What is the gradient of the graph shown?
Answer:
gradient: 1.5
Explanation:
Take two points from the graph: (2, 0), (0, -3)
[tex]\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
So here given:
(x₁ , y₁) = (2, 0)(x₂ , y₂) = (0, -3)Inserting values
[tex]\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5[/tex]
15/16-4/6=
please help I could do this but I’m too lazy so please
in a survey of 200 students 120 were taking mathematics and 50 were taking speech what is the least number of students who could have been taking both courses.
A supermarket purchases chickens wholesale from a farm for $4 each. The store then marks up the chickens 50%. After 10:00 p.m., the supermarket marks down the price of the chickens by 50% to make sure they all sell before the store closes. Which statements are true about the price of a chicken?
The true statements are:
The marked up price of chicken before 10pm is $6
The 50% mark down is taken off the marked up price
What are the true statements?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Price after the mark up= (1 + mark up) x initial price
1.50 x 4 = $6
Price after the mark down = (1 - percentage mark down) x price after mark up
0.50 x $6 = $3
Here are the options:
The marked up price of chicken before 10pm is 6
The 50% mark down is taken off the marked up price
The chickens sell for $4 after 10pm
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IF THREE DIAGONALS ARE DRAWN INSIDE A HEXAGON WITH EACH ONE PASSING THROUGH THE CENTER POINT OF THE HEXAGON, HOW MANY TRIANGLES ARE FORMED?
Answer: 6 triangles
Step-by-step explanation:
hope this helps :)
It's the computer seice can u help me
Answer:
I can help you, just tell me what it is.
Step-by-step explanation:
Step 1: Tell me the problem
Step 2: Wait for a response.
Answer:
yes it can help in some ways I think
Estimate the decimal 61.33 + 53.482 by first rounding each number to nearest whole number
Answer:
it's
answer
is
32.36
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[tex] \sf{x {}^{2} + 6x + 7 = 0 }[/tex]
x² + 6x + 7 = 0
help please it's due today :(
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]
[tex] \bold{ \blue{Answer:} \sf{x = \sqrt{2} - 3, - \sqrt{2 } - 3 }}[/tex]
[tex]\bold{Step \: \: by \: \: step \: \: explanation }[/tex]
1: The expression x² + 6x + 7 fits the form a x²+ bx + c Let's complete the square, where:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{ b = 6} \\ \sf{c = 7}[/tex]
2: Enter the constant k, which is 9 in our case.
[tex] \sf{x {}^{2} + 6x {}^{} + 9 - 9 + 7}[/tex]
3: Use Sum Square (a + b) ² = a² + 2ab + b².
[tex] \sf{(x + 3) {}^{2} - 9 + 7}[/tex]
4: Simplify
[tex] \sf{(x + 3) { }^{2} - 2}[/tex]
5: Substitute the above back into the original equation.
[tex] \sf{( x + 3) {}^{2} - 2 = 0}[/tex]
6: Add 22 to both sides.
[tex] \sf{(x + 3) {}^{2} = 2}[/tex]
7: Take the square root of both sides.
[tex] \sf{x + 3 = ± \sqrt{2}} [/tex]
8: Divide the problem into these 2 equations.
[tex]\sf{x + 3 = \sqrt{2} } \\ \: \: \: \: \: \sf{x + 3 = - \sqrt{2} }[/tex]
9: Solve the 1st equation:
[tex] \sf{ x + 3 = \sqrt{2} } \\ \sf{x = \sqrt{2} - 3 }[/tex]
10: Solve the 2nd equation.
[tex] \sf{ x + 3 = - \sqrt{2} } \\ \sf{x = - \sqrt{2} - 3 } [/tex]
11: Collect all the solutions.
[tex] \sf{x = \sqrt{2} - 3, - \sqrt{2} - 3 }[/tex]
I hope I've helped : )
Find the least common multiple (LCM) of the polynomials z² + 5z + 6 and zx + 2x − 8z-16
Answer:
(z+2)(z+3)(x-8)
Step-by-step explanation:
z² + 5z + 6 can be factored into (z+3)(z+2)
zx + 2x − 8z-16 can be factored into (x-8)(z+2)
the LCM would be (z+2)(z+3)(x-8)
if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first
Please give answer to this problem
The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
Conjugate of a radicalThe conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.
The given roots are
[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]
They have the same numbers but opposite signs in the middle.
Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
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Which equation represents the standard form of the equation y= (x + 3)² - 4?
A. y=x² + 3x-4
B. y=x2² +6x+5
C. y=x² + 6x-4
D. y=x2²+3x+5
Answer:
The answer is B. [tex]y = x^2 + 6x + 5[/tex]
Step-by-step explanation:
Because [tex]y = (x + 3)^2 - 4 = x^2 + 6x + 9 - 4 = x^2 + 6x + 5[/tex]
So the answer in this question is B.
A farmer needs to mix 8 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer will the farmer need to make a mix that contains 80 pounds of soil? ( Remember- 16 ounces = 1 pound)
4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
What is Ratio ?The relationship between two things is called Ratio. It is written in p:q form.
It is given that
For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.
=8/16 = 0.5 pounds of fertiliser
The ratio is 10 : 0.5
Suppose he mixes x pounds of fertilizer for 80 pounds of soil
to determine x
The ratio is 80 : x
As they are in Proportion
10 / 0.5 = 80 /x
x = 80 * 0.5 /10
x = 4 pounds
Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
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Which of the following is a characteristic of all parallelograms?
A. All pairs of consecutive angles are complementary.
B. Both pairs of opposite sides are parallel.
C. The diagonals are congruent.
D. The diagonals are perpendicular.
Edward Nigma is installing square tiles in his bathroom. The blueprint above is a scaled drawing of the tile pattern to be used. If the total area of the shaded region is 22 ft^2, what is the total floor area of the bathroom?
Answer:
H. 99 ft²
Step-by-step explanation:
Area is proportional to the number of tiles.
ProportionThe total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...
total area / shaded area = total tiles / shaded tiles
total area / (22 ft²) = 54/12 . . . . . use given numbers
total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²
The total floor area of the bathroom is 99 square feet.
your family is driving from cincinnati to st louis. the graph relates your distance from st.louis d in miles and travel time h (in hours). The equation of the line is d=360-60h
The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.
What is a distance-time graph?A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.
The slope-intercept form is
y= mx+b−⋯(1)
The y-intercept is 360
⇒b = 360; and m = −60
Substituting the value of m = −60
and b = 360
in (1) above,
⇒y = −60x +360
The x-intercept is
y = 0,
⇒0= −60x+360
hence, x=6
The y-intercept is
x=0
⇒y=−60(0)+360
⇒y=360
In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and
The y - intercept is the distance between Cincinnati and St. Louis.
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find the volume of the sphere
Answer:
523.6
Step-by-step explanation:
Volume of sphere= 4/3πr^3
V=4/3π(5^3)
V=523.6 (correct to 1 dp)
which of the following ordered pairs satisfies the following linear pairs? 3x+2y=-2 x+2y=2
Answer:
-2
Step-by-step explanation:
you will group the like terms and add and subtract the remaining digits
PLEASE HELP
Graph the following exponential function. Show work in how you find the y intercept, talk about the end behavior, and state if it is a growth or decay function. See image.
The y-intercept of the function is -9,25
How to graph the function?The function is given as:
[tex]y = -5(.8)^{x - 1} - 3[/tex]
See attachment for the graph of the function
From the graph, we have the following highlights:
y-intercept = -9,25As x increases, y approaches -3As x decreases, y approaches negative infinityRead more about exponential functions at:
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Tierra, Nico, and Alex had $ 865 altogether.
Tierra spent 2/5 of her money. Nico spent $40,
and Alex spent twice as much as Tierra. If the 3
friends had the same amount of money left, how
much money did Alex have in the beginning?
Alex had $444.231 in the beginning.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let, x = the money Tierra had in the beginning
y = the money Nico had in the beginning
z = the money Alex had in the beginning
Tierra, Nico and Alex had $865 altogether
x + y + z = 865
Tierra spent 2/5 of her money and now she has: x - (2/5)x = 3x/5 left
Nico spent $40 and now has y - 40 left
Alex spent twice as much as Tierra and now has z - 2(2/5)x = z - 4x/5 left
the three friends had the same amount of money left
3x/5 = y - 40
y - 40 = z - 4x/5
by solving the system of equations
x + y + x = 865
3x/5 = y - 40
y - 40 = z - 4x/5
we find
x= $317.308
y = $230.385
z = $444.231
Alex had $444.231 in the beginning.
Hence, Alex had $444.231 in the beginning.
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You want to put in a new concrete patio behind your house. You want it to be 12 ft wide by 14 ft long and it needs to be eight inches thick. You know that an 80 lb. bag of concrete yields 0.60 cubic feet. How many 80 lb. bags of concrete will you need for your patio? (round to the nearest whole number , if needed )
Considering the volume of the rectangular prism, you will need 2240 bags will be needed for the patio.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, the dimensions are:
l = 14 ft, w = 12 ft, h = 8 ft.
Hence the volume is:
V = 14 x 12 x 8 = 1344 ft³
Each bag yields 0.6 ft³, hence the number of bags is:
n = 1344/0.6 = 2240 bags.
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If the Federal Reserve sets the reserve rate to 4%, what is the resulting money
multiplier?
Answer:
The money multiplier is the ratio of money supply to the money base. The money base is the sum of currency in circulation and reserves held by commercial banks.
The reserve rate is the percentage of deposits that commercial banks must hold in reserve.
If the reserve rate is 4%, the money multiplier is 10.
Step-by-step explanation:
A. In 2000, the population of a country was approximately 5.89 million and by 2050 it is projected to grow to 10 million.
Use the exponential growth model A = Ao ekt, in which t is the number of years after 2000 and Ao is in millions, to find
an exponential growth function that models the data.
B. By which year will the population be 11 million?
A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]
B. Using the function, the population will be 11 million by 2059.
What is the exponential growth function for the population?The function is given by:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the population in 2000.k is the exponential growth rate, as a decimal.t is the number of years after 2000.Item a:
We have that:
A(0) = 5.89, A(50) = 10.
We use this to find k, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]10 = 5.89e^{50k}[/tex]
[tex]e^{50k} = \frac{10}{5.89}[/tex]
[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]
[tex]50k = \ln{\frac{10}{5.89}}[/tex]
[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]
k = 0.0106.
Hence the equation is:
[tex]A(t) = 5.89{0.0106t}[/tex]
Item b:
We have to solve for t when A(t) = 11, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]11 = 5.89e^{0.0106t}[/tex]
[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]
[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]
[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]
[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]
t = 58.9
Rounding up, the population will be of 11 million in 2059.
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A ball is dropped off a high cliff, and 2 s later another ball is thrown vertically downward with an initial speed of 30 ms¹. How long will it take the second ball to overtake the first?
HELP FAST PLEASEE
(05.05 MC)
What are the measures of Angles a, b, and c? Show your work and explain your answers.
(PLEASE EXPLAIN WELL)
Answer:
a=30,b=60,c=105
Step-by-step explanation:
a = 30 vertical angle therom
b = 180-120 = 60 using triangle sum therom
c = 180-75 = 105 because a line is always 180 degrees
find x
pls help !!!
Answer: Sorry If I'm wrong but if you are asking for the missing angle on the bottom, I think it is 30 degrees.
Step-by-step explanation: All the angles in a triangle add up to 180 degrees. we already know that one is 50 degrees. The 2nd angle is a bit wider than a 90 degree angle, and the third angle is 30 degrees, so 50 degrees + 100 degrees + 30 degrees add up to 180. So, I think your answer would be 30 degrees.
Answer:
x = 25
Step-by-step explanation:
I added a drawing down below to guide you through!
First, we should remember, that if a line crosses two parallel lines, then the adjacent angles will have the same value. Since Line D and Line E are parallel and line BC is crossing it, angles ABC and 105 will be the same.
Now that we know one of the missing angles, we can find x easily!
All angles in a triangle add up to 180, so in this case, the equation will be: 50 + 105 + x = 180.
155 + x = 180
x = 25.
So x will equal to 25 degrees!
Elaine had StartFraction 5 Over 8 EndFraction of a pizza left after lunch. She told 5 of her friends that they could share the rest. What fraction of the pizza did each of her friends get if they split it evenly?
The fraction of pizza each of her friends get if they split it evenly is 1/8
Division of fractionQuantity of pizza Elaine has = 5/8Number of Elaine friends = 5Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends
= 5/8 ÷ 5
= 5/8 × 1/5
= (5 × 1) / (8 × 5)
= 5/40
= 1/8
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Determine the period.
Using it's concept, it is found that the period of the function is of 20 units.
What is the period of a function?The period of a function is given by the distance between it's repetitions.
Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.
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What is the 25th term given a₁ = 8 and r = 2?
Answer:
134217728
Step-by-step explanation:
The geometric sequence formula is:
[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]
We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:
[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]
Therefore, the 25th term of sequence is 134217728
What are the domain and
range of the function below?
Answer:
2nd answer option
Step-by-step explanation:
the domain is the interval or set of valid x values. the range is the same for valid y values.
so, what is the smallest x value we see in the functional graph ?
x = 0
there is no functional value for any x smaller than that.
and then the function goes on and on to the right in all eternity. that means it goes to infinity.
so, domain = [0, infinity)
please consider the round bracket at the end, because "infinity" is not a number.
now for the range and the y values.
in this case I start to ask for the largest y value.
y = 4
for no x value do we get a larger y value.
but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).
so, the range = (-infinity, 4]
"-infinity" is also not a number and therefore not included (hence the round bracket).
A line with a slope of 3 passes through the points (-10, z) and (-8, 8). What is the value of
z?
Z=?
Answer:
z=2
Step-by-step explanation:
We are given that a line has a slope of 3.
The line passes through the points (-10, z) and (-8, 8)
We want to find the value of z.
To do that, we can calculate the slope.
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Even though we already have 2 points, let's label their values to avoid any confusion.
[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]
Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.
[tex]\frac{8-z}{-8--10}[/tex] = 3
We can simplify this first.
[tex]\frac{8-z}{-8+10}[/tex] = 3
[tex]\frac{8-z}{2}[/tex] = 3
We can multiply both sides by 2 to clear the fraction and make it easier to calculate.
2([tex]\frac{8-z}{2}[/tex]) = 2(3)
Multiply.
8 - z = 6
Subtract 8 from both sides
-z = - 2
Multiply both sides by -1.
-1(-z) = -1(-2)
Multiply.
z = 2