Answer:
7
Step-by-step explanation:
The gradient of a line is a measure of how steep the line is. It is calculated as the change in the y-value (the "rise") divided by the change in the x-value (the "run").
In the equation y = 7x + 8, the coefficient of x (7) is the gradient of the line. This means that for every 1 unit change in the x-value, the y-value changes by 7 units.
So the gradient of the line y = 7x + 8 is 7.
A triangle has side lengths of 2 cm, 8 cm, and x cm. Which measure could be the value of x in centimeters?.
If the side lengths of triangle are 2 cm, 8 cm, and x cm then the measure of x can be 9 , the correct option is (b) .
In the question ,
it is given that ,
the side lengths of the triangle are 2 cm, 8 cm, and x cm .
we know that the sum of two sides of triangle is greater than the third side ,
So , x < 8 + 2 ,
x < 10 ,
and the difference of two sides of triangle is less than the third side ,
So , 8 - 2 < x
6 < x .
So , the side length x can be , 6 < x < 10 .
the options that suits the condition is (b) 9 .
Therefore , the correct option is (b) .
The given question is incomplete , the complete question is
A triangle has side lengths of 2 cm, 8 cm, and x cm. Which measure could be the value of x in centimeters?
(a) 6
(b) 9
(c) 10
(d) 12
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Kanya makes and sells jewellery items. In one week she sells earrings, bracelets and necklace in the ratio of 13:24:15
What fraction of the total items sold were bracelets?
Give your answer in simplest form
The ratio shows how many times one value is contained in another value.
The fraction of the bracelets from the total items is 6/13.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of earrings, bracelets, and necklace is 13:24:15.
This means,
Earrings = 13x
Bracelets = 24x
Necklace = 15x
The fraction of the bracelets from the total items.
= 24x / (13x + 24x + 15x)
= 24x / 52x
= 24/52
= 12/26
= 6/13
Thus,
The fraction of the bracelets from the total items is 6/13.
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swimming pool on a certain hot summers day 553 people use the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1085.25. How many children and how many adult swim at the public pool that day?
The number of children and adults using the swimming pool is x=318, and y=235 respectively.
Given that,
Swimming pool on a certain hot summer day 553 people use the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1085.25.
Here,
let the number of children be x and the number of adults be y,
According to the conditions,
x + y = 553, - - - - - - (1)
1.75x + 2.25y = 1085.25 - -- - - - - -(2)
Solving the above equations by substitution of x from 1 in equation 2.
1.75[y - 553] + 2.25y = 1085.25
x = 318
Now,
x = 553 - 318
x = 235
Thus, the number of children and adults using the swimming pool is x=318, and y=235 respectively.
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HELP PLEASE.
Explore sums of complex numbers by moving points A and B and noticing how the sum of those points written in the expression below corresponds to the sum shown geometrically. Drag the points, A and B, to produce a result of -3 + 4i
This is also written on the attached image
The two points A and B that will be added to produce the complex number -3 + 4i are; -1 + 2i and -2 + 2i.
How to solve Complex Numbers?A complex number is defined as one that has both a real and an imaginary component, whereby both of them are preceded by the letter i which denotes the square root of -1.
Complex numbers are written in the general form; x + iy
Where;
x is the real part.
iy is the imaginary part.
From the graph attached, we can deduce that the two points that were added to obtain the result of -3 + 4i are;
A = -1 + 2i
B = -2 + 2i
Now, let us confirm the sum of the two points A & B;
A + B
= -1 + 2i + -2 + 2i
⇒ -3 + 4i
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Let f(x)=7x and g(x)=7x+2−4. Which transformations are needed to transform the graph of f(x) to the graph of g(x)? Select each correct answer.
Responses
horizontal translation 2 units left
vertical translation 2 units up
vertical translation 4 units down
horizontal translation 2 units right
horizontal translation 4 units left
vertical translation 4 units up
The required answer choice is vertical translation 2 units up and vertical translation 4 units down.
What is translation?
In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the same size as the original shape, and thus the shapes are congruent. They were simply shifted in one or more directions. There is no change in the shape because it is simply moved from one location to another.
The -2 indicates that you need to translate 2 units up, and the -4 indicates that you need to translate 4 units down.
As a result, the answer is vertical translation 2 units up and vertical translation 4 units down.
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Horn lengths of texas longhorn cattle are normally distributed. The mean horn spread is 60 inches with a standard deviation of 4. 5 inches. Calculate the range of horn lengths for the middle 99. 7% of texas longhorn cattle.
The range of horn lengths for the middle 99.7% is (46.5 , 73.5) inches .
In the question ,
it is given that ,
the horn lengths of Texas cattle are Normally Distributed ,
the mean of the horn spread is = 60 inches ,
the standard deviation of horn spread is = 4.5 inches ,
we know that the range for the middle 99.7% is (μ ± 3σ) ,
So , substituting the values in the range formula ,
we get ,
Range = (μ ± 3σ)
= (μ - 3σ , μ + 3σ)
= (60 - 3*4.5 , 60 + 3*4.5)
= (60 - 13.5 , 60 [tex]+[/tex] 13.5)
= (46.5 , 73.5)
Therefore , the range is (46.5 , 73.5) inches .
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Solve the equation for w.
w divided by 4.4 minus 2.8 equals 11.5
62.92
38.28
3.25
1.97
Answer:
62.92
Step-by-step explanation:
which inequality is graphed below?
Answer:x>1
Step-by-step explanation:
X/9=5
PLEASE HELPPPP ASAPPP
Answer:
x = 45
Step-by-step explanation:
2y = x - 4 please help
Answer:
y=1/2x-2
Step-by-step explanation:
11 of 1411 of 14 Items
Question
Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.
Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L.
She fills the cap 314 times in all.
John has a different bottle of detergent that is the same size.
Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L.
He fills his cap 256 times in all.
Who has the greater total change in the amount of detergent in their bottle?
John has the greater total change in the amount of detergent in their bottle.
Given that, Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L. She fills the cap 314 times in all.
Now, the volume of bottle =314×0.26
= 81.64
≈ 82 L
Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L. He fills his cap 256 times in all.
Here, the volume of bottle =256×0.21
= 53.76
≈ 54 L
Hence, John has the greater total change in the amount of detergent in their bottle.
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A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long.
Answer: If you are looking for Area, use the formula A=length x width
If you are looking for Perimeter, use the formula P= 2(length x width)
Step-by-step explanation:
So, the Area would be A=12x9 = 108 meters squared (you're multiplying 12 meters and 9 meters, which squares the unit)
and the Perimeter would be P= 2(12x9) = 216 meters
an ir signal has a percent transmittance of 45%. what does this mean with respect to how the sample interacted with the ir light source? group of answer choices
If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light
The percent transmittance of an IR signal = 45%
The equation of percent transmittance is
Percent transmittance = ( I / Io ) × 100
Where Io is the intensity of the IR signal entering the sample
I is the intensity of the IR signal leaving the sample
If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light
Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample
Therefore, the sample absorbed 55% of the IR light
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i need help with this asap!!! its due tonight!!!! HELPP!!!!
Answer: a
Step-by-step explanation:
I am part of a hole I am twice the value of 1/8 I am percentage what am I
Answer: 25
Step-by-step explanation:
part of a low is anything lower than 1oo
twice of 1/8 = 2/8 = 1/4
Answer:
25%
Step-by-step explanation:
"twice" means two times.
"twice the value of 1/8" is
2 × 1/8
(to multiply a whole number times a fraction, multiply the big number × the top number)
2 × 1/ 8 is 2/8
2/8 is 1/4.
1/4 = .25 = 25%
Since the answer is a percent, change 1/4 to a decimal, .25, change the decimal to a percent.
Or you could change 1/4 to 25/100. Percent means "per hundred" 25/100 is 25%.
Write the equation of the line passing through the points (-3,3) and (3,1).
The equation of the line is?
Answer:
Step-by-step explanation:
Step 1 Find the slope
1-3/3-(-3)
-2/6=1/3
m=-1/3
Use the point slope formula
y-1=-1/3(x-3)
y=-1/3x+2
PLEASE HELP ASAP
I NEED HELP WITH THIS MATH
Step-by-step explanation:
remember :
when multiplying terms with the same base, we add the exponents.
when dividing terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
when putting exponent on exponent, we multiply the exponents.
a negative exponent means 1/...
e.g. 6^-4 = 1/6⁴
1/6^-4 = 1 / 1/6⁴ = 6⁴
so,
1.
(3^-4 × 3²)/3 = 3^-2 × 3^-1 = 3^-3 = 1/3³ = 1/27 =
= 0.037037037...
2.
(4²)^-1 × 4² = 4^-2 × 4² = 4⁰ = 1
3.
(2^-4 / 2^-2)^-1 = (2^-4 × 2²)^-1 = (2^-2)^-1 = 2² = 4
4.
(3^-3)² / (3²)^-1 = 3^-6 / 3^-2 = 3^-6 × 3² = 3^-4 =
= 1/3⁴ = 1/81 = 0.012345679...
the area of a square is 264cm². Find length & perimeter of square.
Answer:
Here,
Given:
Area of a square- 264 sq. cm
To find:
1. The length ( side)
2.Perimeter.
Solution :
Now,
Let the side of the square be x cm.
according to the formula for finding the area of a square:
Area= side× side
264= x× x
264= x^2
√264= x
16.2481= x
16.25= x
hence,
Length= side= 16.25 cm.
Now,
Perimeter of a square:
= 4× side
= 4× 16.25
= 65
Hence,
perimeter of the square= 65 cm
Step-by-step explanation:
I hope I helped you
Please help with this asap Barb was going to buy a shirt which was originally priced for $20. There was a price tag on the shirt that said $12. What percentage was the shirt marked down?
A. 40%
B. 60%
C. 1.33%
D. 1.67%
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
C. x² -8x +16 = 20
Step-by-step explanation:
You want the next step in completing the square after you get x² -8x = 4.
Completing the squareThe constant in a perfect square monic trinomial is the square of half the coefficient of the linear term.
The coefficient of x is -8. Half that is -4, and its square is (-4)² = 16. This will be the value added to the equation in the second step.
x² -8x +16 = 4 +16
x² -8x +16 = 20
__
Additional comment
A monic polynomial has a leading coefficient of 1. We generally work with monic quadratics when completing the square. We do this by factoring the leading coefficient out of the variable terms.
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23.4 is what percent of 288? Round to the nearest tenth..?
It should be noted that 23.4 is 8.1 percent of 288.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
23.4 is what percent of 288 will be calculated thus:
= 23.4 / 288 × 100
= 8.1%
The percentage is 8.1%.
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You work as a server at a restaurant.
You earn $200 in a week, plus an
average of 15% of your sales in tips.
How much food must you sell in
order to make at least $470 this week?
Answer:
It would have saved 445$
Explanation: because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 280$ and the he saved 175$ on the fifth week because 7/8 of 200 is 175 so 280+175 is 445
Step-by-step explanation:
What is the slope of line p?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Slope can be determined by using two points (x1, y1) and (x2, y2) and putting them in rise-over-run format (rise-over-run is equal to slope)
in this case we can use (3, 2) as (x1, y1) and (0, 0) as (x2, y2)
Rise-over-run format is: [tex]\frac{y2 - y1}{x2 - x1}[/tex]
so substitute our number in and you get: [tex]\frac{2-0}{3-0}[/tex]
solve to get: [tex]\frac{2}{3}[/tex]
this is your slope
2) Find y if y = -7x - 6 and
x = 5.
Answer: -41
Step-by-step explanation:
-7x - 6
-7(5) - 6
-35 - 6
-41
If h (x) = 2x^2 - 5x + 7, find the value of h (-3)
if h(x) = 2x² - 5x + 7
h(-3) = 2(-3)² - 5(-3) + 7
= 18 + 15 + 7
= 40
Which function has a period of л?
A. y = cos x
B. y = csc x
C. y = cot x
D. y = sin x
A special machine is used at a construction site to dig holes. A hole is dug to a depth of 4.75 feet when the machine hits rock. The progress slows to 3/5 feet per hour of digging. The depth of the hole must be at least 12 1/2 feet by the end of the day to stay on schedule.
What is the minimum amount of time the machine must continue at its present rate to complete the hole on schedule?
Select from the drop-down menus to correctly complete the statement.
The machine requires at least Choose... hours and Choose... minutes to complete the hole on schedule.
Chose #1: 18 28
Chose#2 9, 15, 45, 55
Answer:
The machine requires at least 9 hours and 45 minutes to complete the hole on schedule.
Step-by-step explanation:
To find this, you can use the formula provided in the previous response:
(required depth - current depth) / digging rate = hours of digging
Plugging in the values from the problem, you get:
(12.5 feet - 4.75 feet) / (3/5 feet per hour) = (7.75 feet) / (3/5 feet per hour)
This simplifies to:
(7.75 feet) / (3/5 feet per hour) = 15.5 hours
Then, to convert this number of hours to hours and minutes, you can divide by the number of minutes in an hour (60 minutes) and round up to the nearest whole number for the number of hours. The remainder will be the number of minutes:
15.5 hours / 60 minutes/hour = 0.258333... hours
Rounding up to the nearest whole number, you get:
0.258333... hours = 1 hour
The remainder is:
15.5 hours - 1 hour = 14.5 hours
14.5 hours / 60 minutes/hour = 0.241666... hours
Rounding up to the nearest whole number, you get:
0.241666... hours = 0 hours
The remainder is:
14.5 hours - 0 hours = 14.5 hours
14.5 hours / 60 minutes/hour = 0.241666... hours
Rounding up to the nearest whole number, you get:
0.241666... hours = 0 hours
The remainder is:
14.5 hours - 0 hours = 14.5 hours
14.5 hours * 60 minutes/hour = 870 minutes
Therefore, the machine requires at least 9 hours and 45 minutes to complete the hole on schedule.
Find the missing length indicated.
Triangle 1's x value is 8 and LN's length is 14 units. Triangle 2's x value is 8 and IH's length is 11 units. Triangle 3's x value is 9 and CB's length is 23 units. Triangle 4's x value is 11 and its IH length is 11 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
ME=EN
MN=ME+EN
MN=2ME
this will be same for all the triangles,
1. 2x-9/2x-2=1/2
2(2x-9)=2x-2
4x-18=2x-2
2x=16
x=8
LN=2x-2
LN=14 units
2. 2x-5/x+14=1/2
2(2x-5)=x+14
4x-10=x+14
3x=24
x=8
IH=2x-5
=11 units
3. (x+14)/(x+19)=1/2
2(x+14)=x+19
2x+28=x+19
x=9
CB=x+14
CB=23 units
4. 2x-11/x+11=1/2
2(2x-11)=x+11
4x-22=x+11
3x=33
x=11
IH=2x-11
IH=11 units
In triangle 1, The value of x is 8 and length of LN is 14 units. In triangle 2, The value of x is 8 and length of IH is 11 units. In triangle 3, The value of x is 9 and length of CB is 23 units. In triangle 4, The value of x is 11 and length of IH is 11 units.
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Express the radical using the imaginary unit, i.
Express your answer in simplified form.
±√-24 = ±
Answer:
2i[tex]\sqrt{6[/tex]
Step-by-step explanation:
So, for right now, ignore the negative. Consider the factors of 24. Both 6 and 4 multiply to 24. This means that [tex]\sqrt{24} = \sqrt{6}[/tex] x [tex]\sqrt{4}[/tex]. [tex]\sqrt{4}[/tex] can simplfy down to just 2. Now let's remember the negative. When taking a negative square root, you need to add an 'I' to the number you take out of the root. So right now you have 2i. Then [tex]\sqrt{6}[/tex] does not have any additional square roots to take out. So your final answer is 2i[tex]\sqrt{6[/tex].
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An equation that goes through (-2,10) and (-10,6)
Answer:
y-10= 1/2(x-2) --- point slope form
Step-by-step explanation:
Point slope form is:
y- y1=m(x-x1)
y1= 10
m= y2-y1/x2-x1
y2= 6
x2= -10
x1= -2
Using point slope form and defining the variables using the given coordinates, the equation can be written.
Answer:
y-6 = -1/3(x-10)
Step-by-step explanation:
Let's use point slope form! The form of this is y-y1 = m(x-x1) where m is the slope.We have points to use, so let's find the slope.
The slope is rise over run, so we take the difference in y and divide it by the difference in x. This gives us [tex](10-6)/(-2-10)[/tex], which simplifies to -1/3. Now we plug in a point, say (-2, 10) for x1 and y1, and -1/3 for the slope, which gives us y-6 = -1/3(x-10)
ALTERNATE WAY:
Another way you could approach this is to plug in both the points to solve for m. Plug in both the y-values(10, 6) for y and y1 and both the x-values(-2, -10) for x and x1.
This gives us [tex]10-6 = m(-2-10)[/tex], which simplifies to [tex]4 = -12m[/tex]. Dividing both sides by -12 gives m = -1/3, which is the slope. Whichever way makes most sense works!
I hope this helps!