Answer:
[tex]26[/tex] and [tex]28[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].
The square of the smaller integer would be [tex]x^{2}[/tex].
Five times the larger integer would be [tex]5\, (x + 2)[/tex].
Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].
The value of this expression should be equal to [tex]536[/tex]. In other words:
[tex]x^{2} - 5\, (x + 2) = 536[/tex].
Rewrite and simplify this quadratic equation:
[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].
[tex]a = 1[/tex].[tex]b = (-5)[/tex].[tex]c = (-546)[/tex]Apply the quadratic formula to find possible values of [tex]x[/tex]:
[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].
[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].
Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.
Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].
Please please please help me really quick i just need help please!
Answer:
54.98 cm squared
To find the area of the shaded region, we first need to know the area of the entire figure and the area of the circle.
To find the area of the circle, we use the formula pi times r^2
r is the radius, which can be found by multiplying the diameter by 1/2
1/2 x 16 = 8
Now we have pi times 8^2
8^2 = 64
Now we have pi times 64
Let's say that pi = 3.141 in this situation. We could be more exact and say 3.14159265... but that is probably not what your teacher wants.
64 x 3.141 = 201.024
So, we have the area of the circle.
Now we need the area of the entire figure.
Well, that's just length times width.
16 x 16 = 256
So, to find the area of the shaded region, we just have to find the difference between 256 and 201.024
256 - 201.024 = 54.976
We can round that to 54.98, or if you want, to 55.
Can someone please help me? I really need this grade and I’m very lost in all of these questions. Thank you.
Answer: See below
Step-by-step explanation:
4) [tex]p(5.8 < x < 8.8)=0.7838[/tex] (By calculator)
5) [tex]p(x \leq 4.8)=0.0032[/tex] (By calculator)
6) [tex]P(x > 9.8 \text { or } x < 5.8)= P(x < 5.8)+P(x > 980)[/tex]
[tex]\begin{array}{ll}\text { Now } \quad & P(x > 9.8)=0.0345 \\\text { and } \quad & P(x < 5.8)=0.0345\end{array}[/tex]
[tex]p(x > 9: 8 \text { or } x < 5.8)=0.069[/tex]
7) No, there are no outliers in the data set
how would you solve this
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's write the equation in standard form ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + {y}^{2} - 2y - 15 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y = 15[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y + 1 = 15 + 1[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} +( {y}^{} - 1 ) {}^{2} = 16[/tex]
Now, it's the required form of circle ~
System of Equations
Explain steps
Answer:
Step 1 : First, solve one linear equation for y in terms of x .
Step 2 : Then substitute that expression for y in the other linear equation. ...
Step 3 : Solve this, and you have the x -coordinate of the intersection.
Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.
Step-by-step explanation:
These are all of the steps
A rocket is launched into the air. the projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the time since launch in seconds and h(t) is the height of the rocket at time t. when will the rocket be 196 feet in the air? after 2.0 seconds after 3.5 seconds after 4.5 seconds after 7.0 seconds
The rocket will attain a height of 196 feet in 3.5 seconds. Then the correct option is B.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
A rocket is launched into the air.
The projectile motion of the rocket can be modeled using
h(t) = 112t – 16t²
where t is the time since the launch in seconds and h(t) is the height of the rocket at time t.
The time required for the rocket to be 196 feet in the air. Then we have
112t – 16t² = 196
16t² – 112t + 196 = 0
4t² – 28t + 49 = 0
On factorization we have
4t² – 28t + 49 = 0
(2t)² – 28t + 7² = 0
(2t – 7)² = 0
2t – 7 = 0
t = 3.5
Thus, the rocket will attain a height of 196 feet in 3.5 seconds.
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:
B. after 3.5 seconds
Step-by-step explanation:
i took the test
also:
196 = 112t - 16t²
-16t² + 112t - 196 = 0
4t² - 28t + 49 = 0
(2t - 7)² = 0
2t - 7 = 0
t = 7/2 = 3.5 sec
PLEASE HELP ASAP!! Also, please explain how to solve. Thank you
By evaluating the given relation, we conclude that the correct options are A, D, and G.
How to check if the points are on the graph?
We have the relation:
k = ∛(V/7)
Such that this relation gives us pairs of the form (V, k).
So, to check if the points belong to the graph of the relation, we need to evaluate the points on the given relation and see if the relation is true.
A) (0, 0) gives:
Evaluating in V = 0
k = ∛(0/7) = 0
So this point belongs.
B) (1, 1) gives:
k= ∛(1/7) = 0.52
So we have the point (1, 0.52) and the point (1, 1) then does not belong to the graph.
We just need to do that for all the points, evaluate V and see if k gives the same value as in the point.
With this method, we will see that the correct options are:
D) (7, 1)
k= ∛(7/7) = 1
G) (56, 2)
k= ∛(56/7) = ∛(8) = 2
If you want to learn more about evaluations, you can read:
https://brainly.com/question/4344214
The price for a gallon of gas is $4.99 how much is it going to cost for 20 gallons ?
Answer:
if one gallon is 4.99, 20 gallons?
write a ratio to make it easier
gallon : price
1 4.99
20 x
cross multiply,
x = 20 × 4.99
x=99.8
Question
Which of the following is NOT in scientific notation?
A. 9.308 x 105
B. 2.758 x 10-6
C. 1.043 x 108
D. 0.316 x 10-4
Answer:
D
Step-by-step explanation:
this is not standard form
Answer:
D
Step-by-step explanation:
The first number should be equal to or greater than one but less than 10
Draw the graph of y = 3x - 1 on the grid use the graph to estimate y when x = 2.5
Answer:
6.5
Step-by-step explanation:
all you have to do is substitute x with 2.5 in the equation and you can find y.
In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 19 students who completed the assignment. There were 15 students who passed the test and also completed the assignment. What is the probability that a student passed the test given that they completed the homework
Answer:
2/9
Step-by-step explanation:
I CANT FIGURE THIS OUT I NEED HELP
Solve and graph the inequality:
[tex]-1/2x + 8\geq 6[/tex]
Answer:
[tex]x\leq 4[/tex]
Step-by-step explanation:
Given:
[tex]-\frac{1}{2}x+8\ge 6[/tex]
Solve:
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]-\frac{1}{2}x+8-8\ge \:6-8[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-\frac{1}{2}x\ge \:-2[/tex]
[tex]Multiply\:both\:sides\:by\:-1[/tex]
[tex]\left(-\frac{1}{2}x\right)\left(-1\right)\le \left(-2\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{1}{2}x\le \:2[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}2[/tex]
[tex]2\cdot \frac{1}{2}x\le \:2\cdot \:2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x\leq 4[/tex]
[tex]\mathrm{Therefore,}[/tex]
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:4\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:4]\end{bmatrix}[/tex]
~lenvy~
A stack of books is 56 inches high. How high is it in feet and inches?
1 foot = 12 inches
56 inches / 12 inches = 4.66 feet = 4 feet and 8 inches
Answer:
4 feet and 8 inches
Step-by-step explanation:
To convert a high number of inches to feet you divide it by 12 since 12 inches makes 1 foot.
So 56÷12 = 4 reminder 8
The remainder we keep it as inches
So our answer is 4 feet and 8 inches.
A rectangle is 2/5 (fraction) inches long and 1/3 inches wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
in2
__/__ in2
Answer:
A = 2/15 in^2
Step-by-step explanation:
To find the area of a rectangle, we multiply length times width
A = l*w
A = 2/5 * 1/3
A = 2/15 in^2
Answer:
[tex]\sf area=\dfrac{2}{15} \ in^2[/tex]
Step-by-step explanation:
Area of a rectangle = width x length
Given:
[tex]\sf length=\dfrac25[/tex][tex]\sf width=\dfrac13[/tex]Substitute these values into the equation are solve:
[tex]\sf \implies area=\dfrac13 \times \dfrac25[/tex]
[tex]\sf \implies area=\dfrac{1 \times 2}{3 \times 5}[/tex]
[tex]\sf \implies area=\dfrac{2}{15} \ in^2[/tex]
AABC has vertices A(-3,-4), B(1,5), and C(4.1). AABC is translated so that B'is located at point (-3, 2). State the
coordinates of A' and C', where AA'B'C' is the translation of AABC.
A. A'(-7, -7), C'(0, -2)
B. A-6, -8), C'(1, -3)
C. A'(-4,-3), C'(1,-4)
D. A'(1,-1), C'(8,4)
Answer:
Step 1: Identify the coordinates of each of the vertices of the triangle.
Step 2: Translate each point by adding the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. For these translations, add a negative number if the horizontal translation is to the left or if the vertical translation is downward.
Step 3: Plot the three translated points and draw the triangle by connecting each pair of points with a straight line.
Step-by-step explanation:
Triangle: A triangle is a three-sided geometric figure made by connecting each pair of points in a set of three with straight lines. The points that define a triangle are known as vertices
Using technology, determine the quarterly payment on a 4 year loan of $16,231 at 5. 1% compounded quarterly. Round your answer to the nearest cent. A. $1,125. 69 c. $1,518. 85 b. $1,127. 86 d. $1,508. 31.
The quarterly payment on a 4-year loan of $16,231 at 5. 1% compounded quarterly is $1508.31.
Principle P= $16,231
Rate of interest r= 5.1% compounded quarterly
Tenure n= 4 year =16 quarters
What is the formula for quarterly payment?The formula for quarterly payment is given as:
Quarterly payment = [tex]\frac{P*r/100(1+r/100)^n}{(1+r/100)^n-1}[/tex]
Where P=principle
r =quarterly rate of interest
n=tenure
Quarterly payment =[tex]\frac{16231*(5.1/100)(1+5.1/100)^16}{(1+5.1/100)^16-1}[/tex]
Quarterly payment =$1508.31
Therefore, the quarterly payment on a 4-year loan of $16,231 at 5. 1% compounded quarterly is $1508.31.
To get more about quarterly payments visit:
https://brainly.com/question/25792915
Given the figure below, find the values of x and z
Answer:
z = 60 and x = 4.25 or 17/4
Step-by-step explanation:
Z = 60°
8x + 86 = 180-60
8x + 86 = 120
8x = 120 - 86
8x = 34
x = 4.25 or 17/4
Theresa entered a photo contest. Each entry was judged by three judges in four different categories. Each category was a percent of the overall score: Originality was 20%, technique was 35%, composition was 20%, and impact was 25%. Entries could earn up to 50 points in each category.
Theresa's scores are shown in the table.
Judge Originality Technique Composition Impact
A 40 45 30 45
B 45 45 40 40
C 35 40 35 40
This equation can be used to find her weighted score for each judge.
weighted score = (weight⋅originality)+(weight⋅technique)+(weight⋅composition)+(weight⋅impact)
What was Theresa's weighted score from each judge?
Enter your answers in the boxes.
Theresa's weighted score for Judge A was
.
Theresa's weighted score for Judge B was
.
Theresa's weighted score for Judge C was
.
Question 2
What is Theresa's overall average score from the three judges?
Enter your answer in the box. Round your answer to the nearest tenth.
points
Step-by-step explanation:
Judge A: 41 (0.20 x 40)+(0.35 x 45)+(0.20 x 30)+(0.25 x 45)
Judge B: 42.75 (0.20 x 45)+(0.35 x 45)+(0.20 x 40)+(0.25 x 40)
Judge C: 38 (0.20 x 35)+(0.35 x 40)+(0.20 x 35)+(0.25 x 40)
Total score: 40.6
PLEASE HELP ASAP ONLY 2 QUESTIONS
Answer:
1. D, 2. B
Step-by-step explanation:
1. D. 1.15b
2. -4(x + 2) - 1/2(2x - 6)
(-4x -8) - (x - 3)
B. - 5x - 5
Hope this helps :)
The regular octagon shown is enlarged so that its side are 3 times
as large. What affect does this have on the perimeter?
Answer:
The perimeter is 2 times greater.
Step-by-step explanation:
Find area of the circle. Use 3.14 as (pie symbol) the diameter is 104. Please help will mark brainliest!!
Answer:
8490.56 yd^2
Step-by-step explanation:
find radius by dividing 104 by 2
we get 52 yd
now the area of circle is [tex]\pi r^{2}[/tex]
we use 3.14 for pi
so 3.14 times 52*52
3.14 times 2704
8490.56
4y + 5 + 2 + 7y answer?
Answer:
11y + 7
Step-by-step explanation:
4y + 5 + 2 + 7y
4y + 7y + 5 + 2 <== combine the like terms
11y + 7
Hope this helps!
Answer:
11y+7
Step-by-step explanation:
4y+5+2+7y
combine like terms
5+2=7
then you have
4y+7+7y
combine the y's
4y+7y=11y
then you got
11y+7
Solve each system by substitution. Show all work.
4x + y = 0
-x - 2y =7
4x + y = 0
-x - 2y =7
with - x - 2y = 7
we have x = -2y - 7
we replace x by this value in the first one
4 * (-2y - 7) + y = 0
- 8y - 28 + y = 0
- 7y = 28
y = 28/(-7)
y = - 4
since 4x + y = 0
we have 4x + (-4) = 0
4x = 4
x = 1
(1 ; -4)
The normal price of a television is £1200
It is reduced to £970
Work out the percentage reduction.
Give your answer to 1 decimal place
Answer:80.8%
Step-by-step explanation:
£1200=100%
£970=
£970*100%/£1200=80.8333333
80.8%
Answer:
19.2%.
Step-by-step explanation:
Reduction = 1200-970 = £230,
% reduction = 230*100/ 1200
= 19,2%
Fill in the table using this function rule y=-10x+1
Answer:
11, 1, -9, -49
Step-by-step explanation:
(Fill in the x value for each one then solve)
Function rule: y = -10x + 1
1. x = -1
fill in: y = (-10) -1 + 1
Solve: 11
Table way: x,y = -1,11
2. x = 0
fill in: y = (-10) 0 + 1
Solve: 1
Table way: x,y = 0,1
3. x = 1
fill in: y = (-10) 1 + 1
Solve: -9
Table way: x,y = 1,-9
4. x = 5
fill in: y = (-10) 5 + 1
Solve: -49
Table way: x,y = 5,-49
*prove de/ae = bd/ce*
triangle proportionality.
i am able to find that the triangles are similar but don’t know how to prove the parallel sides are proportional to the side segments
Explanation:
You can use the definition of similarity to show that corresponding sides are proportional. You cannot prove anything about the proportionality of non-corresponding sides.
Statement . . . . Reason1. BD║CE . . . . given
2. ∠A≅∠A . . . . reflexive property of congruence
3. ∠ABD≅∠ACE . . . . corresponding angles theorem
4. ΔABD ~ ΔACE . . . . AA similarity postulate
5. BD/CE = AD/AE . . . . definition of similarity
_____
Additional comment
Length DE is related to BC in the same way that AD is related to AB. There is no way to prove the ratio you show in your problem statement. You can show that ...
DE/AE = (CE -BD)/CE = 1 -(BD/CE) . . . . the difference is proportional to the corresponding longer side
Explain how many solutions this system of equations has.
Answer:
No solution
Step-by-step explanation:
[tex]\rightarrow \left \{ {{2y = 6x + 4} \atop {y = 3x - 4}} \right. \\\\[/tex]
Multiply the second equation by 2 to make the "x" coordinates the same.
[tex]\rightarrow \left \{ {{2y = 6x + 4} \atop {2(y = 3x - 4)}} \right. \\\\[/tex]
[tex]\rightarrow \left \{ {{2y = 6x + 4} \atop {2y = 6x - 8}} \right. \\\\[/tex]
Subtract 6x from the first equation with the second equation
[tex]\rightarrow \left \{ {{2y = 6x + 4} \atop {-2y = -6x + 8}} \right. \\\\[/tex]
[tex]\rightarrow 0y = 0x + 12[/tex]
Simplify the R.H.S
[tex]\rightarrow 0 \neq 12[/tex]
This system of equation has no solution.
Graph:A triangle has sides with lengths of 12 kilometers, 12 kilometers, and 17 kilometers. Is it a right triangle?
Answer:
no it has to be the same length
Step-by-step explanation:
it has to be the same
please help me with word problems
Answer: c=4
Step-by-step explanation:
70-8.76c=34.96
-70 -70
-----------------------
-8.76c=-35.04
-35.04/-8.76 = 4
c=4
I need help please. Find the volume of the composite solid.
Answer: 150 cubic feet
Step-by-step explanation:
Formula: area of base x height (length x width x height)
Volume of small rectangle: 5 x 2 x 3 = 30
Volume of large rectangle: 10 x 6 x 2 = 120
Add them together: 120 + 30 = 150
Help me plss
4b(9b^5+7b^4)
Step-by-step explanation:
Step by Step Solution

STEP1:Equation at the end of step 1
STEP2:
22b5 Simplify ———— 9b
Dividing exponential expressions :
2.1 b5 divided by b1 = b(5 - 1) = b4
Final result :
4b4 ——— 9