What is the value of x? (7x-8) (6x+11)
we know that
Vertical angles are a pair of opposite and congruent angles formed by intersecting lines
In this problem
[tex](7x-8)=(6x+11)[/tex] --------> by vertical angles
Solve for x
Combine like terms
[tex](7x-6x)=(11+8)[/tex]
[tex]x=19\ degrees[/tex]
therefore
the answer is
the value of x is [tex]19\ degrees[/tex]
Why cant you take the inverse of a matrix with det = 0?
A matrix with a determinant of zero is called a singular matrix and doesn't have an inverse because it indicates the system of equations it represents doesn't have a unique solution, and the transformation it performs is not reversible.
When a matrix has a determinant of zero (det A = 0), it is classified as a singular matrix and is not invertible. This characteristic implies that the matrix cannot be used to find unique solutions for a set of linear equations because such a matrix corresponds to a system of equations that has either no solution or an infinite number of solutions.
The ability to have an inverse matrix is crucial as it allows us to solve matrix equations and essentially 'undo' the transformations applied by the original matrix.
The reason why a zero determinant indicates the absence of an inverse lies in the mathematics of linear transformations.
A determinant of zero suggests that the transformation associated with the matrix collapses the dimensionality of the space, which means some information about the original vectors is lost, and hence, an inverse operation to recover the original vectors cannot exist.
To further illustrate this, consider the matrix equation AB = I, where A is our original matrix and B is its supposed inverse yielding the identity matrix I. It follows from the properties of determinants that det(AB) = det(A) x det(B).
If det(A) is zero, then the product det(A) x det(B) will also be zero, not equal to 1, which is the determinant of the identity matrix. Therefore, B cannot serve as the inverse of A.
In other words, having a non-zero determinant is a prerequisite for a matrix to have an inverse, as it ensures that the system of equations it represents is solvable and that the matrix transformation is reversible.
The width of a rectangle is 9 units less than it length L. Write an expression that shows how wide the rectangle is in terms of L.
Why do two negative numbers multiplied equal a positive?
Please someone help
What does it mean if two angles are congruent?
measures of an angle and five times it’s complement is 298 what is the measure of the angle
What would be an appropriate measure to describe the depth of a lake?
miles
cubic centimeters
milliliters
feet
Answer:
Feet is the appropriate unit.
Step-by-step explanation:
Feet will be an appropriate measure to describe the depth of a lake.
Miles is a very large unit usually used to describe distance between two places.
Cubic centimeters is a unit of volume.
Millimeters is a very small unit used to describe small objects like the diameter of a penny etc.
Therefore, feet is the most appropriate unit to measure the depth of the lake.
A package is in the shape of a triangular prism. The bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. The distance between the bases is 10 centimeters. What is the surface area of the triangular prism? square centimeters
The surface area of the triangular prism is 468 (square cm).
The surface area A of a triangular prism is given by the formula:
[tex]\[ A = 2A_{\text{base}} + P_{\text{base}} \times h \][/tex]
where:
- [tex]\( A_{\text{base}} \)[/tex] is the area of one of the triangular bases,
- [tex]\( P_{\text{base}} \)[/tex] is the perimeter of one of the triangular bases,
- h is the distance between the bases.
The area of a right triangle is given by:
[tex]\[ A_{\text{base}} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
And the perimeter of a right triangle is the sum of the lengths of its three sides.
Given that the legs of the right triangles forming the bases are 9 cm and 12 cm, and the distance between the bases is 10 cm, we can calculate the surface area.
1. Area of the triangular base [tex](\(A_{\text{base}})\)[/tex]:
[tex]\[ A_{\text{base}} = \frac{1}{2} \times 9 \times 12 \][/tex]
2. Perimeter of the triangular base [tex](\(P_{\text{base}})\)[/tex]:
[tex]\[ P_{\text{base}} = 9 + 12 + \sqrt{9^2 + 12^2} \][/tex]
3. Surface area of the triangular prism A:
[tex]\[ A = 2 \times A_{\text{base}} + P_{\text{base}} \times 10 \][/tex]
Calculate each part and find the total surface area.
[tex]\[ A_{\text{base}} = \frac{1}{2} \times 9 \times 12 = 54 \, \text{cm}^2 \][/tex]
[tex]\[ P_{\text{base}} = 9 + 12 + \sqrt{9^2 + 12^2} = 9 + 12 + 15 = 36 \, \text{cm} \][/tex]
[tex]\[ A = 2 \times 54 + 36 \times 10 = 108 + 360 = 468 \, \text{cm}^2 \][/tex]
So, the surface area of the triangular prism is [tex]\(468 \, \text{cm}^2\)[/tex].
One machine can make 138,800 small paper clips in one day.Another machine can make 84,250 large paper clips in one day.How many more small paper clips than large paper clips are made by two machines in one day
The length of a rectangular garden is 3yd more than twice it’s width. The perimeter of the garden is 36yd. What are the width and length of the garden?
12. A race car is running practice laps in preparation for an upcoming race. To judge how
the car is performing, the crew takes measurements of the car’s speed S(t) (in miles per
hour, or mph) every minute. The measurements are given in the table below.
t (minutes) S(t) (mph)
0 201
1 205
2 208
3 214
4 218
5 212
6 219
7 223
8 220
9 221
10 217
11 218
A. Use the trapezoid rule with 4 equal subdivisions to approximate the total distance the car
traveled (in miles) over the first 12 minutes.
B.Find one approximation for Sv(6), including the units. Explain what this quantity means in
the context of the problem.
C. What was the car’s average speed in mph over the first 12 minutes? If the car needs to
have an average speed of 210 mph to qualify for the race, is it currently running fast enough
to qualify?
The student's problem involves the use of the trapezoid rule to approximate total distance traveled by a race car, finding the speed at a particular time point (Sv(6)), and calculating the car's average speed to see if it meets the qualifying speed.
Explanation:To solve this problem, we need to conduct several mathematical operations. Firstly, let's use the trapezoid rule to approximate the total distance the car traveled in 12 minutes. Then we'll find an approximation for Sv(6) and explain its meaning. Finally, we'll calculate the car's average speed and determine if it's fast enough to qualify for the race.
For the trapezoid rule, remember that it's structured as (b-a)/2n [f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn) + f(xn+1)]. We'll create 4 equal subdivisions over the first 12 minutes. Due to the lack of full data set, let's suppose the missing speeds are similar to the closely related ones provided.Sv(6) stands for the velocity, or speed, at the 6th minute, which is 219 mph. This represents how fast the car was going at that specific moment.To get the average speed, add up all the speeds given and divide by the number of measurements. If the resultant speed is at least 210 mph, then the car is fast enough to qualify for the race.Learn more about Trapezoid Rule & Average Speed here:https://brainly.com/question/33247395
#SPJ3
Zoe is taking the measurements of her lawn. her lawn is 64.15 feet long and 22.70 meters wide. one foot is equivalent to 0.3048 meters. which dimension of zoe's lawn is longer, and how many yards longer is it?
Answer:
width of the lawn is greater than the length of the lawn.Step-by-step explanation:
The length of her lawn=64.15 feet.
Width of her lawn=22.70 meters.
we are given that:
1 foot=0.3048 meters.
Hence,
64.15 feet=21.86232 meters.
Hence, length of lawn=21.86232 meters.
Hence, width of the lawn is greater than the length of the lawn.
( since 22.70 meters> 21.862332 meters)
Also 1 meter=1.0936 yards.
so, width of lawn in yards is:
22.70×1.0936=24.82472 yards.
length of lawn is: 23.9086462752 yards.
Hence, width of lawn is 0.9160737 yards more than the length of lawn.
what is the measure on angle A?
- 110
-70
250
55
Calculus: Help ASAP
Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power plus 1, dx. Your work must include the use of substitution and the antiderivative.
Answer:
2.264 (3 d.p.)
Step-by-step explanation:
Given integral:
[tex]\displaystyle \int^0_{-1} \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x[/tex]
First, evaluate the indefinite integral using the method of substitution.
[tex]\textsf{Let} \;\;u = 4x^6+2x[/tex]
Find du/dx and rewrite it so that dx is on its own:
[tex]\dfrac{\text{d}u}{\text{d}x}=24x^5+2 \implies \text{d}x=\dfrac{1}{24x^5+2}\; \text{d}u[/tex]
Rewrite the original integral in terms of u and du, and evaluate:
[tex]\begin{aligned}\displaystyle \int\left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x&=\int \left(u\right)^3\left(12x^5+1\right)\cdot \dfrac{1}{24x^5+2}\; \text{d}u\\\\&=\int \left(u\right)^3\left(12x^5+1\right)\cdot \dfrac{1}{2(12x^5+1)}\; \text{d}u\\\\&=\int \dfrac{u^3\left(12x^5+1\right)}{2(12x^5+1)}\; \text{d}u\\\\&=\displaystyle \int \dfrac{u^3}{2}\; \text{d}u\\\\&=\dfrac{u^{3+1}}{2(3+1)}+C\\\\&=\dfrac{u^4}{8}+C\end{aligned}[/tex]
Substitute back u = 4x⁶ + 2x:
[tex]=\dfrac{(4x^6+2x)^4}{8}+C[/tex]
Therefore:
[tex]\displaystyle \int \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x=\dfrac{(4x^6+2x)^4}{8}+C[/tex]
To evaluate the definite integral, we must first determine any intervals within the given interval -1 ≤ x ≤ 0 where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.
Find the x-intercepts by setting the function to zero and solving for x.
[tex]\left(4x^6+2x\right)^3\left(12x^5+1\right)=0[/tex]
Therefore:
[tex]\begin{aligned}\left(4x^6+2x\right)^3&=0\\4x^6+2x&=0\\x(4x^5+2)&=0\end{aligned}[/tex]
[tex]x=0[/tex]
[tex]\begin{aligned}4x^5+2&=0\\4x^5&=-2\\x^5&=-\frac{1}{2}\\x&=\sqrt[5]{-\dfrac{1}{2}}\end{aligned}[/tex]
[tex]\begin{aligned}12x^5+1&=0\\12x^5&=-1\\x^5&=-\dfrac{1}{12}\\x&=\sqrt[5]{-\dfrac{1}{12}}\end{aligned}[/tex]
Therefore, the curve of the function is:
Below the x-axis between -1 and ⁵√(-1/2).Above the x-axis between ⁵√(-1/2) and ⁵√(-1/12).Below the x-axis between ⁵√(-1/12) and 0.So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.
Integrate the function between -1 and ⁵√(-1/2).
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
[tex]\begin{aligned}A_1&=-\displaystyle \int_{-1}^{\sqrt[5]{-\frac{1}{2}}} \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x\\\\&=-\left[\dfrac{(4x^6+2x)^4}{8}\right]_{-1}^{\sqrt[5]{-\frac{1}{2}}}\\\\&=-\left[\left(\dfrac{\left(4\left(\sqrt[5]{-\frac{1}{2}}\right)^6+2\left(\sqrt[5]{-\frac{1}{2}}\right)\right)^4}{8}\right)-\left(\dfrac{(4(-1)^6+2(-1))^4}{8}\right)\right]\\\\&=-[0-2]\\\\&=2\end{aligned}[/tex]
Integrate the function between ⁵√(-1/2) and ⁵√(-1/12).
[tex]\begin{aligned}A_2&=\displaystyle \int_{\sqrt[5]{-\frac{1}{2}}} ^{\sqrt[5]{-\frac{1}{12}}} \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x\\\\&=\left[\dfrac{(4x^6+2x)^4}{8}\right]_{\sqrt[5]{-\frac{1}{2}}}^{\sqrt[5]{-\frac{1}{12}}}\\\\&=\left(\dfrac{\left(4\left(\sqrt[5]{-\frac{1}{12}}\right)^6+2\left(\sqrt[5]{-\frac{1}{12}}\right)\right)^4}{8}\right)-\left(\dfrac{\left(4\left(\sqrt[5]{-\frac{1}{2}}\right)^6+2\left(\sqrt[5]{-\frac{1}{2}}\right)\right)^4}{8}\right)\\\\\end{aligned}[/tex]
[tex]\begin{aligned}&=\dfrac{625}{648\sqrt[5]{12^4}}-0\\\\&=0.132117398...\end{aligned}[/tex]
Integrate the function between ⁵√(-1/12) and 0.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
[tex]\begin{aligned}A_3&=-\displaystyle \int_{\sqrt[5]{-\frac{1}{12}}}^0 \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x\\\\&=-\left[\dfrac{(4x^6+2x)^4}{8}\right]_{\sqrt[5]{-\frac{1}{12}}}^0\\\\&=-\left[\left(\dfrac{(4(0)^6+2(0))^4}{8}\right)-\left(\dfrac{\left(4\left(\sqrt[5]{-\frac{1}{12}}\right)^6+2\left(\sqrt[5]{-\frac{1}{12}}\right)\right)^4}{8}\right)\right]\\\\&=-\left[0-\dfrac{625}{648\sqrt[5]{12^4}}\right]\\\\&=\dfrac{625}{648\sqrt[5]{12^4}}\\\\&=0.132117398...\\\\\end{aligned}[/tex]
To evaluate the definite integral, sum A₁, A₂ and A₃:
[tex]\begin{aligned}\displaystyle \int^0_{-1} \left(4x^6+2x\right)^3\left(12x^5+1\right)\;\text{d}x&=2+2\left( \dfrac{625}{648\sqrt[5]{12^4}}\right)\\\\&=2+ \dfrac{625}{324\sqrt[5]{12^4}}\right}\\\\&=2.264\; \sf (3\;d.p.)\end{aligned}[/tex]
Write the ratio using fraction notation and reduce.
20 minutes to 1 hour
(a) 20
(b )1/3
(c) 1/20
(d) 3
If PR = 4x – 2 and RS = 3x – 5, which expression represents PS? x – 7 x – 3 7x – 7 7x + 3
we have that
[tex]PR = 4x - 2\\RS = 3x - 5[/tex]
we know that
[tex]PS=PR+RS[/tex]
substitute the values of PR and RS in the formula above
[tex]PS=(4x-2)+(3x-5)[/tex]
Combine like terms
[tex]PS=(7x-7)[/tex]
therefore
the answer is
[tex]PS=(7x-7)[/tex]
The expression which represents PS is; 7x -7
Addition of algebraic expressionsAccording to the question;
The segment, PR = 4x – 2 and RS = 3x – 5.We are required to find; PS.From observation;
PS = PR + RSPS = 4x -2 + 3x -5PS = 4x + 3x -2 -5PS = 7x -7.Read more on addition of algebraic expressions;
https://brainly.com/question/2164351
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
a.14.6
b.15.5
c.21.0
d.21.6
HELPS PLS ryad borrowed $1450 and made 18 payment of $95.25 how much did he pay in interest?
The length of a rectangle is four more than five times its width. its perimeter is 4444 inches. find its dimensions (length and width).
How many lines of symmetry does a regular polygon with 12 sides have?
A local charity sponsors a 5K race to raise money. It receives $25 per race entry and $5,000 in donations, but it must spend $5 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise more than $25,000. Show your work!
Question 1 options:
Spell check
they receive 25 per entry but 5 goes towards the cost of the race
so 25-5 = 20 per entry is for the charity
so 20x + 5000 = 25000
subtract 5000 from each side
20x= 20000
divide both sides by 20
x = 20000/ 20
x = 1000
they need at least 1000 entries to make 25000
so to make more than 25000, they need 1001 entries
Combine like terms.
9 + 3x – 9x + 16
A.19x
B.3x + 16
C.25 – 6x
D.18x + 3x + 16
Does a regular hexagon have 2 parallel sides
which of the following equations represents a proportional relationship? Choose all that apply.
A. x=2y
B.a = 1/3b
C.4x=y-2
D.7/3x=n
E.1/2=1/4
The options A, B, and D have a proportional relationship.
What is a proportional relationship?It is the relationship between two variables where their ratios are equivalent.
Consider the first equation, x = 2y.
It can be written like the ratio of x and y.
i.e [tex]\frac{x}{y} -\frac{2}{1}[/tex]
So, option A is proportional at x = 2 and y = 1.
For option B, It can rewrite as
[tex]\frac{a}{b} =\frac{1}{3}[/tex]
So, option B is proportional when a = 1 and b = 3.
Option C is not proportional since it can't be written as a ratio.
Option D can be written as
[tex]\frac{7}{3} =\frac{n}{x}[/tex]
It is proportional when n = 7 and x = 3.
Option E is not proportional since it is not equal.
Therefore the proportional options are A,B, and D.
To learn more about proportional relationship, use the link given below:
https://brainly.com/question/29765554
#SPJ2
Point G is between points F and H. FH = 102, FG = 5x + 9, and HG = 9x − 5. Show your work.
A.) What is the value of x ?
B.) What is the length of ̅̅̅̅FG?
C.) What is HG?
Alvin's age is three times elga's age. the sum of their ages is 32 . what is elga's age
Final answer:
Elga's age is determined by setting up an equation E + 3E = 32 and solving for E. After simplifying, we find that Elga is 8 years old.
Explanation:
To solve this problem, we can use algebra to set up two equations based on the information given that Alvin's age is three times Elga's age and the sum of their ages is 32.
Let's let E represent Elga's age. According to the problem, Alvin's age will be 3E because it is three times Elga's age. We can write the following equation to represent the sum of their ages:
E + 3E = 32
Combining like terms, we have:
4E = 32
Dividing both sides by 4 to solve for E, we get:
E = 32 / 4
Therefore, Elga's age is:
E = 8
Elga is 8 years old.
The measures of the 3 sides of a triangle can be represented by algebraic expressions x, 3x-1, and 4x＋2.the perimeter of the triangle is 81inches. What are the lengths of the sides of the triangle?
1/4=1/4h + 4
I understand how to do the 2-step equations, but not the ones with 2 fractions.
PLZ HELP!!!! WILL GIVE BRAINLIEST ANSWER!!!
△E′F′G′ is the image of △EFG under a dilation through point C.
What scale factor was used in the dilation?
the correct answer is - 1/2
Answer: The value of the scale factor is [tex]-\frac{1}{2}[/tex].
Explanation:
It is given that the △E′F′G′ is the image of △EFG under a dilation through point C.
We know that the length of sides of image are in the proportion of length of sides of preimage. That proportion factor is also known as scale factor.
It is given that the length of FG is 8 cm and the length of F'G' is 4 cm.
[tex]k=\frac{F'G'}{FG} =\frac{4}{8} =\frac{1}{2}[/tex]
Therefore the side of image and preimage are in proportion of [tex]\frac{1}{2}[/tex].
Since the image and preimage are not on the same side of the center of dilation it means the factor must be negative. So,
[tex]k=-\frac{1}{2}[/tex].
Therefore, [tex]-\frac{1}{2}[/tex] is the scale factor of dilation.