ANSWER
[tex]x ^{2} = - 4(y - 1).[/tex]
EXPLANATION
Since the parabola has the (0, 0) and the directrix at y=2.
The equation is of the form
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is half way between the directrix and the focus.
The vertex will be at (0,1)
and is the distance from the vertex to the focus which is 1.
[tex]{(x - 0)}^{2} = - 4(1)(y - 1)[/tex]
[tex]x ^{2} = - 4(y - 1)[/tex]
Help please asap!
Allen has a recipe for a pitcher of fruit punch that requires 3 and 1/2 cups of pineapple juice. Which question about the recipe is best modeled with a division expression?
How much pineapple juice is needed to make 5 pitchers of punch?
How much punch can be made from 5 cups of pineapple juice?
How many cups of fruit punch does the recipe make if there are a total of 12 cups of other ingredients?
How many cups of other ingredients are needed if the recipe makes a total of 12 cups of fruit punch?
Answer:
I think the answer is "How much pineapple juice is needed to make 5 pitchers of punch?"
Step-by-step explanation:
I believe it's the second one, from 5 cups of juice, since you would divide 5 by 3 1/2
Find the height of a rectangular prism if the surface area is 3,834 square meters and the length of the base is 14.2 meters and the width of the base is 15 meters
Answer:
The height of the rectangular prism is [tex]58.36\ m[/tex]
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the rectangular base
P is the perimeter of the rectangular base
H is the height of the prism
Find the area of the base B
[tex]B=14.2*15=213\ m^{2}[/tex]
Find the perimeter of the base P
[tex]P=2(14.2+15)=58.4\ m[/tex]
we have
[tex]SA=3,834\ m^{2}[/tex]
substitute and solve for H
[tex]SA=2B+PH[/tex]
[tex]3,834=2(213)+(58.4)H[/tex]
[tex]3,834=426+(58.4)H[/tex]
[tex]H=(3,834-426)/(58.4)[/tex]
[tex]H=58.36\ m[/tex]
need the answer please.
Answer: Option A.
Step-by-step explanation:
You need to remember the Quotient property of powers, which states the following:
[tex]\frac{p^m}{p^n}=p^{(m-n)}[/tex]
Then, given the expression [tex]\frac{a^3b^2}{a^2b}[/tex], you need to apply this property to simplify this expression.
Therefore, you get:
[tex]=a^{(3-2)}b^{(2-1)}\\\\=a^1b^1\\\\=ab[/tex]
As you can observe, this matches with the option A.
Answer:
The correct answer is option A. ab
Step-by-step explanation:
Points to remember
Identities
Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾
X⁻ᵃ = 1/Xᵃ
Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾
To find the correct answer
It is given that,
a³b²/a²b
By using above identities we can write,
a³b²/a²b = a⁽³ ⁻ ²⁾b⁽² ⁻ ¹⁾
= a¹b¹ = ab
Therefore the answer is ab
The correct option is option A. ab
Am a 5 digit number My tens digit is the sum of my hundreds digit and thousands digit. My tens digit is twice my one digit. My hundreds digit is 1 more than zero. My thousands digit is seven times my hundreds digit. My ten thousands digit is the same as my ones digit.
Answer:
47184
Step-by-step explanation:
1+0=1
7*1=7
7+1=8
4*2=8
Please help me with this
Answer: y=12.287
Step-by-step explanation:
Answer:
y = 12.3 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle to solve for y
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]
Multiply both sides by 15
15 × cos35° = y, thus
y ≈ 12.3 cm
At Bayside High School, 55% of the student body are boys. Thirty-five percent of the boys are on honor roll, and 40% of girls are on honor roll. What percent of the student body is on honor roll? Round to the nearest percent. A) 18% B) 19% C) 37% D) 63%
Answer:
37%
Step-by-step explanation:
35% of 55% is equal to the percent of boys on honor roll in the student body.
100 - 55 = 45%, which is the percent of girls in the student body.
40% of 45% is equal to the percent of girls on honor roll in the student body.
35% * 55% = 19.25%
40% * 45% = 18%
Adding them up, we get:
19.25 + 18 = 37.25%
Round it to the nearest percent.
37.25 --> 37%
Rounded to the nearest percent, 37% of the student body is on honor roll.
A recipe asks that the following three ingredients be mixed together as follows: add 1/2 of a teaspoon of baking soda, and every 1/4 of a teaspoon of salt. Which of the following rates is a unit rate equivalent to the ratios shown above?
A. 1 teaspoon of baking soda per 2 teaspoons of salt
B. 1/2 teaspoon of salt per 1 teaspoon of baking soda
C. 2 teaspoons of salt per 1 teaspoon of baking soda
D. 2 teaspoons of salt per 1 cup of flour
Answer:
B. 1/2 tespoon of salt per 1 teaspoon of baking soda.
Step-by-step explanation:
If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.
Answer:
B. 1/2 tespoon of salt per 1 teaspoon of baking soda.
Step-by-step explanation:
If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.
Harper wrote the expression 15-6+7 to represent "15 minus the sum of 6 and7 evaluate 15 -6+7 and then explain why Harper expression is incorrect
Answer:
15-6+7=16. The expression should be written as 15-(6+7).
Step-by-step explanation:
The sum of 6 and 7 is (6+7). 15 minus the sum of 6 and 7 would then be written as 15-(6+7), because this way you subtract the entire sum from 15. The expression 15-6+7 just subtracts 6 from 15, then adds 7 onto this number, which is not the same thing as subtracting 6+7 from 15.
The expression 15 - 6 + 7 does not represent '15 minus the sum of 6 and 7'. The correct expression should be 15 - (6 + 7). Evaluating Harper's expression gives 16, while the correct expression gives 2.
Explanation:The expression 15 - 6 + 7 does not properly relay the concept of '15 minus the sum of 6 and 7'. To correctly express this idea, parentheses should be used: 15 - (6 + 7).
To evaluate Harper's expression, one would operate in the order of their entry: 15 - 6 is 9, then, add 7 to 9 and the result is 16.
However, in the correct expression 15 - (6 + 7), the sum of 6 and 7 equals 13 is computed first, according to the order of operations (PEMDAS/BODMAS). Then, subtract this sum from 15 to get 2.
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If [tex]f(x) = 2x^2+5\sqrt{(x-2)}[/tex] complete the following statement:
f(6) = ____
Answer: 82
Simply pug in 6 for [tex]x[/tex]
[tex]2(6)^2+5\sqrt{(6-2)} \\72+5\sqrt{4} \\72+5(2)\\72+10=\\82[/tex]
Hope this helps and have a great day!!!
[tex]Sofia[/tex]
For this case we have a function of the form [tex]y = f (x).[/tex]
Where:[tex]f (x) = 2x ^ 2 + 5 \sqrt {x-2}[/tex]
We must find the value of the function when x = 6, that is, f (6):
Then, replacing the value of "x"[tex]f (6) = 2 (6) ^ 2 + 5 \sqrt {6-2}\\f (6) = 2 * 36 + 5 \sqrt {4}\\f (6) = 72 + 5 (2)\\f (6) = 72 + 10\\f (6) = 82[/tex]
So, [tex]f (6) = 82[/tex]
ANswer:
[tex]f (6) = 82[/tex]
calculate the value of c
Answer:
14.2
Step-by-step explanation:
For this case, we have to define trigonometric relations in a rectangle triangle that, the tangent of an angle is given by the leg opposite the angle on the leg adayed to it. According to the figure we have:[tex]tg (35) = \frac {c} {5}\\c = tg (35) * 5\\c = 0.70020754 * 5[/tex]
[tex]c = 3.5010377[/tex]
Answer:
Option D
At a game show there are 8 people ( including you and your friend in the front row.
Answer:
c because is right
Step-by-step explanation:
Find a possible phase shift for the sinusoidal graph shown.
3.2 right
7.2 right
0.8 left
0.4 right
The phase shift is 7.2 right
jacob has golf scores of 120, 112, 130, 128, and 124. He wants to have an average golf score of 118. What is the first step in determining what Jacob needs to score in his next golf game?
a. Find the sum of all the numbers in the problem, 120+112+130+128+124+118.
b. Find the average score for the five golf games that Jacob has played.
c. Determine the number of points that he needs in his next golf game.
d. Determine how many total points are needed to have an average of 118.
Answer:
d
Step-by-step explanation:
Here the sum of 5+1 golf scores, divided by 6, must be 118:
120 + 112 + 130 + 128 + 124 + x
--------------------------------------------- = 118
6
Here, 120 + 112 + 130 + 128 + 124 + x is the total number of points needed to have an average of 118. Answer d is the correct one.
Answer:
Jacob has golf scores of 120, 112, 130, 128, and 124.
He wants to have an average golf score of 118.
a. Find the sum of all the numbers in the problem, 120+112+130+128+124+118.
[tex]120+112+130+128+124+118[/tex]
= 732
b. Find the average score for the five golf games that Jacob has played.
[tex]\frac{120+112+130+128+124}{5}[/tex]
= 122.8
c. Determine the number of points that he needs in his next golf game.
Jacob will need a golf score of 94 in next game to achieve the average of 118.
Total score = [tex]120+112+130+128+124+x[/tex]
number of matches = 6
Average score = [tex]\frac{614+x}{6}=118[/tex]
[tex]614+x=708[/tex]
[tex]x=708-614[/tex]
x = 94
d. Determine how many total points are needed to have an average of 118.
Total points needed are [tex]614+94=708[/tex]
problem is in the pictures
Answer:
(-5, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}6x+3y=-21&\text{divide both sides by (-3)}\\2x+5y=5\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-y=7\\2x+5y=5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=12\qquad\text{divide both sides by 4}\\.\qquad\qquad y=3\\\\\text{Put it to the second equation:}\\2x+5(3)=5\\2x+15=5\qquad\text{subtract 15 from both sides}\\2x=-10\qquad\text{divide both sides by 2}\\x=-5[/tex]
A triangle is acute provided all the angles have a measure of less than 90 degrees.
A.Conjunction
Step-by-step explanation:
The scale of quantities should always start at zero. True False
Answer:
The correct answer option is true.
Step-by-step explanation:
We are given the following statement and we are to tell if its true or not:
'The scale of quantities should always start at zero'.
To get the correct and accurate measure of any quantity, the scale of that very quantity should always start from zero.
If it does not start from zero, there can be errors in the measure. Therefore, the given statement is true.
Please help me with this
first use the formula it is 1/3 × base area × height =volume of pyramid
so we just need to replace some of the information given in the statement to our formula
so it's going to be,i'll let the height as unknown X
128=1/3 × (8 × 8) × X
so it's going to be
128=64/3X
so X is 128 ÷ 64/3=6cm
Answer:
I'm Sure the answer is 6 cm.
Danny, Amira, and Tyler shared a sum of money in the ratio 6 : 4 : 3. Amira used 1/2 of her money to buy a watch that costs $30, and Danny gave 1/3 of his money to his sister. How much money did they have left altogether?
Answer:
$135
Step-by-step explanation:
step 1
Let
x----> amount of money shared by Danny
y----> amount of money shared by Amira
z----> amount of money shared by Tyler
we know that
x/y=6/4 ----> x=1.5y ----> equation A
x/z=6/3 ---> z=x/2 ---> equation B
Amira used 1/2 of her money to buy a watch that costs $30
so
(1/2)y=$30
y=$60
Substitute the value of y in the equation A and solve for x
x=1.5y ----> x=1.5(60)=$90
Substitute the value of x in the equation B and solve for z
z=x/2 -----> z=90/2=$45
so
The amount of money shared by Danny was $90
The amount of money shared by Amira was $60
The amount of money shared by Tyler was $45
step 2
Find out how much money they have left in total.
Danny gave 1/3 of his money to his sister ----> left --> (2/3)($90)=$60
Amira used 1/2 of her money -----> left --> $60/2=$30
Tyler --------> left ----> $45
Total=$60+$30+$45=$135
Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.
The question deals with dividing a sum of money among Danny, Amira, and Tyler by the ratio 6 : 4 : 3, calculating how much Amira spent, and how much Danny gave away.
Let's assume the total sum of money is M, shared according to the ratio 6x : 4x : 3x, which means:
Danny has 6x of MAmira has 4x of MTyler has 3x of MSince Amira spent 1/2 of her money on a watch costing $30, we can deduce:
(1/2) × 4x = $302x = $30x = $15Therefore, the total sum of money M is 6x + 4x + 3x = 13x, which gives us:
M = 13 × $15M = $195Danny gave away 1/3 of his share to his sister, which is:
(1/3) × 6x = 2x2x = 2 × $152x = $30After spending and giving money away, they have left:
Danny: 6x - 2x = 4x = $60Amira: 4x - (1/2) × 4x = 2x = $30Tyler: 3x = $45Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.
The perimeter of a rectangle is 36 inches. If the width of the rectangle is 6 inches, what is the length?
Perimeter = 2w+2l. 2(6)+2l = 36 subtract 12 to get 2l=24 then divide by 2 so the length is 12 inches
The admission fee at fair is $1.50 for children and $4 for adults. On a certain day 2200 people enter the fair and $5050 is collected. Write the system of equations for this scenario if a is the number of adults and c is the number of children
1.50c +4A =2200$ would be the correct awnser
During a hike,3 friends equally shared 1/2 pound of trail mix .What amount of trail mix,in pounds,did each friend receive?
[tex]\bf \cfrac{1}{2}\div 3\implies \cfrac{1}{2}\div \cfrac{3}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{3}\implies \cfrac{1}{6}[/tex]
3 friends equally shared 1/2 pound of trail mix, during the hike.
Total quantity of trail mix = 1/2 pound
Quantity shared by each friend is 1/3 rd of the trial mix
= 1/3 * 1/2 pound
= 1/6 pound
Therefore, during the hike, each friend shared 1/6 pound of the trail mix.
Hope this helps ..!!
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Find the area of the circle.. PLEASE HELP
Answer:
The area is 154 cm²
Step-by-step explanation:
Since the formula for the area of a circle is pi times the radius squared, divide the diameter in half to get the radius (7). Then, square the radius (49). Next, multiply that by pi (153.938). After that round to the nearest whole number (154). Hope that helps!
-Kyra
Answer:
A = 154 cm^2
Step-by-step explanation:
We know the diameter of the circle
We need to find the radius
d = 2r
14 = 2r
Divide by 2
14/2 = 2r/2
7=r
Now we can use the formula for area
A = pi r^2
A = pi (7)^2
A = 49pi
Replace pi with 3.14
A = 49(3.14)
A = 153.83
Rounding to the nearest whole number
A = 154 cm^2
Find the volume of the prism.
A. 168 units^3
B. 210 units^2
C. 210 units^3
D. 168 units^2
ANSWER
A. 168 units^3
EXPLANATION
The volume of a pyramid is given by the formula:
[tex]Volume= base \: area \: \times \: vertical \: height[/tex]
Area of triangular base
[tex] = \frac{1}{2} bh[/tex]
[tex] = \frac{1}{2} \times 8 \times 6[/tex]
[tex] = 24 \: {units}^{2} [/tex]
The height of the prism is 7 units.
The volume
[tex] = 24 \times 7[/tex]
[tex] = 168 {units}^{3} [/tex]
Answer:
168
Step-by-step explanation:
claire thinks that if she draws a parallelogram with 2 congruent sides, it must be a rhombus. Jacob that she would need to draw a parallelogram with at least 3 congruent sides before she could be sure it was a rhombus. who is correct, if anyone, and why?
Answer:
See below.
Step-by-step explanation:
Neither are correct: a parallelogram with 3 congruent sides could be a square. Also a parallelogram will have 2 pairs of congruent sides but it does not have to be a rhombus.
Answer with explanation:
A rhombus has all sides equal that is four congruent sides.
Statement of Claire
If she draws a parallelogram with 2 congruent sides, it must be a rhombus.
As Rhombus has four Congruent sides.2 Congruent sides does not Guarantee that the Parallelogram will be Rhombus.If Adjacent sides are congruent than Claire statement will be right otherwise not.
Statement of Jacob
If Jacob draws a parallelogram with at least 3 congruent sides ,it must be a rhombus.
Yes ,three congruent sides Guarantees that Parallelogram will be a rhombus because in a Parallelogram opposite sides are equal to each other.So congruency of three sides in a Parallelogram guarantees that this Parallelogram will be a rhombus.
So, we can Conclude that Jacob is correct.
What is the value of tan theta in the unit circle below? A.1/2 B.sqrt3/3. C.sqrt3/2. D.sqrt3
if you don't have a Unit Circle, this is a good time to get one, you can find many online.
Check the picture below.
Answer:
B . √3/3.
Step-by-step explanation:
Tan theta = opposite side/ adjacent
= 1/2 / √3/2
= 1/2 * 2/√3
= 1 /√3
= √3/3.
Suppose \nabla f (x,y) = 3 y \sin(xy) \vec{i} + 3 x \sin(xy)\vec{j}, \vec{f} = \nabla f(x,y), and c is the segment of the parabola y = 3 x^2 from the point (1,3) to (4,48). then
I'll assume you're supposed to compute the line integral of [tex]\nabla f[/tex] over the given path [tex]C[/tex]. By the fundamental theorem of calculus,
[tex]\displaystyle\int_C\nabla f(x,y)\cdot\mathrm d\vec r=f(4,48)-f(1,3)[/tex]
so evaluating the integral is as simple as evaluting [tex]f[/tex] at the endpoints of [tex]C[/tex]. But first we need to determine [tex]f[/tex] given its gradient.
We have
[tex]\dfrac{\partial f}{\partial x}=3y\sin(xy)\implies f(x,y)=-3\cos(xy)+g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y}=3x\sin(xy)=3x\sin(xy)+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C[/tex]
and we end up with
[tex]f(x,y)=-3\cos(xy)+C[/tex]
for some constant [tex]C[/tex]. Then the value of the line integral is [tex]-3\cos192+3\cos3[/tex].
This question involves vector calculus and requires finding the line integral along a segment of a parabola.
Explanation:The given question is related to the subject of Mathematics. It involves the application of vector calculus and requires analyzing a segment of the parabola using vector analysis and gradient fields.
To find the ∫f vector, we need to evaluate the partial derivatives of f(x, y) and multiply them with the corresponding unit vectors. Plugging in the given values, we find that ∫f = 3y·sin(xy)·ᵢ + 3x·sin(xy)·ᵢ.
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If two times a certain number is added to 11, the result is 20.
Which of the following equations could be used to solve the problem?
2x = 20
2(x + 11) = 20
2x = 11 + 20
2x + 11 = 20
Answer:
2x + 11 = 20
Step-by-step explanation:
let's start by assigning the variable x to certain number , if we two times a certain number we got 2x, and if we added to 11 the result is 20. So, ordering the equation we will obtain:
2x + 11 = 20
ANSWER
2x+11=20
EXPLANATION
Let the number be x.
Two times this number is 2x
If 11 is added to two times the number, the expression becomes;
2x+11
If the result is 20, then we equate the expression to 20 to get:
2x+11=20
The correct choice is the last option;
Help! Help! Help!
What is the distance between the vertices of the graphs corresponding to y = (x - 3)2 and y = x2 - 4?
A.0
B.1
C.5
D.13
Answer:
C.5
Step-by-step explanation:
y = (x - 3)^2
This is in the form y= a(x-h)^2 +k where (h,k) is the vertex
The vertex is at (3,0)
y = x^2 - 4
This is in the form y= a(x-h)^2 +k where (h,k) is the vertex
The vertex is at (0,-4)
The distance between the points is found by
d = sqrt( (x2-x1)^2 + (y2-y2)^2)
= sqrt(( 0-3)^2 + (-4-0)^2)
= sqrt( 9 + 16)
= sqrt(25)
= 5
Use ABC to find the value of sin A.
a. 12/37
b. 37/12
c. 35/37
d. 12/35
Answer:
a. 12/37
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
sin(A) = BC/AB = 12/37
The value of sin A in triangle ABC, where AB = 37 and BC = 12, is 12/37.
In a right-angled triangle, the sine of one of the non-right angles (A in this case) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The hypotenuse is the side opposite the right angle (side AB in this case).
To find the value of sin A in triangle ABC, we can use the formula:
sin A = BC / AB
Given that AB = 37 and BC = 12, we have:
sin A = 12 / 37
So, the correct answer is: a. 12/37
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What is the area of the cross section that is parallel to side PQRS in this rectangular box?
The area of the cross section that is parallel to side PQRS in this rectangular box is: A. 12 square units.
In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
A represent the area of a rectangle.
W represent the width of a rectangle.
L represent the length of a rectangle.
By substituting the given side lengths into the formula for the area of a rectangle (PQRS), we have the following;
Area of rectangle = PQ × QR
Area of rectangle = 4 × 3
Area of rectangle = 12 square units.
Complete Question:
What is the area of the cross section that is parallel to side PQRS in this rectangular box?
A. 12 square units
B. 16 square units C. 30 square units D. 40 square units
The volume of the rectangular box is 60 cubic units.
Given that the area of one side of the box is 12 and the area of another side is 15, and both dimensions are integers greater than 1, we can find the dimensions and the volume of the box as follows:
Possible dimensions:
For the side with area 12, the possible integer dimensions are (3, 4) and (4, 3) since 3 x 4 = 4 x 3 = 12.
For the side with area 15, the possible integer dimensions are (3, 5) and (5, 3) since 3 x 5 = 5 x 3 = 15.
Valid dimensions combination:
We need to find a combination of dimensions where the two sides mentioned above are not the same.
The only valid combination is (3, 4) for the side with area 12 and (5, 3) for the side with area 15.
Volume of the box:
The volume of the box is calculated by multiplying the length, width, and height.
In this case, the volume is 3 (length) x 4 (width) x 5 (height) = 60 cubic units.
Therefore, the volume of the rectangular box is 60 cubic units.
Question
The dimensions of a rectangular box are integers greater than 1. If the area of one side of this box is 12 and the area of another side 15, what is the volume of the box?