Answer:
Step-by-step explanation:
From the problem statement, we can setup the following equation:
[tex]35M = 1015[/tex]
where [tex]M[/tex] is the number of months that Rachel has saved up money.
Dividing both sides by 35, we get the answer:
[tex]M = 29[/tex]
(5,-3), (5,8). Find slope
Answer: 0 slope, horizontal line.
Step-by-step explanation:
when using y2-y1/x2-x1, you would get 8-(-3)/5-5. This simplifies to 11/0, which means that the line would have 0 slope. A line with 0 slope is a horizontal line.
Round 503.782 to the nearest tenth
The value 503.782 to the nearest tenth is 503.8
Rounding up to the nearest tenth means we want only a digit to be placed after the decimal point.
Given the value 503.782, this value to the nearest tenth will be 503.8.
Note that 1 was added to the value "7" after the decimal point. This was because the adjacent value "8" is more than 4.
Hence the value 503.782 to the nearest tenth is 503.8
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Final answer:
To round 503.782 to the nearest tenth, the digit in the hundredths place is 8, which is greater than or equal to 5. Therefore, the rounded number is 503.8.
Explanation:
To adjust 503.782 to the closest 10th, we really want to take a gander at the digit in the hundredths place, which is the second digit after the decimal point. It is 7 in this instance.
Since 7 is more prominent than or equivalent to 5, we gather together the digit in the tenths place, which is the primary digit after the decimal point. For this situation, it is 8.
Therefore, 503.8 is obtained by rounding 503.782 to the nearest tenth.
To round 503.782 to the nearest tenth, we look at the digit in the hundredths place, which is 8. Since 8 is greater than or equal to 5, we round up. Therefore, the rounded number is 503.8.
the dimension of a rectangular plot is [7p+4q] and [3p+8p] unita respectively. Find the area of the plot when p=2 and q=1
Answer:
The area of the rectangular plot is 396 square unit.
Step-by-step explanation:
let [7p +4q ]= length of the rectangular plot. And
[ 3p+8p ] = width of the rectangular plot
given that p=2 and q=1
substitute them in the expression for the length
length=7(2)+4(1)
length=14+4
length=18units
again subject the values for p and q into the expression for the width
width=3(2)+8(2)
width=6+16
width=22units
but mathematically,
Area of a rectangular plot
= Length×width
A=L×W
given L=18units and W=22units
A=18units × 22units
A=396 square unit.
A number is 20 less than its square. Find all such numbers.
Answer:
Step-by-step explanation:
[tex]x = x^{2} - 20[/tex]
[tex]x^{2} - x - 20 = 0[/tex]
[tex](x - 5)(x + 4) = 0[/tex]
[tex]x = -4, 5[/tex]
The two numbers are 5 and -4.
To find a number that is 20 less than its square, we can set up an equation where the number is represented by x. The equation then becomes x = x^2 - 20.
By re-arranging the equation, we get x^2 - x - 20 = 0. This is a quadratic equation which can be solved by factoring or using the quadratic formula.
The factored form of the equation is (x - 5)(x + 4) = 0. Therefore, the solutions for x are 5 and -4, meaning 5 and -4 are the numbers that are 20 less than their squares.
. Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%." Is she correct?
Marcy is correct if Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.
As we know,
The ratio of two integers is stated as a fraction of a hundred parts. It is a metric for comparing two sets of data
= (70% + 100%)/2
= 170%/2
= 85%
Thus, Marcy is correct if Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%.
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Final answer:
To raise her score to 85%, Marcy needs to get an average of 1.83 on the final exam. Since it is not possible to score more than 100%, her claim of needing a 100% is not correct.
Explanation:
To determine whether Marcy can raise her score to 85% by getting a 100% on the final exam, we need to calculate the average needed on the final exam.
To find the average Marcy needs, we can use the formula: Final Average = (Current Average * Weight) + (Final Exam Score * (1 - Weight)), where the weight represents the percentage of the final exam in the overall grade.
Let's assume the weight of the final exam is 30%. Plugging in the values, we get:
85% = (70% * 0.7) + (Final Exam Score * 0.3)
Solving for the Final Exam Score:
85% - (70% * 0.7) = Final Exam Score * 0.3
0.55 = Final Exam Score * 0.3
Final Exam Score = 0.55 / 0.3
Final Exam Score = 1.83
Since it is not possible to score more than 100% on the final exam, Marcy's claim of needing to get a 100% on the final to raise her score to 85% is not correct.
an electrician charges $322 for 7 hours of work. how much does the electrician charge per hour?
Answer:
The electrician charges $46 per hour
Step-by-step explanation:
we know that
An electrician charges $322 for 7 hours of work
so
using proportion
Find out how much does the electrician charge per hour
Let
x ----> the charge per hour
[tex]\frac{322}{7}\frac{\$}{h}=\frac{x}{1}\frac{\$}{h}\\\\x=322/7\\\\x=\$46[/tex]
therefore
The electrician charges $46 per hour
The electrician charges $46 per hour.
The total charge is $322, and the total number of hours worked is 7.
To find the charge per hour, use the formula:
Charge per hour = Total charge / Number of hours
Substitute the given values into the formula:
Charge per hour = 322 / 7
Perform the division:
322 divided by 7 equals 46. Therefore, the electrician charges $46 per hour.
So, the calculation is:
Charge per hour = 46
test the continuity of f(x)=1÷(x-3) at x doesnot equal to 3
Good evening ,
____________________
Step-by-step explanation:
it’s a rational function then it’s continue at all real numbers except when x=3
[tex]\frac{1}{x-3}[/tex] ; x≠3.
:)
I need help with this! Angle RELATIONSHIPs
Answer:
The measures of the labeled angles are 58°.
Step-by-step explanation:
Since the two angles are opposite angles, they have to be equal, meaning:
[tex]2x = 87 - x[/tex]
Solve by adding x to both sides and dividing by 3.
[tex]3x = 87 \\ x = 29[/tex]
If x = 29°, then 2x= 58°.
Since opposite angels are equal, the other angle is also 58°.
This can be checked:
[tex]87 - 29 = 58[/tex]
Lake Victoria has the largest surface area is 26828 square miles. How much larger is the surface area of Lake Superior 31700
Answer:
[tex]4,872\ mi^2[/tex]
Step-by-step explanation:
The complete question is
Lake Victoria has the largest surface area of all lakes in Africa. Its surface area is 26,828 square miles. How much larger is the surface area of Lake Superior than that of Lake Victoria?
we know that
Lake Superior has a surface area of 31,700 square miles----> see the attached figure
To find out how much larger is the surface area of Lake Superior than that of Lake Victoria, subtract the surface area of Lake Victoria from the surface area of Lake Superior
so
[tex]31,700-26,828=4,872\ mi^2[/tex]
what is 12^2 *12^-4.
Answer:
[tex]\large\boxed{12^{-2}=\dfrac{1}{144}}[/tex]
Step-by-step explanation:
[tex]12^2\cdot12^{-4}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=12^{2+(-4)}=12^{-2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{12^2}=\dfrac{1}{12\cdot12}=\dfrac{1}{144}[/tex]
Answer:
Step-by-step explanation:
This is the same to have 12^2/12^4
This is equal to have 1/12^2
1/144=0,0069
Write the function representing the graph
Answer:
The function representing the graph is described by two equations, depending on the "x" value
f(x) = (1/3)x + 3 , if x is greater than -3.
f(x) = -x - 5 , if x is less than -3.
Step-by-step explanation:
First, you have to realize that the graph is described by two functions depending on the "x" value and that it is not defined in x= -3.
Then, for "x" values greater than -3, we look at the right line and we took 2 couple of points (-3,2) and (0,3). Using the formula for the slope and the interception with y axis.....
Slope = y2- y1 / x2- x1 = 3 - 2/ 0 - (-3) ⇒ slope = 1/3.
Interception with "y" axis y= 3
⇒ f(x) = (1/3) x + 3.
For "x" values minor than -3, we have to look the left line. Here we used the slope formula and points (-3, -2) and (-5, 0)
Slope = 0 - (-2)/ -5 - (-3) =-1. So, f(x) = -x + b.
Finally we use one of the points to replace in the formula of f(x) to find "b".
-2 = - (-3) + b ⇒ b = -5. ⇒ f(x) = - x -5
Summarizing, f(x) = (1/3)x + 3 , if x is greater than -3.
f(x) = -x - 5 , if x is less than -3.
f(x) = 3x + 4 and g(x) = 5x - 10
fx for whichf(x) = g(x).
Answer:
x =7
Step-by-step explanation:
f(x) = 3x + 4 g(x) = 5x - 10f (x) = g (x)
3x + 4 = 5x - 10
4 + 10 = 5x - 3x
14 = 2x
14/2 = x
7 = x
What is the measure of <T?
72°
156°
48°
132°
Answer:
132°
Step-by-step explanation:
24+24+T=180
48+T=180
T=132°
Complete the place value chart for the following number.Write its number name and tell the value of the underlined digit.
6.325 the underlined digit is 2
Answer:
two hundredths
Step-by-step explanation:
6 is in the ones place. 3 is in the tenths place. 2 is in the hundredths place
5 is in the thousandths place.
Answer:
two hundredths
Step-by-step explanation:
its two places after the decimal point
Todd and Agnes are making desserts. Todd buys
peaches and a carton of vanilla yogurt. Agnes
buys apples and a jar of honey. They bought
the same number of pieces of fruit. Is there a
situation in which they pay the same amount for
their purchases? Explain.
apples
peaches=
$1.25 ea. For peaches
$1 ea. For the apples
YOGUR
HONEY=
$4 for yogurt
$6 for honey
Answer:
If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases
Step-by-step explanation:
Let
x ----> the number of pieces of fruit
y ----> the total pay for the purchase
we know that
Todd
[tex]y=1.25x+4[/tex] ----> equation A (peaches plus a carton of vanilla yogurt)
Agnes
[tex]y=1.00x+6[/tex] ----> equation B (apples plus a jar of honey)
Equate equation A and equation B and solve for x
[tex]1.25x+4=1.00x+6[/tex]
[tex]1.25x-1.00=6-4[/tex]
[tex]0.25x=2[/tex]
[tex]x=8\ pieces\ of\ fruits[/tex]
therefore
If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases
What is the simplified portion of the grouping?
5 + 4 – (102 – 8 × 3) × 4
Answer:
-303 is your answer.
Step-by-step explanation:
What you have to do is PEMDAS.
5 + 4 – (102 – 8 × 3) × 4=
5 + 4 - (102 - 24) × 4=
5 + 4 - 78 × 4=
5 + 4 - 312=
9 - 312=
-303 is your answer.
Answer: 76
Step-by-step explanation:
1,084.9 in expanded form
Answer:
1000+80+4+0.9
Step-by-step explanation:
Keep in mind that expanded form means to expand the number by adding the individual places values to form a mathematical expression. In other words, numbers are expanded to show the value of each of its digits.
For the thousands place:
1,084.9 ---> 1,000.0
Hundreds place:
Because the value is 0, you needn't to include it in the expression.
Tens place:
1,084.9 ---> 80.0
Ones place:
1,084.9 ---> 4
Tenths place:
1,084.9 ---> 0.9
The value of the equation is A = 1,000 + 80 + 9 + 0.40 = 1,084.90
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as A
Now , the value of A is
A = 1,084.90 be equation (1)
On simplifying the equation , we get
1 x 1000 = 1000
0 x 100 = 0
8 x 10 = 80
4 x 1 = 4
0.90 x 1 = 0.90
Substituting the values in the equation , we get
A = 1,000 + 80 + 9 + 0.40
On further simplification , we get
A = 1,084.90
Hence , the equation is solved
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Please help thank you.
Answer:
21
Explanation:
Look at the graph and add up all of the numbers. Hope this helps!
The course length of the Boston Marathon is about 4.2×104 meters. The course length of the Iditarod Trail Invitational ultra-marathon is about 1.6×106 meters. About how many times as long is the course of the Iditarod Trail ultra-marathon as that of the Boston Marathon?
The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.
Explanation:To find out how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon.
Length of Iditarod Trail ultra-marathon = 1.6x106 meters
Length of Boston Marathon = 4.2x104 meters
Dividing the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon:
1.6x106 / 4.2x104 = 38.09524
The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.
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The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.
Explanation:To determine how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail (1.6×106 meters) by the length of the Boston Marathon (4.2×104 meters). Performing the division, we get:
(1.6×106 meters) / (4.2×104 meters)
= 38.095
The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.
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Convert 2.46 Kilometers to centimeters.
Answer:
246000cm
Why: The km to cm formula is:
km/ 0.000010000
Nine more than the quotient of two and a number x
I really need help!!
Answer:
2/x + 9
Step-by-step explanation:
2/x is a fraction, but it also means divided by. More than means flip the addition to the end of the equation.
what is 0.00000000055 in scirntific notation
Answer:
5.5 x 10^-10
Step-by-step explanation:
There are 9 zeros descending from the decimal(so that's why its negative) then you count the five as a "number" and then it equals 10. Don't add the last five just one.
This should be a very simple question on interior angles adding up to 180º, however, I'm continuously getting it wrong. Help!
Answer:
58°
Step-by-step explanation:
65°+57°=122°
180°-122°=58°
what the area of this figure
Let's first start by finding the area of the bigger rectangle.
Area = Length × Width
Area = (4) (3)
Area = 12 ft².
Now, let's find the area of the smaller rectangle.
Area = Length × Width
Area = (4) (1)
Area = 4 ft².
Finally, we need to add the areas of both of the figures to fo find the area of the whole figure.
12 ft² + 4 ft² = 18 ft².
Is this statement true or false?
The range of a list of numbers is the number of numbers in the list.
A:false
B:true
Answer:
A:False
Step-by-step explanation:
Which of the following assist the floor leaders in getting party members to vote in a certain way in both houses of Congress
Answer:
The majority leader and minority leader are elected by their respective party conferences to serve as the chief Senate spokesmen for their parties and to manage and schedule the legislative and executive business of the Senate.
Plz Brainliest?
Anyway, Hope that Helped!
Answer:
Whips
Explanation:
Johann wants to find a rectangular solar panel with an area of 128 cm. If the
width of a panel is 20 cm, what must be the length? Is this an example of
direct variation or inverse variation?
Answer:
The length of rectangular panel is 6.4 cm.
Step-by-step explanation:
We are given the following information in the question:
Area of rectangular solar panel = 128 square cm
Width of panel = 20 cm
We have to find the length of the panel
Formula:
[tex]\text{Area of rectangular panel} = \text{Width}\times \text{Length}\\\Rightarrow 128 = 20\times \text{Length}\\\\\text{Length} = \displaystyle\frac{128}{20} = 6.4\text{ cm}[/tex]
Hence, the length of rectangular panel is 6.4 cm.
This is an example of direct variation as greater would be length and breadth, the greater would be the area.
a certain fish can swim 5 1/2 times faster than a person. if a person can swim 5 2/7 miles per hour, how fast can the fish swim? estimate the answer. then find the exact answer.
I'd estimate about 29 or 30 miles per hour.
The exact answer is 29.0675 miles per hour
5 2/7 x 5 1/2 = 29.0675.
The fish can swim approximately 29 miles per hour, with the exact speed being 29 1/14 miles per hour. This is determined by converting the mixed numbers to improper fractions, multiplying them together, then converting the product back to a mixed number.
Explanation:The subject of this question is mathematics, specifically a real-world application of multiplication of fractions. If a person can swim at a rate of 5 2/7 miles per hour, and the fish swims 5 1/2 times faster, we have to multiply the person's speed by the speed multiplier which is the speed of the fish relative to the person.
Step-by-step explanation:
First, change the mixed numbers to improper fractions. 5 2/7 becomes 37/7 and 5 1/2 becomes 11/2. Multiply the fractions: (37/7) * (11/2), which gives us 407/14. Convert back to a mixed number for the final answer: 29 1/14 miles per hour.
So the fish can swim approximately 29 miles per hour and the exact speed is 29 1/14 miles per hour.
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What is the absolute value of 0?
It's 0.
By definition, the absolute value of a number [tex]x[/tex] is
[tex]|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}[/tex]
so it follows that |0| = 0.
Intuitively, the quantity [tex]|a-b|[/tex] can be thought of as "the distance between the numbers [tex]a[/tex] and [tex]b[/tex] on the real line". If [tex]a=b=0[/tex], asking about |0| is the same as asking "how far away is 0 from 0 on the number line?" to which we answer, 0.
The absolute value of any number is the positive version of that number.
However, there is an exception which I have provided in the image attached.
An equiangular triangle is also known as:
acute
right.
regular
obtuse
Answer:
acute
Step-by-step explanation:
because in a equiangular triangle all the angles are exactly 60° ..
soo..
then.. 60° is an acute angle as it is less than 90° ...
thus, an equiangular triangle is also known a s acute triangle