Answer:
The lowest of three consecutive numbers is [tex]-32[/tex]
Step-by-step explanation:
The question in English
Find the lowest of three consecutive numbers, if the sum of one-half of the lowest number plus one-third of the highest number exceeds the middle number by five.
Let
x-----> the lowest consecutive number
x+1-----> the middle consecutive number
x+2-----> the highest consecutive number
[tex]\frac{x}{2}+\frac{x+2}{3}=(x+1)+5[/tex]
solve for x
[tex]\frac{x}{2}+\frac{x+2}{3}=(x+1)+5\\ \\ \frac{3x+2x+4}{6}=x+6\\ \\5x+4=6x+36\\ \\6x-5x=4-36\\ \\x=-32[/tex]
if W(4,6) and V(-3,-2) what is the length of VW
Answer:
[tex]\large\boxed{VW=\sqrt{113}}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points W(4, 6) and V(-3, -2). Substitute:
[tex]VW=\sqrt{(-3-4)^2+(-2-6)^2}=\sqrt{(-7)^2+(-8)^2}=\sqrt{49+64}=\sqrt{113}[/tex]
Billy has been to three more than four times as many baseball games as Brendan. Brendan has been to 11 baseball games. Complete the equation below to find out how many baseball games Billy has been to.
11 x __ + __ = __
Answer:11x4+3=47
Step-by-step explanation:
Answer:
47
Step-by-step explanation:
11 x 4 + 3 = 47
One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 square meters, what are the lengths of the diagonals?
Answer:
20m and 40m
Step-by-step explanation:
The area (A) of a kite is calculated using the formula
A = [tex]\frac{1}{2}[/tex] product of diagonals
Let one diagonal be d then the other diagonal is 2d ( twice as long )
Hence
[tex]\frac{1}{2}[/tex] × 2d × d = 400
d² = 400 ← take the square root of both sides
d = [tex]\sqrt{400}[/tex] = 20
and 2d = 2 × 20 = 40
The diagonals are 20m and 40m in length
The lengths of the diagonals of a kite, where the area is 400 square meters and one diagonal is twice the length of the other, are 20 meters for the shorter diagonal and 40 meters for the longer diagonal.
Explanation:You asked how the lengths of the diagonals of a kite can be determined given that the area is 400 square meters and one diagonal is twice as long as the other. To find the diagonals, we'll use the formula for the area of a kite, which is Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
Let's denote the shorter diagonal as d, which means the longer diagonal is 2d. Plugging these into the area formula gives us:
400 m2 = (d * 2d) / 2
Multiplying both sides by 2 gives us 800 m2 = d * 2d, which simplifies to 800 m2 = 2d2.
Dividing both sides by 2 gives us 400 m2 = d2. Taking the square root of both sides, we find that d = 20 meters. Hence, the longer diagonal is 2 * 20 meters = 40 meters.
The lengths of the diagonals of the kite are 20 meters and 40 meters.
Jacob made a banner for a sporting event in the shape of a parallelogram. The area of the banner is 127 1/2 square centimeters. The height of the banner is 4 1/4 centimeters. What is the base of the banner?
Answer:
30 cm
Step-by-step explanation:
The area of a parallelogram is given by [tex]A=bh[/tex]
Where
A is the area
b is the base, and
h is the height
Since A and h are given, we plug that in and find the base. Shown below:
[tex]A=bh\\127\frac{1}{2}=b(4\frac{1}{4})\\b=\frac{127\frac{1}{2}}{4\frac{1}{4}}\\b=\frac{\frac{255}{2}}{\frac{17}{4}}\\b=\frac{255}{2}*\frac{4}{17}=30[/tex]
Hence, the base is 30 centimeters
Joe spends $1.75 every time he buys a snack with his lunch. He has $16.25 to spend. Write an inequality showing how many times (x) that Joe can buy a snack with his lunch.
Answer:
16.25=1.75x
Step-by-step explanation:
so write it like this to that the bigger number(16.25) is on the left then write the other number(1.75)then put the X by the 1.75
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive birds nest in the trees.The height of the camera above the water can be modeled by the equation y=-16t^2+400, where t represents the seconds after the camera is dropped. How long will it take before Kay sees the splash from the camera hitting the water.
Answer:
5 seconds it will hit the water.
Step-by-step explanation:
y=-16t²+400
add -16t² to both sides
-16t²=-400
divide both sides by 16
t²=-25
t=√25
t=5
Answer:
t=5
Step-by-step explanation:
t=√25=t=5
■ ■I_____II need the answer please
Answer:
22 degrees
Step-by-step explanation:
Since both triangles correspond, side x is correspondent to 22 degrees, Since that is also the only given piece of information, that is your answer.
a circular swimming pool has a circumference of 188.4 feet. if kelly swims across the pool. how far will she swim
Answer:
C.) 60 feet
Step-by-step explanation:
Knowing that the formula for finding the circumference of a circle is [tex]\pi d[/tex] or [tex]2\pi r[/tex], we are able to set up the equation to be:
[tex]188.4=3.14d[/tex]
[tex]\frac{188.4}{3.14} =d[/tex]
[tex]60=d[/tex]
and done! :)
use the substituition method to solve the system of equation. choose the correct ordered pair 2x+y=8 y= -x+5
The answer is:
[tex]x=3\\y=2[/tex]
Ordered pair: (3,2)
Why?The substitution method for solving system of equations consists in finding the solution by isolating and substituting each variable value into the given equations, doing that, all the variable value can be found.
So, we are given two equations:
[tex]2x+y=8\\y= -x+5[/tex]
We need to substitute (y) into the first equation,so:
[tex]2x+(-x+5)=8[/tex]
[tex]2x-x+5=8[/tex]
[tex]x+5=8[/tex]
[tex]x=8-5[/tex]
[tex]x=3[/tex]
Now that we know "x" we need to substitute it into the second equation, so:
[tex]y=-(3)+5[/tex]
[tex]y=2[/tex]
Hence,
[tex]x=3\\y=2[/tex]
So, the ordered pair will be: (3,2)
Have a nice day!
Answer:
Ordered pair = (3, 2)
Step-by-step explanation:
We are given the following equations and we are to solve them by substitution method:
[tex]2x+y=8[/tex] --- (1)
[tex]y= -x+5[/tex] --- (2)
Substituting the value of y from equation (2) to (1):
[tex]2x+(-x+5) = 8[/tex]
[tex]2x-x+5=8[/tex]
[tex]x = 8-5[/tex]
x = 3
Substituting this value of x in equation (2):
[tex]y = -(3)+5[/tex]
y = 2
So the ordered pair is (3, 2).
Find the surface area of the shape below
Answer:
464 in²
Step-by-step explanation:
Surface area of a figure is the total area of its sides.
We shall assume that the shape is a solid.
2 × (5 × 10) = 2 × 50 = 100
2 × 1/2 × 4(10+16) = 4 × 26 = 104
10 × 10 = 100
10 × 16 = 160
Total area = 100 + 104 + 100 + 160
= 464 in²
The surface area of a shape can be found by using specific formulas that differ depending on the shape's dimensions and type. For a sphere, the formula is A = 4πr², while for a rectangle, it's A = length × width. Other shapes like a cylinder require calculating the area of each side then adding them together.
Explanation:In order to find the surface area of a shape, we first need to know the dimensions and type of the shape. For example, to find the area of a sphere, you'd use the formula A = 4πr², where 'r' is the radius of the sphere. To find the area of a rectangle, you'd use A = length × width.
If we're talking about a more complex shape, like a cylinder, we need to calculate the area of each face or side separately and then add them together for the total surface area. For example, the total surface area of a cylinder is given by A = 2πr(r + h), where 'r' is the radius of the base and 'h' is the height of the cylinder.
These are just a few examples. The calculation of the surface area will depend on the specific dimensions and type of the shape in question.
Learn more about Surface Areahttps://brainly.com/question/12448114
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Need help don’t understand
Answer:
4 units left and 2 units up
Step-by-step explanation:
Translation notation is the words you would use to describe the translation of the point or shape. It says that the point was translated 4 units left and 2 units up, and that is the translation notation.
1. 8397 divided by 27
2. 9396 by 18
3. 8442 by 14
4. 7854 by 23
5a. 7533 by 34
5b. explain the calculation
1. 311
2. 522
3. 603
4. 341.47826087
5. 221.558823
5b. All i did was divide the regular way or u could just put it in a calculator?
Juan pulled a red card from the deck of regular playing cards. This probability is 2652 or 12 . He puts the card back into the deck. Will his chance of pulling a red card next time change?
Answer:
no
Step-by-step explanation:
if he randomly pulls it out it's still the same number of red cards and also the total number of cards as always
can't change
Brendan needs to answer 0.70 of the test questions correctly to pass the test. What percent is this??
That would be 70 percent.
(-1, 1) is a solution to the following system of equations:
True or false
no its not l. the top is 3 the bottom is one
Write the quadratic equation in general quadratic form below.
17x2 = 12x
Answer: [tex]\bold{\dfrac{12\pm \sqrt{144-0}}{2(17)}}[/tex]
Step-by-step explanation:
[tex]17x^2=12x\quad \rightarrow \quad 17x^2-12x+0=0\quad \rightarrow \quad a=17,\ b=-12,\ c=0\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(17)(0)}}{2(17)}\\\\\\.\ =\dfrac{12\pm \sqrt{144-0}}{2(17)}[/tex]
Answer:
General quadratic form is 17x²- 12x + 0 = 0.
Step-by-step explanation:
Given : 17x² = 12x.
To find : Write the quadratic equation in general quadratic form below.
Solution : We have given that 17x² = 12x.
General quadratic form is : [tex]ax^{2} + bx + c = 0[/tex].
We have 17x² = 12x.
Convert it in to general quadratic form
On subtracting both sides by 12x .
17x²- 12x + 0 = 0.
Here a = 17 , b = - 12 , c = 0 .
Therefore, General quadratic form is 17x²- 12x + 0 = 0.
A princess hat for a costume is shaped like a cone. The base of the cone is 12 in across and the height is 8
in. The slant height of the outside edge, which is unknown, is the hypotenuse of the right triangle formed with
the radius and the height of the cone.
(a) Sketch the princess hat. Label the known lengths as described and label the unknown length as x.
(b) What is the slant height of the outside edge?
Answer:
Part a) The drawn in the attached figure
Part b)The slant height of the outside edge is [tex]x=10\ in[/tex]
Step-by-step explanation:
Part a) The drawn in the attached figure
Part b) What is the slant height of the outside edge?
we have that
The diameter of the base of the cone is 12 in
so
[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
Applying the Pythagoras Theorem find the slant height x
[tex]x^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]x^{2}=6^{2}+8^{2}[/tex]
[tex]x^{2}=100[/tex]
[tex]x=10\ in[/tex]
NEED HELP !! BASIC MATH
Step-by-step explanation:
350-40x>40
Now you subtract 350 from both sides. -40x is greater than negative 310. Divide by -40 on both sides and flip the sign since you are dividing by a negative. x<31/4 or 7.75, so round down and she can only have 7 exhibits
Answer:
she can have at most seven exhibits
Step-by-step explanation:
do 350-40 because that is the amount of space needed for a walkwaynext do 310/40 because that is the amount of space is needed for each exhibitround 7.75 down because you can't have part of an exhibit:)how do you solve this?
3x(x+4)=0
Answer:
3x=0 or x+4=0
x=0 or x=−4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x2+12x=0
Step 2: Factor left side of equation.
3x(x+4)=0
Step 3: Set factors equal to 0.
3x=0 or x+4=0
x=0 or x=−4
How to do this ?? How
Answer:
The answer in the procedure
Step-by-step explanation:
we have
x+2y > 6
Isolate the variable y
y > -0.5x+3
The solution of this inequality is the shaded area above the dashed line
The equation of the dashed line is y=-0.5x+3
The slope of the dashed line is negative (m=-0.5)
The y-intercept of the dashed line is 3 (value of y when the value of x is equal to zero)
The x-intercept of the dashed line is 6 (value of x when the value of y is equal to zero)
Plot the intercepts to draw the dashed line and shaded the area above the dashed line
see the attached figure
Can you help me please
Answer:
[tex]\large\boxed{A=(120+32\pi)cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
We have the half of circle and a triangle.
The fromula of an area of a circle:
[tex]A_O=\pi r^2[/tex]
r - radius
We have r = 8cm. Substitute:
[tex]A_O=\pi(8)^2=64\pi\ cm^2[/tex]
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b- base
h - height
We have b = 8cm + 8cm = 16cm and h = 15cm. Substitute:
[tex]A_\triangle=\dfrac{(16)(15)}{2}=(8)(15)=120\ cm^2[/tex]
The area of the figure:
[tex]A=\dfrac{1}{2}A_O+A_\triangle[/tex]
Substitute:
[tex]A=\dfrac{1}{2}(64\pi)+120=32\pi+120=(120+32\pi)cm^2[/tex]
HELP ASAP! GIVING BRAINLIEST!!
∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side BC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side AC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units.
∠ABC ≈ °
A) 55.21
B) 85.16
C) 105.26
D) 114.11
Answer:
AB is A
BC is B
AC is D
Step-by-step explanation:
To find the length of each side, use the formula for the distance between coordinate pairs.
We can find the distance using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (2,1) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(2--3)^2+(1-6)^2} \\d=\sqrt{(2+3)^2+(-5)^2} \\d=\sqrt{25+25}\\d=\sqrt{50}[/tex]
BC
We then substitute (2,1) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9-2)^2+(5-1)^2} \\d=\sqrt{(-7)^2+(4)^2} \\d=\sqrt{49+16}\\d=\sqrt{65}[/tex]
AC
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9--3)^2+(5-6)^2} \\d=\sqrt{(12)^2+(-1)^2} \\d=\sqrt{144+1}\\d=\sqrt{145}[/tex]
What is the degree measure of SRP? Please show work!
well, we have a missing point of R, but since is part of one of the tangent lines, we can safely assume is the point where the PR of 5 inches is at.
what is the angle at point R? namely the ∡SRP, well, SR is a tangent, RP is a radius line, they both touch/intersect at point R, thus R is the point of tangency for those two, and the point of tangency is always a 90° angle.
x/2+3=-5 what does x equal?
x/2+3=-5
x/2 = -5+3
x/2 = -2
x = -2(2)
x = -4
Answer:
X = - 16
PLEASE RATE AND THANKS ME IF THIS HELPED
what value of x makes the equation sin x=cos43
Answer:
0.55511330152
Step-by-step explanation:
Answer:
x = 47
Step-by-step explanation:
Using the cofunction identity
cos x = sin(90 - x), hence
cos43 = sin (90 - 43) = sin47
Solve for the roots in the equation below.
x4 + 3x2 - 4 = 0
Answer: x = {1, -1, 2i, -2i}
Step-by-step explanation:
x⁴ + 3x² - 4 = 0
∧
-1 +4 = 3 this works!
(x² - 1)(x² + 4) = 0
x² - 1 = 0 and x² + 4 = 0
x² = 1 and x² = -4
x = ±1 and x = ± 2i
x = 1, -1 and x = 2i, -2i
A sphere and a cylinder have the same radius and height. The volume of the cylinder is Amie found the volume of the sphere.
Answer:
The answer is the first
Amie should have multiplied 54 by 2/3
Step-by-step explanation:
* Lets start with the rule of the volume of each solid
∵ Volume the sphere = 4/3 π r³
∵ Volume the cylinder = π r² h
∵ The radii and the heights of the sphere and the cylinder are equal
∴ The ratio between there volumes are
4/3 π r³ : π r² h
- Lets divide each part by π r²
∴ 4/3 r : h
∵ The height of the sphere = the diameter of it = 2r
∴ The height of the cylinder = 2r
∴ The ratio will be:
4/3 r : 2r
- Now divide each part by 2r
∵ (4/3)r ÷ 2r = 2/3
∵ 2r ÷ 2r = 1
∴ The ratio is 2/3 : 1
∴ The volume of the sphere = 2/3 the volume of the cylinder
∵ The volume of the cylinder = 54 m³
∴ The volume of the sphere = 2/3 × 54 = 36 m³
∴ The answer is Amie should have multiplied 54 by 2/3
Answer:
The answer is Amie should have multiplied 54 by 2/3
Step-by-step explanation:
Help please 2 questions(25 points)
First one is C and second one is A
PLS HELP ASAP. IM TIMED
Read the following statement:
Line segment CD is congruent to line segment EF.
Which of the following is an equivalent statement?
EXPLANE HOW YOU GOT IT AND WHY
CD overbar similar to EF overbar
CD overbar equal to EF overbar
CD overbar element to EF overbar
CD overbar congruent to EF overbar
Here is your answer
d. CD overbar congruent to EF overbar.
REASON:
Since, line segment CD is congruent to line segment EF and im geometry an overbar represents a line segment.
So, we can say that CD overbar means line segment CD and EF overbar means line segment EF.
Hence, the statement is justified.
HOPE IT IS USEFUL
Here is your answer
d. CD overbar congruent to EF overbar.
REASON:
Since line segment CD is congruent to line segment EF and in geometry an overbar represents a line segment.
So, we can say that CD overbar means line segment CD and EF overbar means line segment EF.
Hence, the statement is justified.
hope this helps :)
remember to love urself <3