 28 = \dfrac{75}{x}}[/tex]
[tex]\mathbf{x = \dfrac{75}{0.5317}}[/tex]
x = 141 ft
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Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine! Payton is overcome with emotion and needs your help to save her dog. You can repel down and successfully rescue Willow, but you must calculate how much rope is needed.
The ravine is 153 feet deep the repel line will be the diagonal distance from the top of the ravine to Willow The anchor and repel line form a 35 degree angle; this is angle A in the image below.
(a) Calculate the length of the repel line using one of the 3 trigonometry ratios taught (sin, cos, tan) Round your answer to the nearest whole number. Show all needed math for calculating this length.
The length of the repel line using one of the 3 trigonometry ratios will be 186.78 feet.
How to calculate the length?From the information given, Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine.
The length will be calculated thus:
Cos 35° = 153/AC.
AC = 153/cos 35°
AC = 153/0.819
AC = 186.78 feet.
Therefore, the length is 186.78 feet.
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Find the equation of
the line that cuts through (0, 5) and (1, 2)?
a. y=-3x+5
C.
y =-57+3
b. y = 3x+5
d.
Y=--X+3
Please select the best answer from the choices provided
Watch help video
Kaylee owns a small business selling clothing. She knows that in the
last week 3
customers paid cash, 21 customers used a debit card, and 46 customers used a credit
card.
Based on these results,
debit card as a
express the probability that the next customer will
pay with
The probability the next customer pays using a debit card based on the last three weeks is 30% or 0.3.
What is a probability?This is the chance or likelood for an event to occur. For example, if in a city it has snowed every year on December 25th, there is a high probability it will snow this year and in the next years.
How to calcuate the probability?Total of a specific outcome/ total of outcomes
Based on this, let's calculate the probability the next customer pays using the debit card:
Total that pay with debit card: 21 customersTotal of customers: 70 customers21/ 70 =0.3 or 30%Learn more about probability in: https://brainly.com/question/11234923
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Please help! Due in 10 minutes! I'll mark brianliest!
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Solve the system of equations below using elimination.
4x + 4y = -37
2x + 5y = -17
Part A: What is the x-value?
Part B: What is the y-value?
Part C: In one paragraph, using your own words, explain the work you did to find the answers to parts A and B.
Answer:
Step-by-step explanation:
4x + 4y = -37
2x + 5y = -17
we are told to use elimination , instead of substitution,
meaning get rid of the x or y in one of the equations.
Part C : let's multiply (2x + 5y = -17 ) * (-2) so we get
-4x - 10y = 34 , then add
4x + 4y = -37
0x -6y = -3 now we have only one variable , y
because both sides have a minus sign, we can just drop it
6y = 3 ( divide both sides by 6)
y = 3/6
Part B : y = 1/2 we now know y
plug in the y value into 1st equation.
4x + 4(1/2) = -37
now solve for x
4x + 2 = -37
4x = -39
Part A : x = - 39/4
please helpppppppppp
Answer:
THE ANSWER IS “your net worth”
Step-by-step explanation:
What is the length of segment np? 1 unit 2 units 3 units 4 units
Answer:
2 units
Step-by-step explanation:
Answer:
The answer is 2 units
Step-by-step explanation:
Kira's purple scarf is 3 1/2 feet long. Her red scarf is 1 1/3 times as long as her purple
scarf. How many feet long is Kira's red scarf?
Answer:
4.55 or 4.7 depending on how you round
Step-by-step explanation:
3 1/2=3.5
1 1/3= 1.3
3.5x1.3=4.55
if x=15 degrees and the measure of Arc YZ is 3 centimeters, what is the circumference of the circle?
A- 24
B- 45
C- 60
D- 72
The circumference of the circle is 72cm.
Arc length formula[tex]Arc length = 2\pi r(\frac{x}{360} )[/tex]
where
r is the radius of the circle
x is the central angle of the arc
Circumference of the circleCircumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It is calculated as
circumference of the circle = 2πr
According to the given question we have
central angle of the arc, x = 15 degrees
Arc length = 3 cm
Let r be the radius of the given circle.
Then,
Arc length = 2πr[tex](\frac{15}{360} )[/tex]
⇒ 3 ×[tex]\frac{360}{15}[/tex] = circumference of the circle ( circumference or circle =2πr)
⇒ circumference of the circle = 72 cm
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need help please!!!!!!
At Ashley Furniture Store, there is a marble table that you want to
purchase for your mother. The length of the table is (-8x+2) and the width
of your rug is (3x-4). What is the total area of the table? Solve the
problem using the best method. Write the answer as a trinomial.
Step-by-step explanation:
in my opinion
total area = the width × the length
= (3x-4)(-8x+2)
= -24x²+6x+32x -8
= -24x² + 38x -8
A triangle is reduced.
A triangle has a base of 16 inches, height of 12 inches, and side length of 20 inches. A smaller triangle has a base of 12 inches, height of 9 inches, and side length of blank.
Not drawn to scale
What is the perimeter of the reduced triangle, in inches?
15
21
36
48
Answer:
c.) 36
Step-by-step explanation:
The triangle was reduced by 36 inches
A circle with a radius of 6 m has an arc of 4 pi m. What is the measure of the centra angle?
Answer: Since the arc length is given (4 ) and the radius is given (6), the central angle can be found
Arc Length = theta * r
4 pi = theta * 6 Divide by 6
4 pi / 6 = theta
theta = (2/3) pi
Step-by-step explanation:
slove for x 10(2x-4)=100x A.x=7 B.x=3 C.x=1/2 D.x=-1/2
Answer:
The answer is D. x=-1/2
Step-by-step explanation:
multiply the parantheses by 10 that'll give us 20x-40=100x2. move terms, that'll give us 20x-100x=403. subtract 100x from 20x, that'll give us -80x=404. divide both sides by -80, which is x=-1/2Answer:
D. x = -1/2Step-by-step explanation:
10(2x - 4) = 100x1. Divide both sides by 10.
10/10 (2x - 4) = 100x/102x - 4 = 10x2. Add 4 to both sides.
2x - 4 +4 = 10x + 42x = 10x + 43. Subtract 10x from both sides.
2x - 10x = 10x + 4 - 10x-8x = 44. Divide both sides by -8.
-8x/-8 = 4/-8x = -1/2The answer is D.
What is the value of the expression
below when a
8, b = 16, and c = -4 ?
Answer:
35
Step-by-step explanation:
5*³√8-（-4）*√16+9=5*2+4*4+9=35
Cynthia is flying a kite in her back pasture. She let out 50 meters of kite string and the string makes an angle of elevation with the ground of 42. How high is the kite flying to the nearest tenth of a meter
The required kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.
To find the height at which the kite is flying, we can use trigonometry, specifically the tangent function. The tangent of the angle of elevation (42 degrees) is the ratio of the height (h) of the kite to the distance from Cynthia to the kite (50 meters).
The formula for the tangent of an angle is:
[tex]tan(angle) = opposite/adjacent[/tex]
In this case, the angle is 42 degrees, the opposite side is the height of the kite (h), and the adjacent side is the length of the string (50 meters).
[tex]tan(42^o) = h / 50[/tex]
To find the height (h), we can rearrange the equation:
[tex]h = 50 * tan(42^o)[/tex]
Now, let's calculate the height:
[tex]h =50 * tan(42^o)[/tex]
h ≈ 50 meters * 0.9004
h ≈ 45.02 meters (rounded to two decimal places)
So, the kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.
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10.
(08.04 MC)
The graph of the function C(x) = −0.34x2 + 12x + 62 is shown. The function models the production cost, C, in thousands of dollars for a tire company to manufacture a tire, where x is the number of tires produced, in thousands:
graph of a parabola opening down passing through points negative 4 and 57 hundredths comma zero, zero comma 62, 1 and 12 hundredths comma 75, 17 and 65 hundredths comma 167 and 55 hundredths, 34 and 18 hundredths comma 75, and 39 and 87 hundredths comma zero
If the company wants to keep its production costs under $75,000, then which constraint is reasonable for the model? (1 point)
−4.57 ≤ x ≤ 39.87
1.12 ≤ x ≤ 34.18
−4.57 ≤ x ≤ 1.12 and 34.18 ≤ x ≤ 39.87
0 ≤ x < 1.12 and 34.18 < x ≤ 39.87
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Answer:
1.12 ≤ x ≤ 34.18
Step-by-step explanation:
This constraint ensures that the number of tires produced, represented by x, falls within the range where the production costs, represented by C(x), are below $75,000.
help v qucik pleaseeeeee
[tex](x - 4) {}^{2} + (y - 1) {}^{2} = r {}^{2} [/tex]
passes through ( 4 , -4 )
[tex](4 - 4) {}^{2} + ( - 4 - 1) {}^{2} = r {}^{2} [/tex]
[tex]r {}^{2} = ( - 5) {}^{2} [/tex]
[tex]r {}^{2} = 25[/tex]
[tex]r = \sqrt{25} = 5[/tex]
Your radius is 5 units
[tex]c = 2\pi \: r \\ c = 2 \times 3.14 \times 5 \\ c = 31.4[/tex]
To Draw:Place your center at the point x=4 and y=1
Then take your radius 5 units by going straight down left right or up by 5 units
AND DRAW