Please help I only have part A incorrect I can’t figure it out
By similarity ratio of triangles, we have;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
PS/PR = PR/PQ
PQ/RQ = RQ/SQ
How to solve similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Thus, applying the concept of similar triangle ratio we can say that;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
Similarly, by similarity ratio of triangles, we have;
PS/PR = PR/PQ
We also have;
PQ/RQ = RQ/SQ
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A kite is shown below.
Find the size of angle BCD.
A
117°
B
55°
D
C
PLEASE DO IT FOR 20 points
The angle measures are given as follows:
x = 118º.y = 35º.What are supplementary angles?Two angles are called supplementary when the sum of their measures is of 180º.
On a trapezoid, consecutive interior angles are supplementary, hence the pairs of supplementary angles are given as follows:
y and 145º.x and 62º.Hence the value of y is obtained as follows:
y + 145 = 180
y = 35º.
(as the two angles are supplementary we know that the sum of their measures is of 180º).
The value of x is obtained as follows:
x + 62 = 180
x = 118º.
(as the two angles are supplementary we know that the sum of their measures is of 180º).
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Two docks are located on an east-west line 2599 ft apart. From dock A, the bearing of a coral reef is 58°23′. From dock B, the bearing of the coral reef is 328°23′. Find the distance from dock A to the coral reef.
Therefore , the solution of the given problem of trigonometry comes out to be it is roughly 5193 feet from pier A to the coral reef.
What is a trigonometry?Relationships between mathematics but also cubic splines When the different fields were combined, astrophysics is thought to have been born in the third century BC. With the aid of exact angle mathematical techniques, many metric issues can be resolved or the outcomes of calculating them can be ascertained. The study of the six fundamental trigonometric formulas is known as trigonometry.
Here,
The north-south distance from pier A to the coral reef, x sin(31°37′), is the other side of the triangle (relative to angle ). The east-west path from dock A to the edge of the coral reef, which is equal to x cos(31°37′), forms the opposite side of the triangle. We're looking for x's number.
The Pythagorean theory allows us to write:
=> (x cos(31°37′) + 2599) + (x sin(61°37′)) = (x sin(31°37′))
By condensing and rearrangeing, we obtain:
=> x² - 5198x + 6790401 = 0
We can use the quadratic formula to answer the following quadratic equation:
=> x = (-(-5198) ± √(-5198)^2 - 4(1)(6790401))) / (2(1))
=> x = (5198 + √(26857604)) / 2
=> x = (5198 ± 5188) / 2
=> x = 5193 or x = 5
The negative answer x = 5 does not make logic in this situation because x is a measure of distance. Consequently, it is roughly 5193 feet from pier A to the coral reef.
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Triangle NMO is drawn with vertices N(−4, −2), M(−1, −1), O(−4 , −5). Determine the image coordinates of N′M′O′ if the preimage is translated 3 units to the left. N′(−7, −2), M′(−4, −1), O′(−7, −5) N′(−4, −5), M′(−1, −4), O′(−4, −8) N′(−4, 1), M′(−1, 2), O′(−4, −2) N′(−1, −2), M′(2, −1), O′ (−1, −5)
Answer: N′(−7, −2), M′(−4, −1), O′(−7, −5)
Step-by-step explanation:
im right and youre wromng
A dish contains 2 bacteria. The bacteria quadruple in number every 16 minutes. The number of bacteria in the dish over time can be represented by the expression 2×4t16.
Which equivalent expression could also be used to represent the number of bacteria in the dish for any time, t, in minutes?
Responses
4t8
8t16
2×2t8
4×2t16
If the bacteria in a dish that contains 2 bacteria quadruple every 16 minutes can be represented by the expression 2×4t/16, an equivalent expression for the number of bacteria in the dish for any time, t, in minutes is B. 8t/16.
What is an equivalent expression?An equivalent expression depicts two algebraic expressions that have the same value when the values for the variables are plugged in.
An algebraic expression is the combination of variables, values, constants, and numbers using mathematical operands without the equal symbol (=).
2×4t/16 = 8t/16
2×4t/16 ≠ 4t8
2×4t/16 ≠ 2×2t8
2×4t/16 ≠ 4×2t16
Thus, 2×4t/16 = 8t/16 as equivalent expressions.
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this is due tomorrow
The number line graph A is correct, thus, option C is true.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, an inequality x ≥ -5.
The inequality x ≥ -5 means that x is greater than or equal to -5.
In other words, any value of x that is equal to or greater than -5 satisfies the inequality.
For example, x = -5, x = 0, x = 10, and x = 100 all satisfy the inequality x ≥ -5 because they are greater than or equal to -5.
On a number line, the solution set for this inequality would include all the values of x to the right of -5, including -5 itself,
because the dot at -5 would be filled in to indicate that it is included in the solution set.
The part of the number line to the left of -5 would not be included because those values of x are less than -5, which does not satisfy the inequality.
Therefore, the Option C is correct.
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g(t)= 200(1.12)^t For each function below, enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.
Answer:
Percent rate of change per unit, t ≈ 10.99%
Step-by-step explanation:
The percent rate of change per unit, t, for a function is equal to the derivative of the function with respect to t, divided by the function value at t.
For the given function g(t) = 200(1.12)^t, the derivative with respect to t is:
g'(t) = ln(1.12) * 200(1.12)^t
The function value at t is:
g(t) = 200(1.12)^t
Therefore, the percent rate of change per unit, t, is:
g'(t) / g(t) = [ln(1.12) * 200(1.12)^t] / [200(1.12)^t] = ln(1.12) ≈ 0.1099
Multiplying by 100 to express the answer as a percentage, rounded to the nearest tenth of a percent, we get:
Percent rate of change per unit, t ≈ 10.99%
help on this of math
The required value of x for the given figure is 2√7 units.
What is right angled triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular edges. The foundation of geometry is the relationship between the sides and other angles of the right triangle.
According to question:In the given figure we have two triangle big and small triangle.
To find the value of x;
first we use Pythagoras theorem in big triangle.
So; let base of big triangle is b
9² = 7² + b²
b² = 81 - 49
b = √32
Now in small triangle;
(√32)² = x² + 2²
32 = x² + 4
x² = 28
x = √28
x = 2√7 units.
Thus, required value of x is 2√7 units.
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why the nature of the roots depend on the value of the discriminant
The value of a discriminant determines the kind of roots in a quadratic equation, and the sign of a discriminant indicates whether the roots were real or complex, unique or recurring.
What does a math quadratic equation mean?Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd quadratic problem, which is guaranteed by the algebraic basic theorem. The solution could be straightforward or difficult.
How do you determine whether an equation is quadratic?To put it another way, if a twice the square of a expression that comes after b plus b times the same expression never squared plus c equals 0.
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Review the graph of function f(x). On a coordinate plane, a graph approaches x = negative 3 in quadrant 2, has inflection point (negative 1, 0) and approaches x = 1 in quadrant 4. A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1. Which statement describes Limit of f (x) as x approaches 1?
The correct statement regarding the limit of f(x) as x -> 1 is given as follows:
lim x -> 1 f(x) = -∞.
How to calculate the lateral limits?To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.
If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.
From quadrant 2, the function approaches x = 1 on quadrant 4, hence the limit to the left is given as follows:
lim x -> 1^- f(x) = -∞.
A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1, hence the limit to the right is given as follows:
lim x -> 1^+ f(x) = -∞.
As the lateral limits are equal, the limit of the function is given as follows:
lim x -> 1 f(x) = -∞.
Missing InformationThe problem describes the graph of the function.
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please help i really need ittt!!!!!!!!!!!!!!!!!!!!!!!!!
A 2.5 m ramp is used to load a truck 1.0 m off of the ground. A man uses 600 N of force to load a box weighing 1200 N. What is the efficiency of the ramp? What is the mechanical advantage of the ramp?
Answer:
To find the efficiency of the ramp, we need to compare the work output to the work input. Work input is the force applied to the ramp multiplied by the distance over which the force is applied, and work output is the weight of the box multiplied by the distance it is lifted.
The force applied to the ramp is 600 N, and the distance over which it is applied is the length of the ramp, which is 2.5 m. So the work input is:
work input = force x distance = 600 N x 2.5 m = 1500 J
The weight of the box is 1200 N, and the distance it is lifted is 1.0 m (the height of the truck). So the work output is:
work output = weight x distance = 1200 N x 1.0 m = 1200 J
The efficiency of the ramp is the ratio of work output to work input:
efficiency = work output / work input = 1200 J / 1500 J = 0.8 = 80%
So the efficiency of the ramp is 80%.
To find the mechanical advantage of the ramp, we need to compare the output force to the input force. The output force is the weight of the box, which is 1200 N. The input force is the force applied to the ramp, which is 600 N.
So the mechanical advantage of the ramp is:
mechanical advantage = output force / input force = 1200 N / 600 N = 2
So the mechanical advantage of the ramp is 2.
A water balloon is dropped at 144 feet.
A) After how many seconds does the water balloon touch the ground.
B) Suppose the initial height is adjusted by k feet. How does this affect part (a)?
when k _ 0, the water balloon will take more than _ seconds to hit the ground when k _ 0, the water balloon will take less than _ seconds to hit the ground
Answer: I dont understand the answer that much but off of what i understand i think the answer is A
Step-by-step explanation: I am not sure but i think so
Answer the following questions using the image below
a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.
b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?
a) The altitude οf the plane is apprοximately 10,780 meters.
b) The pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.
What are trigοnοmetric functiοns?Trigοnοmetric functiοns are mathematical fοrmulas that cοnnect a triangle's angles and side ratiοs. Sine, cοsine, and tangent are the three fundamental trigοnοmetric functiοns; they are alsο knοwn as sin, cοs, and tan, respectively. These functiοns are emplοyed in the study οf physics, engineering, and οther branches οf science as well as in the study οf geοmetry, trigοnοmetry, and οther branches οf mathematics. They can be used tο sοlve issues invοlving angles and distances, such as determining a building's height, the separatiοn between twο οbjects, οr the speed οf a mοving οbject.
a) The Pythagοrean theοrem, which relates the three sides οf a right triangle, can be used tο determine the plane's altitude. In this instance, the slant range serves as the hypοtenuse οf a right triangle, with the grοund range serving as οne οf the legs and the height serving as the οther leg. As a result, we have:
altitude² + grοund range² = slant range²
Substituting the given values, we get:
altitude² + (10.15 km)² = (14.5 km)²
Simplifying and sοlving fοr altitude, we get:
altitude² = (14.5 km)² - (10.15 km)²
altitude² = 116.205 km²
altitude = √116.205 km² ≈ 10.78 km ≈ 10,780 m
Therefοre, the altitude οf the plane is apprοximately 10,780 meters.
b) If the plane descends suddenly at a rate οf 750 meters per minute, its altitude will decrease by 750 meters every minute. Tο find hοw much time the pilοt has befοre he has tο land, we can divide the initial altitude by the rate οf descent. Therefοre, we have:
time = initial altitude/rate οf descent
Substituting the initial altitude and rate οf descent, we get:
time = 10,780 m / 750 m/min
Simplifying, we get:
time = 14.3733 min ≈ 14.4 min
Therefοre, the pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.
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Simplify the radical: √32x
(I understand how to simplify radicals I just don’t know how to do it with an unknown variable in it)
The expression when evaluated is 4√2x
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
√32x
Express 32 as the product of 16 and 2
So, we have
√32x = √(16 * 2x)
Take the LCM of 16
So, we have the following representation
√32x = 4√2x
Hence, the solution is 4√2x
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Guys i need help with these. THIS QUESTION IS EASY PLS HELP:)
(5[tex]\sqrt{3}[/tex])^2
= (25 x 3)
= 75
(2[tex]\sqrt{5}[/tex])^2
= (4 x 5)
= 20
help pls with my homework
Answer:
300.20
Step-by-step explanation:
because it was a nice guesss
Part B
Interest can be calculated on money invested and money borrowed. Based on her four options, in which account should
Brianna choose to invest her summer earnings?
Use your answers from Part A to justify your response. Explain your reasoning using complete sentences.
Based on the four options, Brianna should choose to invest her summer earnings in the Account 4 (compounded continuously) because interest is at highest in the account after like 3 years.
Why is interest higher when compounded continuously is used?Interest is higher in compounded continuously because it is calculated more frequently than in other compounding methods, such as annually or semi-annually. In continuous compounding, interest is calculated and added to the principal an infinite number of times over a given period, which results in a higher effective interest rate than other compounding methods.
This means that the amount of interest earned on an investment or loan increases more rapidly, which can result in greater returns for investors or higher costs for borrowers. Continuous compounding is often used in financial markets where small changes in interest rates can have significant impacts on returns, such as in the case of short-term bonds or options trading.
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Line m has a linear equation of y = 2x + 1 and line t has a linear equation of y = -2x - 4.
Are the lines parallel, perpendicular, or intersecting?
They are intersecting
a) Not parallel because they share different slopes
b) Not perpendicular, they dont intersect creating a right angle. This is because neither of the slopes are a reciprocal of each other.
Simply the expression 7h+(6.3d)-15+4d-3.4h
Answer:
See below.
Step-by-step explanation:
We are asked to simplify the expression provided.
An easy way to simplify this expression is by Combining Like Terms.
What is Combining Like Terms?Combining Like Terms means adding terms that are similar, whether that's natural numbers, or variables.
For example, 8x + 9x are like terms since they both have the same variables. There's no exponents or any other variables that make these terms different from each other.
Using what we've learned, let's combine like terms for our problem now.
Combine Like Terms:
[tex]7h+6.3d-15+4d-3.4h[/tex]
[tex]7h - 3.4h = 3.6h[/tex]
[tex]6.3d + 4d = 10.3d[/tex]
-15 has no like terms.
We should have;
[tex]10.3d-15+3.6h[/tex]
This will be our final answer. There's no more like terms to combine and we can't simplify this expression further.
A skateboard ramp is 4.1 feet high and 6 feet long along the horizontal. To the nearest
tenth of a degree, what is the measure of the angle that the ramp makes with a
horizontal line?
34.3°
55.7°
90°
46.9⁰
Answer: :)
Step-by-step explanation:
To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).
We can use the tangent function to find this angle:
tan(theta) = opposite/adjacent
In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:
tan(theta) = 4.1/6
Using a calculator, we can solve for theta:
theta = tan^-1(4.1/6)
theta ≈ 34.3°
Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.
the product of a 5 and a number plus 11 is 36
Answer:
Step-by-step explanation:
5*x+11=36
5*x=36-11
x=25/5
x=5
5 is the answer
Hey there!
Guide to follow
• Product = multiply/multiplication
• Sum = add/addition
• Quotient = divide/division
• Difference = subtract/subtraction
• Is = equal to/equivalent to
Question reads….
“The product of a 5 and a number plus 11 is 36”
We are not sure what the unknown number is, so we will label it as “w”
Your equation:
5 * w + 11 = 36
SOLVING for the answer to the equation:
5 * w + 11 = 36
5w + 11 = 36
SUBTRACT to both sides
5w + 11 - 11 = 36 - 11
SIMPLIFY it
5w = 25
DIVIDE 5 to BOTH SIDES
5w/5 = 25/5
SIMPLIFY it
w = 25/5
w = 5
Therefore, your unknown number should be: 5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
John has three more pet birds than he has cats. If he has 11 pets in all, how many cats does he have?
Answer:
4 cats
Step-by-step explanation:
Let b represent birds and c represent cats
b = c + 3
c + b = 11
c + (c + 3) = 11
2c + 3 = 11
2c = 8
c = 4.
John has 4 cats
b = (4) + 3
b = 7
John has 7 birds
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All items produced in a factory are checked for defects. of the 300 items checked 3% more found to be defective. how many at the items check to work correctly?
72 items were checked to work correctly.
What is the solution of algebraic expression?
Finding the value of the variable is part of solving an algebraic statement. We must do certain algebraic operations to determine the value of one of the variables in the linear equations before we can substitute that value to get the value of another variable.
Then the percentage of defective items in the checked batch is x + 3%.
We know that out of 300 items, this percentage represents the number of defective items. So we can write:
(x + 3%) * 300 = number of defective items
Simplifying this equation, we get:
3x + 9 = number of defective items
number of items checked - number of defective items = number of items checked to work correctly
Substituting the equation we derived above for the number of defective items, we get:
300 - (3x + 9) = number of items checked to work correctly
Simplifying this equation, we get:
291 - 3x = number of items checked to work correctly
3x = number of defective items in a batch of 300 items with the normal percentage of defects
Substituting this expression for the number of defective items in our previous equation, we get:
291 - 3x = number of items checked to work correctly
Now we can solve for x:
3x = number of defective items in a batch of 300 items with the normal percentage of defects = x/100 * 300
3x = 3 * (300 - number of items checked to work correctly - number of defective items)
3x = 900 - 3(3x + 9)
3x = 900 - 9x - 27
12x = 873
x = 73
So the normal percentage of defective items is 73%.
Now we can find the number of items checked to work correctly:
291 - 3x = 291 - 3(73) = 72
Therefore, 72 items were checked to work correctly.
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solve: 5−3|x+8|=20
(multiple choice)
x= -5
No solution
x= -13
x= 8
the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given an algebraic expression:
5 - 3|x + 8| = 20
First, we can begin by adding 3|x+8| to both sides of the equation, giving us:
5-20 = 3|x+8|
Simplifying the left-hand side, we get:
-15 = 3|x+8|
Next, we can divide both sides by 3, giving us:
-5 = |x+8|
Now we have an absolute value equation, which has two possible solutions depending on whether x+8 is positive or negative.
If x+8 is positive, then we have:
-5 = x+8
Solving for x, we get:
x = -13
If x+8 is negative, then we have:
-5 = -(x+8)
Solving for x, we get:
x = -5
Therefore, the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.
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cos x = 0.4505 find angle x
We can calculate the value of {x} as 63.2°.
What are trigonometric functions?There are six major trigonometric functions as -
Sine(x) Cosine(x)Tangent(x) Cotangent(x)Secant(x) Cosecant(x)We can write the relation between them as -
Sine = 1/cosecantCosine = 1/secantTangent = 1/CotangentAlso the following trigonometry relations hold true -
sin²Ф + cos²Ф = 11 + tan²Ф = sec²Ф1 + cot²Ф = cosec²ФGiven is that -
cos{x} = 0.4505
We have -
cos{x} = 0.4505
{x} = cos⁻¹(0.4505)
{x} = cos⁻¹{cos(63.2)}
{x} = 63.2°
Therefore, we can calculate the value of {x} as 63.2°.
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The list below shows the number of books returned to a library during each of 10 weeks
393, 393, 496, 400, 458, 482, 491, 511, 507, 509
Which two measures of these data best describe the typical number of books that were
returned to the library each week?
A Mean and median
B Mean and range
C Mode and median
D Mode and range
Answer: The answer is the letter B
Step-by-step explanation:
Mean is the overall average of numbers or books and range is the length from greatest to least
PLS HELP- A satellite can move at 17,000 miles per hour. How many hours will it take to reach a star that is three light years away? Recall that 1 light year = 9.5 ∙ 1012 kilometers and 1 kilometer = 0.62 miles. Show your work.
Answer:
3.465 x 10⁸ hours
or
346,500,000 hours
Step-by-step explanation:
Distance to travel to star = 9.5 x 10¹² kilometers
1 kilometer = 0.62mile
Therefore
9.5 x 10¹² km = 9.5 x x 10¹ x 0.6 miles
= 5.89 x 10¹² miles
Speed of satellite = 17,000 mph
In scientific notation
17,000 = 17 x 10³ = 1.7 x 10⁴ mph
Time taken to reach star at distance of 5.89 x 10¹² miles
= 5.89 x 10¹² miles/1.7 x 10⁴ mph = 5.89/1.7 x 10¹²/10⁴
= 3.465 x 10¹²⁻⁴
= 3.465 x 10⁸ hours
= 346,500,000 hours
Suppose that during a test drive of two cars, one car travels 234 miles in the same time that a second car travels 180 miles. If the speed of the first car is 12 miles per hour faster than the speed of the second car, find the speed of both cars.
Answer:
Let's denote the speed of the second car as x (in miles per hour). Then the speed of the first car is 12 miles per hour faster, which is x + 12.
We know that both cars traveled the same amount of time, so we can use the formula:
distance = speed × time
For the first car, we have:
234 = (x + 12) × time
For the second car, we have:
180 = x × time
We want to find the speeds of both cars, so we need to solve for x and x + 12. We can start by solving for time in both equations:
time = 234 / (x + 12)
time = 180 / x
Since both expressions are equal to time, we can set them equal to each other:
234 / (x + 12) = 180 / x
To solve for x, we can cross-multiply and simplify:
234x = 180(x + 12)
234x = 180x + 2160
54x = 2160
x = 40
Therefore, the speed of the second car is 40 miles per hour, and the speed of the first car is x + 12 = 52 miles per hour.
Step-by-step explanation:
Answer:
Let x = speed of first car x + 12 = speed of second
Step-by-step explanation:
Solve for x 2x+3-4=10
Answer:
x = 5.5
Step-by-step explanation:
2x + 3 - 4 = 10
2x - 1 = 10
2x = 11
x = 5.5
Let's check
2(5.5) + 3 - 4 = 10
11 + 3 - 4 = 10
14 - 4 = 10
10 = 10
So, x = 5.5 is the correct answer.
Answer: x = 5.5
Step-by-step explanation:
To solve, we will isolate the variable x.
Given:
2x + 3 - 4 = 10
Combine like terms on the left side:
2x - 1 = 10
Add 1 to both sides of the equation:
2x = 11
Divide both sides of the equation by 2:
x = 5.5
y=3x-19 5x+y=5 substitution
Answer:
x = 3
y = -10
Step-by-step explanation:
5x + y = 5 y = 3x - 19
5x + 3x - 19 = 5
8x - 19 = 5
8x = 24
x = 3
Now put x in to solve for y
y = 3(3) - 19
y = 9 - 19
y = -10
Let's check
5(3) - 10 = 5
15 - 10 = 5
5 = 5
So, x = 3 and y = -10 is the correct answer.