Answer:
The correct answer is 5
Step-by-step explanation:
To find this, start by multiplying them in any order. For ease, we'll multiply the first and last.
-2/3 * -3 = 2
Now we take that and multiply it by the remaining term.
2 * 2 1/2 = 5
Final answer:
Multiplying −2/3 by 2 1/2 and then by −3 results in the answer 5 after converting the mixed number to an improper fraction, considering the signs during multiplication, and simplifying the result.
Explanation:
To multiply the given numbers and write the answer in simplest form, let's break down the math step by step.
Firstly, convert the mixed number 2 1/2 into an improper fraction. To do this, multiply the whole number by the denominator of the fraction and add the numerator. This gives us 2 x 2 + 1 = 5, so 2 1/2 becomes 5/2.
Now, let's look at the multiplication operation:
−2/3 × (5/2) × (−3) = ( −2 × 5 × −3 ) / ( 3 × 2 )
When multiplying, we multiply the numerators together and the denominators together, which results in:
(−2 × 5 × −3) / (3 × 2) = (+2 × 5 × 3) / 6 = 30 / 6
When considering the signs, remember that when two numbers with the same sign multiply, the result is positive (e.g., −2 × −3 = +6), and when two numbers with opposite signs multiply, the answer is negative (e.g., −3 × 2 = −6).
The final step is to simplify the fraction 30/6, which simplifies to 5, since 30 divided by 6 equals 5.
Therefore, the answer is 5.
A company is evaluating a new biology program that is supposed to improve test scores. The box plots show the the results of biology test given before and after using the program. With the data, what is the most reasonable answer to the question: does the program improve test scores?
Answer:
No, because the median test score decreased 5 points.
Step-by-step explanation:
The middle line is is the median so, if the pre-test is 60 and the post-test is 55 then there is a 5 point difference.
15 Points! Math help
Answer:
7Step-by-step explanation:
[tex]\dfrac{5^{11}}{5^x}=5^4\qquad\text{multiply both sides by}\ 5^x\\\\5^{11}=5^4\cdot5^x\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\5^{11}=5^{4+x}\iff11=4+x\qquad\text{subtract 4 from both sides}\\\\11-4=4-4+x\\\\7=x\to x=7[/tex]
This is the mathematical relation relating the three sides, a, b, c, of a right triangle.
Answer:
It is the famous Pythagorean theorem which is this equation:
a^2 + b^2 = c^2,
where a and b are the legs and c is the hypotenuse.
Answer:
Pythagorean theorem
Step-by-step explanation:
Find the surface area of the rectangular prism. A. 69.26 ft^2 B. 70.78 ft^2 C. 71.88 ft^2 D. 72.88 ft^2
Answer:
D
Step-by-step explanation:
The surface area of the rectangular prism is the sum of all the 6 faces.
There are 2 faces with length 3 ft and width 3.4 feet. Hence,Area = 2 (3*3.4) = 20.4
There are 2 faces with length 3 ft and width 4.1 ft. Hence,Area = 2 (3*4.1) = 24.6
There are 2 faces with length 3.4 ft and width 4.1 ft. Hence,Area = 2 (3.4*4.1) = 27.88
Thus, Surface Area = 20.4 + 24.6 + 27.88 = 72.88 ft ^2
Answer:
The correct answer option is D. 72.88 ft^2.
Step-by-step explanation:
We are given a diagram of a rectangular prism with width 3 ft, length 3.4 ft and height 4.1 ft and we are to find its surface area.
We know that the surface area of a rectangular prism is given by:
[tex]2(wl \times hl \times hw)[/tex]
So substituting the given values in the above formula to get:
Surface area of rectangular prism = [tex]2[(3 \times 3.4) + (4.1 \times 3.4) + (4.1 \times 3)][/tex] = 72.88 ft^2
an amphitheater was 19 seats in the front row, 22 in the second, 25 in the third, and so on, for 24 rows
how many seats are in the theater?
Answer:
Answer: 572
Step-by-step explanation:
Select the domain and range of F. F = {(x, y ) | x + y = 10}. Domain: {10} Range: {10} Set F is not a function and does not contain a domain or range Domain: All Real Numbers Range: All Real Numbers
The equation x + y = 10 represents a linear relationship that spans all real numbers in both x and y directions. Thus, the domain and the range for this function are both all real numbers.
Explanation:The equation for the set F is x + y = 10, which is a straight line on a graph. This line extends infinitely in both directions, meaning that there is no restriction on the possible values of x (the domain) and y (the range). Therefore, the correct answer for both domain and range would be 'All Real Numbers'.
To visualize this, imagine you plug in any number for x and solve the equation for y. Similarly, you can do the same, guessing a y-value and solving for x. No matter the number chosen, there will always be a corresponding number on the other side, whether positive, negative, or zero.
Remember that a domain is the set of all inputs (or 'x' values) that a function can accept, and a range is the set of all possible outputs (or 'y' values) that the function can produce. In this example, the function can handle and generate all real numbers, so its domain and range are all real numbers.
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A car left Sacramento, California, and traveled at an average speed of 95 km/h to Redding California. The distance between the two cities is 260 km. How many hours was the car traveling?
About 2 hours
(About 2 hours and 25 minutes exactly)
I added minutes anyways
260 divided by 95 = 2 Remainder 25
Hrs Mins
What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm?
Answer:
The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=BHL[/tex]
Convert the given dimensions to an improper fractions
[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]
[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]
[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]
substitute in the formula
[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]
Convert to mixed number
[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]
what is the answer to -42-34+15= 61
Answer:
-61
Step-by-step explanation:
-42-34=-76= -61
Which exponential function goes through the points (1, 8) and (4, 64)? f(x) = 4(2)x f(x) = 2(4)x f(x) = 4(2)−x f(x) = 2(4)−x
Answer:
y = 4(2^x)
Step-by-step explanation:
To write the exponential values, compare the y values. Notice they are multiples of 8 and they are increasing. This means the base is likely 2 or 4 since each of these numbers has the same multiples. Our options also only include base 2 and 4.
Try 4^1 = 4 and 4^4 = 256.
Try 2^1 = 2 and 2^4 = 16.
None of these give the exact values in the points. This means there is an initial value multiplied to them as well.
When x = 1 and the base is 4, the value is too small. But when x = 4, the value is too large. This cannot be reconciled.
When x = 1 and x = 4 for the base 2, both values are too small and could be multiplied by the same number to get the right values.
2*4 = 8
16*4 = 64
The initial value is 4 so the function is [tex]y = 4(2^x)[/tex]
EASY! WILL MARK BRAINEST!! What is f(3) for the function f(x)=7x+5
Answer:
26 is the answer
Step-by-step explanation:
The measures of the three angles of a triangle are given by 3x + 1, 2x − 3, and 9x. What is the measure of the smallest angle?
Answer:
23°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
3x + 1 +2x - 3 + 9x = 180 ( simplify left side )
14x - 2 = 180 ( add 2 to both sides )
14x = 182 ( divide both sides by 14 )
x = 13
The 3 angles are
3x + 1 = (3 × 13) + 1 = 39 + 1 = 40°
2x - 3 = (2 × 13) - 3 = 26 - 3 = 23° ← smallest angle
9x = 9 × 13 = 117°
Find the difference 5x/x^2-x-6 (-) 4/x^2+4x+4
The difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].
To subtract the two rational expressions [tex]\( \frac{5x}{x^2-x-6} \) and \( \frac{4}{x^2+4x+4} \)[/tex], we need to find a common denominator.
First, factor the denominators:
1. x²-x-6 = (x-3)(x+2)
2. x²+4x+4 = (x+2)²
The common denominator will be (x-3)(x+2)(x+2).
Now, rewrite the expressions with the common denominator:
1. [tex]\( \frac{5x}{(x-3)(x+2)} \)[/tex]
2. [tex]\( \frac{4}{(x+2)^2} \)[/tex]
To subtract, the numerators remain the same, so the expression becomes:
[tex]\[ \frac{5x}{(x-3)(x+2)} - \frac{4}{(x+2)^2} \][/tex]
To combine the fractions, we need to rewrite the first fraction with the common denominator:
[tex]\[ \frac{5x(x+2)}{(x-3)(x+2)(x+2)} - \frac{4(x-3)}{(x-3)(x+2)(x+2)} \][/tex]
Now, we can subtract the fractions:
[tex]\[ \frac{5x(x+2) - 4(x-3)}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 10x - 4x + 12}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \][/tex]
So, the difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].
To find the difference between the two rational expressions, we first need to factorize the denominators and simplify where possible. Let's break it down step by step:
1. Factorize the denominators:
[tex]\(x^2 - x - 6 = (x - 3)(x + 2)\) \(x^2 + 4x + 4 = (x + 2)^2\)[/tex]
2. We rewrite the expressions with common denominators:
[tex]\(\frac{5x}{(x - 3)(x + 2)} - \frac{4}{(x + 2)^2}\)[/tex]
3. To simplify these, we need a common denominator, The least common denominator is [tex]\((x - 3)(x + 2)^2\).[/tex], so to get it, we multiply (x + 2) with Expression 1 and (x - 3) with Expression 2 on both numerator and denominator. We get:
[tex]\(\frac{5x(x + 2)}{(x - 3)(x + 2)^2} - \frac{4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]
4. We combine the fractions:
[tex]\(\frac{5x(x + 2) - 4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]
[tex]\(= \frac{5x^2 + 10x - 4x + 12}{(x - 3)(x + 2)^2}\) \(= \frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\)[/tex]
So, the difference between the two rational expressions is [tex]\(\frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\).[/tex]
In a cafeteria,
3
-
8
of the students are eating salads , and
1
-
4
are eating sandwiches. There are 24 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
The number of students not eating salads and sandwiches are 9
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here: 3/8 of the students in the cafeteria eat salads and 1/4 of the students eat sandwiches.
∴3/8×24+1/4×24=9+6
=15
Thus the number of students eating lunches other than salads or sandwiches are 24-15=9
Hence, The number of students not eating salads and sandwiches are 9
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Complete the square and write the equation in standard form. Then give the center and radius of the circle. 10x2 + 10y2 = 100
2 + y2 = 10 (0, 0), r = 10
x2 + y2 = 100 (0, 0), r = 10
x2 + y2 = 10 (0, 0),
r = 10‾‾‾√
(x - 10)2 +(y - 10)2 = 10 (10, 10),
r = 10‾‾‾√
Answer:
Center: (0,0)
Radius: [tex]r=\sqrt{10}[/tex]
Step-by-step explanation:
The given circle has equation
[tex]10x^2+10y^2=100[/tex]
In order to complete the square, we must make sure the coefficient of the quadratic terms are unity.
We divide through by 10 to obtain;
[tex]x^2+y^2=10[/tex]
The coefficient of the linear terms of both variables are zero.
Therefore the equation can be rewritten as;
[tex](x-0)^2+(y-0)^2=10[/tex]
Comparing to [tex](x-h)^2+(y-k)^2=r^2[/tex]
We have (h,k)=(0,0) to the center of the circle and [tex]r=\sqrt{10}[/tex] to be the radius of the circle.
Answer:
Equation: x² + y² = 10
center = (0, 0)
radius = √10
Step-by-step explanation:
The general equation of a circle is ;
(x - a)² + (y - b)² = r²
Where (a, b) is the coordinate of the center of the circle, and r is its radius.
Where the center is (0,0), the equation becomes,
x² + y² = r²
In our case we have;
10x² + 10y² = 100
dividing both side by ten,
x² + y² = 10
∴ center = (0, 0)
radius = √10
Which of the following steps were applied to ABC obtain A' B'C'?
A Shifted 4 units left and 3 units down
B. Shifted 3 units left and 3 units down
C. Shifted 3 units left and 2 units down
D. Shifted 4 units left and 2 units down
D. Shifted 4 units left and 2 units down
The answer to your problem is d.
Which of the following side lengths can form a triangle?
A) 2in, 3in, and 7in
B) 21cm, 23cm, and 44cm
C) 12mm, 36mm, and 53mm
D) 14ft, 17ft, and 30ft
Answer :
D
Solution :
14ft + 17ft = 30ft
31ft = 30ft
On a number line, show all values of x that have the absolute value less than 3
Unfilled circle on 3, filled circle on 0, line connecting the circles.
•—————o
0 3
The values of x that have the absolute value less than 3 are plotted in the figure attached.
What is the number line?The number line should be represented in the straight line that have the zero point in the middle, having the positive and negative numbers that should be listed on the other side.
Given that to plot all values of x that have the absolute value less than 3,
It can be written as |x| ≤ 3
We can say that,
The values of x that have the absolute value greater than 3 are -3 and 3. It should be located into the equal intervals.
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what is 0.5357142857 in degrees
Answer:
Do you mean like a "degree" of a circle?
Step-by-step explanation:
Answer:
Are you talking about the degrees of a circle?
Step-by-step explanation:
What is the degree of the function f(x)= x(x+1)2 (2x-3)(x+2)2
Answer:
6
Step-by-step explanation:
Given equation is [tex]f(x)= x(x+1)^2 (2x-3)(x+2)^2[/tex].
Now we need to find about what is the degree of the give function.
We know that degree of polynomial function is the highest exponent of the variable (x).
So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.
Second choice will be easier.
Degree of [tex]x[/tex] = 1
Degree of [tex](x+1)^2[/tex] = 2
Degree of [tex](2x-3)[/tex] = 1
Degree of [tex](x+2)^2[/tex] = 2
Hence degree of the given polynomial function = 1+2+1+2=6
QUICKK
Solve for x. You must write your answer in fully simplified form.
To solve divide both sides by 4 to cancel out the 4 on the x side to get x alone. Then just do -10/4. That gives you 2.5 so (X=2.5). Hope I helped and have a great day and night
Answer:
-5/2
Step-by-step explanation:
We start with 4x = -10 and want to solve this for x.
We divide both sides by 4 (which isolates x), obtaining:
x = -10/4
and then we reduce this to x = -5/2.
Brooke paints the outsides of the square walls and triangular ceilings of her treehouse. What area does she paint?
Answer:
Broke paints [tex]216\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of the outsides of the square walls and triangular ceilings of her tree house is equal to the area of four squares and four triangles
so
[tex]A=4[(6)^{2} +\frac{1}{2}(6)(6)]\\ \\A=4[36+18]\\ \\A=216\ ft^{2}[/tex]
The surface area of the square walls and triangular ceiling she painted is 216 ft²
How to find the surface area of the painted region?
The surface area of the painted region can be found as follows:
area of the square = l²
where
l = side lengthTherefore,
l = 6 ft
area of the square = 6² = 36 ft²
Area of the triangular region = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangular region = 1 / 2 × 6 × 6 = 36 / 2 = 18 ft²
Therefore,
area of the painted region = 18(4) + 36(4) = 144 + 72 = 216 ft²
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Which is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8y
Answer:
b
Step-by-step explanation:
The first morning Courtney walked on a beach for 20 minutes . She finished 30 minutes before high tide at what time did Courtney start her walk
Martha walked for 0.67 hours.
Here's how we can calculate it:
Total time spent hiking:
12:30 AM - 11:30 PM = 1 hour (since 12:30 AM is midnight and the same as 00:30 AM)
Convert hours to minutes: 1 hour * 60 minutes/hour = 60 minutes
Time spent running:
Subtract the walking time from the total time: 60 minutes - 20 minutes = 40 minutes
Convert running time to hours:
Divide minutes by minutes per hour: 40 minutes / 60 minutes/hour = 0.67 hours
Therefore, Martha walked for 0.67 hours.
Question
If Martha went on a hiking trip at 11:30 PM, and walked for 20 minutes, and ran the rest, and came back at 12:30 AM, how many hours did Martha WALK?
The losing candidate in a mayoral election received 10,200 votes, which represented 30% of all votes cast in the election.
A. Dorian claims that the total number of votes cast in the mayoral election was 3,060. Dorian made a mistake in his calculations. Why is his claim not reasonable? Explain your answer.
B. Find the total number of votes cast in the mayoral election. Explain how you found your answer.
well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.
B)
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x[/tex]
A)
Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.
Final answer:
Dorian's claim is incorrect because dividing 10,200 votes by 30% (or 0.30) gives 34,000 votes, which is the correct total number of votes cast in the mayoral election. Therefore, the calculation shows that the total votes are much higher than Dorian's claim of 3,060 votes.
Explanation:
A. Dorian's claim that the total number of votes cast in the mayoral election was 3,060 is not reasonable because if the losing candidate received 10,200 votes which represented 30%, then the total votes should be much higher than 3,060. To find the total, you would divide the number of votes the candidate received by the percentage they represent.
B. To find the total number of votes cast in the mayoral election, you would set up the equation 10,200 = 0.30 * Total Votes. Dividing 10,200 by 0.30 gives the total number of votes cast, which is 34,000.
Equation: Total Votes = 10,200 votes / 0.30 = 34,000 votes
A jewelry store is having a going-out-of-business sale. All merchandise is marked 40% off the regular price. The regular price of a watch is $59.95 what is the amount of the discount and the sale price
Answer:
$35.97
Step-by-step explanation:
the regular price is 59.95
40% discount so
let's say the price now is x and i am gonna do fractions
x/59.95 = 40%/100
100 x X = 100x
59.95 x 40 = 2398
i divide 2398 by 100 which equal 23.98
40% is 23.98 and then i do 59.95 - 23.96 = 35.97
DONE!
The discount amount on the watch is $23.98 and the sale price after applying the 40% discount off the regular price of $59.95 is $35.97.
When a jewelry store is having a going-out-of-business sale, and all merchandise is marked 40% off the regular price, we can calculate the amount of the discount and the sale price using percentage formulas. For example, if a watch has a regular price of $59.95, we multiply this price by 40% (or 0.40) to find the discount amount.
To find the discount amount: $59.95 times 0.40 = $23.98
Next, to find the sale price, we subtract the discount amount from the regular price.
To find the sale price: $59.95 - $23.98 = $35.97
Therefore, the discount amount is $23.98, and the sale price of the watch is $35.97.
The price of a gallon of milk went from $2.70 to $3.50 in four years. Find the rate of change of the price of the milk
milk went up to a $1.20
Answer:
The rate of change in price is
$0.2 per year
Step-by-step explanation:
This problem bothers on rates
Given data
Initial price of milk = $2.7
Final price of milk = $3. 5
Time duration = 4 years
Hence the rate of the change of price can be estimated as follows
= Δ in price/Δin time
= (Final price - initial price)/4
=3.5-2.7/4
=0.8/4
=$0.2 per year
Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth. A. 69.18 m^2 B. 79.18 m^2 C. 89.18 m^2 D. 99.18 m^2
Answer: OPTION B
Step-by-step explanation:
Use the following formula:
[tex]SA=\frac{pl}{2}+B[/tex]
Where p is the perimeter of the base, l is the slant height and B is the area of the base.
The perimeter is:
[tex]p=6*s=6*3m=18m[/tex]
Where s is the lenght of a side.
The slant height is given:
[tex]l=6,2m[/tex]
The area of the base is:
[tex]B=\frac{3\sqrt{3}s^2}{2}=\frac{3\sqrt{3}(3m)^2}{2}=23.382m^2[/tex]
Where s is the length of a side.
Substitute values. Then, the result is:
[tex]SA=\frac{(18m)(6.2m)}{2}+23.382m^2=79.18m^2[/tex]
Answer:
The correct answer option is B. 79.18 m^2.
Step-by-step explanation:
We are given a diagram of a regular hexagonal pyramid with height 5.6 m, slant height 6.2 m and base edge length 3m.
We know that the surface area of a regular hexagonal pyramid is given by:
[tex]\frac{PI}{2} +B[/tex]
where P = perimeter of the base, I = slant height and B = base area.
Perimeter of base = [tex]3 \times 6[/tex] = 18 m^2
Base area (area of hexagon) = [tex]\frac{3\sqrt{3} }{2} a^2[/tex] = [tex]\frac{3\sqrt{3} }{2} 3^2[/tex] = 23.38 m^2
Surface area of hexagonal pyramid = [tex]\frac{18 \times 6.2}{2} +23.38[/tex] = 79.18 m^2
Factor.
x2−6x+9
Question 2 options:
(x−3)2
(x+3)2
(x−9)2
Answer:
(x-3)²
Step-by-step explanation:
x²-6x+9
x² can be written as (x)²
9 can be written as 3²
(x)²-6x +(3)
we can break 6x as 2(3)(x)
by using square formula
(a+b)²= a²-2ab+b²
Putting all the values back in expression we get
(x)²-2(3)(x)+(3)²
by closing formula we get
(x-3)²
Answer:
(x-3)2
Step-by-step explanation:
i took the test
(please for the sake of me passing highschool please god in heaven help me i dont want to fail highschool)
How long does it take Heather to do a single push-up?
A.
4 seconds
B.
14 seconds
C.
3 seconds
D.
2 seconds
Your answer is D. 2 seconds because her distance from the floor is consistent. Every push-up is 2 seconds apart, therefore it’s D.