The value of x is 4.
What are vertical angles?
The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Here, we have
Given the following parameters
m∠A= (6x +29)° and
m∠B = (7x+25)°
Now, we equate both angles to find the value of x and we get
6x+29 = 7x + 25
6x-7x = 25 - 29
-x = -4
x = 4
Hence, the value of x is 4.
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Rectangle P Q R S has P Q=3 and Q R=4. Points T and V are on side P S such that P T=U S=1
Determine the measure of angle T Q U in degrees and rounded to 1 decimal place
The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
Solution:
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]
= [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]
= 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = [tex]sin^{-1}[/tex](0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = (0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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multiply 1/2 x 1/4 equals ?
Answer:
1/8 or 0.125
Step-by-step explanation:
1/2×1/8
multiply the numerators 1×1=1 and multiply the denominators 2×4=8
Final answer =1/8 or 0.125
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $700, 3 prizes of $100, 5 prizes of $10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
This raffle's expected value per ticket is $ 0.25.
Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.
To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.
⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X
⇒ (500 + 600 + 50 + 100) / 5000 = X
⇒ 1250/5000 = X
Apply the division operation, and we get
⇒ 0.25 = X
Therefore, this raffle's expected value per ticket is $ 0.25.
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Find the equivalent measure.
19 qt L
Click the icon to view the customary and metric unit equivalents.
-
19 qtL
(Type an integer or decimal rounded to the nearest tenth as needed.)
The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
What is the equivalent measure?
In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.
The unit "qt" stands for quart, which is a unit of volume.
It is equal to 32 fluid ounces or 0.946 liters.
Therefore, 19 quarts is equal to 19 * 32 = 1932= 608 fluid ounces,
or 19 * 0.946 = 190.946 =18.094 liters.
Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
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Please help, math modeling with distribution and statistics
The probability of having fewer than three television sets in the apartment is 0.7
How to find the probability of having fewer than three television setsProbability is solved by finding the ratio of required outcome to the total sample
In the given problem the total sample space is the sum of the frequencies which
sum of the frequencies
= 1 + 6 + 14 + 7 + 2
= 30
The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added
= 1 + 6 + 14
= 21
The probability P(X < 3) = 0.7
= 21 / 30
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Yesterday, Jack drove 39 1/2 miles. He used 1 1/4
gallons of gasoline. What is the unit rate for miles per gallon?
Answer:
31 [tex]\frac{3}{5}[/tex] miles per gallon.
Step-by-step explanation:
[tex]\frac{39\frac{1}{2} }{1\frac{1}{4} }[/tex]
39 [tex]\frac{1}{2}[/tex] ÷ 1 [tex]\frac{1}{4}[/tex]
[tex]\frac{79}{2}[/tex] ÷ [tex]\frac{5}{4}[/tex]
[tex]\frac{79}{2}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{158}{5}[/tex] = 31 [tex]\frac{3}{5}[/tex] miles per gallon or 31.6 miles per gallon
The chalk circle around a pitcher's mound has a diameter of 18 ft.
What is the area of the pitcher's circle?
Answer:
Exact area = 81π ft²
Approximate area = 254 ft²
Step-by-step explanation:
A = πr²
A = π × (9 ft)²
A = 81π ft²
A = 81(3.14) ft²
A = 254 ft²
[tex] \Large{\boxed{\sf A = 81 \pi \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]
[tex] \\ [/tex]
Explanation:The area of a circle is given by the following formula:
[tex] \Large{\sf A = \pi \times r^2 } [/tex]
Where:
A is the area of the circle.r is its radius.[tex] \\ [/tex]
We know that the diameter of a circle is twice its radius. Therefore, we can find the value of the circle's radius by dividing its diameter by 2.
[tex] \sf Diameter =2 \times radius \Longleftrightarrow radius = \dfrac{Diameter}{2} \\ \\ \\ \star \: \sf r = \dfrac{18 \ ft}{2} = \boxed{\sf 9 \ ft} [/tex]
[tex] \\ [/tex]
Now, substitute the value of the radius into the formula:
[tex] \sf A = \pi \times (9 \ ft)^2 = \boxed{\boxed{\sf 81 \pi \ \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number occupants of a randomly-selected car on his street. Which of the following could be his model?
The option that can be the model when Dwayne has collected data on the number of occupants of cars travelling on the road is Table B.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true
Given the information, the probability for a will be illustrated as:
a. = 0.6 + 0.2 + 0.2 + 0.1 + 0.05 = 1.15 > 1
b. = 0.5 + 0.25 + 0.05 + 0.06 + 0.04 = 1
c. 2 + 1 + 0.1 + 0.1 + 0.4 = 3.6 > 1
d. 0.5 + 0.25 + 0.25 + 0.125 + 0.125 = 1.25 > 1
e. 0.5 + 0.2 + 0.1 + 0.05 + 0.05 = 0.9 < 1
The correct option that illustrates this is Table B.
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(7) The sum of five consecutive even integers is at least 400 . What is the minimum value of the first even integer? Choose from the following solutions:
A 80
B 70
C 76
D 82
Answer:
C 76
Step-by-step explanation:
let x = 1st number
let x+ 2 = 2nd number
let x + 4 = 3rd number
let x + 6 = 4th number
Let x + 8 = 5th number
x + x + 2 + x+ 4 + x + 6 + x + 8 = 400 Combine like terms
5x + 20 = 400 Subtract 20 from each side
5x = 380 Divide both sides by 5
x = 76
Check:
76 + 78 + 80 + 82 + 84 = 400
What is the area of the polygon below?
A. 147 square units
B. 111 square units
C. 120 square units
D. 156 square units
Answer:
A. 147
Step-by-step explanation:
Divide the polygon into rectangles.
You will have 2 rectangles:
1) 3 x 10
2) 9 x 13
Now you just need to find the area of this 2 rectangles and add them up.
(Please Help!) For each quantity decide whether circumference or area would be needed to calculate it.
A: The distance around a ferris wheel
B:The amount of paint needed to paint a bullseye
C: The amount of whipped cream needed to go around the edge of a pie
D The amount of material needed to make a drum head (the part of the drum you hit).
The quantities we need circumference for are: A and C.
The quantities we need area for are: B and D.
What is the Circumference and Area of a Circular Shape?The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.
On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².
Therefore:
For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.
For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.
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What is the sign of {-z}/{-y} when z>0 and y>0 ?
Choose 1 answer:
A Positive
(B) Negative
Zero
(A) Positive
When z and y are both positive, the expression{ [tex]\frac{-z}{-y}[/tex] }is equal to [tex]\frac{-z}{-y}[/tex]. Since both z and y are positive, -z is negative and -y is negative, so the expression [tex]\frac{-z}{-y}[/tex] is equal to the positive number [tex]\frac{z}{\\y}[/tex].
Therefore, the sign of {-z}/{-y} when z>0 and y>0 is positive.
So the correct answer is:
(A) Positive
What is sign?
In mathematics, a sign is a symbol that is used to represent the relative size or value of a number or expression. The most common signs used in mathematics are the plus (+) and minus (-) signs, which are used to represent positive and negative numbers, respectively.
For example, the number 5 is a positive number, and it is represented using the plus sign. On the other hand, the number -5 is a negative number, and it is represented using the minus sign.
In addition to the plus and minus signs, there are also other signs used in mathematics, such as the equal sign (=), which is used to indicate that two quantities are equal, and the inequality signs (>, <, ≥, ≤), which are used to indicate that one quantity is greater than or less than another.
Overall, signs play a vital role in mathematics as they help to indicate the size and value of numbers and expressions, and they are essential for performing various mathematical operations and solving mathematical problems.
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easy proportional relationship help wanted
Answer:
y = [tex]\frac{1}{8}[/tex]x
Step-by-step explanation:
You need to find the unit rate. In a proportional relationship, you can find this by taking any point on the line and putting it the form y/x
Look at point (16,2) y/x = 2/16 = 1/8
What is slope-intercept form?
O not this one
O a² +6² = = C
O Ax+By = C
O y = mx + b
Answer:
O y = mx + b
Step-by-step explanation:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
A person jogs 4 miles in 1/5 hour what’s the persons speed in miles per hour
Answer:
Below
Step-by-step explanation:
WOW! THIS is not 'jogging' :
4 miles / 1/5 hr = 20 m/hr
Cedric deposited $796.00 in a savings account that earned 2.5% simple interest annually. Determine the amount of interest Cedric's account earned after 1 year and 9 months. (4 points)
$37.81
$34.83
$348.25
$295.56
The of interest earned by Cedric's account after 1 year and 9 months is $34.83.
What is the amount of interest in Cedric's account after 1 year and 9 months?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $796Interest rate r = 2.5%Elapsed time t = 12months + 9months = 21 monthsInterest I = ?Plug the given values into the above formula and solve for interest.
I = P × r × t
I = $796 × 2.5% × 21/12
I = $796 × 0.025 × 1.75
I = $796 × 0.025 × 1.75
I = $34.83
Therefore, the interest earned in the account is $34.83.
Option B is the correct answer.
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A scuba diver is at an elevation of −18 ft. She then descends 30 ft deeper. What is the scuba diver’s new elevation?
Answer: -48
Step-by-step explanation:
-18-30 = -48
Lucas is 5 inches taller than Tamika, and the sum of their heights is 137 inches?
Answer:
Lucas 71 inches
Tamika 66 inches
Equals how many CC? Please I need help
1. 177.441177
2. 354.882354
3. 118.294118
4. 473.176472
5. 236.588236
By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is (a) greater than zero. (b) less than zero. (c) 0.93 . (d) 6.4 (e) Can't tell without seeing the data.
As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.
Regression line:
In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.
Given,
Here we need to find the correlation between the height and the arm span by using the given least square regression line.
Let us consider the following situation,
"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."
While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.
So, here y is the dependent variable and the x is the independent value.
This means that the value x is smaller comparatively y value.
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Solve the following
(d). m(x)=xcos(-x)
By solving the following trigonometric function of m(x)= x cos(-x) we get m(x) = cos(x).
What is trigonometry ?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles. The ratios used to study this relationship are called trigonometric ratios, namely, sine, cosine, tangent, cotangent, secant, cosecant.Given that;
m(x) = x cos(-x)
m(x) = x cos (x) [ we know that cos(-x) = cos(x) ]
m(x)/x = x cos(x)/x [divide both sides by x]
m = cos(x)
Therefore, m(x)=x cos(-x) ⇒cos(x)
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Three varieties of coffee Coffee A, Coffee B, and Coffee C are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $10.39 per lb, are needed as Coffee A, which sells for $14.99 per lb. Coffee B retails for $13.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.61 per lb?
Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let a pounds of coffee A needed
Let b pounds of coffee B needed
Let c pounds of coffee C needed
c= 2a.................(1)
a+ b+c= 55..........(2)
and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61
1499a + 1399 b + 1039 c = 69,355...............(3)
Subtract (2) from (3), we get
1499 a+ 1399 b + 1039 c= 69355
- 1039 a - 1039 b - 1039 c = 57145
_____________________________
460 a + 360 b = 12210
46a+ 36 b = 1221
b= 1221/ 36 - 46 a/ 36
b= 407 / 12 - 23 a / 18
Put b in Equation (2)
a + 407 / 12 - 23 a / 18 + 2a= 55
-5a / 18 + 2a + 407/ 12 = 55
31a/ 18 = 253/ 12
a= 4554 / 372
a = 2277/ 186
a= 759/ 62
a= 12.241
and, c=2a = 24.482
b= 33.91 - 15.641
b= 18.269
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which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
y<-3/2 x²+9 x+21/2
y<3/2 x²+9 x-21/2
y<-3/2 x²-9 x+21/2
y<3/2 x²-9 x-21/2
The inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) quadratic function is
y < 3/2 x² + 9 x - 21/2How to show the inequality requiredThe problem seeks the inequality that will be less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
Therefore the quadratic function should have zeros at -7 and 1
Substituting the point (2, 27/2) to the quadratic function to check the one that gives the points shows that
3/2 x² + 9 x - 21/2 at x = 2
3/2 * 2² + 9 * 2 - 21/2
= 27/2
Solving for the zeros in the quadratic function 3/2 x² + 9 x - 21/2
shows that the zero are at
x = -7 and
Therefore the inequality that meets the condition is y < 3/2 x² + 9 x - 21/2
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Find two positive numbers whose difference is 11 and whose product is 1692.
The positive numbers are 36 and 47.
What is a positive number?
Any positive number is one that is higher than zero.
A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, increasing bigger as you move to the right.
Assume that the positive numbers be x and y.
Given that the difference x and y is 11.
Therefore x - y = 11
x = y + 11 ....(i)
The product of the numbers is 1692.
xy = 1692 .....(ii)
Putting x = y - 11 in equation (ii):
(y + 11)y = 1692
y² +11y = 1692
y² +11y - 1692 = 0
y² +47y - 36y - 1692 = 0
y(y + 47) - 36(y+47) = 0
(y + 47) (y-36)=0
y = -47 and 36
Since the numbers are positive, thus y = 36.
The value of x is 36 + 11 = 47
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Use synthetic division to find the quotient and remainder when -x^4+2 x^3+12 x^2-16 is divided by x+2 by completing the parts below.
Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]
What is synthetic division?
Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.
Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]
First we find x from the divisor,
x+2=0
x=-2
Next, we arrange it in the division form with only the coefficients of the dividend terms.
[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]
[tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]
----------------------------------
[tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]
Therefore, we get the remainder as 24
And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].
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Kyle needs 164 beads for a project. The beads are sold in packs of 2, 5, or 10. What is the least number of packs Kyle needs to buy. Explain
Answer: 17 packs
Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.
If there are 20 voters and 5 candidates , how many total points would there be in a Borda count
Answer:
25
Step-by-step explanation:
Graph the polygon with the given vertices and its image after a reflection in the line y = x.
A(6, - 3), B(1, - 2), C(4, 1)
The image of the polygon after a reflection in the line y=x is having vertices at A'(-3, 6), B'(-2, 1) and C'(1, 4) as shown in the diagram attached.
What is a reflection?A reflection is a sort of transformation that creates a new shape by flipping a shape, called the preimage, across a line, called the line of reflection (called the image). You may imagine what would occur if the form were turned over the line to graph a reflection.
A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image).
You can picture what would happen if you flipped the form over the line in order to graph a reflection.
If a point A(x, y) is reflected about the line y = x,
the new point would be at A'(y, x)
Given the polygon with vertices at A(6, -3), B(1, -2) and C(4, 1).
The image of the polygon after a reflection in the line y=x has vertices at:
A'(-3, 6), B'(-2, 1) and C'(1, 4)
The image of the polygon is attached.
Therefore, according to the attached graphic, the vertices of the polygon's image after a reflection in the line y=x are located at A'(-3, 6), B'(-2, 1), and C'(1, 4).
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You are investing money at 10.5 percent annual interest, compounded continuously. It will take you ______ years to double your investment.
let's take it from the basic of one dolla!, how long will it take for $1 to become $2, namely double, at 10.5%?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ t=years \end{cases} \\\\\\ 2=1e^{0.105\cdot t} \implies \log_e(2)=\log_e(e^{0.105t})\implies \log_e(2)=0.105t \\\\\\ \ln(2)=0.105t\implies \cfrac{\ln(2)}{0.105}=t\implies 6.6\approx t\qquad \textit{about 6 years and 219 days}[/tex]
Solve each equation.
|x+5|=-3
Answer:
No solution
Step-by-step explanation:
The absolute value function outputs non-negative values.
Answer: No solutions
This is because absolute value is never negative. It represents distance, and negative distance does not make sense.
The smallest possible output of |x+5| is zero.