The error occurred in step 1
The error is not finding the absolute value of aThe correct solution which is the absolute value of a is a = 3/2 or a = -7/2The justification for solving the equation -2(t + 3) + 4 = 12 + 6t is below;
original equationDistributive propertyAddition property of equalitySubtraction property of equalityCombine like termsDivision property of equalitySolutionSimplified solutionHow to solve absolute value equation?2 |a + 1| = 5
Step 1:
2 |a + 1| = 5 or 2 |a + 1| = -5
2a + 2 = 5 or 2a + 2 = -5
combine like terms
2a = 5 - 2 or 2a = -5 - 2
2a = 3 or 2a = -7
divide both sides by 2
a = 3/2 or a = -7/2
2.
-2(t + 3) + 4 = 12 + 6t original equation
-2t - 6 + 4 = 12 + 6t Distributive property
-2t - 2 = 12 + 6t Addition property of equality
-2t - 2 - 6t = 12 + 6t - 6t Subtraction property of equality
-8t - 2 + 2 = 12 + 2 combine like terms
-8t / -8 = 14 / -8 Division property of equality
t = 14/-8 solution
t = 7/-4 simplified solution
Therefore, the equation -2(t + 3) + 4 = 12 + 6t has a simplified solution of t = 7/-4
Read more on absolute value equation:
https://brainly.com/question/5012769
#SPJ1
Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Answer: 2y – 4x = –10
Step-by-step explanation: trust.
help me using trigonometry
2. If two figures are the same shape and the same
size, then the figures are
If two figures are the same shape and the same size, then the figures are Congruent.
Those figures that are exactly the same size and shape are said to be congruent.
Additionally, if the dimensions of one of the figures match those of its mirror image, it will also be true.
Additionally, two figures are said to be congruent if they entirely overlap when one is placed over the other and the top figure cannot be seen through the bottom.
To learn more about two figures which is of same shape and size
https://brainly.in/question/14652545
Given the Trapezoid, BATS, where B (-4, 2), A (-2, 6), T (6, 6), S (8, 2). Graph and find the approximate area of BATS.
The graph of the trapezoid is shown below. The area is calculated as: D. 40 square units.
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the formula used is given below:
Area of a trapezoid = 1/2 * (a + b) * h, where,
a = length of one of the basesb = length of one baseh = height of the trapezoid.The trapezoid BATS with the following vertices, B (-4, 2), A (-2, 6), T (6, 6), S (8, 2), ahs been plotted in the graph shown in the image attached below.
1 unit = 1 box, therefore, we have the following:
a = length of AT = 8 units.
b = length of BS = 12 units
h = 4 units
Plug in the values:
Area of trapezoid BATS = 1/2 * (8 + 12) * 4
Area of trapezoid BATS = 1/2 * (20) * 4
= 10 * 4
Area of trapezoid BATS = 40 square units.
Learn more about the area of trapezoid on:
https://brainly.com/question/1463152
#SPJ1
Which polynomial is prime?
O x² +7
Ox²-25
O3x²-27
O 2x²-8
Explanation:
All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.
3 ft
5 ft
4 ft
5 ft
Find the area of this figure.
Round your answer to the
nearest hundredth. Use
3.14 to approximate ™.
A = [?] ft²
The area of the given figure is 52.26 ft².
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given question,
The radius of semicircle r = 3 ft.
Height of the triangle = 4 ft.
Lateral side of triangle = 5 ft.
And the base of triangle = 2 x 3 = 6 feet
To find the area of the given figure, individually find area of semicircle and triangle.
Area of semicircle = π x r² = 3.14 x 3 × 3 = 28.26 square feet.
Area of triangle having height 4 feet and base 6 feet.
Area of triangle = base x height = 4 x 6 = 24 square feet.
The Area of the whole figure = Area of semicircle + area of triangle
= 28.26 +24
= 52.26 ft²
The required area of figure is 52.26 ft².
To know more about Triangle on:
https://brainly.com/question/2773823
#SPJ1
7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
To learn more about the congruence of triangle from the given link. https://brainly.com/question/1675117
#SPJ1
the gas tank on scooter holds 8.4 Liters of gas. how many milliliters is this?
Answer: 8,400 milliliters of gas
Step-by-step explanation:
1 liter = 1000 milliliter
8.4 Liters x 1000
= 8,400 milliliters
The answer is 8400 millileters
21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
To learn more about linear inequality visit,
https://brainly.com/question/18881247
#SPJ1
Solve for c.
4(c + 17) = 16
C =
Please help
Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
To know more about Slope on:
https://brainly.com/question/16941905
#SPJ1
one and four seventh plus three and two fifths equals blank
a
five and thirty four thirty fifths
b
four and six twelfths
c
four and thirty four thirty fifths
d
four and eight thirty fifths
Answer:
a. four and thirty four thirty fifths
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do
not have brown hair, while 80% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest
marginal relative frequency and its interpretation?
A. 0.56; Individuals with brown eyes
B. 0.70; Individuals with brown eyes
C. 0.80; Individuals with brown hair
D. 0.83; Individuals with brown hair
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C
What is the marginal relative frequency?Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.
Read more about the marginal relative frequency
https://brainly.com/question/9553384
#SPJ1
a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
Read more about randomized controlled trial
https://brainly.com/question/14209363
#SPJ1
24.7% of the products in the local shop are specialty soaps. 76% of those soaps are made with fresh herbs. if there are 350 bars of specialty soap in the shop, approximately how many of them are not made with fresh herbs? round your answer up to nearest whole number
we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs? well, just 76% of those 350
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266[/tex]
Calculate the area of a cylinder with a diameter of 14 and a height of 20.
Answer:
The answer is 2990.8
Step-by-step explanation:
Answer:
volume = 980π = 3078.790801
Step-by-step explanation:
14 ÷ 2 = 7 = radius
π x [tex]r^{2}[/tex]= = 49π = area
area x 20 = volume
volume = 980π = 3078.790801
passes through (-2,6) with a slope of - 1/4
The equation of the line is y = x/4 + 13/2 .
What is a slope?A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1/4
And (x₁ ,y₁) = (-2,6)
then the equation of line is
y - y₁ = m (x - x₁)
y - 6 = (1/4) (x +2)
y = x/4 + 13/2
Therefore, the equation is y = x/4 + 13/2.
To learn more about the slope;
brainly.com/question/3605446
#SPJ1
The temperature cooled by 4° on the firt day of the year together on the 1t 2 day of the year the temperature heated up 7°
Answer:
If the temperature cooled by 4° on the first day of the year, and then heated up 7° on the second day, the net change in temperature would be a 3° increase. This means that the temperature increased by a total of 3° over the two days.
Step-by-step explanation:
On the first day of the year, the temperature starts at a certain degree (let's call it X).
On the same day, the temperature cools by 4°. This means that the temperature becomes X - 4°.
On the second day of the year, the temperature starts at X - 4° (the temperature from the previous day).
On the second day, the temperature heats up by 7°. This means that the temperature becomes (X - 4°) + 7° = X + 3°.
The net change in temperature over the two days is X + 3° - X = 3°.
I hope this helps to clarify the example! Let me know if you have any further questions.
Please help with this
Answer:
1. x = {-3, 3}
2. a = {-12, -2}
3. v = {-7, 10}
4. m = {-8, 8}
5. k = {-11, 1}
6. y = {-13, 19}
Step-by-step explanation:
|-2x| = 6
means that
-2x = 6 or -2x = -6
x = -3 or x = 3
|a + 7| = 5
means that
a + 7 = 5 or a + 7 = -5
a = -2 or a = -12
|8v-12| = 68
means that
8v-12 = 68 or 8v-12 = -68
8v = 80 or 8v = -56
v = 10 or v = -7
| m / -4 | + 1 = 3
| m / -4 | = 2
means that
m/-4 = 2 or m/-4 = -2
m = -8 or m = 8
3|k + 5| = 18
|k+5| = 6
means that
k + 5 = 6 or k + 5 = -6
k = 1 or k = -11
|2y - 6| / 4 = 8
|2y - 6| = 32
means that
2y - 6 = 32 or 2y - 6 = -32
y = 19 or m = -13
Kim and her friends watched the server making smoothies. The table shows the number of mango's that were used for each of the different sizes of smoothies that the friends ordered.
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Which statement is correct based on the data?
The statement that is correct based on the data is that the table shows a proportional relationship
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Express properly
So, we have
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Start by checking if the table has a constant rate
This is represented as
Constant rate = Smoothie Size/Mango Used
So, we have
Constant rate = 8/1 = 8
Constant rate = 24/3 = 8
Constant rate = 32/4 = 8
See that the constant rate is the same for all values
Hence, the table shows a proportional relationship
Read more about proportional relationship at
https://brainly.com/question/14425347
#SPJ1
solve the system by graphing y=-x+10 y=x+8
Answer:
Step-by-step explanation:
I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...
Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
More can be learned about reflection at https://brainly.com/question/26642069
#SPJ1
please help almost done with this thing. also, will mark brainliest for the best answer
The functions for this problem are classified as follows:
Land: Linear function.Car: Linear function.How to classify a function as exponential or linear?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For the land function, the rates are given as follows:
36.9/30 = 1.23.44.1/36.9 = 1.20.51.1/44.1 = 1.16.58.1/51.1 = 1.14.The differences are given as follows:
36.9 - 30 = 6.9.44.1 - 36.9 = 7.2.51.1 - 44.1 = 7.58.1 - 51.1 = 7.Neither are exactly the same, however the variations for the differences are less, meaning that it can be classified as a linear function.
For the car, the rates are given as follows:
12.1/9 = 1.344.15/12.1 = 1.24.17.9/15 = 1.19.20.9/17.9 = 1.17.The differences are given as follows:
12.1 - 9 = 3.1.15 - 12.1 = 2.9.17.9 - 15 = 2.9.20.9 - 17.9 = 3.Again less change on the differences, hence also linear.
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
read the picture plsss
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
To know more about volume:
https://brainly.com/question/15265703
#SPJ1
2) the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. the bls reported in february 2012 that the labor force participation rate in the united states was 66.9% (calculatedrisk). a marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. what are the expected value and the standard error for a labor participation rate in the company's sample?
The expected value and the standard error for a labor participation rate in the company's sample is 0.0043
In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.
The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).
A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.
We have to find the expected value and the standard error for a labor participation rate in the company's sample.
Working age people sample n = 120
The labor force participation rate in the United States was 66.9% = 0.669
The Expected value is μ = p = 0.669
The standard error:
SE = √p(1-p)/n
SE = √0.669(1-0.669)/120
SE = √0.669*0.331/120
SE = √0.2214/120
SE = √0.001845
SE = 0.043
Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.
To learn more about standard error link is here
brainly.com/question/13179711
#SPJ4