Answer:
The length of the radius of the sphere is 11.0 units
Step-by-step explanation:
we know that
To calculate the radius of the sphere, we can use the distance formula
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}[/tex]
where
d is the length of the radius
(x_1,y_1,z_1) is the center of the sphere
and
(x_2,y_2,z_2) is one point on the surface of the sphere
we have
[tex](x_1,y_1,z_1)=(0,0,0)[/tex]
[tex](x_2,y_2,z_2)=(4,9,-5)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-0)^{2}+(9-0)^{2}+(-5-0)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(9)^{2}+(-5)^{2}}[/tex]
[tex]d=\sqrt{122}[/tex]
[tex]d=11.0\ units[/tex]
therefore
The length of the radius of the sphere is 11.0 units
a quadrilateral has sides that measure 12 centimeters, 10 centimeters, 10 centimeters, and 5 centimeters. The side that measures 12 centimeters is parallel to the side that measures 5 centimeters. What is the figure l?
Answer:
Trapezium.
Step-by-step explanation:
Some of the properties of a trapezium include:
- A pair of opposite parallel sides (the long and short base)
- Has 4 sides (meaning it is a quadrilateral)
-
write (-3, -5) (-1, -19) in point slope form
Answer:
(y + 5) = -7(x + 3)
Step-by-step explanation:
Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find Slope
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{-19 - (-5)}{-1 - (-3)}[/tex]
m = [tex]\frac{-19 + 5}{-1 + 3}[/tex]
m = [tex]\frac{-14}{2}[/tex]
m = -7
Step 2: Put into point slope form
Point Slope Form: (y - y1) = m(x - x1)
(y - (-5)) = -7(x - (-3))
(y + 5) = -7(x + 3)
Two parallel lines are crossed by a transversal.
What is the value of x?
Answer:
x = 115°
Step-by-step explanation:
A bookcase has two shelves. The top shelf has 10 more than 1/3 the number of books on the bottom shelf. There are 12 books on the bottom shelf. How many books are on the top shelf?
a.4
b.14
c.40
d.46
Show your work below!!!
Answer: b.14
Step-by-step explanation:
We have two shelves, the top shelf [tex]s_{t}[/tex] and the bottom shelf [tex]s_{b}[/tex].
Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:
[tex]s_{t}=10+\frac{1}{3}s_{b}[/tex] (1)
Then, we are told there are 12 books on the bottom shelf:
[tex]s_{b}=12[/tex] (2)
Substituting (2) in (1):
[tex]s_{t}=10+\frac{1}{3}(12)[/tex] (3)
[tex]s_{t}=10+\frac{12}{3}[/tex] (4)
[tex]s_{t}=14[/tex] (5) This is the number of books on the top shelf
Hence, the correct option is b.
PLEASE HELP I HAVE NO IDEA IM GONNA FAIL
Yo sup??
Dude chill....u will pass for sure :)
SA of composite figure=sum of SA of individual faces
=SA of 2 triangles+SA of rectangle 1+SA of lower cuboid
=2*1/2*8*10+2*9*14+3*10*14+2*10*10
=80+252+420+200
=952 ft^2
Hope this helps.
4(960+2-125)+5 what is the solution to this mathematical expression?
Answer:
3353
Step-by-step explanation:
1. Simplify 960 + 2 to 962.
4 · (962 − 125) + 5
2. Simplify 962 − 125 to 837.
4 · 837 + 5
3. Simplify 4 · 837 to 3348.
3348 + 5
4. Simplify
3353
Answer: 3353
Step-by-step explanation:
4 × 960 = 3840
4 × 2 = 8
4 × -125 = -500
-500 + 8 + 3840 = 3348
3348 + 5 = 3353
I NEED HELP FAST PLEASE WILL GIVE BRAINIEST
Gavin deposited money into his savings account that is compounded annually at an interest rate of 9%. Gavin
thought the equivalent quarterly interest rate would be 2.25%. Is Gavin correct? If he is, explain why. If he is
not correct, state what the equivalent quarterly interest rate is and show how you got your answer.
Answer:
He is correct.
Step-by-step explanation:
9÷4=2.25
The equivalent quarterly interest rate is 2.25%. The annual interest is converted quarterly by dividing the annual rate by 4.
What is the definition of simple interest?Simple interest is a notion employed in various industries, including banking, finance, and automobiles.
Gavin put money into his savings account, which is compounded annually at an interest rate of 9%
The corresponding quarterly interest rate is, 2.25%.
The annual interest is converted quarterly as;
[tex]\rm n= \frac{9}{4} \\\\ n= 2.25\%[/tex]
Hence, the equivalent quarterly interest rate is 2.25%.
To learn more about simple interests, refer to;
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4 sisters love barrettes. they have a value pack that contains 92 barrettes. how many barrettes can each sister have if they share equally?
Answer:
23
Step-by-step explanation:
92÷4=23
There are a total of 92 barrettes and 4 sisters so you divide the total amount of barrettes with the total amount of people present.
Answer:
23 barrettes
Step-by-step explanation:
92 divided by 4=23 There are a total of 92 barrettes and 4 sisters so you divide the total amount of barrettes with the total amount of people present.
In another way :
So you have 92 then you divide 92 by 4 and that equals 23
List the next four multiples of the unit fraction 1/2 4th grade
Step-by-step explanation:
We have:
The unit fraction = [tex]\dfrac{1}{2}[/tex]
To find, the next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] = ?
∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex]
The first multiple = [tex]\dfrac{1}{2}\times 2= \dfrac{2}{2} =1[/tex]
The second multiple = [tex]\dfrac{1}{2}\times 3= \dfrac{3}{2}[/tex]
The third multiple = [tex]\dfrac{1}{2}\times 4= \dfrac{4}{2} =2[/tex]
The fourth multiple = [tex]\dfrac{1}{2}\times 5= \dfrac{5}{2}[/tex]
∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] are
[tex]\dfrac{2}{2}[/tex] ( 1), [tex]\dfrac{3}{2}[/tex], [tex]\dfrac{4}{2}[/tex] (2) and [tex]\dfrac{5}{2}[/tex].
The first four multiples: [tex]\frac{1}{2}, 1, \frac{3}{2}, 2[/tex]. A multiple of a fraction is found by multiplying that fraction by whole numbers.
To find the next four multiples of the unit fraction [tex]\frac{1}{2}[/tex], we can begin by understanding what a multiple of a fraction means.
Let's calculate the first four multiples of [tex]\frac{1}{2}[/tex]:
First multiple: [tex]1 \times \frac{1}{2} = \frac{1}{2}[/tex]
Second multiple: [tex]2 \times \frac{1}{2} = \frac{2}{2} = 1[/tex]
Third multiple: [tex]3 \times \frac{1}{2} = \frac{3}{2}[/tex]
Fourth multiple: [tex]4 \times \frac{1}{2} = \frac{4}{2} = 2[/tex]
what expressions are equivalent to 162x^4 - 144x^2 +32
Answer:
2x((3x-2)x(3x+2))²
Final answer:
The correct equivalent expressions for 162x⁴-144x²+32 are 2(81x⁴ - 72x² + 16) and 2(9x² - 4)², which correspond to options A and C.
Explanation:
The expression 162x⁴-144x²+32 can be factored by first taking out the greatest common factor (GCF), which is 2, resulting in 2(81x⁴ - 72x² + 16). If we look at the inside expression, we can recognize that it is a perfect square trinomial because 81x⁴ is the square of 9x² and 16 is the square of 4, and the middle term (-72x²) is twice the product of 9x² and 4. Consequently, the expression inside the parentheses can be written as the square of a binomial, resulting in 2(9x² - 4)². Therefore, the equivalent expressions for 162x⁴ - 144x² + 32 are:
2(81x⁴ - 72x² + 16)2(9x² - 4)²Thus, the answers are A and C from the options provided.
I need now plz
Select all the functions whose graphs include the point (16, 4).
A. y=2x
B. y=x2
C. y=x+12
D. y=x−12
E. y=14x
The functions whose graphs include the point (16, 4) is y = x−12.
Option: D.
Step-by-step explanation:
To find the function that passes through the point (16,4).
Substitute the point in all the equations and equate the final values to find the correct equation.
A. y=2x.
Substitute (16,4).
4=2(16).
4≠32.
Thus the equation doesn't contains the point (16,4).
B. y=[tex]x^2[/tex].
Substitute (16,4).
4=[tex]16^2[/tex].
4≠ 256.
Thus the equation doesn't contains the point (16,4)
C. y=x+12.
4=16+12.
4≠28.
Thus the equation doesn't contains the point (16,4)
D. y=x−12.
4=16-12.
4=4.
Thus the equation contains the point (16,4)
E. y=14x.
4=14(16).
4≠224.
Thus the equation doesn't contains the point (16,4)
∴The functions whose graphs include the point (16, 4) is y = x−12.
Answer:
Step-by-step explanation:
There are 2 answers to this question. I know one of them wich is D but the other one I think it;s A
what is the volume of a hemisphere with a radius of 2.3m round to the nearest tenth of a cubic meter
Answer: [tex]25.5 m^{3}[/tex]
Step-by-step explanation:
If the volume of a sphere is
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Where [tex]r=2.3 m[/tex] is the radius
The volume of a hemisphere is half the volume of the total sphere:
[tex]V_{hemisphere}=\frac{V}{2}=\frac{\frac{4}{3} \pi r^{3}}{2}[/tex]
[tex]V_{hemisphere}=\frac{2}{3} \pi r^{3}[/tex]
Solving this equation:
[tex]V_{hemisphere}=\frac{2}{3} \pi (2.3 m)^{3}[/tex]
Finally:
[tex]V_{hemisphere}=25.48m^{3} \approx 25.5 m^{3}[/tex]
The volume is approximately 12.8 cubic meters.
To find the volume of a hemisphere, we can use the formula for the volume of a sphere and then take half of that volume.
The formula for the volume of a sphere is:
V = (4/3)πr³
Since we only need the volume of a hemisphere, we'll divide by 2:
V = (1/2) * (4/3)πr³
Given the radius (r) is 2.3 meters, we substitute the value into the formula:
V = (1/2) * (4/3)π (2.3)³
First, calculate the cube of the radius:
2.33 = 2.3 * 2.3 * 2.3 = 12.167
Next, plug this back into the formula:
V = (1/2) * (4/3)π * 12.167
Then, calculate the constant part of this equation:
(4/3)π ≈ 4.18879
So:
V = (1/2) * 4.18879 * 12.167 = 25.5288
Finally, divide by 2:
V ≈ 12.7644
Rounding to the nearest tenth, the volume of the hemisphere is 12.8 cubic meters.
Brian's kite is flying above a field at the end of a 40 m string. If the angle of elevation
to the kite measures 70°, how high is the kite above the ground? Round your answer
to the nearest tenth of a meter.
Answer:
who ever answers right will get Brainlyeist!!!!! PLEASE HELP ME OUT!!!
3. Find the area of the triangle.
A. 21.2 in
B. 10.5 in
C. 21 in
D. 42 in
Please help! Thank you!
Answer:
1. 7/10 + 3 6/10= 4 13/10= 5 3/10
if 3x > or = 2x+5 then what is 3x-10 > or = 2x -__
To save time, you dont need to write "> or ="
You can simply write ">=" without the quotes.
So 3x >= 10 means "3x is greater than or equal to 10"
-----------------------------------
we start with 3x >= 2x+5
we want 3x-10 on the left hand side. We already have a 3x. So if we stick a -10 on the left side, we need to do the same thing to the right side to balance things out. We can subtract 10 from both sides to do this
3x >= 2x+5
3x-10 >= 2x+5-10 ... subtract 10 from both sides
3x-10 >= 2x-5
So it looks like a 5 will go in the blank because the negative portion is already taken care of.
Answer:
The answer is 10
Step-by-step explanation:
Name the restrictions on x then solve showing your steps
2/x-3=5/x
Answer:
x=5
Step-by-step explanation:
The given equation is [tex]\frac{2}{x-3}=\frac{5}{x}[/tex]
The denominator is never equal to zero.
Therefore [tex]x-3\ne0[/tex] or [tex]x\ne 0[/tex]
[tex]x\ne3[/tex] or [tex]x\ne 0[/tex]
Let us now cross multiply to get:
[tex]2x=5(x-3)[/tex]
Expand to get:
[tex]2x=5x-15[/tex]
Group similar terms to get:
[tex]5x-2x=15[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
what 2 numbers multiply to get -120 and add to get -14
Answer:
-20 and 6
Step-by-step explanation:
-20 x 6 = -120
and if you add -20 and 6, you get -14.
what is the inequality for 5(x+3)−8<17
Answer:
x< 2
Step-by-step explanation:
We are given the inequality;
5(x+3)−8<17
First we take 8 to the other side;
5(x+3)<17 + 8, notice the sign changes like with an equation
Opening the brackets;
5x + 15 < 25
We then take 15 to the other side;
5x < 25 -15
5x < 10
x < 2
Thus, the solution of the inequality is x< 2
calculate the length of the circumference of a circle with a radius of 3cm
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
use the formula [tex]C=2\pi r[/tex]
r = radius
plug in numbers into the equation to get
[tex]2\pi (3)[/tex] which equals [tex]6\pi[/tex]
Answer:
The answer was 9.42 units
Step-by-step explanation:
Advanced question!
I need smart people
Answer:
3/2
Step-by-step explanation:
Scale factor=side of second triangle/side of first triangle
Scale factor=12/8
=3/2
Step-by-step explanation:
[tex]Scale \: factor = \frac{8}{12} = \frac{2}{3} \\ [/tex]
The retail price of a product is $77.30 per square metre. Trade price is retail less 12.5%. Calculate the trade price of 5.35m of the product.
(Answer should be in $ pls)
Answer: $1935.56
Step-by-step explanation:
T.P=R.P-(12% of R.P)
R.P=$77.30 per 1m²
When m =5.35, m²=5.35²=28.6225
R.P= $(77.30×28.6225)
R.P=$2212.52
12.5% of R.P=0.125×$2212.52=$276.565
Therefore,
T.P = $2212.52-$276.565 = $1935.96
Note: T.P is Trade Price and R.P is Retail Price.
Hope this helps?
Draw a rectangle that has the area of 56 sq.cm.
Answer:
draw an 8 x 7 rectangle
Step-by-step explanation:
note that
area of rectangle = length x width.
we also know that 56 = 8 x 7
hence you simply need to draw a rectangle and label the long side "8 cm" and the short side "7 cm"
The lengths of the sides of a triangle are 11.25 inches, 9.25 inches, and 10.25 inches. What is the perimeter of the triangle?
Perimeter of the triangle is 30.75 inches.
Step-by-step explanation:
Step 1: Given sides of the triangle = 11.25 in, 9.25 in, 10.25 inStep 2: Formula for perimeter of triangle = length of sides of the triangleStep 3: Substitute in the formulaPerimeter = 11.25 + 9.25 + 10.25
= 30.75 inches
Nine times a number y subtracted from 95 equals 37
Answer:
y = 6.44
Step-by-step explanation:
"nine times number y" : 9y
"subtracted from 95" : (95 - 9y)
"equals 37" : (95 - 9y) = 37
solving for y
95 - 9y = 37 (subtract 95 from both sides)
-9y = 37 - 95
-9y = -58 (divide both sides by -9)
y = -58/ -9
y = 6.44
The required algebraic expression that is nine times a number y subtracted from 95 equals 37. is 95 - 9y = 37.
Given that,
To determine the algebraic expression for nine times a number y subtracted from 95 equals 37.
The algebraic expression consists of constant and variable. eg x, y, z etc.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The number be y
Nine-time of y = 9y
Subtraction of 9y from 95 is equal to 37,
95 - 9y = 37
Thus, the required algebraic expression that is nine times a number y subtracted from 95 equals 37. is 95 - 9y = 37.
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For which pairs of functions is (f•g)(x)=x of functions is (f•g)(x)=x
Answer:
Option A
Step-by-step explanation:
The complete question is shown in the attachment.
Note that: [tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
We need to multiply all the functions to see which of them satisfy the given criteria.
Option A
[tex]x^2\cdot \frac{1}{x} =\frac{x^2}{x}=x[/tex]
Option B
[tex]\frac{2}{x} \cdot \frac{2}{c} =\frac{4}{cx}[/tex]
Option C
[tex]\frac{x-2}{3} \cdot 2-3x =\frac{-3x^2+8x-4}{3}[/tex]
Option D
[tex]\frac{1}{2x-2} \cdot \frac{1}{2x+2} =\frac{1}{4(x^2-1)}[/tex]
The correct choice is A
Marc was born on his grandmother’s 56th birthday. In how many years will Marcs grandmother be 5 times as Marc will be then?
Answer:
Therefore 70 year Marc's grandmother be 5 times of as Marc will be after (70-56) = 14 year.
Step-by-step explanation:
Given, Marc was born on his grandmother's 56th birthday.
Let , x year will Marc's grandmother be 5 times as Marc will be then.
At that time the age of Marc will be = (x-56) year
According to the problem,
x= 5(x-56)
⇔x = 5x - 280
⇔x-5x= -280
⇔-4x=-280
⇔x=70
Therefore 70 year Marc's grandmother be 5 times of as Marc will be after (70-56) = 14 year.
san
R
APOR is a right triangle. IF RO = 8, what is PO?
mios
16
Answer:
PQ = 16
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex], then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{RQ}{PQ}[/tex] = [tex]\frac{8}{PQ}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
PQ = 8 × 2 = 16
What is the slope of the line?
Answer:
(-5,4) (6,-2)
(-2-4)/(6+5)= -6/11
Answer:
-3/5
Step-by-step explanation:
Solve the equation for the given variable. Select the answer that best
describes your solution.
4(2x + 7) + 3 = 8x +31
Infinitely many solutions
No solution
One solution
Answer:infinitely many solutions
Step-by-step explanation: 4*2x= 8x and (7*4)+3 = 31. 8x+31 is equal to itself, therefore any value of x makes the equation true.
(-6,5) and (4,-1) equation
Answer:
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]
Step-by-step explanation:
The correct question is
Write an equation for the line passing through (-6,5) and (4,-1)
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-6,5) and (4,-1)
substitute
[tex]m=\frac{-1-5}{4+6}[/tex]
[tex]m=\frac{-6}{10}[/tex]
[tex]m=-\frac{3}{5}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{5}[/tex]
[tex]point\ (-6,5)[/tex]
substitute
[tex]y-5=-\frac{3}{5}(x+6)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-5=-\frac{3}{5}x-\frac{18}{5}[/tex]
[tex]y=-\frac{3}{5}x-\frac{18}{5}+5[/tex]
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]