Answer:
Step-by-step explanation:
We can use algebra to solve for the unknown number. Let's call the number "x".
The equation can be written as:
9 + x * (-7) = -19
Expanding the product on the left side:
9 + -7x = -19
Subtracting 9 from both sides:
-7x = -28
Dividing both sides by -7:
x = 4
So the number x is 4.
please, help with this one
r log a + y log c
The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:
[tex]log a^b = blog a[/tex]
Using this rule, we can write the expression as:
[tex]r log a + y log c = log a^r + log c^y[/tex]
Now we can use the rule that says:
log a + log b = log ab
to combine the two logarithms:
[tex]log a^r + log c^y = log (a^r c^y)[/tex]
Therefore, the expression r log a + y log c simplifies to:
[tex]r log a + y log c = log (a^r c^y)[/tex]
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Which expressions are equivalent to the given complex number?
45 + 2i
C
(13 + 4i) + (32 - 6i)
000
(13 + 4i) + 2(7 + 2i)(2 -i)
(2 - 8i) + 2(9 + 6i)(1 - i)
4i) + (36
2i)
(2 + 8i) + (30 - 6i)
0 (9 + 4i) + 2(4 + 7i)(1 - 2i)
The equivalent expressions of 45 + 2i are (13 + 4i) + (32 - 6i) and (9 + 4i) + 2(4 + 7i)(1 - 2i)
How to determine the equivalent expressionsFrom the question, we have the following parameters that can be used in our computation:
Complex number: 45 + 2i
Next, we test the options:
(13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i
(13 + 4i) + (32 - 6i) = 45 - 2i --- true
(13 + 4i) + 2(7 + 2i)(2 -i) = (13 + 4i) + 2(14 - 7i + 4i - 2)
(13 + 4i) + 2(7 + 2i)(2 -i) = 13 + 4i + 28 - 14i + 8i - 4
(13 + 4i) + 2(7 + 2i)(2 -i) = 37 - 2i --- false
(2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i
(2 + 8i) + (30 - 6i) = 32 + 2i--- false
(9 + 4i) + 2(4 + 7i)(1 - 2i) = (9 + 4i) + 2(4 - 8i + 7i + 14)
(9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 8 - 16i + 14i + 28
(9 + 4i) + 2(4 + 7i)(1 - 2i) = 45+ 2i --- true
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What are the coordinates of (-5,6) after a dilation of 2 centered at the origin
Answer:
(-10, 12).
Step-by-step explanation:
A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).
So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).
So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).
first combine like terms in 3/4a + 8 - 1/4a - 2
1/2a+6 is the simplified form of the expression 3/4a + 8 - 1/4a - 2
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 3/4a + 8 - 1/4a - 2
Three by four times of a plus eight minus one by four times of a minus 2.
In the given expression a is a variable and plus and minus signs are the operators.
3/4a + 8 - 1/4a - 2
3/4a and - 1/4a are the like terms
Add the like terms
3/4a - 1/4a +8 - 2
2/4 a +6
1/2a+6
Hence, 1/2a+6 is the simplified form of the expression 3/4a + 8 - 1/4a - 2
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The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
The ratio of stars to red stripes is 50 to 7
How to write a ratio to represent the ratio of stars to red stripes.from the question, we have the following parameters that can be used in our computation:
Number of stars = 50
Red stripes = 7
White stripes = 6
Using the above as a guide, we have the following:
Ratio = Stars : Red stripes
substitute the known values in the above equation, so, we have the following representation
Stars : Red stripes = 50 : 7
Hence, the ratio is 50 : 7
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If your car gets 24 miles per gallon, how much does it cost to drive 450 miles when gasoline costs $2.70 per gallon?
Answer:
Cost $50.63
Step-by-step explanation:
To calculate the cost, we need to find out how many gallons of gasoline the car will consume in 450 miles. We can use the formula:
Gallons = Total miles / Miles per gallon
Gallons = 450 miles / 24 miles per gallon
Gallons = 18.75
Next, we multiply the number of gallons by the cost per gallon to get the total cost:
Total cost = Gallons * Cost per gallon
Total cost = 18.75 gallons * $2.70 per gallon
Total cost = $50.63
So, it will cost $50.63 to drive 450 miles when gasoline costs $2.70 per gallon and your car gets 24 miles per gallon.
PLease help question below
The statement that is true about the graphs is Graph A is a linear function because it has a constant rate of change
What is a graph?A graph is a pictorial representation of a function.
How to find which statemnt is true?Given the graphs A and B, to determine which statement is true, we need to find the characteristics of each graph.
Characteristics of graph AGraph A is a linear graphGraph A has a constant rate of changeGraph A has only one x interceptGraph A has only one y - interceptCharacteristics of graph BGraph B is not a linear graphGraph B does not have a constant rate of changeGraph B has multiple x interceptsGraph B has only one y - interceptComparing all the statements with the given characteristics of both graphs, we see that the statement that is true is Graph A is a linear function because it has a constant rate of change
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A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function
fix) to model the situation where x is the number of 30-minute time periods.
since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]
sandy ran for 22 minutes. Gary ran 7 minutes longer than sandy did. Herbert ran 12 minutes less than Gary. who ran the longest
Answer:
So Gary ran the longest
Step-by-step explanation:
Gary ran for 22 minutes + 7 minutes = 29 minutes.
Herbert ran for 29 minutes - 12 minutes = 17 minutes.
So Gary ran the longest, followed by Sandy and then Herbert.
How many rotational symmetries does this figure have?
The figure: F
The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.
What is rotational symmetry ?The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.
When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.
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Find the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h]
The rate of change of the function on the interval specified as in the task content is; 7.
What is the rate of change of the function on the given interval?It follows from the task content that the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h] is to be determined.
Since the function is a linear function, it follows that the rate of change is a constant and hence is given by;
f'(x) = 7.
Ultimately, the rate of change of the function on the given interval is; 7.
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Examine the triangle below, solve for t, round to the nearest whole number.
T
37
46°
A
84°
t
D
In the triangle, the nearest whole number of the side t is 28.
What is the sine rule of a triangle?The sine rule states that the ratios of the sides to their corresponding opposite angles are equal to a particular value. This value gives the circumradius of that triangle.
The sum of three angles in a triangle is 180°.
Find the angle ∠T for ∠A=46° and ∠D=84°.
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
The sine rule for triangle ABC is [tex]\[\frac{a}{{\sin A }} = \frac{{37}}{{\sin B }} = \frac{c}{{\sin C }} = 2R\][/tex], where R is the circumradius and a, b, and c are the opposite sides of the angles ∠A, ∠B, and ∠C, respectively.
On applying the sine rule to triangle ADT, the result becomes [tex]\[\frac{a}{{\sin 46^\circ }} = \frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }} = 2R\][/tex].
Take the equation [tex]\frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }}[/tex] and find t.
[tex]\[\begin{array}{l}t = \frac{{37\sin 50^\circ }}{{\sin 84^\circ }}\\ \approx 28.4997\\ \approx 28\end{array}\][/tex]
Therefore, the nearest round whole number of t is 28.
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can someone explain why 4(8x + 2) = 4(7x + 2 + x)
On solving the provided question, we cans ay that the equation is 4(8x + 2) = 4(7x + 2 + x); when we put x = , LHS = RHS
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation is
4(8x + 2) = 4(7x + 2 + x)
32x + 8 = 28x + 8 + 8x
36x - 32x = 0
4x = 0
x = 0
when we put x = , LHS = RHS
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Martina has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Answer:
Step-by-step explanation:
Martina has been given 5 bands and asked to place a vote for her favorite and second favorite bands. The number of different votes possible can be calculated using combinations.
A combination is a way of selecting items from a set, where order does not matter and repetition is not allowed. To find the number of combinations, we can use the formula:
C(n, k) = n! / (k! * (n - k)!)
where:
n is the number of items
k is the number of items being selected
! denotes factorial, which is the product of all positive integers up to that number
Step-by-step, the calculation is as follows:
Determine the number of items and the number of items being selected:
n = 5 (the number of bands)
k = 2 (the number of bands Martina is voting for)
Calculate the number of combinations using the formula:
C(n, k) = n! / (k! * (n - k)!)
C(5, 2) = 5! / (2! * (5 - 2)!)
C(5, 2) = 120 / (2 * 3!)
C(5, 2) = 120 / (2 * 6)
C(5, 2) = 120 / 12
C(5, 2) = 10
So, there are 10 different votes possible for Martina's favorite and second favorite bands from the list of 5 bands.
Hual takes out a $3200 student loan at 6.4% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and
borrows another $12,400 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and
payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.6%. Find the total
amount of interest that will accrue until payments begin.
(a) Find the total amount of interest that will accrue for loan 1 (community college).
The total amount of interest that will accrue for loan 1 (community college) is $_____ Round your answer to two decimal
places, if necessary.
Part 2 of 3
A ALEKS-Erika Ramirez - Test 2-Chapter 7
(b) Find the total amount of interest that will accrue for loan 2 (state university).
The total amount of interest that will accrue for loan 2 (state university) is $____
Answer:
a) $4096 b) $1884,8 ■■ im not 100% sure
Step-by-step explanation:
a) 3200×0.064×2=$4096 in intrest
b) 12,400×0.076×2=$1884,8 in intrest
A line passes through the origin and (4, 6). What are two other points on this line?
Two other points on this line are (1, 1.5) and (2, 3)
How to determine the two other points on this line?From the question, we have the following parameters that can be used in our computation:
A line passes through the originAnd it passes through (4, 6).This means that the slope (m) of the line is
m = 6/4
Evaluate
m = 1.5
For the other points, we have
f(2) = 2 * 1.5 = 3
f(1) = 1 * 1.5 = 1.5
So, we have (1, 1.5) and (2, 3)
Hence, the points are (1, 1.5) and (2, 3)
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Please help me with this question
Answer:
= 7022cm
Step-by-step explanation:
The Perimeter of a rectangle =
[tex] = 2(l) + 2(w)[/tex]
From the question
L= 15.47m
w= 19.64m
therefore perimeter of a rectangle
=
[tex] = 2(15.47) + 2(19.64) \\ = 30.94 + 39.28 \\ = 70.22 m[/tex]
Also since rectangle are in centimetres
than if. 1 m = 100cm
than 70.22m = ?
therefore 70.22/1 = 100cm
=7022cm
therefore the Perimeter of a rectangle = 7022
A pharmaceutical company is carrying out
a trial for a new flea prevention
medication that is designed to work for
dogs or cats. They recruit pet owners and
ask them what flea prevention they
currently use. They randomly assign half of
the dogs in the study to the new flea
prevention medication, and the other half
of the dogs in the study will receive their
current prevention. A similar process is
carried out with the cats in the study.
What type of experiment design is this?
Choose 1 answer:
A
B
A randomized block design where the
pet types (dogs and cats) are the blocks
A systematic cluster design
A matched pairs design where the new
and existing flea medications are the pair
In the experiment in which researcher randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention, this type of experiment design is a randomized block design where the pet types (dogs and cats) are the blocks.
What is randomized block design in experiment design?Randomized block design is a type of experimental design that is used to control for the effects of extraneous variables. It involves dividing the subjects or treatments into groups, or blocks, that are similar with respect to the extraneous variable.
These blocks are then randomly assigned to the treatments being tested. By controlling for the extraneous variable in this way, the randomized block design can reduce error and increase the accuracy of the results.
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Answer:
answer B (Khan)
Step-by-step explanation:
A randomized block design where the pet types (dogs and cats) are the blocks
Mrs. Imperiale's credit card has an APR of 13.2%. She does not ever pay her balance off in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 31 days long. She is planning to purchase $7,400 worth of new kitchen cabinets this billing cycle. She will use her tax refund to pay off her entire bill next month. If she purchases the kitchen cabinets on the last day of the billing cycle instead of the first day, how much would she save in finance charges? Round to the nearest ten dollars.
If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would save in finance charges Round to the nearest ten dollars is $80.
What is the amount saved?Finance charge if bought on the first day
Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 7400 × 0.011
Finance charge= $81.40
Finance charge if bought on the last day
Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 238.709677 × 0.011
Finance charge= $2.625
Finance charge = $2.63
Savings = $81.40 - $2.63
Savings = $78.77
Savings = $80 ( Approximately)
Therefore the savings is $80.
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n
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
11
18
24
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
The value of the length of hypotenuse when base length is 11cm and angle is 24°: 12.04 cm
What is trigonometry?Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.
There are 6 commonly used functions in trigonometry with their name and abbreviations-
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)
Given that,
The length of hypotenuse = x
The length of base = 11 cm
The angle = 24°
It is known that,
cosФ = base/hypotenuse
= 11/x
cos24° = 11/x
x = 11/cos24°
= 12.4
Therefore, the length of the hypotenuse is approximately 12.04cm.
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johns orchard yielded a harvest of 460 apples and 340 oranges .He managed to sell 20%of the apples and 30%of the oranges. Which fruit notched up a better sale?
Answer:
oranges
Step-by-step explanation:
20% of 460 = 92
30% of 340 = 102
Find the area of the figure pictured below.
The area of the composite figure is 41 ft square.
How to find the area of a figure?The figure is a composite figure. A composite figure is a figure that has two or more shapes.
Therefore, the area of the composite figure is the sum of the individual area of the shapes.
Therefore,
area of the figure = area of rectangle 1 + area of rectangle 2
area of rectangle 1 = lw
where
l = lengthw = widthTherefore,
area of rectangle 1 = 2 × 4 = 8 ft²
area of rectangle 2 = 11 × 3 = 33 ft²
Hence,
area of the figure = = 8 + 33
area of the figure = 41 ft²
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What is b in this? Y=-1/3+b
Or how do i graph it?
NEED ASAP
The equation of line passing through the points (-2, 4) & (4, 2) is :
y = -1/3 x + 6
The value of b = 6
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is any point on the line.
To find the slope of the line, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two given points.
Plugging in the values for the given points, we get:
m = (2 - 4) / (4 - (-2))
m = -2 / 6
m = -1/3
Next, we can use one of the given points to write the equation in point-slope form:
y - 4 = -1/3 (x - (-2))
y - 4 = -1/3 x + 2
y = -1/3 x + 6
This is the equation of the line passing through the two given points (-2, 4) and (4, 2).
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Give the domain of
s(x)=6/25-x^2
Answer: The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
In this case, the function s(x) = 6/25 - x^2 has no restrictions on the input values for x, so the domain of the function is all real numbers.
Therefore, the domain of the function s(x) = 6/25 - x^2 is:
(-∞, ∞)
This means that the function can be evaluated for any real value of x.
Step-by-step explanation:
Graph the image of square CDEF after a dilation with a scale factor of
1
2
, centered at the origin.
Answer:
Step-by-step explanation:
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin, you would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, you would plot each of the new vertices and connect them to form the image square.
The solution is given below.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin,
we would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, we would plot each of the new vertices and connect them to form the image square.
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how to solve this question
What is your monthly take-home pay if your take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance?
Round intermediate calculations and the final answer to the nearest cent; use 365 days in a year.
Your monthly take-home pay is $
The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.
We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.
Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.
In a week there are 20 hours
So, in 4 weeks, there will be 80 hours
Take - home pay before deductions = 80 * $11.66 = $932.8
Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94
This is equal to ¢ 68094.
Hence, the monthly take-home pay is ¢ 68094.
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The shape of the distribution of the number of clase friends for the males is best characterized as
The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).
What are shapes called in math?Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza
What are the basic shapes?The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.
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Find the sum of the infinite geometric series, if possible. (Round your answer to three decimal places.)
∞
Σ
n = 0 6(0.75)n
STEP 1: Determine the first term of the infinite geometric series.
a1 =
24
STEP 2: Find the common ratio of the infinite geometric series.
r =
STEP 3: Based on your results from Step 1 and Step 2, the Sum of an Infinite Geometric Series Formula may be applied to this series. What guarantees the formula will work in this case?
The common ratio has an absolute value less than 1.
The first term of the series has an absolute value less than 1.
The common ratio has an absolute value less than the first term of the series.
The common ratio is less than the first term of the series.
The common ratio is less than one.
The first term of the series has an absolute value greater than the common ratio.
The first term of the series is positive.
STEP 4: Compute the sum of the series using the Sum of an Infinite Geometric Series Formula. Round your answer to three decimal places.
Sn =
STEP 1: a1 = 6.
STEP 2: r = 0.75
STEP 3: The common ratio is less than one.
STEP 4: The sum of the Sum of the Infinite Geometric series is Sn = 24
How to find the sum of the infinite geometric series?Since we have the expression for the sum of the infinite geometric series
[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]
STEP 1:
The first term of the infinite geometric series is 6. Thus, a1 = 6.
STEP 2:
The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75
STEP 3:
The common ratio is less than one.
Because Sn = a/(1 - r) is the formula we use when the common ratio is less than 1.
STEP 4:
Sn = a/(1 - r)
Sn = 6/(1 - 0.75) = 24
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Evaluate the expression when c equals 3 and y = -7. -2c+y
Answer: That’s easy… The answer is -13
Step-by-step explanation: -2 x 3 + -7 = ?
-2 x 3 = -6
-6 + -7 = -13
