Answer:
The product is the difference of squares is [tex]$$\left(m-7\right)\left(m+7\right)={{m}^2}-49$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (m-7)(m+7).We have to multiply the given expression.Square the first term m. Square the last term 7 .[tex]$$\begin{aligned}&(m-7)(m+7)=(m)^{2}-(7)^{2} \\&(m-7)(m+7)=m^{2}-49\end{aligned}$$[/tex]
Beth wanted to buy vegetables. She noticed that brand A of black beans was on sale for 4 cans for 87 cents. Brand B was 3 cans for 79 cents. Which was a better buy?
Answer:
Brand A
Step-by-step explanation:
If you divide both brands to find how much one can costs, brand B costs more per can.
79 ÷ 3 = 26.34
87 ÷ 4 = 21.75
That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.
The function f(x) is given by the set of ordered pairs.
The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6
What is the equation about?Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6) can have input functions of (as domain) 2,3,4 and output functions of (as range) of 4,5,6.
So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
See full question below
The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
The answer choices are :
f (-10) = 1 values x = -10, f (x) = y = 1, ordered pairs (-10,1)
f (2) = - 10 values x = 2, f (x) = y = -10, ordered pairs (2, -10)
f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
f (1) = - 10 values x = 1, f (x) = y = -10, ordered pairs (1, -10)
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Use the figure to decide the type of angle pair that describes ∠5 and ∠6.
Reason:
These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).
What are the coordinates of the endpoints of the segment T'V'?It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.
On this note, given that the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).
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What is 12.1975 rounded to the nearest thousandth?
Answer:
12.198
hope it helps
12.198
To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.
A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer
As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.
Note that 2,3,5 and 7 are the smallest primes, then use the reasoning from
(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.
But no such integers k, l, m, and n exist such that (k + 1)(l + 1)(m + 1) (n + 1) = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors
Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents, that, when 1 is added to each and all are multiplied together, would equal 20. Put another way, we are looking for k, l and m ≥ 1 such that (k + 1)(l + 1)(m + 1) = 20
Note that the only possibility here is when we have 2 *2 *5 = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) = 2^4 * 3 * 5 = 240
Now......the only remaining possibility is that this number is composed of the two smallest primes, 2 and 3, and we are looking for some k and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities are when k = 4 and l = 5, or vice-versa
So this number would factor as either 2^3 * 3^4 = 648 or 2^4 * 3^3 = 432 and both are > 240.
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Write an equation of the line that passes through a pair of points: on a coordinate plane, a line goes through (0, 2) and (2, 0). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 please select the best answer from the choices provided a b c d
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
Equation of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the coordinate points (0, 2) and (2, 0)
Slope = 0-2/2-0
Slope = -1
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
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Answer:
c
Step-by-step explanation:
Myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. The vapor trails from two other jets flying from another direction crossed over the parallel trails. She printed her picture and labeled the angles and lines.
Parallel lines c and d are cut by transversals a and b. All angles are described clockwise, from uppercase left. The intersection of lines c and b form angles: 2, 4, 3, 1. The intersection of lines d and b form angles: 6, 8, 7, 5. The intersection of lines c and a form angles: 10, 12, 11, 9. The intersection of lines a and d form angles: 14, 16, 15, 13.
Assume lines c and d are parallel and Angle2 measures 98°. Which statements are true? Select three options.
mAngle3 = mAngle6 = 98°
mAngle3 = mAngle14 = 98°
mAngle4 = mAngle8 = 82°
mAngle4 = mAngle12 = 82°
mAngle5 = mAngle8 = 82°
Options 1, 3 and 5. The true statements based on the fact that c and d are parallel are:
m<3 = m<6 = 98 degrees m<4 = m<8 = 82degreesm<5 = m<8 = 82 degrees How to solve for the anglesThe sum of the angles m<4 + m<3 = 180
m<4 + 82 = 180
m<4 = 180 - 82= 98
From the question we have the first as alternate interior angles. The second is corresponding angles and the last option is vertical angles.
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Suppose a and b are real numbers such that 17^a=16 and 17^b=4. What is 1/(2^a-b) ?
Since
[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]
it follows that
[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]
Then
[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]
so that
[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]
We also have
[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]
so we can go on to say
[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]
Which statement about the following graph is correct?
O
The graph is symmetric about the line x = -1.
The graph is symmetric about the line y = -1.
The graph is not symmetric.
The graph is symmetric about the line x-1.
Answer:
the graph is symmetric about the line y=-1
Step-by-step explanation:
A function is symmetric about y=a when the following is true for all points: f(a-x) = f(a+x). By just looking at the graph, it appears to be symmetric about y=-1, and it can be further proven, by finding the difference of two points, that have the same y-value. So for example if you look at (0, 1) and (-2, 1). The difference between 0 and -1 is 1, and the difference between -2 and -1, is also 1. And this appears to be true for all the other values as well. So the graph is symmetric about the line y=-1
Answer:
The graph is symmetric about the line x=-1
Step-by-step explanation:
How to find the size of an exterior angle of a regular polygon
Answer:
exterior angle of a polygon = 360° ÷ number of sidesStep-by-step explanation:
exterior angle of a polygon = 360° ÷ number of sides
7n-(4n-3) combining like terms with negative coefficient and distribution
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation/Question:}[/tex]
[tex]\mathbf{7n - (4n - 3)}[/tex]
[tex]\huge\textbf{Convert equation/question to:}[/tex]
[tex]\mathbf{= 7n - 1(4n - 3)}[/tex]
[tex]\huge\textbf{Solving the equation/question:}[/tex]
[tex]\mathbf{= 7n - 1(4n) - 1(-3)}[/tex]
[tex]\mathbf{= 7n - 4n + 3}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{= (7n - 4n) + 3}[/tex]
[tex]\mathbf{= 7n - 4n + 3}[/tex]
[tex]\mathbf{= 3n + 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{3n + 3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Terrell brought 42 muffins to school for his birthday He gave one each to the 17students in his class and to the 19 student in the other third grade class
Answer:
The expression is 42-17-19 OR 42-(17+19).
Step-by-step explanation:
First, we can indicate that we can use subtraction because is giving them away for his birthday.
"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".
That represents taking away 17 and 19 means that it is subtracting them.
Hope this helps. (:
A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching
The probability that the colour changes, while she is watching, is 1/7
Concept: Event probability = number of favorite results /Total number of results
It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3 seconds, and then red for 30 seconds.
This means that the traffic light passes through 63 seconds to complete one-time cycle.
It is also given that Leah chooses a random 3 second time interval to watch the light.
We should find the probability that the color changes while Leah is looking.
The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.
Now let time t=0
The light changes at three different times: t=30,t = 33 and t = 63
This means that the light will change if Leah watches at intervals [27,30]
, [30,33] or [60,63]
Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.
That makes a total of 9 seconds out of 63
⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds
=9/63=17
∴ The probability that Leah observes the color change is 1/7
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3. Donnell is doing market research for a major brand by surveying customers at a local mall.
The probability of a customer agreeing to take the survey is 22%. What is the probability that
one of the first five customers agrees to take the survey?
29%
54%
071%
74%
71% is the required probability here.
What is a probability simple definition?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as
x ` Bin (n = 5 , p = 0.22 )
Thus the probability here is computed as
P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵
= 0.71 %
Therefore 71% is the required probability here.
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Sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved?
The equation which he have solved is [tex]10/x^{2} -1=15/3x-3[/tex] as in this 1 is the extraneous solution.
Given four equations in which first equation is [tex]10/x^{2} -1=15/3x-3[/tex],second is (x+2)/(x+3)=6x/8, third is (4x-4)/(x+6)=x-1/10, fourth is 4/x-1=x+2/10.
We have to find such a equation which have a valid solution and one extraneous solution.
We have to solve these equation:
[tex]10/x^{2} -1=15/3x-3[/tex]
The above exprssion is not defined for x=1 so 1 is an extraneous solution. Simplifying the above equation by doing cross multiplication.
10(3x-3)=15([tex]x^{2} -1[/tex])
30(x-1)=15(x-1)(x+1) [We know that [tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]
2=x+1
x=1
In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.
Hence the correct equation which Sean solves is option A which is [tex]10/x^{2} -1=15/3x-3[/tex].
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The given question is incomplete as it should include the given figure.
Answer:see photo #15
Step-by-step explanation:
The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (0, 8) as its solution? (1 point) Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D
The pair of equations that has (0, 8) as its solution is: A. equation A and equation C.
What is the Solution to a System of equations?The solution to a system of linear equations that are graphed is the pair of x and y coordinates of the points where two lines intersect.
In the graph given, the lines representing equations A and C intersect at point (0, 8). Therefore, the pair of equation that has a solution of (0, 8) is: A. equation A and equation C.
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Lines DE and AB intersect at point C.
D
A
C
B
(2x+2) E
(5x + 3)*
E
What is the value of x?
O12
25
38
52
Answer:
25
Step-by-step explanation:
2x+2+5x+3=180
7x=175
x=24
Find the condition of the expression:√3-2x-x^2
Answer:
-1 <= x <= 1
Step-by-step explanation:
√((1-2x+x^2)+2-2x^2)
= √((1-x)^2 + 2*(1-x)(1+x) )
điều kiện là 1 - x > =0 và 1+x >=0
giải 2 bất phương trình trên ta thu đc kết ququả
f(x) = ^3√4x
g(x) = 3x + 5
Find (f/g)(x). Include any restrictions on the domain.
The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
How to Simplify Algebraic Functions?Given the functions;
f(x) = ∛4x
g(x) = 2x + 3
We want to find the resulting function (f/g)(x);
(f/g)(x) = f(x)/g(x)
Thus, (f/g)(x) = ∛4x/(2x + 3)
Restriction to the function occurs at the point where the denominator is equal to zero.
Thus;
2x + 3 = 0
2x = -3
x = -3/2
Thus, the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
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A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.
Group of answer choices
27
664
544
385
The sample size suggested by this statement is 664 option second is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
At 99% confidence Z = 2.576
By using the MOE formula:
0.05 = 2.376×√(0.5(0.5)/n)
After calculating
n = 663.57 ≈ 664
Thus, the sample size suggested by this statement is 664 option second is correct.
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Mark is investing his money. he thinks that he should make $10 for every $100 he invests. how much does he expect to make on an investment of $500?
What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers
The difference is 2003.
The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).
The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).
Knowing this, plug 2003 for n,
SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003
The difference is 2003.
A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.
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6. The difference between 2 number is 36.
The larger number is 4 times as great as the
smaller. What are the 2 numbers?
Answer: 48 and 12.
Step-by-step explanation:
Let the smaller number is x. Hence, the larger number is 4*x.
The difference between 2 number is 36.
So,
4*x-x=36
3*x=36\ |:3
x=12.
4*x=12*4
4*x=48.
Good luck an' have a nice day!
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
These problems are solved using the trigonometric function. Trigonometric functions provides the ratio of different sides of a right-angle triangle.
What are Trigonometric functions?The trigonometric function refer to function that are periodic in nature and which lend insight to the relationship between angles and the sides of a triangle that is right angled.
The solutions to x in the respective problems is given as follows:
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) It is to be noted that for right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
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Triangle WXY has the interior and exterior angles shown below.
Triangle X W Y. Angle W is (2 x minus 13) degrees and angle Y is x degrees. The exterior angle to angle X is 122 degrees.
What is Measure of angle W?
45 degrees
58 degrees
68 degrees
77 degrees
The correct option is last one 77 degrees.
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
Given:
Exterior angle = 122°
∠W = (2x-13)°
∠Y= x°
To Find:
∠W = (2x-13)° = ?
Solution:
Exterior Angle Property:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Angle W and Angle Y are the interior angles of Exterior angle 122°.
∴
Substituting the values we get
Now Substitute 'x' in angle W we get
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
The length of the hypotenuse of a right triangle is 7 feet, and the length of one leg is 4 feet. what is the length of the other leg to the nearest tenth of a foot
The length of the other leg to the nearest tenth of a foot is 5.7 feet.
What is Pythagorean theorem?
A theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.The Pythagoras theorem equation is expressed as, [tex]c^{2} = a^{2} + b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.We can use the Pythagorean Theorem to find the length of the other leg
[tex]a^{2} + b^{2} = c^{2}[/tex]
"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.
So,
[tex]b^{2} = c^{2} - a^{2}[/tex]
= 7² - 4²
b = [tex]\sqrt{49 - 16}[/tex]
[tex]b = \sqrt{33}[/tex] ⇒ 5.7 feet
Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.
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Identify the slope and y-intercept of the line whose equation is given. write the y-intercept as an ordered pair. y = negative 2 x + 5 a. slope = negative 2; y-intercept (0, 5) b. slope = 2; y-intercept (0, 5) c. slope = 5; y-intercept (0, 2) d. slope = negative 5; y-intercept (0, 2) please select the best answer from the choices provided a b c d
The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.
The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.
The y-intercept of a line is the point at which the line intersects the y-axis.
The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.
In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.
Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,
m = -2, and b = 5.
Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.
Thus, we get the slope = -2, and the y-intercept = (0, 5).
The option representing the answer is option A.
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StartLayout 1st row StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot space c greater-than-or-equal-to 0 and d greater-than-or-equal-to 0. 2nd row = StartRoot StartFraction 25 times 10 c squared times c Over 9 d Superscript 6 Baseline EndFraction EndRoot. 3rd Row = StartFraction StartRoot 25 EndRoot times StartRoot c squared EndRoot times StartRoot 10 c EndRoot Over StartRoot 9 d Superscript 6 Baseline EndRoot EndFraction EndLayout
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot ?
The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³
How to simplify algebra problems?We are given the algebra problems as;
√(250c³/9d⁶)
Now 250c³ can be broken down into 250 = 25c² × 10c
Thus, we now have;
√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶
When we breakdown the above expression, we have;
5c * (√10c)]/3d³
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Answer:
the answer is a
Step-by-step explanation:
i got it right
evaluate
3x³ 2x² + 7y for x = -3 and y = -7.
-
Answer:
2511
Step-by-step explanation: