Answer:
2k + 5
Step-by-step explanation:
Since this is a subtraction problem, you need to change it to an addition problem. When you do this, you also need to change the sign of each term in the second set of parentheses.
(-4k - 1) - (-6k - 6)
(-4k - 1) + (6k + 6)
Remove the parentheses and add like terms.
-4k - 1 + 6k + 6
2k +5
Write an exponential expression equivalent to 8^3 that has a base of 2.
Answer:
2^9
Step-by-step explanation:
8 is [tex]2^3\\[/tex], so we can replace [tex]8^3[/tex] for [tex](2^3)^3[/tex]
Exponents separated by parenthesis, multiply.
So [tex](2^3)^3=2^9[/tex]
Colin has 29,820 in a saving account that earn 7% interest per year how much will he have in four years
EXPLANATION
Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:
[tex]Simple\text{ Interest = P}\cdot r\cdot t[/tex]Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,
Plugging in the numbers into the expression:
[tex]\text{Interest}=29,820\cdot0.07\cdot4[/tex]Multiplying numbers:
[tex]\text{Interest}=8,349[/tex]Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169
In conclusion, Colin will have $38,169 after 4 years
In the triangle below, ZABC is a right angle. Given that BDI AC, which statement must be true? (Hint: Look at your notes about similar right triangles). B AB AC AB AD DC DC BD BD AB BC DB BC DC AD DB DC
In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, the length of the altitude is the geometric mean of the lengths of the two segments.
According to this
[tex]\frac{AD}{DB}=\frac{DB}{DC}[/tex]Which is the fourth option.
Lana and raul are participating in a walk-a-thon at the local community college track to raise money. lana can walk around the track in 4 minutes. raul can walk around the track in 6 minutes. lana and raul started walking at the same time. question: how many minutes will it be until they complete a lap at the same time?
The minutes will it be until they complete a lap at the same time is 2.4 minutes
How to calculate the time?From the information, Lana can walk around the track in 4 minutes and Raul can walk around the track in 6 minutes.
Lana will cover a distance of 1/4 while Raul will be represented as 1/6.
This will be illustrated as:
1/4 + 1/6 = 1
3/12 + 2/12 = 1
5x/12 = 1
Cross multiply
5x = 12
x = 12/5
x = 2.4 minutes
Note that x = number of minutes
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A baker has four containers. Three of the containers contain 3/4 pounds of sugar. The fourth container has 1/3 pound of sugar. How many total pounds of sugar does the baker have?
The baker has 13/3 pounds of sugar.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
We have been given two fractions.
The three containers have 3/4 pounds of sugar and fourth one have 1/2 pounds of sugar.
To find the total sugar, we have to add both the fractions
Total pounds of sugar = Sugar in three containers + sugar in fourth container
= 3/4 + 1/3
= (9 + 4)/3
= 13/3 pounds
So, the total sugar the baker has is 13/3 pounds.
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Order of Operations
If you do not use the proper order of operations, you will not get
the correct answer.
Write which operation should be done first.
1.6 + 3 × 2
2.13 – 1 + 4 ÷ 2
3.5 × (7 – 2) + 1
4.(19 + 23) – (4 × 5)
For questions 5 through 8, evaluate the expression for x = 6 and y = 17.
5.4x + 5y
6.12x + (20 – y)
7.x ÷ 3 + y
8.4y ÷ 2 + (8x + 10)
9.Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts
for her family, how much money does she have left?
10.Carlos solved 20 – (2 × 6) + 8 ÷ 4 = 29. Is this the correct answer?
To answer this question, we need to apply the rules of "PEMDAS".
Thus:
- we first deal with the numbers in the "Parentheses" or brackets
- then we perform the "Multiplication" operation
- and then we perform the "Subtraction" operation
This is done as follows:
[tex]6\times14-(9+8)\times2[/tex]- by dealing with the numbers in the parentheses, we get:
[tex]6\times14-(17)\times2[/tex]- now, by dealing with the multiplication, we have:
[tex]84-34[/tex]- finally, we deal with the subtraction, as follows:
[tex]50[/tex]please help thank you
Solve the given linear equation.14x + 4 = 8x + 23x =
We have to solve this linear equation for x:
[tex]\begin{gathered} 14x+4=8x+23 \\ 14x-8x+4-4=8x-8x+23-4 \\ 6x+0=0x+19 \\ 6x=19 \\ x=\frac{19}{6} \\ x\approx3.16\ldots \end{gathered}[/tex]The answer is x=19/6
Help me with this question please
Answer:
65
Step-by-step explanation:
First find the area of the triangles
a*b/2 is the equation for triangles
5*6/2 is 15
multiply 15*2 because there are two triangles
15*2=30
Now find the area of the rectangle
5*7=35
Then add.
30+35=65
:)
Write the equation of the line that passes through
the given point and is parallel to the given line.
SEE EXAMPLE 1
15. (5, −4); y = ≤⁄x − 4
17. (-3, 2); y=-4
16. (2, 7); 3x - y = 5
18. (6, 4); 2x + 3y = 18
Answer:
I'll do #17 as an example of how to do the others. #15 doesn't make sense. What is "= ≤⁄x?"
Step-by-step explanation:
17. (-3, 2); y=-4
y=4 is a horizontal line, where all values of y are 4, regardless of x. A horizontal line has a slope of 0. [Y does not depend on x].
That leaves us with y =0x + b
For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0]. Since y=0 regardless of x, b must be 2.
The parallel line that goes through (-3,2) is:
y = 0*x + 2, or
y = 2
please help with the question below (please add an explanation)
In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.
First, let's calculate the volume of the upper part.
The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.
[tex]V_{upper}=7cm\times3cm\times3cm=63cm^3[/tex]Hence, the volume of the upper figure is 63 cm³.
Let's now calculate the volume of the lower figure.
The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.
[tex]V_{lower}=5cm\times4cm\times3cm=60cm^3[/tex]The volume of the lower figure is 60 cm³.
Let's add the volume of the two figures to get the volume of the entire irregular figure.
[tex]V_{irregular}=V_{upper}+V_{lower}[/tex][tex]V_{irregular}=63cm^3+60cm^3=123cm^3[/tex]Therefore, the entire volume of the given irregular figure is 123 cm³.
Sheila can wash her car in 15 minutes. It takes Bob twice as long to wash the same
car. How long does it take them to wash the car working together
Both Sheila and Bob together can wash the car in 10 minutes
Calculating work :
The formulas to find work and time is given by
Time Taken = 1 / Rate of Work
Rate of Work = 1 / Time Taken
If a work can be done in x number of days, then the work can be done in one day = 1/x
Total Work done = Number of Days × Efficiency ( of the person or machine )
Given that,
Sheila can wash her car in 15 minutes
Let us consider washing the car is 1 unit of work
Then the work can done by Sheila in 1 minute = 1/15
Bob take twice as long as Sheila to wash the same
Bob can wash the same car in 30 minutes
Then the work can done by Bob in 1 minute = 1/30
From above calculation,
The work can be done by Sheila and Bob = (1/15 + 1/30)
= (2+1) /30 = 3/30 = 1/10
So the efficiency of Both Sheila and Bob per minute = 1/10
Let Both can complete the work in x minutes
As we know Total Work done = time × Efficiency
⇒ 1 = x × 1/10
⇒ x = 1 × 10
⇒ x = 10 minutes
Therefore,
Both Sheila and Bob together can wash the car in 10 minutes
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a license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. these six characters may appear in any order, except that the two letters must appear next to each other. how many distinct license plates are possible?
33,800,000 are total distinct six characters license plates possible such that the two letters must appear next to each other. We can solve it by using combination formula ( ⁿCr ) .
Total number of digits are 10 i.e., 0,1,2,3,4,5,6,7,8,9. We have given the option to select any four digits out of 10 with repetition. So, we use combination formula
ⁿ C r = n!/(r! ×(n-r)! )
For 1ˢᵗ digit, the number ways to choose the 1ˢᵗ digit is ¹⁰C ₁= 10
For 1ˢᵗ letter, the number of ways to choose the 1ˢᵗ letter is ²⁶C ₁= 26
There are 10×10×10×10 = 10⁴ ways to choose four digits . In a similar way, the total number of letters for choice is 26 ; i.e., from A to Z. We were given the task of choosing two letters from a list of 26 , which were not necessarily distinct .
There are 26×26 = 26²ways to choose the two letters . For the letters to be next to each other, they can be the 1ˢᵗ and 2ⁿᵈ, 2ⁿᵈand 3ʳᵈ, 3ʳᵈand 4ᵗʰ, 4ᵗʰand 5ᵗʰ, 5ᵗʰ and 6ᵗʰ characters . So, there are 6-1 = 5 are choices for the positions of the letters .
Therefore, numbers of distinct license plates is 5×10⁴× 26² = 33,800,000
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help me out please will give brainleist
Answer: A z=9
Step-by-step explanation:
Answer:
z = 12
Step-by-step explanation:
To understand the equation, you must first know that m∠a = 108°. It equals that because a regular five-sided polygon has an interior angle of 108° each.
Next, you would want to group all constants to the right side of the equation. By doing so, you want to subtract 72 from both sides.
(3z + 72) - 72 = 108 - 72
3z = 36
Lastly, you want to isolate the z by dividing 36 by 3.
z = 36 ÷ 3
z = 12
PLSS HELP I DO NOT UNDERSTAND THIS PLSSS bc
Average rate of change is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate of change, in simplest form, is -1/6.
What is meant by average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
The formula for calculating the gradient of a function exists expressed as:
[tex]$m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinate points from the table (6, 53) and (24, 50).
Substitute the coordinate into the expression:
[tex]$m=\frac{50-53}{24-6} \\[/tex]
[tex]$&m=\frac{-1}{6} \\[/tex]
Therefore, the average rate of change, in simplest form is -1/6.
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Tom’s car has 11 1/9 gallons of gas. If he uses 3/8 of the gas, how much gas does the car have left?
Answer:
10.736
Step-by-step explanation:
11 1/9 - 3/8 =10/53/72
= 10.736
The flag of Colombia is a rectangle that is 66 ft. long with three horizontal stripes
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Below is a scale illustration of the Colombian flag that ranges from 1 cm to 2 ft.
How are scale illustrations created?It is already stated that all measurements would be done using a fixed scale for a given scale drawing. Let the scale, for illustration, be K feet to s inches.
1ft ; s/k in
Thus, all foot measures will be multiplied by s/k to obtain the relevant lengths in the drawing.
Since the ratio is 2:1, there are 1 centimeter for every 2 feet.
This indicates that to reach 33, we must divide 66 by 2.
66/2 = 3
As a result, the scale drawing of the Colombian flag is attached below and has a scale of 1 cm to 2 ft.
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Part A Write the multiplication expression shown by the model. Do not solve the problem.
Explain the expression written in Part B. Include the final product and how it is shown with the model.
The multiplication model represented by the image is given as follows:
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
What is a multiplication operation?A multiplication operation is equivalent to consecutive additions.
For the green squares, the following addition is obtained:
10 + 10 + 10 + 10 + 6.
(which is the number of squares painted green).
Considering a multiplication with consecutive additions, it is written as follows:
4 x 10 + 6.
For the red squares, the expression is:
4 + 4 x 10 + 2 = 4 x 10 + 6.
For the blue squares, the expression is:
8 + 3 x 10 + 8
3 x 10 + 16
For the white squares, the expression is:
2 + 6 x 10
Hence the total model is calculated as follows:
4 x 10 + 6 + 4 x 10 + 6 + 3 x 10 + 16 + 2 + 6 x 10
(4 x 10)(6 + 6) + (3 x 10) + (6 x 10) + 18.
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
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What is the slope of a line perpendicular to the line whose equation is 3x+y=8
Answer:
slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + y = 8 ( subtract 3x from both sides )
y = - 3x + 8 ← in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
If a rectangle is drawn and another rectangle is drawn so that the sides are twice asbig as the first rectangle, what happens to the area? (remember k^2 for area)A.) quadruplesB.) doublesC.) triplesD.) not enoughInformation
Let the rectangle with side as x and y.
Determine the area of the rectangle.
[tex]\begin{gathered} A=x\cdot y \\ =xy \end{gathered}[/tex]The sides of the rectangle is increased by twice means that new sides are 2x and 2y.
Determine the area of new rectangle.
[tex]\begin{gathered} A^{\prime}=2x\cdot2y \\ =4xy \\ =4A \end{gathered}[/tex]So new area is four times the previous rectangle.
Thus correct answer is option A quadruples.
at a tree farm,there are nine rows of 36 Spruce trees . in each row 14 of the spruce trees are blue spruce how many Spruce tree‘s are not blue spruce?
Answer: 198
Step-by-step explanation:
9 * 36 = 324
9 * 14 = 126
324 - 126 = 198
Hope this helps!
you want to rearrange the furniture in your room. you use a coordinate plane to plan your changes. the vertices of the dresser are given below. Give the coordinates of the dresser after rotating the dresser 180* about the origin, translating 2 units left and 3 units up.
A(-1,-1), B(2,-1), C(2,1), D(-1,1) HELP ASAP!!! I NEED IT RIGHT NOW PLEASE ANYONE!!!
The coordinates of the dresser
i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)
after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes
A(3, 2), B(0, 2), C(0,0), D(3, 0)
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The coordinates of the vertices of the dresser.
A(-1,-1), B(2,-1), C(2,1), D(-1,1).
Now,
Rotating 180 degrees the coordinates become,
A(2, 1), B(-1, 1), C(-1, -1), D(2, -1)
Translating 2 units left.
The coordinates become:
A(2-2, 1-2), B(-1-2, 1-2), C(-1-2, -1-2), D(2-2, -1-2)
A(0, -1), B(-3, -1), C(-3, -3), D(0, -3)
Translating 3 units up.
The coordinates become:
A(0+3, -1+3), B(-3+3, -1+3), C(-3+3, -3+3), D(0+3, -3+3)
A(3, 2), B(0, 2), C(0,0), D(3, 0)
Thus,
The coordinates of the dresser
i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)
after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes
A(3, 2), B(0, 2), C(0,0), D(3, 0)
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Select all ratios equivalent to 3:6
18:9. 4:8. 11:12
Answer:
4:8
Step-by-step explanation:
Equivalent ratios have the same simplified ratio.
The simplified ratio of 3:6 is 1:2. We can get it by dividing both sides of the ratio by a common factor of 3.
18:9 is incorrect because its simplified ratio is 2:1. Equivalent ratios have the same order.
4:8 is correct because dividing both sides of the ratio by 4 gives us 1:2.
11:12 is incorrect because it can not be simplified to give 1:2.
which of the following expressions does not represent 7 + 7 + 7 + 7 + 7
7 + 7 + 7 + 7 + 7 means 7 is added 5 times
It could be written as
5(7)
7 x 5 and
7 . 5
But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7
Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7
This makes the correct option to be the third option. That is 7^5
Which expression is equivalent to 6(−3.1y − 10.8)?
−18.6y − 64.8
−18.6y − 10.8
2.9y − 4.8
2.9y − 10.8
Answer:
The answer for the question is = -18.6y - 64.8
The opposite of the opposite by of 2 is to the_of zero and is written as _
Recall that the opposite of 2 is
[tex]-2.[/tex]Therefore, the opposite of the opposite of 2 is
[tex]-(-2)=2.[/tex]Now, recall that a horizontal number line is of the form:
Therefore, 2 is to the right of zero.
Answer:
On a horizontal number line, the opposite of the opposite of 2 is to the right of zero and is written as 2.
ramone scores 40 on his history test and 40 on his chemistry test. the class means for both tests is 30. the standard deviation for the history test is 10 and the standard deviation for the chemistry test is 5. on which test did he do better in relation to his peers and why?
Ramones’s Chemistry test was much better as it has higher Z-Score than history
For History test, Test score (x) = 40
Mean (μₓ) = 30, Standard deviation (σₓ) = 10
For Chemistry test, Test score (Y) = 40
Mean (μ) =30, Standard deviation (σ) =5
Ramones’s Z-score for History test is given by,
Z-Score = (x-μₓ)/σₓ =(40-30)/10 = 1
Ramones’s Z-score for chemistry test is given by,
Z-Score = (y-μ)/σ =(40-30)/5 = 2
Thus, Ramones’s Chemistry test was much better, because Chemistry test has higher z-score.
Difference in the mean score (α) =μₓ -μ =0
Difference in Z-Score= Z- Zₓ =1
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refrigerant r-410a is a mixture of refrigerants r-32 and r-125. it takes 60 pounds of r-32 and 40 pounds of r-125 to make 100 pounds of r-410a. find the ratio of r-32 to r-125. fill in the blanks with the correct answer.
The ratio of r-32 to r-125 is 3:2
A ratio in math displays how many times one number is contained in another. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). When both sides of a ratio are whole numbers and cannot be divided by a whole number, the ratio is in its simplest form.
Given,
Refrigerant r-32 and r-125 are the two main constituents of refrigerant r-410.
60 pounds of r-32 and 40 pounds of r-125 make up to 100 pounds of r-410.
The ratio of r-32 to r-125 = 60/40 =3/2.
Hence, the required ratio of r-32 to r-125 is 3:2
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9th grade math HHhH HHhH
Answer:y=-x+3
Step-by-step explanation:
variables Review find r if 2r+10=22
EXPLANATION
If the equation is 2r+10=22
Subtracting -10 to both sides:
2r = 22 - 10
Subtracting numbers:
2r = 12
Dividing both sides by 2:
r = 12/2
Simplifying:
r=6
The answer is r=6