2x+6-4x-1=13
2x+5=13
2x=8
x=4
A gasoline pump fills an automobile tank at the rate of .7 gallon every 2 seconds. At this rate, how long would it take to fill a 28- gallon tank?
Help!!
Answer:
80 seconds
Step-by-step explanation:
rate x time = gallons
[tex]\frac{.7}{2}[/tex]t = 28 Multiply both sides by [tex]\frac{2}{.7}[/tex]
t = 80
16 divided by 200 times 100
[tex]16 : (200 \cdot 100) =[/tex]
[tex]16 : 20000 = 0.0008[/tex]
Answer:
8
Step-by-step explanation:
To solve this problem we use PEMDAS; Parenthesis, Exponents, Multiply, divide, add, subtract
Let's set up an equation:
16/200*100
Now let's solve:
16/200=0.08
Now we multiply 0.08 by 100
0.08*100=8
Thus, our answer is 8
X
. You deposit money in an account that earns Simple interest at an annual rate of 6%. After 8 years.
Y
the account earns $360 in interest. How much money did you deposit in the account?
Answer:
$750
Step-by-step explanation:
I = interest
p = principle
r = rate
t = time
I = prt Plug in what you know and solve for p
360 = p (.06)(8)
360 =p.48 Divide both sides by .48
750 = p
The principal is deposited in the account is $750.
Given that, rate of interest =6%, time period = 8 years and simple interest = $360.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 360 = (P×6×8)/100
⇒ 360 = 48P/100
⇒ 48P = 36000
⇒ P = 36000/48
⇒ P = $750
Therefore, the principal is deposited in the account is $750.
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A pharmacist mixes 5g of a power with 45cm of water to make a prescription medicine . how much powder should she mix with 81cm of water to make a larger amount of the same medicine.
The pharmacist should mix 9 g of a power to make a larger amount of the medicine
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
mass(1) = 5gvolume(1) = 45 cm3volume(2)= 81 cm3mass(2) = ?Calculating the rate of the medicine with the 1st mixed:
rate = mass(1)/ volume(1)
rate = 5g / 45cm3
rate = 0.11 g/cm3
Calculating how much power the pharmacist needs for the volume(2):
mass(2) = rate * volume(2)
mass(2) = 0.11 g/cm3 * 81 cm3
mass(2) = 9 g
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Calculus help please
Step-by-step explanation:
THE POINT WHERE
[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]
Now we have point (-4,17)
the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point
f'(x) =m
f'(-4)=2(-4)
f'(-4)=-8
The gradient therefore is -8
the general equation of a straight line is given by
[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]
HOPE THIS HELPS!!
if 5 out of 30 students scored an A on a quiz.what percent did not get an A on the quiz?Round to the nearest whole percent.
PLEASE SHOW WORK
Answer:
83 %
Step-by-step explanation:
If 5 out of 30 got an A, that means that
30 -5 = 25
25 out of 30 did not get and A
25/30 = .8333333 = 83.33333 %
Rounding to the nearest whole percent
83 %
Which of the following is not a rational number?
Α. 0
B. √2
C. 3/4
D. √4
Answer: B
Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.
Answer:
B
Step-by-step explanation:
1. A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head
speed was 99 miles per hour. Was the baseball faster than the club head?
The baseball was faster than the club head will be incorrect.
What is conversion?Conversion means to convert the same thing into different units.
A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head speed was 99 miles per hour.
We know that in one mile, there are 5280 feet. And in one hour, there are 3600 seconds.
Then the speed of the golfer's drive will be
⇒ 99 x 5280 feet / 3600 seconds
⇒ 145.2 feet per second
The speed of the club head is faster than the baseball.
The baseball was faster than the club head will be incorrect.
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Triangle ABC has the following angle measures:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
What is m∠A?
pleaseee help
The measure of angle A in the triangle is 18°
How to determine the measure of angle A?The angles in the triangle are given as:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
The sum of angles in a triangle is 180
So, we have
m∠A + m∠B + m∠C = 180
Substitute the known values in the above equation
So, we have:
2x − 24 + x + 8 + 4x + 49 = 180
Evaluate the like terms
7x = 147
Divide both sides by 7
x = 21
Substitute x = 21 in m∠A = (2x − 24)°
m∠A = (2 * 21 − 24)°
Evaluate
m∠A = 18°
Hence, the measure of angle A in the triangle is 18°
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h) Suppose that a cold drink costs R4,50 now but will cost double in eight years' time. What will the average inflation rate be?
average inflation rate of cold drink will be 100%
WHAT IS INFLATION RATE ?Inflation is the term used to describe an increase in the price of goods and services that households buy. It is determined by how quickly these prices fluctuate. Prices frequently rise with time, but they can also fall (a situation called deflation).
CALCULATIONYou will subtract the starting price (A) from the later price (B), and divide it by the starting date (A). Then multiply the result by 100 to get the inflation rate percentage.
FORMULA FOR FINDING AVERAGE INFLATION = ((B-A)/A)*100
plugging in the values =
∵ given in the question that cost will double in the next 8 years i.e.
= Rs. 4.50 * 2
= Rs.9.00
∴ when we plug in the values in the formula we get
= ((9-4.5)/4.5) * 100
= 100 % inflation rate
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find the circumference of a circle whose area is equal of 64 π centimeters square
The circumference of the given circle is: 16πcm.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Given: Area of a circle = 64π cm²
To find: Circumference of the circle.
Finding:
We know that the formula of the area of a circle = πr²,
On comparing it with the given value, we get:
πr² = π(64)
πr² = π(8)²
8² = r²
r = 8cm (as the side of a circle can never be negative).
Also, the formula of the circumference of a circle = 2πr
Thus, for the circle having radius 8 cm, circumference = 2π(8) = 16πcm.
Hence, The circumference of the given circle is: 16πcm.
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Identify the rule(s) of algebra illustrated by the statement. (Select all that apply.) 1 · (1 + x) = 1 + x
The rule(s) of algebra illustrated by the statement is the identity property of algebra
How to identify the rule(s) of algebra illustrated by the statement.?The statement is given as:
1 · (1 + x) = 1 + x
The identity property of algebra states that:
1 * a = a or a * 1 = a
In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x
This can be illustrated as
1 * a = a
The rule(s) of algebra that illustrates the above equation is the identity property of algebra
Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra
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given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2 49a 108$ and $2a 9$.
Odd Multiples of 7767 are 1, 3, 9, 863, 2589, 7767.The greatest common divisor of [tex]$6a^2 49a 108$[/tex] = 6×1×49×1×108= 31,752 and
2a9=2×1×9=18
What do you mean by Greatest Common Divisor?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor (GCD) in mathematics. The greatest common divisor of two numbers x and y is shown for x and y. As an illustration, the GCD of 8 and 12 equals 4, or. The words "divisor" and "factor" can be swapped out in the name "largest common divisor" so that alternative names such as "highest common factor" (HCF), etc. can be used instead. In the past, the term biggest common measure has been used to refer to the same idea.
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a tripod has three legs each of length 5 feet. when the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. in setting up the tripod, the lower 1 foot of one leg breaks off. let $h$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. then $h$ can be written in the form $\frac{m}{\sqrt{n}}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. find $\lfloor m \sqrt{n} \rfloor$. (the notation $\lfloor x \rfloor$ denotes the greatest integer that is less than or equal to $x$.)
The value of [m + √n] is 183.
We note that AO=3. From this we can derive that the side length of the equilateral is 3√3. We now use 3D coordinate geometry.A is (0, 0, 0), B is (3√3, 0, 0), C is ((3√3)/2, 9/2, 0), T is ((3√3)/2, 3/2, 4), and S is ((3√3)/10, 3/10, 4/5).We know three points of the SCB plane, so we can write out the equation for the plane. Plane SCB can be expressed as (4√3)x + 4y + 39z - 36 = 0.Applying the distance between a point and a plane formula(ax + by + cz + d)/(√(a² + b² +c²)Put T's coordinates in this in (x, y, z), and replace the values of a, b, c, and d with plane equation coefficients.We get the distance equal to 144/(√1585).A distance of the form m/(√n) is given to us.We have to calculate [m + √n] = [144 + √1585] = 183.To learn more about plane, visit :
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natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. a radio tracker costs $650 and a gps tracker costs $1400. natalie wants to buy at least 9 radio trackers and more than 3 gps trackers. the following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of gps trackers. x ≥ 9 y > 3 650x 1400y ≤ 15000 which yellow shaded region corresponds to natalie's possible choices?
Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.
What do you mean by GPS?Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.
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Find the surface area of a cube with side length og 6 1/2 inches.
PLEASE SHOW WORK
The surface area of a cube with side length of 6 1/2 inches is 253.5 square in
Surface area of cubeThe formula for calculating the surface area of cube is expressed as:
Surface area = 6L^2
where
L is the side length of the cube
Substitute
SA = 6(13/2)^2
SA = 6 * 169/4
SA = 3 * 169/2
SA = 253.5 square in
Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in
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The price of an item has been reduced by $6.18. The new sale price is $30.55. What was the original price?
Answer:
30.55 + 6.18 = $36.73
Step-by-step explanation:
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your bedroom sock drawer contains 4 green socks and 6 yellow socks that are mixed together. the light in your room is broken so you must select your socks in the dark. what is the probability you will select two socks of the same color on your first try?
The probability of selecting two socks of same color is 0.96.
According to the given question.
Total number of green socks = 4
Total number of yellow socks = 6
So, the total number of socks in a drawer = 4 + 6 = 10
Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.
So, the probability of selecting a green scoks = 4/10 = 2/5
And the probability of selecting a yellow socks = 6/10 = 3/5
Therefore, the probability of selecting two socks of same color
= probability of selecting both the green socks or probability of selecting both the yellow socks
= [( 2/5) + (2/5)] × [(3/5)+(3/5)]
= (4/5) × (6/5)
= 24/25
= 0.96
Hence, the probability of selecting two socks of same color is 0.96.
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I need help solving. Im stuck please help me.
will give u brainliest <3
89 degrees
Step-by-step explanation:Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.
Setting Up an Equation
To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.
14 + 77 + a = 180This is only one equation that you could set up to represent this situation.
Solving For a
Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.
91 + a = 180Next, subtract 91 from both sides.
a = 89To check our answer we can plug it back into the original equation.
14 + 77 + 89 = 180180 = 180This means that the missing angle must be 89 degrees.
What transformation is represented by the rule
(1, y) → (1, y+3)?
O translation 3 units down
O translation 3 units right
O translation 3 units up
O translation 3 units left
What is P(AC)? I don’t know the answer to this
P(ac) means that it's 100%
write a ratio and sentence comparing the number of jeans bought to the cost
In words, the ratio of the number of jeans bought to the cost is four to thirty two.
How to write a ratio?
We are told that you just bought 4 pairs of jeans for $32.
Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;
4 :32
Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.
Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.
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Complete question is;
You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:
h(x) = (x − 1)2 − 9.
See attachment for the graph of the function and the features
How to use the drawing tool(s) to form the correct answer on the provided graph?The function is given as
h(x) =(x - 1)^2 - 9
The x-intercept
Set h(x) to 0
So, we have
(x - 1)^2 - 9 = 0
Add 9 to both sides
(x - 1)^2 = 9
Take the square root of both sides
x - 1 = ±3
This gives
x = 1 ± 3
Expand
x = (1 - 3, 1 + 3)
Evaluate
x = (-2, 4)
Hence, the x-intercepts are x =2 and x = 4
The y-intercept
Set x to 0
So, we have
h(0) = (0 - 1)^2 - 9
Evaluate
h(0) = -8
Hence, the y-intercept is h(x) =-8
The vertex
We have
h(x) =(x - 1)^2 - 9
Expand
h(x) = x^2 - 2x + 1 - 9
Differentiate
h'(x) = 2x - 2
Set to 0 and solve for x
2x - 2 = 0
This gives
x = 1 --- this represents the axis of symmetry
Substitute x = 1 in h(x) =(x - 1)^2 - 9
h(1) =(1 - 1)^2 - 9
Evaluate
h(1) = -9
Hence, the vertex of the function is (1, -9)
See attachment for the graph of the function and the features
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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running
How to illustrate the information?From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.
The equation is
3w + 6r ≥ 36
3w + 6r ≤ 90
The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking; and 12 hours running.
This will be:
3w + 6r ≤ 90
3(2) + 6(12)
6 + 72 = 78
Therefore, 78 is less than 90.
The correct option is A.
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Louis sets off a firework. The height of the firework at the time t seconds is given by h (t) 16t^2+128t.
Use the quadratic formula to estimate when into the trip the rocket is 64 feet high.
A
at about 0.4 seconds and about 7.6 seconds
B
at about 0.8 second and about 5.2 seconds
C
at about 1.1 seconds and about 6.8 seconds
D
at about 0.5 seconds and about 7.5 seconds
The option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
What is a quadratic equation ?
A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.
The height of firework is represented by a quadratic equation which is 16t² + 128t.
Let's find out that at what time the rocket will be at height of 64 feet.
So,
16t² + 128t = 64 feet
or
16t² + 128t - 64 = 0
or
t² + 8t - 4 = 0
We know that quadratic equation is in form ax² + bx + c = 0.
Using the quadratic formula to find value of t :
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
t = [ -8 ± √(8² - (4 × 1 × - 4))] / ( 2 × 1 )
t = [ - 8 ± 8.94 ] / 2
t = -4 ± 4.47
So , the value of t can be either -4 + 4.47 or -4 - 4.47 which is equal to 0.47 or - 8.47 seconds. Time can't be negative , so t = 0.47 or 0.5 seconds.
Therefore , the option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
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In ΔUVW, w = 3 inches, ∠W=23° and ∠U=73°. Find the length of u, to the nearest 10th of an inch.
The length of u by using sine rule is 7.4 to the nearest 10th of an inch.
What is sine rule?In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.
Formulas for sine rule:
If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :
[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]
In the given question,
Sine rule will be used to get the unknown side of the triangle.
According to the rule;
[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]
Given w = 3 in, ∠W=23° and ∠U=73°, substitute into the equation above to get u we have;
we can write the eq. as
[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]
[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]
Hence, length of u is 7.4 inches to the nearest 10th of an inch.
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How do we find the "rate of change"
Answer: To find the average rate of change, divide the change in y-values by the change in x-values
Step-by-step explanation:
I need help with this question
Answer:
x= 32
Step-by-step explanation:
3x-2+3x-10= 180 (sum of angles in straight line)
6x-12=180
6x=192
6x/6= 192/ 6
x = 32
Step-by-step explanation:
3x - 2 ° + 3x - 10° = 180°
reason : being angle in linear pair ...
6x - 12 = 180°
6x = 180° + 12
6x = 192°
[tex] x = \frac{192}{6} \\ [/tex]
x = 32°
Now ,
3x - 2 °
= 3 × 32 - 2
= 96 - 2
= 94°
Again ,
= 3x - 10°
= 3 × 32 - 10°
= 86°
☘☘☘...
If p and q are negative integers such that [tex]p^2 \ \textgreater \ q^2[/tex],
then [tex]p^3[/tex] ________ [tex]q^3\\[/tex].
a) >
b) <
c) =
d) none of these
By compatibility principle of inequalities we complete the following sentence:
If p and q are negative integers such that p² > q², then p³ < q³. (Correct choice: B)
What is the relationship between two distinct negative integers?
According to the statement, the elements p and q are negative integers such that p² > q². By the sign law, the product of two negative numbers is always equal to a positive number, then by compatibility principle:
p² > q² Given
p · p > q · q Definition of power
p < q Compatibility principle
p³ < q³ Compatibility principle / Result
Please notice that the inequality symbol, that is, from "<" to ">" and viceversa, changes when the compatibility principle is applied in the given inequality.
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