Answer:
[tex]x = - \frac{7}{4} \: \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]8 {x}^{2} + 14x - 4x - 7 = 0 \\ 2x(4x + 7) - (4x + 7) = 0 \\ (4x + 7)(2x - 1) = 0[/tex]
Answer:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
When factoring trinomials of the form ax² + bx + c:
multiply the leading coefficient and the last term.find the product factors that add to give you the coefficient of the middle term.rewrite the polynomial with those factors replacing the middle term.1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
4x + 7 = 02x - 1 = 0
Case 1:
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x = [tex]\bold{-\dfrac{7}{4}}[/tex]
Case 2:
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x = [tex]\bold{\dfrac{1}{2}}[/tex]
Solutions:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
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What is the area of the kite?
A. 1,500 ft^2
B. 640 ft^2
C. 320 ft^2
D. 160 ft^2
thank you ! :)
(x-1)(x+1)= выполнить умножение
Answer:
x^2-1^2
Step-by-step explanation:
formula:
(a-b)(a+b)=a^2-b^2
what is the answer to a math problem I had it on khan academy but the problem I
1 2/7 divided by (-2 1/4)
hat is the answer to a math problem I had it on khan academy but the problem I
1 2/7 divided by (-2 1/4)
Answer:
-4/7
Step-by-step explanation:
1 2/7 divided by (-2 1/4)
1 2/7 = 9/7
-2 1/4 = -9/4
9/7 divided by -9/4 =
9/7 multiplied by -4/9 =
9's cancel out
1/7 multiplied by -4/1 =
-4/7
The first number in a pattern is 6. The pattern follows the rule "Add 1, Multiply by 2" Which of the following shows the next four numbers in the pattern?
A - 7, 8, 9, 18
B - 12, 13, 26 27
C - 7, 14, 15, 30
D - 12 14. 28, 28
Answer:
C
Step-by-step explanation:
Remark
You must do the changes in order. Add 1 then multiply by 2
First entry: 6Add 1: 6 + 1 = 7Multiply by 2 = 2*7 = 14Add 1: 14 + 1 = 15Multiply by 2: 15 * 2 = 30Answer: 7 14 15 30
Paige is working on an art project. She draws two rectangles that are connected. The total area of the two rectangles is 56 centimeters. The
dimensions of the smaller rectangle are 2 centimeters by 7 centimeters.
Answer:
2 * 21
3 * 14
6 * 7
Step-by-step explanation:
7 * 2 = 14
56 - 14 = 42
Multiples of 42 = 2,3,6,7, 14, 21
The possible dimensions of the larger rectangle are:
21 centimeters by 2 centimeters
14 centimeters by 3 centimeters
7 centimeters by 6 centimeters
Let the dimensions of the larger rectangle be length L and width W.
We know that the total area of the two rectangles is 56 square centimeters.
Area of the smaller rectangle = 2 cm * 7 cm = 14 square centimeters
Area of the larger rectangle = Total area - Area of the smaller rectangle
Area of the larger rectangle = 56 square centimeters - 14 square centimeters
Area of the larger rectangle = 42 square centimeters
Now, we need to find the possible dimensions of the larger rectangle with an area of 42 square centimeters.
To find the possible dimensions, we can list all the pairs of whole numbers (L, W) whose product is 42.
7 * 2 = 14
56 - 14 = 42
Multiples of 42 = 2,3,6,7, 14, 21
Remember that the length (L) should be greater than or equal to the width (W) to avoid counting duplicates.
The possible dimensions are:
L = 42, W = 1 (42 cm * 1 cm = 42 square centimeters)
L = 21, W = 2 (21 cm * 2 cm = 42 square centimeters)
L = 14, W = 3 (14 cm * 3 cm = 42 square centimeters)
L = 7, W = 6 (7 cm * 6 cm = 42 square centimeters)
So, the possible dimensions of the larger rectangle are:
42 centimeters by 1 centimeter
21 centimeters by 2 centimeters
14 centimeters by 3 centimeters
7 centimeters by 6 centimeters
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a prototype rocket burns 159 gallons of liquid hydrogen fuel each second during a regular launch. Make a table that shows how many gallons of fuel are burned after 2,3,5 and 10 seconds.
Answer:
Seconds: 2 || 3 || 5 || 10 ||
---------------------||-------||--------||--------||
Gallons: 312 || 486 || 780 || 1560 ||
Kevin is running a marathon. His time comes to 26 miles in 2 2/3 hours. What is his speed in miles per hour?
how do i divide 431.25 by 61
Answer:
7.070 to the nearest thousandth
Step-by-step explanation:
You could use a calculator or do it manually using long division:
61)431 .2500(7.0695 <---------Quotient
427
425
367
580
549
310
305
There are 20 students in a class.
12 of the students are girls.
Find the ratio of the number of girls to the number of boys.
Give your ratio in the form n : 1.
Answer:
1.5:1
Step-by-step explanation:
the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1
20 POINTS!!! WILL GIVE BRAINLIEST!!!
Answer:
equivalent. not equivalent. not equivalent
Step-by-step explanation:
PROVE :
sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4
Step-by-step explanation:
[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]
[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]
[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]
[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]
If set A contains seven distinct numbers and set B contains three distinct letters, how many elements are in (A U B)?
=======================================================
Explanation:
Let's use an example to see why this is
A = {1,2,3,4,5,6,7}
B = {x,y,z}
A U B = {1,2,3,4,5,6,7, x,y,z}
We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).
There are 7 items in set A, and 3 items in set B.
Therefore, we have 7+3 = 10 items in set A U B
The symbol U refers to the set union operator.
If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.
The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.
-----------------
If you want a formula to write down on a notecard or reference sheet, then it would be
n(A U B) = n(A)+n(B)
where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region
What is the equation of a line that passes through (-6,2) and has a slope of -(1)/(2)?
Answer:
y= -1/2x+5
Step-by-step explanation:
(5 1/6-x)*2 7/10-1 3/14=3 2/7
Answer:
3.5
Step-by-step explanation:
B) State whether the given pairs are complementary, supplementary or neither.
1) 25°, 155°
2) 46°, 44°
3) 68°, 108°
4) 180, 72⁰
6) 19⁰, 161°
5) 320, 58⁰.
Answer:
1st answer supplementary angles
2nd answer complementary angles
3rd answer neither
4th ananswe complementary angles
5th answer complementary angles
6th answer supplementary angles
hope you find this helpful
Write a rule for the nth term of the geometric sequence for which a1=−6 and a5=−486
The geometric rule for the nth term of the geometric sequence for which a1 =−6 and a5=−486 is -6 × 3^(n - 1)
The nth term of a geometric sequenceFirst term, a1 = -6
Fifth term, a5 = -486
a5 = ar^(n - 1)
-486 = -6 × r^(5-1)
-486 = -6r⁴
r⁴ = -486 / 6
r⁴ = 81
r = 4√81
r = 3
Geometric rule:
nth term = ar^(n-1)
nth term = -6 × 3^(n - 1)
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41 Buying music
LV
Dave loves music. He wants to listen to his favorite
singer's new CD. So he goes to Itunes and buys his
songs. One song costs 1,29 € and the album 9,99 €.
There are 8 songs on the album.
. What's the best choice?
Answer:
theUse the Distance and Midpoint Formulas to find the length and midpoint of the segments with indicated endpoints. Show your solution and answer inside the box.
Endpoints
Distance
Midpoint
1. (-5,8) and (9,4)
2. (6 ,- 3) and (10,11)
3. (2,1) and (-16,13)
4. (3,0) and (9 ,- 13)
5. (-3 ,- 10) & (-7 ,- 2)
what the 2 soultion answer to
y = 6x − 4
y = 5x − 3
[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]
The volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. What is the volume of a cube with side 4 inches?
Volume is a three-dimensional scalar quantity. The volume of the cube with side length of 4 inches is 64 inches³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. Therefore, the volume of cube with side 4 inches will be,
Volume of the cube = (4 in)³ = 64 in³
Hence, the volume of the cube with side length of 4 inches is 64 inches³.
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what are the key features of the graph of a trigonometric function? How do you find them from a graph or an equation?
Answer:
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).
can someone help with this please
Answer:
Step-by-step explanation:
1. Sally makes $600 dollars a week and earns 20% commission on her sales. If she sells $5000 dollars worth of furniture one week. What does she make in total? (Think weekly salary PLUS commission = total salary)
Answer:
20% of sales : $1000
and salary+commission : $1000+ 600
So total salary : $1600
Use technology or a z-score table to answer the question.
The weights of boxes of rice produced at a factory are normally distributed with a
mean of 20 ounces and a standard deviation of 1.5 ounces. Consider a shipment of 1500 boxes of rice.
How many of the boxes will weigh 18 ounces or less?
138 boxes
154 boxes
632 boxes
781 boxes
The number of boxes will weigh 18 ounces or less will be 138. Then the correct option is A.
What is a normal distribution?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The weights of boxes of rice produced at a factory are normally distributed with a mean of 20 ounces and a standard deviation of 1.5 ounces.
Consider a shipment of 1500 boxes of rice.
Then the number of the boxes will weigh 18 ounces or less will be
z = (18 - 20) / 1.5
z = -1.33
Then the probability will be
P(x ≤ 18) = P(z ≤ -1.33)
P(x ≤ 18) = 1 - P(z > -1.33)
P(x ≤ 18) = 1 - [1 - P(z < -1.33)]
P(x ≤ 18) = P(z < -1.33)
P(x ≤ 18) = 0.091211
Then the number of the boxes will weigh 18 ounces or less will be
⇒ 0.091211 x 1500
⇒ 136.8
approximately 138 boxes.
Then the correct option is A.
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What is the volume of this sphere?
Use 3.14 and round your answer to the nearest
hundredth.
18mm
cubic millimeters
Work Shown:
[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\[/tex]
I get the part A of the question its just the part B that i would really appreciate for someone to explain
Step-by-step explanation:
650065 = (a² + 1)(c² + 1)
and
650065 = (ac - 1)² + (a + c)² = the sum of 2 squared numbers (ac - 1)² and (a + c)².
we see that 5 and 13 and therefore 5×13=65 are all factor of 650065. and then 650065/65 = 10001.
and we know that 65 = (64 + 1) = (8² + 1)
and 10001 = (10000 + 1) = (100² + 1)
so, a = 8, c = 100
that means the 2 squared numbers summing up to 650065 are
(ac - 1)² = (8×100 - 1)² = 799² = 638,401
(a + c)² = (8 + 100)² = 108² = 11,664
650,065 = 638,401 + 11,664 = 799² + 108²
Find the area of the triangle ?
Answer:
16 cm²/m²
Step-by-step explanation:
The formula to find the area of a triangle is:
Area of the triangle = [tex]\frac{1}{2}[/tex] × base × height
Where base = 8 and height = 4
So, the area of the triangle = [tex]\frac{1}{2}[/tex] × 8 × 4 = 16 cm²/m²
Which of the following equations describes the graph?
y=-x^2+1
An equation that describes the graph is [tex]y=-x^{2} +1[/tex]
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is parabola?"It is a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. "
For given question,
The graph describes the parabola.
The parabola opens downward, so the equation of the parabola would be,
[tex]y=-x^{2}[/tex]
We know that, for a function f(x) is transformed to f(x) + c if c > 0 then the graph of the function moves up by c units.
if c < 0 then the graph of the function moves down by c units.
As the graph of the parabola moves down by 1 unit, the equation of the parabola would be,
[tex]y=-x^2+1[/tex]
Therefore, the equation that describes the graph is [tex]y=-x^{2} +1[/tex]
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The table shows the monthly low temperature for several cities in December. The monthly low temperature in Toledo in December was 212°F. Which of the cities in the table, if any, had a lower December temperature than Toledo? Explain your reasoning.
Please this is urgent, please.
Of these cities, the place that has the lowest temperature than Toledo is Youngstown.
What is the temperature of Youngstown?The town is known to have a temperature that is less than 20. This shows that the temperature has fallen below all other temperatures in the table.
Hence it can be concluded that the lowest table here is the temperature of Youngstown at -20 degrees.
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Solve y = ax² + c for x.
Answer:
[tex]x =\pm\sqrt{\dfrac{y-c}a}[/tex]
Step-by-step explanation:
[tex]~~~~~~y= ax^2 +c\\\\\implies ax^2 = y-c\\\\\implies x^2 =\dfrac{y-c}{a}\\\\\implies x =\pm\sqrt{\dfrac{y-c}a}[/tex]
Find the measure of the angle between u = 6i - 3j and
v = 2i+j to the nearest tenth of a degree.
Answer:
θ = 53.1° (to the nearest tenth)
Step-by-step explanation:
FORMULA :
Let θ be the measure of the angle between U and V :
[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]
========================
[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]
…………………………………………………
Then
[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]
[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]