Answer:
See below.
Step-by-step explanation:
We know that the equation [tex]4x+16y=36[/tex] is a true equation for a particular value of x.
Now, let's see what happens if we divide everything by 4. In other words:
[tex]\frac{4x+16}{4}=\frac{36}{4}[/tex]
Divide:
[tex]x+4=9[/tex]
So, we get [tex]x+4=9[/tex].
When we divided everything by 4, we used the division property of equality. Under this property, the equation remains the same even if we divided since we did the same thing to both sides of the equation.
Therefore, [tex]x+4y=9[/tex] is also true for the same value of x because it is just a simplified version of [tex]4x+16y=36[/tex].
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SOLVE!!!!!!!!!!!
Answer:
Range of the function is {7,5,2,0}
Step-by-step explanation:
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Answer:
{7, 5, 2, 0}
Step-by-step explanation:
The domain is essentially all the [tex]x[/tex] values of the function, where the range is the value of [tex]h(x)[/tex].
So in order to solve this we simply plug in each number into the equation and get:
[tex]h(x)=|-2-5| = |-7|=7[/tex]
[tex]h(x)=|0-5| = |-5|=5[/tex]
[tex]h(x)=|3-5| = |-2|=2[/tex]
[tex]h(x)=|5-5|=|0|=0[/tex]
Therefore the range is: {7, 5, 2, 0}
PLEASE ANSWER (100points)
When evaluating (6 x + 9) squared minus 5 for x = 1, the given value of 1 is substituted for what part of the expression?
the exponent
the constant
the variable
any numerical value
Answer:
the variable
Step-by-step explanation:
Given expression:
[tex](6x+9)^2-5[/tex]
When evaluating the expression for [tex]x=1[/tex], we need substitute 1 for the variable ([tex]x[/tex]) in the expression.
Evaluating the expression for [tex]x=1[/tex]:
[tex]\implies (6\cdot1+9)^2-5[/tex]
[tex]\implies (6+9)^2-5[/tex]
[tex]\implies (15)^2-5[/tex]
[tex]\implies 225-5[/tex]
[tex]\implies 220[/tex]
Answer:
Variable
As variable is x and we have to substitute x=1Step-by-step explanation:
Let's find the value
[tex]\\ \rm\Rrightarrow (6x+9)^2-5[/tex]
[tex]\\ \rm\Rrightarrow (6+9)^2-5[/tex]
[tex]\\ \rm\Rrightarrow 14^2-5[/tex]
[tex]\\ \rm\Rrightarrow 196-5[/tex]
[tex]\\ \rm\Rrightarrow 191[/tex]
Which polynomials are in standard form?
Choose all answers that apply:
(Choice A, Checked)
A
t^4-1t
4
−1t, start superscript, 4, end superscript, minus, 1
(Choice B, Checked)
B
-2t^2+3t+4−2t
2
+3t+4minus, 2, t, squared, plus, 3, t, plus, 4
(Choice C, Checked)
C
4t-74t−74, t, minus, 7
(Choice D)
D
None of the above
Answer:
a c
Step-by-step explanation:
Which model shows 764 = 4?
Identify the domain of the function show in the graph.
A.-1 <x <0
B.x>0
C.x is all real numbers.
D.-1 <x<1
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[tex]
x \: \: is \: \: all \: \: real \: \: numbers.[/tex]
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Thus the correct answer is (( C )) .
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On the way to visit my aunt, I left my house and drove 15 miles up the freeway before remembering I left my wallet at home. I immediately exited the freeway and headed back in the opposite direction toward my house. However, 3/4th of the way back, I ran out of gas and my car stopped on the side of the freeway. What is my displacement?
Answer:
3.75 miles
Step-by-step explanation:
Displacement is the shortest distance from the initial to the final position. So to calculate you do 15 - (3/4 of 15) = 3.75
Congruent Triangle are?
Answer:
Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as the three sides and three angles of another triangle.
Answer:
have exactly the same size and shape
Step-by-step explanation:
triangles are congruent when they have three sides
Courtney has 4/15 bags of flour o use in her donut shop. each bag of flour will make 12.5 batches of doughnut . how many batches of doughnuts willcourtney be ableto make
Answer: [tex]3\frac{1}{3}[/tex]
Solve the inequality
Answer:
t > 28
Step-by-step explanation:
[tex]\dfrac{t}{4} > 7[/tex]
Multiply both sides by 4:
[tex]\implies t > 28[/tex]
Please help with this question :)
CS = x, and since AB = BC = CD = DA = 1cm -> SD = 1 - x
We see that angle DSP = angle APQ (because they simultaneously equal to 90 when added angle DPS)
So, triangle DSP = triangle APQ (equal hypotenuse - square side and equal angle.)
Similarly, we can prove triangle SCE and QBE in the same way
So, all 4 of the triangles are equal to each other.
-> SD = CE = BQ = AP = 1-x
Calculate the area of 4 triangles : [ x(1-x) : 2 ] x 4 = x(1-x) x 2
Area (PQRS) = 1 - [ x(1-x)] x 2 = 1 - 2x + 2x(squared) = [tex]2x^{2} -2x + 1[/tex]
ii) Half area of PQRS = [tex]x^{2} -x+1[/tex]
= [tex]x^{2} -\frac{1}{2} x-\frac{1}{2} x + \frac{1}{2} = x(x-\frac{1}{2} )- \frac{1}{2}(x-\frac{1}{2} ) + \frac{1}{4} = (x-\frac{1}{2})^{2} + \frac{1}{4}[/tex]
We have : [tex](x-\frac{1}{2}) ^{2}[/tex]
has the smallest value of 0 -> The smallest half value of PQRS = 1/4 -> The smallest value of PQRS = 1/2
Suppose an exponential function can be written in the form y=ab^x, and we know the common ratio b and some point (ℎ,k). True or false: The function can also be written as y=k·b^x-h.
Answer:
true
Step-by-step explanation:
y = ab^x
the coordinates of the point are x and y values.
so, we can express "a" by these values :
k = ab^h
a = k/(b^h) = k × b^-h
now we use this identity in the original equation and get
y = k × b^-h × b^x = k×b^(x-h)
and that is exactly the same as the proposed form.
which of these is the correct way to write 21000 in words?
Answer:
Twenty-one Thousand
Step-by-step explanation:
If two witches were watching two watches, which witch would watch which watch?
Answer:
Wouldn't both of the witch watch whichever watch they felt like watching?
Step-by-step explanation:
Which point would not be a solution to the system of linear inequalities shown below?
Answer:
The coordinates (12,7) would NOT be a solution to the system of linear inequalities shown below.
Step-by-step explanation:
If you do the graphing and you look at all your options of coordinates, (12,7) is the only one that is not in the shaded areas or in the lines of the inequalities. Therefore, (12,7) should be the answer to that question. :)
which expression is equivalent to 2×-17?
is it
A) -17+2×
B) -2×+17
C) -2×-17
D) 17+2×
Answer:
B because based by what I'm seeing it is the same answer to the other equation. Which is -34.
Help me solve problem 7
Answer:
3-2r + 1 - 13
Step-by-step explanation:
3-2r + 1 - 13
Answers:
Compound inequality: 1 < x < 6Graph: Open hole at 1 and 6, shading in between (see diagram below)Interval notation: (1,6)=============================================
Work Shown:
3 < 2x+1 < 13
3-1 < 2x+1-1 < 13-1 .... subtract 1 from all sides
2 < 2x < 12
2/2 < 2x/2 < 12/2 ... divide both sides by 2
1 < x < 6
The value of x is between 1 and 6, excluding both endpoints.
Since we exclude both endpoints, the graph will have open holes at 1 and 6 on the number line. The shading is between the open holes. The graph is below.
Converting 1 < x <6 to interval notation leads to (1, 6)
The curved parenthesis in interval notation indicate "exclude the endpoint".
Tyler painted 9/2 square yards of wall area with 3 gallons of paint. How many gallons of paint does it take to paint each square yard wall?
Answer:
He would need 3/4 a gallon to paint the wall
Step-by-step explanation:
Using the fact that cos(52) = 0.6157, find the measure of angle B if sin(B) = 0.6157.
===============================================
Work Shown:
If cos(A) = sin(B), then A+B = 90, where A & B are both acute angles in degree form.
In this case, A = 52, so,
A+B = 90
B = 90-A
B = 90-52
B = 38
Telling us that
cos(A) = cos(52) = 0.6157
sin(B) = sin(38) = 0.6157
cos(52) = sin(38)
f [ x ] = [ x - 3] [ x + 8 ]
Answer:
f [ x ] = [ x - 3] [ x + 8 ] = x^2 + 5x - 24
Step-by-step explanation:
f (x)=[ x - 3] [ x + 8 ]
x [ x + 8 ] -3[ x + 8 ]
x^2 + 8x - 3x - 24
x^2 + 5x - 24
how do we calculate percentage that were increase
Answer:
here you go
Step-by-step explanation:
First: work out the difference (increase) between the two numbers you are comparing.
Increase = New Number - Original Number.
Then: divide the increase by the original number and multiply the answer by 100.
% increase = Increase ÷ Original Number × 100.
Which interval on the graph could be described as linear constant?
Find the roots of the equation 9x^2-1-(3x -2)^2=0
Answer: 5/12
Step-by-step explanation:
What is 1/4 of a 3.5 radius of a circle?
Answer:
Let us divide the circle into 4 equal parts because they have told that 1/4 th part so there are 4 equal parts because,fractions represent equal parts of a whole or a collection.
Let us take a circle with centre 'O'
Now, the 1/4th part of circle is a sector with angle 90° & radius 3.5cm
We can find the area of sector in 2 methods
Method 1 :
Formula :
Here , r is radius & θ is the angle in sector where θ is measured in degrees
Hence , area of sector = 9.6cm²
Method 2 :
Formula:
Here , r is radius & θ is angle in sector where θ is measured in radians
First we have to convert 90° into radians
We know that π radians = 180°
90 ° = π/2 radians
Substituting
Hence , area of sector = 9.6 cm²
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Can somebody help me solve this The diameter of a cylinder is 1 yd. The height is 12 yd. What is the volume of the cylinder type you answer with yards
Answer:
9.42
Step-by-step explanation:
Volume of cylinder= πr^2h
3.14 × 0.5 × 0.5 × 129.42 cube.ydAnswer:
37.68 yd
Step-by-step explanation:
= [tex]\pi[/tex]r²h
= (3.14)(1)²(12)
= 3.14 x 1 x 12
= 3.14 x 12
= 37.68 yd
Addison has a balance of $3,450 on her credit card that has an APR of 18%. She currently pays the minimum monthly payment of $86. 25. If Addison wants to pay off her balance in 24 months, determine the monthly payments she would need to make. Choose the following modification with the least cuts to her current expenses that will allow Addison to pay off her balance in 24 months. Income Wages $2,278. 00 Expenses Rent $950. 00 Utilities $232. 45 Food/Clothes $445. 00 Entertainment $270. 00 Car $200. 00 Credit Card $86. 25 Cell Phone $77. 89 Net Income $16. 41 a. Addison can eliminate $73 from Food/Clothes and $100 from Entertainment. B. Addison can eliminate $45 from Food/Clothes and $41 from Entertainment. C. Addison can eliminate $25 from Food/Clothes and $22 from Entertainment. D. The minimum payment is enough to pay off the balance within 24 months.
Addison needs to cut $45 from Food/Clothes and $41 from Entertainment, to pay the revised monthly payment.
It is given that
Addison has a balance of $3,450 on her credit card.
APR = 18%
Current monthly payment = $86.25
She wants to choose a monthly payment for 24 months.
So for 24 months,
A revised monthly payment using formula,
[tex]M = \frac{P.\frac{R}{12}. (1+\frac{R}{12} )^N }{(1+\frac{R}{12})N -1}[/tex]
R = 0.18
P = 3450
N = 24
Revised montly payment M = $172.24
Current monthly payment = $86.25
Difference = $86
So, she needs to cut the expenses by $86
If she cut $45 from Food/Clothes and $41 from Entertainment, she can easily pay the revised monthly payment.
Therefore, Addison needs to cut $45 from Food/Clothes and $41 from Entertainment, to pay the revised monthly payment.
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You want to determine the probability that in a litter of 5 kittens, there will be more female than male kittens. Which describes one trial of a simulation you could use to model this problem?
The trial of stimulation that can model the probability of the gender of the kittens is tossing a coin five times and count the number of heads.
What is probability?Probability simply means the chance of the occurrence of an event. It's the numerical description of how likely an event will occur.
In this case, from the complete question, the trial of stimulation that can model the probability is to toss a coin five times and count the number of heads. The gender of the kittens can be allocated to the head or tail of the coin.
This is important to determine the probability that in a litter of 5 kittens, there will be more female than male kittens.
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Find the distance between the points.
(5 ,10) and (negative 3 ,10)
Answer:
8 unit difference x, stays the same on y
Step-by-step explanation:
5 to -3 = 8 units
NEED HELP ASAP!!!!!!!!!
Steve has 12 biscuits in a tin.
There are 7 digestive, 2 chocolate and 3 ginger biscuits.
Steve takes two biscuits at random from the tin.
Work out the probability that he chooses two different types of biscuits.
Answer:
There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.
The probability of choosing a digestive then a chocolate is as follows:
7/12 * 5/11 =0.265
The probability of choosing a chocolate then a digestive is as follows:
5/12*7/11 = 0.265
Therefore the combined probability is 0.53 or 53%
Probability of digestive and chocolate
7/12×2/11=14/132=7/66And
2/12×7/11=7/66Probability of digestive and ginger
7/12×3/11=21/132=7/44And
3/12×7/11=7/44Probability of ginger and chocolate
2/12×3/11=6/132=3/66=1/22What is the width of the prism?
2 ft
w
4 ft
Volume = 24 cubic feet
Answer:
3 ft
Step-by-step explanation:
(I assumed that this was a rectangular prism based on the dimensions given, but do correct me if I assumed incorrectly.)
The formula for finding the volume of a rectangular prism is: [tex]V=w*h*l[/tex]
In this case, we already know that the volume of the prism is 24, so we can plug 24 in for V:
[tex]24=w*h*l[/tex]
We also already know the height and the length because they gave it to us, so we can plug it in as follows:
[tex]24=w*2*4[/tex]
Then we can multiply 2 and 4 on the right side:
[tex]24=w*8[/tex]
Then, to get the w alone, we can divide by 8 on both sides:
[tex]3=w[/tex]
Now that gives us that the width of the rectangular prism is 3ft.
In a setting where a situation is described for which optimal parameters are sought, how do we develop a function that models the situation and use calculus to find the desired maximum or minimum
In order to develop a function that models the situation regarding the optimal parameters, the following are needed:
Introduce the variables.Find an equation relating to the variable.Maximize the quantity.Look that the critical points to determine the extrema.Wnat is a function?It should be noted that a function simply means the relation or expression that has to do with two or more variables.
In this case, to develop a function that models the situation regarding the optimal parameters, one has to introduce the variables and find an equation relating to the variable.
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