Using PEDMAS to evaluate the given expression, the value is -23
What is the value of the expression?To substitute 1 in for x and evaluate the expression 7x - 6(3 + 2x), we replace every instance of x with 1 and simplify the expression.
Starting with the expression: 7x - 6(3 + 2x)
We substitute x with 1: 7(1) - 6(3 + 2(1))
Simplifying the inner parentheses: 7 - 6(3 + 2)
Continuing the simplification: 7 - 6(5)
Further simplification: 7 - 30
Finally, performing the subtraction: -23
Therefore, when we substitute 1 in for x, the value of the expression 7x - 6(3 + 2x) is -23.
In this evaluation, we followed the order of operations PEMDAS by simplifying the parentheses first, then performing the multiplication and subtraction to obtain the final result of -23.
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6(x + 3) = -84
Show work
Answer: -14
Step-by-step explanation:
1) Distribute
6(x+3) =-84
6*x + 6*3 =-84
6x + 18 = -84
2) Addition/Subtraction Inverse
6x + 18 =-84
-18. -18
3) Divide/Multiply Inverse
6x = -84
-84/6x = -14
Answer:
x = -17
Step-by-step explanation:
6(x + 3) = -84
6x + 18 = -84
6x = -84 - 18
6x = -102
x = -102 : 6
x = -17
------------------------------------
check6(-17 + 3) = -84
-102 + 18 = -84
-102 = -84 - 18
-102 = -102
the answer is good
Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable.
12 -7
(12 - 7) is a Numerical expression.
Numerical and Variable expressions:An expression written having a variable in it is referred to as a variable expression. A numerical expression is an expression made up of numbers and operations.
Expressions that use numbers to perform operations are an example of a numerical expressions like 2(3 + 8). If there is at least one variable and one operation must be present in an algebraic expression such as 2(x + 8y) is an example of variable expression.
Here we have the expression (12 - 7)
As we can see there are only numerical values but there are no variables in the given equation, So the given expression is a Numerical expression
Therefore,
(12 - 7) is a Numerical expression.
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Need help ASAP……………..
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
what is y=x-1 if y=x+5
Answer:
I think your question is incorrect
Is it possible to have a triangle with the following sides 3cm 5cm 7cm?
One can create a triangle with the sides 3 cm, 5 cm and 7 cm.
We can check the possibility of constructing a triangle through side-side-side. It states that the sum of any two sides of triangle should be greater than third side of the triangle. Therefore, let us say 3 cm is side a, 5 cm is side b and 7 cm is side c.
Now, checking the rule.
Side a + side b > side c
3 + 5 > 7
Add the digits on left
8 > 7
Side b + side c > side a
5 + 7 > 8
Add the digits on left
12 > 8
side c + side a > side b
8 + 5 > 7
Add the digits on left
13 > 7
The side-side-side rule of triangle is followed in all the cases, and hence triangle formation is possible.
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please hurry and help me on this!!!
Answer: Try the answer A
What was the principal for continuously compounded account earning 3.9% for 15 years that
now has a balance of $2,656,586.66?
$4,768,549.11
$1,496,548.42
$1,480,000
This problem is related to the concept of continuous compounding, which is a method of calculating the interest earned on an account over a certain period of time. The formula for calculating the principal amount for a continuously compounded account earning 3.9% for 15 years is as follows:
P = A/ (1 + r)^t
Where P is the principal, A is the balance after 15 years, r is the rate of interest and t is the number of years.
In this problem, P = $4,768,549.11, A = $2,656,586.66, r = 3.9% and t = 15.
Therefore, the principal for the continuously compounded account earning 3.9% for 15 years is $4,768,549.11
Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden’s width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Write expressions to represent the length and width of Melissa’s vegetable garden in terms of x.
Enter the correct answer in the box.
y = ____
The expressions to represent the length and width of Melissa’s vegetable garden in terms of x include the following:
y = 3x + 2.
y = x + 5
How to write the required expressions?In order to write the expressions representing the length and width of Melissa’s vegetable garden, we would assign variables to its dimensions as follows;
Let the variable x represent the length of the tomato square patch.Let the variable y represent the length of the rectangular vegetable garden.Since Melissa wants the length of her rectangular vegetable garden to exceed three (3) times the length of the tomato square patch by 2 feet, the length of the rectangular vegetable garden with respect to its length is given by:
y = 3x + 2.
For the width, an expression for the rectangular vegetable garden's width with respect to the width of the tomato square patch is given by:
y = x + 5
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The total charge on 4 particles is −36 units. All the particles have the same charge. What is the charge on each particle? (3 points) a −9 units b −8 units c 8 units d 9 units
52.8% as fraction in simplest form
Answer:
66/125
Step-by-step explanation:
%52.8 = 52.8/100
= 0.528
0.528/1 x 1000/1000
=528/1000
=66/125
Quarter 2 Assessment
The line models the temperature on a certain winter day since sunrise. What is the y-intercept of the
line? What does the y-intercept represent?
Temperature (degrees Celsius)
10-
6
4
0
Temperature Since Sunrise
2
6
4
Hours after Sunrise
00-
8
10
I
The y-intercept is
What does the y-intercept represent?
O
O
O
O
The rate the temperature increases
The temperature at sunrise
The temperature at sunset
The rate the temperature decreases
The point on a line where it crosses the y-axis is known as the y-intercept.
Graphs and charts are useful visual aids because they make information accessible and quick to understand. Therefore, it is not unexpected that print and electronic media frequently use graphs. When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
The temperature initially climbs to 5 degrees Celsius.
formula for a line
A line's y-intercept, also known as the point where the x-coordinate equals zero, is where the line intersects the y-axis.
You can see from the graph that the line intersects the y-axis at y = 5. This demonstrates that the temperature initially increases to 5 degrees Celsius.
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Complete question -
Assignment is due tonight!!!! Please help
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game.
The inequality for Erik to win is
|x- y| ≤ 10
And for Nita to win
|x- y| ≥ 10
What is Inequality ?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Inequalities define the connection between two values that are not equal. 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. The different inequality symbols, characteristics, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples.
In the problem let the number chosen by Erik and Nita be x and y respectively .
here both x,y ≤ 20
so the inequality for Erik to win is
|x- y| ≤ 10
And for Nita to win
|x- y| ≥ 10
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A student solved the following problem and made an error:
Triangles ABC and DEF. Angles A and F are congruent and measure 135 degrees. The coordinates for the vertices are at A 0, 2 and B 2, 4 and C 0, 0 and D 2, 0 and E 4, 4 and F 4, 2.
Line 1 segment AC equals 2, segment DF equals 2, segment AC is congruent to segment DF
Line 2 ∠A ≅ ∠F
Line 3 Length of segment AB.
A (0, 2)
B (2, 4)
d equals square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared, then d equals the square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment AB = 2.83
Line 4 Length of segment FD.
D (2, 0)
F (4, 2)
d equals the square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared then d equals the square root of quantity 2 minus 4 all squared plus quantity 0 minus 2 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment FD = 2.83
Line 5 segment AC is congruent to segment FD
Line 6 triangle ABC is congruent to triangle FDE by SAS
In which line did the student make the first mistake?
Triangle ABC is congruent to triangle FDE by SAS congruence. Therefore, students did mistake in line 1.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, in triangles ABC and DEF
∠A≅∠F=135°
The coordinates for the vertices are at A(0, 2), B(2, 4) and C(0, 0)
In triangle DEF, we have D(2, 0), E(4, 4) and F(4, 2)
AC= 2 units and DF= 2 units
AC≅DF
Length of segment AB.
A (0, 2) and B (2, 4)
Here, d=√[(x₂-x₁)²+(y₂-y₁)²]
= √[(2-0)²+(4-2)²]
= √8
AB = 2.83
Length of segment FD.
D (2, 0)
F (4, 2)
Here, d=√[(4-2)²+(2-0)²]
FD= = 2.83
AC≅FD
Triangle ABC is congruent to triangle FDE by SAS congruence
Hence, students did mistake in line 1.
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Is my birthday divisible by 3?
Yes, your birthday is divisible by 3.
To check if a number is divisible by 3, the sum of its digits must be divisible by 3. To determine the sum of the digits of your birthday, we can use the formula:
Birthday = abc
Sum of digits = a + b + c
For example, if your birthday is the 7th of December, 2020:
Birthday = 07122020
Sum of digits = 0 + 7 + 1 + 2 + 2 + 0 + 2 + 0 = 14
Since 14 is divisible by 3, your birthday is divisible by 3.
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Find the missing side length. Tell if the side lengths form a Pythagorean triple. Also, identify the correct explanation.
The missing side length is 17 and the side lengths 8, 15, and 17 form a Pythagorean triple.
Side lengths: 8, 15
Missing side length: 17
Yes, the side lengths form a Pythagorean triple. The side lengths 8, 15, and 17 form a Pythagorean triple because 8^2 + 15^2 = 17^2.
To answer this question, we first need to determine if the side lengths 8, 15 and the missing side length form a Pythagorean triple. To do this, we use the Pythagorean theorem which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. If this is true, then the side lengths form a Pythagorean triple.
In this case, we can plug in the side lengths 8 and 15 into the Pythagorean theorem. 8^2 + 15^2 = 17^2. Since the equation is true, this means that the side lengths 8, 15 and 17 form a Pythagorean triple. Therefore, the missing side length is 17.
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Given right triangle abcabc with altitude \overline{bd} bd drawn to hypotenuse \overline{ac} ac. If ac=16ac=16 and dc=4,dc=4, what is the length of \overline{bc}? bc ?.
The length of bc is 8. The result is obtained by using the concept of conditions for similar triangles.
How are the conditions for similar triangles?For two or more similar triangles, it has two conditions.
Corresponding angles of the triangles are equal.Corresponding sides of the triangles are in proportion to each other.A right triangle abc with altitude bd drawn to hypotenuse ac has the length of sides as follow
ac = 16dc = 4Find the length of bc!
Observe the picture of triangles in the attachment! If we drawn a perpendicular line to the hypotenuse, we'll have three similar triangles.
The corresponding sides of the two triangles are
[tex]\frac{\overline{ac}}{\overline{bc}} = \frac{\overline{bc}}{\overline{dc}} = \frac{\overline{ab}}{\overline{bd}}[/tex]
The length of bc is
[tex]({\overline{bc})^{2} = \overline{ac} \times {\overline{dc}[/tex]
[tex]({\overline{bc})^{2} = 16 \times 4[/tex]
[tex]({\overline{bc})^{2} = 64[/tex]
[tex]{\overline{bc} = \sqrt{64}[/tex]
[tex]{\overline{bc} = 8[/tex]
Hence, the length side of bc on the right triangle is 8.
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What does a residual of 2 mean?
The observed frequency of the cell is fewer than the expected frequency, according to a typical rule of thumb for interpreting the standardized residual: If the residual is less than -2. If the observed frequency is more than the expected frequency, it is greater than 2.
The meaning of a negative residual?
A negative residual indicates an excessively high anticipated value, and a positive residual indicates an excessively low expected value. A regression line's goal is to reduce the total amount of residuals.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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ASAP
If f(x)= 3x-4, which of these is the inverse of f(x)?
O A. f-¹(x)=X-4/3
B. f¹(x)=x+4/3
OC. F¹(x) = x/3+4
OD. ¹(x)=x/3-4
Answer:
Step-by-step explanation:
f(x)=−3x−4
f
(x)=−3x−4 as an equation.
y=−3x−4 Interchange the variables.
x=−3y−4 Solve for y
y=−x3−4
3 Replace y with f−1(x) to show the final answer.
f−1(x)=−x3−43 Verify if f−1(x)=−x3−43
is the inverse of (x)=−3x−4.
F−1(x)=−x3−43
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
k = 2
The coordinates of the points after dilation is P'(6,10), Q'(8,0), and R'(2,2).
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 2. The coordinates of the points after dilation is,
P(3,5) = P'(6,10)
Q(4,0) = Q'(8,0)
R(1,1) = R'(2,2)
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If mary had 456 apple, and her iter had half of mary apple, and they both give half of their apple to their mom, nhow many apple doe the girl till have?
Answer:
Mary:228
iter:114
Step-by-step explanation:
Mary's "iter" would have 228 apples (half of what mary has) and would be left with 114 after giving half to her mother.
Mary would be left with 228 apples because 456/2=228.
621 x 99 = 621 x ----- - 621 x ---------(1 Point)
a) 90 ,9
b) 100 ,1
c) 98 ,1
d) 0 ,100
621 × 99 = 621 × 100 - 621 x 1
option b is correct.
Do the segments 15 12 and 9 form a right triangle?
It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 15 and 12
15 + 12 > 9
27 > 9
Now we add 15 and 9
15 + 9 > 12
24 > 12
Now we add 12 and 9
12 + 9 > 15
21 > 15
It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.
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6. Keith's charge account uses the unpaid-balance method to compute the finance charge
at a monthly periodic rate of 1.5%. His previous balance was $200. During the month,
he charged $178.62, made a $200 payment.
a. What is Kieth's unpaid balance?
b. What is Kieth's finance charge?
c. What is Kieth's new balance?
Keith's unpaid balance is $178.62, finance charge is $2.6795 and new balance is $181.2995
Kieth's unpaid balanceTo find Keith's unpaid balance, we need to find the difference between the previous balance and the payments made during the month.
Keith's previous balance was $200.
During the month, he charged $178.62, made a $200 payment.
So, Keith's unpaid balance is:
$200 (previous balance) - $200 (payment) + $178.62 (charges) = $178.62
Finance chargeTo find Keith's finance charge, we need to multiply the unpaid balance by the monthly periodic rate (1.5% in this case).
Keith's finance charge is:
$178.62 (unpaid balance) * 0.015 (monthly periodic rate) = $2.6795
New balanceTo find Keith's new balance, we need to add the finance charge to the unpaid balance.
Keith's new balance is:
$178.62 (unpaid balance) + $2.6795 (finance charge) = $181.2995
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What are coordinates of G?
The coordinates of point G are (5, 6).
To find the coordinates of point G, we need to find the average of the x-coordinates and the average of the y-coordinates of points A and B.
To find the x-coordinate of G: (x1 + x2) / 2 = (3 + 7) / 2 = 5To find the y-coordinate of G: (y1 + y2) / 2 = (4 + 8) / 2 = 6Therefore, the coordinates of point G are (5, 6).
Key points:
To find the midpoint of a line segment, take the average of the x-coordinates and y-coordinates of the two endpoints.Midpoint coordinates = ((x1+x2)/2, (y1+y2)/2)The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment.To find the coordinates of point G, we need to find the average of the x-coordinates and the average of the y-coordinates of points A and B.Learn more about coordinates here:
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What is an exponent of 4 called?
The exponent of 4 is called as a Biquadrate or fourth power of Exponent which is written as [tex]x^{4}[/tex] and read as number x raised to power 4 .
What is Exponent ?
The Exponent is defined as a method of expressing large numbers in terms of powers. which means, that exponent refers to how many times the number multiplied by itself.
The exponents of numbers are as follows :
(i) the exponent of 2 is called "Squared" ,
(ii) the exponent of 3 is called "Cube" ;
(iii) the exponent of 4 is called "Biquadrate" .
Some Examples of "exponent of 4 " are : 2⁴ , 3⁴ .
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Draw any line egment pq take any point r on it. Through R draw a perpendicular to pq
Perpendicular drawn through point R on the given line segment PQ.
Constructed figure is attached.
Step of construction :
Constructed figure is attached.
Draw a line segment PQ of any measurement.Take a point R on the line segment PQ.Draw an arc through point R on line segment PQ such that it intersect PQ at point A and B.Now take more than half the measure of arc AB .Take A as center and draw an arc in the upper half plane of line segment PQ.Take B as center and with the same measure draw an arc in the upper half plane of line segment PQ such that it intersect the previous arc and name it C.Join RC which represent the perpendicular drawn through point R on line segment PQ.Therefore, perpendicular line drawn through point R on line segment PQ using above steps of construction.
The above question is incomplete , the complete question is :
Draw any line segment PQ take any point R on it. Through R draw a perpendicular to PQ.
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Do sides 7cm 24cm 25cm form a right angled triangle *?
Given, sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of the sides of the, we will get 49, 576, and 625. Therefore, the above equation satisfies, Pythagoras theorem. Hence, it is right angled triangle.
Which are side of a right triangle 7 24 and 25?Yes, 7, 24, 25 is a Pythagorean Triple and sides of a right triangle. Yes, 9, 40, 41 is a Pythagorean Triple and sides of a right triangle. No, 11, 56, 57 do not represent the sides of a right triangle.The triangle is therefore not acute. Thirteen plus seven equals twenty, and twenty is more than nine. The Triangle Inequality Theorem is satisfied by this set of side lengths. A triangle is formed by these lengths. No, not in the traditional sense of the word (Euclidean geometry). A "degenerate triangle" is possible, but it isn't exactly a triangle in the sense that we often think of triangle 8 + 7 = 15 the length of any two sides added together.To learn more about side of a right triangle refer to:
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i need help on question 7 please!!!
For a single serving, 1 4/5 pounds of chicken is needed.
What is the fraction?
A fraction is a way of representing a part of a whole. It consists of two parts: the numerator and the denominator. The numerator represents the number of parts being considered, and the denominator represents the number of parts in the whole.
To find out how many pounds of chicken will be needed for a single serving, we need to divide the amount of chicken needed for 4 servings by the number of servings.
The amount of chicken needed for 4 servings is 4 4/5 pounds. To convert it to a single serving we will divide it by 4.
(4 4/5) / 4 = (4 + 4/5) / 4 = 4/4 + 4/5*4/4 = 1 + 4/5 = 1 4/5 pounds
Hence, for a single serving, 1 4/5 pounds of chicken is needed.
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If the length of each side of a square is represented by 3x + 5, which expression represents the perimeter?
(1)
2)
3)
4) 9x² + 6x + 25
6x +10
12x + 20
12x² + 20
The expression that represents the perimeter is 12x+20 the correct option is C
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those of equal length n sides).
Given;
The length of each side of square= 3x+5
Perimeter of square= 4a
where, a is the length of each side
So,
perimeter= 4 x (3x+5)
= (4 x 3x) + (4 x 5)
= 12x +20
Therefore, the perimeter will be12x+20
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What is the quotient of 2.506 × 108 and 8.95 × 104
* expressed in scientific
notation?
The quotient of 2.506 × 10^8 and 8.95 × 10^4 expressed in scientific
notation is 2.8 x 10^3.
What is the quotient?
Quotient is the result of the division process. Scientific notation is a method that is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is expressed as a power of 10. For example, 1000 in scientific notation is 1 x 10³.
(2.506 x 10^8) ÷ (8.95 x 10^4)
= (2.506 / 8.95) x 10^8 - 4
0.28 x 10^4
2.8 x 10^4 - 1
= 2.8 x 10^3
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