Find the solutions of the quadratic equation 14x^2+9x+10=014x
2
+9x+10=014, x, start superscript, 2, end superscript, plus, 9, x, plus, 10, equals, 0.
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i
28
9
​ ±
28
479
​
​ istart fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i

(Choice B)
B
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i−
28
9
​ ±
28
479
​
​ iminus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i

(Choice C)
C
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}−
28
9
​ ±
28
479
​
​ minus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction

(Choice D)
D
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}
28
9
​ ±
28
479
​
​

Answer:

2 first blank and left second blank

Step-by-step explanation:

Your translation is off. You are going to reflect it across the x-axis so you just need your points of your pre-image and image to be lined up.

To do that you will shift your pre-image 2 units left.

You need to get rid of that negative sign on 2 and after the word unit(s) put left.

So actually you did marvelous.

Answer:

1) The equation of the line in point slope form is equal to [tex]y-11=\frac{4}{3}(x-9)[/tex]

2) The equation of the line in slope intercept form is equal to [tex]y=\frac{4}{3}x-1[/tex]

3) The equation of the line in standard form is equal to [tex]4x-3y=-3[/tex]

Step-by-step explanation:

we have that the line passes through the points

(9,11) and (21,27)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{27-11}{21-9}[/tex]

[tex]m=\frac{16}{12}[/tex]

[tex]m=\frac{4}{3}[/tex]

step 2

Find the equation of the line into point slope form

The equation of the line is

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

[tex]point (9,11)[/tex]

substitute

[tex]y-11=\frac{4}{3}(x-9)[/tex] -----> equation of the line into point slope form

step 3

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

[tex]y-11=\frac{4}{3}(x-9)[/tex]

[tex]y=\frac{4}{3}x-12+11[/tex]

[tex]y=\frac{4}{3}x-1[/tex] -----> equation of the line in slope intercept form

step 4

Find the equation of the line in standard form

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

[tex]y=\frac{4}{3}x-1[/tex]

Multiply by 3 both sides to remove the fraction

[tex]3y=4x-3[/tex]

[tex]4x-3y=-3[/tex] ----> equation of the line in standard form

Answer:

D $1298

Step-by-step explanation:

10% of 5200 is 520

1% is 52

0.5% is 26

700+520+52+26 = 1298

Answer:

50/27

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{\frac{-2}{3}}{6}\div\dfrac{\frac{-3}{5}}{10}=\dfrac{50}{27}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{-2}{3}}{6}\div\dfrac{\frac{-3}{5}}{10}=\left(\dfrac{-2}{3}\div6\right)\div\left(\dfrac{-3}{5}\div10\right)=\left(\dfrac{-2\!\!\!\!\diagup^1}{3}\cdot\dfrac{1}{6\!\!\!\!\diagup_3}\right)\div\left(\dfrac{-3}{5}\cdot\dfrac{1}{10}\right)\\\\=\left(-\dfrac{1}{9}\right)\div\left(-\dfrac{3}{50}\right)=\dfrac{1}{9}\cdot\dfrac{50}{3}=\dfrac{50}{27}[/tex]

Answer:

The answer to this is -5

Step-by-step explanation:

To do this, just do -125 to the 1/3 power. This is because you need to do the reverse of the order of operations.

Answer:

Step-by-step explanation:

[tex]x=4\\\\-25x>100\qquad\text{change the signs}\\25x<-100\qquad\text{divide both sides by 25}\\x<-4\qquad\bold{NOT}\to4<-4\qquad\bold{FALSE}\\\\-25x\geq100\qquad\text{change the signs}\\25x\leq-100\qquad\text{divide both sides by 25}\\x\leq-4\qquad\bold{NOT}\to4\leq-4\qquad\bold{FALSE}\\\\25x<100\qquad\text{divide both sides by 25}\\x<4\qquad\bold{NOT}\to4<4\qquad\bold{FALSE}\\\\25x\leq100\qquad\text{divide both sides by 25}\\x\leq4\qquad\bold{YES}\to4\leq4\qquad\bold{TRUE}[/tex]

Put the value of x = 4 to each inequality:

-25x > 100 → -25(4) > 100 → -100 > 100 FALSE

-25x ≥ 100 → -25(4) ≥ 100 → -100  ≥ 100 FALSE

25x < 100 → 25(4) < 100 → 100 < 100 FALSE

25x ≤ 100 → 25(4) ≤ 100 → 100 ≤ 100 TRUE

Answer:

180 -88 = 92 degrees

Step-by-step explanation:

Solution: x ≥ -5

Domain Definition: The domain of a function is the set of input or argument values for which the function is real and defined

squareroot 2x + 10  ⇒  2x + 10 ≥ 0

Solve 2x + 10 ≥ 0:

Subtract 10 from both sides

2x + 10 - 10 ≥ 0 - 10

Simplify

2x ≥ -10

Divide both sides by 2

2x / 2  ≥  -10 / 2

Simplify

2x / 2

Divide the numbers: 2 / 2 = 1

= x

Note: x has the same value as 1

Divide the numbers: -10 / 2 = -5

= -5

The function domain is

x ≥ -5

Answer:

[tex]\boxed{\text{C. }x \geq -5}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x-values that will make the function work.

The definition automatically eliminate options B and D.

Your function is

[tex]y = \sqrt{2x + 10}[/tex]

The number under the radical cannot be negative, because the square root of a negative number is imaginary.

Thus, we must have

[tex]\begin{array}{rcr}2x+ 10 & \geq & 0\\2x & \geq & -10\\x & \geq & -5\\\end{array}\\\\\text{The domain is }\boxed{\mathbf{x \geq -5}}[/tex]

The graph of your function shows that the range is x ≥ -5.

14.5...?

Hope this helps!

Answer:

The correct answer option is B. 21.

Step-by-step explanation:

We are given a figure where the line KL is intersecting another line MN such that angle from K to N is equal to the angle opposing it which is the angle measuring [tex](5x)[/tex].

Measure of angle K - N = 90° + 15° = 105°

Since angle K - N = angle M - L, we can write it as:

105° = 5x

x = 105/5

x = 21

Therefore, the correct answer option is B. 21.

Answer:

The correct answer is option B

21

Step-by-step explanation:

From the figure we can see a number of line segments

To find the value of x

Let the point of intersection of line segments be 'o'

From the figure we get, <KON and <MOL are vertically opposite angles

m<KON = m<MOL

90 + 15  = 5x

5x = 105

x = 105/5 = 21

Therefore the value of x = 21

Answer:

Step-by-step explanation:

Here we are going to use the rule which says that

i) equal arc segments subtends equal angles at the circle

ii) The Angle subtended by any arc segment at center is double to that of the angle subtended by the same arc at its circumference.

For more details please refer to the image attached to this problem.

Let us say that the angle subtended by arc mAB at center O = 6∅

Hence , ∠AOB=6∅

Hence ∠ADB = 3∅ ( Rule ii as discussed above )

Also as length of arc mCD = x , the angle subtended by it on the center will be in the same ratio as it was subtended by arc with length 6x

Hence

∠COD=∅

Hence

∠CAD=∅/2

Hence in ΔATD

∠ATD + ∠ADT +∠DAT = 180°

∠ATD + 3∅+∅/2= 180°

∠ATD = 180° - (3∅+∅/2)    ----------(A)

Also

∠ATD + ∠ATB = 180°

From (A)

180° - (3∅+∅/2) +∠ATB =  180°

∠ATB = (3∅+∅/2)

∠ATB = (6∅+∅)/2

∠ATB = (7∅)/2

However , in order to find the exact value of∠ATB  we need to evaluate  ∅, and to find it , we must have some value of x .

Answer:

C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SSS.Then , corresponding angles of the triangles are congruent by CPCTC.

Step-by-step explanation:

We have to explain one way through which we can verify that the corresponding angles of the two triangles are congruent.

A. Use the slope formula to prove that the slopes of corresponding sides are opposite reciprocals . Therefore, the corresponding angles of the triangles are congruent.

In this option we are given that by slopes formula the slopes of corresponding sides are opposite reciprocals .It means sides are perpendicular but not give any information about congruency of two triangles through which we can say corresponding angles of two triangles are congruent.Hence, it is false.

B.Use the distance formula to prove that two corresponding sides of the triangles have same lengths. Therefore, corresponding angles of the triangles are congruent by CPCTC.

In this option we are given information about only two corresponding sides of two triangles . It is not sufficient to prove that corresponding angles of two triangles are congruent.Hence, it is false.

C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore,the two triangles are congruent by SSS. Then, corresponding angles of the triangles are congruent by CPCTC.

In this option we have complete information through which we can verify that corresponding angles of two triangles are congruent.Hence, it is correct.

D.Use the distance formula to prove that two corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SAS.Then, all corresponding angles of the triangles are congruent.

In this option we have no complete information through which we can two triangles are congruent by SAS. Therefore, In this option  explaination are not given properly.Hence , it is false.

The required Paola needs to use 18 cups of water.

To determine the number of cups of water Paola needs to use, we need to know the ratio of water to iced tea mix. Typically, a common ratio for making iced tea is 1 tablespoon of iced tea mix per 1 cup of water.

A ratio is a comparison of two quantities or values, typically expressed in the form of a fraction or with a colon (:). It shows the relative sizes or amounts of two or more things in relation to each other.

Given that Paola uses 18 tablespoons of iced tea mix, she would need an equal amount of cups of water.

Therefore, Paola needs to use 18 cups of water.

Learn more about ratios here:

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Answer:

2x+3y-5=0

Step-by-step explanation:

We have been given two points  (4,-1) and (-2,3). Now we need to find about

what is the equation of the line that passes through (4,-1) and (-2,3).

Slope of the line through the points  (4,-1) and (-2,3)  is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{3-\left(-1\right)}{-2-4}=\frac{3+1}{-6}=\frac{4}{-6}=-\frac{2}{3}[/tex]

Now plug the slope [tex]m=-\frac{2}{3}[/tex] and point (4,-1) into point slope formula

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y--1=-\frac{2}{3}\left(x-4\right)[/tex]

[tex]y=-\frac{2}{3}x+\frac{5}{3}[/tex]

or we can rewrite that as 2x+3y-5=0

Hence final answer is 2x+3y-5=0

The answer is:

The second option

[tex]2x+3y-5=0[/tex]

To know which is the equation of the line, we need to follow the next steps:

Find the slope of the line:

We are given the points:

[tex](-2,3)\\(4,1)[/tex]

Where,

[tex]x_1=4\\y_1=-1\\x_2=-2\\y_2=3[/tex]

Also, we know that we can calculate the slope of a function using the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, using the slope formula, and substituting the given points, we have:

[tex]m=\frac{3-(-1)}{-2-4}[/tex]

[tex]m=\frac{4}{-6}[/tex]

[tex]m=-\frac{2}{3}[/tex]

Find the "b" value:

In order to find "b" we need to substitute any of the given points, we know that line pass through both of the given points, so, substituting the point (4,-1), we have:

Writing the slope form of the function,

[tex]y=mx+b[/tex]

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]-1=-\frac{2}{3}*(4)+b\\\\b=-1+\frac{2}{3}*(4)=-1+\frac{8}{3}=\frac{-3+8}{3}=\frac{5}{3}[/tex]

Now that we know the slope and "b", we can write the equation of the line in slope-intercept form:

Writing the equation of the equation, we have:

[tex]y=-\frac{2}{3}x+\frac{5}{3}[/tex]

Then, by multiplying each side of the equation by 3 in order to simplify the fractions, we have:

[tex]3y=(3)*(-\frac{2}{3}x)+(3)*(\frac{5}{3})[/tex]

[tex]3y=-2x+5[/tex]

Rewriting the equation, we have:

[tex]2x+3y-5=0[/tex]

Hence, we have that the correct option is the second option, the equation of the line that passes through the given points is:

[tex]2x+3y-5=0[/tex]

Have a nice day!

Answer:

b 43.5 cm^2

Step-by-step explanation:

The area of a trapezoid is found by using the formula

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases

A = 1/2(13 +16) *3

A = 1/2 (29)*3

A = 43.5 cm^2

I believe it would be (A)

A mean is an arithmetic average of a set of observations. The higher mean score out of two grades will be of grade 6.

A mean is an arithmetic average of a set of observations. it is given by the formula,

[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]

The mean of the 6th grade will be,

[tex]\rm Mean_1 = \dfrac{(70 \times 6)+(80 \times 4)+(90 \times 6)+(100 \times 4)}{20} = \dfrac{1680}{20} = 84[/tex]

The mean of the 7th grade will be,

[tex]\rm Mean_2 = \dfrac{(50 \times 5)+(60 \times 7)+(70 \times 4)+(80 \times 4)}{20} = \dfrac{1270}{20} = 63.5[/tex]

Hence, the higher mean score out of two grades will be of grade 6.

Learn more about Mean:

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Answer:

Slope: 7

y-intercept:-6

Step-by-step explanation:

The equation of the line in Slope-intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

You have the equation of the given line:

[tex]y=7x-6[/tex]

You can observe that it is written in Slope-intercept form, therefore, you can identify that the slope and the y-intercept are the following:

[tex]m=7\\b=-6[/tex]

A. The slope is 7.

B. The line rises steeply right 7 units for every 1 unit increase in x.

Here's how to find the slope and y-intercept directly from the equation:

Understanding the Slope-Intercept Form:

The equation of a line can be written in *slope-intercept form* as `y = mx + b`, where:

`m` represents the slope of the line.

`b` represents the y-intercept, which is the point where the line crosses the y-axis.

Identifying Slope and Y-Intercept:

In the given equation, `y = 7x - 6`, we can directly identify the values:

The slope `m` is the coefficient of `x`, which is 7.

The y-intercept `b` is the constant term, which is -6.

Interpreting the Slope:

A slope of 7 indicates that for every 1 unit increase in `x`, the `y` value increases by 7 units. This means the line rises steeply from left to right.

Question:

Find the slope and y-intercept of the line whose equation is y= 7x-6.

What is the slope? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The slope is ______ (Type an integer or a fraction.)

B. The slope is undefined.

Answer:

B

Step-by-step explanation:

The question is on inverse of functions

f(x)=2x-9 -----------to find f ⁻(x)

replace f(x) with y;

f(x)=2x-9----------------y=2x-9

replace y with x and x with y

y=2x-9------------------x=2y-9

solve for y

x=2y-9

x+9=2y

(x+9)/2 =y

replace y with g(x) or f ⁻(x)

g(x)=x+9 /2

Answer:

(only ii right?)

Since we have the total number is 360° and our section is 72°, we know that the percentage of students who choose the cinema should be the number that we have divided to the total amount and then multiply the result by 100 ( it's fine if you write 100%, but when you actually calculate it, it's only 100, not 100%):

(72/360) . 100 = 20%

Answer:

y = 23

Step-by-step explanation:

Since it's a rhombus, we know that the two diagonals are perpendicular.

That means that angle 1 is necessary a right angle, so it's worth 90 degrees since it's at the meeting point of the two perpendicular diagonals.

So, we have

∠1 = 4y - 2

All we have to do is to replace ∠1 by its value (90) and solve the mini-equation:

90 = 4y - 2

92 = 4y

y = 23

7/8 because there are 8 pieces of pizza and they eat 7 slices of pizza.

Answer:

Andy = 84 and Bart = 105

Step-by-step explanation:

Given that the ratio is 4 : 5 = 4x : 5x

Andy loses 9 thus 4x - 9

ratio 4x - 9 : 5x = 5 : 7, that is

[tex]\frac{4x-9}{5x}[/tex] = [tex]\frac{5}{7}[/tex] ( cross- multiply )

25x = 7(4x - 9) ← distribute

25x = 28x - 63 ( subtract 28x from both sides )

- 3x = - 63 ( divide both sides by 3 )

x = 21

Hence

Andy = 4x = 4 × 21 = 84 marbles

Bart = 5x = 5 × 21 = 105 marbles

Answer:

add 15

Step-by-step explanation:

i think im not super sure

Answer:

Red triangle on the diagram

Step-by-step explanation:

The center of dilation is point D(-5,1). The scale factor is 1/2. This means that all distances need to be halved.

If triangle ABC has vertices A(-1,7), B(7,9) and C(3,1), then the image triangle has vertices at points E(-3,4), G(1,5) and F(-1,1).

Points E, G and F are midpoints of the segments DA, DB and DC (see attached diagram for details).

Answer: first option

Step-by-step explanation:

You can observe in the figure that the total budget is $1,695.00 and the car is $272.00

Then, you know that the total budget represents the 100%, then, to calculate what percent of the total budget the car is, you need to divide  $272.00 by  $1,695.00 and multiply this by 100:

[tex]\%car=\frac{ \$272.00}{ \$1,695.00}*100\\\\\%car=16.04\%[/tex]

Rounded to the nearest tenth:

[tex]\%car=16.0\%[/tex]

Answer:

16%

Step-by-step explanation:

We have been given a table for the budget of June month.

Using that table we need to calculate about what percent of the total budget is the car. Then round the answer to the nearest tenth.

From table we see that budget for the car = $272

From table we see that total budget for June month = $1695

then required percent is given by formula :

[tex]percent=\frac{part}{whole}\cdot 100\%[/tex]

[tex]percent=\frac{272}{1695}\cdot 100\%[/tex]

[tex]percent=\frac{27200}{1695} \%[/tex]

[tex]percent=16.0471976401 \%[/tex]

Which is approx 16%.

The answer is To this problem is the answer choice A

Answer:

So the correct option is option a.

Step-by-step explanation:

An ordered pair is written in the following form: (x, y). It means, first the independent variable and secondly the dependent variable.

In the diagram, the first circle represents the independent variable, and the second circle represents the dependent variable.

Then, the set of ordered pairs is:

(0, 2) ; (2, 6) ; (4, 10).

So the correct option is option a.

Answer:

1). This is a right angle triangle = TRUE

2). The hypotenuse of the triangle has a length of 21 = FALSE ("C" is the hypotenuse which makes 21 and 20 the leg of the triangle)

3). One of the legs has a length of 20 = TRUE

4). The length of "c" can be found by 202 + c2 = 212 = FALSE (To calculate the hypotenuse of the triangle you should use the formula a² + b² = c² )

"A" and "C" are the correct answers <3

Answer:

m<2 = 56°

Step-by-step explanation:

m<1 and m<2 are supplementary angles and sum = 180

so

m<1 + m< 2 = 180

If m< 1 = 10x + 4 and m <2 = 5x-4, find m< 2

10x + 4 + 5x - 4 = 180

15x = 180

  x = 12

m<2 = 5(12) -4 = 56

Answer

m<2 = 56°

Answer: 56°

Step-by-step explanation:

Answer:

the answer is 1,648

SA= 2 (lw +lh + wh)

SA = 2 (384 + 120 + 320)

SA = 2 (824)

SA = 1,648 sq. cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

420(0.882)^16 ~ 56.3 grams left

Answer: 56.3

Step-by-step explanation: