Answers
We can rewrite the sum of logarithms as:
log(8) + log(3) = log(24)
How to write this a single logarithm?
Remember that if we have two logarithms of the same base, then we can write:
log(a) + log(b) = log(a*b)
Here the base of the logarithms is the same, then we can use that rule, we can rewrite the given sum as:
log(8) + log(3) = log(8*3) = log(24)
That is the expression rewritten as a single logarithm.
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Related Questions
This is my last one please help
Answers
Answer:
d
Step-by-step explanation:
Simon has $315 to buy gifts for 5 people. Each gift costs $m, with a $4 packing fee per gift and a $10 shipping fee per order. The inequality 5(m+4) +10 $315. O No, because the total cost is $335, and $335 > $315. O Yes, because the total cost is $285, and $285 < $315. O Yes, because the total cost is $305, and $305 ≤ $315.
Answers
The true statement of the inequality is (d) Yes, because the total cost is $305, and $305 ≤ $315.
How to determine the true statement of the inequalityFrom the question, we have the following parameters that can be used in our computation:
Simon has $315 to buy gifts for 5 people. Each gift costs $m, with a $4 packing fee per gift $10 shipping fee per order. The inequality 5(m+4) +10 <= $315The cost of each gift is $55
So, we have
5(55+4) +10 <= $315
When expanded, we have
305 <= $315
The above inequality is true
Hence, the solution is (d)
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When rounding to the nearest 10, which of the numbers below will round to 90? Select all that apply.
Answers
Therefore , the solution of the given problem of rational numbers comes out to be 92 and 95 are the numbers that, when rounded to the closest 10, will equal 90.
What exactly is rational numbers?Any number that can be expressed as a ratio (not a portion) of two integers is considered rational. A reasonable fraction is one that has a nonzero denominator. 1/2, 1/5, but also 3/4 are a few examples of rational integers. "0" may additionally be expressed in a variety of forms as an actual function, like 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. It makes logical that there are seven. When two parameters are divided, a rational number results.
Here,
We glance at the digit in the ones spot to round a number up to the nearest 10. In that case, we round down to the prior multiple of 10 if the digit is 0, 1, 2, 3, or 4. We round up to the following multiple of 10 if that number is 5, 6, 7, 8, or 9.
Finding numbers with a ones place digit between 5 and 9 will enable us to round to the closest 10 and arrive at 90. The figures that would round to 90 are as follows:
=>92
=> 95
As a result, 92 and 95 are the numbers that, when rounded to the closest 10, will equal 90.
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Solve : select all answer that apply
|x/5| = 1
x=3
x= -1
x=-6
x= 5
x=-5
Answers
The correct solution for the given absolute function |x/5| = 1 is: x = 5 and x = -5.
Explain about the absolute function?The variable inside this absolute value bars makes up an essential algebraic function known as the absolute value function.
This same absolute value function is likewise referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number. Such operations are frequently used to determine the separation between two points. Beyond a certain point, all of these functions change (becoming rising or decreasing).The given function is-
|x/5| = 1
Solving the bars will give:
x/5 = 1 and x/5 = -1
So,
x = 5 and x = -5 are the solution of the absolute function.
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What would the hypotenuse have to be if the legs of a right triangle are 9 and 5?
Answers
Answer:
10.3
Step-by-step explanation:
Let's say
a leg = 9
b leg = 5
The formula to find the hypotenuse is [tex]\sqrt{a^{2}+b^{2} } = \sqrt{9^{2} +5^{2} } = \sqrt{81+25} = \sqrt{106} = 10.246\\[/tex]
Round [tex]10.246[/tex] to get [tex]10.3[/tex]
Solve by Completing the Square
Matalea created a rectangle where the length was eight more than the width. She then determined that the area of a rectangle could be found by using the function A(x)= x2+8x where x is the width of the rectangle. If the area of the rectangle is 33 in^2, what is the width of the rectangle?
Answers
The width of the rectangle is calculated as: 11 inches
How to use completing the square?The formula for area of a rectangle is:
A = l*w.
Since the area is 33 in², then;
33 = x(x + 8) would be the equation to solve for x.
Now, you need to put the equation in standard form.
x² + 8x - 33 = 0.
To complete the square you need to add 33 to both sides.
Now you have x² + 8x = 33
Take the coefficient for the x term (8) and divide by 2. Now square it. That would be 4², so 16.
Now you have x² + 8x + 16 = 49
(x + 4)² = 49
Take the square root of both sides and you have;
x + 4 = 7.
Therefore, x = 3 (the short side) and 11 is the long side.
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Are rhombuses also rectangle?? Explain
Answers
Answer:
No, rhombuses are not necessarily rectangles. While both shapes are quadrilaterals with opposite sides parallel, there is an additional requirement for a rectangle that is not present in a rhombus. Specifically, a rectangle must have all interior angles measuring 90 degrees, while a rhombus can have any angle between 0 and 180 degrees.
On the other hand, all rectangles are parallelograms, while not all parallelograms are rectangles. Similarly, all squares are both rhombuses and rectangles, but not all rhombuses or rectangles are squares. In summary, a rhombus is a quadrilateral with four equal sides, while a rectangle is a quadrilateral with four right angles. While there is some overlap between the definitions, they are not equivalent.
Answer:
Rhombuses are not rectangles
Step-by-step explanation:
This is because rhombuses do not have 4 right angles.
A square would be a rectangle because its a quadrilateral with 4 right angles
while a rectangle wouldn't be a square because it doesn't have 4 equal sides
A rhombus is a quadrilateral that has 4 equal sides but doesn't have 4 right angles, making it not a rectangle
Find the equation of the line with slope 4/5 and y-intercept (0,−4).
Answers
Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).
what is slope ?Slope is a mathematical term that describes how steep a path is. It gives an explanation of the rate of rise or decline of the line as it moves horizontally along the x-axis. The percentage of the difference in the y-coordinate to the change in the x-coordinate at all between the two locations on a line is known as the slope of the line. In other terms, it is the line's "rise" over its "run". The letter "m" stands for slope, and the following formula is used to determine it:
m = (y2 - y1)/(x2 - x1) (x2 - x1)
given
In slope-intercept form, a line's equation is written as y = mx + b, where m is the slope and b is the y-intercept.
Given that the y-intercept is (0, -4) and the slope is 4/5, we can enter these numbers into the slope-intercept form to obtain:
y = (4/5)x - 4
Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).
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measure the diameter of the tin which is 750 gram
Answers
The approximate diameter of the tin would be 12.9 centimeters.
What is diameter?Diameter is a straight line passing through the center of a circle, or any other curved shape, and connecting two points on the circumference. It is the longest line that can be drawn within a circle and its length is twice the radius. It is also used in measuring the size of objects and distances in the universe. The term is also used in geometry to refer to the size or width of a triangle, square, or other shapes.
To measure the diameter of a tin which is 750 gram, one needs to use a ruler or measuring tape. First, one needs to weigh the tin using a scale or balance. Once the weight is known, it can be used to calculate the approximate diameter of the tin.
To find the diameter, one needs to use the formula: Diameter = 2 x (cube root of volume). The volume of the tin can be calculated by multiplying the weight of the tin (in grams) by 0.52.
Therefore, for a tin weighing 750 grams, the approximate volume would be 390 cubic centimeters. To find the diameter, one needs to take the cube root of 390, which is 6.47.
Therefore, the approximate diameter of the tin would be 12.9 centimeters.
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Pls help me find the surface are and volume
Answers
Let me solve it down for you :)
Surface area:The shape is a cuboid, so its dimensions will be:
Length (L) = 12mBreadth (B) = 5m Height (H) = 10m[tex] \sf \: Surface \: area \: of \: cuboid = 2(lb + bh + hl)[/tex]
[tex] \sf \: S.A. = 2(12 \times 5 + 5 \times 10 + 12 \times 10)[/tex]
[tex] \sf \: S.A. = 2(60+ 50 + 120)[/tex]
[tex] \sf \: S.A. = 2(230)[/tex]
[tex] \sf \: S.A. = 460 \: {m}^{2} [/tex]
Volume:Dimensions of the cuboid:
Length (L) = 12mBreadth (B) = 5m Height (H) = 10m[tex] \sf \: Volume = l \times b \times h[/tex]
[tex] \sf \: Volume = 12\times 5 \times 10[/tex]
[tex] \sf \: Volume = 600 \: {m}^{3} [/tex]
Convert m to cm, according to the question:
600 Cubic meter =
600,000,000 Cubic Centimeters
4.A pizza was cut into equal slices. Ben ate 4 of the slices. The amount Ben ate was of the whole pizza.
Which equation represents a way to find the total number of slices that were in the whole pizza?
A. 3.x=4
B. 4.x=
C. 3+x=4
D. x= 4.3
Answers
Based on the information, we can infer that the expression that tells us how many slices the entire pizza had is x = 4 * 3 (option D).
How to find the correct expression?To find the correct expression we must take into account the information that the statement gives us:
Ben ate 4 slices.Ben ate 1/3 of the pizza.Based on the above, if Ben ate 1/3 of the pizza, we must multiply 4 * 3 to find the total number of slices on the pizza.
x = 4 * 3x = 12So the pizza had 12 slices. To check this result we can divide it by 3 to find out if 1/3 of 12 is equal to 4.
12 / 3 = 4Note: This question is incomplete. Here is the complete information:
4. A pizza was cut into equal slices. Ben ate 4 of the slices. The amount Ben ate was 1/3 of the whole pizza. Which equation represents a way to find the total number of slices that were in the whole pizza?
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Here is summary information on the alcohol percentage
for a sample of 25 beers:
lower fourth ¼4:35 median ¼5 upper fourth ¼5:95
The bottom three are 3.20 (Heineken Premium
Light), 3.50 (Amstel light), 4.03 (Shiner Light)
and the top three are 7.50 (Terrapin All-American
Imperial Pilsner), 9.10 (Great Divide Hercules
Double IPA), 11.60 (Rogue Imperial Stout).
a. Are there any outliers in the sample? Any
extreme outliers?
b. Construct a boxplot that shows outliers, and
comment on any interesting features.
Answers
a. Rogue Imperial Stout (11.6) is an extreme outlier.
b. This suggests that there may be more beers with lower alcohol percentages in the sample than higher percentages.
How does math define a percentage?When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.
According to the given information:To determine if there are any outliers in the sample, we need to calculate the interquartile range (IQR), which is the difference between the upper quartile (Q3) and lower quartile (Q1).
IQR = Q3 - Q1
= 5.95 - 4.35
= 1.6
We then use the following rule to identify outliers:
Mild outliers: values that are less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR).
Extreme outliers: values that are less than Q1 - 3(IQR) or greater than Q3 + 3(IQR).
Using this rule, we have:
Mild outliers: None.
Extreme outliers: Rogue Imperial Stout (11.6) is an extreme outlier.
b. The boxplot below shows the distribution of alcohol percentage for the sample of 25 beers. The box represents the interquartile range (IQR), with the lower and upper whiskers extending to the smallest and largest values within 1.5 times the IQR from the lower and upper quartiles, respectively. Any values beyond the whiskers are considered outliers.
Another interesting feature of the boxplot is that the distribution appears slightly skewed to the right, with the median (5) closer to the lower quartile (4.35) than the upper quartile (5.95). This suggests that there may be more beers with lower alcohol percentages in the sample than higher percentages.
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As x
approaches
As x approaches
As x approaches
-co, y approaches -co. As x approaches ∞o, y approaches co
co, y approaches 0. As x approaches -00, y approaches ∞
0, y approaches -co. As x approaches co, y approaches co
Answers
No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.
YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.
No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.
Explain about the domain and range of function?The range of values that we are permitted to enter into our function is known as that of the domain of function. The x values for a formula like make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.A function's domain and range are its constituent parts. The range of a function has been the set of all potential outputs, whereas the domain of a function has been the collection of each of the inputs.Thus, correct options are-
No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.
YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.
No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.
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Translation: 4 left and 2 down
Answers
Answer: (2,0) = (-2,-2) (2,2) = (-2,0) (1,0) = (-3,-2) (0,2) = (-4,0)
Step-by-step explanation:
How is solving a word problem similar to specific tasks you do at school, at home, or at a job? What types of addition problems might be necessary in the next job you expect to have? How can knowing how to problem solve in this way be helpful in the real world? Use the Text Editor to write at least 200 words answering these questions.
Answers
Answer:
Solving a word problem is similar to specific tasks we do in various areas of our lives, such as school, home, or job, in that it requires critical thinking, attention to detail, and logical reasoning. In school, we solve math problems to understand different concepts, and in our job, we solve various problems related to our work to improve efficiency and productivity. Similarly, in our personal lives, we encounter problems and challenges that require problem-solving skills.
Addition problems are crucial in almost every job. For example, in accounting, addition is necessary when calculating profit and loss or taxes. In the retail sector, addition is necessary when calculating inventory or the total amount of sales. Even in fields such as medicine, addition is necessary when calculating dosages and other related calculations.
Knowing how to problem solve in this way can be incredibly helpful in the real world. Being able to identify the problem, analyze it, and find a suitable solution can make us more effective and efficient in our personal and professional lives. The ability to solve problems can also help us develop critical thinking skills, which can be useful in various situations.
In conclusion, solving word problems is an essential skill that can be applied to various areas of our lives. Being proficient in addition problems is essential for success in most jobs. Developing problem-solving skills can make us more effective and efficient in our personal and professional lives, and critical thinking skills can help us analyze problems and identify the best solutions.
Solve the following 2x+18=42
Answers
Answer:
the solution to the equation 2x + 18 = 42 is x = 12.
Step-by-step explanation:
To solve for x in the equation 2x + 18 = 42, you can follow these steps:
Subtract 18 from both sides of the equation:
2x + 18 - 18 = 42 - 18
2x = 24
Divide both sides of the equation by 2:
2x/2 = 24/2
x = 12
Therefore, the solution to the equation 2x + 18 = 42 is x = 12.
Answer:
[tex] \sf \: x = 12[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 2x + 18 = 42
Then the value of x will be,
→ 2x + 18 = 42
→ 2x = 42 - 18
→ 2x = 24
→ x = 24 ÷ 2
→ [ x = 12 ]
Hence, the value of x is 12.
if 20% of 200 people know how to ski, how many people know how to ski
Answers
Answer:
200 x 20% = 200 x 20/100 = 40.
Answer is 40.
14. Kellen is taking a 17-question test that is worth 100 points. There are two types of questions,
multiple-choice questions and free response questions. If the multiple choice questions are worth
5 points each and the free response questions are worth 10 points each, write a system of equations
that can be used to determine the number of multiple choice questions, m, and the number of free
response questions, f? Find the total number of free response and multiple-choice questions.
Answers
Answer:
ehhhhhhhhhhh
Step-by-step explanation:
Which of the following rational functions is graphed below?
Answers
Answer: B
Step-by-step explanation: Expressions that include x within the denominator can be solved to find values that cannot be expressed within the domain of the graph. Because there are clear vertical asymptotes at x=1 and x=5, the graph is formed around these areas. The main difference between B and C is that in order for the answer to be C, the graph must pass through y=1, and the graph displayed does not represent that.
A social worker at a large high school wants to estimate the number of days students are absent. He randomly
selects 45 students and records the number of days each one is absent. The social worker constructs a 95%
confidence interval for the true mean number of days students at this school are absent. Which of the following
would decrease the margin of error?
O using a sample of size 30
O using a sample of size 40
constructing a 90% confidence interval
O constructing a 99% confidence interval
Answers
Answer:
The answer is C.)
Step-by-step explanation:
Suppose that prices increase 2.5% each year for 10 years. How much will a jacket that costs $100 today cost in 10 years? Hint: Think of the cost as the balance in a savings account with an APY of 2.5% and an initial investment of $100. (Enter your answer to the nearest dollar and do not include a dollar sign or decimal points in your answer.)
Answers
Answer:
Step-by-step explanation:
If the price of the jacket increases 2.5% each year for 10 years, we can think of the price increase as the interest earned on an initial investment of $100 with an annual percentage yield (APY) of 2.5%. We can use the formula for compound interest to calculate the future value of the investment after 10 years:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (as a decimal), and n is the number of compounding periods (years).
In this case, PV = $100, r = 0.025 (2.5% expressed as a decimal), and n = 10. Plugging these values into the formula, we get:
FV = $100 x (1 + 0.025)^10
FV ≈ $128
Therefore, the jacket that costs $100 today will cost approximately $128 in 10 years if the price increases 2.5% each year.
A rectangular field is 100 meters wide and 150 meters long.
Give the length and width of another rectangular field that has the same perimeter but a smaller area.
Answers
Answer:
perimeter of first ️
2(100+150) = 500 m
A projectile is thrown into the air. The equation y=-3x² - 12x + 96 represents the path of the projectile, where x represents the amount of time in seconds. How long is the projectile in the air, in seconds?
Answers
As this is when it hits the ground, the projectile is in the air for 6 seconds.
Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.
What is a projectile?Objects that are thrown, shot, or launched with a certain initial velocity and then move against the forces of gravity and air resistance are known as projectiles. Projectiles can be anything from arrows and bullets to rocks and water balloons. Typically, a bow, slingshot, gun, or cannon is used to fire them. When projectiles are launched, gravity, air resistance, and other forces influence their trajectories.
from the question:
We must discover the moment the missile strikes the ground in order to calculate how long it was in the air. The height of the missile above the earth would be zero at that point.
Thus we must resolve the following equation:
y = -3x² - 12x + 96 = 0
We can use the quadratic formula to solve this equation in the quadratic form:
x = (-b ± √(b² - 4ac)) / 2a
where a = -3, b = -12, and c = 96.
Plugging in these values, we get:
x = (-(-12) ± √((-12)² - 4(-3)(96))) / 2(-3)
x = (12 ± √(144 + 1152)) / (-6)
x = (12 ± √1296) / (-6)
x = (12 ± 36) / (-6)
So, the solutions are:
x = -2 or x = 6
Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.
As a result, the missile is in the air for 6 seconds before it strikes the earth.
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Please help! 14 points, one right answer.
Answers
Answer:
C. [tex]\frac{n+4}{2}[/tex]
Step-by-step explanation:
"the sum of a number (n) and 4" --> n + 4
"divided by 2" --> this means the whole expression will be divided by 2
Therefore, the final answer is the third option!
Hope this helps!! :)
What’s 4/9 /8? I’m having trouble with this problem because I wasn’t paying attention in class lol
Answers
Answer:
To divide by a fraction, we can multiply by its reciprocal.
So,
4/9 /8 = 4/9 x 1/8 = 4/72 = 1/18
Adam needs to build a shed and he can only use triangular frames that form a right triangle for the corner walls. Which of the following dimensions for a triangular frame should Adam use?
25 in., 60 in., 65 in.
40 in., 44 in., 58 in.
50 in., 110 in., 130 in.
130 in., 50 in., 60 in.
Answers
The only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.
What is a valid triangle?
A valid triangle is a three-sided polygon that satisfies the following conditions:
The sum of the lengths of any two sides of the triangle is greater than the length of the third side.
The lengths of all three sides of the triangle are greater than zero.
Adam should use the dimensions 40 in., 44 in., 58 in. for a triangular frame to form a right triangle.
To determine if a right triangle can be formed, we need to check if the Pythagorean theorem is satisfied, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse).
Let's check each set of dimensions:
For 25 in., 60 in., 65 in.:
25^2 + 60^2 = 625 + 3600 = 4225
65^2 = 4225
The Pythagorean theorem is satisfied, so a right triangle can be formed. However, this triangle is not a valid option for Adam because the lengths are too short for building walls.
For 40 in., 44 in., 58 in.:
40^2 + 44^2 = 1600 + 1936 = 3536
58^2 = 3364
The Pythagorean theorem is not satisfied, so a right triangle cannot be formed using these dimensions.
For 50 in., 110 in., 130 in.:
50^2 + 110^2 = 2500 + 12100 = 14600
130^2 = 16900
The Pythagorean theorem is satisfied, so a right triangle can be formed.
For 130 in., 50 in., 60 in.:
50^2 + 60^2 = 2500 + 3600 = 6100
130^2 = 16900
The Pythagorean theorem is satisfied, so a right triangle can be formed.
Out of the options given, only the dimensions 50 in., 110 in., 130 in. and 130 in., 50 in., 60 in. satisfy the Pythagorean theorem, but both are too large for building walls.
Therefore, the only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.
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Help Plsss! I’ll give brainliest
Answers
How do I solve 1/6 + 3/4 - 2/3
Answers
[tex]\cfrac{1}{6}+\cfrac{3}{4}-\cfrac{2}{3}\implies \cfrac{(2)1~~ + ~~(3)3~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{2+9-8}{12}\implies \cfrac{3}{12}\implies \cfrac{1}{4}[/tex]
4.A pizza was cut into equal slices. Ben ate 4 of the slices. The amount Ben ate was 2/3 of the whole pizza.
Which equation represents a way to find the total number of slices that were in the whole pizza?
A. 2/3.x=4
B. 4.x=2/3
C. 2/3+x=4
D. x= 4.2/3
Answers
The equation that represent the whole slices is as follows:
2 / 3 x = 4 .
Therefore, the answer is A.
How to find the equation to represent an expression?A pizza was cut into equal slices. Ben ate 4 of the slices. The amount Ben ate was 2/3 of the whole pizza.
Therefore, the equation that represent a way to find the total number of slices that were in the whole pizza can be calculated as follows:
Let
x = amount of the whole pizza
Therefore,
2 / 3 x = 4
cross multiply
2x = 4(3)
2x = 12
x = 12 /2
x = 6
Therefore, the whole slice is 6.
Hence, the equation is 2 / 3 x = 4
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What is the sum of 9 16 9 16 and 5 16 5 16 ? A. 14 32 14 32 B. 10 16 10 16 C. 12 16 12 16 D. 14 16
Answers
Answer:
A
Step-by-step explanation:
Arrange the 4 set of numbers above each other and add the corresponding numbers.
9 and 5, 16 and 16, 9 and 5, 16 and 16
Answer:
the sum of 9 16 9 15 and 5 16 5 16 is 14 32 14 32 which is (A)
Step-by-step explanation:
9 16 9 16+
5 16 5 16
14 32 14 32