Answer:
[tex]t=\frac{8x-24}{7}\\[/tex]
Step-by-step explanation:
[tex]\frac{7}{8}t+3=x\\\frac{7}{8}t=x-3\\7t=8x-24\\t=\frac{8x-24}{7}[/tex]
Pretty simple, basic algebra.
1. Switch the sides to make it easier to read
2. Subtract 3 on both sides
3. Divide both sides by 8 to cancel the denominator
4. Divide both sides by 7 to isolate the y
How many integer solutions are there to the equation x³ + 2x² -41x-25-17 on the interval 0≤x≤10?
The solution in the given interval is x =6
What is inequalities?A "equal to" symbol on both sides of an equation is not necessarily necessary for it to be balanced. It may also refer to a connection when two things are "not equal to," i.e., where one is better or worse than the other. Any relationship between two numbers or other mathematical expressions that leads to an unfair comparison is referred to in mathematics as an inequality. Certain algebraic mathematical expressions are known as inequalities.
Equation is :
[tex]x^{3} +2x^{2} -41x -25 =17\\x^{3} +2x^{2} -41x -42\\Put x =-1\\-1^{3} -2(-1)^{2} -41(-1) -42=0\\So, (-1) is the solution of the given equation and (x+1) must divide the equation so,\\\frac{x^{3} +2x^{2} -41x -42}{(x+1)} =x^{2} +x-42\\So we can write \\(x+1)(x^{2} +x-42)=0\\(x+1)(x^{2} +7x-6x-42)=0\\(x+1)(x-6)(x+7)=0\\So the solution of the equation are\\x_{1} =-1\\x_{2} =+6\\x_{3} =-7\\[/tex]
We need to find the integer solution in the interval 0≤x≤10
So total no. of solution in the given interval is 1
The solution in the given interval is x =6
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There are 2 different maps of North Carolina. The scale on the first map is 1 cm to 2 km. The distance from Durham to Cary is 15 cm. The scale of the second map is 1 cm to 5 km. What is the distance from Durham to Cary on the second map
The distance from Durham to Cary on the second map is 75 km
The scale of the first map:
1 cm = 2 km
The scale of the second map:
1 cm = 5 km
Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.
Distance from Durham to Cary = 15 cm
Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary
= 5*15
= 75 km
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HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
The equation of the straight line is 3y + 2x = 15
The generic form of a straight line, Ax + By = C, is also the typical form for two-variable linear equations.
Standard form is used, for instance, in the linear equation 4x+7y= 1. This method makes it easy to find the two intercepts (x and y) of an equation.
Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient or slope of the line and c denotes the location of its y-axis intersection.
Two geometrical objects are perpendicular if they cross at a right angle.
We are aware that the product of the slopes of two lines when they are perpendicular equals -1.
The given straight line is of the form y =3/2 x - 1 .
Slope of the straight line = 3/2
Slope of the perpendicular(90°) line (m) = -2/3
The equation of a line is formulated by :
y -y₁ = m (x - x₁ )
The straight line passes through (-3 , 7)
∴y - 7 = -(2/3) (x + 3 )
or, -2x - 6 = 3y - 21
or, 3y + 2x = 15
Therefore the equation of the straight line is 3y + 2x = 15 .
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PLEASE HELP! this is probably easy, THANK YOU! please let me know if you can’t see properly it is a little hard to see thank you
Design a pseudocode and the corresponding flow chart for calculating; the area of a circle,the perimeter of a rectangle, the perimeter of a square
See below for the pseudocode and the flowchart is added as an attachment
What is a pseudocode and a flowchart?Flowcharts and pseudocodes are used as prototypes of actual programs.
Flowcharts are in graphical form, while pseudocodes are in the form of texts.The flowchart and pseudocode do not conform to programming syntaxHow to design the pseudocode and the flowchart?Area of circle
The pseudocode is as follows:
StartInput radius, rCalculate Area, A = pi * r^2Display AreaStopPerimeter of rectangle
The pseudocode is as follows:
StartInput dimensions, l and bCalculate Perimeter, P = 2 * (l + b)Display PerimeterStopPerimeter of square
The pseudocode is as follows:
StartInput dimensions, lCalculate Perimeter, P = 4 * lDisplay PerimeterStopSee attachment for the flowcharts
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Rewrite 7x + 49 using a common factor.
Here are some options it gave me.
(A) . 7(x + 7)
(B). 7(x + 49)
(C). 7x(x + 7)
(D). 7x(x + 49)
7x + 49 rewritten using common factor is 7(x + 7)
How to find common factors?A common factor is a whole number which is a factor of two or more numbers.
In other words, common factors of two or more numbers are a number which divides each of the given numbers exactly.
For example the common factor of 24 and 36 are 1, 2, 3, 4, 6 and 12.
Therefore,
rewriting 7x + 49 using common factors is as follows:
7x + 49 = 7(x + 7 )
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Simplify (2√5)²
Please help fast!
Answer:
20
Step-by-step explanation:
Simplify the following:
(2 sqrt(5))^2
Multiply each exponent in 2 sqrt(5) by 2:
2^2×5^(2/2)
2/2 = 1:
2^2×5
2^2 = 4:
4×5
4×5 = 20:
Answer: 20
f(x)=x-7; vertical stretch of 3 g(x)
The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:
g(x) = 3x - 21.
How are vertical stretches and compression applied to the graph of a function f(x)?Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:
g(x) = a x f(x).
Then the value of the constant determines if it is an stretch or a compression.
If the absolute value of the constant a is greater than 1, it is a stretch. If the absolute value of the constant a is less than 1, it is a compression.For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:
a = 3.
Then the definition of function g(x) is given by:
g(x) = 3f(x)
g(x) = 3(x - 7)
g(x) = 3x - 21.
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3) Margaret invests $3,500 in a savings account that offers 5% simple interest per
annum. How much interest will she get after 8 years?
Margaret invests $3,500 in a savings account that offers 5% simple interest per annum. So interest she will get after 8 years is
What is simple interest ?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Given that : Margaret invests $3,500 in a savings account that offers 5% simple interest per annum.
S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]
P = $3,500
R=5%
T=8 years
S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]
S.I = [tex]\frac{(3500)(5)(8)}{100}[/tex]
S.I = 1400
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9(4)^2 + 24(4) + 20 = 4
Answer:
Step-by-step explanation:
a=96.5 rounded to 1 DP
b= 6.48 rounded to 2 DP
Find the maximum of a - b
Help im litteraly failing
The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)
The graph of the system of equations is shown below
Solving system of linear of linear equationsFrom the question, we are to determine the apparent solution to the given system of linear equations
The given system of equations is
y = -2x + 3
y = 1/3x - 4
Set the two equations equal
That is,
-2x + 3 = 1/3x - 4
Multiply through by 3
-6x + 9 = x - 12
Add 6x to both sides of the equation
-6x + 6x + 9 = x + 6x - 12
9 = 7x - 12
Add 12 to both sides of the equation
9 + 12 = 7x - 12 + 12
21 = 7x
x = 21/7
x = 3
Substitute the value of x into the first equation
y = -2x + 3
y = -2(3) + 3
y = - 6 + 3
y = - 3
The solution is (3, -3)
The graph is shown below
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Find the surface area of the figure
In one year, a school uses 11,280 pieces of white paper, 3,580 fewer pieces of blue paper than white paper, and 3,600 fewer pieces of yellow paper than blue paper. how many pieces of paper does the school use in all?
The school uses a total of 23,080 pieces of paper in one year.
To calculate the total number of pieces of paper used by the school we use addition. We also use subtraction to find the pieces of blue paper and yellow paper.
As the pieces of blue paper are 3580 fewer than white paper, we find the pieces of blue paper by subtracting 3580 from 11,280.
blue paper = 11280 - 3580 = 7700
As the pieces of yellow paper are 3600 fewer than blue paper, we subtract 3600 from the total number of pieces of blue paper.
Yellow paper = 7700 - 3600 = 4100
Now, the total number of pieces can be found by the addition of white, blue, and yellow pieces of paper.
Total pieces = White papers + Blue papers + Yellow papers
Total pieces = 11,280 + 7700 + 4100
Total pieces = 23,080
Therefore, 23,080 pieces of paper were used by the school in one year.
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Which table of ordered pairs represents a proportional relationship?
need this answer ASAP
Answer:
It's the 3rd one
Step-by-step explanation:
2x7=14 7x4=28 7x6=42
Answer:
The third table, since x/y = 7.
A scientist needs 1.8 liters of a 22% alcohol solution. She has available a 33% and a
17% solution. How many liters of the 23% and how many liters of the 17%
solutions should she mix to make the 22% solution?
Step-by-step explanation:
the approach of the other answer is basically correct, but we need to use the correct numbers.
so, I assume that the 33% of the first solution is correct, and not the 23% mentioned later.
x = liters of the 33% solution.
y = liters of the 17% solution.
we know that
x + y = 1.8
and therefore
x = 1.8 - y
and then we want to enforce the desired result (ab% are simply 0.ab)
0.33x + 0.17y = 0.22×1.8
we use the identity from above in this equation :
0.33(1.8 - y) + 0.17y = 0.396
0.594 - 0.33y + 0.17y = 0.396
0.198 - 0.16y = 0
0.198 = 0.16y
y = 1.2375 liters
x = 1.8 - y = 1.8 - 1.2375 = 0.5625 liters
if the first solution is truly only 23%, then we only need to change the number :
0.23(1.8 - y) + 0.17y = 0.396
0.414 - 0.23y + 0.17y = 0.396
0.018 - 0.06y = 0
0.018 = 0.06y
y = 0.3 liters
x = 1.8 - y = 1.8 - 0.3 = 1.5 liters
There are 15 squares and 6 triangles. What is the simplest ratio of triangles to total shapes?
Answer: 2:7
Step-by-step explanation:
[tex]\displaystyle\\\frac{6}{15+6} =\\\\\frac{6}{21} =\\\\\frac{2(3)}{7(3)} =\\\\\frac{2}{7} =\\\\2:7[/tex]
The ratio of triangles to total shapes in simplest form is 2 : 7.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, There are 15 squares and 6 triangles.
Therefore, The total number of shapes is (15 + 6) = 21.
So, The ratio of triangles to total shapes is,
triangle/total shapes = 5/15 + 6.
triangles/total shapes = 6/21.
triangles : total shapes = 6 : 21 = 2 : 7
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A rock is dropped into a pond, creating a circular ripple. The radius of the ripple increases steadily at 6 cm/s. A toy boat is floating on the pond, 2.00 m east and 1.00 m north of the spot where the rock is dropped. How long does the ripple take to reach the boat?
Answer: 28.87 seconds
Step-by-step explanation:
Check attached image for explaination
what property does 5(a) = a(5) belong to?
Associative Property
Commutative Property
Inverse Property
Identity Property
Answer:
Commutative Property for Multiplication
Answer:
Commutative Property for Multiplication
Step-by-step explanation:
Which statement cannot be assumed based on the diagram?
A) <GBE and <DBC are adjacent
B) <DBC is vertical to <FDE
C) <EDF and <EDC are adjacent
D) <ABG and <GBD are adjacent.
help please :)
The statement that cannot be assumed based on the diagram is ∠DBC is vertical to ∠FDE.
(A) ∠GBE and ∠DBC are adjacent angles. As we can see from the diagram, they have a common ray starting from the point B.(B) We cannot say that ∠DBC is vertical to ∠FDE from the diagram as we have no such direct relation between the angles.(C) ∠EDF and ∠EDC are adjacent angles. As we can see from the diagram, they have a common ray starting from the point D.(D) ∠ABG and ∠GBD are adjacent angles. As we can see from the diagram, they have a common ray starting from the point B.To learn more about angles, visit :
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What Property’s are used in each step?
Step 1 5x+9+5x+12=(5x+9)+(5x+12)
Step 2 = 5x+(9 +5x)+12
Step 3 = 5x+(5x+9)+12
Step 4 =(5x+5x)+(9+12)
Step 5 = (5 + 5)x+ (9 + 12)
Step 6 = 10x + 21
The property used is Distributive property
What is Distributive property ?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
Given, equation
5x+9+5x+12
Step 1 =(5x+9)+(5x+12)
Step 2 = 5x+(9 +5x)+12
Step 3 = 5x+(5x+9)+12
Step 4 =(5x+5x)+(9+12)
Step 5 = (5 + 5)x+ (9 + 12)
Step 6 = 10x + 21
The property used in this equation is called Distributive property
Hence, the property use in here Distributive property
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how many whole numbers are there between 121and176
TO KNOW HOW MANY WHOLE NUMBERS THERE ARE BETWEEN 121 AMD 176 WE CAN SIMPLY GET THEIR DIFFERENCE.
THE DIFFERENCE IS THE NUMBER OF WHOLE NUMBERS INBETWEEN 121 AND 176.
[tex] = 176 - 121 \\ = 55[/tex]
THERE ARE 55 WHOLE NUMBERS BETWEEN 121 AND 176.
Answer:
54
Step-by-step explanation:
Whole numbers are 0,1,2,3,... Following that pattern forever.
Take a simpler example. How many whole numbers between 2 and 5? It would be just 3 numbers; 3 and 4.
We could subtract 5-2 to get 3 and then subtract 1 more to get the answer of 3
What if I wanted to know the number of whole numbers between 3 and 7?
The numbers would be 4,5,6.
7-3 = 4 and then subtract 1 more to get the answer that there are 3 whole numbers between 3 and 7.
176 - 121 = 55 take one more away to get 54
Justin runs at a constant rate, traveling 17 km in 2 hours.
Write an equation that shows the relationship between d, the distance he runs in kilometers, and h, the time he spends running in hours.
The relationship between the distance that Justin runs, in kilometers, and the running time, in hours, is equal to d = (17 / 2) · t.
How to define the model to describe the distance travelled by Justin at a constant rate
In this problem we find that the distance that Justin runs (d), in kilometers, is directly proportional to the running time (t), in hours. That is:
d ∝ t
d = k · t
Where:
d - Distance, in kilometers.t - Time, in hoursk - Speed, in kilometers per hour.If we know that d = 17 km and t = 2 h, then the relationship between distance and time is described below:
k = 17 km / 2 h
k = 17 / 2 km / h
d = (17 / 2) · t
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the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06. each student does homework independently. in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?
the probability that at least 5 will do their homework on time in a class of 50 students is 0.1
How do you calculate probability?
Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.
the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.
each student does homework independently.
in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?
probability = event occur/ total number of outcomes
= 5/50= 1/10=0.1
thus the probability becomes 0.1
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To enroll in lessons to learn about pottery wheel throwing, you must pay an rollment of $20 for each lesson. The pottery studio also charges you $2.99 pe pound for the amount of clay used.To enroll in lessons to learn about pottery wheel throwing, you must pay an enrollment of $20 for each lesson. The pottery studio also charges you $2.99 per pound for the amount of clay used. Write an expression for the total cost of a person using c pounds of clay during a lesson. Use the expression to calculate the cost of a lesson where Sam uses 3.5 pounds of clay.
Answer:
cost per day = 2.99(c)+20
sam's lessons cost $30.47 per day
Step-by-step explanation:
2.99 (price of clay used per pound) * c (pounds of clay used) + 20 (cost of lesson)
2.99(c)+20
since sam uses 3.5 pounds of clay per lesson that's 2.99(3.5)+20, which is equal to 30.47
Determine whether the graph is linear or non linear and explain
The given graph represents a non-linear function.
What are linear and non-linear functions?When a function is plotted on a graph, a linear function produces a straight line, whereas a nonlinear function does not (it is curved in some way). While the slope of a nonlinear function is continuously changing, the slope of a linear function is constant.Take two points in the graph and calculate the slope:
Slope of (-2,1) and (0,2) = (2-1)/(0-(-2) = 1/2
Slope of (2,1) and (0,2) = (2-1)/(0-2) = 1/(-2)
As the slope of the given graph is variable, it is a non-linear function.
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HELP ASAP, ITS DUE TODAY AT MIDNIGHT!!!!! 92 POINTS!!!!!!!!!!!
The relationship is that number sense can be used to solve area models or partial products.
What is number sense?Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.
Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.
In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.
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Use the following information to find x: AB = 4x + 5; BC = 13; and B is the midpoint of AC
The numerical value of x is 2 as segment AB equals segment BC.
What is the numerical value of x ?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
B is the midpoint of ACSegment AB = 4x + 5Segment BC = 13Given that B is the midpoint of segment AC, this means that segment AB is equal to segment BC.
Hence
Segment AB = Segment BC
4x + 5 = 13
Solve for x
Subtract 5 from both sides
4x + 5 - 5 = 13 -5
4x = 8
Divide both sides by 4
4x/4 = 8/4
x = 8/4
x = 2
Therefore, the value of x is 2.
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. TEST SCORES Benjamin's test scores for the quarter so far are 78, 82, 95, and 88. What does he need to score on the fifth test of the quarter in order to have an average test score of 87?
write the fraction for the following
Answer:
A- 2/4
simplified-1/2
B- 3/5
C- 4/9
D-3/3 which=1
so basically D is 1
hope this helped
please mark as brainliest and have a good day!
Step-by-step explanation: