Answer:
y-5=3x+2
Step-by-step explanation:
1) to make up the equation through the given two points:
[tex]\frac{x+8}{-6+8}= \frac{y+1}{5+1}; \ => \ y=3x+24[/tex]
2) to change that equation according to the condition:
y-5=3x+24-5; ⇔ y-5=3x+19.
P.S. the way suggested above is not the shortest one.
A diver is standing on a platform 24ft. Above the pool. He jumps from the platform with an initial upward velocity of 8ft/s. Use the formula h(t)=-16^2+vt+s, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How long will it take for him to hit the water?
Answer:
He will take 1.5 seconds to hit the water
Step-by-step explanation:
* The formula h(t) = -16t² + vt + s
- h is the his height above the water
- v is his initial up-word velocity
- s is his starting height
- t is the time
* When he hits the water h(t) = 0
- because h is his height above the water
∴ -16t² + vt + s = 0
∵ v = 8 ft/s
∵ s = 24 ft
∴ -16t² + 8t + 24 = 0 ⇒ × (-1)
∴ 16t² - 8t - 24 = 0 ⇒ ÷ 8
∴ 2t² - t - 3 = 0 ⇒ by using factorization
∴ (2t - 3)(t + 1) = 0
∴ 2t - 3 = 0 ⇒ 2t = 3 ⇒ t = 3/2 = 1.5 sec
∴ t + 1 = 0 ⇒ t = -1 ⇒ rejected the time is positive value
* He will take 1.5 seconds to hit the water
Answer: The answers is 1.5 second
Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE? A) The y-coordinates have the same value. B) The x-coordinates have the same absolute value. C) The x-coordinates are opposite numbers. D) Both points are 4 units above the y-axis.
Answer:
A) The y-coordinates have the same value.
Step-by-step explanation:
Answer:
D) Both points are 4 units above the y-axis.
Step-by-step explanation:
Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE?
A) The y-coordinates have the same value. TRUE. The y-coordinates have the value 4.
B) The x-coordinates have the same absolute value. TRUE. 3 and -3 have the same absolute value, |-3| = |3| = 3.
C) The x-coordinates are opposite numbers. TRUE. 3 and -3 are opposite numbers.
D) Both points are 4 units above the y-axis. NOT TRUE. Both points are 4 units above the x-axis.
Joyce paid $96.00 for an item at the store that was 20 percent off the original price. What was the original price?
Answer:
$120
Step-by-step explanation:
✯Hello✯
↪ If we know that the original price was 20% more than what was payed for it we can form an equation
↪ 80%(x)=96 when we solve this x=120
↪ The original price was 120
↪ We can check this by working out 20% of 120 which is 24 and 120-24-96
HOPE THIS HELPS
❤Gianna❤
Find the zeroes of the following equation:
1/x = x - 1
What is special about one of the zeroes?
Answer: [tex]\bold{x=\dfrac{1\pm \sqrt5}{2}}[/tex]
both zeros are irrational numbers
Step-by-step explanation:
Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.
[tex]\dfrac{1}{x}=x-1\qquad \text{Restriction: }x\neq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=\dfrac{-(-1)\pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}\\\\\\x=\dfrac{1\pm \sqrt5}{2}[/tex]
write the quadratic question f(x)=3x^2-24x+49 in the form of f(x)= a(x-h)^2+k
Answer:
f(x) = 3(x -4)^2 +1
Step-by-step explanation:
Usually you start by factoring the leading coefficient from the first two terms:
f(x) = 3(x^2 -8x) +49
Now, you add the square of half the x-coefficient inside parentheses, and subtract the same quantity outside.
f(x) = 3(x^2 -8x +(-4)^2) -3(-4)^2 +49
= 3(x -4)^2 -48 +49
f(x) = 3(x -4)^2 +1 . . . . . . . . the vertex form you desire
Plz help me with questions 9&10. Show your work and explain how you got your answer so I understand because I just don’t understand this math we’re doing.
Answer:
10.) 116.6
Step-by-step explanation:
10.) add 100^2 + 60^2 = c^2
10,000 + 3600 = c^2
√13,600 = √c^2
116.6 = c
hope this helps!!
Please help me! I will give brainliest to the person who answers correctly.
In triangle XYZ provide the following ratios:
sin X ____ (express in fractional form, don't simplify)
XY ____ (to the nearest tenth)
cos X ____ X (express in fractional form, don't simplify)
tan X ____ (express in fractional form, don't simplify)
Thanks!
Answer:
sin(X) = 6/7.5XY = 4.5cos(X) = 4.5/7.5tan(X) = 6/4.5Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
_____
Comment on the triangle and ratios
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
[tex]64 {x}^{2}- 25y^{2} [/tex]
Factor.
[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 64x^2-25y^2~~ \begin{cases} 64=8\cdot 8\\ \qquad 8^2\\ 25=5\cdot 5\\ \qquad 5^2 \end{cases}\implies 8^2x^2-5^2y^2\implies (8x)^2-(5y)^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8x-5y)(8x+5y)~\hfill[/tex]
Please help it would be a greatly supported.
Answer:
D. N = w² + 8w + 12
Step-by-step explanation:
The current size is w by w+4, so the area is ...
A = w(w+4)
When each dimension is increased by 2, the new size is (w+2) by (w+4+2). The latter dimension can be simplified to (w+6). Now, the new area is ...
N = (w+2)(w+6) = w² +8w +12 . . . . . . . matches choice D
Mr. Yarmus purchased 3 cups of coffee for his friends. He paid $7.29 in total, including an 8 percent sales in tax. What was the cost per cup of coffee, excluding tax???? PLZZ I will give you 100 pointd
Answer:
$2.25
Step-by-step explanation:
Let c represent the cost of a cup of coffee. Then the total amount paid for 3 cups is ...
3c + 3c·0.08 = 7.29
3.24c = 7.29
c = 7.29/3.24 = 2.25
A cup of coffee costs $2.25.
_____
Comment on "I will give you 100 pointd"
I don't know what a "pointd" is, but I suggest you not make promises you cannot keep.
Given: m
KL
=25°, m
MJ
=85°
Find: m∠MEJ
Answer:
30°
Step-by-step explanation:
If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.
If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.
Thus, the measure of the angle ELM is 180°-42.5°=137.5°.
Consider triangle EML. In this triangle,
m∠MEL=180°-137.5°-12.5°=30°.
Thus, m∠MEJ=30°.
Answer:
30°
Step-by-step explanation:
x=(a-b)/2 because of secants exterior angles
x=(85-25)/2 Substitution
x=60/2 Algebra
x=30° Answer
the equation of a circle is x + 4 squared plus y - 5 squared equals 121 what is the center and radius of the circle
The center of the circle is (-4, 5) while the radius is 11 units.
Georgia will use the pattern shown to make a square pyramid out of cardboard. The square pyramid will not have a bottom. How much cardboard will she need if a = 14 in. and b = 9 in.? PLEASE HELP
Answer:
252 square inches
Step-by-step explanation:
Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches. The area of a triangle is ...
A = (1/2)bh
so one face of Georgia's pyramid will have an area of ...
A = (1/2)(9 in)(14 in) = 63 in^2
Then all four faces will have a total area of ...
(63 in^2) · 4 = 252 in^2
_____
Comment on the pattern
The pattern shown includes the base of the pyramid. The problem text says the base is not included. We have assumed that the base is not included. (For Georgia's pyramid, a different pattern would be more to the point: see attachment.)
252 square inches of cardboard she needed if a = 14 in. and b = 9 in
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The square pyramid will not have a bottom.
We have to find the lateral surface area as the base area is not included.
Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches.
The area of lateral face is A = (1/2)bh
A = (1/2)(9 in)(14 in)
= 63 square inches
There are four faces so, 4×63 = 252 square inches
Lateral surface area is 252 square inches
Hence, 252 square inches of cardboard she needed if a = 14 in. and b = 9 in
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Evelyn sold 11 boxes of chocolate cookies. Each box contained 12 cookies. Round to the nearest ten and then multiply to find the total number of cookies.
Answer: 100 cookies approximately.
Step-by-step explanation:
To round to the nearest ten:
- If the digit located in the units place of the number is [tex]<5[/tex], then you must round the number down.
- If the digit located in the units place of the number is [tex]\geq5[/tex], then you must round the number up.
The digit located in the units place of the number 11 is 1 and [tex]1<5[/tex], therefore you must round the number down to: 10
The digit located in the units place of the number 12 is 2 and [tex]2<5[/tex], therefore you must round the number down to: 10
Multiply 10 by 10 to estimate the total number of cookies:
[tex]Total_{(cookies)}=10*10\\Total_{(cookies)}=100[/tex]
(100 cookies approximately)
Hello,
I propose this exercise if anyone can answer me.
Let ABC be a right triangle, of hypotenuse BC = a, where [tex]A\widehat{B}C=x[/tex].
Let A' be the symmetric of A with respect to BC.
Determine x so that:
-the area of the triangle AA'C is maximum
Show and justify all the steps (take the picture).
Thank you.
Answer:
for fixed AC, x = 45° maximizes the areafor fixed AB, x → 90° maximizes the areaStep-by-step explanation:
Call the point of intersection of AA' and BC point X. Then ...
CX = AC·cos(90°-x) = AC·sin(x)
and the area of AA'C is ...
area = AC·CX·sin(90°-x) = AC²·sin(x)cos(x) = (1/2)AC²·sin(2x)
Obviously, area is maximized for 2x = π/2, or x = π/4 when AC is fixed.
___
On the other hand, ...
AC = AB·tan(x)
so the area of the triangle is ...
area = (1/2)AC²·sin(2x) = (1/2)(AB·tan(x))²·sin(2x) = AB²·sin(x)³/cos(x)
For fixed AB, area approaches infinity as x approaches 90°.
_____
Comment on the attachments
The attached diagrams show AC=1 and B free to move. Values of x around 45° are shown. The number in the middle of the figure is the approximate area of ΔAA'C.
a snowman is made of three spherical snowballs with a diameters of 3 feet, 2 feet, and 1 foot. what is the total volume of the snowman?represent your answer in terns of pi
Answer:
The total volume of the snowman is [tex]6\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
step 1
Find the volume of the spherical snowball with a diameter of 3 feet
Find the radius
[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (1.5)^{3}[/tex]
[tex]V1=\frac{9}{2}\pi\ ft^{3}[/tex]
step 2
Find the volume of the spherical snowball with a diameter of 2 feet
Find the radius
[tex]r=2/2=1\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (1)^{3}[/tex]
[tex]V2=\frac{4}{3}\pi\ ft^{3}[/tex]
step 3
Find the volume of the spherical snowball with a diameter of 1 feet
Find the radius
[tex]r=1/2=0.5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (0.5)^{3}[/tex]
[tex]V3=\frac{1}{6}\pi\ ft^{3}[/tex]
step 4
Find the total volume
[tex]V=V1+V2+V3[/tex]
substitute the values
[tex]V=\frac{9}{2}\pi+\frac{4}{3}\pi+\frac{1}{6}\pi=\frac{27+8+1}{6}\pi=6\pi\ ft^{3}[/tex]
at track practice Bethany ran 5 more miles this week than last week. write an expression to show the total miles she ran both weeks
Answer:
x+5=m
Let x be the number of miles that were run the first time.
Add five to the original number
M is the total number of miles for both weeks
The perimeter of a rectangle is 14.
Write the function that describes its area in terms of one of the sides
If one side is a, the formula will be S=______
To express the area of a rectangle with a perimeter of 14 in terms of one side, use the function S = 7a - a² where S is the area and a is one side length.
Explanation:To find the function that describes the area of a rectangle in terms of one of its sides with a given perimeter, we can follow these steps. Let's say one side length is a; we will then call the other side length b. The perimeter of a rectangle is given by the formula P = 2a + 2b, where P is the perimeter, and a and b are the lengths of the sides of the rectangle.
Given that the perimeter is 14, we can express b in terms of a as follows:
b = (14 - 2a) / 2
Next, to find the area (S) in terms of a, we multiply the two side lengths together.
S = a × b
Substitute b into the area formula:
S = a × ((14 - 2a) / 2)
Simplifying the formula gives us the function for the area in terms of side a:
S = (14a - 2a²) / 2
Which simplifies further to:
S = 7a - a²
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What are the critical values X2/L and X2/R that correspond to a 99% confidence level and a sample size of 30?
13.787, 53.672
13.121, 52.336
14.257, 49.588
19.768, 39.087
Answer:
c
Step-by-step explanation:
2.6 repeated simplified as a fraction Please help asap!!!
Answer:
8/3
Step-by-step explanation:
Let S represent the value of 2.666...(repeated). Then 10S will have the value 26.666...(repeated). Subtracting S from 10S, we have ...
10S -S = 26.666... - 2.666... = 24
9S = 24
S = 24/9 = 8/3
The improper fraction equivalent of 2.666...(repeated) is 8/3.
_____
In general, if the number of repeated digits is n, you do this procedure multiplying the number by 10^n before you do the subtraction. The result is a fraction with (10^n)-1 as a denominator. That is, for a 2-digit repeat, the denominator will be 99; for a 6-digit repeat, 999999.
Knowing this, you can immediately recognize that 0.6...(repeated) = 6/9 = 2/3. Then your number 2.666...(repeated) is 2 2/3 = 8/3.
The repeating decimal 2.6 (2.66...) can be simplified as a fraction by setting it equal to a variable, multiplying by a power of 10 to eliminate the decimal, subtracting the original equation, and solving for the variable. This process results in the simplified fraction 8/3.
Explanation:The number 2.6 repeated refers to the number where the digit 6 repeats indefinitely. To simplify it as a fraction, we can do the following steps:
Let's call the repeating decimal x. So, x = 2.66...Next, to eliminate the decimal, you multiply by a power of 10. Here, because there is one repeating digit, we multiply by 10. So, 10x = 26.66...Subtract the two equations: 10x - x = 26.66... - 2.66..., which simplifies to: 9x = 24.Finally, solve for x by dividing both sides by 9, you get x = 24/9. This fraction can be simplified to 8/3.Learn more about Repeating Decimals here:https://brainly.com/question/31325113
A cubical tank with an edge length of 20 cm is filled with 3.75 liters of water. How much more water is needed to fill the tank completely? Give your answer in liters.
Answer:
4.25 Liters
Step-by-step explanation:
Edge of Cubical tank
= 20 cm
= 20 (0.01 m)……………..1 meter = 100 cm
= 0.2 m
Volume of Tank
= ( Edge ) ^ 3
= ( 0.2 m ) ^3
= 0.008 m^3
= 8 liters…………….. 1 m^3 = 1000 Liters
Volume required to fill the tank
= 8 - 3.75
= 4.25 Liters
2 2/7 divided 2 1/2=
Answer: [tex]\frac{32}{35}[/tex]
Step-by-step explanation:
We need to convert the mixed numbers into fractions.
The new numerator will be the sum of the numerator of the fractional part and the product obtained by multiplying the denominator of the fractional part by the whole number part.
The new denominator will the the same denominator of the fractional part.
Then:
[tex]2\ \frac{2}{7}=\frac{2+(2*7)}{7}=\frac{16}{7}[/tex]
[tex]2\ \frac{1}{2}=\frac{1+(2*2)}{2}=\frac{5}{2}[/tex]
Dividing the fractions, we get:
[tex]\frac{\frac{16}{7}}{\frac{5}{2}}=\frac{16*2}{7*5}=\frac{32}{35}[/tex]
f(x)=9x^3+2x2-5x+4 and g(x) =5x^3-7x+4.What is f(x)-g(x)?
show all steps and final answer
Answer:
The answer is 4x^3 + 2x^2 + 2x
Step-by-step explanation:
To find a subtracted function, simply change all of the signs in the second function and then combine like terms.
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
f(x) - g(x) = 4x^3 + 2x^2 + 2x
Solve for p; 8+p=w I can find 1p or p by ____________ on both sides of the equation
PLZ show your work Thank You
Answer:
p = w - 8
Step-by-step explanation:
I can find 1p or p by subtracting 8 on both sides of the equation.
We need to isolate the variable p here, so we subtract 8 from both sides.
Every square meter of solar paneling produces 0.2 kilowatts of electricity. Which of the following models this situation?
*tap the picture for the answer choices.
Answer:
B) linear function with a positive rate of change
Step-by-step explanation:
Each increase by 1 m^2 in area produces the same 0.2 kW increase in power, so the relationship between area and power is linear. Since they both go up (or both go down), the "rate of change" is positive. (If it were negative, one would go down when the other went up.)
The best description is that of B.
f(x)=2x is transformed to g(x)=5⋅2x. How was the graph affected?
shifted up by 5 units
shifted down by 5 units
stretched by a factor of 5 units
compressed by a factor of 5 units
Answer:
vertically stretched by a factor of 5
Step-by-step explanation:
Multiplying the function value by 5 makes each vertical coordinate 5 times the value it was, so it is 5 times as far away from the x-axis. This has the appearance of stretching the graph vertically by a factor of 5.
_____
Comment on the answer choices
The stretch factor is a "pure number", a ratio of new units to old units. It is "5", not "5 units."
For example, if f(x) is 1 ft (1 unit, where the unit is a foot), then g(x) = 5 ft, the value of f(x) multiplied by 5. It is not 5 ft^2, as you would get if f(x) were multiplied by 5 units, or 5 ft.
The diagonals of kite KITE intersect at point P. If M
The diagonals of kite KITE intersect at point P. This would be at 44 degrees then.
Answer: 44 degrees
..._..._..._..._..._..._
appreciate
What is the total surface area of the figure shown?
3(20×9)+3((24-9)×8)+(10×8)+(9×10)+((20-8)×10)+((24-9)×10)
=3(180)+3(15×8)+80+90+(12×10)+(15×10)
=540+3(120)+170+120+150
=920+360
=1280
Answers
[tex] {1280cm}^{2} [/tex]
Answer:
[tex]S=1964 in^{2}[/tex]
Step-by-step explanation:
The surface of a rectangular prims is defined as
[tex]S=2lw+2wh+2lh[/tex]
Where [tex]l[/tex] is length, [tex]w[/tex] is width and [tex]h[/tex] is height.
In this case, we have a figure formed by two rectangular prism. We are gonna call Surface 1 to the bottoming prism.
Its diemensions are:
[tex]l=24in\\w=10in\\h=8in[/tex]
So, the Surface 1 is
[tex]S_{1}=2(24)(10)+2(10)(8)+2(24)(8)= 480+160+384=1024in^{2}[/tex]
Now, the dimensions of Surface 2 are
[tex]l=9in\\w=10in\\h=20in[/tex]
Replacing all values, its surface is
[tex]S_{2}= 2(9)(10)+2(10)(20)+2(9)(20)=180+400+360=940in^{2}[/tex]
Therefore, the total surface of the whole figure is
[tex]S=1024+940=1964 in^{2}[/tex]
Which function has the same y-intercept as the line graphed below?
A. y=16-3x/4
B. 24+3y=6x
C. 4y+x=16
D. y+4=2x
Answer:
D. y + 4 = 2x
Step-by-step explanation:
The graph has a y-intercept at (0, -4).
A. y=16 - 3x/4
if x = 0, y = 16. FALSE.
B. 24 + 3y = 6x
If x = 0, 24 + 3y = 0
3y = -24
y = -8. FALSE.
C. 4y + x = 16
If x = 0, 4y = 16
y = 4. FALSE.
D. y + 4 = 2x
If x = 0, y + 4 = 0
y = -4. TRUE.
y = 4 + 2x has the same y-intercept as the graphed line.
10 is 20% of, please answer
Answer:
50
Step-by-step explanation:
20% is the same as 0.2 times something.
So you can create the equation 0.2x = 10. The solution of this equation is x=50.