Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
We can represent each ratio as a fraction, then use the cross products property to find the value of x.
[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]
Hope this helped!
evaluate 5!+2!. Thank you!
Answer:
122
Step-by-step explanation:
5!=5 x 4 x 3 x 2 x 1 = 120
2!=2 x 1 = 2
120+2=122
if the morning temperature started at -7 celsius but warmed during the day to 24 celsius . What is the temperature change
Answer:
31° change
Step-by-step explanation:
If we want to find the change between two numbers, we need to imagine it like a number line.
<-------------0------------->
Let's plot -7 and 24 on this number line.
<----------[tex]-7[/tex]--0------------24>
If we want to get from -7 to 0, we increase by 7. To get from 0 to 24, we increase by 24.
So the total change is [tex]7 + 24 = 31[/tex].
Hope this helped!
Given triangle ABC is similar to triangle DEF , calculate the value of BC. Picture is below
Hello! :)
Answer:
[tex]\huge\boxed{BC = 6.4 }[/tex]
Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:
[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]
Let BC = x:
[tex]\frac{8}{15} = \frac{x}{12}[/tex]
Cross multiply:
[tex]8 * 12 = 15 * x[/tex]
[tex]96 = 15x[/tex]
[tex]x = 6.4[/tex]
Therefore, BC = 6.4 units.
Hope this helped you!
Complete the point-slope equation of the line through (8,−8) (9,8) Use exact numbers. y-8=
Answer:
y-8=16(x-9)
Step-by-step explanation:
slope m=y2-y1/x2-x1
m=8+8/9-8 ⇒ m=16
y-8=m(x-x1)
y-8=16(x-9)
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(8, −8) and (9, 8)
The equation of the line that is passing through (8, −8) and (9, 8) will be given as,
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
Simplify the equation, then we have
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
(y + 8) = 16(x − 8)
y + 8 = 16x − 128
y = 16x − 120
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
More about the line passing through two points link is given below.
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what’s the equation of line ?
y =__x + __
Answer:
y=3/4x-2
Step-by-step explanation:
two points from graph (0-2) and (8,4)
find slope m: y2-y1/x2-x1
m=4+2/8-0
m=6/8=3/4
x=0 then y=b=-2
y=3/4x-2
A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 2 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Answer:
16. 1 miles
Step-by-step explanation:
Using Pythagorean Theorem,
a^2 + b^2 = c^2
Since the road that goes from his home to work directly is c^2...
Plug in the rest of the numbers
16^2 + 2^2 = c^2
256 + 4 = c^2
260 = c^2
The reverse square of 260 is
16. 1 miles
Claire and Richard are both artists who use square canvases. Claire
uses the polynomial 50%? + 250 to decide how much to charge for her paintings
and Richard uses the polynomial 40x² + 350 to decide how much to charge for
his paintings. In each polynomial, x is the height of the painting in feet.
a. How much does Claire charge for a 20-foot-tall painting?
b. How much does Richard charge for a 15-foot-tall painting?
c. To the nearest tenth, for what height will both Claire and Richard charge
the same amount for a painting? Explain how to find the answer.
d. When both Claire and Richard charge the same amount for a painting,
how much does each charge?
Answer:
A. [tex]Claire = 20250[/tex]
B. [tex]Richard = 9350[/tex]
C. Height = 3.2 feet
D. Charges = $760
Step-by-step explanation:
Given
[tex]Claire = 50x^2 + 250[/tex]
[tex]Richard = 40x^2 + 350[/tex]
Solving (a): Claire's 20ft charges
In this case, x = 20
Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(20)^2 + 250[/tex]
[tex]Claire = 50(400) + 250[/tex]
[tex]Claire = 20000 + 250[/tex]
[tex]Claire = 20250[/tex]
Solving (b): Richard's 15ft charges
In this case, x = 15
Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(15)^2 + 350[/tex]
[tex]Richard = 40(225) + 350[/tex]
[tex]Richard = 9000 + 350[/tex]
[tex]Richard = 9350[/tex]
Solving (c): Height which they both charge the same;
This implies that
[tex]50x^2 + 250 = 40x^2 + 350[/tex]
Solving for x [Collect Like Terms\
[tex]50x^2 - 40x^2 = 350 - 250[/tex]
[tex]10x^2 = 100[/tex]
Divide both sides by 10
[tex]x^2 = 10[/tex]
Take square roots of both sides
[tex]x = \sqrt{10}[/tex]
[tex]x = 3.2ft[/tex] (Approximated)
Hence; Height = 3.2 feet
Solving (d): How much they charge when the charge the same amount.
Substitute 3.2 for x in any of the given equation
[tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(3.2)^2 + 250[/tex]
[tex]Claire = 50*10.24 + 250[/tex]
[tex]Claire = 512 + 250[/tex]
[tex]Claire = 762[/tex]
[tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(3.2)^2 + 350[/tex]
[tex]Richard = 40 * 10.24 + 350[/tex]
[tex]Richard = 409.6 + 350[/tex]
[tex]Richard = 759.6[/tex]
The reason for the difference is due to approximation
Hence, they both charge approximately 760
Keenan currently does a total of 8 pushups each day. He plans to increase the number of pushups he does each day by 2 pushups until he is doing a total of 30 pushups each day. Which equation can we use to determine x, the number of days that it will take Keenan to reach his goal? In an expression
Answer:
Number of push up = 8 + 2x
Step-by-step explanation:
Keenan can do 8 push ups each day. He plans to do 2 extra day until he is doing 30 push ups. Each day he does an additional 2 push up, on the first day he does 8 + 2 = 10 push up, on the second day he does 10 + 2 = 12 push ups. This can be represented by the expression:
Number of push up = 8 + 2x
where x is the number of days.
To do 30 push ups, we can calculate the number of days needed:
30 = 8 + 2x
2x = 30 - 8
2x = 22
x = 11
Answer:
8+2x its from khan academy
Step-by-step explanation:
give person above brainliest :)
[tex]\frac{63,756×60}{70×5,280}[/tex]
Answer:
[tex]1035[/tex]
Step-by-step explanation:
(63756×60)/(70×5280)
=1035
Choose all properties that were used to simplify the following problem:
(38 +677) + (-38)
[677 + 38) + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The properties 1‚ 2‚ 4‚ and 5. are used
The properties used to simplify problem are 1 , 2 and 4.
A problem which is simplified is given ; (38 +677) + (-38).
What are the correct options ?
How will you represent the associative properties of addition ?
Associative properties are represented by ; (A + B ) + C = A + ( B + C ).
As per the data given in question ;
Let's check which options are suitable.
( 38 + 677 ) + ( -38 ) = 38 + ( 677 - 38 )
(A + B ) + C = A + ( B + C )
So , this is the associative property.
677 + 0 = 677
A + 0 = A
So , this is the additive identity.
677 + [38 + (-38)]
Here ; 38 + ( -38 ) represents ;
A + (-A) = 0.
So , this is the additive inverse.
Thus , the properties used to simplify problem are 1 , 2 and 4.
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Nala has 'n' marbles. Paul has three times as many marbles as Nala. Nala loses 5 marbles and Paul buys 10 marbles. Together they now have 105 marbles. Write down and solve an inequality in 'n'
Answer:
Step-by-step explanation:
Nala's marbles = n
Paul's marbles = 3n
nala loses 5 marbles
so nala's marbles = n - 5
paul buys 10 marbles
so paul's marbles = 3n + 10
Total marbles = 105
so,
n - 5 + 3n + 10 = 105
By transposing,
n + 3n = 105 - 10 + 5
4n = 100
n = 100 / 4
n = 25
Hope this helps
plz mark as brainliest!!!!!!!
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
-7.5 and 5.4
Answer:
Step-by-step explanation:
m
Classify the triangle.
B) isosceles
Step-by-step explanation:If the median to the base is perpendicular to the base =>
= > isosceles triangle
A man gave his 8000$ as pocket money and his son 1000$ less.Express the girls money as a percentage of the total sum of money.
Answer:
About 89%
Step-by-step explanation:
8000 + 1000 = 9000.
To find the girls money as a percentage of the total sum of money, you must take 8000 and divide it by 9000.
8000/9000 = .8888 = 88.88 = 88.9% or about 89%.
Find the vertex of the parabola.
f (x) = x squared minus 6 x + 13
a.
( 4, 0)
c.
( 3, 4)
b.
(0, 3)
d.
( 4, 3)
Answer:
The vertex is (3,4)
Step-by-step explanation:
f (x) = x^2 - 6 x + 13
Completing the square
-6/2 = -3 and squaring it = 9
= x^2 -6x +9 +4
= ( x-3) ^2 +4
The equation is now in vertex form
a( x-h) ^2 +k
where the vertex is ( h,k)
The vertex is (3,4)
Answer:
C on edge
Step-by-step explanation:
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be times the original volume.
Answer:
The answer is below
Step-by-step explanation:
From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch
The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³
While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25
The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³
Volume of the flask = The volume of the cylinder + The volume of the sphere = 2.36 + 47.71 = 50.07 in³
If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025
The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³
While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125
The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³
New Volume of the flask = The new volume of the cylinder + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³
The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125
The resulting volume would be 0.125 times the original volume
Answer:
50.07 and 8 times
Step-by-step explanation:
1) Calculate volume of each figure using according formulas.
You should get:
Sphere: 47.71in^3
Cylinder: 2.36in^3
Now let's add, and you should get 50.07.
2) Let's dilate the dimensions/flask by 2 (multiply by 2)
4.5 * 2 = 9
1 * 2 = 2
3 * 2 = 6
Now with these dimensions you should get:
Sphere: 381.7in^3
Cylinder: 18.85in^3
This should add up to 400.55in^3
Divide new by original. 400.55 / 50.07 = 8
So it is 8 times larger.
I REALLY need help with these 3 questions plz!!!!
Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
sandra is playing a trivia game.on her first turn she lost 75 points. on her second turn,she lost 35 points. on her third turn,she scored 100 points. What is sandras score after three turns?
Answer: -10 points
Step-by-step explanation:
She lost 110,so that loss -the gain(100) is the total score at the end of three games
a 6 foot tall man casts a shadow that is 9 ft long. At the same time, a tree nearby casts a 48 ft shadow. how tall is the tree
Answer:
32 ft tall
Step-by-step explanation:
Since a 6 ft man casts a shadow 9 ft long, the shadow is 3/2 of the actual object/person.
SINCE THE TREE'S SHADOW IS AT THE SAME TIME, THE HEIGHT IS THE SAME RULE.
We know the tree's shadow is 48 ft.
--> 48/3 = 16
16 x 2 = 32
32 ft tall
Hope this helps!
Answer: 32ft tall
Step-by-step explanation:
The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?
Answer:
5 hours
Step-by-step explanation:
From the question, we are told that:
Time required to drive a fixed distance varies inversely as the Speed
T ∝ 1/S
k = proportionality constant hence,
T =k × 1/S
T = k/S
Step 1
Find k
It takes 2 hr at a speed of 200 km/h to drive a fixed distance
T = 2 hours, S = 200km/h
T = k/S
2 = k / 200
k = 2 × 200
k = 400
Step 2
How long will it take to drive the same distance at a speed of 80 km/h?
S = 80km/h
T = k/S
k = 400
T = 400/80
T = 5
Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr
2x-15=3(2x+3)
It’s multi step equations
Answer:
x = -6
Step-by-step explanation:
Hello!
2x - 15 = 3(2x + 3)
Distribute the 3
3 * 2x = 6x
3 * 3 = 9
2x - 15 = 6x + 9
Subtract 2x from both sides
-15 = 4x + 9
Subtract 9 from both sides
-24 = 4x
Divide both sides by 4
-6 = x
Hope this helps!
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get
Answer:
3x(x+8)=0
x=0,-8
This is how to solve for x.
Which of the following terms correctly describe the object below?
Check all that apply.
a. polyhedron
b. pyramid
c. prism
d. solid
e. cube
f. polygon
*will mark brainliest :))
Answer:
The given figure is:
a. Polyhedron
c. prism
d. solid
Step-by-step explanation:
First of all, let us consider the given image.
It is a 3 dimensional figure.
It has 2 equal bases which are pentagonal.
Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces.
The faces can be of 'n' number of edges (Polygonal faces).
Its edges are straight, has sharp corners which are also known as vertices.
The given image is a polyhedron as per above definition.
b. Pyramid:
It is also a 3D shape which can have a polygonal base and its faces are triangular which converge on the top to one point.
The given image does not converge to a point on the top, so not a pyramid.
c. Prism:
It is a 3D shape which has it two bases as polygonal structure.
The two bases are equal in shape and size.
There are faces on the body of prism which are formed by joining the edges of the bases.
The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height.
So, the given image is a Solid.
e. Cube:
Cube is a 3D figure, which has all its faces in square shape.
All the sides are equal for a cube.
The given image is not a cube.
f. Polygon:
A polygon is a closed figure in 2 dimensions which has n number of sides.
The given image is not a polygon.
Answer: The given figure is:
a. Polyhedron
c. prism
d. solid
The given figure is a Polyhedron, prism and solid.
What is a polyhedron?A polyhedron is a three-dimensional geometry having plane surfaces connected together with sharp edges and pointed vertices.
First of all, let us consider the given image. It is a 3-dimensional figure. It has 2 equal bases which are pentagonal. Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in the following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces. The faces can be of 'n' number of edges (Polygonal faces). Its edges are straight, has sharp corners which are also known as vertices. The given image is a polyhedron as per the above definition.
c. Prism:
It is a 3D shape which has it two bases as a polygonal structure.The two bases are equal in shape and size. There are faces on the body of prism which are formed by joining the edges of the bases. The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height. So, the given image is a Solid.
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How would I solve this? (y-z) ÷ z y=-2 and z=4/5
Answer:
-3.5
Step-by-step explanation:
The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5
Answer:
[tex]\large\boxed{-3.5}[/tex]
Step-by-step explanation:
(y - z) ÷ z y = -2 and z = 4/5
Substitute in the given values for y and z into the equation
(y - z) ÷ z
(-2 - 4/5) ÷ 4/5
Subtract inside the parenthesis (-2 - 4/5)
-2.8 ÷ 4/5
Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)
4/5 = (4 * 20) / (5 * 20) = 80 / 100
80 / 100
Divide numerator and denominator by 10
8/10 = 0.8
Substitute into previous equation
-2.8 ÷ 4/5 = -2.8 ÷ 0.8
Divide
[tex]\large\boxed{-3.5}[/tex]
Hope this helps :)
The linear scale factor of two shapes is 3:4. If the area of the smallest shape is 72^2 what is the area of the big shape?
Answer:
[tex]\boxed{6912 units^2}[/tex]
Step-by-step explanation:
Hey there!
Well using the given ratio,
3:4
And the area of the small shape we need to do,
72*72 = 5184
Now we can make the following fractions,
[tex]\frac{3}{4}[/tex] = [tex]\frac{5184}{x}[/tex]
Now we can solve,
3*x = 3x
4 * 5184 = 20736
3x = 20736
20736 / 3
x = 6912
So the area of the bigger shape is 6912 units^2
Hope this helps :)
Ali was supposed to meet his friend in th evening every sunday. The first time he came at 4.30,the next time at5. 20,then at 6.30.Then at8. 00.When did he turn up the last time after that?
Answer:
9:50
Step-by-step explanation:
Given the following information :
First meeting = 4:30
Second meeting = 5:20
Third meeting = 6:30
Fourth meeting = 8:00
Frim careful observation of the meeting times :
Difference between the ;
Second and first meeting:
5:20 - 4:30 = 50 minutes
After that 20 minutes is added to the subsequent meetings as observed from the third and fourth meetings
6:30 - 5:20 = 70 minutes
8:00 - 6:30 = 90 minutes
Therefore, next meeting time :
(90 + 20) minutes = 110 minutes
8:00 + 110 minutes = 9:50
a shop has a sale and reduces all the prices by 15k in naira.find the sale price of an article of an article marked at 750naira
Answer:
Question (i):
Reduce = 15% of Rs 40 = 0.15 x 40 = Rs 6
Price after reduced = Rs 40 - Rs 6 = Rs 36
Answer: Rs 36
-
Question (ii):
Reduce = 15% x 20.40 = 0.15 x 20.40 = Rs 3.60
Price after reduced = Rs 20.40 - Rs 3.60 = Rs 17.34
Answer: Rs 17.34
-
A 10 gram sample of a substance that’s used to detect explosives has a k-value of 0.1356.Find the substances half life in days.Round your answer to the nearest tenth.
Answer:
t ≈ 5.1 days
Step-by-step explanation:
A 10 gram sample of a substance thats used to detect explosives has a k-value of 0.1356. Find the substances half-life in days. round your answer to the nearest tenth. N=N₀ e^-kt N₀= initial mass (at time t = 0) N = mass at time t k= a positive constant that depends on the substance itself and on the units used to measure time t=time in days
The initial condition is that, at time t = 0, the amount of substance contains originally 10 grams
Find the value of N₀
N=N₀ e^-kt
We substitute:
10 = N₀ {e^(-0.1356)*0}
10 = N₀ (e^0)
10=N₀(1)
10=N₀
N₀ = 10
When the substance is in half-life
That is, half of the original substance (5 grams)
Find t
N=N₀ e^-kt
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Bring down t by multiplying natural log on both sides
ln(0.5) = -0.1356*t
Divide both sides by -0.1356
t = -(ln(0.5) / 0.1356
t ≈ 5.11 days
To the nearest tenth
t ≈ 5.1 days
Answer:
5.1 days in Plato
Step-by-step explanation:
solve for v. 27= -v/2
Answer:
v = -54
Step-by-step explanation:
27= -v/2
Multiply each side by -2
27 *-2= -v/2 *-2
-54 = v
Answer:
-54
Step-by-step explanation:
[tex]27=\frac{-v}{2}[/tex] .... Equation to start with
[tex]27 x 2= \frac{-v}{2} x2[/tex] ..... Cancelling out the denominator and multiplying on the other side
[tex]54 = -v[/tex] .... Multipling
[tex]-54 =v[/tex] ..... Solving for v, not -v, so bring the negative over to the other side
Hope you understood:)
